LMFDB - Embedded newform 252.4.i.a.25.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(25,252)]

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, 4, 4]))

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

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.i (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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.18
Character	$\chi$	$=$	252.25
Dual form			252.4.i.a.121.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.59994 + 3.74705i) q^{3} +(-10.9363 + 18.9422i) q^{5} +(-13.2752 - 12.9139i) q^{7} +(-1.08080 + 26.9784i) q^{9} +O(q^{10})$	\(q+(3.59994 + 3.74705i) q^{3} +(-10.9363 + 18.9422i) q^{5} +(-13.2752 - 12.9139i) q^{7} +(-1.08080 + 26.9784i) q^{9} +(7.44740 + 12.8993i) q^{11} +(-29.1283 - 50.4518i) q^{13} +(-110.347 + 27.2120i) q^{15} +(21.1706 - 36.6685i) q^{17} +(-0.154699 - 0.267947i) q^{19} +(0.598848 - 96.2322i) q^{21} +(-32.8000 + 56.8112i) q^{23} +(-176.704 - 306.061i) q^{25} +(-104.980 + 93.0708i) q^{27} +(53.5988 - 92.8358i) q^{29} -32.5889 q^{31} +(-21.5240 + 74.3425i) q^{33} +(389.799 - 110.232i) q^{35} +(122.131 + 211.536i) q^{37} +(84.1850 - 290.769i) q^{39} +(26.7692 + 46.3657i) q^{41} +(-135.107 + 234.012i) q^{43} +(-499.209 - 315.516i) q^{45} -371.613 q^{47} +(9.46373 + 342.869i) q^{49} +(213.612 - 52.6773i) q^{51} +(-101.709 + 176.166i) q^{53} -325.787 q^{55} +(0.447103 - 1.54426i) q^{57} -599.543 q^{59} -892.529 q^{61} +(362.743 - 344.187i) q^{63} +1274.22 q^{65} +941.511 q^{67} +(-330.953 + 81.6141i) q^{69} -897.389 q^{71} +(-249.033 + 431.337i) q^{73} +(510.701 - 1763.92i) q^{75} +(67.7136 - 267.416i) q^{77} -283.997 q^{79} +(-726.664 - 58.3164i) q^{81} +(483.481 - 837.413i) q^{83} +(463.054 + 802.034i) q^{85} +(540.813 - 133.366i) q^{87} +(370.959 + 642.520i) q^{89} +(-264.842 + 1045.92i) q^{91} +(-117.318 - 122.112i) q^{93} +6.76735 q^{95} +(-375.482 + 650.355i) q^{97} +(-356.050 + 186.977i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.59994	+	3.74705i	0.692810	+	0.721121i
$3$	3.59994	+	3.74705i	0.692810	+	0.721121i
$4$		0			0
$5$	−10.9363	+	18.9422i	−0.978171	+	1.69424i	−0.309122	+	0.951022i	$0.600035\pi$
$5$	−10.9363	+	18.9422i	−0.978171	+	1.69424i	−0.669048	+	0.743219i	$0.733298\pi$
$6$		0			0
$7$	−13.2752	−	12.9139i	−0.716795	−	0.697284i
$7$	−13.2752	−	12.9139i	−0.716795	−	0.697284i
$8$		0			0
$9$	−1.08080	+	26.9784i	−0.0400296	+	0.999198i
$10$		0			0
$11$	7.44740	+	12.8993i	0.204134	+	0.353571i	0.949857	−	0.312686i	$-0.101229\pi$
$11$	7.44740	+	12.8993i	0.204134	+	0.353571i	−0.745722	+	0.666257i	$0.767895\pi$
$12$		0			0
$13$	−29.1283	−	50.4518i	−0.621442	−	1.07637i	−0.989217	−	0.146455i	$-0.953214\pi$
$13$	−29.1283	−	50.4518i	−0.621442	−	1.07637i	0.367775	−	0.929915i	$-0.380120\pi$
$14$		0			0
$15$	−110.347	+	27.2120i	−1.89944	+	0.468408i
$16$		0			0
$17$	21.1706	−	36.6685i	0.302036	−	0.523142i	−0.674561	−	0.738219i	$-0.735667\pi$
$17$	21.1706	−	36.6685i	0.302036	−	0.523142i	0.976597	+	0.215077i	$0.0690003\pi$
$18$		0			0
$19$	−0.154699	−	0.267947i	−0.00186792	−	0.00323533i	0.865090	−	0.501617i	$-0.167261\pi$
$19$	−0.154699	−	0.267947i	−0.00186792	−	0.00323533i	−0.866958	+	0.498381i	$0.833928\pi$
$20$		0			0
$21$	0.598848	−	96.2322i	0.00622282	−	0.999981i
$22$		0			0
$23$	−32.8000	+	56.8112i	−0.297360	+	0.515042i	−0.975531	−	0.219862i	$-0.929439\pi$
$23$	−32.8000	+	56.8112i	−0.297360	+	0.515042i	0.678171	+	0.734904i	$0.262773\pi$
$24$		0			0
$25$	−176.704	−	306.061i	−1.41364	−	2.44849i
$26$		0			0
$27$	−104.980	+	93.0708i	−0.748275	+	0.663388i
$28$		0			0
$29$	53.5988	−	92.8358i	0.343208	−	0.594454i	−0.641818	−	0.766857i	$-0.721820\pi$
$29$	53.5988	−	92.8358i	0.343208	−	0.594454i	0.985027	+	0.172402i	$0.0551530\pi$
$30$		0			0
$31$	−32.5889			−0.188811			−0.0944054	−	0.995534i	$-0.530095\pi$
$31$	−32.5889			−0.188811			−0.0944054	+	0.995534i	$0.530095\pi$
$32$		0			0
$33$	−21.5240	+	74.3425i	−0.113541	+	0.392162i
$34$		0			0
$35$	389.799	−	110.232i	1.88251	−	0.532362i
$36$		0			0
$37$	122.131	+	211.536i	0.542652	+	0.939902i	0.998751	+	0.0499722i	$0.0159133\pi$
$37$	122.131	+	211.536i	0.542652	+	0.939902i	−0.456098	+	0.889929i	$0.650753\pi$
$38$		0			0
$39$	84.1850	−	290.769i	0.345651	−	1.19385i
$40$		0			0
$41$	26.7692	+	46.3657i	0.101967	+	0.176612i	0.912495	−	0.409088i	$-0.134153\pi$
$41$	26.7692	+	46.3657i	0.101967	+	0.176612i	−0.810528	+	0.585700i	$0.800820\pi$
$42$		0			0
$43$	−135.107	+	234.012i	−0.479153	+	0.829917i	−0.999714	−	0.0239069i	$-0.992389\pi$
$43$	−135.107	+	234.012i	−0.479153	+	0.829917i	0.520561	+	0.853824i	$0.325723\pi$
$44$		0			0
$45$	−499.209	−	315.516i	−1.65373	−	1.04521i
$46$		0			0
$47$	−371.613			−1.15331			−0.576653	−	0.816990i	$-0.695641\pi$
$47$	−371.613			−1.15331			−0.576653	+	0.816990i	$0.695641\pi$
$48$		0			0
$49$	9.46373	+	342.869i	0.0275911	+	0.999619i
$50$		0			0
$51$	213.612	−	52.6773i	0.586502	−	0.144633i
$52$		0			0
$53$	−101.709	+	176.166i	−0.263601	+	0.456570i	−0.967196	−	0.254031i	$-0.918244\pi$
$53$	−101.709	+	176.166i	−0.263601	+	0.456570i	0.703595	+	0.710601i	$0.251577\pi$
$54$		0			0
$55$	−325.787			−0.798712
$56$		0			0
$57$	0.447103	−	1.54426i	0.00103895	−	0.00358847i
$58$		0			0
$59$	−599.543			−1.32295			−0.661473	−	0.749969i	$-0.730068\pi$
$59$	−599.543			−1.32295			−0.661473	+	0.749969i	$0.730068\pi$
$60$		0			0
$61$	−892.529			−1.87339			−0.936694	−	0.350149i	$-0.886131\pi$
$61$	−892.529			−1.87339			−0.936694	+	0.350149i	$0.886131\pi$
$62$		0			0
$63$	362.743	−	344.187i	0.725418	−	0.688309i
$64$		0			0
$65$	1274.22			2.43151
$66$		0			0
$67$	941.511			1.71677			0.858387	−	0.513002i	$-0.171467\pi$
$67$	941.511			1.71677			0.858387	+	0.513002i	$0.171467\pi$
$68$		0			0
$69$	−330.953	+	81.6141i	−0.577421	+	0.142394i
$70$		0			0
$71$	−897.389			−1.50001			−0.750004	−	0.661434i	$-0.769948\pi$
$71$	−897.389			−1.50001			−0.750004	+	0.661434i	$0.769948\pi$
$72$		0			0
$73$	−249.033	+	431.337i	−0.399275	+	0.691565i	−0.993637	−	0.112633i	$-0.964071\pi$
$73$	−249.033	+	431.337i	−0.399275	+	0.691565i	0.594362	+	0.804198i	$0.297405\pi$
$74$		0			0
$75$	510.701	−	1763.92i	0.786275	−	2.71574i
$76$		0			0
$77$	67.7136	−	267.416i	0.100217	−	0.395777i
$78$		0			0
$79$	−283.997			−0.404457			−0.202229	−	0.979338i	$-0.564818\pi$
$79$	−283.997			−0.404457			−0.202229	+	0.979338i	$0.564818\pi$
$80$		0			0
$81$	−726.664	−	58.3164i	−0.996795	−	0.0799950i
$82$		0			0
$83$	483.481	−	837.413i	0.639384	−	1.10745i	−0.346184	−	0.938167i	$-0.612523\pi$
$83$	483.481	−	837.413i	0.639384	−	1.10745i	0.985568	−	0.169279i	$-0.0541441\pi$
$84$		0			0
$85$	463.054	+	802.034i	0.590886	+	1.02344i
$86$		0			0
$87$	540.813	−	133.366i	0.666451	−	0.164349i
$88$		0			0
$89$	370.959	+	642.520i	0.441816	+	0.765247i	0.997824	−	0.0659292i	$-0.0210011\pi$
$89$	370.959	+	642.520i	0.441816	+	0.765247i	−0.556008	+	0.831177i	$0.687668\pi$
$90$		0			0
$91$	−264.842	+	1045.92i	−0.305088	+	1.20486i
$92$		0			0
$93$	−117.318	−	122.112i	−0.130810	−	0.136155i
$94$		0			0
$95$	6.76735			0.00730858
$96$		0			0
$97$	−375.482	+	650.355i	−0.393036	+	0.680758i	−0.992848	−	0.119383i	$-0.961908\pi$
$97$	−375.482	+	650.355i	−0.393036	+	0.680758i	0.599813	+	0.800141i	$0.295242\pi$
$98$		0			0
$99$	−356.050	+	186.977i	−0.361459	+	0.189817i
$100$		0			0
$101$	532.567	+	922.432i	0.524677	+	0.908767i	0.999587	+	0.0287326i	$0.00914714\pi$
$101$	532.567	+	922.432i	0.524677	+	0.908767i	−0.474910	+	0.880034i	$0.657520\pi$
$102$		0			0
$103$	−667.712	+	1156.51i	−0.638754	+	1.10635i	0.346953	+	0.937883i	$0.387216\pi$
$103$	−667.712	+	1156.51i	−0.638754	+	1.10635i	−0.985707	+	0.168472i	$0.946117\pi$
$104$		0			0
$105$	1816.30	+	1063.77i	1.68812	+	0.988695i
$106$		0			0
$107$	827.736	+	1433.68i	0.747853	+	1.29532i	0.948850	+	0.315728i	$0.102249\pi$
$107$	827.736	+	1433.68i	0.747853	+	1.29532i	−0.200997	+	0.979592i	$0.564418\pi$
$108$		0			0
$109$	818.445	−	1417.59i	0.719200	−	1.24569i	−0.242117	−	0.970247i	$-0.577842\pi$
$109$	818.445	−	1417.59i	0.719200	−	1.24569i	0.961317	−	0.275444i	$-0.0888250\pi$
$110$		0			0
$111$	−352.974	+	1219.15i	−0.301828	+	1.04249i
$112$		0			0
$113$	495.164	+	857.649i	0.412222	+	0.713990i	0.995132	−	0.0985468i	$-0.0314194\pi$
$113$	495.164	+	857.649i	0.412222	+	0.713990i	−0.582910	+	0.812537i	$0.698086\pi$
$114$		0			0
$115$	−717.420	−	1242.61i	−0.581737	−	1.00760i
$116$		0			0
$117$	1392.59	−	731.307i	1.10038	−	0.577858i
$118$		0			0
$119$	−754.576	+	213.389i	−0.581276	+	0.164381i
$120$		0			0
$121$	554.572	−	960.548i	0.416659	−	0.721674i
$122$		0			0
$123$	−77.3668	+	267.220i	−0.0567149	+	0.195889i
$124$		0			0
$125$	4995.89			3.57477
$126$		0			0
$127$	−268.123			−0.187339			−0.0936695	−	0.995603i	$-0.529860\pi$
$127$	−268.123			−0.187339			−0.0936695	+	0.995603i	$0.529860\pi$
$128$		0			0
$129$	−1363.23	+	336.177i	−0.930432	+	0.229448i
$130$		0			0
$131$	577.763	−	1000.71i	0.385339	−	0.667426i	−0.606478	−	0.795101i	$-0.707418\pi$
$131$	577.763	−	1000.71i	0.385339	−	0.667426i	0.991816	+	0.127675i	$0.0407513\pi$
$132$		0			0
$133$	−1.40657	+	5.55483i	−0.000917028	+	0.00362154i
$134$		0			0
$135$	−614.873	−	3006.40i	−0.391999	−	1.91667i
$136$		0			0
$137$	1422.24	+	2463.40i	0.886938	+	1.53622i	0.843477	+	0.537166i	$0.180505\pi$
$137$	1422.24	+	2463.40i	0.886938	+	1.53622i	0.0434608	+	0.999055i	$0.486162\pi$
$138$		0			0
$139$	−895.343	−	1550.78i	−0.546345	−	0.946298i	−0.998521	−	0.0543689i	$-0.982685\pi$
$139$	−895.343	−	1550.78i	−0.546345	−	0.946298i	0.452176	−	0.891929i	$-0.350648\pi$
$140$		0			0
$141$	−1337.79	−	1392.45i	−0.799021	−	0.831672i
$142$		0			0
$143$	433.861	−	751.469i	0.253715	−	0.439447i
$144$		0			0
$145$	1172.34	+	2030.56i	0.671433	+	1.16296i
$146$		0			0
$147$	−1250.68	+	1269.77i	−0.701731	+	0.712442i
$148$		0			0
$149$	1509.15	−	2613.93i	0.829764	−	1.43719i	−0.0684601	−	0.997654i	$-0.521809\pi$
$149$	1509.15	−	2613.93i	0.829764	−	1.43719i	0.898224	−	0.439539i	$-0.144858\pi$
$150$		0			0
$151$	1147.80	+	1988.05i	0.618587	+	1.07142i	0.989744	+	0.142854i	$0.0456280\pi$
$151$	1147.80	+	1988.05i	0.618587	+	1.07142i	−0.371157	+	0.928570i	$0.621039\pi$
$152$		0			0
$153$	966.374	+	610.778i	0.510632	+	0.322735i
$154$		0			0
$155$	356.401	−	617.305i	0.184689	−	0.319891i
$156$		0			0
$157$	−1598.16			−0.812402			−0.406201	−	0.913784i	$-0.633147\pi$
$157$	−1598.16			−0.812402			−0.406201	+	0.913784i	$0.633147\pi$
$158$		0			0
$159$	−1026.25	+	253.077i	−0.511867	+	0.126228i
$160$		0			0
$161$	1169.08	−	330.608i	0.572276	−	0.161836i
$162$		0			0
$163$	−1774.44	−	3073.42i	−0.852668	−	1.47686i	−0.878792	−	0.477205i	$-0.841650\pi$
$163$	−1774.44	−	3073.42i	−0.852668	−	1.47686i	0.0261245	−	0.999659i	$-0.491683\pi$
$164$		0			0
$165$	−1172.82	−	1220.74i	−0.553355	−	0.575968i
$166$		0			0
$167$	163.423	+	283.058i	0.0757250	+	0.131160i	0.901401	−	0.432985i	$-0.142540\pi$
$167$	163.423	+	283.058i	0.0757250	+	0.131160i	−0.825676	+	0.564144i	$0.809206\pi$
$168$		0			0
$169$	−598.421	+	1036.50i	−0.272381	+	0.471778i
$170$		0			0
$171$	7.39598	−	3.88394i	0.00330751	−	0.00173691i
$172$		0			0
$173$	−1284.29			−0.564410			−0.282205	−	0.959354i	$-0.591066\pi$
$173$	−1284.29			−0.564410			−0.282205	+	0.959354i	$0.591066\pi$
$174$		0			0
$175$	−1606.64	+	6344.97i	−0.694004	+	2.74077i
$176$		0			0
$177$	−2158.32	−	2246.52i	−0.916550	−	0.954004i
$178$		0			0
$179$	−1653.35	+	2863.69i	−0.690377	+	1.19577i	0.281338	+	0.959609i	$0.409222\pi$
$179$	−1653.35	+	2863.69i	−0.690377	+	1.19577i	−0.971714	+	0.236159i	$0.924111\pi$
$180$		0			0
$181$	−770.605			−0.316457			−0.158228	−	0.987403i	$-0.550578\pi$
$181$	−770.605			−0.316457			−0.158228	+	0.987403i	$0.550578\pi$
$182$		0			0
$183$	−3213.06	−	3344.35i	−1.29790	−	1.35094i
$184$		0			0
$185$	−5342.62			−2.12323
$186$		0			0
$187$	630.662			0.246624
$188$		0			0
$189$	2595.54	+	120.164i	0.998930	+	0.0462467i
$190$		0			0
$191$	−623.980			−0.236385			−0.118193	−	0.992991i	$-0.537710\pi$
$191$	−623.980			−0.236385			−0.118193	+	0.992991i	$0.537710\pi$
$192$		0			0
$193$	−490.806			−0.183052			−0.0915258	−	0.995803i	$-0.529174\pi$
$193$	−490.806			−0.183052			−0.0915258	+	0.995803i	$0.529174\pi$
$194$		0			0
$195$	4587.13	+	4774.58i	1.68457	+	1.75341i
$196$		0			0
$197$	1450.03			0.524420			0.262210	−	0.965011i	$-0.415549\pi$
$197$	1450.03			0.524420			0.262210	+	0.965011i	$0.415549\pi$
$198$		0			0
$199$	764.991	−	1325.00i	0.272506	−	0.471995i	−0.696997	−	0.717074i	$-0.745481\pi$
$199$	764.991	−	1325.00i	0.272506	−	0.471995i	0.969503	+	0.245079i	$0.0788141\pi$
$200$		0			0
$201$	3389.39	+	3527.89i	1.18940	+	1.23800i
$202$		0			0
$203$	−1910.41	+	540.249i	−0.660513	+	0.186789i
$204$		0			0
$205$	−1171.02			−0.398965
$206$		0			0
$207$	−1497.22	−	946.291i	−0.502726	−	0.317738i
$208$		0			0
$209$	2.30422	−	3.99102i	0.000762613	−	0.00132088i
$210$		0			0
$211$	−197.910	−	342.790i	−0.0645720	−	0.111842i	0.831932	−	0.554878i	$-0.187235\pi$
$211$	−197.910	−	342.790i	−0.0645720	−	0.111842i	−0.896504	+	0.443036i	$0.853902\pi$
$212$		0			0
$213$	−3230.55	−	3362.57i	−1.03922	−	1.08169i
$214$		0			0
$215$	−2955.13	−	5118.44i	−0.937387	−	1.62360i
$216$		0			0
$217$	432.625	+	420.848i	0.135339	+	0.131655i
$218$		0			0
$219$	−2512.75	+	619.652i	−0.775323	+	0.191197i
$220$		0			0
$221$	−2466.65			−0.750792
$222$		0			0
$223$	−1046.56	+	1812.69i	−0.314272	+	0.544335i	−0.979282	−	0.202499i	$-0.935094\pi$
$223$	−1046.56	+	1812.69i	−0.314272	+	0.544335i	0.665011	+	0.746834i	$0.268427\pi$
$224$		0			0
$225$	8448.01	−	4436.41i	2.50311	−	1.31449i
$226$		0			0
$227$	1587.17	+	2749.06i	0.464071	+	0.803794i	0.999159	−	0.0410019i	$-0.0130550\pi$
$227$	1587.17	+	2749.06i	0.464071	+	0.803794i	−0.535088	+	0.844796i	$0.679722\pi$
$228$		0			0
$229$	526.744	−	912.347i	0.152001	−	0.263273i	−0.779962	−	0.625827i	$-0.784762\pi$
$229$	526.744	−	912.347i	0.152001	−	0.263273i	0.931963	+	0.362554i	$0.118095\pi$
$230$		0			0
$231$	1245.79	−	708.955i	0.354834	−	0.201930i
$232$		0			0
$233$	−325.786	−	564.277i	−0.0916005	−	0.158657i	0.816584	−	0.577226i	$-0.195865\pi$
$233$	−325.786	−	564.277i	−0.0916005	−	0.158657i	−0.908185	+	0.418570i	$0.862532\pi$
$234$		0			0
$235$	4064.06	−	7039.17i	1.12813	−	1.95398i
$236$		0			0
$237$	−1022.37	−	1064.15i	−0.280212	−	0.291663i
$238$		0			0
$239$	−2779.44	−	4814.13i	−0.752247	−	1.30293i	−0.946731	−	0.322025i	$-0.895637\pi$
$239$	−2779.44	−	4814.13i	−0.752247	−	1.30293i	0.194484	−	0.980906i	$-0.437697\pi$
$240$		0			0
$241$	1062.16	+	1839.71i	0.283899	+	0.491728i	0.972342	−	0.233563i	$-0.0750386\pi$
$241$	1062.16	+	1839.71i	0.283899	+	0.491728i	−0.688442	+	0.725291i	$0.741705\pi$
$242$		0			0
$243$	−2397.43	−	2932.78i	−0.632903	−	0.774231i
$244$		0			0
$245$	−6598.20	−	3570.45i	−1.72058	−	0.931052i
$246$		0			0
$247$	−9.01228	+	15.6097i	−0.00232161	+	0.00402115i
$248$		0			0
$249$	4878.33	−	1203.01i	1.24157	−	0.306176i
$250$		0			0
$251$	2121.21			0.533425			0.266713	−	0.963776i	$-0.414063\pi$
$251$	2121.21			0.533425			0.266713	+	0.963776i	$0.414063\pi$
$252$		0			0
$253$	−977.098			−0.242805
$254$		0			0
$255$	−1338.29	+	4622.36i	−0.328655	+	1.13515i
$256$		0			0
$257$	−1336.92	+	2315.62i	−0.324494	+	0.562041i	−0.981410	−	0.191924i	$-0.938527\pi$
$257$	−1336.92	+	2315.62i	−0.324494	+	0.562041i	0.656916	+	0.753964i	$0.271861\pi$
$258$		0			0
$259$	1110.44	−	4385.37i	0.266407	−	1.05210i
$260$		0			0
$261$	2446.63	+	1546.34i	0.580239	+	0.366729i
$262$		0			0
$263$	128.040	+	221.771i	0.0300200	+	0.0519962i	0.880645	−	0.473777i	$-0.157110\pi$
$263$	128.040	+	221.771i	0.0300200	+	0.0519962i	−0.850625	+	0.525773i	$0.823776\pi$
$264$		0			0
$265$	−2224.64	−	3853.19i	−0.515693	−	0.893207i
$266$		0			0
$267$	−1072.12	+	3703.04i	−0.245741	+	0.848773i
$268$		0			0
$269$	−2488.24	+	4309.76i	−0.563981	+	0.976844i	0.433163	+	0.901316i	$0.357398\pi$
$269$	−2488.24	+	4309.76i	−0.563981	+	0.976844i	−0.997144	+	0.0755280i	$0.975936\pi$
$270$		0			0
$271$	−195.292	−	338.256i	−0.0437754	−	0.0758213i	0.843308	−	0.537431i	$-0.180605\pi$
$271$	−195.292	−	338.256i	−0.0437754	−	0.0758213i	−0.887083	+	0.461610i	$0.847272\pi$
$272$		0			0
$273$	−4872.53	+	2772.87i	−1.08022	+	0.614732i
$274$		0			0
$275$	2631.98	−	4558.72i	0.577143	−	0.999640i
$276$		0			0
$277$	3461.28	+	5995.12i	0.750789	+	1.30040i	0.947441	+	0.319931i	$0.103660\pi$
$277$	3461.28	+	5995.12i	0.750789	+	1.30040i	−0.196652	+	0.980473i	$0.563007\pi$
$278$		0			0
$279$	35.2220	−	879.194i	0.00755802	−	0.188659i
$280$		0			0
$281$	−4011.11	+	6947.44i	−0.851540	+	1.47491i	0.0282788	+	0.999600i	$0.490997\pi$
$281$	−4011.11	+	6947.44i	−0.851540	+	1.47491i	−0.879818	+	0.475310i	$0.842336\pi$
$282$		0			0
$283$	−4382.91			−0.920625			−0.460313	−	0.887757i	$-0.652263\pi$
$283$	−4382.91			−0.920625			−0.460313	+	0.887757i	$0.652263\pi$
$284$		0			0
$285$	24.3621	+	25.3576i	0.00506345	+	0.00527037i
$286$		0			0
$287$	243.393	−	961.210i	0.0500593	−	0.197695i
$288$		0			0
$289$	1560.11	+	2702.20i	0.317548	+	0.550010i
$290$		0			0
$291$	−3788.63	+	934.289i	−0.763207	+	0.188209i
$292$		0			0
$293$	2188.84	+	3791.18i	0.436427	+	0.755914i	0.997411	−	0.0719126i	$-0.0229103\pi$
$293$	2188.84	+	3791.18i	0.436427	+	0.755914i	−0.560984	+	0.827827i	$0.689577\pi$
$294$		0			0
$295$	6556.77	−	11356.7i	1.29407	−	2.24139i
$296$		0			0
$297$	−1982.37	−	661.032i	−0.387303	−	0.129148i
$298$		0			0
$299$	3821.64			0.739167
$300$		0			0
$301$	4815.57	−	1361.81i	0.922143	−	0.260775i
$302$		0			0
$303$	−1539.19	+	5316.26i	−0.291829	+	1.00796i
$304$		0			0
$305$	9760.95	−	16906.5i	1.83249	−	3.17397i
$306$		0			0
$307$	−954.574			−0.177461			−0.0887303	−	0.996056i	$-0.528281\pi$
$307$	−954.574			−0.177461			−0.0887303	+	0.996056i	$0.528281\pi$
$308$		0			0
$309$	−6737.24	+	1661.42i	−1.24035	+	0.305874i
$310$		0			0
$311$	1038.41			0.189334			0.0946672	−	0.995509i	$-0.469821\pi$
$311$	1038.41			0.189334			0.0946672	+	0.995509i	$0.469821\pi$
$312$		0			0
$313$	−3253.47			−0.587531			−0.293766	−	0.955878i	$-0.594908\pi$
$313$	−3253.47			−0.587531			−0.293766	+	0.955878i	$0.594908\pi$
$314$		0			0
$315$	2552.59	+	10635.3i	0.456579	+	1.90232i
$316$		0			0
$317$	3801.51			0.673545			0.336773	−	0.941586i	$-0.390665\pi$
$317$	3801.51			0.673545			0.336773	+	0.941586i	$0.390665\pi$
$318$		0			0
$319$	1596.69			0.280242
$320$		0			0
$321$	−2392.27	+	8262.74i	−0.415962	+	1.43670i
$322$		0			0
$323$	−13.1003			−0.00225672
$324$		0			0
$325$	−10294.2	+	17830.1i	−1.75699	+	3.04319i
$326$		0			0
$327$	8258.14	−	2036.48i	1.39656	−	0.344397i
$328$		0			0
$329$	4933.25	+	4798.96i	0.826684	+	0.804181i
$330$		0			0
$331$	10227.0			1.69827			0.849136	−	0.528174i	$-0.177123\pi$
$331$	10227.0			1.69827			0.849136	+	0.528174i	$0.177123\pi$
$332$		0			0
$333$	−5838.90	+	3066.25i	−0.960871	+	0.504594i
$334$		0			0
$335$	−10296.6	+	17834.3i	−1.67930	+	2.90863i
$336$		0			0
$337$	−2838.47	−	4916.37i	−0.458816	−	0.794693i	0.540082	−	0.841612i	$-0.318393\pi$
$337$	−2838.47	−	4916.37i	−0.458816	−	0.794693i	−0.998899	+	0.0469191i	$0.985060\pi$
$338$		0			0
$339$	−1431.09	+	4942.89i	−0.229281	+	0.791921i
$340$		0			0
$341$	−242.702	−	420.373i	−0.0385427	−	0.0667579i
$342$		0			0
$343$	4302.14	−	4673.89i	0.677241	−	0.735761i
$344$		0			0
$345$	2073.44	−	7161.53i	0.323567	−	1.11758i
$346$		0			0
$347$	−7685.36			−1.18897			−0.594484	−	0.804107i	$-0.702644\pi$
$347$	−7685.36			−1.18897			−0.594484	+	0.804107i	$0.702644\pi$
$348$		0			0
$349$	86.5373	−	149.887i	0.0132729	−	0.0229893i	−0.859313	−	0.511451i	$-0.829108\pi$
$349$	86.5373	−	149.887i	0.0132729	−	0.0229893i	0.872586	+	0.488461i	$0.162442\pi$
$350$		0			0
$351$	7753.48	+	2585.44i	1.17906	+	0.393163i
$352$		0			0
$353$	942.322	+	1632.15i	0.142081	+	0.246092i	0.928280	−	0.371881i	$-0.121287\pi$
$353$	942.322	+	1632.15i	0.142081	+	0.246092i	−0.786199	+	0.617974i	$0.787954\pi$
$354$		0			0
$355$	9814.10	−	16998.5i	1.46726	−	2.54137i
$356$		0			0
$357$	−3516.01	−	2059.25i	−0.521252	−	0.305286i
$358$		0			0
$359$	−2708.37	−	4691.04i	−0.398169	−	0.689648i	0.595331	−	0.803480i	$-0.297021\pi$
$359$	−2708.37	−	4691.04i	−0.398169	−	0.689648i	−0.993500	+	0.113832i	$0.963687\pi$
$360$		0			0
$361$	3429.45	−	5939.99i	0.499993	−	0.866013i
$362$		0			0
$363$	5595.65	−	1379.91i	0.809079	−	0.199522i
$364$		0			0
$365$	−5446.98	−	9434.45i	−0.781118	−	1.35294i
$366$		0			0
$367$	−4868.80	−	8433.01i	−0.692505	−	1.19945i	−0.971014	−	0.239021i	$-0.923174\pi$
$367$	−4868.80	−	8433.01i	−0.692505	−	1.19945i	0.278509	−	0.960434i	$-0.410160\pi$
$368$		0			0
$369$	−1279.80	+	672.078i	−0.180552	+	0.0948157i
$370$		0			0
$371$	3625.20	−	1025.18i	0.507307	−	0.143463i
$372$		0			0
$373$	1860.91	−	3223.19i	0.258322	−	0.447427i	−0.707470	−	0.706743i	$-0.750164\pi$
$373$	1860.91	−	3223.19i	0.258322	−	0.447427i	0.965793	+	0.259316i	$0.0834971\pi$
$374$		0			0
$375$	17984.9	+	18719.9i	2.47663	+	2.57784i
$376$		0			0
$377$	−6244.97			−0.853137
$378$		0			0
$379$	−8509.84			−1.15335			−0.576677	−	0.816972i	$-0.695651\pi$
$379$	−8509.84			−1.15335			−0.576677	+	0.816972i	$0.695651\pi$
$380$		0			0
$381$	−965.227	−	1004.67i	−0.129790	−	0.135094i
$382$		0			0
$383$	−1341.16	+	2322.96i	−0.178930	+	0.309916i	−0.941514	−	0.336973i	$-0.890597\pi$
$383$	−1341.16	+	2322.96i	−0.178930	+	0.309916i	0.762584	+	0.646889i	$0.223930\pi$
$384$		0			0
$385$	4324.90	+	4207.18i	0.572513	+	0.556929i
$386$		0			0
$387$	−6167.23	−	3897.88i	−0.810072	−	0.511990i
$388$		0			0
$389$	1643.32	+	2846.32i	0.214189	+	0.370987i	0.953022	−	0.302903i	$-0.0979557\pi$
$389$	1643.32	+	2846.32i	0.214189	+	0.370987i	−0.738832	+	0.673890i	$0.764622\pi$
$390$		0			0
$391$	1388.79	+	2405.45i	0.179627	+	0.311123i
$392$		0			0
$393$	5829.64	−	1437.61i	0.748261	−	0.184524i
$394$		0			0
$395$	3105.87	−	5379.52i	0.395628	−	0.685248i
$396$		0			0
$397$	−97.0380	−	168.075i	−0.0122675	−	0.0212479i	0.859826	−	0.510586i	$-0.170572\pi$
$397$	−97.0380	−	168.075i	−0.0122675	−	0.0212479i	−0.872094	+	0.489338i	$0.837238\pi$
$398$		0			0
$399$	−25.8778	+	14.7266i	−0.00324689	+	0.00184775i
$400$		0			0
$401$	5165.94	−	8947.67i	0.643329	−	1.11428i	−0.341356	−	0.939934i	$-0.610886\pi$
$401$	5165.94	−	8947.67i	0.643329	−	1.11428i	0.984685	−	0.174344i	$-0.0557805\pi$
$402$		0			0
$403$	949.260	+	1644.17i	0.117335	+	0.203230i
$404$		0			0
$405$	9051.64	−	13126.8i	1.11057	−	1.61056i
$406$		0			0
$407$	−1819.11	+	3150.79i	−0.221548	+	0.383732i
$408$		0			0
$409$	14702.9			1.77753			0.888764	−	0.458364i	$-0.151565\pi$
$409$	14702.9			1.77753			0.888764	+	0.458364i	$0.151565\pi$
$410$		0			0
$411$	−4110.48	+	14197.3i	−0.493321	+	1.70390i
$412$		0			0
$413$	7959.07	+	7742.42i	0.948282	+	0.922469i
$414$		0			0
$415$	10575.0	+	18316.4i	1.25085	+	2.16654i
$416$		0			0
$417$	2587.67	−	8937.62i	0.303881	−	1.04959i
$418$		0			0
$419$	−4639.95	−	8036.63i	−0.540994	−	0.937029i	−0.998847	−	0.0480010i	$-0.984715\pi$
$419$	−4639.95	−	8036.63i	−0.540994	−	0.937029i	0.457854	−	0.889028i	$-0.348618\pi$
$420$		0			0
$421$	−699.555	+	1211.66i	−0.0809839	+	0.140268i	−0.903673	−	0.428224i	$-0.859140\pi$
$421$	−699.555	+	1211.66i	−0.0809839	+	0.140268i	0.822689	+	0.568492i	$0.192473\pi$
$422$		0			0
$423$	401.639	−	10025.5i	0.0461663	−	1.15238i
$424$		0			0
$425$	−14963.7			−1.70788
$426$		0			0
$427$	11848.5	+	11526.0i	1.34284	+	1.30628i
$428$		0			0
$429$	4377.67	−	1079.55i	0.492671	−	0.121494i
$430$		0			0
$431$	−5433.50	+	9411.10i	−0.607245	+	1.05178i	0.384447	+	0.923147i	$0.374392\pi$
$431$	−5433.50	+	9411.10i	−0.607245	+	1.05178i	−0.991692	+	0.128632i	$0.958941\pi$
$432$		0			0
$433$	12094.8			1.34235			0.671175	−	0.741299i	$-0.265790\pi$
$433$	12094.8			1.34235			0.671175	+	0.741299i	$0.265790\pi$
$434$		0			0
$435$	−3388.23	+	11702.7i	−0.373456	+	1.28989i
$436$		0			0
$437$	20.2966			0.00222178
$438$		0			0
$439$	−525.009			−0.0570782			−0.0285391	−	0.999593i	$-0.509086\pi$
$439$	−525.009			−0.0570782			−0.0285391	+	0.999593i	$0.509086\pi$
$440$		0			0
$441$	−9260.28	−	115.257i	−0.999923	−	0.0124454i
$442$		0			0
$443$	−2533.48			−0.271714			−0.135857	−	0.990728i	$-0.543379\pi$
$443$	−2533.48			−0.271714			−0.135857	+	0.990728i	$0.543379\pi$
$444$		0			0
$445$	−16227.7			−1.72868
$446$		0			0
$447$	15227.4	−	3755.13i	1.61126	−	0.397341i
$448$		0			0
$449$	5224.90			0.549172			0.274586	−	0.961563i	$-0.411459\pi$
$449$	5224.90			0.549172			0.274586	+	0.961563i	$0.411459\pi$
$450$		0			0
$451$	−398.722	+	690.607i	−0.0416299	+	0.0721052i
$452$		0			0
$453$	−3317.30	+	11457.7i	−0.344063	+	1.18837i
$454$		0			0
$455$	−16915.6	−	16455.2i	−1.74289	−	1.69545i
$456$		0			0
$457$	−19319.7			−1.97755			−0.988774	−	0.149416i	$-0.952261\pi$
$457$	−19319.7			−1.97755			−0.988774	+	0.149416i	$0.952261\pi$
$458$		0			0
$459$	1190.28	+	5819.82i	0.121040	+	0.591821i
$460$		0			0
$461$	−5334.33	+	9239.33i	−0.538925	+	0.933446i	0.460037	+	0.887900i	$0.347836\pi$
$461$	−5334.33	+	9239.33i	−0.538925	+	0.933446i	−0.998962	+	0.0455460i	$0.985497\pi$
$462$		0			0
$463$	5895.26	+	10210.9i	0.591741	+	1.02493i	0.993998	+	0.109398i	$0.0348924\pi$
$463$	5895.26	+	10210.9i	0.591741	+	1.02493i	−0.402257	+	0.915527i	$0.631774\pi$
$464$		0			0
$465$	3596.10	−	886.809i	0.358634	−	0.0884404i
$466$		0			0
$467$	8864.03	+	15353.0i	0.878327	+	1.52131i	0.853176	+	0.521623i	$0.174673\pi$
$467$	8864.03	+	15353.0i	0.878327	+	1.52131i	0.0251503	+	0.999684i	$0.491994\pi$
$468$		0			0
$469$	−12498.8	−	12158.6i	−1.23058	−	1.19708i
$470$		0			0
$471$	−5753.29	−	5988.39i	−0.562840	−	0.585840i
$472$		0			0
$473$	−4024.77			−0.391246
$474$		0			0
$475$	−54.6722	+	94.6950i	−0.00528112	+	0.00914716i
$476$		0			0
$477$	−4642.73	−	2934.35i	−0.445652	−	0.281666i
$478$		0			0
$479$	−4059.22	−	7030.77i	−0.387203	−	0.670656i	0.604869	−	0.796325i	$-0.293226\pi$
$479$	−4059.22	−	7030.77i	−0.387203	−	0.670656i	−0.992072	+	0.125669i	$0.959892\pi$
$480$		0			0
$481$	7114.92	−	12323.4i	0.674454	−	1.16819i
$482$		0			0
$483$	5447.43	+	3190.44i	0.513182	+	0.300559i
$484$		0			0
$485$	−8212.76	−	14224.9i	−0.768912	−	1.33179i
$486$		0			0
$487$	−1188.84	+	2059.14i	−0.110619	+	0.191598i	−0.916020	−	0.401132i	$-0.868617\pi$
$487$	−1188.84	+	2059.14i	−0.110619	+	0.191598i	0.805401	+	0.592731i	$0.201950\pi$
$488$		0			0
$489$	5128.38	−	17713.1i	0.474260	−	1.63806i
$490$		0			0
$491$	5751.08	+	9961.17i	0.528600	+	0.915562i	0.999444	+	0.0333458i	$0.0106163\pi$
$491$	5751.08	+	9961.17i	0.528600	+	0.915562i	−0.470844	+	0.882217i	$0.656050\pi$
$492$		0			0
$493$	−2269.43	−	3930.77i	−0.207323	−	0.359093i
$494$		0			0
$495$	352.111	−	8789.21i	0.0319721	−	0.798072i
$496$		0			0
$497$	11913.1	+	11588.8i	1.07520	+	1.04593i
$498$		0			0
$499$	−620.939	+	1075.50i	−0.0557055	+	0.0964847i	−0.892533	−	0.450981i	$-0.851074\pi$
$499$	−620.939	+	1075.50i	−0.0557055	+	0.0964847i	0.836828	+	0.547466i	$0.184407\pi$
$500$		0			0
$501$	−472.316	+	1631.35i	−0.0421189	+	0.145476i
$502$		0			0
$503$	−11235.6			−0.995964			−0.497982	−	0.867187i	$-0.665925\pi$
$503$	−11235.6			−0.995964			−0.497982	+	0.867187i	$0.665925\pi$
$504$		0			0
$505$	−23297.2			−2.05289
$506$		0			0
$507$	−6038.08	+	1489.01i	−0.528917	+	0.130433i
$508$		0			0
$509$	5237.61	−	9071.81i	0.456096	−	0.789982i	−0.542654	−	0.839956i	$-0.682581\pi$
$509$	5237.61	−	9071.81i	0.456096	−	0.789982i	0.998751	+	0.0499742i	$0.0159139\pi$
$510$		0			0
$511$	8876.20	−	2510.13i	0.768415	−	0.217302i
$512$		0			0
$513$	41.1784	+	13.7311i	0.00354400	+	0.00118176i
$514$		0			0
$515$	−14604.6	−	25295.9i	−1.24962	−	2.16441i
$516$		0			0
$517$	−2767.55	−	4793.54i	−0.235429	−	0.407775i
$518$		0			0
$519$	−4623.38	−	4812.31i	−0.391028	−	0.407007i
$520$		0			0
$521$	5727.49	−	9920.30i	0.481623	−	0.834196i	−0.518154	−	0.855287i	$-0.673381\pi$
$521$	5727.49	−	9920.30i	0.481623	−	0.834196i	0.999778	+	0.0210913i	$0.00671407\pi$
$522$		0			0
$523$	3118.16	+	5400.82i	0.260703	+	0.451551i	0.966429	−	0.256934i	$-0.0827123\pi$
$523$	3118.16	+	5400.82i	0.260703	+	0.451551i	−0.705726	+	0.708485i	$0.749379\pi$
$524$		0			0
$525$	−29558.8	+	16821.4i	−2.45724	+	1.39837i
$526$		0			0
$527$	−689.924	+	1194.98i	−0.0570277	+	0.0987748i
$528$		0			0
$529$	3931.82	+	6810.11i	0.323155	+	0.559720i
$530$		0			0
$531$	647.985	−	16174.7i	0.0529570	−	1.32189i
$532$		0			0
$533$	1559.49	−	2701.11i	0.126733	−	0.219509i
$534$		0			0
$535$	−36209.4			−2.92611
$536$		0			0
$537$	−16682.4	+	4113.93i	−1.34059	+	0.330594i
$538$		0			0
$539$	−4352.29	+	2675.56i	−0.347804	+	0.213812i
$540$		0			0
$541$	2831.35	+	4904.04i	0.225008	+	0.389725i	0.956322	−	0.292316i	$-0.0944259\pi$
$541$	2831.35	+	4904.04i	0.225008	+	0.389725i	−0.731314	+	0.682041i	$0.761093\pi$
$542$		0			0
$543$	−2774.14	−	2887.50i	−0.219244	−	0.228203i
$544$		0			0
$545$	17901.5	+	31006.3i	1.40700	+	2.43700i
$546$		0			0
$547$	2868.71	−	4968.75i	0.224236	−	0.388388i	−0.731854	−	0.681462i	$-0.761345\pi$
$547$	2868.71	−	4968.75i	0.224236	−	0.388388i	0.956090	+	0.293073i	$0.0946780\pi$
$548$		0			0
$549$	964.645	−	24079.0i	0.0749910	−	1.87189i
$550$		0			0
$551$	−33.1668			−0.00256434
$552$		0			0
$553$	3770.12	+	3667.50i	0.289913	+	0.282022i
$554$		0			0
$555$	−19233.1	−	20019.1i	−1.47099	−	1.53110i
$556$		0			0
$557$	11093.9	−	19215.1i	0.843917	−	1.46171i	−0.0426420	−	0.999090i	$-0.513577\pi$
$557$	11093.9	−	19215.1i	0.843917	−	1.46171i	0.886559	−	0.462616i	$-0.153089\pi$
$558$		0			0
$559$	15741.7			1.19106
$560$		0			0
$561$	2270.35	+	2363.12i	0.170863	+	0.177845i
$562$		0			0
$563$	−1903.23			−0.142472			−0.0712359	−	0.997459i	$-0.522694\pi$
$563$	−1903.23			−0.142472			−0.0712359	+	0.997459i	$0.522694\pi$
$564$		0			0
$565$	−21661.0			−1.61289
$566$		0			0
$567$	8893.54	+	10158.2i	0.658719	+	0.752389i
$568$		0			0
$569$	25705.4			1.89390			0.946948	−	0.321387i	$-0.104149\pi$
$569$	25705.4			1.89390			0.946948	+	0.321387i	$0.104149\pi$
$570$		0			0
$571$	−10158.3			−0.744504			−0.372252	−	0.928132i	$-0.621414\pi$
$571$	−10158.3			−0.744504			−0.372252	+	0.928132i	$0.621414\pi$
$572$		0			0
$573$	−2246.29	−	2338.08i	−0.163770	−	0.170462i
$574$		0			0
$575$	23183.6			1.68143
$576$		0			0
$577$	6646.28	−	11511.7i	0.479529	−	0.830568i	−0.520195	−	0.854047i	$-0.674141\pi$
$577$	6646.28	−	11511.7i	0.479529	−	0.830568i	0.999724	+	0.0234788i	$0.00747422\pi$
$578$		0			0
$579$	−1766.87	−	1839.07i	−0.126820	−	0.132002i
$580$		0			0
$581$	−17232.6	+	4873.25i	−1.23051	+	0.347980i
$582$		0			0
$583$	−3029.88			−0.215240
$584$		0			0
$585$	−1377.18	+	34376.4i	−0.0973322	+	2.42956i
$586$		0			0
$587$	3658.10	−	6336.02i	0.257216	−	0.445512i	−0.708279	−	0.705933i	$-0.750528\pi$
$587$	3658.10	−	6336.02i	0.257216	−	0.445512i	0.965495	+	0.260421i	$0.0838614\pi$
$588$		0			0
$589$	5.04148	+	8.73210i	0.000352683	+	0.000610866i
$590$		0			0
$591$	5220.04	+	5433.35i	0.363323	+	0.378170i
$592$		0			0
$593$	9022.95	+	15628.2i	0.624837	+	1.08225i	0.988572	+	0.150747i	$0.0481677\pi$
$593$	9022.95	+	15628.2i	0.624837	+	1.08225i	−0.363736	+	0.931502i	$0.618499\pi$
$594$		0			0
$595$	4210.21	−	16627.0i	0.290087	−	1.14561i
$596$		0			0
$597$	7718.78	−	1903.48i	0.529160	−	0.130493i
$598$		0			0
$599$	2400.65			0.163753			0.0818764	−	0.996642i	$-0.473909\pi$
$599$	2400.65			0.163753			0.0818764	+	0.996642i	$0.473909\pi$
$600$		0			0
$601$	−2367.41	+	4100.47i	−0.160680	+	0.278306i	−0.935113	−	0.354350i	$-0.884702\pi$
$601$	−2367.41	+	4100.47i	−0.160680	+	0.278306i	0.774433	+	0.632656i	$0.218035\pi$
$602$		0			0
$603$	−1017.58	+	25400.4i	−0.0687218	+	1.71540i
$604$		0			0
$605$	12129.9	+	21009.6i	0.815126	+	1.41184i
$606$		0			0
$607$	−738.545	+	1279.20i	−0.0493849	+	0.0855371i	−0.889661	−	0.456621i	$-0.849059\pi$
$607$	−738.545	+	1279.20i	−0.0493849	+	0.0855371i	0.840276	+	0.542158i	$0.182393\pi$
$608$		0			0
$609$	−8901.70	−	5213.52i	−0.592307	−	0.346901i
$610$		0			0
$611$	10824.5	+	18748.5i	0.716712	+	1.24138i
$612$		0			0
$613$	9807.86	−	16987.7i	0.646225	−	1.11929i	−0.337793	−	0.941221i	$-0.609680\pi$
$613$	9807.86	−	16987.7i	0.646225	−	1.11929i	0.984017	−	0.178073i	$-0.0569864\pi$
$614$		0			0
$615$	−4215.62	−	4387.89i	−0.276407	−	0.287702i
$616$		0			0
$617$	1950.95	+	3379.15i	0.127297	+	0.220485i	0.922629	−	0.385690i	$-0.126036\pi$
$617$	1950.95	+	3379.15i	0.127297	+	0.220485i	−0.795331	+	0.606175i	$0.792703\pi$
$618$		0			0
$619$	−6132.59	−	10622.0i	−0.398206	−	0.689714i	0.595298	−	0.803505i	$-0.297034\pi$
$619$	−6132.59	−	10622.0i	−0.398206	−	0.689714i	−0.993505	+	0.113791i	$0.963701\pi$
$620$		0			0
$621$	−1844.12	−	9016.77i	−0.119166	−	0.582658i
$622$		0			0
$623$	3372.85	−	13320.1i	0.216903	−	0.856597i
$624$		0			0
$625$	−32548.4	+	56375.4i	−2.08310	+	3.60803i
$626$		0			0
$627$	23.2496	−	5.73343i	0.00148086	−	0.000365185i
$628$		0			0
$629$	10342.3			0.655603
$630$		0			0
$631$	6023.19			0.379999			0.190000	−	0.981784i	$-0.439151\pi$
$631$	6023.19			0.379999			0.190000	+	0.981784i	$0.439151\pi$
$632$		0			0
$633$	571.988	−	1975.61i	0.0359154	−	0.124049i
$634$		0			0
$635$	2932.26	−	5078.83i	0.183249	−	0.317397i
$636$		0			0
$637$	17022.7	−	10464.7i	1.05881	−	0.650904i
$638$		0			0
$639$	969.898	−	24210.1i	0.0600447	−	1.49881i
$640$		0			0
$641$	−7189.35	−	12452.3i	−0.442999	−	0.767297i	0.554911	−	0.831909i	$-0.312752\pi$
$641$	−7189.35	−	12452.3i	−0.442999	−	0.767297i	−0.997910	+	0.0646126i	$0.979419\pi$
$642$		0			0
$643$	−5286.35	−	9156.23i	−0.324220	−	0.561565i	0.657134	−	0.753773i	$-0.271768\pi$
$643$	−5286.35	−	9156.23i	−0.324220	−	0.561565i	−0.981354	+	0.192208i	$0.938435\pi$
$644$		0			0
$645$	8540.74	−	29499.1i	0.521382	−	1.80082i
$646$		0			0
$647$	−2315.06	+	4009.80i	−0.140671	+	0.243650i	−0.927750	−	0.373203i	$-0.878259\pi$
$647$	−2315.06	+	4009.80i	−0.140671	+	0.243650i	0.787078	+	0.616853i	$0.211593\pi$
$648$		0			0
$649$	−4465.04	−	7733.67i	−0.270059	−	0.467755i
$650$		0			0
$651$	−19.5158	+	3136.10i	−0.00117494	+	0.188807i
$652$		0			0
$653$	65.6264	−	113.668i	0.00393287	−	0.00681192i	−0.864052	−	0.503402i	$-0.832081\pi$
$653$	65.6264	−	113.668i	0.00393287	−	0.00681192i	0.867985	+	0.496590i	$0.165415\pi$
$654$		0			0
$655$	12637.1	+	21888.2i	0.753854	+	1.30571i
$656$		0			0
$657$	−11367.6	−	7184.68i	−0.675028	−	0.426638i
$658$		0			0
$659$	−11474.1	+	19873.7i	−0.678250	+	1.17476i	0.297258	+	0.954797i	$0.403928\pi$
$659$	−11474.1	+	19873.7i	−0.678250	+	1.17476i	−0.975508	+	0.219965i	$0.929406\pi$
$660$		0			0
$661$	21485.0			1.26425			0.632124	−	0.774867i	$-0.282183\pi$
$661$	21485.0			1.26425			0.632124	+	0.774867i	$0.282183\pi$
$662$		0			0
$663$	−8879.81	−	9242.68i	−0.520156	−	0.541412i
$664$		0			0
$665$	−89.8381	−	87.3927i	−0.00523876	−	0.00509615i
$666$		0			0
$667$	3516.08	+	6090.03i	0.204113	+	0.353533i
$668$		0			0
$669$	−10559.8	+	2604.08i	−0.610262	+	0.150493i
$670$		0			0
$671$	−6647.02	−	11513.0i	−0.382422	−	0.662375i
$672$		0			0
$673$	−5004.17	+	8667.48i	−0.286622	+	0.496444i	−0.973001	−	0.230800i	$-0.925866\pi$
$673$	−5004.17	+	8667.48i	−0.286622	+	0.496444i	0.686379	+	0.727244i	$0.259199\pi$
$674$		0			0
$675$	47035.8	+	15684.3i	2.68209	+	0.894355i
$676$		0			0
$677$	2676.12			0.151922			0.0759612	−	0.997111i	$-0.475797\pi$
$677$	2676.12			0.151922			0.0759612	+	0.997111i	$0.475797\pi$
$678$		0			0
$679$	13383.2	−	3784.68i	0.756408	−	0.213907i
$680$		0			0
$681$	−4587.14	+	15843.7i	−0.258120	+	0.891527i
$682$		0			0
$683$	−5218.41	+	9038.56i	−0.292353	+	0.506370i	−0.974366	−	0.224970i	$-0.927772\pi$
$683$	−5218.41	+	9038.56i	−0.292353	+	0.506370i	0.682013	+	0.731340i	$0.261105\pi$
$684$		0			0
$685$	−62216.2			−3.47030
$686$		0			0
$687$	5314.86	−	1310.66i	0.295160	−	0.0727873i
$688$		0			0
$689$	11850.5			0.655251
$690$		0			0
$691$	−8037.81			−0.442508			−0.221254	−	0.975216i	$-0.571015\pi$
$691$	−8037.81			−0.442508			−0.221254	+	0.975216i	$0.571015\pi$
$692$		0			0
$693$	7141.25	+	2115.82i	0.391448	+	0.115979i
$694$		0			0
$695$	39166.9			2.13768
$696$		0			0
$697$	2266.88			0.123191
$698$		0			0
$699$	941.566	−	3252.10i	0.0509489	−	0.175974i
$700$		0			0
$701$	−13759.8			−0.741368			−0.370684	−	0.928759i	$-0.620877\pi$
$701$	−13759.8			−0.741368			−0.370684	+	0.928759i	$0.620877\pi$
$702$		0			0
$703$	37.7871	−	65.4491i	0.00202726	−	0.00351132i
$704$		0			0
$705$	41006.5	−	10112.3i	2.19063	−	0.540217i
$706$		0			0
$707$	4842.23	−	19123.0i	0.257582	−	1.01725i
$708$		0			0
$709$	6558.60			0.347410			0.173705	−	0.984798i	$-0.444426\pi$
$709$	6558.60			0.347410			0.173705	+	0.984798i	$0.444426\pi$
$710$		0			0
$711$	306.943	−	7661.77i	0.0161903	−	0.404133i
$712$		0			0
$713$	1068.91	−	1851.41i	0.0561447	−	0.0972454i
$714$		0			0
$715$	9489.65	+	16436.6i	0.496353	+	0.859709i
$716$		0			0
$717$	8032.97	−	27745.3i	0.418406	−	1.44514i
$718$		0			0
$719$	482.525	+	835.757i	0.0250280	+	0.0433498i	0.878268	−	0.478168i	$-0.158699\pi$
$719$	482.525	+	835.757i	0.0250280	+	0.0433498i	−0.853240	+	0.521518i	$0.825366\pi$
$720$		0			0
$721$	23799.1	−	6730.21i	1.22930	−	0.347637i
$722$		0			0
$723$	−3069.79	+	10602.8i	−0.157907	+	0.545399i
$724$		0			0
$725$	−37884.6			−1.94069
$726$		0			0
$727$	−15860.1	+	27470.5i	−0.809104	+	1.40141i	0.104382	+	0.994537i	$0.466714\pi$
$727$	−15860.1	+	27470.5i	−0.809104	+	1.40141i	−0.913485	+	0.406871i	$0.866620\pi$
$728$		0			0
$729$	2358.66	−	19541.2i	0.119832	−	0.992794i
$730$		0			0
$731$	5720.57	+	9908.32i	0.289443	+	0.501330i
$732$		0			0
$733$	−6288.08	+	10891.3i	−0.316856	+	0.548811i	−0.979830	−	0.199831i	$-0.935961\pi$
$733$	−6288.08	+	10891.3i	−0.316856	+	0.548811i	0.662974	+	0.748642i	$0.269294\pi$
$734$		0			0
$735$	−10374.5	−	37577.2i	−0.520637	−	1.88579i
$736$		0			0
$737$	7011.81	+	12144.8i	0.350452	+	0.607001i
$738$		0			0
$739$	11332.3	−	19628.2i	0.564095	−	0.977042i	−0.433038	−	0.901376i	$-0.642558\pi$
$739$	11332.3	−	19628.2i	0.564095	−	0.977042i	0.997133	−	0.0756659i	$-0.0241083\pi$
$740$		0			0
$741$	−90.9342	+	22.4247i	−0.00450816	+	0.00111173i
$742$		0			0
$743$	2879.78	+	4987.93i	0.142192	+	0.246285i	0.928322	−	0.371777i	$-0.121251\pi$
$743$	2879.78	+	4987.93i	0.142192	+	0.246285i	−0.786130	+	0.618062i	$0.787918\pi$
$744$		0			0
$745$	33009.1	+	57173.4i	1.62330	+	2.81164i
$746$		0			0
$747$	22069.5	+	13948.6i	1.08096	+	0.683203i
$748$		0			0
$749$	7525.99	−	29721.7i	0.367148	−	1.44994i
$750$		0			0
$751$	−6157.19	+	10664.6i	−0.299173	+	0.518183i	−0.975947	−	0.218008i	$-0.930044\pi$
$751$	−6157.19	+	10664.6i	−0.299173	+	0.518183i	0.676774	+	0.736191i	$0.263377\pi$
$752$		0			0
$753$	7636.24	+	7948.29i	0.369562	+	0.384664i
$754$		0			0
$755$	−50210.7			−2.42034
$756$		0			0
$757$	−55.0545			−0.00264332			−0.00132166	−	0.999999i	$-0.500421\pi$
$757$	−55.0545			−0.00264332			−0.00132166	+	0.999999i	$0.500421\pi$
$758$		0			0
$759$	−3517.50	−	3661.24i	−0.168218	−	0.175092i
$760$		0			0
$761$	−8679.25	+	15032.9i	−0.413433	+	0.716087i	−0.995263	−	0.0972240i	$-0.969004\pi$
$761$	−8679.25	+	15032.9i	−0.413433	+	0.716087i	0.581830	+	0.813311i	$0.302337\pi$
$762$		0			0
$763$	−29171.6	+	8249.52i	−1.38412	+	0.391419i
$764$		0			0
$765$	−22138.0	+	11625.6i	−1.04628	+	0.549444i
$766$		0			0
$767$	17463.7	+	30248.0i	0.822135	+	1.42398i
$768$		0			0
$769$	−16709.4	−	28941.4i	−0.783556	−	1.35716i	−0.929858	−	0.367919i	$-0.880070\pi$
$769$	−16709.4	−	28941.4i	−0.783556	−	1.35716i	0.146302	−	0.989240i	$-0.453263\pi$
$770$		0			0
$771$	−13489.6	+	3326.58i	−0.630112	+	0.155388i
$772$		0			0
$773$	−5857.11	+	10144.8i	−0.272530	+	0.472036i	−0.969509	−	0.245056i	$-0.921194\pi$
$773$	−5857.11	+	10144.8i	−0.272530	+	0.472036i	0.696979	+	0.717092i	$0.254527\pi$
$774$		0			0
$775$	5758.60	+	9974.18i	0.266910	+	0.462301i
$776$		0			0
$777$	20429.8	−	11626.2i	0.943260	−	0.536793i
$778$		0			0
$779$	8.28237	−	14.3455i	0.000380933	−	0.000659795i
$780$		0			0
$781$	−6683.22	−	11575.7i	−0.306203	−	0.530359i
$782$		0			0
$783$	3013.49	+	14734.4i	0.137540	+	0.672496i
$784$		0			0
$785$	17477.9	−	30272.7i	0.794668	−	1.37640i
$786$		0			0
$787$	10601.1			0.480163			0.240082	−	0.970753i	$-0.422826\pi$
$787$	10601.1			0.480163			0.240082	+	0.970753i	$0.422826\pi$
$788$		0			0
$789$	−370.053	+	1278.14i	−0.0166974	+	0.0576716i
$790$		0			0
$791$	4502.16	−	17780.0i	0.202374	−	0.799220i
$792$		0			0
$793$	25997.9	+	45029.7i	1.16420	+	2.01646i
$794$		0			0
$795$	6429.53	−	22207.1i	0.286833	−	0.990699i
$796$		0			0
$797$	14497.3	+	25110.1i	0.644319	+	1.11599i	0.984458	+	0.175618i	$0.0561924\pi$
$797$	14497.3	+	25110.1i	0.644319	+	1.11599i	−0.340140	+	0.940375i	$0.610474\pi$
$798$		0			0
$799$	−7867.26	+	13626.5i	−0.348340	+	0.603342i
$800$		0			0
$801$	−17735.1	+	9313.44i	−0.782320	+	0.410829i
$802$		0			0
$803$	−7418.58			−0.326023
$804$		0			0
$805$	−6522.96	+	25760.6i	−0.285595	+	1.12788i
$806$		0			0
$807$	−25106.5	+	6191.33i	−1.09515	+	0.270069i
$808$		0			0
$809$	−7738.82	+	13404.0i	−0.336319	+	0.582522i	−0.983737	−	0.179613i	$-0.942515\pi$
$809$	−7738.82	+	13404.0i	−0.336319	+	0.582522i	0.647418	+	0.762135i	$0.275849\pi$
$810$		0			0
$811$	−9983.84			−0.432281			−0.216141	−	0.976362i	$-0.569347\pi$
$811$	−9983.84			−0.432281			−0.216141	+	0.976362i	$0.569347\pi$
$812$		0			0
$813$	564.421	−	1949.47i	0.0243482	−	0.0840971i
$814$		0			0
$815$	77623.1			3.33622
$816$		0			0
$817$	83.6038			0.00358008
$818$		0			0
$819$	−27930.9	−	8275.44i	−1.19168	−	0.353073i
$820$		0			0
$821$	19163.3			0.814620			0.407310	−	0.913290i	$-0.366467\pi$
$821$	19163.3			0.814620			0.407310	+	0.913290i	$0.366467\pi$
$822$		0			0
$823$	32806.3			1.38950			0.694749	−	0.719252i	$-0.255515\pi$
$823$	32806.3			1.38950			0.694749	+	0.719252i	$0.255515\pi$
$824$		0			0
$825$	26556.7	−	6548.98i	1.12071	−	0.276371i
$826$		0			0
$827$	6282.43			0.264161			0.132081	−	0.991239i	$-0.457834\pi$
$827$	6282.43			0.264161			0.132081	+	0.991239i	$0.457834\pi$
$828$		0			0
$829$	−14335.8	+	24830.3i	−0.600605	+	1.04028i	0.392124	+	0.919912i	$0.371740\pi$
$829$	−14335.8	+	24830.3i	−0.600605	+	1.04028i	−0.992729	+	0.120367i	$0.961593\pi$
$830$		0			0
$831$	−10003.6	+	34551.7i	−0.417594	+	1.44234i
$832$		0			0
$833$	12772.9	+	6911.72i	0.531276	+	0.287487i
$834$		0			0
$835$	−7148.98			−0.296288
$836$		0			0
$837$	3421.18	−	3033.07i	0.141282	−	0.125255i
$838$		0			0
$839$	8476.77	−	14682.2i	0.348809	−	0.604155i	−0.637229	−	0.770674i	$-0.719920\pi$
$839$	8476.77	−	14682.2i	0.348809	−	0.604155i	0.986038	+	0.166520i	$0.0532529\pi$
$840$		0			0
$841$	6448.84	+	11169.7i	0.264416	+	0.457982i
$842$		0			0
$843$	−40472.2	+	9980.58i	−1.65354	+	0.407769i
$844$		0			0
$845$	−13089.0	−	22670.8i	−0.532870	−	0.922958i
$846$		0			0
$847$	−19766.5	+	5589.82i	−0.801870	+	0.226763i
$848$		0			0
$849$	−15778.2	−	16423.0i	−0.637818	−	0.663882i
$850$		0			0
$851$	−16023.5			−0.645452
$852$		0			0
$853$	22605.7	−	39154.3i	0.907392	−	1.57165i	0.0897183	−	0.995967i	$-0.471403\pi$
$853$	22605.7	−	39154.3i	0.907392	−	1.57165i	0.817674	−	0.575682i	$-0.195263\pi$
$854$		0			0
$855$	−7.31414	+	182.572i	−0.000292559	+	0.00730272i
$856$		0			0
$857$	3129.37	+	5420.22i	0.124734	+	0.216046i	0.921629	−	0.388072i	$-0.126859\pi$
$857$	3129.37	+	5420.22i	0.124734	+	0.216046i	−0.796895	+	0.604118i	$0.793526\pi$
$858$		0			0
$859$	18220.1	−	31558.1i	0.723704	−	1.25349i	−0.235801	−	0.971801i	$-0.575771\pi$
$859$	18220.1	−	31558.1i	0.723704	−	1.25349i	0.959505	−	0.281691i	$-0.0908952\pi$
$860$		0			0
$861$	4477.90	−	2548.30i	0.177243	−	0.100866i
$862$		0			0
$863$	9394.86	+	16272.4i	0.370573	+	0.641851i	0.989654	−	0.143476i	$-0.0458280\pi$
$863$	9394.86	+	16272.4i	0.370573	+	0.641851i	−0.619081	+	0.785327i	$0.712495\pi$
$864$		0			0
$865$	14045.4	−	24327.3i	0.552089	−	0.956246i
$866$		0			0
$867$	−4508.95	+	15573.6i	−0.176623	+	0.610043i
$868$		0			0
$869$	−2115.04	−	3663.35i	−0.0825636	−	0.143004i
$870$		0			0
$871$	−27424.7	−	47500.9i	−1.06688	−	1.84788i
$872$		0			0
$873$	−17139.7	−	10832.8i	−0.664479	−	0.419971i
$874$		0			0
$875$	−66321.6	−	64516.3i	−2.56238	−	2.49263i
$876$		0			0
$877$	−370.186	+	641.181i	−0.0142535	+	0.0246877i	−0.873064	−	0.487605i	$-0.837871\pi$
$877$	−370.186	+	641.181i	−0.0142535	+	0.0246877i	0.858811	+	0.512293i	$0.171204\pi$
$878$		0			0
$879$	−6326.04	+	21849.7i	−0.242744	+	0.838421i
$880$		0			0
$881$	30941.1			1.18324			0.591618	−	0.806218i	$-0.298489\pi$
$881$	30941.1			1.18324			0.591618	+	0.806218i	$0.298489\pi$
$882$		0			0
$883$	19722.2			0.751646			0.375823	−	0.926691i	$-0.377360\pi$
$883$	19722.2			0.751646			0.375823	+	0.926691i	$0.377360\pi$
$884$		0			0
$885$	66158.0	−	16314.8i	2.51286	−	0.619678i
$886$		0			0
$887$	−12393.4	+	21466.0i	−0.469142	+	0.812578i	−0.999378	−	0.0352725i	$-0.988770\pi$
$887$	−12393.4	+	21466.0i	−0.469142	+	0.812578i	0.530236	+	0.847850i	$0.322103\pi$
$888$		0			0
$889$	3559.39	+	3462.50i	0.134284	+	0.130628i
$890$		0			0
$891$	−4659.52	−	9807.74i	−0.175196	−	0.368767i
$892$		0			0
$893$	57.4883	+	99.5727i	0.00215428	+	0.00373133i
$894$		0			0
$895$	−36163.1	−	62636.3i	−1.35061	−	2.33933i
$896$		0			0
$897$	13757.7	+	14319.9i	0.512102	+	0.533029i
$898$		0			0
$899$	−1746.72	+	3025.41i	−0.0648014	+	0.112239i
$900$		0			0
$901$	4306.48	+	7459.05i	0.159234	+	0.275801i
$902$		0			0
$903$	22438.6	+	13141.8i	0.826920	+	0.484308i
$904$		0			0
$905$	8427.55	−	14597.0i	0.309548	−	0.536154i
$906$		0			0
$907$	−19748.5	−	34205.3i	−0.722973	−	1.25223i	−0.959803	−	0.280676i	$-0.909442\pi$
$907$	−19748.5	−	34205.3i	−0.722973	−	1.25223i	0.236829	−	0.971551i	$-0.423892\pi$
$908$		0			0
$909$	−25461.3	+	13370.8i	−0.929041	+	0.487879i
$910$		0			0
$911$	−6977.61	+	12085.6i	−0.253764	+	0.439531i	−0.964559	−	0.263867i	$-0.915002\pi$
$911$	−6977.61	+	12085.6i	−0.253764	+	0.439531i	0.710795	+	0.703399i	$0.248335\pi$
$912$		0			0
$913$	14402.7			0.522081
$914$		0			0
$915$	98488.3	−	24287.5i	3.55838	−	0.877509i
$916$		0			0
$917$	−20593.0	+	5823.56i	−0.741594	+	0.209718i
$918$		0			0
$919$	−11048.1	−	19136.0i	−0.396567	−	0.686874i	0.596733	−	0.802440i	$-0.296465\pi$
$919$	−11048.1	−	19136.0i	−0.396567	−	0.686874i	−0.993300	+	0.115566i	$0.963132\pi$
$920$		0			0
$921$	−3436.41	−	3576.84i	−0.122946	−	0.127970i
$922$		0			0
$923$	26139.5	+	45274.9i	0.932168	+	1.61456i
$924$		0			0
$925$	43162.0	−	74758.8i	1.53423	−	2.65736i
$926$		0			0
$927$	−30479.1	−	19263.7i	−1.07990	−	0.682529i
$928$		0			0
$929$	−43564.6			−1.53854			−0.769272	−	0.638922i	$-0.779381\pi$
$929$	−43564.6			−1.53854			−0.769272	+	0.638922i	$0.779381\pi$
$930$		0			0
$931$	90.4069	−	55.5775i	0.00318256	−	0.00195648i
$932$		0			0
$933$	3738.23	+	3890.99i	0.131173	+	0.136533i
$934$		0			0
$935$	−6897.10	+	11946.1i	−0.241240	+	0.417840i
$936$		0			0
$937$	−39176.1			−1.36588			−0.682938	−	0.730476i	$-0.739298\pi$
$937$	−39176.1			−1.36588			−0.682938	+	0.730476i	$0.739298\pi$
$938$		0			0
$939$	−11712.3	−	12190.9i	−0.407047	−	0.423681i
$940$		0			0
$941$	6360.84			0.220359			0.110179	−	0.993912i	$-0.464857\pi$
$941$	6360.84			0.220359			0.110179	+	0.993912i	$0.464857\pi$
$942$		0			0
$943$	−3512.12			−0.121284
$944$		0			0
$945$	−30661.7	+	47851.1i	−1.05548	+	1.64719i
$946$		0			0
$947$	−29442.1			−1.01029			−0.505143	−	0.863036i	$-0.668560\pi$
$947$	−29442.1			−1.01029			−0.505143	+	0.863036i	$0.668560\pi$
$948$		0			0
$949$	29015.6			0.992505
$950$		0			0
$951$	13685.2	+	14244.4i	0.466639	+	0.485707i
$952$		0			0
$953$	−9082.56			−0.308723			−0.154361	−	0.988014i	$-0.549332\pi$
$953$	−9082.56			−0.308723			−0.154361	+	0.988014i	$0.549332\pi$
$954$		0			0
$955$	6824.02	−	11819.5i	0.231225	−	0.400494i
$956$		0			0
$957$	5747.98	+	5982.87i	0.194154	+	0.202088i
$958$		0			0
$959$	12931.4	−	51068.9i	0.435429	−	1.71960i
$960$		0			0
$961$	−28729.0			−0.964351
$962$		0			0
$963$	−39573.0	+	20781.4i	−1.32422	+	0.695403i
$964$		0			0
$965$	5367.59	−	9296.93i	0.179056	−	0.310134i
$966$		0			0
$967$	−20971.3	−	36323.4i	−0.697407	−	1.20795i	−0.969362	−	0.245635i	$-0.921003\pi$
$967$	−20971.3	−	36323.4i	−0.697407	−	1.20795i	0.271955	−	0.962310i	$-0.412330\pi$
$968$		0			0
$969$	−47.1603	−	49.0875i	−0.00156348	−	0.00162737i
$970$		0			0
$971$	−6125.00	−	10608.8i	−0.202431	−	0.350621i	0.746880	−	0.664959i	$-0.231551\pi$
$971$	−6125.00	−	10608.8i	−0.202431	−	0.350621i	−0.949311	+	0.314338i	$0.898218\pi$
$972$		0			0
$973$	−8140.68	+	32149.3i	−0.268220	+	1.05926i
$974$		0			0
$975$	−103869.	+	25614.4i	−3.41176	+	0.841352i
$976$		0			0
$977$	−22152.2			−0.725396			−0.362698	−	0.931907i	$-0.618144\pi$
$977$	−22152.2			−0.725396			−0.362698	+	0.931907i	$0.618144\pi$
$978$		0			0
$979$	−5525.36	+	9570.21i	−0.180379	+	0.312426i
$980$		0			0
$981$	37359.6	+	23612.4i	1.21590	+	0.768488i
$982$		0			0
$983$	−3017.43	−	5226.35i	−0.0979056	−	0.169577i	0.812912	−	0.582387i	$-0.197881\pi$
$983$	−3017.43	−	5226.35i	−0.0979056	−	0.169577i	−0.910818	+	0.412809i	$0.864548\pi$
$984$		0			0
$985$	−15858.0	+	27466.8i	−0.512972	+	0.888493i
$986$		0			0
$987$	−222.540	+	35761.2i	−0.00717681	+	1.15328i
$988$		0			0
$989$	−8863.00	−	15351.2i	−0.284962	−	0.493568i
$990$		0			0
$991$	−10448.3	+	18097.1i	−0.334917	+	0.580093i	−0.983469	−	0.181077i	$-0.942042\pi$
$991$	−10448.3	+	18097.1i	−0.334917	+	0.580093i	0.648552	+	0.761170i	$0.275375\pi$
$992$		0			0
$993$	36816.7	+	38321.2i	1.17658	+	1.22466i
$994$		0			0
$995$	16732.3	+	28981.2i	0.533116	+	0.923383i
$996$		0			0
$997$	577.230	+	999.791i	0.0183361	+	0.0317590i	0.875048	−	0.484036i	$-0.160830\pi$
$997$	577.230	+	999.791i	0.0183361	+	0.0317590i	−0.856712	+	0.515795i	$0.827496\pi$
$998$		0			0
$999$	−32509.1	−	10840.3i	−1.02957	−	0.343316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.i.a.25.18	✓	48
3.2	odd	2		756.4.i.a.613.24		48
7.2	even	3		252.4.l.a.205.2	yes	48
9.4	even	3		252.4.l.a.193.2	yes	48
9.5	odd	6		756.4.l.a.361.1		48
21.2	odd	6		756.4.l.a.289.1		48
63.23	odd	6		756.4.i.a.37.24		48
63.58	even	3	inner	252.4.i.a.121.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.i.a.25.18	✓	48	1.1	even	1	trivial
252.4.i.a.121.18	yes	48	63.58	even	3	inner
252.4.l.a.193.2	yes	48	9.4	even	3
252.4.l.a.205.2	yes	48	7.2	even	3
756.4.i.a.37.24		48	63.23	odd	6
756.4.i.a.613.24		48	3.2	odd	2
756.4.l.a.289.1		48	21.2	odd	6
756.4.l.a.361.1		48	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(3.59994 + 3.74705i) q^{3} +(-10.9363 + 18.9422i) q^{5} +(-13.2752 - 12.9139i) q^{7} +(-1.08080 + 26.9784i) q^{9} +O(q^{10})\)	\(q+(3.59994 + 3.74705i) q^{3} +(-10.9363 + 18.9422i) q^{5} +(-13.2752 - 12.9139i) q^{7} +(-1.08080 + 26.9784i) q^{9} +(7.44740 + 12.8993i) q^{11} +(-29.1283 - 50.4518i) q^{13} +(-110.347 + 27.2120i) q^{15} +(21.1706 - 36.6685i) q^{17} +(-0.154699 - 0.267947i) q^{19} +(0.598848 - 96.2322i) q^{21} +(-32.8000 + 56.8112i) q^{23} +(-176.704 - 306.061i) q^{25} +(-104.980 + 93.0708i) q^{27} +(53.5988 - 92.8358i) q^{29} -32.5889 q^{31} +(-21.5240 + 74.3425i) q^{33} +(389.799 - 110.232i) q^{35} +(122.131 + 211.536i) q^{37} +(84.1850 - 290.769i) q^{39} +(26.7692 + 46.3657i) q^{41} +(-135.107 + 234.012i) q^{43} +(-499.209 - 315.516i) q^{45} -371.613 q^{47} +(9.46373 + 342.869i) q^{49} +(213.612 - 52.6773i) q^{51} +(-101.709 + 176.166i) q^{53} -325.787 q^{55} +(0.447103 - 1.54426i) q^{57} -599.543 q^{59} -892.529 q^{61} +(362.743 - 344.187i) q^{63} +1274.22 q^{65} +941.511 q^{67} +(-330.953 + 81.6141i) q^{69} -897.389 q^{71} +(-249.033 + 431.337i) q^{73} +(510.701 - 1763.92i) q^{75} +(67.7136 - 267.416i) q^{77} -283.997 q^{79} +(-726.664 - 58.3164i) q^{81} +(483.481 - 837.413i) q^{83} +(463.054 + 802.034i) q^{85} +(540.813 - 133.366i) q^{87} +(370.959 + 642.520i) q^{89} +(-264.842 + 1045.92i) q^{91} +(-117.318 - 122.112i) q^{93} +6.76735 q^{95} +(-375.482 + 650.355i) q^{97} +(-356.050 + 186.977i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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