LMFDB - Embedded newform 252.4.b.e.55.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(55,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("252.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.b (of order $2$, degree $1$, 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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 2x^{10} - 6x^{9} + 56x^{7} - 448x^{6} + 448x^{5} - 3072x^{3} - 8192x^{2} - 32768x + 262144 $ x^12 - x^11 - 2x^10 - 6x^9 + 56x^7 - 448x^6 + 448x^5 - 3072x^3 - 8192x^2 - 32768x + 262144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.7
Root			$-0.951271 + 2.66366i$ of defining polynomial
Character	$\chi$	$=$	252.55
Dual form			252.4.b.e.55.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951271 - 2.66366i) q^{2} +(-6.19017 - 5.06772i) q^{4} +10.8462i q^{5} +(15.1344 - 10.6748i) q^{7} +(-19.3872 + 11.6677i) q^{8} +O(q^{10})$	\(q+(0.951271 - 2.66366i) q^{2} +(-6.19017 - 5.06772i) q^{4} +10.8462i q^{5} +(15.1344 - 10.6748i) q^{7} +(-19.3872 + 11.6677i) q^{8} +(28.8905 + 10.3176i) q^{10} +45.0243i q^{11} +40.3676i q^{13} +(-14.0371 - 50.4674i) q^{14} +(12.6364 + 62.7401i) q^{16} -8.11855i q^{17} +53.3328 q^{19} +(54.9654 - 67.1397i) q^{20} +(119.929 + 42.8303i) q^{22} +55.7907i q^{23} +7.36043 q^{25} +(107.526 + 38.4005i) q^{26} +(-147.781 - 10.6181i) q^{28} +169.210 q^{29} +262.968 q^{31} +(179.139 + 26.0238i) q^{32} +(-21.6251 - 7.72294i) q^{34} +(115.781 + 164.150i) q^{35} -354.930 q^{37} +(50.7339 - 142.060i) q^{38} +(-126.550 - 210.277i) q^{40} -42.7783i q^{41} +23.1555i q^{43} +(228.171 - 278.708i) q^{44} +(148.607 + 53.0721i) q^{46} +437.834 q^{47} +(115.098 - 323.112i) q^{49} +(7.00176 - 19.6057i) q^{50} +(204.572 - 249.882i) q^{52} -388.515 q^{53} -488.341 q^{55} +(-168.863 + 383.538i) q^{56} +(160.965 - 450.718i) q^{58} -649.834 q^{59} +916.217i q^{61} +(250.154 - 700.457i) q^{62} +(239.728 - 452.410i) q^{64} -437.834 q^{65} +736.636i q^{67} +(-41.1426 + 50.2552i) q^{68} +(547.379 - 152.249i) q^{70} -600.682i q^{71} +673.579i q^{73} +(-337.634 + 945.413i) q^{74} +(-330.139 - 270.276i) q^{76} +(480.624 + 681.414i) q^{77} -585.232i q^{79} +(-680.490 + 137.056i) q^{80} +(-113.947 - 40.6938i) q^{82} +856.883 q^{83} +88.0553 q^{85} +(61.6784 + 22.0272i) q^{86} +(-525.331 - 872.896i) q^{88} -920.574i q^{89} +(430.915 + 610.938i) q^{91} +(282.732 - 345.354i) q^{92} +(416.499 - 1166.24i) q^{94} +578.457i q^{95} +638.990i q^{97} +(-751.171 - 613.949i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + 5 q^{4} - 10 q^{7} - 25 q^{8}+O(q^{10}) $ 12 * q - q^2 + 5 * q^4 - 10 * q^7 - 25 * q^8	$ 12 q - q^{2} + 5 q^{4} - 10 q^{7} - 25 q^{8} - 56 q^{10} - 101 q^{14} + 41 q^{16} + 84 q^{19} + 172 q^{20} - 182 q^{22} - 216 q^{25} + 300 q^{26} - 379 q^{28} - 200 q^{29} + 384 q^{31} + 159 q^{32} + 164 q^{34} + 84 q^{35} - 244 q^{37} + 268 q^{38} + 316 q^{40} - 190 q^{44} + 894 q^{46} + 280 q^{47} - 424 q^{49} + 1771 q^{50} + 796 q^{52} + 16 q^{53} - 212 q^{55} + 1759 q^{56} - 570 q^{58} + 1168 q^{59} - 384 q^{62} + 2705 q^{64} - 280 q^{65} + 1552 q^{68} + 2592 q^{70} - 1622 q^{74} + 788 q^{76} - 968 q^{77} - 3060 q^{80} + 2540 q^{82} - 968 q^{83} - 852 q^{85} + 258 q^{86} - 2186 q^{88} - 1648 q^{91} - 4298 q^{92} - 4256 q^{94} - 3137 q^{98}+O(q^{100}) $ 12 * q - q^2 + 5 * q^4 - 10 * q^7 - 25 * q^8 - 56 * q^10 - 101 * q^14 + 41 * q^16 + 84 * q^19 + 172 * q^20 - 182 * q^22 - 216 * q^25 + 300 * q^26 - 379 * q^28 - 200 * q^29 + 384 * q^31 + 159 * q^32 + 164 * q^34 + 84 * q^35 - 244 * q^37 + 268 * q^38 + 316 * q^40 - 190 * q^44 + 894 * q^46 + 280 * q^47 - 424 * q^49 + 1771 * q^50 + 796 * q^52 + 16 * q^53 - 212 * q^55 + 1759 * q^56 - 570 * q^58 + 1168 * q^59 - 384 * q^62 + 2705 * q^64 - 280 * q^65 + 1552 * q^68 + 2592 * q^70 - 1622 * q^74 + 788 * q^76 - 968 * q^77 - 3060 * q^80 + 2540 * q^82 - 968 * q^83 - 852 * q^85 + 258 * q^86 - 2186 * q^88 - 1648 * q^91 - 4298 * q^92 - 4256 * q^94 - 3137 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	0.951271	−	2.66366i	0.336325	−	0.941746i
$2$	0.951271	−	2.66366i	0.336325	−	0.941746i
$3$		0			0
$3$		0			0
$4$	−6.19017	−	5.06772i	−0.773771	−	0.633465i
$5$			10.8462i			0.970112i	0.874483	+	0.485056i	$0.161201\pi$
$5$			10.8462i			0.970112i	−0.874483	+	0.485056i	$0.838799\pi$
$6$		0			0
$7$	15.1344	−	10.6748i	0.817179	−	0.576384i
$7$	15.1344	−	10.6748i	0.817179	−	0.576384i
$8$	−19.3872	+	11.6677i	−0.856802	+	0.515646i
$9$		0			0
$10$	28.8905	+	10.3176i	0.913599	+	0.326273i
$11$			45.0243i			1.23412i	0.786916	+	0.617061i	$0.211677\pi$
$11$			45.0243i			1.23412i	−0.786916	+	0.617061i	$0.788323\pi$
$12$		0			0
$13$			40.3676i			0.861228i	0.902536	+	0.430614i	$0.141703\pi$
$13$			40.3676i			0.861228i	−0.902536	+	0.430614i	$0.858297\pi$
$14$	−14.0371	−	50.4674i	−0.267970	−	0.963427i
$15$		0			0
$16$	12.6364	+	62.7401i	0.197443	+	0.980314i
$17$		−	8.11855i		−	0.115826i	−0.998322	−	0.0579129i	$-0.981555\pi$
$17$		−	8.11855i		−	0.115826i	0.998322	−	0.0579129i	$-0.0184446\pi$
$18$		0			0
$19$	53.3328			0.643968			0.321984	−	0.946745i	$-0.395650\pi$
$19$	53.3328			0.643968			0.321984	+	0.946745i	$0.395650\pi$
$20$	54.9654	−	67.1397i	0.614532	−	0.750644i
$21$		0			0
$22$	119.929	+	42.8303i	1.16223	+	0.415066i
$23$			55.7907i			0.505790i	0.967494	+	0.252895i	$0.0813827\pi$
$23$			55.7907i			0.505790i	−0.967494	+	0.252895i	$0.918617\pi$
$24$		0			0
$25$	7.36043			0.0588835
$26$	107.526	+	38.4005i	0.811058	+	0.289652i
$27$		0			0
$28$	−147.781	−	10.6181i	−0.997429	−	0.0716654i
$29$	169.210			1.08350			0.541751	−	0.840539i	$-0.317762\pi$
$29$	169.210			1.08350			0.541751	+	0.840539i	$0.317762\pi$
$30$		0			0
$31$	262.968			1.52356			0.761782	−	0.647834i	$-0.224325\pi$
$31$	262.968			1.52356			0.761782	+	0.647834i	$0.224325\pi$
$32$	179.139	+	26.0238i	0.989612	+	0.143763i
$33$		0			0
$34$	−21.6251	−	7.72294i	−0.109078	−	0.0389551i
$35$	115.781	+	164.150i	0.559157	+	0.792755i
$36$		0			0
$37$	−354.930			−1.57703			−0.788515	−	0.615015i	$-0.789150\pi$
$37$	−354.930			−1.57703			−0.788515	+	0.615015i	$0.789150\pi$
$38$	50.7339	−	142.060i	0.216582	−	0.606454i
$39$		0			0
$40$	−126.550	−	210.277i	−0.500234	−	0.831194i
$41$		−	42.7783i		−	0.162948i	−0.996675	−	0.0814738i	$-0.974037\pi$
$41$		−	42.7783i		−	0.162948i	0.996675	−	0.0814738i	$-0.0259627\pi$
$42$		0			0
$43$			23.1555i			0.0821206i	0.999157	+	0.0410603i	$0.0130736\pi$
$43$			23.1555i			0.0821206i	−0.999157	+	0.0410603i	$0.986926\pi$
$44$	228.171	−	278.708i	0.781773	−	0.954927i
$45$		0			0
$46$	148.607	+	53.0721i	0.476326	+	0.170110i
$47$	437.834			1.35882			0.679412	−	0.733757i	$-0.262235\pi$
$47$	437.834			1.35882			0.679412	+	0.733757i	$0.262235\pi$
$48$		0			0
$49$	115.098	−	323.112i	0.335563	−	0.942018i
$50$	7.00176	−	19.6057i	0.0198040	−	0.0554533i
$51$		0			0
$52$	204.572	−	249.882i	0.545558	−	0.666393i
$53$	−388.515			−1.00692			−0.503459	−	0.864019i	$-0.667939\pi$
$53$	−388.515			−1.00692			−0.503459	+	0.864019i	$0.667939\pi$
$54$		0			0
$55$	−488.341			−1.19724
$56$	−168.863	+	383.538i	−0.402951	+	0.915222i
$57$		0			0
$58$	160.965	−	450.718i	0.364409	−	1.02038i
$59$	−649.834			−1.43392			−0.716960	−	0.697115i	$-0.754467\pi$
$59$	−649.834			−1.43392			−0.716960	+	0.697115i	$0.754467\pi$
$60$		0			0
$61$			916.217i			1.92311i	0.274615	+	0.961554i	$0.411450\pi$
$61$			916.217i			1.92311i	−0.274615	+	0.961554i	$0.588550\pi$
$62$	250.154	−	700.457i	0.512412	−	1.43481i
$63$		0			0
$64$	239.728	−	452.410i	0.468219	−	0.883612i
$65$	−437.834			−0.835487
$66$		0			0
$67$			736.636i			1.34320i	0.740914	+	0.671600i	$0.234393\pi$
$67$			736.636i			1.34320i	−0.740914	+	0.671600i	$0.765607\pi$
$68$	−41.1426	+	50.2552i	−0.0733716	+	0.0896226i
$69$		0			0
$70$	547.379	−	152.249i	0.934632	−	0.259960i
$71$		−	600.682i		−	1.00405i	−0.864852	−	0.502027i	$-0.832588\pi$
$71$		−	600.682i		−	1.00405i	0.864852	−	0.502027i	$-0.167412\pi$
$72$		0			0
$73$			673.579i			1.07995i	0.841681	+	0.539976i	$0.181567\pi$
$73$			673.579i			1.07995i	−0.841681	+	0.539976i	$0.818433\pi$
$74$	−337.634	+	945.413i	−0.530395	+	1.48516i
$75$		0			0
$76$	−330.139	−	270.276i	−0.498283	−	0.407931i
$77$	480.624	+	681.414i	0.711328	+	1.00850i
$78$		0			0
$79$		−	585.232i		−	0.833465i	−0.909029	−	0.416732i	$-0.863175\pi$
$79$		−	585.232i		−	0.833465i	0.909029	−	0.416732i	$-0.136825\pi$
$80$	−680.490	+	137.056i	−0.951014	+	0.191542i
$81$		0			0
$82$	−113.947	−	40.6938i	−0.153455	−	0.0548034i
$83$	856.883			1.13319			0.566597	−	0.823995i	$-0.308260\pi$
$83$	856.883			1.13319			0.566597	+	0.823995i	$0.308260\pi$
$84$		0			0
$85$	88.0553			0.112364
$86$	61.6784	+	22.0272i	0.0773367	+	0.0276192i
$87$		0			0
$88$	−525.331	−	872.896i	−0.636369	−	1.05740i
$89$		−	920.574i		−	1.09641i	−0.836343	−	0.548206i	$-0.815311\pi$
$89$		−	920.574i		−	1.09641i	0.836343	−	0.548206i	$-0.184689\pi$
$90$		0			0
$91$	430.915	+	610.938i	0.496398	+	0.703777i
$92$	282.732	−	345.354i	0.320400	−	0.391366i
$93$		0			0
$94$	416.499	−	1166.24i	0.457006	−	1.27967i
$95$			578.457i			0.624720i
$96$		0			0
$97$			638.990i			0.668862i	0.942420	+	0.334431i	$0.108544\pi$
$97$			638.990i			0.668862i	−0.942420	+	0.334431i	$0.891456\pi$
$98$	−751.171	−	613.949i	−0.774283	−	0.632839i
$99$		0			0
$100$	−45.5623	−	37.3006i	−0.0455623	−	0.0373006i
$101$			1502.61i			1.48035i	0.672415	+	0.740175i	$0.265257\pi$
$101$			1502.61i			1.48035i	−0.672415	+	0.740175i	$0.734743\pi$
$102$		0			0
$103$	945.506			0.904500			0.452250	−	0.891891i	$-0.350621\pi$
$103$	945.506			0.904500			0.452250	+	0.891891i	$0.350621\pi$
$104$	−470.998	−	782.616i	−0.444088	−	0.737902i
$105$		0			0
$106$	−369.583	+	1034.87i	−0.338652	+	0.948261i
$107$		−	1060.20i		−	0.957883i	−0.877847	−	0.478941i	$-0.841021\pi$
$107$		−	1060.20i		−	0.957883i	0.877847	−	0.478941i	$-0.158979\pi$
$108$		0			0
$109$	−1895.91			−1.66601			−0.833007	−	0.553262i	$-0.813383\pi$
$109$	−1895.91			−1.66601			−0.833007	+	0.553262i	$0.813383\pi$
$110$	−464.545	+	1300.78i	−0.402660	+	1.12749i
$111$		0			0
$112$	860.980	+	814.642i	0.726384	+	0.687289i
$113$	−1094.02			−0.910770			−0.455385	−	0.890295i	$-0.650498\pi$
$113$	−1094.02			−0.910770			−0.455385	+	0.890295i	$0.650498\pi$
$114$		0			0
$115$	−605.116			−0.490673
$116$	−1047.44	−	857.510i	−0.838382	−	0.686361i
$117$		0			0
$118$	−618.168	+	1730.94i	−0.482263	+	1.35039i
$119$	−86.6638	−	122.869i	−0.0667601	−	0.0946504i
$120$		0			0
$121$	−696.186			−0.523055
$122$	2440.49	+	871.571i	1.81108	+	0.646789i
$123$		0			0
$124$	−1627.82	−	1332.65i	−1.17889	−	0.965124i
$125$			1435.60i			1.02724i
$126$		0			0
$127$		−	146.769i		−	0.102548i	−0.998685	−	0.0512742i	$-0.983672\pi$
$127$		−	146.769i		−	0.102548i	0.998685	−	0.0512742i	$-0.0163282\pi$
$128$	−977.019	−	1068.92i	−0.674665	−	0.738124i
$129$		0			0
$130$	−416.499	+	1166.24i	−0.280995	+	0.786817i
$131$	−1140.05			−0.760359			−0.380179	−	0.924913i	$-0.624138\pi$
$131$	−1140.05			−0.760359			−0.380179	+	0.924913i	$0.624138\pi$
$132$		0			0
$133$	807.158	−	569.316i	0.526237	−	0.371173i
$134$	1962.15	+	700.740i	1.26495	+	0.451752i
$135$		0			0
$136$	94.7251	+	157.396i	0.0597251	+	0.0992398i
$137$	−1338.39			−0.834648			−0.417324	−	0.908758i	$-0.637032\pi$
$137$	−1338.39			−0.834648			−0.417324	+	0.908758i	$0.637032\pi$
$138$		0			0
$139$	−495.774			−0.302525			−0.151263	−	0.988494i	$-0.548334\pi$
$139$	−495.774			−0.302525			−0.151263	+	0.988494i	$0.548334\pi$
$140$	115.166	−	1602.86i	0.0695235	−	0.967617i
$141$		0			0
$142$	−1600.01	−	571.411i	−0.945563	−	0.337688i
$143$	−1817.52			−1.06286
$144$		0			0
$145$			1835.28i			1.05112i
$146$	1794.19	+	640.756i	1.01704	+	0.363215i
$147$		0			0
$148$	2197.08	+	1798.69i	1.22026	+	0.998994i
$149$	1860.24			1.02280			0.511398	−	0.859344i	$-0.329128\pi$
$149$	1860.24			1.02280			0.511398	+	0.859344i	$0.329128\pi$
$150$		0			0
$151$		−	873.260i		−	0.470629i	−0.971919	−	0.235314i	$-0.924388\pi$
$151$		−	873.260i		−	0.470629i	0.971919	−	0.235314i	$-0.0756119\pi$
$152$	−1033.97	+	622.273i	−0.551753	+	0.332059i
$153$		0			0
$154$	2272.26	−	632.010i	1.18899	−	0.330707i
$155$			2852.20i			1.47803i
$156$		0			0
$157$		−	1372.07i		−	0.697471i	−0.937221	−	0.348735i	$-0.886611\pi$
$157$		−	1372.07i		−	0.697471i	0.937221	−	0.348735i	$-0.113389\pi$
$158$	−1558.86	−	556.714i	−0.784912	−	0.280315i
$159$		0			0
$160$	−282.259	+	1942.97i	−0.139466	+	0.960034i
$161$	595.553	+	844.357i	0.291529	+	0.413321i
$162$		0			0
$163$		−	2039.67i		−	0.980120i	−0.871689	−	0.490060i	$-0.836975\pi$
$163$		−	2039.67i		−	0.980120i	0.871689	−	0.490060i	$-0.163025\pi$
$164$	−216.789	+	264.805i	−0.103222	+	0.126084i
$165$		0			0
$166$	815.128	−	2282.44i	0.381121	−	1.06718i
$167$	−289.529			−0.134158			−0.0670791	−	0.997748i	$-0.521368\pi$
$167$	−289.529			−0.134158			−0.0670791	+	0.997748i	$0.521368\pi$
$168$		0			0
$169$	567.455			0.258286
$170$	83.7644	−	234.549i	0.0377908	−	0.105818i
$171$		0			0
$172$	117.346	−	143.337i	0.0520205	−	0.0635425i
$173$		−	4070.74i		−	1.78898i	−0.447092	−	0.894488i	$-0.647540\pi$
$173$		−	4070.74i		−	1.78898i	0.447092	−	0.894488i	$-0.352460\pi$
$174$		0			0
$175$	111.396	−	78.5710i	0.0481183	−	0.0339395i
$176$	−2824.83	+	568.944i	−1.20983	+	0.243669i
$177$		0			0
$178$	−2452.10	−	875.715i	−1.03254	−	0.368751i
$179$			2159.77i			0.901837i	0.892565	+	0.450918i	$0.148903\pi$
$179$			2159.77i			0.901837i	−0.892565	+	0.450918i	$0.851097\pi$
$180$		0			0
$181$		−	4516.84i		−	1.85489i	−0.373965	−	0.927443i	$-0.622002\pi$
$181$		−	4516.84i		−	1.85489i	0.373965	−	0.927443i	$-0.377998\pi$
$182$	2037.25	−	566.644i	0.829731	−	0.230783i
$183$		0			0
$184$	−650.951	−	1081.63i	−0.260808	−	0.433362i
$185$		−	3849.63i		−	1.52990i
$186$		0			0
$187$	365.532			0.142943
$188$	−2710.27	−	2218.82i	−1.05142	−	0.860768i
$189$		0			0
$190$	1540.81	+	550.269i	0.588328	+	0.210109i
$191$		−	2750.74i		−	1.04208i	−0.853533	−	0.521039i	$-0.825545\pi$
$191$		−	2750.74i		−	1.04208i	0.853533	−	0.521039i	$-0.174455\pi$
$192$		0			0
$193$	3469.67			1.29405			0.647026	−	0.762468i	$-0.276013\pi$
$193$	3469.67			1.29405			0.647026	+	0.762468i	$0.276013\pi$
$194$	1702.05	+	607.852i	0.629898	+	0.224955i
$195$		0			0
$196$	−2349.92	+	1416.83i	−0.856385	+	0.516338i
$197$	1555.68			0.562627			0.281314	−	0.959616i	$-0.409230\pi$
$197$	1555.68			0.562627			0.281314	+	0.959616i	$0.409230\pi$
$198$		0			0
$199$	−1028.69			−0.366442			−0.183221	−	0.983072i	$-0.558652\pi$
$199$	−1028.69			−0.366442			−0.183221	+	0.983072i	$0.558652\pi$
$200$	−142.698	+	85.8795i	−0.0504515	+	0.0303630i
$201$		0			0
$202$	4002.44	+	1429.39i	1.39411	+	0.497878i
$203$	2560.89	−	1806.28i	0.885415	−	0.624513i
$204$		0			0
$205$	463.981			0.158077
$206$	899.432	−	2518.51i	0.304206	−	0.851809i
$207$		0			0
$208$	−2532.67	+	510.100i	−0.844274	+	0.170044i
$209$			2401.27i			0.794734i
$210$		0			0
$211$		−	1148.26i		−	0.374643i	−0.982299	−	0.187322i	$-0.940019\pi$
$211$		−	1148.26i		−	0.374643i	0.982299	−	0.187322i	$-0.0599806\pi$
$212$	2404.97	+	1968.89i	0.779124	+	0.637847i
$213$		0			0
$214$	−2824.01	−	1008.54i	−0.902082	−	0.322160i
$215$	−251.149			−0.0796661
$216$		0			0
$217$	3979.85	−	2807.13i	1.24502	−	0.878157i
$218$	−1803.53	+	5050.07i	−0.560322	+	1.56896i
$219$		0			0
$220$	3022.92	+	2474.78i	0.926386	+	0.758407i
$221$	327.727			0.0997524
$222$		0			0
$223$	135.249			0.0406141			0.0203070	−	0.999794i	$-0.493536\pi$
$223$	135.249			0.0406141			0.0203070	+	0.999794i	$0.493536\pi$
$224$	2988.95	−	1518.41i	0.891553	−	0.452917i
$225$		0			0
$226$	−1040.71	+	2914.11i	−0.306315	+	0.857714i
$227$	4959.03			1.44997			0.724983	−	0.688766i	$-0.241847\pi$
$227$	4959.03			1.44997			0.724983	+	0.688766i	$0.241847\pi$
$228$		0			0
$229$		−	1158.12i		−	0.334196i	−0.985940	−	0.167098i	$-0.946560\pi$
$229$		−	1158.12i		−	0.334196i	0.985940	−	0.167098i	$-0.0534396\pi$
$230$	−575.629	+	1611.82i	−0.165025	+	0.462089i
$231$		0			0
$232$	−3280.51	+	1974.30i	−0.928346	+	0.558703i
$233$	990.886			0.278606			0.139303	−	0.990250i	$-0.455514\pi$
$233$	990.886			0.278606			0.139303	+	0.990250i	$0.455514\pi$
$234$		0			0
$235$			4748.83i			1.31821i
$236$	4022.58	+	3293.18i	1.10953	+	0.908338i
$237$		0			0
$238$	−409.722	+	113.961i	−0.111590	+	0.0310378i
$239$		−	4178.60i		−	1.13093i	−0.824774	−	0.565463i	$-0.808698\pi$
$239$		−	4178.60i		−	1.13093i	0.824774	−	0.565463i	$-0.191302\pi$
$240$		0			0
$241$			2492.36i			0.666170i	0.942897	+	0.333085i	$0.108090\pi$
$241$			2492.36i			0.666170i	−0.942897	+	0.333085i	$0.891910\pi$
$242$	−662.261	+	1854.40i	−0.175916	+	0.492585i
$243$		0			0
$244$	4643.14	−	5671.54i	1.21822	−	1.48805i
$245$	3504.53	+	1248.38i	0.913862	+	0.325534i
$246$		0			0
$247$			2152.92i			0.554603i
$248$	−5098.22	+	3068.24i	−1.30539	+	0.785619i
$249$		0			0
$250$	3823.96	+	1365.65i	0.967395	+	0.345485i
$251$	121.042			0.0304387			0.0152194	−	0.999884i	$-0.495155\pi$
$251$	121.042			0.0304387			0.0152194	+	0.999884i	$0.495155\pi$
$252$		0			0
$253$	−2511.94			−0.624206
$254$	−390.943	−	139.617i	−0.0965745	−	0.0344896i
$255$		0			0
$256$	−3776.64	+	1585.61i	−0.922032	+	0.387113i
$257$		−	2253.73i		−	0.547018i	−0.961869	−	0.273509i	$-0.911816\pi$
$257$		−	2253.73i		−	0.547018i	0.961869	−	0.273509i	$-0.0881844\pi$
$258$		0			0
$259$	−5371.64	+	3788.80i	−1.28872	+	0.908975i
$260$	2710.27	+	2218.82i	0.646476	+	0.529252i
$261$		0			0
$262$	−1084.50	+	3036.72i	−0.255728	+	0.716065i
$263$			4614.71i			1.08196i	0.841036	+	0.540979i	$0.181946\pi$
$263$			4614.71i			1.08196i	−0.841036	+	0.540979i	$0.818054\pi$
$264$		0			0
$265$		−	4213.90i		−	0.976822i
$266$	−748.638	−	2691.57i	−0.172564	−	0.620416i
$267$		0			0
$268$	3733.07	−	4559.90i	0.850871	−	1.03933i
$269$		−	3549.09i		−	0.804431i	−0.915545	−	0.402216i	$-0.868240\pi$
$269$		−	3549.09i		−	0.804431i	0.915545	−	0.402216i	$-0.131760\pi$
$270$		0			0
$271$	−2467.20			−0.553032			−0.276516	−	0.961009i	$-0.589180\pi$
$271$	−2467.20			−0.553032			−0.276516	+	0.961009i	$0.589180\pi$
$272$	509.359	−	102.589i	0.113546	−	0.0228690i
$273$		0			0
$274$	−1273.18	+	3565.03i	−0.280713	+	0.786026i
$275$			331.398i			0.0726693i
$276$		0			0
$277$	−2926.10			−0.634701			−0.317350	−	0.948308i	$-0.602793\pi$
$277$	−2926.10			−0.634701			−0.317350	+	0.948308i	$0.602793\pi$
$278$	−471.615	+	1320.57i	−0.101747	+	0.284902i
$279$		0			0
$280$	−4159.92	−	1831.52i	−0.887867	−	0.390907i
$281$	−1725.38			−0.366290			−0.183145	−	0.983086i	$-0.558628\pi$
$281$	−1725.38			−0.366290			−0.183145	+	0.983086i	$0.558628\pi$
$282$		0			0
$283$	5607.19			1.17778			0.588892	−	0.808212i	$-0.299564\pi$
$283$	5607.19			1.17778			0.588892	+	0.808212i	$0.299564\pi$
$284$	−3044.09	+	3718.32i	−0.636033	+	0.776907i
$285$		0			0
$286$	−1728.96	+	4841.26i	−0.357466	+	1.00094i
$287$	−456.649	−	647.423i	−0.0939204	−	0.133157i
$288$		0			0
$289$	4847.09			0.986584
$290$	4888.57	+	1745.85i	0.989885	+	0.353517i
$291$		0			0
$292$	3413.51	−	4169.57i	0.684112	−	0.835635i
$293$		−	2141.36i		−	0.426961i	−0.976947	−	0.213480i	$-0.931520\pi$
$293$		−	2141.36i		−	0.426961i	0.976947	−	0.213480i	$-0.0684800\pi$
$294$		0			0
$295$		−	7048.22i		−	1.39106i
$296$	6881.10	−	4141.23i	1.35120	−	0.813189i
$297$		0			0
$298$	1769.59	−	4955.04i	0.343992	−	0.963214i
$299$	−2252.14			−0.435600
$300$		0			0
$301$	247.180	+	350.444i	0.0473330	+	0.0671072i
$302$	−2326.07	−	830.707i	−0.443213	−	0.158284i
$303$		0			0
$304$	673.933	+	3346.11i	0.127147	+	0.631291i
$305$	−9937.46			−1.86563
$306$		0			0
$307$	2698.42			0.501651			0.250825	−	0.968032i	$-0.419298\pi$
$307$	2698.42			0.501651			0.250825	+	0.968032i	$0.419298\pi$
$308$	478.072	−	6653.74i	0.0884438	−	1.23095i
$309$		0			0
$310$	7597.29	+	2713.21i	1.39193	+	0.497097i
$311$	−403.959			−0.0736540			−0.0368270	−	0.999322i	$-0.511725\pi$
$311$	−403.959			−0.0736540			−0.0368270	+	0.999322i	$0.511725\pi$
$312$		0			0
$313$			2206.77i			0.398511i	0.979948	+	0.199255i	$0.0638523\pi$
$313$			2206.77i			0.398511i	−0.979948	+	0.199255i	$0.936148\pi$
$314$	−3654.72	−	1305.21i	−0.656841	−	0.234577i
$315$		0			0
$316$	−2965.79	+	3622.68i	−0.527971	+	0.644911i
$317$	239.465			0.0424281			0.0212140	−	0.999775i	$-0.493247\pi$
$317$	239.465			0.0424281			0.0212140	+	0.999775i	$0.493247\pi$
$318$		0			0
$319$			7618.57i			1.33717i
$320$	4906.91	+	2600.14i	0.857203	+	0.454225i
$321$		0			0
$322$	2815.61	−	783.140i	0.487292	−	0.135536i
$323$		−	432.985i		−	0.0745881i
$324$		0			0
$325$			297.123i			0.0507121i
$326$	−5433.00	−	1940.28i	−0.923024	−	0.329639i
$327$		0			0
$328$	499.126	+	829.353i	0.0840232	+	0.139614i
$329$	6626.35	−	4673.78i	1.11040	−	0.783204i
$330$		0			0
$331$		−	11138.4i		−	1.84961i	−0.380436	−	0.924807i	$-0.624226\pi$
$331$		−	11138.4i		−	1.84961i	0.380436	−	0.924807i	$-0.375774\pi$
$332$	−5304.25	−	4342.45i	−0.876833	−	0.717839i
$333$		0			0
$334$	−275.420	+	771.206i	−0.0451207	+	0.126343i
$335$	−7989.68			−1.30305
$336$		0			0
$337$	−367.966			−0.0594789			−0.0297395	−	0.999558i	$-0.509468\pi$
$337$	−367.966			−0.0594789			−0.0297395	+	0.999558i	$0.509468\pi$
$338$	539.804	−	1511.51i	0.0868682	−	0.243240i
$339$		0			0
$340$	−545.077	−	446.240i	−0.0869440	−	0.0711787i
$341$			11839.9i			1.88026i
$342$		0			0
$343$	−1707.21	−	6118.74i	−0.268749	−	0.963210i
$344$	−270.172	−	448.921i	−0.0423451	−	0.0703611i
$345$		0			0
$346$	−10843.1	−	3872.38i	−1.68476	−	0.601677i
$347$			3110.91i			0.481275i	0.970615	+	0.240638i	$0.0773565\pi$
$347$			3110.91i			0.481275i	−0.970615	+	0.240638i	$0.922643\pi$
$348$		0			0
$349$		−	213.997i		−	0.0328224i	−0.999865	−	0.0164112i	$-0.994776\pi$
$349$		−	213.997i		−	0.0328224i	0.999865	−	0.0164112i	$-0.00522408\pi$
$350$	−103.319	−	371.462i	−0.0157790	−	0.0567299i
$351$		0			0
$352$	−1171.70	+	8065.60i	−0.177421	+	1.22130i
$353$			3794.88i			0.572184i	0.958202	+	0.286092i	$0.0923563\pi$
$353$			3794.88i			0.572184i	−0.958202	+	0.286092i	$0.907644\pi$
$354$		0			0
$355$	6515.10			0.974044
$356$	−4665.21	+	5698.51i	−0.694539	+	0.848372i
$357$		0			0
$358$	5752.89	+	2054.53i	0.849301	+	0.303310i
$359$		−	864.312i		−	0.127066i	−0.997980	−	0.0635330i	$-0.979763\pi$
$359$		−	864.312i		−	0.127066i	0.997980	−	0.0635330i	$-0.0202368\pi$
$360$		0			0
$361$	−4014.61			−0.585306
$362$	−12031.3	−	4296.74i	−1.74683	−	0.623844i
$363$		0			0
$364$	428.627	−	5965.57i	0.0617203	−	0.859013i
$365$	−7305.76			−1.04767
$366$		0			0
$367$	−7818.53			−1.11205			−0.556027	−	0.831164i	$-0.687675\pi$
$367$	−7818.53			−1.11205			−0.556027	+	0.831164i	$0.687675\pi$
$368$	−3500.32	+	704.992i	−0.495833	+	0.0998648i
$369$		0			0
$370$	−10254.1	−	3662.04i	−1.44077	−	0.514542i
$371$	−5879.93	+	4147.31i	−0.822832	+	0.580371i
$372$		0			0
$373$	2332.52			0.323789			0.161894	−	0.986808i	$-0.448240\pi$
$373$	2332.52			0.323789			0.161894	+	0.986808i	$0.448240\pi$
$374$	347.720	−	973.653i	0.0480753	−	0.134616i
$375$		0			0
$376$	−8488.39	+	5108.53i	−1.16424	+	0.700671i
$377$			6830.61i			0.933142i
$378$		0			0
$379$		−	13305.3i		−	1.80329i	−0.432481	−	0.901643i	$-0.642362\pi$
$379$		−	13305.3i		−	1.80329i	0.432481	−	0.901643i	$-0.357638\pi$
$380$	2931.46	−	3580.75i	0.395739	−	0.483391i
$381$		0			0
$382$	−7327.04	−	2616.70i	−0.981372	−	0.350477i
$383$	−8176.19			−1.09082			−0.545410	−	0.838169i	$-0.683626\pi$
$383$	−8176.19			−1.09082			−0.545410	+	0.838169i	$0.683626\pi$
$384$		0			0
$385$	−7390.74	+	5212.94i	−0.978356	+	0.690067i
$386$	3300.59	−	9242.01i	0.435222	−	1.21867i
$387$		0			0
$388$	3238.22	−	3955.45i	0.423701	−	0.517546i
$389$	5660.36			0.737768			0.368884	−	0.929476i	$-0.379740\pi$
$389$	5660.36			0.737768			0.368884	+	0.929476i	$0.379740\pi$
$390$		0			0
$391$	452.940			0.0585835
$392$	1538.55	+	7607.18i	0.198236	+	0.980154i
$393$		0			0
$394$	1479.87	−	4143.80i	0.189226	−	0.529852i
$395$	6347.53			0.808554
$396$		0			0
$397$			4283.65i			0.541538i	0.962644	+	0.270769i	$0.0872779\pi$
$397$			4283.65i			0.541538i	−0.962644	+	0.270769i	$0.912722\pi$
$398$	−978.562	+	2740.08i	−0.123243	+	0.345095i
$399$		0			0
$400$	93.0092	+	461.794i	0.0116261	+	0.0577243i
$401$	12896.4			1.60603			0.803014	−	0.595960i	$-0.203228\pi$
$401$	12896.4			1.60603			0.803014	+	0.595960i	$0.203228\pi$
$402$		0			0
$403$			10615.4i			1.31213i
$404$	7614.81	−	9301.41i	0.937750	−	1.14545i
$405$		0			0
$406$	−2375.22	−	8539.60i	−0.290345	−	1.04387i
$407$		−	15980.5i		−	1.94625i
$408$		0			0
$409$		−	2361.92i		−	0.285549i	−0.989755	−	0.142775i	$-0.954398\pi$
$409$		−	2361.92i		−	0.285549i	0.989755	−	0.142775i	$-0.0456024\pi$
$410$	441.372	−	1235.89i	0.0531654	−	0.148869i
$411$		0			0
$412$	−5852.84	−	4791.56i	−0.699876	−	0.572969i
$413$	−9834.83	+	6936.84i	−1.17177	+	0.826488i
$414$		0			0
$415$			9293.90i			1.09932i
$416$	−1050.52	+	7231.41i	−0.123812	+	0.852282i
$417$		0			0
$418$	6396.17	+	2284.26i	0.748438	+	0.267289i
$419$	12042.1			1.40405			0.702024	−	0.712153i	$-0.252280\pi$
$419$	12042.1			1.40405			0.702024	+	0.712153i	$0.252280\pi$
$420$		0			0
$421$	−16279.4			−1.88458			−0.942290	−	0.334799i	$-0.891332\pi$
$421$	−16279.4			−1.88458			−0.942290	+	0.334799i	$0.891332\pi$
$422$	−3058.58	−	1092.31i	−0.352819	−	0.126002i
$423$		0			0
$424$	7532.22	−	4533.09i	0.862729	−	0.519213i
$425$		−	59.7561i		−	0.00682022i
$426$		0			0
$427$	9780.42	+	13866.4i	1.10845	+	1.57152i
$428$	−5372.80	+	6562.82i	−0.606785	+	0.741182i
$429$		0			0
$430$	−238.911	+	668.975i	−0.0267937	+	0.0750252i
$431$			9006.69i			1.00658i	0.864117	+	0.503291i	$0.167878\pi$
$431$			9006.69i			1.00658i	−0.864117	+	0.503291i	$0.832122\pi$
$432$		0			0
$433$			16445.5i			1.82522i	0.408834	+	0.912609i	$0.365935\pi$
$433$			16445.5i			1.82522i	−0.408834	+	0.912609i	$0.634065\pi$
$434$	−3691.31	−	13271.3i	−0.408268	−	1.46784i
$435$		0			0
$436$	11736.0	+	9607.96i	1.28911	+	1.05536i
$437$			2975.47i			0.325712i
$438$		0			0
$439$	−10058.8			−1.09357			−0.546787	−	0.837272i	$-0.684149\pi$
$439$	−10058.8			−1.09357			−0.546787	+	0.837272i	$0.684149\pi$
$440$	9467.58	−	5697.83i	1.02579	−	0.617349i
$441$		0			0
$442$	311.757	−	872.952i	0.0335492	−	0.0939414i
$443$		−	5894.63i		−	0.632194i	−0.948727	−	0.316097i	$-0.897627\pi$
$443$		−	5894.63i		−	0.632194i	0.948727	−	0.316097i	$-0.102373\pi$
$444$		0			0
$445$	9984.71			1.06364
$446$	128.658	−	360.257i	0.0136595	−	0.0382481i
$447$		0			0
$448$	−1201.24	−	9405.98i	−0.126681	−	0.991944i
$449$	−7506.67			−0.789001			−0.394501	−	0.918896i	$-0.629082\pi$
$449$	−7506.67			−0.789001			−0.394501	+	0.918896i	$0.629082\pi$
$450$		0			0
$451$	1926.06			0.201097
$452$	6772.19	+	5544.21i	0.704728	+	0.576941i
$453$		0			0
$454$	4717.38	−	13209.2i	0.487660	−	1.36550i
$455$	−6626.35	+	4673.78i	−0.682743	+	0.481561i
$456$		0			0
$457$	−4234.60			−0.433450			−0.216725	−	0.976233i	$-0.569537\pi$
$457$	−4234.60			−0.433450			−0.216725	+	0.976233i	$0.569537\pi$
$458$	−3084.84	−	1101.69i	−0.314728	−	0.112398i
$459$		0			0
$460$	3745.77	+	3066.56i	0.379668	+	0.310824i
$461$		−	13411.8i		−	1.35498i	−0.735530	−	0.677492i	$-0.763067\pi$
$461$		−	13411.8i		−	1.35498i	0.735530	−	0.677492i	$-0.236933\pi$
$462$		0			0
$463$		−	14635.2i		−	1.46902i	−0.678598	−	0.734510i	$-0.737412\pi$
$463$		−	14635.2i		−	1.46902i	0.678598	−	0.734510i	$-0.262588\pi$
$464$	2138.20	+	10616.3i	0.213930	+	1.06217i
$465$		0			0
$466$	942.601	−	2639.38i	0.0937020	−	0.262376i
$467$	17234.6			1.70775			0.853876	−	0.520477i	$-0.174246\pi$
$467$	17234.6			1.70775			0.853876	+	0.520477i	$0.174246\pi$
$468$		0			0
$469$	7863.42	+	11148.5i	0.774199	+	1.09763i
$470$	12649.3	+	4517.42i	1.24142	+	0.443347i
$471$		0			0
$472$	12598.5	−	7582.09i	1.22858	−	0.739394i
$473$	−1042.56			−0.101347
$474$		0			0
$475$	392.553			0.0379190
$476$	−86.2036	+	1199.77i	−0.00830071	+	0.115528i
$477$		0			0
$478$	−11130.4	−	3974.98i	−1.06505	−	0.380359i
$479$	−1588.48			−0.151523			−0.0757617	−	0.997126i	$-0.524139\pi$
$479$	−1588.48			−0.151523			−0.0757617	+	0.997126i	$0.524139\pi$
$480$		0			0
$481$		−	14327.7i		−	1.35818i
$482$	6638.80	+	2370.91i	0.627363	+	0.224050i
$483$		0			0
$484$	4309.51	+	3528.08i	0.404725	+	0.331337i
$485$	−6930.60			−0.648870
$486$		0			0
$487$			11023.5i			1.02572i	0.858473	+	0.512858i	$0.171413\pi$
$487$			11023.5i			1.02572i	−0.858473	+	0.512858i	$0.828587\pi$
$488$	−10690.2	−	17762.9i	−0.991643	−	1.64772i
$489$		0			0
$490$	6659.00	−	8147.34i	0.613925	−	0.751141i
$491$		−	583.129i		−	0.0535972i	−0.999641	−	0.0267986i	$-0.991469\pi$
$491$		−	583.129i		−	0.0535972i	0.999641	−	0.0267986i	$-0.00853129\pi$
$492$		0			0
$493$		−	1373.74i		−	0.125497i
$494$	5734.64	+	2048.01i	0.522295	+	0.186527i
$495$		0			0
$496$	3322.96	+	16498.6i	0.300817	+	1.49357i
$497$	−6412.14	−	9090.94i	−0.578720	−	0.820491i
$498$		0			0
$499$			5378.92i			0.482552i	0.970457	+	0.241276i	$0.0775659\pi$
$499$			5378.92i			0.482552i	−0.970457	+	0.241276i	$0.922434\pi$
$500$	7275.25	−	8886.64i	0.650718	−	0.794845i
$501$		0			0
$502$	115.144	−	322.415i	0.0102373	−	0.0286656i
$503$	2956.43			0.262069			0.131035	−	0.991378i	$-0.458170\pi$
$503$	2956.43			0.262069			0.131035	+	0.991378i	$0.458170\pi$
$504$		0			0
$505$	−16297.6			−1.43610
$506$	−2389.53	+	6690.94i	−0.209936	+	0.587843i
$507$		0			0
$508$	−743.784	+	908.524i	−0.0649608	+	0.0793489i
$509$		−	723.267i		−	0.0629828i	−0.999504	−	0.0314914i	$-0.989974\pi$
$509$		−	723.267i		−	0.0629828i	0.999504	−	0.0314914i	$-0.0100257\pi$
$510$		0			0
$511$	7190.31	+	10194.2i	0.622467	+	0.882514i
$512$	630.928	+	11568.0i	0.0544596	+	0.998516i
$513$		0			0
$514$	−6003.17	−	2143.91i	−0.515152	−	0.183976i
$515$			10255.1i			0.877466i
$516$		0			0
$517$			19713.2i			1.67695i
$518$	4982.19	+	17912.4i	0.422596	+	1.51935i
$519$		0			0
$520$	8488.39	−	5108.53i	0.715847	−	0.430815i
$521$			17475.9i			1.46955i	0.678312	+	0.734774i	$0.262712\pi$
$521$			17475.9i			1.46955i	−0.678312	+	0.734774i	$0.737288\pi$
$522$		0			0
$523$	3715.44			0.310640			0.155320	−	0.987864i	$-0.450359\pi$
$523$	3715.44			0.310640			0.155320	+	0.987864i	$0.450359\pi$
$524$	7057.13	+	5777.48i	0.588344	+	0.481661i
$525$		0			0
$526$	12292.0	+	4389.83i	1.01893	+	0.363889i
$527$		−	2134.92i		−	0.176468i
$528$		0			0
$529$	9054.40			0.744177
$530$	−11224.4	−	4008.56i	−0.919919	−	0.328530i
$531$		0			0
$532$	−7881.58	−	566.293i	−0.642312	−	0.0461502i
$533$	1726.86			0.140335
$534$		0			0
$535$	11499.1			0.929253
$536$	−8594.87	−	14281.3i	−0.692615	−	1.15086i
$537$		0			0
$538$	−9453.58	−	3376.15i	−0.757570	−	0.270550i
$539$	14547.9	+	5182.21i	1.16256	+	0.414126i
$540$		0			0
$541$	8909.91			0.708072			0.354036	−	0.935232i	$-0.384809\pi$
$541$	8909.91			0.708072			0.354036	+	0.935232i	$0.384809\pi$
$542$	−2346.97	+	6571.78i	−0.185998	+	0.520815i
$543$		0			0
$544$	211.276	−	1454.35i	0.0166514	−	0.114623i
$545$		−	20563.4i		−	1.61622i
$546$		0			0
$547$			5848.51i			0.457156i	0.973526	+	0.228578i	$0.0734076\pi$
$547$			5848.51i			0.457156i	−0.973526	+	0.228578i	$0.926592\pi$
$548$	8284.89	+	6782.61i	0.645826	+	0.528721i
$549$		0			0
$550$	882.732	+	315.249i	0.0684361	+	0.0244405i
$551$	9024.45			0.697740
$552$		0			0
$553$	−6247.22	−	8857.11i	−0.480396	−	0.681090i
$554$	−2783.51	+	7794.13i	−0.213466	+	0.597727i
$555$		0			0
$556$	3068.93	+	2512.45i	0.234085	+	0.191639i
$557$	2801.60			0.213120			0.106560	−	0.994306i	$-0.466016\pi$
$557$	2801.60			0.213120			0.106560	+	0.994306i	$0.466016\pi$
$558$		0			0
$559$	−934.733			−0.0707245
$560$	−8835.75	+	9338.35i	−0.666747	+	0.704673i
$561$		0			0
$562$	−1641.30	+	4595.83i	−0.123193	+	0.344952i
$563$	−14489.5			−1.08465			−0.542326	−	0.840168i	$-0.682456\pi$
$563$	−14489.5			−1.08465			−0.542326	+	0.840168i	$0.682456\pi$
$564$		0			0
$565$		−	11866.0i		−	0.883549i
$566$	5333.95	−	14935.6i	0.396118	−	1.10917i
$567$		0			0
$568$	7008.59	+	11645.5i	0.517736	+	0.860275i
$569$	−2975.43			−0.219221			−0.109610	−	0.993975i	$-0.534960\pi$
$569$	−2975.43			−0.219221			−0.109610	+	0.993975i	$0.534960\pi$
$570$		0			0
$571$		−	3196.17i		−	0.234248i	−0.993117	−	0.117124i	$-0.962633\pi$
$571$		−	3196.17i		−	0.234248i	0.993117	−	0.117124i	$-0.0373675\pi$
$572$	11250.8	+	9210.70i	0.822410	+	0.673285i
$573$		0			0
$574$	−2158.91	+	600.484i	−0.156988	+	0.0436650i
$575$			410.644i			0.0297827i
$576$		0			0
$577$			381.164i			0.0275010i	0.999905	+	0.0137505i	$0.00437706\pi$
$577$			381.164i			0.0275010i	−0.999905	+	0.0137505i	$0.995623\pi$
$578$	4610.89	−	12911.0i	0.331813	−	0.929112i
$579$		0			0
$580$	9300.71	−	11360.7i	0.665846	−	0.813324i
$581$	12968.4	−	9147.04i	0.926023	−	0.653155i
$582$		0			0
$583$		−	17492.6i		−	1.24266i
$584$	−7859.14	−	13058.8i	−0.556872	−	0.925304i
$585$		0			0
$586$	−5703.85	−	2037.01i	−0.402089	−	0.143598i
$587$	6538.52			0.459751			0.229875	−	0.973220i	$-0.426168\pi$
$587$	6538.52			0.459751			0.229875	+	0.973220i	$0.426168\pi$
$588$		0			0
$589$	14024.8			0.981125
$590$	−18774.1	−	6704.76i	−1.31003	−	0.467849i
$591$		0			0
$592$	−4485.03	−	22268.3i	−0.311374	−	1.54599i
$593$			23421.0i			1.62190i	0.585118	+	0.810948i	$0.301048\pi$
$593$			23421.0i			1.62190i	−0.585118	+	0.810948i	$0.698952\pi$
$594$		0			0
$595$	1332.66	−	939.971i	0.0918215	−	0.0647648i
$596$	−11515.2	−	9427.17i	−0.791410	−	0.647906i
$597$		0			0
$598$	−2142.39	+	5998.93i	−0.146503	+	0.410225i
$599$		−	17506.7i		−	1.19416i	−0.802181	−	0.597081i	$-0.796327\pi$
$599$		−	17506.7i		−	1.19416i	0.802181	−	0.597081i	$-0.203673\pi$
$600$		0			0
$601$			1370.09i			0.0929904i	0.998919	+	0.0464952i	$0.0148052\pi$
$601$			1370.09i			0.0929904i	−0.998919	+	0.0464952i	$0.985195\pi$
$602$	1168.60	−	325.036i	0.0791172	−	0.0220058i
$603$		0			0
$604$	−4425.44	+	5405.63i	−0.298127	+	0.364159i
$605$		−	7550.96i		−	0.507422i
$606$		0			0
$607$	−21991.5			−1.47052			−0.735262	−	0.677783i	$-0.762941\pi$
$607$	−21991.5			−1.47052			−0.735262	+	0.677783i	$0.762941\pi$
$608$	9553.98	+	1387.92i	0.637278	+	0.0925785i
$609$		0			0
$610$	−9453.21	+	26470.0i	−0.627458	+	1.75695i
$611$			17674.3i			1.17026i
$612$		0			0
$613$	−7173.72			−0.472665			−0.236333	−	0.971672i	$-0.575946\pi$
$613$	−7173.72			−0.472665			−0.236333	+	0.971672i	$0.575946\pi$
$614$	2566.92	−	7187.66i	0.168718	−	0.472428i
$615$		0			0
$616$	−17268.5	−	7602.93i	−1.12949	−	0.497290i
$617$	20378.8			1.32969			0.664846	−	0.746981i	$-0.268497\pi$
$617$	20378.8			1.32969			0.664846	+	0.746981i	$0.268497\pi$
$618$		0			0
$619$	272.986			0.0177258			0.00886288	−	0.999961i	$-0.497179\pi$
$619$	272.986			0.0177258			0.00886288	+	0.999961i	$0.497179\pi$
$620$	14454.1	−	17655.6i	0.936278	−	1.14365i
$621$		0			0
$622$	−384.274	+	1076.01i	−0.0247717	+	0.0693634i
$623$	−9826.93	−	13932.3i	−0.631954	−	0.895965i
$624$		0			0
$625$	−14650.8			−0.937649
$626$	5878.08	+	2099.23i	0.375296	+	0.134029i
$627$		0			0
$628$	−6953.26	+	8493.33i	−0.441824	+	0.539683i
$629$			2881.52i			0.182661i
$630$		0			0
$631$		−	24207.1i		−	1.52721i	−0.645686	−	0.763603i	$-0.723428\pi$
$631$		−	24207.1i		−	1.52721i	0.645686	−	0.763603i	$-0.276572\pi$
$632$	6828.33	+	11346.0i	0.429772	+	0.714114i
$633$		0			0
$634$	227.796	−	637.853i	0.0142696	−	0.0399564i
$635$	1591.88			0.0994833
$636$		0			0
$637$	13043.3	+	4646.24i	0.811292	+	0.288996i
$638$	20293.3	+	7247.32i	1.25928	+	0.449724i
$639$		0			0
$640$	11593.7	−	10596.9i	0.716063	−	0.654500i
$641$	26265.0			1.61842			0.809208	−	0.587522i	$-0.199897\pi$
$641$	26265.0			1.61842			0.809208	+	0.587522i	$0.199897\pi$
$642$		0			0
$643$	−20418.1			−1.25227			−0.626137	−	0.779713i	$-0.715365\pi$
$643$	−20418.1			−1.25227			−0.626137	+	0.779713i	$0.715365\pi$
$644$	592.391	−	8244.81i	0.0362477	−	0.504489i
$645$		0			0
$646$	−1153.33	−	411.886i	−0.0702430	−	0.0250858i
$647$	−19530.1			−1.18672			−0.593359	−	0.804938i	$-0.702199\pi$
$647$	−19530.1			−1.18672			−0.593359	+	0.804938i	$0.702199\pi$
$648$		0			0
$649$		−	29258.3i		−	1.76963i
$650$	791.435	+	282.645i	0.0477579	+	0.0170557i
$651$		0			0
$652$	−10336.5	+	12625.9i	−0.620872	+	0.758388i
$653$	−11035.5			−0.661334			−0.330667	−	0.943748i	$-0.607274\pi$
$653$	−11035.5			−0.661334			−0.330667	+	0.943748i	$0.607274\pi$
$654$		0			0
$655$		−	12365.2i		−	0.737633i
$656$	2683.92	−	540.563i	0.159740	−	0.0321729i
$657$		0			0
$658$	−6145.93	−	22096.4i	−0.364123	−	1.30913i
$659$			8634.82i			0.510417i	0.966886	+	0.255209i	$0.0821442\pi$
$659$			8634.82i			0.510417i	−0.966886	+	0.255209i	$0.917856\pi$
$660$		0			0
$661$		−	19201.3i		−	1.12987i	−0.825134	−	0.564936i	$-0.808901\pi$
$661$		−	19201.3i		−	1.12987i	0.825134	−	0.564936i	$-0.191099\pi$
$662$	−29668.9	−	10595.6i	−1.74187	−	0.622071i
$663$		0			0
$664$	−16612.6	+	9997.88i	−0.970923	+	0.584327i
$665$	6174.90	+	8754.58i	0.360079	+	0.510508i
$666$		0			0
$667$			9440.35i			0.548024i
$668$	1792.23	+	1467.25i	0.103808	+	0.0849845i
$669$		0			0
$670$	−7600.35	+	21281.8i	−0.438250	+	1.22715i
$671$	−41252.0			−2.37335
$672$		0			0
$673$	14720.8			0.843160			0.421580	−	0.906791i	$-0.361476\pi$
$673$	14720.8			0.843160			0.421580	+	0.906791i	$0.361476\pi$
$674$	−350.036	+	980.137i	−0.0200042	+	0.0560140i
$675$		0			0
$676$	−3512.64	−	2875.71i	−0.199855	−	0.163616i
$677$		−	3825.44i		−	0.217169i	−0.994087	−	0.108585i	$-0.965368\pi$
$677$		−	3825.44i		−	0.217169i	0.994087	−	0.108585i	$-0.0346318\pi$
$678$		0			0
$679$	6821.07	+	9670.70i	0.385521	+	0.546580i
$680$	−1707.15	+	1027.40i	−0.0962737	+	0.0579400i
$681$		0			0
$682$	31537.6	+	11263.0i	1.77073	+	0.632379i
$683$			4464.38i			0.250109i	0.992150	+	0.125055i	$0.0399106\pi$
$683$			4464.38i			0.250109i	−0.992150	+	0.125055i	$0.960089\pi$
$684$		0			0
$685$		−	14516.5i		−	0.809702i
$686$	−17922.3	−	1273.15i	−0.997486	−	0.0708588i
$687$		0			0
$688$	−1452.78	+	292.602i	−0.0805040	+	0.0162142i
$689$		−	15683.4i		−	0.867186i
$690$		0			0
$691$	21592.4			1.18873			0.594366	−	0.804195i	$-0.297403\pi$
$691$	21592.4			1.18873			0.594366	+	0.804195i	$0.297403\pi$
$692$	−20629.4	+	25198.6i	−1.13325	+	1.38426i
$693$		0			0
$694$	8286.41	+	2959.32i	0.453239	+	0.161865i
$695$		−	5377.25i		−	0.293483i
$696$		0			0
$697$	−347.298			−0.0188735
$698$	−570.016	−	203.569i	−0.0309103	−	0.0110390i
$699$		0			0
$700$	−1087.73	−	78.1538i	−0.0587321	−	0.00421991i
$701$	−25026.4			−1.34841			−0.674204	−	0.738545i	$-0.735513\pi$
$701$	−25026.4			−1.34841			−0.674204	+	0.738545i	$0.735513\pi$
$702$		0			0
$703$	−18929.4			−1.01556
$704$	20369.4	+	10793.6i	1.09048	+	0.577839i
$705$		0			0
$706$	10108.3	+	3609.95i	0.538852	+	0.192440i
$707$	16040.0	+	22741.1i	0.853250	+	1.20971i
$708$		0			0
$709$	−4470.40			−0.236798			−0.118399	−	0.992966i	$-0.537776\pi$
$709$	−4470.40			−0.236798			−0.118399	+	0.992966i	$0.537776\pi$
$710$	6197.62	−	17354.0i	0.327595	−	0.917302i
$711$		0			0
$712$	10741.0	+	17847.4i	0.565360	+	0.939408i
$713$			14671.2i			0.770603i
$714$		0			0
$715$		−	19713.2i		−	1.03109i
$716$	10945.1	−	13369.3i	0.571282	−	0.697815i
$717$		0			0
$718$	−2302.23	−	822.195i	−0.119664	−	0.0427354i
$719$	11835.0			0.613866			0.306933	−	0.951731i	$-0.400697\pi$
$719$	11835.0			0.613866			0.306933	+	0.951731i	$0.400697\pi$
$720$		0			0
$721$	14309.6	−	10093.1i	0.739138	−	0.521339i
$722$	−3818.98	+	10693.6i	−0.196853	+	0.551209i
$723$		0			0
$724$	−22890.1	+	27960.0i	−1.17501	+	1.43526i
$725$	1245.46			0.0638003
$726$		0			0
$727$	27077.9			1.38138			0.690690	−	0.723151i	$-0.257307\pi$
$727$	27077.9			1.38138			0.690690	+	0.723151i	$0.257307\pi$
$728$	−15482.5	−	6816.59i	−0.788214	−	0.347032i
$729$		0			0
$730$	−6949.75	+	19460.1i	−0.352359	+	0.986642i
$731$	187.989			0.00951168
$732$		0			0
$733$			35697.1i			1.79878i	0.437150	+	0.899388i	$0.355988\pi$
$733$			35697.1i			1.79878i	−0.437150	+	0.899388i	$0.644012\pi$
$734$	−7437.54	+	20825.9i	−0.374012	+	1.04727i
$735$		0			0
$736$	−1451.89	+	9994.29i	−0.0727137	+	0.500536i
$737$	−33166.5			−1.65767
$738$		0			0
$739$			10357.8i			0.515585i	0.966200	+	0.257793i	$0.0829952\pi$
$739$			10357.8i			0.515585i	−0.966200	+	0.257793i	$0.917005\pi$
$740$	−19508.9	+	23829.9i	−0.969136	+	1.18379i
$741$		0			0
$742$	5453.62	+	19607.3i	0.269823	+	0.970092i
$743$		−	20402.7i		−	1.00741i	−0.863877	−	0.503704i	$-0.831970\pi$
$743$		−	20402.7i		−	1.00741i	0.863877	−	0.503704i	$-0.168030\pi$
$744$		0			0
$745$			20176.5i			0.992226i
$746$	2218.86	−	6213.03i	0.108898	−	0.304927i
$747$		0			0
$748$	−2262.71	−	1852.42i	−0.110605	−	0.0905495i
$749$	−11317.4	−	16045.5i	−0.552108	−	0.782762i
$750$		0			0
$751$		−	19383.5i		−	0.941830i	−0.882179	−	0.470915i	$-0.843924\pi$
$751$		−	19383.5i		−	0.941830i	0.882179	−	0.470915i	$-0.156076\pi$
$752$	5532.64	+	27469.8i	0.268291	+	1.33207i
$753$		0			0
$754$	18194.4	+	6497.76i	0.878782	+	0.313839i
$755$	9471.54			0.456562
$756$		0			0
$757$	5902.37			0.283389			0.141694	−	0.989910i	$-0.454745\pi$
$757$	5902.37			0.283389			0.141694	+	0.989910i	$0.454745\pi$
$758$	−35440.7	−	12656.9i	−1.69824	−	0.606490i
$759$		0			0
$760$	−6749.28	−	11214.7i	−0.322134	−	0.535262i
$761$		−	16477.6i		−	0.784904i	−0.919772	−	0.392452i	$-0.871627\pi$
$761$		−	16477.6i		−	0.784904i	0.919772	−	0.392452i	$-0.128373\pi$
$762$		0			0
$763$	−28693.4	+	20238.5i	−1.36143	+	0.960264i
$764$	−13940.0	+	17027.6i	−0.660120	+	0.806329i
$765$		0			0
$766$	−7777.77	+	21778.6i	−0.366870	+	1.02728i
$767$		−	26232.3i		−	1.23493i
$768$		0			0
$769$		−	21396.0i		−	1.00333i	−0.865062	−	0.501665i	$-0.832721\pi$
$769$		−	21396.0i		−	1.00333i	0.865062	−	0.501665i	$-0.167279\pi$
$770$	6854.90	+	24645.3i	0.320823	+	1.15345i
$771$		0			0
$772$	−21477.8	−	17583.3i	−1.00130	−	0.819737i
$773$			9499.74i			0.442020i	0.975271	+	0.221010i	$0.0709354\pi$
$773$			9499.74i			0.442020i	−0.975271	+	0.221010i	$0.929065\pi$
$774$		0			0
$775$	1935.56			0.0897127
$776$	−7455.56	−	12388.2i	−0.344896	−	0.573082i
$777$		0			0
$778$	5384.53	−	15077.3i	0.248130	−	0.694790i
$779$		−	2281.49i		−	0.104933i
$780$		0			0
$781$	27045.3			1.23912
$782$	430.868	−	1206.48i	0.0197031	−	0.0551708i
$783$		0			0
$784$	21726.5	+	3138.31i	0.989728	+	0.142962i
$785$	14881.7			0.676625
$786$		0			0
$787$	−9521.98			−0.431286			−0.215643	−	0.976472i	$-0.569185\pi$
$787$	−9521.98			−0.431286			−0.215643	+	0.976472i	$0.569185\pi$
$788$	−9629.92	−	7883.75i	−0.435345	−	0.356405i
$789$		0			0
$790$	6038.22	−	16907.7i	0.271937	−	0.761452i
$791$	−16557.3	+	11678.5i	−0.744262	+	0.524953i
$792$		0			0
$793$	−36985.5			−1.65623
$794$	11410.2	+	4074.91i	0.509991	+	0.182133i
$795$		0			0
$796$	6367.76	+	5213.11i	0.283542	+	0.232128i
$797$		−	6161.99i		−	0.273863i	−0.990580	−	0.136932i	$-0.956276\pi$
$797$		−	6161.99i		−	0.273863i	0.990580	−	0.136932i	$-0.0437241\pi$
$798$		0			0
$799$		−	3554.58i		−	0.157387i
$800$	1318.54	+	191.547i	0.0582718	+	0.00846525i
$801$		0			0
$802$	12268.0	−	34351.7i	0.540147	−	1.51247i
$803$	−30327.4			−1.33279
$804$		0			0
$805$	−9158.05	+	6459.48i	−0.400967	+	0.282816i
$806$	28275.8	+	10098.1i	1.23570	+	0.441304i
$807$		0			0
$808$	−17532.0	−	29131.4i	−0.763336	−	1.26837i
$809$	14824.7			0.644262			0.322131	−	0.946695i	$-0.395601\pi$
$809$	14824.7			0.644262			0.322131	+	0.946695i	$0.395601\pi$
$810$		0			0
$811$	5179.05			0.224243			0.112121	−	0.993695i	$-0.464235\pi$
$811$	5179.05			0.224243			0.112121	+	0.993695i	$0.464235\pi$
$812$	−25006.1	−	1796.69i	−1.08072	−	0.0776496i
$813$		0			0
$814$	−42566.5	−	15201.8i	−1.83287	−	0.654571i
$815$	22122.7			0.950826
$816$		0			0
$817$			1234.95i			0.0528830i
$818$	−6291.36	−	2246.83i	−0.268915	−	0.0960373i
$819$		0			0
$820$	−2872.12	−	2351.33i	−0.122316	−	0.100137i
$821$	−17245.1			−0.733080			−0.366540	−	0.930402i	$-0.619458\pi$
$821$	−17245.1			−0.733080			−0.366540	+	0.930402i	$0.619458\pi$
$822$		0			0
$823$			27833.6i			1.17888i	0.807812	+	0.589441i	$0.200652\pi$
$823$			27833.6i			1.17888i	−0.807812	+	0.589441i	$0.799348\pi$
$824$	−18330.7	+	11031.9i	−0.774977	+	0.466401i
$825$		0			0
$826$	9121.79	+	32795.5i	0.384247	+	1.38148i
$827$		−	33922.5i		−	1.42636i	−0.700980	−	0.713180i	$-0.747254\pi$
$827$		−	33922.5i		−	1.42636i	0.700980	−	0.713180i	$-0.252746\pi$
$828$		0			0
$829$		−	14220.9i		−	0.595794i	−0.954598	−	0.297897i	$-0.903715\pi$
$829$		−	14220.9i		−	0.595794i	0.954598	−	0.297897i	$-0.0962852\pi$
$830$	24755.8	+	8841.02i	1.03528	+	0.369730i
$831$		0			0
$832$	18262.7	+	9677.26i	0.760992	+	0.403243i
$833$	−2623.20	−	934.431i	−0.109110	−	0.0388669i
$834$		0			0
$835$		−	3140.28i		−	0.130148i
$836$	12169.0	−	14864.3i	0.503436	−	0.614942i
$837$		0			0
$838$	11455.3	−	32076.1i	0.472217	−	1.32226i
$839$	1012.97			0.0416825			0.0208413	−	0.999783i	$-0.493366\pi$
$839$	1012.97			0.0416825			0.0208413	+	0.999783i	$0.493366\pi$
$840$		0			0
$841$	4243.08			0.173975
$842$	−15486.1	+	43362.7i	−0.633831	+	1.77479i
$843$		0			0
$844$	−5819.08	+	7107.94i	−0.237323	+	0.289888i
$845$			6154.72i			0.250567i
$846$		0			0
$847$	−10536.3	+	7431.63i	−0.427430	+	0.301480i
$848$	−4909.42	−	24375.5i	−0.198809	−	0.987096i
$849$		0			0
$850$	−159.170	−	56.8442i	−0.00642292	−	0.00229381i
$851$		−	19801.8i		−	0.797646i
$852$		0			0
$853$		−	30869.9i		−	1.23912i	−0.784951	−	0.619558i	$-0.787312\pi$
$853$		−	30869.9i		−	1.23912i	0.784951	−	0.619558i	$-0.212688\pi$
$854$	46239.1	−	12861.0i	1.85278	−	0.515334i
$855$		0			0
$856$	12370.1	+	20554.3i	0.493928	+	0.820716i
$857$			18165.2i			0.724052i	0.932168	+	0.362026i	$0.117915\pi$
$857$			18165.2i			0.724052i	−0.932168	+	0.362026i	$0.882085\pi$
$858$		0			0
$859$	8466.59			0.336294			0.168147	−	0.985762i	$-0.446222\pi$
$859$	8466.59			0.336294			0.168147	+	0.985762i	$0.446222\pi$
$860$	1554.65	+	1272.75i	0.0616433	+	0.0504657i
$861$		0			0
$862$	23990.8	+	8567.80i	0.947945	+	0.338539i
$863$		−	2089.73i		−	0.0824277i	−0.999150	−	0.0412138i	$-0.986878\pi$
$863$		−	2089.73i		−	0.0824277i	0.999150	−	0.0412138i	$-0.0131225\pi$
$864$		0			0
$865$	44152.0			1.73551
$866$	43805.2	+	15644.1i	1.71889	+	0.613866i
$867$		0			0
$868$	−38861.7	−	2792.22i	−1.51965	−	0.109187i
$869$	26349.6			1.02860
$870$		0			0
$871$	−29736.2			−1.15680
$872$	36756.5	−	22121.0i	1.42744	−	0.859073i
$873$		0			0
$874$	7925.65	+	2830.48i	0.306738	+	0.109545i
$875$	15324.8	+	21727.0i	0.592082	+	0.839435i
$876$		0			0
$877$	−11741.7			−0.452096			−0.226048	−	0.974116i	$-0.572581\pi$
$877$	−11741.7			−0.452096			−0.226048	+	0.974116i	$0.572581\pi$
$878$	−9568.61	+	26793.1i	−0.367796	+	1.02987i
$879$		0			0
$880$	−6170.86	−	30638.6i	−0.236386	−	1.17367i
$881$			11269.6i			0.430968i	0.976507	+	0.215484i	$0.0691329\pi$
$881$			11269.6i			0.430968i	−0.976507	+	0.215484i	$0.930867\pi$
$882$		0			0
$883$			34244.0i			1.30510i	0.757746	+	0.652550i	$0.226301\pi$
$883$			34244.0i			1.30510i	−0.757746	+	0.652550i	$0.773699\pi$
$884$	−2028.68	−	1660.83i	−0.0771855	−	0.0631897i
$885$		0			0
$886$	−15701.3	−	5607.38i	−0.595367	−	0.212623i
$887$	6692.54			0.253341			0.126670	−	0.991945i	$-0.459571\pi$
$887$	6692.54			0.253341			0.126670	+	0.991945i	$0.459571\pi$
$888$		0			0
$889$	−1566.73	−	2221.25i	−0.0591072	−	0.0838003i
$890$	9498.16	−	26595.9i	0.357729	−	1.00168i
$891$		0			0
$892$	−837.214	−	685.404i	−0.0314260	−	0.0257276i
$893$	23350.9			0.875038
$894$		0			0
$895$	−23425.2			−0.874882
$896$	−26197.0	−	5747.95i	−0.976765	−	0.214314i
$897$		0			0
$898$	−7140.87	+	19995.2i	−0.265361	+	0.743039i
$899$	44496.9			1.65078
$900$		0			0
$901$			3154.18i			0.116627i
$902$	1832.21	−	5130.38i	0.0676340	−	0.189382i
$903$		0			0
$904$	21210.1	−	12764.8i	0.780350	−	0.469635i
$905$	48990.5			1.79945
$906$		0			0
$907$		−	4516.82i		−	0.165357i	−0.996576	−	0.0826784i	$-0.973653\pi$
$907$		−	4516.82i		−	0.165357i	0.996576	−	0.0826784i	$-0.0263474\pi$
$908$	−30697.2	−	25131.0i	−1.12194	−	0.918504i
$909$		0			0
$910$	6145.93	+	22096.4i	0.223885	+	0.804931i
$911$			17920.4i			0.651733i	0.945416	+	0.325866i	$0.105656\pi$
$911$			17920.4i			0.651733i	−0.945416	+	0.325866i	$0.894344\pi$
$912$		0			0
$913$			38580.5i			1.39850i
$914$	−4028.25	+	11279.5i	−0.145780	+	0.408199i
$915$		0			0
$916$	−5869.04	+	7168.97i	−0.211702	+	0.258591i
$917$	−17254.0	+	12169.8i	−0.621349	+	0.438259i
$918$		0			0
$919$		−	4196.24i		−	0.150622i	−0.997160	−	0.0753108i	$-0.976005\pi$
$919$		−	4196.24i		−	0.150622i	0.997160	−	0.0753108i	$-0.0239949\pi$
$920$	11731.5	−	7060.33i	0.420409	−	0.253013i
$921$		0			0
$922$	−35724.4	−	12758.2i	−1.27605	−	0.455715i
$923$	24248.1			0.864719
$924$		0			0
$925$	−2612.44			−0.0928610
$926$	−38983.2	−	13922.0i	−1.38344	−	0.494068i
$927$		0			0
$928$	30312.1	+	4403.50i	1.07225	+	0.155767i
$929$		−	29450.4i		−	1.04008i	−0.854141	−	0.520041i	$-0.825917\pi$
$929$		−	29450.4i		−	1.04008i	0.854141	−	0.520041i	$-0.174083\pi$
$930$		0			0
$931$	6138.51	−	17232.5i	0.216092	−	0.606629i
$932$	−6133.75	−	5021.54i	−0.215577	−	0.176487i
$933$		0			0
$934$	16394.7	−	45907.0i	0.574360	−	1.60827i
$935$			3964.63i			0.138671i
$936$		0			0
$937$		−	2371.63i		−	0.0826869i	−0.999145	−	0.0413435i	$-0.986836\pi$
$937$		−	2371.63i		−	0.0826869i	0.999145	−	0.0413435i	$-0.0131638\pi$
$938$	37176.1	−	10340.2i	1.29408	−	0.359937i
$939$		0			0
$940$	24065.7	−	29396.1i	0.835041	−	1.01999i
$941$		−	55538.8i		−	1.92403i	−0.272998	−	0.962015i	$-0.588015\pi$
$941$		−	55538.8i		−	1.92403i	0.272998	−	0.962015i	$-0.411985\pi$
$942$		0			0
$943$	2386.63			0.0824173
$944$	−8211.55	−	40770.7i	−0.283118	−	1.40569i
$945$		0			0
$946$	−991.757	+	2777.03i	−0.0340854	+	0.0954429i
$947$			12123.3i			0.416003i	0.978128	+	0.208002i	$0.0666960\pi$
$947$			12123.3i			0.416003i	−0.978128	+	0.208002i	$0.933304\pi$
$948$		0			0
$949$	−27190.8			−0.930084
$950$	373.424	−	1045.63i	0.0127531	−	0.0357101i
$951$		0			0
$952$	3113.77	+	1370.92i	0.106006	+	0.0466721i
$953$	−11939.2			−0.405821			−0.202911	−	0.979197i	$-0.565040\pi$
$953$	−11939.2			−0.405821			−0.202911	+	0.979197i	$0.565040\pi$
$954$		0			0
$955$	29835.0			1.01093
$956$	−21176.0	+	25866.3i	−0.716402	+	0.875078i
$957$		0			0
$958$	−1511.08	+	4231.18i	−0.0509611	+	0.142697i
$959$	−20255.8	+	14287.1i	−0.682057	+	0.481078i
$960$		0			0
$961$	39361.2			1.32124
$962$	−38164.1	−	13629.5i	−1.27906	−	0.456791i
$963$		0			0
$964$	12630.6	−	15428.1i	0.421996	−	0.515463i
$965$			37632.6i			1.25537i
$966$		0			0
$967$		−	24933.9i		−	0.829182i	−0.910008	−	0.414591i	$-0.863925\pi$
$967$		−	24933.9i		−	0.829182i	0.910008	−	0.414591i	$-0.136075\pi$
$968$	13497.1	−	8122.91i	0.448155	−	0.269711i
$969$		0			0
$970$	−6592.87	+	18460.7i	−0.218231	+	0.611071i
$971$	−54351.7			−1.79632			−0.898161	−	0.439668i	$-0.855096\pi$
$971$	−54351.7			−1.79632			−0.898161	+	0.439668i	$0.855096\pi$
$972$		0			0
$973$	−7503.23	+	5292.28i	−0.247217	+	0.174371i
$974$	29362.9	+	10486.4i	0.965965	+	0.344974i
$975$		0			0
$976$	−57483.6	+	11577.7i	−1.88525	+	0.379705i
$977$	−41536.7			−1.36016			−0.680080	−	0.733138i	$-0.738055\pi$
$977$	−41536.7			−1.36016			−0.680080	+	0.733138i	$0.738055\pi$
$978$		0			0
$979$	41448.2			1.35311
$980$	−15367.2	−	25487.6i	−0.500906	−	0.830789i
$981$		0			0
$982$	−1553.26	−	554.713i	−0.0504750	−	0.0180261i
$983$	12193.5			0.395638			0.197819	−	0.980239i	$-0.436614\pi$
$983$	12193.5			0.395638			0.197819	+	0.980239i	$0.436614\pi$
$984$		0			0
$985$			16873.2i			0.545811i
$986$	−3659.18	−	1306.80i	−0.118187	−	0.0422079i
$987$		0			0
$988$	10910.4	−	13326.9i	0.351322	−	0.429136i
$989$	−1291.86			−0.0415357
$990$		0			0
$991$		−	50014.9i		−	1.60320i	−0.597858	−	0.801602i	$-0.703981\pi$
$991$		−	50014.9i		−	1.60320i	0.597858	−	0.801602i	$-0.296019\pi$
$992$	47107.8	+	6843.44i	1.50774	+	0.219032i
$993$		0			0
$994$	−30314.8	+	8431.83i	−0.967332	+	0.269056i
$995$		−	11157.4i		−	0.355489i
$996$		0			0
$997$		−	25494.4i		−	0.809844i	−0.914351	−	0.404922i	$-0.867299\pi$
$997$		−	25494.4i		−	0.809844i	0.914351	−	0.404922i	$-0.132701\pi$
$998$	14327.6	+	5116.81i	0.454442	+	0.162294i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.b.e.55.7		12
3.2	odd	2		84.4.b.b.55.6	yes	12
4.3	odd	2		252.4.b.f.55.8		12
7.6	odd	2		252.4.b.f.55.7		12
12.11	even	2		84.4.b.a.55.5	✓	12
21.20	even	2		84.4.b.a.55.6	yes	12
24.5	odd	2		1344.4.b.g.895.10		12
24.11	even	2		1344.4.b.h.895.10		12
28.27	even	2	inner	252.4.b.e.55.8		12
84.83	odd	2		84.4.b.b.55.5	yes	12
168.83	odd	2		1344.4.b.g.895.3		12
168.125	even	2		1344.4.b.h.895.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.b.a.55.5	✓	12	12.11	even	2
84.4.b.a.55.6	yes	12	21.20	even	2
84.4.b.b.55.5	yes	12	84.83	odd	2
84.4.b.b.55.6	yes	12	3.2	odd	2
252.4.b.e.55.7		12	1.1	even	1	trivial
252.4.b.e.55.8		12	28.27	even	2	inner
252.4.b.f.55.7		12	7.6	odd	2
252.4.b.f.55.8		12	4.3	odd	2
1344.4.b.g.895.3		12	168.83	odd	2
1344.4.b.g.895.10		12	24.5	odd	2
1344.4.b.h.895.3		12	168.125	even	2
1344.4.b.h.895.10		12	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951271 - 2.66366i) q^{2} +(-6.19017 - 5.06772i) q^{4} +10.8462i q^{5} +(15.1344 - 10.6748i) q^{7} +(-19.3872 + 11.6677i) q^{8} +O(q^{10})\)	\(q+(0.951271 - 2.66366i) q^{2} +(-6.19017 - 5.06772i) q^{4} +10.8462i q^{5} +(15.1344 - 10.6748i) q^{7} +(-19.3872 + 11.6677i) q^{8} +(28.8905 + 10.3176i) q^{10} +45.0243i q^{11} +40.3676i q^{13} +(-14.0371 - 50.4674i) q^{14} +(12.6364 + 62.7401i) q^{16} -8.11855i q^{17} +53.3328 q^{19} +(54.9654 - 67.1397i) q^{20} +(119.929 + 42.8303i) q^{22} +55.7907i q^{23} +7.36043 q^{25} +(107.526 + 38.4005i) q^{26} +(-147.781 - 10.6181i) q^{28} +169.210 q^{29} +262.968 q^{31} +(179.139 + 26.0238i) q^{32} +(-21.6251 - 7.72294i) q^{34} +(115.781 + 164.150i) q^{35} -354.930 q^{37} +(50.7339 - 142.060i) q^{38} +(-126.550 - 210.277i) q^{40} -42.7783i q^{41} +23.1555i q^{43} +(228.171 - 278.708i) q^{44} +(148.607 + 53.0721i) q^{46} +437.834 q^{47} +(115.098 - 323.112i) q^{49} +(7.00176 - 19.6057i) q^{50} +(204.572 - 249.882i) q^{52} -388.515 q^{53} -488.341 q^{55} +(-168.863 + 383.538i) q^{56} +(160.965 - 450.718i) q^{58} -649.834 q^{59} +916.217i q^{61} +(250.154 - 700.457i) q^{62} +(239.728 - 452.410i) q^{64} -437.834 q^{65} +736.636i q^{67} +(-41.1426 + 50.2552i) q^{68} +(547.379 - 152.249i) q^{70} -600.682i q^{71} +673.579i q^{73} +(-337.634 + 945.413i) q^{74} +(-330.139 - 270.276i) q^{76} +(480.624 + 681.414i) q^{77} -585.232i q^{79} +(-680.490 + 137.056i) q^{80} +(-113.947 - 40.6938i) q^{82} +856.883 q^{83} +88.0553 q^{85} +(61.6784 + 22.0272i) q^{86} +(-525.331 - 872.896i) q^{88} -920.574i q^{89} +(430.915 + 610.938i) q^{91} +(282.732 - 345.354i) q^{92} +(416.499 - 1166.24i) q^{94} +578.457i q^{95} +638.990i q^{97} +(-751.171 - 613.949i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + 5 q^{4} - 10 q^{7} - 25 q^{8}+O(q^{10}) \) 12 * q - q^2 + 5 * q^4 - 10 * q^7 - 25 * q^8	\( 12 q - q^{2} + 5 q^{4} - 10 q^{7} - 25 q^{8} - 56 q^{10} - 101 q^{14} + 41 q^{16} + 84 q^{19} + 172 q^{20} - 182 q^{22} - 216 q^{25} + 300 q^{26} - 379 q^{28} - 200 q^{29} + 384 q^{31} + 159 q^{32} + 164 q^{34} + 84 q^{35} - 244 q^{37} + 268 q^{38} + 316 q^{40} - 190 q^{44} + 894 q^{46} + 280 q^{47} - 424 q^{49} + 1771 q^{50} + 796 q^{52} + 16 q^{53} - 212 q^{55} + 1759 q^{56} - 570 q^{58} + 1168 q^{59} - 384 q^{62} + 2705 q^{64} - 280 q^{65} + 1552 q^{68} + 2592 q^{70} - 1622 q^{74} + 788 q^{76} - 968 q^{77} - 3060 q^{80} + 2540 q^{82} - 968 q^{83} - 852 q^{85} + 258 q^{86} - 2186 q^{88} - 1648 q^{91} - 4298 q^{92} - 4256 q^{94} - 3137 q^{98}+O(q^{100}) \) 12 * q - q^2 + 5 * q^4 - 10 * q^7 - 25 * q^8 - 56 * q^10 - 101 * q^14 + 41 * q^16 + 84 * q^19 + 172 * q^20 - 182 * q^22 - 216 * q^25 + 300 * q^26 - 379 * q^28 - 200 * q^29 + 384 * q^31 + 159 * q^32 + 164 * q^34 + 84 * q^35 - 244 * q^37 + 268 * q^38 + 316 * q^40 - 190 * q^44 + 894 * q^46 + 280 * q^47 - 424 * q^49 + 1771 * q^50 + 796 * q^52 + 16 * q^53 - 212 * q^55 + 1759 * q^56 - 570 * q^58 + 1168 * q^59 - 384 * q^62 + 2705 * q^64 - 280 * q^65 + 1552 * q^68 + 2592 * q^70 - 1622 * q^74 + 788 * q^76 - 968 * q^77 - 3060 * q^80 + 2540 * q^82 - 968 * q^83 - 852 * q^85 + 258 * q^86 - 2186 * q^88 - 1648 * q^91 - 4298 * q^92 - 4256 * q^94 - 3137 * q^98

Introduction

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