LMFDB - Embedded newform 324.5.d.f.163.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,5,Mod(163,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("324.163");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	324.d (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:	$33.4918680392$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.11
Character	$\chi$	$=$	324.163
Dual form			324.5.d.f.163.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.328300 - 3.98650i) q^{2} +(-15.7844 + 2.61754i) q^{4} +5.66182 q^{5} +52.1456i q^{7} +(15.6169 + 62.0654i) q^{8} +O(q^{10})$	\(q+(-0.328300 - 3.98650i) q^{2} +(-15.7844 + 2.61754i) q^{4} +5.66182 q^{5} +52.1456i q^{7} +(15.6169 + 62.0654i) q^{8} +(-1.85878 - 22.5709i) q^{10} +106.664i q^{11} -122.137 q^{13} +(207.879 - 17.1194i) q^{14} +(242.297 - 82.6328i) q^{16} -122.675 q^{17} -593.624i q^{19} +(-89.3686 + 14.8200i) q^{20} +(425.216 - 35.0178i) q^{22} -546.922i q^{23} -592.944 q^{25} +(40.0976 + 486.900i) q^{26} +(-136.493 - 823.090i) q^{28} +735.866 q^{29} -585.927i q^{31} +(-408.962 - 938.790i) q^{32} +(40.2742 + 489.044i) q^{34} +295.239i q^{35} +2289.29 q^{37} +(-2366.49 + 194.887i) q^{38} +(88.4199 + 351.403i) q^{40} -2868.26 q^{41} -2244.52i q^{43} +(-279.197 - 1683.63i) q^{44} +(-2180.31 + 179.555i) q^{46} -1054.85i q^{47} -318.168 q^{49} +(194.664 + 2363.77i) q^{50} +(1927.87 - 319.699i) q^{52} -4752.60 q^{53} +603.911i q^{55} +(-3236.44 + 814.352i) q^{56} +(-241.585 - 2933.53i) q^{58} +2152.65i q^{59} -66.3319 q^{61} +(-2335.80 + 192.360i) q^{62} +(-3608.23 + 1938.53i) q^{64} -691.518 q^{65} -4104.76i q^{67} +(1936.36 - 321.107i) q^{68} +(1176.97 - 96.9271i) q^{70} -5031.65i q^{71} +2705.16 q^{73} +(-751.574 - 9126.26i) q^{74} +(1553.84 + 9370.03i) q^{76} -5562.06 q^{77} -1381.05i q^{79} +(1371.84 - 467.852i) q^{80} +(941.652 + 11434.4i) q^{82} +3008.36i q^{83} -694.563 q^{85} +(-8947.79 + 736.876i) q^{86} +(-6620.13 + 1665.76i) q^{88} +3186.35 q^{89} -6368.92i q^{91} +(1431.59 + 8632.86i) q^{92} +(-4205.18 + 346.309i) q^{94} -3360.99i q^{95} -4814.06 q^{97} +(104.455 + 1268.38i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + q^{2} + q^{4} + 2 q^{5} + 61 q^{8}+O(q^{10}) $ 22 * q + q^2 + q^4 + 2 * q^5 + 61 * q^8	$ 22 q + q^{2} + q^{4} + 2 q^{5} + 61 q^{8} + 14 q^{10} + 2 q^{13} - 252 q^{14} + q^{16} - 28 q^{17} + 140 q^{20} + 33 q^{22} + 1752 q^{25} + 548 q^{26} - 258 q^{28} - 526 q^{29} + 121 q^{32} - 385 q^{34} - 4 q^{37} - 1395 q^{38} + 2276 q^{40} + 2762 q^{41} + 3357 q^{44} + 1788 q^{46} - 3428 q^{49} - 6375 q^{50} - 1438 q^{52} - 5044 q^{53} + 7506 q^{56} + 4064 q^{58} + 2 q^{61} - 9162 q^{62} + 4513 q^{64} + 2014 q^{65} + 11405 q^{68} - 3666 q^{70} - 1708 q^{73} - 14620 q^{74} - 1581 q^{76} + 3942 q^{77} + 22760 q^{80} - 4243 q^{82} + 1252 q^{85} - 22113 q^{86} - 1995 q^{88} + 6524 q^{89} + 30294 q^{92} - 7524 q^{94} - 5638 q^{97} - 46469 q^{98}+O(q^{100}) $ 22 * q + q^2 + q^4 + 2 * q^5 + 61 * q^8 + 14 * q^10 + 2 * q^13 - 252 * q^14 + q^16 - 28 * q^17 + 140 * q^20 + 33 * q^22 + 1752 * q^25 + 548 * q^26 - 258 * q^28 - 526 * q^29 + 121 * q^32 - 385 * q^34 - 4 * q^37 - 1395 * q^38 + 2276 * q^40 + 2762 * q^41 + 3357 * q^44 + 1788 * q^46 - 3428 * q^49 - 6375 * q^50 - 1438 * q^52 - 5044 * q^53 + 7506 * q^56 + 4064 * q^58 + 2 * q^61 - 9162 * q^62 + 4513 * q^64 + 2014 * q^65 + 11405 * q^68 - 3666 * q^70 - 1708 * q^73 - 14620 * q^74 - 1581 * q^76 + 3942 * q^77 + 22760 * q^80 - 4243 * q^82 + 1252 * q^85 - 22113 * q^86 - 1995 * q^88 + 6524 * q^89 + 30294 * q^92 - 7524 * q^94 - 5638 * q^97 - 46469 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$1$

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 $

$2$	−0.328300	−	3.98650i	−0.0820750	−	0.996626i
$2$	−0.328300	−	3.98650i	−0.0820750	−	0.996626i
$3$		0			0
$3$		0			0
$4$	−15.7844	+	2.61754i	−0.986527	+	0.163596i
$5$	5.66182			0.226473			0.113236	−	0.993568i	$-0.463878\pi$
$5$	5.66182			0.226473			0.113236	+	0.993568i	$0.463878\pi$
$6$		0			0
$7$			52.1456i			1.06420i	0.846683	+	0.532098i	$0.178596\pi$
$7$			52.1456i			1.06420i	−0.846683	+	0.532098i	$0.821404\pi$
$8$	15.6169	+	62.0654i	0.244014	+	0.969772i
$9$		0			0
$10$	−1.85878	−	22.5709i	−0.0185878	−	0.225709i
$11$			106.664i			0.881519i	0.897625	+	0.440760i	$0.145291\pi$
$11$			106.664i			0.881519i	−0.897625	+	0.440760i	$0.854709\pi$
$12$		0			0
$13$	−122.137			−0.722705			−0.361352	−	0.932429i	$-0.617685\pi$
$13$	−122.137			−0.722705			−0.361352	+	0.932429i	$0.617685\pi$
$14$	207.879	−	17.1194i	1.06061	−	0.0873440i
$15$		0			0
$16$	242.297	−	82.6328i	0.946473	−	0.322784i
$17$	−122.675			−0.424481			−0.212240	−	0.977217i	$-0.568076\pi$
$17$	−122.675			−0.424481			−0.212240	+	0.977217i	$0.568076\pi$
$18$		0			0
$19$		−	593.624i		−	1.64439i	−0.569207	−	0.822194i	$-0.692750\pi$
$19$		−	593.624i		−	1.64439i	0.569207	−	0.822194i	$-0.307250\pi$
$20$	−89.3686	+	14.8200i	−0.223422	+	0.0370501i
$21$		0			0
$22$	425.216	−	35.0178i	0.878545	−	0.0723507i
$23$		−	546.922i		−	1.03388i	−0.856022	−	0.516940i	$-0.827071\pi$
$23$		−	546.922i		−	1.03388i	0.856022	−	0.516940i	$-0.172929\pi$
$24$		0			0
$25$	−592.944			−0.948710
$26$	40.0976	+	486.900i	0.0593160	+	0.720266i
$27$		0			0
$28$	−136.493	−	823.090i	−0.174099	−	1.04986i
$29$	735.866			0.874989			0.437495	−	0.899221i	$-0.355866\pi$
$29$	735.866			0.874989			0.437495	+	0.899221i	$0.355866\pi$
$30$		0			0
$31$		−	585.927i		−	0.609705i	−0.952400	−	0.304853i	$-0.901393\pi$
$31$		−	585.927i		−	0.609705i	0.952400	−	0.304853i	$-0.0986072\pi$
$32$	−408.962	−	938.790i	−0.399377	−	0.916787i
$33$		0			0
$34$	40.2742	+	489.044i	0.0348393	+	0.423049i
$35$			295.239i			0.241012i
$36$		0			0
$37$	2289.29			1.67223			0.836117	−	0.548551i	$-0.184820\pi$
$37$	2289.29			1.67223			0.836117	+	0.548551i	$0.184820\pi$
$38$	−2366.49	+	194.887i	−1.63884	+	0.134963i
$39$		0			0
$40$	88.4199	+	351.403i	0.0552624	+	0.219627i
$41$	−2868.26			−1.70628			−0.853142	−	0.521678i	$-0.825306\pi$
$41$	−2868.26			−1.70628			−0.853142	+	0.521678i	$0.825306\pi$
$42$		0			0
$43$		−	2244.52i		−	1.21391i	−0.794736	−	0.606955i	$-0.792391\pi$
$43$		−	2244.52i		−	1.21391i	0.794736	−	0.606955i	$-0.207609\pi$
$44$	−279.197	−	1683.63i	−0.144213	−	0.869643i
$45$		0			0
$46$	−2180.31	+	179.555i	−1.03039	+	0.0848557i
$47$		−	1054.85i		−	0.477526i	−0.971078	−	0.238763i	$-0.923258\pi$
$47$		−	1054.85i		−	0.477526i	0.971078	−	0.238763i	$-0.0767419\pi$
$48$		0			0
$49$	−318.168			−0.132515
$50$	194.664	+	2363.77i	0.0778654	+	0.945509i
$51$		0			0
$52$	1927.87	−	319.699i	0.712968	−	0.118232i
$53$	−4752.60			−1.69192			−0.845960	−	0.533246i	$-0.820972\pi$
$53$	−4752.60			−1.69192			−0.845960	+	0.533246i	$0.820972\pi$
$54$		0			0
$55$			603.911i			0.199640i
$56$	−3236.44	+	814.352i	−1.03203	+	0.259678i
$57$		0			0
$58$	−241.585	−	2933.53i	−0.0718148	−	0.872037i
$59$			2152.65i			0.618399i	0.950997	+	0.309200i	$0.100061\pi$
$59$			2152.65i			0.618399i	−0.950997	+	0.309200i	$0.899939\pi$
$60$		0			0
$61$	−66.3319			−0.0178264			−0.00891319	−	0.999960i	$-0.502837\pi$
$61$	−66.3319			−0.0178264			−0.00891319	+	0.999960i	$0.502837\pi$
$62$	−2335.80	+	192.360i	−0.607648	+	0.0500416i
$63$		0			0
$64$	−3608.23	+	1938.53i	−0.880915	+	0.473275i
$65$	−691.518			−0.163673
$66$		0			0
$67$		−	4104.76i		−	0.914404i	−0.889363	−	0.457202i	$-0.848852\pi$
$67$		−	4104.76i		−	0.914404i	0.889363	−	0.457202i	$-0.151148\pi$
$68$	1936.36	−	321.107i	0.418762	−	0.0694435i
$69$		0			0
$70$	1176.97	−	96.9271i	0.240198	−	0.0197810i
$71$		−	5031.65i		−	0.998145i	−0.866560	−	0.499072i	$-0.833674\pi$
$71$		−	5031.65i		−	0.998145i	0.866560	−	0.499072i	$-0.166326\pi$
$72$		0			0
$73$	2705.16			0.507631			0.253815	−	0.967253i	$-0.418314\pi$
$73$	2705.16			0.507631			0.253815	+	0.967253i	$0.418314\pi$
$74$	−751.574	−	9126.26i	−0.137249	−	1.66659i
$75$		0			0
$76$	1553.84	+	9370.03i	0.269016	+	1.62223i
$77$	−5562.06			−0.938110
$78$		0			0
$79$		−	1381.05i		−	0.221286i	−0.993860	−	0.110643i	$-0.964709\pi$
$79$		−	1381.05i		−	0.221286i	0.993860	−	0.110643i	$-0.0352911\pi$
$80$	1371.84	−	467.852i	0.214350	−	0.0731019i
$81$		0			0
$82$	941.652	+	11434.4i	0.140043	+	1.70053i
$83$			3008.36i			0.436690i	0.975872	+	0.218345i	$0.0700658\pi$
$83$			3008.36i			0.436690i	−0.975872	+	0.218345i	$0.929934\pi$
$84$		0			0
$85$	−694.563			−0.0961333
$86$	−8947.79	+	736.876i	−1.20981	+	0.0996317i
$87$		0			0
$88$	−6620.13	+	1665.76i	−0.854873	+	0.215103i
$89$	3186.35			0.402267			0.201133	−	0.979564i	$-0.435538\pi$
$89$	3186.35			0.402267			0.201133	+	0.979564i	$0.435538\pi$
$90$		0			0
$91$		−	6368.92i		−	0.769100i
$92$	1431.59	+	8632.86i	0.169139	+	1.01995i
$93$		0			0
$94$	−4205.18	+	346.309i	−0.475915	+	0.0391930i
$95$		−	3360.99i		−	0.372409i
$96$		0			0
$97$	−4814.06			−0.511644			−0.255822	−	0.966724i	$-0.582346\pi$
$97$	−4814.06			−0.511644			−0.255822	+	0.966724i	$0.582346\pi$
$98$	104.455	+	1268.38i	0.0108762	+	0.132068i
$99$		0			0
$100$	9359.28	−	1552.05i	0.935928	−	0.155205i
$101$	−7020.93			−0.688259			−0.344130	−	0.938922i	$-0.611826\pi$
$101$	−7020.93			−0.688259			−0.344130	+	0.938922i	$0.611826\pi$
$102$		0			0
$103$			2146.41i			0.202320i	0.994870	+	0.101160i	$0.0322554\pi$
$103$			2146.41i			0.202320i	−0.994870	+	0.101160i	$0.967745\pi$
$104$	−1907.40	−	7580.49i	−0.176350	−	0.700859i
$105$		0			0
$106$	1560.28	+	18946.3i	0.138864	+	1.68621i
$107$			13846.7i			1.20943i	0.796443	+	0.604713i	$0.206712\pi$
$107$			13846.7i			1.20943i	−0.796443	+	0.604713i	$0.793288\pi$
$108$		0			0
$109$	−19384.9			−1.63159			−0.815793	−	0.578344i	$-0.803699\pi$
$109$	−19384.9			−1.63159			−0.815793	+	0.578344i	$0.803699\pi$
$110$	2407.50	−	198.264i	0.198967	−	0.0163855i
$111$		0			0
$112$	4308.94	+	12634.7i	0.343506	+	1.00723i
$113$	13634.4			1.06777			0.533887	−	0.845556i	$-0.320731\pi$
$113$	13634.4			1.06777			0.533887	+	0.845556i	$0.320731\pi$
$114$		0			0
$115$		−	3096.57i		−	0.234145i
$116$	−11615.2	+	1926.16i	−0.863201	+	0.143145i
$117$		0			0
$118$	8581.54	−	706.715i	0.616313	−	0.0507551i
$119$		−	6396.96i		−	0.451731i
$120$		0			0
$121$	3263.82			0.222923
$122$	21.7768	+	264.433i	0.00146310	+	0.0177662i
$123$		0			0
$124$	1533.69	+	9248.52i	0.0997455	+	0.601491i
$125$	−6895.78			−0.441330
$126$		0			0
$127$		−	15689.6i		−	0.972754i	−0.873749	−	0.486377i	$-0.838318\pi$
$127$		−	15689.6i		−	0.972754i	0.873749	−	0.486377i	$-0.161682\pi$
$128$	8912.56	+	13747.8i	0.543979	+	0.839099i
$129$		0			0
$130$	227.025	+	2756.74i	0.0134335	+	0.163121i
$131$		−	8371.86i		−	0.487842i	−0.969795	−	0.243921i	$-0.921566\pi$
$131$		−	8371.86i		−	0.487842i	0.969795	−	0.243921i	$-0.0784338\pi$
$132$		0			0
$133$	30954.9			1.74995
$134$	−16363.6	+	1347.59i	−0.911319	+	0.0750497i
$135$		0			0
$136$	−1915.80	−	7613.87i	−0.103579	−	0.411650i
$137$	−29930.3			−1.59467			−0.797333	−	0.603540i	$-0.793756\pi$
$137$	−29930.3			−1.59467			−0.797333	+	0.603540i	$0.793756\pi$
$138$		0			0
$139$		−	23846.7i		−	1.23424i	−0.786871	−	0.617118i	$-0.788300\pi$
$139$		−	23846.7i		−	1.23424i	0.786871	−	0.617118i	$-0.211700\pi$
$140$	−772.800	−	4660.18i	−0.0394286	−	0.237764i
$141$		0			0
$142$	−20058.7	+	1651.89i	−0.994777	+	0.0819228i
$143$		−	13027.6i		−	0.637078i
$144$		0			0
$145$	4166.34			0.198161
$146$	−888.106	−	10784.2i	−0.0416638	−	0.505918i
$147$		0			0
$148$	−36135.1	+	5992.30i	−1.64970	+	0.273571i
$149$	5273.96			0.237555			0.118778	−	0.992921i	$-0.462102\pi$
$149$	5273.96			0.237555			0.118778	+	0.992921i	$0.462102\pi$
$150$		0			0
$151$		−	33424.0i		−	1.46590i	−0.680281	−	0.732951i	$-0.738142\pi$
$151$		−	33424.0i		−	1.46590i	0.680281	−	0.732951i	$-0.261858\pi$
$152$	36843.5	−	9270.55i	1.59468	−	0.401253i
$153$		0			0
$154$	1826.02	+	22173.2i	0.0769954	+	0.934945i
$155$		−	3317.41i		−	0.138082i
$156$		0			0
$157$	17001.5			0.689742			0.344871	−	0.938650i	$-0.387923\pi$
$157$	17001.5			0.689742			0.344871	+	0.938650i	$0.387923\pi$
$158$	−5505.55	+	453.398i	−0.220540	+	0.0181621i
$159$		0			0
$160$	−2315.47	−	5315.26i	−0.0904480	−	0.207627i
$161$	28519.6			1.10025
$162$		0			0
$163$		−	30843.8i		−	1.16089i	−0.814298	−	0.580447i	$-0.802878\pi$
$163$		−	30843.8i		−	1.16089i	0.814298	−	0.580447i	$-0.197122\pi$
$164$	45273.9	−	7507.80i	1.68330	−	0.279142i
$165$		0			0
$166$	11992.8	−	987.644i	0.435216	−	0.0358413i
$167$			15798.7i			0.566485i	0.959048	+	0.283243i	$0.0914102\pi$
$167$			15798.7i			0.566485i	−0.959048	+	0.283243i	$0.908590\pi$
$168$		0			0
$169$	−13643.5			−0.477698
$170$	228.025	+	2768.88i	0.00789015	+	0.0958090i
$171$		0			0
$172$	5875.12	+	35428.5i	0.198591	+	1.19756i
$173$	47062.8			1.57248			0.786241	−	0.617921i	$-0.212025\pi$
$173$	47062.8			1.57248			0.786241	+	0.617921i	$0.212025\pi$
$174$		0			0
$175$		−	30919.4i		−	1.00961i
$176$	8813.93	+	25844.3i	0.284541	+	0.834334i
$177$		0			0
$178$	−1046.08	−	12702.4i	−0.0330161	−	0.400909i
$179$		−	2545.69i		−	0.0794511i	−0.999211	−	0.0397256i	$-0.987352\pi$
$179$		−	2545.69i		−	0.0794511i	0.999211	−	0.0397256i	$-0.0126484\pi$
$180$		0			0
$181$	5676.58			0.173272			0.0866362	−	0.996240i	$-0.472388\pi$
$181$	5676.58			0.173272			0.0866362	+	0.996240i	$0.472388\pi$
$182$	−25389.7	+	2090.92i	−0.766505	+	0.0631239i
$183$		0			0
$184$	33944.9	−	8541.21i	1.00263	−	0.252281i
$185$	12961.5			0.378715
$186$		0			0
$187$		−	13085.0i		−	0.374188i
$188$	2761.12	+	16650.3i	0.0781214	+	0.471092i
$189$		0			0
$190$	−13398.6	+	1103.41i	−0.371153	+	0.0305655i
$191$			32478.5i			0.890284i	0.895460	+	0.445142i	$0.146847\pi$
$191$			32478.5i			0.890284i	−0.895460	+	0.445142i	$0.853153\pi$
$192$		0			0
$193$	787.434			0.0211397			0.0105699	−	0.999944i	$-0.496635\pi$
$193$	787.434			0.0211397			0.0105699	+	0.999944i	$0.496635\pi$
$194$	1580.46	+	19191.3i	0.0419932	+	0.509918i
$195$		0			0
$196$	5022.11	−	832.818i	0.130730	−	0.0216789i
$197$	24825.9			0.639694			0.319847	−	0.947469i	$-0.396368\pi$
$197$	24825.9			0.639694			0.319847	+	0.947469i	$0.396368\pi$
$198$		0			0
$199$			12008.5i			0.303237i	0.988439	+	0.151619i	$0.0484485\pi$
$199$			12008.5i			0.303237i	−0.988439	+	0.151619i	$0.951551\pi$
$200$	−9259.93	−	36801.3i	−0.231498	−	0.920032i
$201$		0			0
$202$	2304.97	+	27989.0i	0.0564889	+	0.685937i
$203$			38372.2i			0.931161i
$204$		0			0
$205$	−16239.6			−0.386427
$206$	8556.69	−	704.668i	0.201638	−	0.0166054i
$207$		0			0
$208$	−29593.5	+	10092.5i	−0.684020	+	0.233278i
$209$	63318.3			1.44956
$210$		0			0
$211$		−	29750.5i		−	0.668235i	−0.942532	−	0.334117i	$-0.891562\pi$
$211$		−	29750.5i		−	0.668235i	0.942532	−	0.334117i	$-0.108438\pi$
$212$	75017.2	−	12440.1i	1.66913	−	0.276792i
$213$		0			0
$214$	55200.0	−	4545.88i	1.20535	−	0.0992637i
$215$		−	12708.1i		−	0.274917i
$216$		0			0
$217$	30553.5			0.648846
$218$	6364.06	+	77277.9i	0.133912	+	1.62608i
$219$		0			0
$220$	−1580.76	−	9532.40i	−0.0326604	−	0.196950i
$221$	14983.2			0.306774
$222$		0			0
$223$		−	52948.5i		−	1.06474i	−0.846511	−	0.532371i	$-0.821301\pi$
$223$		−	52948.5i		−	1.06474i	0.846511	−	0.532371i	$-0.178699\pi$
$224$	48953.8	−	21325.6i	0.975642	−	0.425016i
$225$		0			0
$226$	−4476.18	−	54353.6i	−0.0876376	−	1.06417i
$227$		−	37635.8i		−	0.730380i	−0.930933	−	0.365190i	$-0.881004\pi$
$227$		−	37635.8i		−	0.730380i	0.930933	−	0.365190i	$-0.118996\pi$
$228$		0			0
$229$	−57238.4			−1.09148			−0.545741	−	0.837954i	$-0.683752\pi$
$229$	−57238.4			−1.09148			−0.545741	+	0.837954i	$0.683752\pi$
$230$	−12344.5	+	1016.61i	−0.233356	+	0.0192175i
$231$		0			0
$232$	11491.9	+	45671.8i	0.213509	+	0.848540i
$233$	−36468.7			−0.671751			−0.335876	−	0.941906i	$-0.609032\pi$
$233$	−36468.7			−0.671751			−0.335876	+	0.941906i	$0.609032\pi$
$234$		0			0
$235$		−	5972.39i		−	0.108147i
$236$	−5634.64	−	33978.3i	−0.101168	−	0.610068i
$237$		0			0
$238$	−25501.5	+	2100.12i	−0.450207	+	0.0370759i
$239$		−	52357.1i		−	0.916600i	−0.888798	−	0.458300i	$-0.848459\pi$
$239$		−	52357.1i		−	0.916600i	0.888798	−	0.458300i	$-0.151541\pi$
$240$		0			0
$241$	−13511.1			−0.232625			−0.116313	−	0.993213i	$-0.537107\pi$
$241$	−13511.1			−0.232625			−0.116313	+	0.993213i	$0.537107\pi$
$242$	−1071.51	−	13011.2i	−0.0182964	−	0.222171i
$243$		0			0
$244$	1047.01	−	173.627i	0.0175862	−	0.00291633i
$245$	−1801.41			−0.0300110
$246$		0			0
$247$			72503.6i			1.18841i
$248$	36365.8	−	9150.34i	0.591275	−	0.148776i
$249$		0			0
$250$	2263.88	+	27490.0i	0.0362221	+	0.439841i
$251$			111309.i			1.76678i	0.468635	+	0.883392i	$0.344746\pi$
$251$			111309.i			1.76678i	−0.468635	+	0.883392i	$0.655254\pi$
$252$		0			0
$253$	58336.8			0.911385
$254$	−62546.5	+	5150.88i	−0.969472	+	0.0798388i
$255$		0			0
$256$	51879.6	−	40043.4i	0.791620	−	0.611013i
$257$	−73913.1			−1.11906			−0.559532	−	0.828809i	$-0.689019\pi$
$257$	−73913.1			−1.11906			−0.559532	+	0.828809i	$0.689019\pi$
$258$		0			0
$259$			119376.i			1.77959i
$260$	10915.2	−	1810.08i	0.161468	−	0.0267763i
$261$		0			0
$262$	−33374.5	+	2748.48i	−0.486197	+	0.0400397i
$263$			7367.96i			0.106521i	0.998581	+	0.0532606i	$0.0169614\pi$
$263$			7367.96i			0.106521i	−0.998581	+	0.0532606i	$0.983039\pi$
$264$		0			0
$265$	−26908.4			−0.383174
$266$	−10162.5	−	123402.i	−0.143627	−	1.74405i
$267$		0			0
$268$	10744.4	+	64791.3i	0.149593	+	0.902084i
$269$	−38604.8			−0.533502			−0.266751	−	0.963765i	$-0.585950\pi$
$269$	−38604.8			−0.533502			−0.266751	+	0.963765i	$0.585950\pi$
$270$		0			0
$271$			12540.3i			0.170753i	0.996349	+	0.0853767i	$0.0272094\pi$
$271$			12540.3i			0.170753i	−0.996349	+	0.0853767i	$0.972791\pi$
$272$	−29723.8	+	10137.0i	−0.401759	+	0.137016i
$273$		0			0
$274$	9826.12	+	119317.i	0.130882	+	1.58929i
$275$		−	63245.7i		−	0.836306i
$276$		0			0
$277$	−92104.7			−1.20039			−0.600195	−	0.799854i	$-0.704910\pi$
$277$	−92104.7			−1.20039			−0.600195	+	0.799854i	$0.704910\pi$
$278$	−95064.9	+	7828.87i	−1.23007	+	0.101300i
$279$		0			0
$280$	−18324.1	+	4610.71i	−0.233726	+	0.0588101i
$281$	22295.9			0.282366			0.141183	−	0.989983i	$-0.454909\pi$
$281$	22295.9			0.282366			0.141183	+	0.989983i	$0.454909\pi$
$282$		0			0
$283$			24997.7i			0.312123i	0.987747	+	0.156062i	$0.0498799\pi$
$283$			24997.7i			0.312123i	−0.987747	+	0.156062i	$0.950120\pi$
$284$	13170.5	+	79421.7i	0.163293	+	0.984697i
$285$		0			0
$286$	−51934.6	+	4276.97i	−0.634929	+	0.0522882i
$287$		−	149568.i		−	1.81582i
$288$		0			0
$289$	−68471.9			−0.819816
$290$	−1367.81	−	16609.1i	−0.0162641	−	0.197493i
$291$		0			0
$292$	−42699.5	+	7080.88i	−0.500792	+	0.0830465i
$293$	−23497.1			−0.273703			−0.136852	−	0.990592i	$-0.543698\pi$
$293$	−23497.1			−0.273703			−0.136852	+	0.990592i	$0.543698\pi$
$294$		0			0
$295$			12187.9i			0.140051i
$296$	35751.5	+	142086.i	0.408048	+	1.62169i
$297$		0			0
$298$	−1731.44	−	21024.7i	−0.0194974	−	0.236754i
$299$			66799.5i			0.747190i
$300$		0			0
$301$	117042.			1.29184
$302$	−133245.	+	10973.1i	−1.46096	+	0.120314i
$303$		0			0
$304$	−49052.8	−	143833.i	−0.530783	−	1.55637i
$305$	−375.559			−0.00403719
$306$		0			0
$307$			32060.0i			0.340163i	0.985430	+	0.170082i	$0.0544031\pi$
$307$			32060.0i			0.340163i	−0.985430	+	0.170082i	$0.945597\pi$
$308$	87793.9	−	14558.9i	0.925471	−	0.153471i
$309$		0			0
$310$	−13224.9	+	1089.11i	−0.137616	+	0.0113331i
$311$			70946.4i			0.733516i	0.930316	+	0.366758i	$0.119532\pi$
$311$			70946.4i			0.733516i	−0.930316	+	0.366758i	$0.880468\pi$
$312$		0			0
$313$	118519.			1.20976			0.604882	−	0.796315i	$-0.293220\pi$
$313$	118519.			1.20976			0.604882	+	0.796315i	$0.293220\pi$
$314$	−5581.58	−	67776.4i	−0.0566106	−	0.687415i
$315$		0			0
$316$	3614.95	+	21799.1i	0.0362016	+	0.218305i
$317$	−134781.			−1.34125			−0.670626	−	0.741795i	$-0.733975\pi$
$317$	−134781.			−1.34125			−0.670626	+	0.741795i	$0.733975\pi$
$318$		0			0
$319$			78490.3i			0.771320i
$320$	−20429.1	+	10975.6i	−0.199503	+	0.107184i
$321$		0			0
$322$	−9362.99	−	113694.i	−0.0903032	−	1.09654i
$323$			72822.8i			0.698011i
$324$		0			0
$325$	72420.4			0.685637
$326$	−122959.	+	10126.0i	−1.15698	+	0.0952804i
$327$		0			0
$328$	−44793.3	−	178020.i	−0.416357	−	1.65471i
$329$	55006.1			0.508181
$330$		0			0
$331$			153740.i			1.40324i	0.712552	+	0.701620i	$0.247539\pi$
$331$			153740.i			1.40324i	−0.712552	+	0.701620i	$0.752461\pi$
$332$	−7874.49	−	47485.2i	−0.0714408	−	0.430806i
$333$		0			0
$334$	62981.6	−	5186.72i	0.564574	−	0.0464943i
$335$		−	23240.4i		−	0.207087i
$336$		0			0
$337$	−22943.7			−0.202024			−0.101012	−	0.994885i	$-0.532208\pi$
$337$	−22943.7			−0.202024			−0.101012	+	0.994885i	$0.532208\pi$
$338$	4479.17	+	54390.0i	0.0392071	+	0.476086i
$339$		0			0
$340$	10963.3	−	1818.05i	0.0948382	−	0.0157271i
$341$	62497.2			0.537467
$342$		0			0
$343$			108611.i			0.923175i
$344$	139307.	−	35052.4i	1.17722	−	0.296211i
$345$		0			0
$346$	−15450.7	−	187616.i	−0.129061	−	1.56718i
$347$		−	7229.43i		−	0.0600406i	−0.999549	−	0.0300203i	$-0.990443\pi$
$347$		−	7229.43i		−	0.0600406i	0.999549	−	0.0300203i	$-0.00955720\pi$
$348$		0			0
$349$	110565.			0.907753			0.453877	−	0.891065i	$-0.350041\pi$
$349$	110565.			0.907753			0.453877	+	0.891065i	$0.350041\pi$
$350$	−123260.	+	10150.9i	−1.00621	+	0.0828641i
$351$		0			0
$352$	100135.	−	43621.5i	0.808165	−	0.352059i
$353$	−61603.4			−0.494374			−0.247187	−	0.968968i	$-0.579506\pi$
$353$	−61603.4			−0.494374			−0.247187	+	0.968968i	$0.579506\pi$
$354$		0			0
$355$		−	28488.3i		−	0.226053i
$356$	−50294.8	+	8340.41i	−0.396847	+	0.0658093i
$357$		0			0
$358$	−10148.4	+	835.752i	−0.0791831	+	0.00652095i
$359$		−	84462.7i		−	0.655354i	−0.944790	−	0.327677i	$-0.893734\pi$
$359$		−	84462.7i		−	0.655354i	0.944790	−	0.327677i	$-0.106266\pi$
$360$		0			0
$361$	−222069.			−1.70401
$362$	−1863.62	−	22629.7i	−0.0142213	−	0.172688i
$363$		0			0
$364$	16670.9	+	100530.i	0.125822	+	0.758738i
$365$	15316.1			0.114965
$366$		0			0
$367$		−	185928.i		−	1.38042i	−0.723607	−	0.690212i	$-0.757517\pi$
$367$		−	185928.i		−	1.38042i	0.723607	−	0.690212i	$-0.242483\pi$
$368$	−45193.7	−	132518.i	−0.333720	−	0.978538i
$369$		0			0
$370$	−4255.27	−	51671.2i	−0.0310831	−	0.377438i
$371$		−	247828.i		−	1.80054i
$372$		0			0
$373$	−85091.3			−0.611600			−0.305800	−	0.952096i	$-0.598924\pi$
$373$	−85091.3			−0.611600			−0.305800	+	0.952096i	$0.598924\pi$
$374$	−52163.3	+	4295.80i	−0.372926	+	0.0307115i
$375$		0			0
$376$	65470.0	−	16473.5i	0.463091	−	0.116523i
$377$	−89876.5			−0.632359
$378$		0			0
$379$			146982.i			1.02326i	0.859206	+	0.511630i	$0.170958\pi$
$379$			146982.i			1.02326i	−0.859206	+	0.511630i	$0.829042\pi$
$380$	8797.53	+	53051.4i	0.0609247	+	0.367392i
$381$		0			0
$382$	129475.	−	10662.7i	0.887280	−	0.0730701i
$383$			186199.i			1.26935i	0.772780	+	0.634674i	$0.218866\pi$
$383$			186199.i			1.26935i	−0.772780	+	0.634674i	$0.781134\pi$
$384$		0			0
$385$	−31491.3			−0.212456
$386$	−258.515	−	3139.11i	−0.00173504	−	0.0210684i
$387$		0			0
$388$	75987.2	−	12601.0i	0.504751	−	0.0837030i
$389$	−256004.			−1.69179			−0.845897	−	0.533347i	$-0.820934\pi$
$389$	−256004.			−1.69179			−0.845897	+	0.533347i	$0.820934\pi$
$390$		0			0
$391$			67093.7i			0.438862i
$392$	−4968.79	−	19747.2i	−0.0323354	−	0.128509i
$393$		0			0
$394$	−8150.35	−	98968.5i	−0.0525029	−	0.637536i
$395$		−	7819.24i		−	0.0501153i
$396$		0			0
$397$	−260735.			−1.65432			−0.827159	−	0.561968i	$-0.810044\pi$
$397$	−260735.			−1.65432			−0.827159	+	0.561968i	$0.810044\pi$
$398$	47871.9	−	3942.39i	0.302214	−	0.0248882i
$399$		0			0
$400$	−143668.	+	48996.6i	−0.897928	+	0.306229i
$401$	53014.0			0.329687			0.164843	−	0.986320i	$-0.447288\pi$
$401$	53014.0			0.329687			0.164843	+	0.986320i	$0.447288\pi$
$402$		0			0
$403$			71563.4i			0.440637i
$404$	110821.	−	18377.6i	0.678986	−	0.112597i
$405$		0			0
$406$	152971.	−	12597.6i	0.928019	−	0.0764251i
$407$			244184.i			1.47411i
$408$		0			0
$409$	147396.			0.881126			0.440563	−	0.897722i	$-0.354779\pi$
$409$	147396.			0.881126			0.440563	+	0.897722i	$0.354779\pi$
$410$	5331.46	+	64739.2i	0.0317160	+	0.385123i
$411$		0			0
$412$	−5618.33	−	33879.9i	−0.0330988	−	0.199594i
$413$	−112251.			−0.658099
$414$		0			0
$415$			17032.8i			0.0988983i
$416$	49949.5	+	114661.i	0.288632	+	0.662566i
$417$		0			0
$418$	−20787.4	−	252419.i	−0.118973	−	1.44467i
$419$		−	232592.i		−	1.32485i	−0.749127	−	0.662426i	$-0.769527\pi$
$419$		−	232592.i		−	1.32485i	0.749127	−	0.662426i	$-0.230473\pi$
$420$		0			0
$421$	−69801.5			−0.393823			−0.196911	−	0.980421i	$-0.563091\pi$
$421$	−69801.5			−0.393823			−0.196911	+	0.980421i	$0.563091\pi$
$422$	−118600.	+	9767.08i	−0.665980	+	0.0548454i
$423$		0			0
$424$	−74220.8	−	294972.i	−0.412852	−	1.64078i
$425$	72739.4			0.402709
$426$		0			0
$427$		−	3458.92i		−	0.0189708i
$428$	−36244.4	−	218563.i	−0.197858	−	1.19313i
$429$		0			0
$430$	−50660.7	+	4172.06i	−0.273990	+	0.0225639i
$431$			147873.i			0.796037i	0.917377	+	0.398019i	$0.130302\pi$
$431$			147873.i			0.796037i	−0.917377	+	0.398019i	$0.869698\pi$
$432$		0			0
$433$	294850.			1.57262			0.786312	−	0.617830i	$-0.211988\pi$
$433$	294850.			1.57262			0.786312	+	0.617830i	$0.211988\pi$
$434$	−10030.7	−	121802.i	−0.0532541	−	0.646657i
$435$		0			0
$436$	305979.	−	50740.7i	1.60960	−	0.266921i
$437$	−324666.			−1.70010
$438$		0			0
$439$			72131.8i			0.374281i	0.982333	+	0.187140i	$0.0599220\pi$
$439$			72131.8i			0.374281i	−0.982333	+	0.187140i	$0.940078\pi$
$440$	−37482.0	+	9431.20i	−0.193605	+	0.0487149i
$441$		0			0
$442$	−4918.98	−	59730.5i	−0.0251785	−	0.305739i
$443$		−	190907.i		−	0.972781i	−0.873741	−	0.486391i	$-0.838313\pi$
$443$		−	190907.i		−	0.972781i	0.873741	−	0.486391i	$-0.161687\pi$
$444$		0			0
$445$	18040.6			0.0911024
$446$	−211080.	+	17383.0i	−1.06115	+	0.0873887i
$447$		0			0
$448$	−101086.	−	188153.i	−0.503658	−	0.937467i
$449$	192859.			0.956639			0.478319	−	0.878186i	$-0.341246\pi$
$449$	192859.			0.956639			0.478319	+	0.878186i	$0.341246\pi$
$450$		0			0
$451$		−	305940.i		−	1.50412i
$452$	−215211.	+	35688.6i	−1.05339	+	0.174684i
$453$		0			0
$454$	−150035.	+	12355.8i	−0.727916	+	0.0599460i
$455$		−	36059.7i		−	0.174180i
$456$		0			0
$457$	−5925.33			−0.0283713			−0.0141857	−	0.999899i	$-0.504516\pi$
$457$	−5925.33			−0.0283713			−0.0141857	+	0.999899i	$0.504516\pi$
$458$	18791.4	+	228181.i	0.0895834	+	1.08780i
$459$		0			0
$460$	8105.41	+	48877.7i	0.0383053	+	0.230991i
$461$	126684.			0.596100			0.298050	−	0.954550i	$-0.403664\pi$
$461$	126684.			0.596100			0.298050	+	0.954550i	$0.403664\pi$
$462$		0			0
$463$			235572.i			1.09891i	0.835524	+	0.549454i	$0.185164\pi$
$463$			235572.i			1.09891i	−0.835524	+	0.549454i	$0.814836\pi$
$464$	178298.	−	60806.7i	0.828153	−	0.282433i
$465$		0			0
$466$	11972.7	+	145383.i	0.0551340	+	0.669485i
$467$			97776.2i			0.448332i	0.974551	+	0.224166i	$0.0719658\pi$
$467$			97776.2i			0.448332i	−0.974551	+	0.224166i	$0.928034\pi$
$468$		0			0
$469$	214045.			0.973105
$470$	−23809.0	+	1960.74i	−0.107782	+	0.00887613i
$471$		0			0
$472$	−133605.	+	33617.6i	−0.599706	+	0.150898i
$473$	239409.			1.07009
$474$		0			0
$475$			351986.i			1.56005i
$476$	16744.3	+	100972.i	0.0739015	+	0.445645i
$477$		0			0
$478$	−208722.	+	17188.8i	−0.913508	+	0.0752300i
$479$			403178.i			1.75722i	0.477543	+	0.878608i	$0.341527\pi$
$479$			403178.i			1.75722i	−0.477543	+	0.878608i	$0.658473\pi$
$480$		0			0
$481$	−279607.			−1.20853
$482$	4435.70	+	53862.1i	0.0190927	+	0.231841i
$483$		0			0
$484$	−51517.6	+	8543.18i	−0.219920	+	0.0364694i
$485$	−27256.3			−0.115873
$486$		0			0
$487$			195207.i			0.823071i	0.911394	+	0.411536i	$0.135007\pi$
$487$			195207.i			0.823071i	−0.911394	+	0.411536i	$0.864993\pi$
$488$	−1035.90	−	4116.92i	−0.00434988	−	0.0172875i
$489$		0			0
$490$	591.403	+	7181.33i	0.00246315	+	0.0299097i
$491$		−	76137.6i		−	0.315818i	−0.987454	−	0.157909i	$-0.949525\pi$
$491$		−	76137.6i		−	0.315818i	0.987454	−	0.157909i	$-0.0504752\pi$
$492$		0			0
$493$	−90272.3			−0.371416
$494$	289036.	−	23802.9i	1.18440	−	0.0975386i
$495$		0			0
$496$	−48416.8	−	141968.i	−0.196803	−	0.577069i
$497$	262379.			1.06222
$498$		0			0
$499$		−	14570.3i		−	0.0585152i	−0.999572	−	0.0292576i	$-0.990686\pi$
$499$		−	14570.3i		−	0.0585152i	0.999572	−	0.0292576i	$-0.00931431\pi$
$500$	108846.	−	18050.0i	0.435384	−	0.0721999i
$501$		0			0
$502$	443735.	−	36542.8i	1.76082	−	0.145009i
$503$		−	280154.i		−	1.10729i	−0.832753	−	0.553645i	$-0.813236\pi$
$503$		−	280154.i		−	1.10729i	0.832753	−	0.553645i	$-0.186764\pi$
$504$		0			0
$505$	−39751.2			−0.155872
$506$	−19152.0	−	232560.i	−0.0748019	−	0.908310i
$507$		0			0
$508$	41068.0	+	247651.i	0.159139	+	0.959649i
$509$	203009.			0.783573			0.391787	−	0.920056i	$-0.371857\pi$
$509$	203009.			0.783573			0.391787	+	0.920056i	$0.371857\pi$
$510$		0			0
$511$			141063.i			0.540219i
$512$	−176665.	−	193672.i	−0.673924	−	0.738801i
$513$		0			0
$514$	24265.7	+	294655.i	0.0918472	+	1.11529i
$515$			12152.6i			0.0458200i
$516$		0			0
$517$	112515.			0.420948
$518$	475895.	−	39191.3i	1.77358	−	0.146060i
$519$		0			0
$520$	−10799.3	−	42919.3i	−0.0399384	−	0.158725i
$521$	−30822.1			−0.113550			−0.0567749	−	0.998387i	$-0.518082\pi$
$521$	−30822.1			−0.113550			−0.0567749	+	0.998387i	$0.518082\pi$
$522$		0			0
$523$			94412.3i			0.345164i	0.984995	+	0.172582i	$0.0552109\pi$
$523$			94412.3i			0.345164i	−0.984995	+	0.172582i	$0.944789\pi$
$524$	21913.7	+	132145.i	0.0798092	+	0.481270i
$525$		0			0
$526$	29372.4	−	2418.90i	0.106162	−	0.00874273i
$527$			71878.5i			0.258808i
$528$		0			0
$529$	−19282.9			−0.0689066
$530$	8834.03	+	107270.i	0.0314490	+	0.381881i
$531$		0			0
$532$	−488606.	+	81025.8i	−1.72638	+	0.286286i
$533$	350322.			1.23314
$534$		0			0
$535$			78397.6i			0.273902i
$536$	254763.	−	64103.5i	0.886763	−	0.223127i
$537$		0			0
$538$	12673.9	+	153898.i	0.0437872	+	0.531702i
$539$		−	33937.0i		−	0.116814i
$540$		0			0
$541$	166561.			0.569087			0.284544	−	0.958663i	$-0.408158\pi$
$541$	166561.			0.569087			0.284544	+	0.958663i	$0.408158\pi$
$542$	49992.0	−	4116.98i	0.170177	−	0.0140146i
$543$		0			0
$544$	50169.4	+	115166.i	0.169528	+	0.389158i
$545$	−109754.			−0.369510
$546$		0			0
$547$		−	295887.i		−	0.988897i	−0.869207	−	0.494448i	$-0.835370\pi$
$547$		−	295887.i		−	0.988897i	0.869207	−	0.494448i	$-0.164630\pi$
$548$	472433.	−	78343.7i	1.57318	−	0.260881i
$549$		0			0
$550$	−252129.	+	20763.6i	−0.833485	+	0.0686399i
$551$		−	436828.i		−	1.43882i
$552$		0			0
$553$	72015.6			0.235492
$554$	30238.0	+	367176.i	0.0985220	+	1.19634i
$555$		0			0
$556$	62419.6	+	376406.i	0.201916	+	1.21761i
$557$	−30600.2			−0.0986312			−0.0493156	−	0.998783i	$-0.515704\pi$
$557$	−30600.2			−0.0986312			−0.0493156	+	0.998783i	$0.515704\pi$
$558$		0			0
$559$			274139.i			0.877298i
$560$	24396.4	+	71535.5i	0.0777948	+	0.228111i
$561$		0			0
$562$	−7319.76	−	88882.9i	−0.0231752	−	0.281414i
$563$			242796.i			0.765992i	0.923750	+	0.382996i	$0.125108\pi$
$563$			242796.i			0.765992i	−0.923750	+	0.382996i	$0.874892\pi$
$564$		0			0
$565$	77195.5			0.241822
$566$	99653.3	−	8206.73i	0.311070	−	0.0256175i
$567$		0			0
$568$	312291.	−	78578.6i	0.967973	−	0.243561i
$569$	296918.			0.917090			0.458545	−	0.888671i	$-0.348371\pi$
$569$	296918.			0.917090			0.458545	+	0.888671i	$0.348371\pi$
$570$		0			0
$571$		−	263786.i		−	0.809058i	−0.914525	−	0.404529i	$-0.867435\pi$
$571$		−	263786.i		−	0.809058i	0.914525	−	0.404529i	$-0.132565\pi$
$572$	34100.3	+	205634.i	0.104224	+	0.628495i
$573$		0			0
$574$	−596252.	+	49103.0i	−1.80970	+	0.149034i
$575$			324294.i			0.980852i
$576$		0			0
$577$	350367.			1.05238			0.526188	−	0.850368i	$-0.323621\pi$
$577$	350367.			1.05238			0.526188	+	0.850368i	$0.323621\pi$
$578$	22479.3	+	272963.i	0.0672864	+	0.817050i
$579$		0			0
$580$	−65763.3	+	10905.6i	−0.195491	+	0.0324184i
$581$	−156873.			−0.464724
$582$		0			0
$583$		−	506931.i		−	1.49146i
$584$	42246.2	+	167897.i	0.123869	+	0.492286i
$585$		0			0
$586$	7714.12	+	93671.5i	0.0224642	+	0.272780i
$587$		−	6888.66i		−	0.0199921i	−0.999950	−	0.00999606i	$-0.996818\pi$
$587$		−	6888.66i		−	0.0199921i	0.999950	−	0.00999606i	$-0.00318190\pi$
$588$		0			0
$589$	−347820.			−1.00259
$590$	48587.1	−	4001.29i	0.139578	−	0.0114947i
$591$		0			0
$592$	554688.	−	189170.i	1.58272	−	0.539771i
$593$	544416.			1.54818			0.774090	−	0.633076i	$-0.218208\pi$
$593$	544416.			1.54818			0.774090	+	0.633076i	$0.218208\pi$
$594$		0			0
$595$		−	36218.4i		−	0.102305i
$596$	−83246.5	+	13804.8i	−0.234355	+	0.0388631i
$597$		0			0
$598$	266296.	−	21930.3i	0.744669	−	0.0613256i
$599$			141764.i			0.395104i	0.980292	+	0.197552i	$0.0632992\pi$
$599$			141764.i			0.395104i	−0.980292	+	0.197552i	$0.936701\pi$
$600$		0			0
$601$	−530760.			−1.46943			−0.734715	−	0.678376i	$-0.762684\pi$
$601$	−530760.			−1.46943			−0.734715	+	0.678376i	$0.762684\pi$
$602$	−38424.9	−	466588.i	−0.106028	−	1.28748i
$603$		0			0
$604$	87488.8	+	527580.i	0.239816	+	1.44615i
$605$	18479.2			0.0504861
$606$		0			0
$607$		−	40663.6i		−	0.110364i	−0.998476	−	0.0551821i	$-0.982426\pi$
$607$		−	40663.6i		−	0.110364i	0.998476	−	0.0551821i	$-0.0175739\pi$
$608$	−557288.	+	242770.i	−1.50755	+	0.656731i
$609$		0			0
$610$	123.296	+	1497.17i	0.000331352	+	0.00402357i
$611$			128837.i			0.345110i
$612$		0			0
$613$	−498556.			−1.32676			−0.663382	−	0.748281i	$-0.730879\pi$
$613$	−498556.			−1.32676			−0.663382	+	0.748281i	$0.730879\pi$
$614$	127807.	−	10525.3i	0.339015	−	0.0279189i
$615$		0			0
$616$	−86861.9	−	345211.i	−0.228912	−	0.909753i
$617$	−90060.9			−0.236573			−0.118287	−	0.992979i	$-0.537740\pi$
$617$	−90060.9			−0.236573			−0.118287	+	0.992979i	$0.537740\pi$
$618$		0			0
$619$		−	172488.i		−	0.450171i	−0.974339	−	0.225086i	$-0.927734\pi$
$619$		−	172488.i		−	0.450171i	0.974339	−	0.225086i	$-0.0722662\pi$
$620$	8683.45	+	52363.5i	0.0225896	+	0.136221i
$621$		0			0
$622$	282828.	−	23291.7i	0.731042	−	0.0602034i
$623$			166154.i			0.428091i
$624$		0			0
$625$	331547.			0.848761
$626$	−38909.9	−	472478.i	−0.0992914	−	1.20568i
$627$		0			0
$628$	−268358.	+	44502.0i	−0.680449	+	0.112839i
$629$	−280838.			−0.709831
$630$		0			0
$631$		−	210621.i		−	0.528985i	−0.964388	−	0.264492i	$-0.914796\pi$
$631$		−	210621.i		−	0.528985i	0.964388	−	0.264492i	$-0.0852044\pi$
$632$	85715.2	−	21567.6i	0.214597	−	0.0539968i
$633$		0			0
$634$	44248.7	+	537306.i	0.110083	+	1.33673i
$635$		−	88831.4i		−	0.220302i
$636$		0			0
$637$	38860.1			0.0957691
$638$	312902.	−	25768.4i	0.768718	−	0.0633061i
$639$		0			0
$640$	50461.3	+	77837.5i	0.123196	+	0.190033i
$641$	−464524.			−1.13056			−0.565278	−	0.824901i	$-0.691231\pi$
$641$	−464524.			−1.13056			−0.565278	+	0.824901i	$0.691231\pi$
$642$		0			0
$643$		−	417977.i		−	1.01095i	−0.862841	−	0.505476i	$-0.831317\pi$
$643$		−	417977.i		−	1.01095i	0.862841	−	0.505476i	$-0.168683\pi$
$644$	−450166.	+	74651.2i	−1.08543	+	0.179997i
$645$		0			0
$646$	290309.	−	23907.7i	0.695656	−	0.0572893i
$647$		−	825841.i		−	1.97282i	−0.164299	−	0.986411i	$-0.552536\pi$
$647$		−	825841.i		−	1.97282i	0.164299	−	0.986411i	$-0.447464\pi$
$648$		0			0
$649$	−229610.			−0.545131
$650$	−23775.6	−	288704.i	−0.0562737	−	0.683324i
$651$		0			0
$652$	80734.8	+	486852.i	0.189918	+	1.14525i
$653$	328545.			0.770493			0.385247	−	0.922814i	$-0.374116\pi$
$653$	328545.			0.770493			0.385247	+	0.922814i	$0.374116\pi$
$654$		0			0
$655$		−	47400.0i		−	0.110483i
$656$	−694972.	+	237013.i	−1.61495	+	0.550762i
$657$		0			0
$658$	−18058.5	−	219282.i	−0.0417090	−	0.506467i
$659$			167361.i			0.385374i	0.981260	+	0.192687i	$0.0617202\pi$
$659$			167361.i			0.385374i	−0.981260	+	0.192687i	$0.938280\pi$
$660$		0			0
$661$	−305233.			−0.698599			−0.349300	−	0.937011i	$-0.613580\pi$
$661$	−305233.			−0.698599			−0.349300	+	0.937011i	$0.613580\pi$
$662$	612886.	−	50473.0i	1.39851	−	0.115171i
$663$		0			0
$664$	−186715.	+	46981.1i	−0.423489	+	0.106558i
$665$	175261.			0.396317
$666$		0			0
$667$		−	402461.i		−	0.904633i
$668$	−41353.7	−	249374.i	−0.0926749	−	0.558853i
$669$		0			0
$670$	−92647.9	+	7629.82i	−0.206389	+	0.0169967i
$671$		−	7075.22i		−	0.0157143i
$672$		0			0
$673$	806065.			1.77967			0.889836	−	0.456281i	$-0.150819\pi$
$673$	806065.			1.77967			0.889836	+	0.456281i	$0.150819\pi$
$674$	7532.41	+	91465.0i	0.0165811	+	0.201342i
$675$		0			0
$676$	215355.	−	35712.5i	0.471262	−	0.0781496i
$677$	−366235.			−0.799065			−0.399533	−	0.916719i	$-0.630828\pi$
$677$	−366235.			−0.799065			−0.399533	+	0.916719i	$0.630828\pi$
$678$		0			0
$679$		−	251032.i		−	0.544490i
$680$	−10846.9	−	43108.3i	−0.0234578	−	0.0932274i
$681$		0			0
$682$	−20517.8	−	249145.i	−0.0441126	−	0.535654i
$683$			398332.i			0.853894i	0.904277	+	0.426947i	$0.140411\pi$
$683$			398332.i			0.853894i	−0.904277	+	0.426947i	$0.859589\pi$
$684$		0			0
$685$	−169460.			−0.361148
$686$	432977.	−	35656.9i	0.920060	−	0.0757696i
$687$		0			0
$688$	−185471.	−	543840.i	−0.391831	−	1.14893i
$689$	580469.			1.22276
$690$		0			0
$691$			351812.i			0.736809i	0.929666	+	0.368405i	$0.120096\pi$
$691$			351812.i			0.736809i	−0.929666	+	0.368405i	$0.879904\pi$
$692$	−742860.	+	123189.i	−1.55130	+	0.257252i
$693$		0			0
$694$	−28820.2	+	2373.42i	−0.0598381	+	0.00492784i
$695$		−	135016.i		−	0.279521i
$696$		0			0
$697$	351864.			0.724285
$698$	−36298.6	−	440769.i	−0.0745039	−	0.904691i
$699$		0			0
$700$	80932.9	+	488046.i	0.165169	+	0.996012i
$701$	−620142.			−1.26199			−0.630994	−	0.775788i	$-0.717353\pi$
$701$	−620142.			−1.26199			−0.630994	+	0.775788i	$0.717353\pi$
$702$		0			0
$703$		−	1.35898e6i		−	2.74980i
$704$	−206772.	−	384867.i	−0.417201	−	0.776543i
$705$		0			0
$706$	20224.4	+	245582.i	0.0405758	+	0.492706i
$707$		−	366111.i		−	0.732443i
$708$		0			0
$709$	314897.			0.626434			0.313217	−	0.949682i	$-0.398593\pi$
$709$	314897.			0.626434			0.313217	+	0.949682i	$0.398593\pi$
$710$	−113569.	+	9352.70i	−0.225290	+	0.0185533i
$711$		0			0
$712$	49760.9	+	197762.i	0.0981585	+	0.390107i
$713$	−320456.			−0.630362
$714$		0			0
$715$		−	73760.0i		−	0.144281i
$716$	6663.45	+	40182.3i	0.0129979	+	0.0783807i
$717$		0			0
$718$	−336711.	+	27729.1i	−0.653143	+	0.0537882i
$719$			361941.i			0.700132i	0.936725	+	0.350066i	$0.113841\pi$
$719$			361941.i			0.700132i	−0.936725	+	0.350066i	$0.886159\pi$
$720$		0			0
$721$	−111926.			−0.215308
$722$	72905.2	+	885278.i	0.139857	+	1.69826i
$723$		0			0
$724$	−89601.6	+	14858.7i	−0.170938	+	0.0283467i
$725$	−436327.			−0.830111
$726$		0			0
$727$		−	308930.i		−	0.584510i	−0.956340	−	0.292255i	$-0.905594\pi$
$727$		−	308930.i		−	0.584510i	0.956340	−	0.292255i	$-0.0944056\pi$
$728$	395289.	−	99462.6i	0.745852	−	0.187671i
$729$		0			0
$730$	−5028.29	−	61057.9i	−0.00943572	−	0.114577i
$731$			275346.i			0.515281i
$732$		0			0
$733$	882544.			1.64259			0.821293	−	0.570506i	$-0.193253\pi$
$733$	882544.			1.64259			0.821293	+	0.570506i	$0.193253\pi$
$734$	−741202.	+	61040.2i	−1.37577	+	0.113298i
$735$		0			0
$736$	−513445.	+	223670.i	−0.947847	+	0.412908i
$737$	437829.			0.806065
$738$		0			0
$739$		−	396910.i		−	0.726781i	−0.931637	−	0.363390i	$-0.881619\pi$
$739$		−	396910.i		−	0.726781i	0.931637	−	0.363390i	$-0.118381\pi$
$740$	−204590.	+	33927.3i	−0.373613	+	0.0619564i
$741$		0			0
$742$	−987966.	+	81361.8i	−1.79446	+	0.147779i
$743$		−	959979.i		−	1.73894i	−0.493988	−	0.869469i	$-0.664461\pi$
$743$		−	959979.i		−	1.73894i	0.493988	−	0.869469i	$-0.335539\pi$
$744$		0			0
$745$	29860.2			0.0537998
$746$	27935.5	+	339217.i	0.0501971	+	0.609536i
$747$		0			0
$748$	34250.5	+	206539.i	0.0612158	+	0.369147i
$749$	−722046.			−1.28707
$750$		0			0
$751$		−	660734.i		−	1.17151i	−0.810488	−	0.585756i	$-0.800798\pi$
$751$		−	660734.i		−	1.17151i	0.810488	−	0.585756i	$-0.199202\pi$
$752$	−87165.6	−	255588.i	−0.154138	−	0.451965i
$753$		0			0
$754$	29506.5	+	358293.i	0.0519009	+	0.630225i
$755$		−	189241.i		−	0.331987i
$756$		0			0
$757$	326842.			0.570356			0.285178	−	0.958475i	$-0.407947\pi$
$757$	326842.			0.570356			0.285178	+	0.958475i	$0.407947\pi$
$758$	585945.	−	48254.2i	1.01981	−	0.0839841i
$759$		0			0
$760$	208601.	−	52488.2i	0.361152	−	0.0908729i
$761$	329626.			0.569183			0.284591	−	0.958649i	$-0.408142\pi$
$761$	329626.			0.569183			0.284591	+	0.958649i	$0.408142\pi$
$762$		0			0
$763$		−	1.01084e6i		−	1.73633i
$764$	−85013.7	−	512654.i	−0.145647	−	0.878290i
$765$		0			0
$766$	742285.	−	61129.3i	1.26507	−	0.104182i
$767$		−	262918.i		−	0.446920i
$768$		0			0
$769$	−599476.			−1.01372			−0.506862	−	0.862027i	$-0.669194\pi$
$769$	−599476.			−1.01372			−0.506862	+	0.862027i	$0.669194\pi$
$770$	10338.6	+	125540.i	0.0174374	+	0.211740i
$771$		0			0
$772$	−12429.2	+	2061.14i	−0.0208549	+	0.00345838i
$773$	−58555.0			−0.0979952			−0.0489976	−	0.998799i	$-0.515603\pi$
$773$	−58555.0			−0.0979952			−0.0489976	+	0.998799i	$0.515603\pi$
$774$		0			0
$775$			347422.i			0.578433i
$776$	−75180.5	−	298786.i	−0.124848	−	0.496178i
$777$		0			0
$778$	84046.1	+	1.02056e6i	0.138854	+	1.68609i
$779$			1.70267e6i			2.80580i
$780$		0			0
$781$	536695.			0.879884
$782$	267469.	−	22026.9i	0.437381	−	0.0360196i
$783$		0			0
$784$	−77091.2	+	26291.1i	−0.125422	+	0.0427737i
$785$	96259.1			0.156208
$786$		0			0
$787$			638842.i			1.03144i	0.856757	+	0.515720i	$0.172476\pi$
$787$			638842.i			1.03144i	−0.856757	+	0.515720i	$0.827524\pi$
$788$	−391863.	+	64982.8i	−0.631076	+	0.104652i
$789$		0			0
$790$	−31171.4	+	2567.06i	−0.0499462	+	0.00411321i
$791$			710975.i			1.13632i
$792$		0			0
$793$	8101.59			0.0128832
$794$	85599.4	+	1.03942e6i	0.135778	+	1.64874i
$795$		0			0
$796$	−31432.7	−	189547.i	−0.0496085	−	0.299152i
$797$	−1.17526e6			−1.85019			−0.925095	−	0.379737i	$-0.876015\pi$
$797$	−1.17526e6			−1.85019			−0.925095	+	0.379737i	$0.876015\pi$
$798$		0			0
$799$			129404.i			0.202701i
$800$	242492.	+	556649.i	0.378893	+	0.869765i
$801$		0			0
$802$	−17404.5	−	211340.i	−0.0270591	−	0.328574i
$803$			288543.i			0.447486i
$804$		0			0
$805$	161473.			0.249177
$806$	285288.	−	23494.3i	0.439150	−	0.0361653i
$807$		0			0
$808$	−109645.	−	435757.i	−0.167945	−	0.667454i
$809$	−215543.			−0.329334			−0.164667	−	0.986349i	$-0.552655\pi$
$809$	−215543.			−0.329334			−0.164667	+	0.986349i	$0.552655\pi$
$810$		0			0
$811$			1.05773e6i			1.60817i	0.594512	+	0.804087i	$0.297345\pi$
$811$			1.05773e6i			1.60817i	−0.594512	+	0.804087i	$0.702655\pi$
$812$	−100441.	−	605684.i	−0.152334	−	0.918616i
$813$		0			0
$814$	973442.	−	80165.7i	1.46913	−	0.120987i
$815$		−	174632.i		−	0.262911i
$816$		0			0
$817$	−1.33240e6			−1.99614
$818$	−48390.0	−	587594.i	−0.0723185	−	0.878153i
$819$		0			0
$820$	256333.	−	42507.8i	0.381221	−	0.0632180i
$821$	−75851.4			−0.112532			−0.0562662	−	0.998416i	$-0.517920\pi$
$821$	−75851.4			−0.112532			−0.0562662	+	0.998416i	$0.517920\pi$
$822$		0			0
$823$		−	657611.i		−	0.970889i	−0.874267	−	0.485445i	$-0.838658\pi$
$823$		−	657611.i		−	0.970889i	0.874267	−	0.485445i	$-0.161342\pi$
$824$	−133218.	+	33520.3i	−0.196204	+	0.0493689i
$825$		0			0
$826$	36852.1	+	447490.i	0.0540135	+	0.655878i
$827$		−	669017.i		−	0.978196i	−0.872229	−	0.489098i	$-0.837326\pi$
$827$		−	669017.i		−	0.978196i	0.872229	−	0.489098i	$-0.162674\pi$
$828$		0			0
$829$	−637042.			−0.926955			−0.463478	−	0.886109i	$-0.653399\pi$
$829$	−637042.			−0.926955			−0.463478	+	0.886109i	$0.653399\pi$
$830$	67901.2	−	5591.86i	0.0985647	−	0.00811708i
$831$		0			0
$832$	440698.	−	236767.i	0.636641	−	0.342038i
$833$	39031.3			0.0562500
$834$		0			0
$835$			89449.4i			0.128293i
$836$	−999443.	+	165738.i	−1.43003	+	0.237143i
$837$		0			0
$838$	−927231.	+	76360.1i	−1.32038	+	0.108737i
$839$		−	1.00773e6i		−	1.43159i	−0.698311	−	0.715795i	$-0.746065\pi$
$839$		−	1.00773e6i		−	1.43159i	0.698311	−	0.715795i	$-0.253935\pi$
$840$		0			0
$841$	−165782.			−0.234394
$842$	22915.9	+	278264.i	0.0323230	+	0.392494i
$843$		0			0
$844$	77873.0	+	469594.i	0.109321	+	0.659232i
$845$	−77247.2			−0.108186
$846$		0			0
$847$			170194.i			0.237234i
$848$	−1.15154e6	+	392721.i	−1.60136	+	0.546125i
$849$		0			0
$850$	−23880.3	−	289976.i	−0.0330524	−	0.401351i
$851$		−	1.25206e6i		−	1.72889i
$852$		0			0
$853$	−193580.			−0.266050			−0.133025	−	0.991113i	$-0.542469\pi$
$853$	−193580.			−0.266050			−0.133025	+	0.991113i	$0.542469\pi$
$854$	−13789.0	+	1135.56i	−0.0189068	+	0.00155703i
$855$		0			0
$856$	−859402.	+	216242.i	−1.17287	+	0.295116i
$857$	923728.			1.25772			0.628858	−	0.777520i	$-0.283523\pi$
$857$	923728.			1.25772			0.628858	+	0.777520i	$0.283523\pi$
$858$		0			0
$859$			725649.i			0.983423i	0.870758	+	0.491712i	$0.163629\pi$
$859$			725649.i			0.983423i	−0.870758	+	0.491712i	$0.836371\pi$
$860$	33263.9	+	200590.i	0.0449755	+	0.271214i
$861$		0			0
$862$	589495.	−	48546.6i	0.793351	−	0.0653348i
$863$		−	444700.i		−	0.597097i	−0.954394	−	0.298549i	$-0.903497\pi$
$863$		−	444700.i		−	0.597097i	0.954394	−	0.298549i	$-0.0965025\pi$
$864$		0			0
$865$	266461.			0.356124
$866$	−96799.2	−	1.17542e6i	−0.129073	−	1.56732i
$867$		0			0
$868$	−482270.	+	79975.1i	−0.640105	+	0.106149i
$869$	147308.			0.195068
$870$		0			0
$871$			501343.i			0.660844i
$872$	−302731.	−	1.20313e6i	−0.398129	−	1.58227i
$873$		0			0
$874$	106588.	+	1.29428e6i	0.139536	+	1.69436i
$875$		−	359585.i		−	0.469662i
$876$		0			0
$877$	−576603.			−0.749683			−0.374841	−	0.927089i	$-0.622303\pi$
$877$	−576603.			−0.749683			−0.374841	+	0.927089i	$0.622303\pi$
$878$	287554.	−	23680.9i	0.373018	−	0.0307191i
$879$		0			0
$880$	49902.9	+	146326.i	0.0644407	+	0.188954i
$881$	−1.16458e6			−1.50044			−0.750219	−	0.661190i	$-0.770052\pi$
$881$	−1.16458e6			−1.50044			−0.750219	+	0.661190i	$0.770052\pi$
$882$		0			0
$883$			12142.2i			0.0155731i	0.999970	+	0.00778655i	$0.00247856\pi$
$883$			12142.2i			0.0155731i	−0.999970	+	0.00778655i	$0.997521\pi$
$884$	−236501.	+	39219.0i	−0.302641	+	0.0501871i
$885$		0			0
$886$	−761053.	+	62674.9i	−0.969499	+	0.0798411i
$887$			1.29477e6i			1.64568i	0.568273	+	0.822840i	$0.307612\pi$
$887$			1.29477e6i			1.64568i	−0.568273	+	0.822840i	$0.692388\pi$
$888$		0			0
$889$	818142.			1.03520
$890$	−5922.72	−	71918.8i	−0.00747723	−	0.0907951i
$891$		0			0
$892$	138595.	+	835763.i	0.174188	+	1.05040i
$893$	−626187.			−0.785238
$894$		0			0
$895$		−	14413.3i		−	0.0179935i
$896$	−716887.	+	464751.i	−0.892966	+	0.578901i
$897$		0			0
$898$	−63315.8	−	768835.i	−0.0785162	−	0.953411i
$899$		−	431164.i		−	0.533485i
$900$		0			0
$901$	583026.			0.718188
$902$	−1.21963e6	+	100440.i	−1.49905	+	0.123451i
$903$		0			0
$904$	212927.	+	846225.i	0.260551	+	1.03550i
$905$	32139.8			0.0392415
$906$		0			0
$907$		−	684812.i		−	0.832448i	−0.909262	−	0.416224i	$-0.863353\pi$
$907$		−	684812.i		−	0.832448i	0.909262	−	0.416224i	$-0.136647\pi$
$908$	98513.1	+	594059.i	0.119487	+	0.720540i
$909$		0			0
$910$	−143752.	+	11838.4i	−0.173593	+	0.0142958i
$911$			717669.i			0.864743i	0.901695	+	0.432372i	$0.142323\pi$
$911$			717669.i			0.864743i	−0.901695	+	0.432372i	$0.857677\pi$
$912$		0			0
$913$	−320883.			−0.384951
$914$	1945.29	+	23621.3i	0.00232858	+	0.0282756i
$915$		0			0
$916$	903476.	−	149824.i	1.07678	−	0.178562i
$917$	436556.			0.519160
$918$		0			0
$919$			441444.i			0.522691i	0.965245	+	0.261345i	$0.0841661\pi$
$919$			441444.i			0.522691i	−0.965245	+	0.261345i	$0.915834\pi$
$920$	192190.	−	48358.8i	0.227068	−	0.0571347i
$921$		0			0
$922$	−41590.3	−	505026.i	−0.0489249	−	0.594089i
$923$			614551.i			0.721364i
$924$		0			0
$925$	−1.35742e6			−1.58646
$926$	939108.	−	77338.2i	1.09520	−	0.0901929i
$927$		0			0
$928$	−300941.	−	690823.i	−0.349451	−	0.802179i
$929$	1.26657e6			1.46757			0.733783	−	0.679384i	$-0.237753\pi$
$929$	1.26657e6			1.46757			0.733783	+	0.679384i	$0.237753\pi$
$930$		0			0
$931$			188872.i			0.217906i
$932$	575638.	−	95458.3i	0.662701	−	0.109896i
$933$		0			0
$934$	389785.	−	32100.0i	0.446819	−	0.0367969i
$935$		−	74084.8i		−	0.0847434i
$936$		0			0
$937$	377258.			0.429694			0.214847	−	0.976648i	$-0.431075\pi$
$937$	377258.			0.429694			0.214847	+	0.976648i	$0.431075\pi$
$938$	−70271.1	−	853292.i	−0.0798677	−	0.969822i
$939$		0			0
$940$	15633.0	+	94270.9i	0.0176924	+	0.106690i
$941$	−1.29154e6			−1.45858			−0.729288	−	0.684207i	$-0.760148\pi$
$941$	−1.29154e6			−1.45858			−0.729288	+	0.684207i	$0.760148\pi$
$942$		0			0
$943$			1.56872e6i			1.76409i
$944$	177879.	+	521580.i	0.199610	+	0.585298i
$945$		0			0
$946$	−78598.0	−	954405.i	−0.0878273	−	1.06647i
$947$			1.17881e6i			1.31444i	0.753697	+	0.657222i	$0.228269\pi$
$947$			1.17881e6i			1.31444i	−0.753697	+	0.657222i	$0.771731\pi$
$948$		0			0
$949$	−330401.			−0.366867
$950$	1.40319e6	−	115557.i	1.55478	−	0.128041i
$951$		0			0
$952$	397030.	−	99900.6i	0.438076	−	0.110229i
$953$	613396.			0.675391			0.337695	−	0.941255i	$-0.390353\pi$
$953$	613396.			0.675391			0.337695	+	0.941255i	$0.390353\pi$
$954$		0			0
$955$			183887.i			0.201625i
$956$	137047.	+	826428.i	0.149952	+	0.904251i
$957$		0			0
$958$	1.60727e6	−	132363.i	1.75129	−	0.144224i
$959$		−	1.56073e6i		−	1.69704i
$960$		0			0
$961$	580211.			0.628260
$962$	91795.0	+	1.11465e6i	0.0991903	+	1.20445i
$963$		0			0
$964$	213265.	−	35365.9i	0.229491	−	0.0380567i
$965$	4458.31			0.00478757
$966$		0			0
$967$			47416.0i			0.0507075i	0.999679	+	0.0253537i	$0.00807121\pi$
$967$			47416.0i			0.0507075i	−0.999679	+	0.0253537i	$0.991929\pi$
$968$	50970.7	+	202570.i	0.0543963	+	0.216185i
$969$		0			0
$970$	8948.25	+	108657.i	0.00951031	+	0.115482i
$971$		−	746340.i		−	0.791586i	−0.918340	−	0.395793i	$-0.870470\pi$
$971$		−	746340.i		−	0.791586i	0.918340	−	0.395793i	$-0.129530\pi$
$972$		0			0
$973$	1.24350e6			1.31347
$974$	778193.	−	64086.5i	0.820294	−	0.0675536i
$975$		0			0
$976$	−16072.0	+	5481.19i	−0.0168722	+	0.00575408i
$977$	−286711.			−0.300369			−0.150185	−	0.988658i	$-0.547987\pi$
$977$	−286711.			−0.300369			−0.150185	+	0.988658i	$0.547987\pi$
$978$		0			0
$979$			339869.i			0.354606i
$980$	28434.2	−	4715.26i	0.0296067	−	0.00490969i
$981$		0			0
$982$	−303523.	+	24996.0i	−0.314752	+	0.0259208i
$983$		−	582712.i		−	0.603041i	−0.953460	−	0.301521i	$-0.902506\pi$
$983$		−	582712.i		−	0.603041i	0.953460	−	0.301521i	$-0.0974942\pi$
$984$		0			0
$985$	140560.			0.144873
$986$	29636.4	+	359871.i	0.0304840	+	0.370163i
$987$		0			0
$988$	−189781.	−	1.14443e6i	−0.194419	−	1.17240i
$989$	−1.22758e6			−1.25504
$990$		0			0
$991$		−	918794.i		−	0.935558i	−0.883845	−	0.467779i	$-0.845054\pi$
$991$		−	918794.i		−	0.935558i	0.883845	−	0.467779i	$-0.154946\pi$
$992$	−550062.	+	239622.i	−0.558970	+	0.243502i
$993$		0			0
$994$	−86138.9	−	1.04597e6i	−0.0871820	−	1.05864i
$995$			67989.9i			0.0686749i
$996$		0			0
$997$	−1.39525e6			−1.40366			−0.701830	−	0.712344i	$-0.747633\pi$
$997$	−1.39525e6			−1.40366			−0.701830	+	0.712344i	$0.747633\pi$
$998$	−58084.7	+	4783.45i	−0.0583178	+	0.00480264i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.5.d.f.163.11		22
3.2	odd	2		324.5.d.e.163.12		22
4.3	odd	2	inner	324.5.d.f.163.12		22
9.2	odd	6		108.5.f.a.91.19		44
9.4	even	3		36.5.f.a.7.19	yes	44
9.5	odd	6		108.5.f.a.19.4		44
9.7	even	3		36.5.f.a.31.4	yes	44
12.11	even	2		324.5.d.e.163.11		22
36.7	odd	6		36.5.f.a.31.19	yes	44
36.11	even	6		108.5.f.a.91.4		44
36.23	even	6		108.5.f.a.19.19		44
36.31	odd	6		36.5.f.a.7.4	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.4	✓	44	36.31	odd	6
36.5.f.a.7.19	yes	44	9.4	even	3
36.5.f.a.31.4	yes	44	9.7	even	3
36.5.f.a.31.19	yes	44	36.7	odd	6
108.5.f.a.19.4		44	9.5	odd	6
108.5.f.a.19.19		44	36.23	even	6
108.5.f.a.91.4		44	36.11	even	6
108.5.f.a.91.19		44	9.2	odd	6
324.5.d.e.163.11		22	12.11	even	2
324.5.d.e.163.12		22	3.2	odd	2
324.5.d.f.163.11		22	1.1	even	1	trivial
324.5.d.f.163.12		22	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	324.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.328300 - 3.98650i) q^{2} +(-15.7844 + 2.61754i) q^{4} +5.66182 q^{5} +52.1456i q^{7} +(15.6169 + 62.0654i) q^{8} +O(q^{10})\)	\(q+(-0.328300 - 3.98650i) q^{2} +(-15.7844 + 2.61754i) q^{4} +5.66182 q^{5} +52.1456i q^{7} +(15.6169 + 62.0654i) q^{8} +(-1.85878 - 22.5709i) q^{10} +106.664i q^{11} -122.137 q^{13} +(207.879 - 17.1194i) q^{14} +(242.297 - 82.6328i) q^{16} -122.675 q^{17} -593.624i q^{19} +(-89.3686 + 14.8200i) q^{20} +(425.216 - 35.0178i) q^{22} -546.922i q^{23} -592.944 q^{25} +(40.0976 + 486.900i) q^{26} +(-136.493 - 823.090i) q^{28} +735.866 q^{29} -585.927i q^{31} +(-408.962 - 938.790i) q^{32} +(40.2742 + 489.044i) q^{34} +295.239i q^{35} +2289.29 q^{37} +(-2366.49 + 194.887i) q^{38} +(88.4199 + 351.403i) q^{40} -2868.26 q^{41} -2244.52i q^{43} +(-279.197 - 1683.63i) q^{44} +(-2180.31 + 179.555i) q^{46} -1054.85i q^{47} -318.168 q^{49} +(194.664 + 2363.77i) q^{50} +(1927.87 - 319.699i) q^{52} -4752.60 q^{53} +603.911i q^{55} +(-3236.44 + 814.352i) q^{56} +(-241.585 - 2933.53i) q^{58} +2152.65i q^{59} -66.3319 q^{61} +(-2335.80 + 192.360i) q^{62} +(-3608.23 + 1938.53i) q^{64} -691.518 q^{65} -4104.76i q^{67} +(1936.36 - 321.107i) q^{68} +(1176.97 - 96.9271i) q^{70} -5031.65i q^{71} +2705.16 q^{73} +(-751.574 - 9126.26i) q^{74} +(1553.84 + 9370.03i) q^{76} -5562.06 q^{77} -1381.05i q^{79} +(1371.84 - 467.852i) q^{80} +(941.652 + 11434.4i) q^{82} +3008.36i q^{83} -694.563 q^{85} +(-8947.79 + 736.876i) q^{86} +(-6620.13 + 1665.76i) q^{88} +3186.35 q^{89} -6368.92i q^{91} +(1431.59 + 8632.86i) q^{92} +(-4205.18 + 346.309i) q^{94} -3360.99i q^{95} -4814.06 q^{97} +(104.455 + 1268.38i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + q^{2} + q^{4} + 2 q^{5} + 61 q^{8}+O(q^{10}) \) 22 * q + q^2 + q^4 + 2 * q^5 + 61 * q^8	\( 22 q + q^{2} + q^{4} + 2 q^{5} + 61 q^{8} + 14 q^{10} + 2 q^{13} - 252 q^{14} + q^{16} - 28 q^{17} + 140 q^{20} + 33 q^{22} + 1752 q^{25} + 548 q^{26} - 258 q^{28} - 526 q^{29} + 121 q^{32} - 385 q^{34} - 4 q^{37} - 1395 q^{38} + 2276 q^{40} + 2762 q^{41} + 3357 q^{44} + 1788 q^{46} - 3428 q^{49} - 6375 q^{50} - 1438 q^{52} - 5044 q^{53} + 7506 q^{56} + 4064 q^{58} + 2 q^{61} - 9162 q^{62} + 4513 q^{64} + 2014 q^{65} + 11405 q^{68} - 3666 q^{70} - 1708 q^{73} - 14620 q^{74} - 1581 q^{76} + 3942 q^{77} + 22760 q^{80} - 4243 q^{82} + 1252 q^{85} - 22113 q^{86} - 1995 q^{88} + 6524 q^{89} + 30294 q^{92} - 7524 q^{94} - 5638 q^{97} - 46469 q^{98}+O(q^{100}) \) 22 * q + q^2 + q^4 + 2 * q^5 + 61 * q^8 + 14 * q^10 + 2 * q^13 - 252 * q^14 + q^16 - 28 * q^17 + 140 * q^20 + 33 * q^22 + 1752 * q^25 + 548 * q^26 - 258 * q^28 - 526 * q^29 + 121 * q^32 - 385 * q^34 - 4 * q^37 - 1395 * q^38 + 2276 * q^40 + 2762 * q^41 + 3357 * q^44 + 1788 * q^46 - 3428 * q^49 - 6375 * q^50 - 1438 * q^52 - 5044 * q^53 + 7506 * q^56 + 4064 * q^58 + 2 * q^61 - 9162 * q^62 + 4513 * q^64 + 2014 * q^65 + 11405 * q^68 - 3666 * q^70 - 1708 * q^73 - 14620 * q^74 - 1581 * q^76 + 3942 * q^77 + 22760 * q^80 - 4243 * q^82 + 1252 * q^85 - 22113 * q^86 - 1995 * q^88 + 6524 * q^89 + 30294 * q^92 - 7524 * q^94 - 5638 * q^97 - 46469 * q^98

Introduction

L-functions

Modular forms

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