LMFDB - Embedded newform 324.5.d.e.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.e.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	$-0.536122\pi$
$5$	−5.66182			−0.226473			−0.113236	+	0.993568i	$0.536122\pi$
$6$		0			0
$7$		−	52.1456i		−	1.06420i	−0.846683	−	0.532098i	$-0.821404\pi$
$7$		−	52.1456i		−	1.06420i	0.846683	−	0.532098i	$-0.178596\pi$
$8$	−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	$-0.431924\pi$
$17$	122.675			0.424481			0.212240	+	0.977217i	$0.431924\pi$
$18$		0			0
$19$			593.624i			1.64439i	0.569207	+	0.822194i	$0.307250\pi$
$19$			593.624i			1.64439i	−0.569207	+	0.822194i	$0.692750\pi$
$20$	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	$-0.644134\pi$
$29$	−735.866			−0.874989			−0.437495	+	0.899221i	$0.644134\pi$
$30$		0			0
$31$			585.927i			0.609705i	0.952400	+	0.304853i	$0.0986072\pi$
$31$			585.927i			0.609705i	−0.952400	+	0.304853i	$0.901393\pi$
$32$	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	$-0.174694\pi$
$41$	2868.26			1.70628			0.853142	+	0.521678i	$0.174694\pi$
$42$		0			0
$43$			2244.52i			1.21391i	0.794736	+	0.606955i	$0.207609\pi$
$43$			2244.52i			1.21391i	−0.794736	+	0.606955i	$0.792391\pi$
$44$	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	$-0.179028\pi$
$53$	4752.60			1.69192			0.845960	+	0.533246i	$0.179028\pi$
$54$		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	$0.151148\pi$
$67$			4104.76i			0.914404i	−0.889363	+	0.457202i	$0.848852\pi$
$68$	−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	$0.0352911\pi$
$79$			1381.05i			0.221286i	−0.993860	+	0.110643i	$0.964709\pi$
$80$	−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	$-0.564462\pi$
$89$	−3186.35			−0.402267			−0.201133	+	0.979564i	$0.564462\pi$
$90$		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	$-0.388174\pi$
$101$	7020.93			0.688259			0.344130	+	0.938922i	$0.388174\pi$
$102$		0			0
$103$		−	2146.41i		−	0.202320i	−0.994870	−	0.101160i	$-0.967745\pi$
$103$		−	2146.41i		−	0.202320i	0.994870	−	0.101160i	$-0.0322554\pi$
$104$	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	$-0.679269\pi$
$113$	−13634.4			−1.06777			−0.533887	+	0.845556i	$0.679269\pi$
$114$		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	$0.161682\pi$
$127$			15689.6i			0.972754i	−0.873749	+	0.486377i	$0.838318\pi$
$128$	−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	$-0.206244\pi$
$137$	29930.3			1.59467			0.797333	+	0.603540i	$0.206244\pi$
$138$		0			0
$139$			23846.7i			1.23424i	0.786871	+	0.617118i	$0.211700\pi$
$139$			23846.7i			1.23424i	−0.786871	+	0.617118i	$0.788300\pi$
$140$	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	$-0.537898\pi$
$149$	−5273.96			−0.237555			−0.118778	+	0.992921i	$0.537898\pi$
$150$		0			0
$151$			33424.0i			1.46590i	0.680281	+	0.732951i	$0.261858\pi$
$151$			33424.0i			1.46590i	−0.680281	+	0.732951i	$0.738142\pi$
$152$	−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	$0.197122\pi$
$163$			30843.8i			1.16089i	−0.814298	+	0.580447i	$0.802878\pi$
$164$	−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	$-0.787975\pi$
$173$	−47062.8			−1.57248			−0.786241	+	0.617921i	$0.787975\pi$
$174$		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	$-0.603632\pi$
$197$	−24825.9			−0.639694			−0.319847	+	0.947469i	$0.603632\pi$
$198$		0			0
$199$		−	12008.5i		−	0.303237i	−0.988439	−	0.151619i	$-0.951551\pi$
$199$		−	12008.5i		−	0.303237i	0.988439	−	0.151619i	$-0.0484485\pi$
$200$	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	$0.108438\pi$
$211$			29750.5i			0.668235i	−0.942532	+	0.334117i	$0.891562\pi$
$212$	−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	$0.178699\pi$
$223$			52948.5i			1.06474i	−0.846511	+	0.532371i	$0.821301\pi$
$224$	−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	$-0.390968\pi$
$233$	36468.7			0.671751			0.335876	+	0.941906i	$0.390968\pi$
$234$		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	$-0.310981\pi$
$257$	73913.1			1.11906			0.559532	+	0.828809i	$0.310981\pi$
$258$		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	$-0.414050\pi$
$269$	38604.8			0.533502			0.266751	+	0.963765i	$0.414050\pi$
$270$		0			0
$271$		−	12540.3i		−	0.170753i	−0.996349	−	0.0853767i	$-0.972791\pi$
$271$		−	12540.3i		−	0.170753i	0.996349	−	0.0853767i	$-0.0272094\pi$
$272$	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	$-0.545091\pi$
$281$	−22295.9			−0.282366			−0.141183	+	0.989983i	$0.545091\pi$
$282$		0			0
$283$		−	24997.7i		−	0.312123i	−0.987747	−	0.156062i	$-0.950120\pi$
$283$		−	24997.7i		−	0.312123i	0.987747	−	0.156062i	$-0.0498799\pi$
$284$	−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	$-0.456302\pi$
$293$	23497.1			0.273703			0.136852	+	0.990592i	$0.456302\pi$
$294$		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	$-0.945597\pi$
$307$		−	32060.0i		−	0.340163i	0.985430	−	0.170082i	$-0.0544031\pi$
$308$	−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	$-0.266025\pi$
$317$	134781.			1.34125			0.670626	+	0.741795i	$0.266025\pi$
$318$		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	$-0.752461\pi$
$331$		−	153740.i		−	1.40324i	0.712552	−	0.701620i	$-0.247539\pi$
$332$	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	$-0.420494\pi$
$353$	61603.4			0.494374			0.247187	+	0.968968i	$0.420494\pi$
$354$		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	$0.242483\pi$
$367$			185928.i			1.38042i	−0.723607	+	0.690212i	$0.757517\pi$
$368$	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	$-0.829042\pi$
$379$		−	146982.i		−	1.02326i	0.859206	−	0.511630i	$-0.170958\pi$
$380$	−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	$-0.179066\pi$
$389$	256004.			1.69179			0.845897	+	0.533347i	$0.179066\pi$
$390$		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	$-0.552712\pi$
$401$	−53014.0			−0.329687			−0.164843	+	0.986320i	$0.552712\pi$
$402$		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	$-0.940078\pi$
$439$		−	72131.8i		−	0.374281i	0.982333	−	0.187140i	$-0.0599220\pi$
$440$	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	$-0.658754\pi$
$449$	−192859.			−0.956639			−0.478319	+	0.878186i	$0.658754\pi$
$450$		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	$-0.596336\pi$
$461$	−126684.			−0.596100			−0.298050	+	0.954550i	$0.596336\pi$
$462$		0			0
$463$		−	235572.i		−	1.09891i	−0.835524	−	0.549454i	$-0.814836\pi$
$463$		−	235572.i		−	1.09891i	0.835524	−	0.549454i	$-0.185164\pi$
$464$	−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	$-0.864993\pi$
$487$		−	195207.i		−	0.823071i	0.911394	−	0.411536i	$-0.135007\pi$
$488$	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	$0.00931431\pi$
$499$			14570.3i			0.0585152i	−0.999572	+	0.0292576i	$0.990686\pi$
$500$	−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	$-0.628143\pi$
$509$	−203009.			−0.783573			−0.391787	+	0.920056i	$0.628143\pi$
$510$		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	$-0.481918\pi$
$521$	30822.1			0.113550			0.0567749	+	0.998387i	$0.481918\pi$
$522$		0			0
$523$		−	94412.3i		−	0.345164i	−0.984995	−	0.172582i	$-0.944789\pi$
$523$		−	94412.3i		−	0.345164i	0.984995	−	0.172582i	$-0.0552109\pi$
$524$	−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	$0.164630\pi$
$547$			295887.i			0.988897i	−0.869207	+	0.494448i	$0.835370\pi$
$548$	−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	$-0.484296\pi$
$557$	30600.2			0.0986312			0.0493156	+	0.998783i	$0.484296\pi$
$558$		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	$-0.651629\pi$
$569$	−296918.			−0.917090			−0.458545	+	0.888671i	$0.651629\pi$
$570$		0			0
$571$			263786.i			0.809058i	0.914525	+	0.404529i	$0.132565\pi$
$571$			263786.i			0.809058i	−0.914525	+	0.404529i	$0.867435\pi$
$572$	−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	$-0.781792\pi$
$593$	−544416.			−1.54818			−0.774090	+	0.633076i	$0.781792\pi$
$594$		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	$0.0175739\pi$
$607$			40663.6i			0.110364i	−0.998476	+	0.0551821i	$0.982426\pi$
$608$	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	$-0.462260\pi$
$617$	90060.9			0.236573			0.118287	+	0.992979i	$0.462260\pi$
$618$		0			0
$619$			172488.i			0.450171i	0.974339	+	0.225086i	$0.0722662\pi$
$619$			172488.i			0.450171i	−0.974339	+	0.225086i	$0.927734\pi$
$620$	−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	$0.0852044\pi$
$631$			210621.i			0.528985i	−0.964388	+	0.264492i	$0.914796\pi$
$632$	−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	$-0.308769\pi$
$641$	464524.			1.13056			0.565278	+	0.824901i	$0.308769\pi$
$642$		0			0
$643$			417977.i			1.01095i	0.862841	+	0.505476i	$0.168683\pi$
$643$			417977.i			1.01095i	−0.862841	+	0.505476i	$0.831317\pi$
$644$	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	$-0.625884\pi$
$653$	−328545.			−0.770493			−0.385247	+	0.922814i	$0.625884\pi$
$654$		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	$-0.369172\pi$
$677$	366235.			0.799065			0.399533	+	0.916719i	$0.369172\pi$
$678$		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	$-0.879904\pi$
$691$		−	351812.i		−	0.736809i	0.929666	−	0.368405i	$-0.120096\pi$
$692$	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	$-0.282647\pi$
$701$	620142.			1.26199			0.630994	+	0.775788i	$0.282647\pi$
$702$		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	$0.0944056\pi$
$727$			308930.i			0.584510i	−0.956340	+	0.292255i	$0.905594\pi$
$728$	−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	$0.118381\pi$
$739$			396910.i			0.726781i	−0.931637	+	0.363390i	$0.881619\pi$
$740$	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	$0.199202\pi$
$751$			660734.i			1.17151i	−0.810488	+	0.585756i	$0.800798\pi$
$752$	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	$-0.591858\pi$
$761$	−329626.			−0.569183			−0.284591	+	0.958649i	$0.591858\pi$
$762$		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	$-0.484397\pi$
$773$	58555.0			0.0979952			0.0489976	+	0.998799i	$0.484397\pi$
$774$		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	$-0.827524\pi$
$787$		−	638842.i		−	1.03144i	0.856757	−	0.515720i	$-0.172476\pi$
$788$	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	$-0.123985\pi$
$797$	1.17526e6			1.85019			0.925095	+	0.379737i	$0.123985\pi$
$798$		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	$-0.447345\pi$
$809$	215543.			0.329334			0.164667	+	0.986349i	$0.447345\pi$
$810$		0			0
$811$		−	1.05773e6i		−	1.60817i	−0.594512	−	0.804087i	$-0.702655\pi$
$811$		−	1.05773e6i		−	1.60817i	0.594512	−	0.804087i	$-0.297345\pi$
$812$	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	$-0.482080\pi$
$821$	75851.4			0.112532			0.0562662	+	0.998416i	$0.482080\pi$
$822$		0			0
$823$			657611.i			0.970889i	0.874267	+	0.485445i	$0.161342\pi$
$823$			657611.i			0.970889i	−0.874267	+	0.485445i	$0.838658\pi$
$824$	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	$-0.716477\pi$
$857$	−923728.			−1.25772			−0.628858	+	0.777520i	$0.716477\pi$
$858$		0			0
$859$		−	725649.i		−	0.983423i	−0.870758	−	0.491712i	$-0.836371\pi$
$859$		−	725649.i		−	0.983423i	0.870758	−	0.491712i	$-0.163629\pi$
$860$	−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	$-0.229948\pi$
$881$	1.16458e6			1.50044			0.750219	+	0.661190i	$0.229948\pi$
$882$		0			0
$883$		−	12142.2i		−	0.0155731i	−0.999970	−	0.00778655i	$-0.997521\pi$
$883$		−	12142.2i		−	0.0155731i	0.999970	−	0.00778655i	$-0.00247856\pi$
$884$	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	$0.136647\pi$
$907$			684812.i			0.832448i	−0.909262	+	0.416224i	$0.863353\pi$
$908$	−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	$-0.915834\pi$
$919$		−	441444.i		−	0.522691i	0.965245	−	0.261345i	$-0.0841661\pi$
$920$	−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	$-0.762247\pi$
$929$	−1.26657e6			−1.46757			−0.733783	+	0.679384i	$0.762247\pi$
$930$		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	$-0.239852\pi$
$941$	1.29154e6			1.45858			0.729288	+	0.684207i	$0.239852\pi$
$942$		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	$-0.609647\pi$
$953$	−613396.			−0.675391			−0.337695	+	0.941255i	$0.609647\pi$
$954$		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	$-0.991929\pi$
$967$		−	47416.0i		−	0.0507075i	0.999679	−	0.0253537i	$-0.00807121\pi$
$968$	−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	$-0.452013\pi$
$977$	286711.			0.300369			0.150185	+	0.988658i	$0.452013\pi$
$978$		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	$0.154946\pi$
$991$			918794.i			0.935558i	−0.883845	+	0.467779i	$0.845054\pi$
$992$	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.e.163.11		22
3.2	odd	2		324.5.d.f.163.12		22
4.3	odd	2	inner	324.5.d.e.163.12		22
9.2	odd	6		36.5.f.a.31.19	yes	44
9.4	even	3		108.5.f.a.19.19		44
9.5	odd	6		36.5.f.a.7.4	✓	44
9.7	even	3		108.5.f.a.91.4		44
12.11	even	2		324.5.d.f.163.11		22
36.7	odd	6		108.5.f.a.91.19		44
36.11	even	6		36.5.f.a.31.4	yes	44
36.23	even	6		36.5.f.a.7.19	yes	44
36.31	odd	6		108.5.f.a.19.4		44

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
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

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