LMFDB - Embedded newform 304.5.r.d.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,5,Mod(65,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("304.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	304.r (of order $6$, degree $2$, not 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:	$31.4244687775$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Character	$\chi$	$=$	304.145
Dual form			304.5.r.d.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-14.4186 + 8.32460i) q^{3} +(10.1950 + 17.6583i) q^{5} -80.1603 q^{7} +(98.0979 - 169.911i) q^{9} +O(q^{10})$	\(q+(-14.4186 + 8.32460i) q^{3} +(10.1950 + 17.6583i) q^{5} -80.1603 q^{7} +(98.0979 - 169.911i) q^{9} +190.229 q^{11} +(121.151 + 69.9466i) q^{13} +(-293.997 - 169.739i) q^{15} +(222.065 + 384.628i) q^{17} +(330.795 + 144.552i) q^{19} +(1155.80 - 667.303i) q^{21} +(291.978 - 505.721i) q^{23} +(104.622 - 181.211i) q^{25} +1917.92i q^{27} +(-612.149 - 353.424i) q^{29} +491.210i q^{31} +(-2742.85 + 1583.58i) q^{33} +(-817.238 - 1415.50i) q^{35} -1361.94i q^{37} -2329.11 q^{39} +(215.533 - 124.438i) q^{41} +(1046.30 + 1812.24i) q^{43} +4000.45 q^{45} +(-363.989 + 630.447i) q^{47} +4024.68 q^{49} +(-6403.75 - 3697.21i) q^{51} +(-718.890 - 415.051i) q^{53} +(1939.40 + 3359.13i) q^{55} +(-5972.96 + 669.495i) q^{57} +(2639.64 - 1524.00i) q^{59} +(-2847.99 + 4932.87i) q^{61} +(-7863.56 + 13620.1i) q^{63} +2852.43i q^{65} +(-738.492 - 426.368i) q^{67} +9722.41i q^{69} +(-1755.53 + 1013.56i) q^{71} +(4240.19 + 7344.22i) q^{73} +3483.75i q^{75} -15248.9 q^{77} +(6527.58 - 3768.70i) q^{79} +(-8019.96 - 13891.0i) q^{81} +1667.35 q^{83} +(-4527.93 + 7842.60i) q^{85} +11768.5 q^{87} +(-3824.73 - 2208.21i) q^{89} +(-9711.51 - 5606.94i) q^{91} +(-4089.13 - 7082.58i) q^{93} +(819.923 + 7315.01i) q^{95} +(-6169.95 + 3562.22i) q^{97} +(18661.1 - 32322.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−14.4186	+	8.32460i	−1.60207	+	0.924955i	−0.610997	+	0.791633i	$0.709231\pi$
$3$	−14.4186	+	8.32460i	−1.60207	+	0.924955i	−0.991073	+	0.133323i	$0.957435\pi$
$4$		0			0
$5$	10.1950	+	17.6583i	0.407802	+	0.706333i	0.994643	−	0.103369i	$-0.0329621\pi$
$5$	10.1950	+	17.6583i	0.407802	+	0.706333i	−0.586841	+	0.809702i	$0.699629\pi$
$6$		0			0
$7$	−80.1603			−1.63593			−0.817963	−	0.575271i	$-0.804896\pi$
$7$	−80.1603			−1.63593			−0.817963	+	0.575271i	$0.804896\pi$
$8$		0			0
$9$	98.0979	−	169.911i	1.21109	−	2.09766i
$10$		0			0
$11$	190.229			1.57214			0.786072	−	0.618135i	$-0.212112\pi$
$11$	190.229			1.57214			0.786072	+	0.618135i	$0.212112\pi$
$12$		0			0
$13$	121.151	+	69.9466i	0.716870	+	0.413885i	0.813600	−	0.581425i	$-0.197505\pi$
$13$	121.151	+	69.9466i	0.716870	+	0.413885i	−0.0967294	+	0.995311i	$0.530838\pi$
$14$		0			0
$15$	−293.997	−	169.739i	−1.30665	−	0.754397i
$16$		0			0
$17$	222.065	+	384.628i	0.768391	+	1.33089i	0.938435	+	0.345456i	$0.112276\pi$
$17$	222.065	+	384.628i	0.768391	+	1.33089i	−0.170044	+	0.985437i	$0.554391\pi$
$18$		0			0
$19$	330.795	+	144.552i	0.916331	+	0.400422i
$19$	330.795	+	144.552i	0.916331	+	0.400422i
$20$		0			0
$21$	1155.80	−	667.303i	2.62087	−	1.51316i
$22$		0			0
$23$	291.978	−	505.721i	0.551944	−	0.955995i	−0.446190	−	0.894938i	$-0.647220\pi$
$23$	291.978	−	505.721i	0.551944	−	0.955995i	0.998134	−	0.0610570i	$-0.0194472\pi$
$24$		0			0
$25$	104.622	−	181.211i	0.167396	−	0.289938i
$26$		0			0
$27$			1917.92i			2.63089i
$28$		0			0
$29$	−612.149	−	353.424i	−0.727882	−	0.420243i	0.0897650	−	0.995963i	$-0.471388\pi$
$29$	−612.149	−	353.424i	−0.727882	−	0.420243i	−0.817647	+	0.575720i	$0.804722\pi$
$30$		0			0
$31$			491.210i			0.511145i	0.966790	+	0.255572i	$0.0822639\pi$
$31$			491.210i			0.511145i	−0.966790	+	0.255572i	$0.917736\pi$
$32$		0			0
$33$	−2742.85	+	1583.58i	−2.51868	+	1.45416i
$34$		0			0
$35$	−817.238	−	1415.50i	−0.667133	−	1.15551i
$36$		0			0
$37$		−	1361.94i		−	0.994840i	−0.867510	−	0.497420i	$-0.834281\pi$
$37$		−	1361.94i		−	0.994840i	0.867510	−	0.497420i	$-0.165719\pi$
$38$		0			0
$39$	−2329.11			−1.53130
$40$		0			0
$41$	215.533	−	124.438i	0.128217	−	0.0740262i	−0.434520	−	0.900662i	$-0.643082\pi$
$41$	215.533	−	124.438i	0.128217	−	0.0740262i	0.562737	+	0.826636i	$0.309748\pi$
$42$		0			0
$43$	1046.30	+	1812.24i	0.565873	+	0.980121i	0.996968	+	0.0778142i	$0.0247941\pi$
$43$	1046.30	+	1812.24i	0.565873	+	0.980121i	−0.431095	+	0.902307i	$0.641873\pi$
$44$		0			0
$45$	4000.45			1.97553
$46$		0			0
$47$	−363.989	+	630.447i	−0.164775	+	0.285399i	−0.936575	−	0.350466i	$-0.886023\pi$
$47$	−363.989	+	630.447i	−0.164775	+	0.285399i	0.771800	+	0.635865i	$0.219357\pi$
$48$		0			0
$49$	4024.68			1.67625
$50$		0			0
$51$	−6403.75	−	3697.21i	−2.46203	−	1.42146i
$52$		0			0
$53$	−718.890	−	415.051i	−0.255924	−	0.147758i	0.366550	−	0.930398i	$-0.380539\pi$
$53$	−718.890	−	415.051i	−0.255924	−	0.147758i	−0.622474	+	0.782641i	$0.713872\pi$
$54$		0			0
$55$	1939.40	+	3359.13i	0.641123	+	1.11046i
$56$		0			0
$57$	−5972.96	+	669.495i	−1.83840	+	0.206062i
$58$		0			0
$59$	2639.64	−	1524.00i	0.758300	−	0.437805i	−0.0703852	−	0.997520i	$-0.522423\pi$
$59$	2639.64	−	1524.00i	0.758300	−	0.437805i	0.828685	+	0.559715i	$0.189090\pi$
$60$		0			0
$61$	−2847.99	+	4932.87i	−0.765383	+	1.32568i	0.174660	+	0.984629i	$0.444117\pi$
$61$	−2847.99	+	4932.87i	−0.765383	+	1.32568i	−0.940044	+	0.341054i	$0.889216\pi$
$62$		0			0
$63$	−7863.56	+	13620.1i	−1.98124	+	3.43162i
$64$		0			0
$65$			2852.43i			0.675132i
$66$		0			0
$67$	−738.492	−	426.368i	−0.164511	−	0.0949807i	0.415484	−	0.909601i	$-0.363612\pi$
$67$	−738.492	−	426.368i	−0.164511	−	0.0949807i	−0.579995	+	0.814620i	$0.696946\pi$
$68$		0			0
$69$			9722.41i			2.04209i
$70$		0			0
$71$	−1755.53	+	1013.56i	−0.348251	+	0.201063i	−0.663915	−	0.747808i	$-0.731106\pi$
$71$	−1755.53	+	1013.56i	−0.348251	+	0.201063i	0.315664	+	0.948871i	$0.397773\pi$
$72$		0			0
$73$	4240.19	+	7344.22i	0.795682	+	1.37816i	0.922406	+	0.386223i	$0.126220\pi$
$73$	4240.19	+	7344.22i	0.795682	+	1.37816i	−0.126724	+	0.991938i	$0.540446\pi$
$74$		0			0
$75$			3483.75i			0.619334i
$76$		0			0
$77$	−15248.9			−2.57191
$78$		0			0
$79$	6527.58	−	3768.70i	1.04592	−	0.603862i	0.124415	−	0.992230i	$-0.460295\pi$
$79$	6527.58	−	3768.70i	1.04592	−	0.603862i	0.921504	+	0.388368i	$0.126961\pi$
$80$		0			0
$81$	−8019.96	−	13891.0i	−1.22237	−	2.11720i
$82$		0			0
$83$	1667.35			0.242031			0.121016	−	0.992651i	$-0.461385\pi$
$83$	1667.35			0.242031			0.121016	+	0.992651i	$0.461385\pi$
$84$		0			0
$85$	−4527.93	+	7842.60i	−0.626703	+	1.08548i
$86$		0			0
$87$	11768.5			1.55482
$88$		0			0
$89$	−3824.73	−	2208.21i	−0.482859	−	0.278779i	0.238748	−	0.971082i	$-0.423263\pi$
$89$	−3824.73	−	2208.21i	−0.482859	−	0.278779i	−0.721607	+	0.692303i	$0.756596\pi$
$90$		0			0
$91$	−9711.51	−	5606.94i	−1.17275	−	0.677085i
$92$		0			0
$93$	−4089.13	−	7082.58i	−0.472786	−	0.818890i
$94$		0			0
$95$	819.923	+	7315.01i	0.0908502	+	0.810528i
$96$		0			0
$97$	−6169.95	+	3562.22i	−0.655750	+	0.378598i	−0.790656	−	0.612261i	$-0.790260\pi$
$97$	−6169.95	+	3562.22i	−0.655750	+	0.378598i	0.134906	+	0.990858i	$0.456927\pi$
$98$		0			0
$99$	18661.1	−	32322.0i	1.90400	−	3.29782i
$100$		0			0
$101$	4715.99	−	8168.34i	0.462307	−	0.800739i	−0.536769	−	0.843729i	$-0.680355\pi$
$101$	4715.99	−	8168.34i	0.462307	−	0.800739i	0.999075	+	0.0429906i	$0.0136886\pi$
$102$		0			0
$103$			10562.9i			0.995655i	0.867276	+	0.497828i	$0.165869\pi$
$103$			10562.9i			0.995655i	−0.867276	+	0.497828i	$0.834131\pi$
$104$		0			0
$105$	23566.9	+	13606.4i	2.13759	+	1.23414i
$106$		0			0
$107$		−	7399.42i		−	0.646294i	−0.946349	−	0.323147i	$-0.895259\pi$
$107$		−	7399.42i		−	0.646294i	0.946349	−	0.323147i	$-0.104741\pi$
$108$		0			0
$109$	2132.42	−	1231.15i	0.179482	−	0.103624i	−0.407567	−	0.913175i	$-0.633623\pi$
$109$	2132.42	−	1231.15i	0.179482	−	0.103624i	0.587049	+	0.809551i	$0.300290\pi$
$110$		0			0
$111$	11337.6	+	19637.2i	0.920183	+	1.59380i
$112$		0			0
$113$			10832.4i			0.848336i	0.905584	+	0.424168i	$0.139433\pi$
$113$			10832.4i			0.848336i	−0.905584	+	0.424168i	$0.860567\pi$
$114$		0			0
$115$	11906.9			0.900335
$116$		0			0
$117$	23769.3	−	13723.2i	1.73638	−	1.00250i
$118$		0			0
$119$	−17800.8	−	30831.9i	−1.25703	−	2.17724i
$120$		0			0
$121$	21546.2			1.47164
$122$		0			0
$123$	−2071.79	+	3588.45i	−0.136942	+	0.237190i
$124$		0			0
$125$	17010.3			1.08866
$126$		0			0
$127$	10358.2	+	5980.32i	0.642211	+	0.370780i	0.785466	−	0.618905i	$-0.212424\pi$
$127$	10358.2	+	5980.32i	0.642211	+	0.370780i	−0.143255	+	0.989686i	$0.545757\pi$
$128$		0			0
$129$	−30172.4	−	17420.0i	−1.81314	−	1.04681i
$130$		0			0
$131$	−4254.48	−	7368.98i	−0.247916	−	0.429403i	0.715032	−	0.699092i	$-0.246412\pi$
$131$	−4254.48	−	7368.98i	−0.247916	−	0.429403i	−0.962947	+	0.269690i	$0.913079\pi$
$132$		0			0
$133$	−26516.7	−	11587.4i	−1.49905	−	0.655060i
$134$		0			0
$135$	−33867.2	+	19553.2i	−1.85828	+	1.07288i
$136$		0			0
$137$	−10606.7	+	18371.3i	−0.565118	+	0.978813i	0.431921	+	0.901911i	$0.357836\pi$
$137$	−10606.7	+	18371.3i	−0.565118	+	0.978813i	−0.997039	+	0.0769012i	$0.975497\pi$
$138$		0			0
$139$	3499.47	−	6061.26i	0.181122	−	0.313713i	−0.761141	−	0.648587i	$-0.775360\pi$
$139$	3499.47	−	6061.26i	0.181122	−	0.313713i	0.942263	+	0.334874i	$0.108694\pi$
$140$		0			0
$141$		−	12120.2i		−	0.609639i
$142$		0			0
$143$	23046.5	+	13305.9i	1.12702	+	0.650687i
$144$		0			0
$145$		−	14412.7i		−	0.685503i
$146$		0			0
$147$	−58030.4	+	33503.8i	−2.68547	+	1.55046i
$148$		0			0
$149$	4887.00	+	8464.53i	0.220125	+	0.381268i	0.954846	−	0.297102i	$-0.0960200\pi$
$149$	4887.00	+	8464.53i	0.220125	+	0.381268i	−0.734721	+	0.678370i	$0.762687\pi$
$150$		0			0
$151$		−	23140.1i		−	1.01487i	−0.861690	−	0.507435i	$-0.830594\pi$
$151$		−	23140.1i		−	1.01487i	0.861690	−	0.507435i	$-0.169406\pi$
$152$		0			0
$153$	87136.5			3.72235
$154$		0			0
$155$	−8673.95	+	5007.91i	−0.361039	+	0.208446i
$156$		0			0
$157$	−78.4250	−	135.836i	−0.00318167	−	0.00551081i	0.864430	−	0.502753i	$-0.167679\pi$
$157$	−78.4250	−	135.836i	−0.00318167	−	0.00551081i	−0.867612	+	0.497242i	$0.834346\pi$
$158$		0			0
$159$	13820.5			0.546677
$160$		0			0
$161$	−23405.1	+	40538.8i	−0.902939	+	1.56394i
$162$		0			0
$163$	−6507.51			−0.244929			−0.122464	−	0.992473i	$-0.539080\pi$
$163$	−6507.51			−0.244929			−0.122464	+	0.992473i	$0.539080\pi$
$164$		0			0
$165$	−55926.9	−	32289.4i	−2.05425	−	1.18602i
$166$		0			0
$167$	1607.08	+	927.850i	0.0576242	+	0.0332694i	0.528535	−	0.848911i	$-0.322741\pi$
$167$	1607.08	+	927.850i	0.0576242	+	0.0332694i	−0.470911	+	0.882181i	$0.656075\pi$
$168$		0			0
$169$	−4495.44	−	7786.34i	−0.157398	−	0.272621i
$170$		0			0
$171$	57011.3	−	42025.4i	1.94970	−	1.43721i
$172$		0			0
$173$	−12698.6	+	7331.51i	−0.424289	+	0.244963i	−0.696911	−	0.717158i	$-0.745443\pi$
$173$	−12698.6	+	7331.51i	−0.424289	+	0.244963i	0.272622	+	0.962121i	$0.412109\pi$
$174$		0			0
$175$	−8386.56	+	14525.9i	−0.273847	+	0.474316i
$176$		0			0
$177$	−25373.3	+	43947.9i	−0.809899	+	1.40279i
$178$		0			0
$179$			36402.8i			1.13613i	0.822983	+	0.568066i	$0.192308\pi$
$179$			36402.8i			1.13613i	−0.822983	+	0.568066i	$0.807692\pi$
$180$		0			0
$181$	16226.0	+	9368.06i	0.495283	+	0.285952i	0.726763	−	0.686888i	$-0.241024\pi$
$181$	16226.0	+	9368.06i	0.495283	+	0.285952i	−0.231481	+	0.972840i	$0.574357\pi$
$182$		0			0
$183$		−	94833.6i		−	2.83178i
$184$		0			0
$185$	24049.5	−	13885.0i	0.702688	−	0.405697i
$186$		0			0
$187$	42243.3	+	73167.5i	1.20802	+	2.09235i
$188$		0			0
$189$		−	153741.i		−	4.30394i
$190$		0			0
$191$	−33191.2			−0.909820			−0.454910	−	0.890537i	$-0.650329\pi$
$191$	−33191.2			−0.909820			−0.454910	+	0.890537i	$0.650329\pi$
$192$		0			0
$193$	25666.2	−	14818.4i	0.689045	−	0.397820i	−0.114209	−	0.993457i	$-0.536433\pi$
$193$	25666.2	−	14818.4i	0.689045	−	0.397820i	0.803254	+	0.595637i	$0.203100\pi$
$194$		0			0
$195$	−23745.4	−	41128.2i	−0.624467	−	1.08161i
$196$		0			0
$197$	10015.4			0.258068			0.129034	−	0.991640i	$-0.458812\pi$
$197$	10015.4			0.258068			0.129034	+	0.991640i	$0.458812\pi$
$198$		0			0
$199$	−15024.9	+	26023.8i	−0.379406	+	0.657151i	−0.990976	−	0.134039i	$-0.957205\pi$
$199$	−15024.9	+	26023.8i	−0.379406	+	0.657151i	0.611570	+	0.791191i	$0.290538\pi$
$200$		0			0
$201$	14197.4			0.351412
$202$		0			0
$203$	49070.0	+	28330.6i	1.19076	+	0.687486i
$204$		0			0
$205$	4394.74	+	2537.30i	0.104574	+	0.0603760i
$206$		0			0
$207$	−57284.9	−	99220.4i	−1.33690	−	2.31558i
$208$		0			0
$209$	62927.0	+	27498.1i	1.44060	+	0.629520i
$210$		0			0
$211$	2919.83	−	1685.76i	0.0655832	−	0.0378645i	−0.466850	−	0.884337i	$-0.654611\pi$
$211$	2919.83	−	1685.76i	0.0655832	−	0.0378645i	0.532433	+	0.846472i	$0.321278\pi$
$212$		0			0
$213$	16874.9	−	29228.2i	0.371948	−	0.644234i
$214$		0			0
$215$	−21334.1	+	36951.8i	−0.461528	+	0.799390i
$216$		0			0
$217$		−	39375.6i		−	0.836195i
$218$		0			0
$219$	−122275.	−	70595.7i	−2.54947	−	1.47194i
$220$		0			0
$221$			62130.8i			1.27210i
$222$		0			0
$223$	−73449.5	+	42406.1i	−1.47699	+	0.852743i	−0.999662	−	0.0259799i	$-0.991729\pi$
$223$	−73449.5	+	42406.1i	−1.47699	+	0.852743i	−0.477332	+	0.878723i	$0.658396\pi$
$224$		0			0
$225$	−20526.4	−	35552.8i	−0.405461	−	0.702278i
$226$		0			0
$227$			67190.2i			1.30393i	0.758249	+	0.651965i	$0.226055\pi$
$227$			67190.2i			1.30393i	−0.758249	+	0.651965i	$0.773945\pi$
$228$		0			0
$229$	2825.04			0.0538709			0.0269354	−	0.999637i	$-0.491425\pi$
$229$	2825.04			0.0538709			0.0269354	+	0.999637i	$0.491425\pi$
$230$		0			0
$231$	219868.	−	126941.i	4.12038	−	2.37890i
$232$		0			0
$233$	37395.6	+	64771.0i	0.688824	+	1.19308i	0.972219	+	0.234075i	$0.0752061\pi$
$233$	37395.6	+	64771.0i	0.688824	+	1.19308i	−0.283394	+	0.959003i	$0.591461\pi$
$234$		0			0
$235$	−14843.5			−0.268783
$236$		0			0
$237$	−62745.9	+	108679.i	−1.11709	+	1.93486i
$238$		0			0
$239$	66754.9			1.16866			0.584329	−	0.811517i	$-0.301358\pi$
$239$	66754.9			1.16866			0.584329	+	0.811517i	$0.301358\pi$
$240$		0			0
$241$	−80582.6	−	46524.4i	−1.38742	−	0.801026i	−0.394395	−	0.918941i	$-0.629046\pi$
$241$	−80582.6	−	46524.4i	−1.38742	−	0.801026i	−0.993024	+	0.117915i	$0.962379\pi$
$242$		0			0
$243$	96735.5	+	55850.3i	1.63822	+	0.945829i
$244$		0			0
$245$	41031.8	+	71069.1i	0.683578	+	1.18399i
$246$		0			0
$247$	29965.3	+	40650.7i	0.491162	+	0.666306i
$248$		0			0
$249$	−24040.9	+	13880.0i	−0.387751	+	0.223868i
$250$		0			0
$251$	15858.6	−	27467.9i	0.251720	−	0.435992i	−0.712280	−	0.701896i	$-0.752337\pi$
$251$	15858.6	−	27467.9i	0.251720	−	0.435992i	0.963999	+	0.265904i	$0.0856705\pi$
$252$		0			0
$253$	55542.9	−	96203.1i	0.867735	−	1.50296i
$254$		0			0
$255$		−	150773.i		−	2.31869i
$256$		0			0
$257$	−88876.1	−	51312.7i	−1.34561	−	0.776888i	−0.357985	−	0.933727i	$-0.616536\pi$
$257$	−88876.1	−	51312.7i	−1.34561	−	0.776888i	−0.987624	+	0.156840i	$0.949869\pi$
$258$		0			0
$259$			109173.i			1.62748i
$260$		0			0
$261$	−120101.	+	69340.3i	−1.76305	+	1.01790i
$262$		0			0
$263$	−1395.16	−	2416.48i	−0.0201703	−	0.0349359i	0.855764	−	0.517366i	$-0.173088\pi$
$263$	−1395.16	−	2416.48i	−0.0201703	−	0.0349359i	−0.875934	+	0.482430i	$0.839754\pi$
$264$		0			0
$265$		−	16925.9i		−	0.241023i
$266$		0			0
$267$	73529.8			1.03143
$268$		0			0
$269$	46391.5	−	26784.1i	0.641112	−	0.370146i	−0.143931	−	0.989588i	$-0.545974\pi$
$269$	46391.5	−	26784.1i	0.641112	−	0.370146i	0.785043	+	0.619442i	$0.212641\pi$
$270$		0			0
$271$	−35263.1	−	61077.4i	−0.480155	−	0.831653i	0.519586	−	0.854418i	$-0.326086\pi$
$271$	−35263.1	−	61077.4i	−0.480155	−	0.831653i	−0.999741	+	0.0227652i	$0.992753\pi$
$272$		0			0
$273$	186702.			2.50510
$274$		0			0
$275$	19902.2	−	34471.7i	0.263170	−	0.455824i
$276$		0			0
$277$	30787.7			0.401252			0.200626	−	0.979668i	$-0.435702\pi$
$277$	30787.7			0.401252			0.200626	+	0.979668i	$0.435702\pi$
$278$		0			0
$279$	83461.8	+	48186.7i	1.07221	+	0.619040i
$280$		0			0
$281$	34056.5	+	19662.5i	0.431307	+	0.249015i	0.699903	−	0.714237i	$-0.253226\pi$
$281$	34056.5	+	19662.5i	0.431307	+	0.249015i	−0.268596	+	0.963253i	$0.586560\pi$
$282$		0			0
$283$	46361.9	+	80301.2i	0.578880	+	1.00265i	0.995608	+	0.0936181i	$0.0298433\pi$
$283$	46361.9	+	80301.2i	0.578880	+	1.00265i	−0.416728	+	0.909031i	$0.636823\pi$
$284$		0			0
$285$	−72716.7	−	98646.9i	−0.895250	−	1.21449i
$286$		0			0
$287$	−17277.2	+	9974.99i	−0.209754	+	0.121101i
$288$		0			0
$289$	−56865.3	+	98493.6i	−0.680850	+	1.17927i
$290$		0			0
$291$	59308.2	−	102725.i	0.700372	−	1.21308i
$292$		0			0
$293$		−	32227.5i		−	0.375398i	−0.982227	−	0.187699i	$-0.939897\pi$
$293$		−	32227.5i		−	0.375398i	0.982227	−	0.187699i	$-0.0601030\pi$
$294$		0			0
$295$	53822.5	+	31074.4i	0.618472	+	0.357075i
$296$		0			0
$297$			364844.i			4.13613i
$298$		0			0
$299$	70747.0	−	40845.8i	0.791345	−	0.456883i
$300$		0			0
$301$	−83871.7	−	145270.i	−0.925726	−	1.60340i
$302$		0			0
$303$			157035.i			1.71045i
$304$		0			0
$305$	−116142.			−1.24850
$306$		0			0
$307$	−145054.	+	83746.9i	−1.53905	+	0.888571i	−0.540155	+	0.841566i	$0.681634\pi$
$307$	−145054.	+	83746.9i	−1.53905	+	0.888571i	−0.998895	+	0.0470050i	$0.985032\pi$
$308$		0			0
$309$	−87932.0	−	152303.i	−0.920937	−	1.59511i
$310$		0			0
$311$	−119476.			−1.23526			−0.617632	−	0.786467i	$-0.711908\pi$
$311$	−119476.			−1.23526			−0.617632	+	0.786467i	$0.711908\pi$
$312$		0			0
$313$	−43061.2	+	74584.1i	−0.439539	+	0.761303i	−0.997654	−	0.0684603i	$-0.978191\pi$
$313$	−43061.2	+	74584.1i	−0.439539	+	0.761303i	0.558115	+	0.829763i	$0.311525\pi$
$314$		0			0
$315$	−320677.			−3.23182
$316$		0			0
$317$	10116.6	+	5840.80i	0.100673	+	0.0581238i	0.549491	−	0.835499i	$-0.314822\pi$
$317$	10116.6	+	5840.80i	0.100673	+	0.0581238i	−0.448818	+	0.893623i	$0.648155\pi$
$318$		0			0
$319$	−116449.	−	67231.7i	−1.14433	−	0.660682i
$320$		0			0
$321$	61597.2	+	106689.i	0.597793	+	1.03541i
$322$		0			0
$323$	17859.3	+	159333.i	0.171183	+	1.52722i
$324$		0			0
$325$	25350.2	−	14635.9i	0.240002	−	0.138565i
$326$		0			0
$327$	−20497.7	+	35503.1i	−0.191695	+	0.332025i
$328$		0			0
$329$	29177.4	−	50536.8i	0.269560	−	0.466892i
$330$		0			0
$331$		−	55406.4i		−	0.505713i	−0.967504	−	0.252856i	$-0.918630\pi$
$331$		−	55406.4i		−	0.505713i	0.967504	−	0.252856i	$-0.0813700\pi$
$332$		0			0
$333$	−231407.	−	133603.i	−2.08684	−	1.20484i
$334$		0			0
$335$		−	17387.4i		−	0.154933i
$336$		0			0
$337$	8509.02	−	4912.69i	0.0749238	−	0.0432573i	−0.462070	−	0.886843i	$-0.652893\pi$
$337$	8509.02	−	4912.69i	0.0749238	−	0.0432573i	0.536994	+	0.843586i	$0.319560\pi$
$338$		0			0
$339$	−90175.4	−	156188.i	−0.784673	−	1.35909i
$340$		0			0
$341$			93442.6i			0.803593i
$342$		0			0
$343$	−130155.			−1.10630
$344$		0			0
$345$	−171682.	+	99120.4i	−1.44240	+	0.832770i
$346$		0			0
$347$	−46427.5	−	80414.9i	−0.385582	−	0.667848i	0.606268	−	0.795261i	$-0.292666\pi$
$347$	−46427.5	−	80414.9i	−0.385582	−	0.667848i	−0.991850	+	0.127413i	$0.959333\pi$
$348$		0			0
$349$	55430.4			0.455090			0.227545	−	0.973768i	$-0.426930\pi$
$349$	55430.4			0.455090			0.227545	+	0.973768i	$0.426930\pi$
$350$		0			0
$351$	−134152.	+	232358.i	−1.08889	+	1.88601i
$352$		0			0
$353$	135398.			1.08658			0.543289	−	0.839545i	$-0.317179\pi$
$353$	135398.			1.08658			0.543289	+	0.839545i	$0.317179\pi$
$354$		0			0
$355$	−35795.5	−	20666.5i	−0.284035	−	0.163988i
$356$		0			0
$357$	513327.	+	296369.i	4.02770	+	2.32539i
$358$		0			0
$359$	114033.	+	197510.i	0.884790	+	1.53250i	0.845954	+	0.533256i	$0.179032\pi$
$359$	114033.	+	197510.i	0.884790	+	1.53250i	0.0388363	+	0.999246i	$0.487635\pi$
$360$		0			0
$361$	88530.3	+	95634.4i	0.679325	+	0.733837i
$362$		0			0
$363$	−310667.	+	179364.i	−2.35766	+	1.36120i
$364$		0			0
$365$	−86457.8	+	149749.i	−0.648961	+	1.12403i
$366$		0			0
$367$	−6326.61	+	10958.0i	−0.0469720	+	0.0813578i	−0.888555	−	0.458769i	$-0.848290\pi$
$367$	−6326.61	+	10958.0i	−0.0469720	+	0.0813578i	0.841584	+	0.540127i	$0.181624\pi$
$368$		0			0
$369$		−	48828.4i		−	0.358608i
$370$		0			0
$371$	57626.4	+	33270.6i	0.418672	+	0.241720i
$372$		0			0
$373$		−	131514.i		−	0.945267i	−0.881259	−	0.472634i	$-0.843303\pi$
$373$		−	131514.i		−	0.945267i	0.881259	−	0.472634i	$-0.156697\pi$
$374$		0			0
$375$	−245265.	+	141604.i	−1.74411	+	1.00696i
$376$		0			0
$377$	−49441.6	−	85635.4i	−0.347865	−	0.602519i
$378$		0			0
$379$			32713.9i			0.227747i	0.993495	+	0.113874i	$0.0363259\pi$
$379$			32713.9i			0.227747i	−0.993495	+	0.113874i	$0.963674\pi$
$380$		0			0
$381$	−199135.			−1.37182
$382$		0			0
$383$	−97145.8	+	56087.1i	−0.662257	+	0.382354i	−0.793136	−	0.609044i	$-0.791553\pi$
$383$	−97145.8	+	56087.1i	−0.662257	+	0.382354i	0.130880	+	0.991398i	$0.458220\pi$
$384$		0			0
$385$	−155463.	−	269269.i	−1.04883	−	1.81662i
$386$		0			0
$387$	410559.			2.74128
$388$		0			0
$389$	30127.2	−	52181.9i	0.199095	−	0.344842i	−0.749140	−	0.662411i	$-0.769533\pi$
$389$	30127.2	−	52181.9i	0.199095	−	0.344842i	0.948235	+	0.317569i	$0.102866\pi$
$390$		0			0
$391$	259353.			1.69644
$392$		0			0
$393$	122688.	+	70833.7i	0.794356	+	0.458622i
$394$		0			0
$395$	133098.	+	76844.1i	0.853055	+	0.492512i
$396$		0			0
$397$	−46336.5	−	80257.2i	−0.293997	−	0.509217i	0.680754	−	0.732512i	$-0.261652\pi$
$397$	−46336.5	−	80257.2i	−0.293997	−	0.509217i	−0.974751	+	0.223295i	$0.928319\pi$
$398$		0			0
$399$	478794.	−	53667.0i	3.00748	−	0.337102i
$400$		0			0
$401$	72522.6	−	41871.0i	0.451009	−	0.260390i	−0.257247	−	0.966346i	$-0.582816\pi$
$401$	72522.6	−	41871.0i	0.451009	−	0.260390i	0.708256	+	0.705956i	$0.249482\pi$
$402$		0			0
$403$	−34358.5	+	59510.7i	−0.211555	+	0.366425i
$404$		0			0
$405$	163528.	−	283238.i	0.996968	−	1.72680i
$406$		0			0
$407$		−	259080.i		−	1.56403i
$408$		0			0
$409$	270576.	+	156217.i	1.61749	+	0.933861i	0.987565	+	0.157208i	$0.0502494\pi$
$409$	270576.	+	156217.i	1.61749	+	0.933861i	0.629929	+	0.776653i	$0.283084\pi$
$410$		0			0
$411$		−	353186.i		−	2.09083i
$412$		0			0
$413$	−211595.	+	122164.i	−1.24052	+	0.716216i
$414$		0			0
$415$	16998.7	+	29442.6i	0.0987007	+	0.170955i
$416$		0			0
$417$			116527.i			0.670121i
$418$		0			0
$419$	−44501.4			−0.253481			−0.126741	−	0.991936i	$-0.540452\pi$
$419$	−44501.4			−0.253481			−0.126741	+	0.991936i	$0.540452\pi$
$420$		0			0
$421$	−6107.91	+	3526.40i	−0.0344610	+	0.0198961i	−0.517132	−	0.855906i	$-0.673000\pi$
$421$	−6107.91	+	3526.40i	−0.0344610	+	0.0198961i	0.482671	+	0.875802i	$0.339667\pi$
$422$		0			0
$423$	71413.0	+	123691.i	0.399114	+	0.691285i
$424$		0			0
$425$	92931.8			0.514501
$426$		0			0
$427$	228296.	−	395420.i	1.25211	−	2.16872i
$428$		0			0
$429$	−443065.			−2.40743
$430$		0			0
$431$	−298250.	−	172195.i	−1.60556	−	0.926970i	−0.990347	−	0.138609i	$-0.955737\pi$
$431$	−298250.	−	172195.i	−1.60556	−	0.926970i	−0.615212	−	0.788361i	$-0.710930\pi$
$432$		0			0
$433$	−162902.	−	94051.7i	−0.868863	−	0.501639i	−0.00189304	−	0.999998i	$-0.500603\pi$
$433$	−162902.	−	94051.7i	−0.868863	−	0.501639i	−0.866970	+	0.498360i	$0.833936\pi$
$434$		0			0
$435$	119980.	+	207811.i	0.634059	+	1.09822i
$436$		0			0
$437$	169688.	−	125084.i	0.888565	−	0.654998i
$438$		0			0
$439$	−246263.	+	142180.i	−1.27782	+	0.737749i	−0.976447	−	0.215757i	$-0.930778\pi$
$439$	−246263.	+	142180.i	−1.27782	+	0.737749i	−0.301372	+	0.953507i	$0.597445\pi$
$440$		0			0
$441$	394813.	−	683835.i	2.03008	−	3.51621i
$442$		0			0
$443$	159902.	−	276958.i	0.814791	−	1.41126i	−0.0946874	−	0.995507i	$-0.530185\pi$
$443$	159902.	−	276958.i	0.814791	−	1.41126i	0.909478	−	0.415752i	$-0.136482\pi$
$444$		0			0
$445$		−	90051.1i		−	0.454746i
$446$		0			0
$447$	−140928.	−	81364.6i	−0.705312	−	0.407212i
$448$		0			0
$449$			242152.i			1.20114i	0.799571	+	0.600572i	$0.205060\pi$
$449$			242152.i			1.20114i	−0.799571	+	0.600572i	$0.794940\pi$
$450$		0			0
$451$	41000.7	−	23671.8i	0.201576	−	0.116380i
$452$		0			0
$453$	192632.	+	333648.i	0.938710	+	1.62589i
$454$		0			0
$455$		−	228652.i		−	1.10447i
$456$		0			0
$457$	−377100.			−1.80561			−0.902806	−	0.430048i	$-0.858497\pi$
$457$	−377100.			−1.80561			−0.902806	+	0.430048i	$0.858497\pi$
$458$		0			0
$459$	−737685.	+	425902.i	−3.50143	+	2.02155i
$460$		0			0
$461$	183728.	+	318226.i	0.864517	+	1.49739i	0.867526	+	0.497391i	$0.165709\pi$
$461$	183728.	+	318226.i	0.864517	+	1.49739i	−0.00300966	+	0.999995i	$0.500958\pi$
$462$		0			0
$463$	306531.			1.42992			0.714962	−	0.699163i	$-0.246444\pi$
$463$	306531.			1.42992			0.714962	+	0.699163i	$0.246444\pi$
$464$		0			0
$465$	83377.7	−	144414.i	0.385606	−	0.667889i
$466$		0			0
$467$	349891.			1.60435			0.802174	−	0.597090i	$-0.203676\pi$
$467$	349891.			1.60435			0.802174	+	0.597090i	$0.203676\pi$
$468$		0			0
$469$	59197.8	+	34177.8i	0.269128	+	0.155381i
$470$		0			0
$471$	2261.56	+	1305.71i	0.0101945	+	0.00588581i
$472$		0			0
$473$	199037.	+	344742.i	0.889634	+	1.54089i
$474$		0			0
$475$	60803.0	−	44820.4i	0.269487	−	0.198650i
$476$		0			0
$477$	−141043.	+	81431.3i	−0.619891	+	0.357894i
$478$		0			0
$479$	−190061.	+	329196.i	−0.828366	+	1.43477i	0.0709527	+	0.997480i	$0.477396\pi$
$479$	−190061.	+	329196.i	−0.828366	+	1.43477i	−0.899319	+	0.437293i	$0.855937\pi$
$480$		0			0
$481$	95262.8	−	165000.i	0.411750	−	0.713171i
$482$		0			0
$483$		−	779352.i		−	3.34071i
$484$		0			0
$485$	−125806.	−	72634.1i	−0.534832	−	0.308785i
$486$		0			0
$487$			403593.i			1.70171i	0.525402	+	0.850854i	$0.323915\pi$
$487$			403593.i			1.70171i	−0.525402	+	0.850854i	$0.676085\pi$
$488$		0			0
$489$	93829.3	−	54172.4i	0.392393	−	0.226548i
$490$		0			0
$491$	49364.3	+	85501.5i	0.204762	+	0.354659i	0.950057	−	0.312076i	$-0.101024\pi$
$491$	49364.3	+	85501.5i	0.204762	+	0.354659i	−0.745295	+	0.666735i	$0.767691\pi$
$492$		0			0
$493$		−	313933.i		−	1.29164i
$494$		0			0
$495$	761003.			3.10582
$496$		0			0
$497$	140724.	−	81247.2i	0.569713	−	0.328924i
$498$		0			0
$499$	139342.	+	241348.i	0.559605	+	0.969264i	0.997529	+	0.0702519i	$0.0223803\pi$
$499$	139342.	+	241348.i	0.559605	+	0.969264i	−0.437925	+	0.899012i	$0.644286\pi$
$500$		0			0
$501$	−30895.9			−0.123091
$502$		0			0
$503$	100529.	−	174122.i	0.397336	−	0.688205i	−0.596061	−	0.802939i	$-0.703268\pi$
$503$	100529.	−	174122.i	0.397336	−	0.688205i	0.993396	+	0.114734i	$0.0366016\pi$
$504$		0			0
$505$	192319.			0.754118
$506$		0			0
$507$	129636.	+	74845.5i	0.504325	+	0.291172i
$508$		0			0
$509$	−446326.	−	257686.i	−1.72273	−	0.994617i	−0.913172	−	0.407575i	$-0.866375\pi$
$509$	−446326.	−	257686.i	−1.72273	−	0.994617i	−0.809556	−	0.587043i	$-0.800292\pi$
$510$		0			0
$511$	−339895.	−	588715.i	−1.30168	−	2.25457i
$512$		0			0
$513$	−277239.	+	634438.i	−1.05346	+	2.41076i
$514$		0			0
$515$	−186523.	+	107689.i	−0.703264	+	0.406030i
$516$		0			0
$517$	−69241.3	+	119929.i	−0.259050	+	0.448688i
$518$		0			0
$519$	122064.	−	211421.i	0.453161	−	0.784897i
$520$		0			0
$521$		−	168184.i		−	0.619598i	−0.950802	−	0.309799i	$-0.899738\pi$
$521$		−	168184.i		−	0.619598i	0.950802	−	0.309799i	$-0.100262\pi$
$522$		0			0
$523$	−211960.	−	122375.i	−0.774908	−	0.447393i	0.0597146	−	0.998215i	$-0.480981\pi$
$523$	−211960.	−	122375.i	−0.774908	−	0.447393i	−0.834623	+	0.550822i	$0.814314\pi$
$524$		0			0
$525$		−	279259.i		−	1.01318i
$526$		0			0
$527$	−188933.	+	109081.i	−0.680279	+	0.392759i
$528$		0			0
$529$	−30582.3	−	52970.1i	−0.109285	−	0.189286i
$530$		0			0
$531$		−	598004.i		−	2.12087i
$532$		0			0
$533$	34816.1			0.122553
$534$		0			0
$535$	130661.	−	75437.4i	0.456499	−	0.263560i
$536$		0			0
$537$	−303039.	−	524879.i	−1.05087	−	1.82016i
$538$		0			0
$539$	765612.			2.63531
$540$		0			0
$541$	279693.	−	484443.i	0.955626	−	1.65519i	0.222696	−	0.974888i	$-0.428514\pi$
$541$	279693.	−	484443.i	0.955626	−	1.65519i	0.732930	−	0.680304i	$-0.238152\pi$
$542$		0			0
$543$	−311941.			−1.05797
$544$		0			0
$545$	43480.3	+	25103.3i	0.146386	+	0.0845159i
$546$		0			0
$547$	−311215.	−	179680.i	−1.04013	−	0.600517i	−0.120257	−	0.992743i	$-0.538372\pi$
$547$	−311215.	−	179680.i	−1.04013	−	0.600517i	−0.919869	+	0.392225i	$0.871705\pi$
$548$		0			0
$549$	558764.	+	967808.i	1.85389	+	3.21103i
$550$		0			0
$551$	−151408.	−	205399.i	−0.498706	−	0.676541i
$552$		0			0
$553$	−523253.	+	302100.i	−1.71105	+	0.987873i
$554$		0			0
$555$	−231174.	+	400405.i	−0.750504	+	1.29991i
$556$		0			0
$557$	−185546.	+	321376.i	−0.598056	+	1.03586i	0.395052	+	0.918659i	$0.370727\pi$
$557$	−185546.	+	321376.i	−0.598056	+	1.03586i	−0.993108	+	0.117204i	$0.962607\pi$
$558$		0			0
$559$			292740.i			0.936826i
$560$		0			0
$561$	−1.21818e6	−	703317.i	−3.87067	−	2.23473i
$562$		0			0
$563$		−	482764.i		−	1.52306i	−0.648128	−	0.761532i	$-0.724448\pi$
$563$		−	482764.i		−	1.52306i	0.648128	−	0.761532i	$-0.275552\pi$
$564$		0			0
$565$	−191282.	+	110437.i	−0.599208	+	0.345953i
$566$		0			0
$567$	642883.	+	1.11351e6i	1.99970	+	3.46359i
$568$		0			0
$569$			412772.i			1.27493i	0.770480	+	0.637464i	$0.220017\pi$
$569$			412772.i			1.27493i	−0.770480	+	0.637464i	$0.779983\pi$
$570$		0			0
$571$	132966.			0.407820			0.203910	−	0.978990i	$-0.434635\pi$
$571$	132966.			0.407820			0.203910	+	0.978990i	$0.434635\pi$
$572$		0			0
$573$	478571.	−	276303.i	1.45760	−	0.841543i
$574$		0			0
$575$	−61094.9	−	105819.i	−0.184786	−	0.320059i
$576$		0			0
$577$	−64062.9			−0.192422			−0.0962111	−	0.995361i	$-0.530672\pi$
$577$	−64062.9			−0.192422			−0.0962111	+	0.995361i	$0.530672\pi$
$578$		0			0
$579$	−246715.	+	427322.i	−0.735932	+	1.27467i
$580$		0			0
$581$	−133655.			−0.395945
$582$		0			0
$583$	−136754.	−	78954.9i	−0.402349	−	0.232296i
$584$		0			0
$585$	484659.	+	279818.i	1.41620	+	0.817643i
$586$		0			0
$587$	181684.	+	314686.i	0.527279	+	0.913274i	0.999495	+	0.0317912i	$0.0101212\pi$
$587$	181684.	+	314686.i	0.527279	+	0.913274i	−0.472215	+	0.881483i	$0.656546\pi$
$588$		0			0
$589$	−71005.5	+	162490.i	−0.204673	+	0.468378i
$590$		0			0
$591$	−144408.	+	83373.9i	−0.413443	+	0.238702i
$592$		0			0
$593$	321097.	−	556157.i	0.913118	−	1.58157i	0.103485	−	0.994631i	$-0.467001\pi$
$593$	321097.	−	556157.i	0.913118	−	1.58157i	0.809633	−	0.586936i	$-0.199666\pi$
$594$		0			0
$595$	362960.	−	628665.i	1.02524	−	1.77577i
$596$		0			0
$597$		−	500304.i		−	1.40374i
$598$		0			0
$599$	138783.	+	80126.6i	0.386798	+	0.223318i	0.680772	−	0.732496i	$-0.261645\pi$
$599$	138783.	+	80126.6i	0.386798	+	0.223318i	−0.293974	+	0.955813i	$0.594978\pi$
$600$		0			0
$601$			136738.i			0.378564i	0.981923	+	0.189282i	$0.0606160\pi$
$601$			136738.i			0.378564i	−0.981923	+	0.189282i	$0.939384\pi$
$602$		0			0
$603$	−144889.	+	83651.7i	−0.398475	+	0.230059i
$604$		0			0
$605$	219665.	+	380470.i	0.600135	+	1.03946i
$606$		0			0
$607$		−	490140.i		−	1.33028i	−0.746719	−	0.665140i	$-0.768372\pi$
$607$		−	490140.i		−	1.33028i	0.746719	−	0.665140i	$-0.231628\pi$
$608$		0			0
$609$	−943363.			−2.54357
$610$		0			0
$611$	−88195.2	+	50919.5i	−0.236245	+	0.136396i
$612$		0			0
$613$	−141164.	−	244504.i	−0.375668	−	0.650676i	0.614759	−	0.788715i	$-0.289253\pi$
$613$	−141164.	−	244504.i	−0.375668	−	0.650676i	−0.990427	+	0.138039i	$0.955920\pi$
$614$		0			0
$615$	−84488.1			−0.223380
$616$		0			0
$617$	−92331.6	+	159923.i	−0.242538	+	0.420088i	−0.961437	−	0.275027i	$-0.911313\pi$
$617$	−92331.6	+	159923.i	−0.242538	+	0.420088i	0.718898	+	0.695115i	$0.244647\pi$
$618$		0			0
$619$	−341765.			−0.891962			−0.445981	−	0.895042i	$-0.647145\pi$
$619$	−341765.			−0.891962			−0.445981	+	0.895042i	$0.647145\pi$
$620$		0			0
$621$	969932.	+	559990.i	2.51512	+	1.45210i
$622$		0			0
$623$	306592.	+	177011.i	0.789922	+	0.456062i
$624$		0			0
$625$	108032.	+	187117.i	0.276562	+	0.479019i
$626$		0			0
$627$	−1.13623e6	+	127358.i	−2.89023	+	0.323959i
$628$		0			0
$629$	523839.	−	302438.i	1.32403	−	0.764426i
$630$		0			0
$631$	375876.	−	651037.i	0.944031	−	1.63511i	0.186351	−	0.982483i	$-0.440334\pi$
$631$	375876.	−	651037.i	0.944031	−	1.63511i	0.757680	−	0.652626i	$-0.226333\pi$
$632$		0			0
$633$	−28066.6	+	48612.8i	−0.0700459	+	0.121323i
$634$		0			0
$635$			243878.i			0.604820i
$636$		0			0
$637$	487594.	+	281513.i	1.20165	+	0.693776i
$638$		0			0
$639$			397712.i			0.974017i
$640$		0			0
$641$	−80029.8	+	46205.2i	−0.194776	+	0.112454i	−0.594217	−	0.804305i	$-0.702538\pi$
$641$	−80029.8	+	46205.2i	−0.194776	+	0.112454i	0.399440	+	0.916759i	$0.369204\pi$
$642$		0			0
$643$	−72545.3	−	125652.i	−0.175464	−	0.303912i	0.764858	−	0.644199i	$-0.222809\pi$
$643$	−72545.3	−	125652.i	−0.175464	−	0.303912i	−0.940322	+	0.340287i	$0.889476\pi$
$644$		0			0
$645$		−	710392.i		−	1.70757i
$646$		0			0
$647$	−436812.			−1.04348			−0.521742	−	0.853103i	$-0.674718\pi$
$647$	−436812.			−1.04348			−0.521742	+	0.853103i	$0.674718\pi$
$648$		0			0
$649$	502137.	−	289909.i	1.19216	−	0.688292i
$650$		0			0
$651$	327786.	+	567742.i	0.773443	+	1.33964i
$652$		0			0
$653$	−159196.			−0.373341			−0.186671	−	0.982423i	$-0.559770\pi$
$653$	−159196.			−0.373341			−0.186671	+	0.982423i	$0.559770\pi$
$654$		0			0
$655$	86749.2	−	150254.i	0.202201	−	0.350222i
$656$		0			0
$657$	1.66381e6			3.85455
$658$		0			0
$659$	467947.	+	270169.i	1.07752	+	0.622107i	0.930227	−	0.366986i	$-0.119610\pi$
$659$	467947.	+	270169.i	1.07752	+	0.622107i	0.147294	+	0.989093i	$0.452944\pi$
$660$		0			0
$661$	424337.	+	244991.i	0.971197	+	0.560721i	0.899601	−	0.436713i	$-0.143857\pi$
$661$	424337.	+	244991.i	0.971197	+	0.560721i	0.0715964	+	0.997434i	$0.477191\pi$
$662$		0			0
$663$	−517214.	−	895841.i	−1.17664	−	2.03800i
$664$		0			0
$665$	−65725.3	−	586374.i	−0.148624	−	1.32596i
$666$		0			0
$667$	−357468.	+	206384.i	−0.803500	+	0.463901i
$668$		0			0
$669$	706027.	−	1.22287e6i	1.57750	−	2.73231i
$670$		0			0
$671$	−541772.	+	938376.i	−1.20329	+	2.08416i
$672$		0			0
$673$			360606.i			0.796165i	0.917350	+	0.398082i	$0.130324\pi$
$673$			360606.i			0.796165i	−0.917350	+	0.398082i	$0.869676\pi$
$674$		0			0
$675$	347548.	+	200657.i	0.762794	+	0.440399i
$676$		0			0
$677$		−	382851.i		−	0.835320i	−0.908603	−	0.417660i	$-0.862850\pi$
$677$		−	382851.i		−	0.835320i	0.908603	−	0.417660i	$-0.137150\pi$
$678$		0			0
$679$	494586.	−	285549.i	1.07276	−	0.619357i
$680$		0			0
$681$	−559331.	−	968790.i	−1.20608	−	2.08899i
$682$		0			0
$683$			356692.i			0.764631i	0.924032	+	0.382315i	$0.124873\pi$
$683$			356692.i			0.764631i	−0.924032	+	0.382315i	$0.875127\pi$
$684$		0			0
$685$	−432543.			−0.921824
$686$		0			0
$687$	−40733.2	+	23517.3i	−0.0863049	+	0.0498282i
$688$		0			0
$689$	−58062.8	−	100568.i	−0.122309	−	0.211846i
$690$		0			0
$691$	12388.6			0.0259458			0.0129729	−	0.999916i	$-0.495870\pi$
$691$	12388.6			0.0259458			0.0129729	+	0.999916i	$0.495870\pi$
$692$		0			0
$693$	−1.49588e6	+	2.59094e6i	−3.11480	+	5.39499i
$694$		0			0
$695$	142709.			0.295448
$696$		0			0
$697$	95724.7	+	55266.7i	0.197042	+	0.113762i
$698$		0			0
$699$	−1.07839e6	−	622606.i	−2.20709	−	1.27426i
$700$		0			0
$701$	221308.	+	383316.i	0.450361	+	0.780048i	0.998408	−	0.0563992i	$-0.0179619\pi$
$701$	221308.	+	383316.i	0.450361	+	0.780048i	−0.548047	+	0.836447i	$0.684629\pi$
$702$		0			0
$703$	196871.	−	450522.i	0.398355	−	0.911603i
$704$		0			0
$705$	214023.	−	123566.i	0.430608	−	0.248612i
$706$		0			0
$707$	−378035.	+	654777.i	−0.756299	+	1.30995i
$708$		0			0
$709$	−28163.6	+	48780.8i	−0.0560268	+	0.0970413i	−0.892679	−	0.450694i	$-0.851177\pi$
$709$	−28163.6	+	48780.8i	−0.0560268	+	0.0970413i	0.836652	+	0.547735i	$0.184510\pi$
$710$		0			0
$711$		−	1.47881e6i		−	2.92531i
$712$		0			0
$713$	248416.	+	143423.i	0.488652	+	0.282123i
$714$		0			0
$715$			542617.i			1.06141i
$716$		0			0
$717$	−962514.	+	555708.i	−1.87227	+	1.08096i
$718$		0			0
$719$	336623.	+	583048.i	0.651158	+	1.12784i	0.982842	+	0.184448i	$0.0590496\pi$
$719$	336623.	+	583048.i	0.651158	+	1.12784i	−0.331685	+	0.943390i	$0.607617\pi$
$720$		0			0
$721$		−	846726.i		−	1.62882i
$722$		0			0
$723$	1.54919e6			2.96365
$724$		0			0
$725$	−128089.	+	73952.1i	−0.243688	+	0.140694i
$726$		0			0
$727$	−224483.	−	388817.i	−0.424732	−	0.735658i	0.571663	−	0.820488i	$-0.306298\pi$
$727$	−224483.	−	388817.i	−0.424732	−	0.735658i	−0.996395	+	0.0848305i	$0.972965\pi$
$728$		0			0
$729$	−560491.			−1.05466
$730$		0			0
$731$	−464693.	+	804872.i	−0.869624	+	1.50623i
$732$		0			0
$733$	456840.			0.850269			0.425134	−	0.905130i	$-0.360227\pi$
$733$	456840.			0.850269			0.425134	+	0.905130i	$0.360227\pi$
$734$		0			0
$735$	−1.18324e6	−	683146.i	−2.19028	−	1.26456i
$736$		0			0
$737$	−140483.	−	81107.8i	−0.258636	−	0.149323i
$738$		0			0
$739$	350426.	+	606956.i	0.641664	+	1.11140i	0.985061	+	0.172205i	$0.0550891\pi$
$739$	350426.	+	606956.i	0.641664	+	1.11140i	−0.343397	+	0.939190i	$0.611578\pi$
$740$		0			0
$741$	−770459.	−	336678.i	−1.40318	−	0.613166i
$742$		0			0
$743$	184519.	−	106532.i	0.334244	−	0.192976i	−0.323480	−	0.946235i	$-0.604853\pi$
$743$	184519.	−	106532.i	0.334244	−	0.192976i	0.657724	+	0.753259i	$0.271519\pi$
$744$		0			0
$745$	−99646.4	+	172593.i	−0.179535	+	0.310964i
$746$		0			0
$747$	163564.	−	283301.i	0.293120	−	0.507699i
$748$		0			0
$749$			593140.i			1.05729i
$750$		0			0
$751$	−678803.	−	391907.i	−1.20355	−	0.694869i	−0.242207	−	0.970225i	$-0.577871\pi$
$751$	−678803.	−	391907.i	−1.20355	−	0.694869i	−0.961343	+	0.275355i	$0.911205\pi$
$752$		0			0
$753$			528066.i			0.931319i
$754$		0			0
$755$	408615.	−	235914.i	0.716837	−	0.413866i
$756$		0			0
$757$	70481.2	+	122077.i	0.122993	+	0.213031i	0.920947	−	0.389688i	$-0.127417\pi$
$757$	70481.2	+	122077.i	0.122993	+	0.213031i	−0.797953	+	0.602719i	$0.794084\pi$
$758$		0			0
$759$			1.84949e6i			3.21047i
$760$		0			0
$761$	−274938.			−0.474751			−0.237376	−	0.971418i	$-0.576287\pi$
$761$	−274938.			−0.474751			−0.237376	+	0.971418i	$0.576287\pi$
$762$		0			0
$763$	−170936.	+	98689.8i	−0.293619	+	0.169521i
$764$		0			0
$765$	888360.	+	1.53868e6i	1.51798	+	2.62922i
$766$		0			0
$767$	426394.			0.724804
$768$		0			0
$769$	430243.	−	745203.i	0.727547	−	1.26015i	−0.230369	−	0.973103i	$-0.573993\pi$
$769$	430243.	−	745203.i	0.727547	−	1.26015i	0.957917	−	0.287046i	$-0.0926732\pi$
$770$		0			0
$771$	1.70863e6			2.87435
$772$		0			0
$773$	−585004.	−	337752.i	−0.979038	−	0.565248i	−0.0770584	−	0.997027i	$-0.524553\pi$
$773$	−585004.	−	337752.i	−0.979038	−	0.565248i	−0.901980	+	0.431779i	$0.857886\pi$
$774$		0			0
$775$	89012.7	+	51391.5i	0.148200	+	0.0855634i
$776$		0			0
$777$	−908823.	−	1.57413e6i	−1.50535	−	2.60734i
$778$		0			0
$779$	89285.1	−	10007.8i	0.147131	−	0.0164916i
$780$		0			0
$781$	−333954.	+	192809.i	−0.547501	+	0.316100i
$782$		0			0
$783$	677838.	−	1.17405e6i	1.10561	−	1.91498i
$784$		0			0
$785$	1599.09	−	2769.71i	0.00259498	−	0.00449464i
$786$		0			0
$787$			625269.i			1.00953i	0.863258	+	0.504763i	$0.168420\pi$
$787$			625269.i			1.00953i	−0.863258	+	0.504763i	$0.831580\pi$
$788$		0			0
$789$	40232.5	+	23228.3i	0.0646284	+	0.0373132i
$790$		0			0
$791$		−	868329.i		−	1.38781i
$792$		0			0
$793$	−690075.	+	398415.i	−1.09736	+	0.633562i
$794$		0			0
$795$	140901.	+	244048.i	0.222936	+	0.386136i
$796$		0			0
$797$			445179.i			0.700839i	0.936593	+	0.350420i	$0.113961\pi$
$797$			445179.i			0.700839i	−0.936593	+	0.350420i	$0.886039\pi$
$798$		0			0
$799$	−323317.			−0.506448
$800$		0			0
$801$	−750396.	+	433241.i	−1.16957	+	0.675250i
$802$		0			0
$803$	806608.	+	1.39709e6i	1.25093	+	2.16667i
$804$		0			0
$805$	−954463.			−1.47288
$806$		0			0
$807$	−445934.	+	772381.i	−0.684737	+	1.18600i
$808$		0			0
$809$	814331.			1.24424			0.622120	−	0.782922i	$-0.286272\pi$
$809$	814331.			1.24424			0.622120	+	0.782922i	$0.286272\pi$
$810$		0			0
$811$	−187546.	−	108280.i	−0.285146	−	0.164629i	0.350605	−	0.936523i	$-0.385976\pi$
$811$	−187546.	−	108280.i	−0.285146	−	0.164629i	−0.635751	+	0.771895i	$0.719309\pi$
$812$		0			0
$813$	1.01689e6	+	587102.i	1.53848	+	0.888244i
$814$		0			0
$815$	−66344.3	−	114912.i	−0.0998823	−	0.173001i
$816$		0			0
$817$	84147.3	+	750727.i	0.126065	+	1.12470i
$818$		0			0
$819$	−1.90536e6	+	1.10006e6i	−2.84059	+	1.64002i
$820$		0			0
$821$	329918.	−	571435.i	0.489463	−	0.847775i	−0.510464	−	0.859899i	$-0.670526\pi$
$821$	329918.	−	571435.i	0.489463	−	0.847775i	0.999926	+	0.0121247i	$0.00385949\pi$
$822$		0			0
$823$	−258797.	+	448250.i	−0.382085	+	0.661790i	−0.991360	−	0.131169i	$-0.958127\pi$
$823$	−258797.	+	448250.i	−0.382085	+	0.661790i	0.609275	+	0.792959i	$0.291460\pi$
$824$		0			0
$825$			662712.i			0.973682i
$826$		0			0
$827$	−629102.	−	363212.i	−0.919835	−	0.531067i	−0.0362527	−	0.999343i	$-0.511542\pi$
$827$	−629102.	−	363212.i	−0.919835	−	0.531067i	−0.883582	+	0.468276i	$0.844875\pi$
$828$		0			0
$829$			1.02389e6i			1.48986i	0.667144	+	0.744929i	$0.267516\pi$
$829$			1.02389e6i			1.48986i	−0.667144	+	0.744929i	$0.732484\pi$
$830$		0			0
$831$	−443916.	+	256295.i	−0.642834	+	0.371140i
$832$		0			0
$833$	893741.	+	1.54800e6i	1.28802	+	2.23091i
$834$		0			0
$835$			37837.9i			0.0542692i
$836$		0			0
$837$	−942101.			−1.34476
$838$		0			0
$839$	349973.	−	202057.i	0.497177	−	0.287045i	−0.230370	−	0.973103i	$-0.573994\pi$
$839$	349973.	−	202057.i	0.497177	−	0.287045i	0.727547	+	0.686058i	$0.240660\pi$
$840$		0			0
$841$	−103823.	−	179827.i	−0.146792	−	0.254251i
$842$		0			0
$843$	−654730.			−0.921313
$844$		0			0
$845$	91662.5	−	158764.i	0.128374	−	0.222351i
$846$		0			0
$847$	−1.72715e6			−2.40749
$848$		0			0
$849$	−1.33695e6	−	771888.i	−1.85481	−	1.07088i
$850$		0			0
$851$	−688760.	−	397656.i	−0.951062	−	0.549096i
$852$		0			0
$853$	−467080.	−	809006.i	−0.641938	−	1.11187i	−0.985000	−	0.172556i	$-0.944797\pi$
$853$	−467080.	−	809006.i	−0.641938	−	1.11187i	0.343062	−	0.939313i	$-0.388536\pi$
$854$		0			0
$855$	1.32333e6	+	578274.i	1.81024	+	0.791045i
$856$		0			0
$857$	−531230.	+	306706.i	−0.723305	+	0.417600i	−0.815968	−	0.578097i	$-0.803795\pi$
$857$	−531230.	+	306706.i	−0.723305	+	0.417600i	0.0926632	+	0.995698i	$0.470462\pi$
$858$		0			0
$859$	403471.	−	698833.i	0.546797	−	0.947081i	−0.451694	−	0.892173i	$-0.649180\pi$
$859$	403471.	−	698833.i	0.546797	−	0.947081i	0.998491	−	0.0549079i	$-0.0174865\pi$
$860$		0			0
$861$	166076.	−	287651.i	0.224027	−	0.388026i
$862$		0			0
$863$		−	464046.i		−	0.623073i	−0.950234	−	0.311537i	$-0.899156\pi$
$863$		−	464046.i		−	0.623073i	0.950234	−	0.311537i	$-0.100844\pi$
$864$		0			0
$865$	−258924.	−	149490.i	−0.346052	−	0.199793i
$866$		0			0
$867$		−	1.89352e6i		−	2.51903i
$868$		0			0
$869$	1.24174e6	−	716918.i	1.64434	−	0.949358i
$870$		0			0
$871$	−59646.1	−	103310.i	−0.0786222	−	0.136178i
$872$		0			0
$873$			1.39779e6i			1.83406i
$874$		0			0
$875$	−1.36355e6			−1.78097
$876$		0			0
$877$	994485.	−	574166.i	1.29300	−	0.746515i	0.313817	−	0.949484i	$-0.398392\pi$
$877$	994485.	−	574166.i	1.29300	−	0.746515i	0.979185	+	0.202969i	$0.0650590\pi$
$878$		0			0
$879$	268281.	+	464677.i	0.347226	+	0.601414i
$880$		0			0
$881$	403904.			0.520387			0.260194	−	0.965556i	$-0.416214\pi$
$881$	403904.			0.520387			0.260194	+	0.965556i	$0.416214\pi$
$882$		0			0
$883$	439905.	−	761938.i	0.564206	−	0.977234i	−0.432917	−	0.901434i	$-0.642516\pi$
$883$	439905.	−	761938.i	0.564206	−	0.977234i	0.997123	−	0.0757999i	$-0.0241510\pi$
$884$		0			0
$885$	−1.03473e6			−1.32111
$886$		0			0
$887$	1.13862e6	+	657385.i	1.44722	+	0.835551i	0.998315	−	0.0580305i	$-0.0184821\pi$
$887$	1.13862e6	+	657385.i	1.44722	+	0.835551i	0.448901	+	0.893581i	$0.351815\pi$
$888$		0			0
$889$	−830318.	−	479384.i	−1.05061	−	0.606569i
$890$		0			0
$891$	−1.52563e6	−	2.64247e6i	−1.92174	−	3.32855i
$892$		0			0
$893$	−211538.	+	155934.i	−0.265269	+	0.195541i
$894$		0			0
$895$	−642813.	+	371128.i	−0.802488	+	0.463317i
$896$		0			0
$897$	−680050.	+	1.17788e6i	−0.845193	+	1.46392i
$898$		0			0
$899$	173606.	−	300694.i	0.214805	−	0.372053i
$900$		0			0
$901$		−	368673.i		−	0.454143i
$902$		0			0
$903$	2.41863e6	+	1.39640e6i	2.96616	+	1.71251i
$904$		0			0
$905$			382031.i			0.466446i
$906$		0			0
$907$	962112.	−	555475.i	1.16953	−	0.675228i	0.215960	−	0.976402i	$-0.430712\pi$
$907$	962112.	−	555475.i	1.16953	−	0.675228i	0.953569	+	0.301174i	$0.0973786\pi$
$908$		0			0
$909$	−925258.	−	1.60259e6i	−1.11979	−	1.93953i
$910$		0			0
$911$			374866.i			0.451689i	0.974163	+	0.225844i	$0.0725141\pi$
$911$			374866.i			0.451689i	−0.974163	+	0.225844i	$0.927486\pi$
$912$		0			0
$913$	317179.			0.380508
$914$		0			0
$915$	1.67460e6	−	966832.i	2.00018	−	1.15481i
$916$		0			0
$917$	341041.	+	590700.i	0.405572	+	0.702470i
$918$		0			0
$919$	−122774.			−0.145370			−0.0726851	−	0.997355i	$-0.523157\pi$
$919$	−122774.			−0.145370			−0.0726851	+	0.997355i	$0.523157\pi$
$920$		0			0
$921$	1.39432e6	−	2.41503e6i	1.64378	−	2.84710i
$922$		0			0
$923$	−283580.			−0.332868
$924$		0			0
$925$	−246798.	−	142489.i	−0.288442	−	0.166532i
$926$		0			0
$927$	1.79475e6	+	1.03620e6i	2.08855	+	1.20582i
$928$		0			0
$929$	−501460.	−	868554.i	−0.581038	−	1.00639i	−0.995357	−	0.0962560i	$-0.969313\pi$
$929$	−501460.	−	868554.i	−0.581038	−	1.00639i	0.414318	−	0.910132i	$-0.364020\pi$
$930$		0			0
$931$	1.33135e6	+	581776.i	1.53600	+	0.671207i
$932$		0			0
$933$	1.72268e6	−	994589.i	1.97898	−	1.14256i
$934$		0			0
$935$	−861344.	+	1.49189e6i	−0.985266	+	1.70653i
$936$		0			0
$937$	−198281.	+	343432.i	−0.225840	+	0.391166i	−0.956571	−	0.291499i	$-0.905846\pi$
$937$	−198281.	+	343432.i	−0.225840	+	0.391166i	0.730731	+	0.682665i	$0.239179\pi$
$938$		0			0
$939$		−	1.43387e6i		−	1.62621i
$940$		0			0
$941$	−613338.	−	354111.i	−0.692660	−	0.399908i	0.111947	−	0.993714i	$-0.464291\pi$
$941$	−613338.	−	354111.i	−0.692660	−	0.399908i	−0.804608	+	0.593806i	$0.797624\pi$
$942$		0			0
$943$		−	145333.i		−	0.163433i
$944$		0			0
$945$	2.71481e6	−	1.56739e6i	3.04001	−	1.75515i
$946$		0			0
$947$	529694.	+	917457.i	0.590643	+	1.02302i	0.994146	+	0.108045i	$0.0344592\pi$
$947$	529694.	+	917457.i	0.590643	+	1.02302i	−0.403503	+	0.914978i	$0.632207\pi$
$948$		0			0
$949$			1.18635e6i			1.31728i
$950$		0			0
$951$	−194489.			−0.215048
$952$		0			0
$953$	638361.	−	368558.i	0.702879	−	0.405807i	−0.105540	−	0.994415i	$-0.533657\pi$
$953$	638361.	−	368558.i	0.702879	−	0.405807i	0.808419	+	0.588608i	$0.200324\pi$
$954$		0			0
$955$	−338385.	−	586100.i	−0.371026	−	0.642636i
$956$		0			0
$957$	2.23871e6			2.44441
$958$		0			0
$959$	850236.	−	1.47265e6i	0.924490	−	1.60126i
$960$		0			0
$961$	682234.			0.738731
$962$		0			0
$963$	−1.25724e6	−	725867.i	−1.35571	−	0.782717i
$964$		0			0
$965$	523337.	+	302148.i	0.561987	+	0.324463i
$966$		0			0
$967$	−728564.	−	1.26191e6i	−0.779138	−	1.34951i	−0.932439	−	0.361327i	$-0.882324\pi$
$967$	−728564.	−	1.26191e6i	−0.779138	−	1.34951i	0.153301	−	0.988180i	$-0.451010\pi$
$968$		0			0
$969$	−1.58389e6	−	2.14869e6i	−1.68686	−	2.28837i
$970$		0			0
$971$	1.43261e6	−	827117.i	1.51946	−	0.877261i	0.519723	−	0.854335i	$-0.326035\pi$
$971$	1.43261e6	−	827117.i	1.51946	−	0.877261i	0.999737	−	0.0229255i	$-0.00729806\pi$
$972$		0			0
$973$	−280519.	+	485872.i	−0.296303	+	0.513212i
$974$		0			0
$975$	−243677.	+	422060.i	−0.256333	+	0.443982i
$976$		0			0
$977$		−	401114.i		−	0.420222i	−0.977677	−	0.210111i	$-0.932617\pi$
$977$		−	401114.i		−	0.420222i	0.977677	−	0.210111i	$-0.0673826\pi$
$978$		0			0
$979$	−727576.	−	420066.i	−0.759124	−	0.438281i
$980$		0			0
$981$		−	483095.i		−	0.501989i
$982$		0			0
$983$	−700254.	+	404292.i	−0.724684	+	0.418396i	−0.816474	−	0.577382i	$-0.804074\pi$
$983$	−700254.	+	404292.i	−0.724684	+	0.418396i	0.0917903	+	0.995778i	$0.470741\pi$
$984$		0			0
$985$	102107.	+	176855.i	0.105241	+	0.182282i
$986$		0			0
$987$			971562.i			0.997324i
$988$		0			0
$989$	1.22199e6			1.24932
$990$		0			0
$991$	−657314.	+	379501.i	−0.669308	+	0.386425i	−0.795814	−	0.605541i	$-0.792957\pi$
$991$	−657314.	+	379501.i	−0.669308	+	0.386425i	0.126507	+	0.991966i	$0.459624\pi$
$992$		0			0
$993$	461236.	+	798884.i	0.467762	+	0.810187i
$994$		0			0
$995$	−612717.			−0.618890
$996$		0			0
$997$	−802426.	+	1.38984e6i	−0.807262	+	1.39822i	0.107491	+	0.994206i	$0.465718\pi$
$997$	−802426.	+	1.38984e6i	−0.807262	+	1.39822i	−0.914753	+	0.404013i	$0.867615\pi$
$998$		0			0
$999$	2.61208e6			2.61731

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.d.145.1		40
4.3	odd	2		152.5.n.a.145.20	yes	40
19.8	odd	6	inner	304.5.r.d.65.1		40
76.27	even	6		152.5.n.a.65.20	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.5.n.a.65.20	✓	40	76.27	even	6
152.5.n.a.145.20	yes	40	4.3	odd	2
304.5.r.d.65.1		40	19.8	odd	6	inner
304.5.r.d.145.1		40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	304.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-14.4186 + 8.32460i) q^{3} +(10.1950 + 17.6583i) q^{5} -80.1603 q^{7} +(98.0979 - 169.911i) q^{9} +O(q^{10})\)	\(q+(-14.4186 + 8.32460i) q^{3} +(10.1950 + 17.6583i) q^{5} -80.1603 q^{7} +(98.0979 - 169.911i) q^{9} +190.229 q^{11} +(121.151 + 69.9466i) q^{13} +(-293.997 - 169.739i) q^{15} +(222.065 + 384.628i) q^{17} +(330.795 + 144.552i) q^{19} +(1155.80 - 667.303i) q^{21} +(291.978 - 505.721i) q^{23} +(104.622 - 181.211i) q^{25} +1917.92i q^{27} +(-612.149 - 353.424i) q^{29} +491.210i q^{31} +(-2742.85 + 1583.58i) q^{33} +(-817.238 - 1415.50i) q^{35} -1361.94i q^{37} -2329.11 q^{39} +(215.533 - 124.438i) q^{41} +(1046.30 + 1812.24i) q^{43} +4000.45 q^{45} +(-363.989 + 630.447i) q^{47} +4024.68 q^{49} +(-6403.75 - 3697.21i) q^{51} +(-718.890 - 415.051i) q^{53} +(1939.40 + 3359.13i) q^{55} +(-5972.96 + 669.495i) q^{57} +(2639.64 - 1524.00i) q^{59} +(-2847.99 + 4932.87i) q^{61} +(-7863.56 + 13620.1i) q^{63} +2852.43i q^{65} +(-738.492 - 426.368i) q^{67} +9722.41i q^{69} +(-1755.53 + 1013.56i) q^{71} +(4240.19 + 7344.22i) q^{73} +3483.75i q^{75} -15248.9 q^{77} +(6527.58 - 3768.70i) q^{79} +(-8019.96 - 13891.0i) q^{81} +1667.35 q^{83} +(-4527.93 + 7842.60i) q^{85} +11768.5 q^{87} +(-3824.73 - 2208.21i) q^{89} +(-9711.51 - 5606.94i) q^{91} +(-4089.13 - 7082.58i) q^{93} +(819.923 + 7315.01i) q^{95} +(-6169.95 + 3562.22i) q^{97} +(18661.1 - 32322.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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