LMFDB - Embedded newform 950.2.f.d.493.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(493,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("950.493");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.13
Character	$\chi$	$=$	950.493
Dual form			950.2.f.d.607.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.267657 - 0.267657i) q^{3} +1.00000i q^{4} +0.378524 q^{6} +(-0.709827 + 0.709827i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.85672i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.267657 - 0.267657i) q^{3} +1.00000i q^{4} +0.378524 q^{6} +(-0.709827 + 0.709827i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.85672i q^{9} -5.59543 q^{11} +(0.267657 + 0.267657i) q^{12} +(-2.99477 + 2.99477i) q^{13} -1.00385 q^{14} -1.00000 q^{16} +(2.20326 - 2.20326i) q^{17} +(-2.02001 + 2.02001i) q^{18} +(3.84194 + 2.05900i) q^{19} +0.379980i q^{21} +(-3.95657 - 3.95657i) q^{22} +(-5.89692 - 5.89692i) q^{23} +0.378524i q^{24} -4.23524 q^{26} +(1.56759 + 1.56759i) q^{27} +(-0.709827 - 0.709827i) q^{28} -9.34335 q^{29} +3.46410i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.49766 + 1.49766i) q^{33} +3.11588 q^{34} -2.85672 q^{36} +(6.61320 + 6.61320i) q^{37} +(1.26073 + 4.17260i) q^{38} +1.60314i q^{39} +9.14029i q^{41} +(-0.268687 + 0.268687i) q^{42} +(0.927191 + 0.927191i) q^{43} -5.59543i q^{44} -8.33950i q^{46} +(4.20858 - 4.20858i) q^{47} +(-0.267657 + 0.267657i) q^{48} +5.99229i q^{49} -1.17943i q^{51} +(-2.99477 - 2.99477i) q^{52} +(2.44104 - 2.44104i) q^{53} +2.21691i q^{54} -1.00385i q^{56} +(1.57943 - 0.477216i) q^{57} +(-6.60675 - 6.60675i) q^{58} +12.5001 q^{59} -2.00000 q^{61} +(-2.44949 + 2.44949i) q^{62} +(-2.02778 - 2.02778i) q^{63} -1.00000i q^{64} -2.11801 q^{66} +(-5.72134 - 5.72134i) q^{67} +(2.20326 + 2.20326i) q^{68} -3.15670 q^{69} +13.9114i q^{71} +(-2.02001 - 2.02001i) q^{72} +(-4.33274 - 4.33274i) q^{73} +9.35248i q^{74} +(-2.05900 + 3.84194i) q^{76} +(3.97179 - 3.97179i) q^{77} +(-1.13359 + 1.13359i) q^{78} -5.47180 q^{79} -7.73101 q^{81} +(-6.46316 + 6.46316i) q^{82} +(-5.53597 - 5.53597i) q^{83} -0.379980 q^{84} +1.31125i q^{86} +(-2.50081 + 2.50081i) q^{87} +(3.95657 - 3.95657i) q^{88} +8.99513 q^{89} -4.25154i q^{91} +(5.89692 - 5.89692i) q^{92} +(0.927191 + 0.927191i) q^{93} +5.95183 q^{94} -0.378524 q^{96} +(9.16155 + 9.16155i) q^{97} +(-4.23719 + 4.23719i) q^{98} -15.9846i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{6}+O(q^{10}) $ 32 * q - 8 * q^6	$ 32 q - 8 q^{6} - 24 q^{11} - 32 q^{16} + 32 q^{26} + 56 q^{36} - 64 q^{61} + 72 q^{66} + 4 q^{76} - 32 q^{81} + 8 q^{96}+O(q^{100}) $ 32 * q - 8 * q^6 - 24 * q^11 - 32 * q^16 + 32 * q^26 + 56 * q^36 - 64 * q^61 + 72 * q^66 + 4 * q^76 - 32 * q^81 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.267657	−	0.267657i	0.154532	−	0.154532i	−0.625607	−	0.780139i	$-0.715149\pi$
$3$	0.267657	−	0.267657i	0.154532	−	0.154532i	0.780139	+	0.625607i	$0.215149\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	0.378524			0.154532
$7$	−0.709827	+	0.709827i	−0.268289	+	0.268289i	−0.828411	−	0.560121i	$-0.810755\pi$
$7$	−0.709827	+	0.709827i	−0.268289	+	0.268289i	0.560121	+	0.828411i	$0.310755\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			2.85672i			0.952240i
$10$		0			0
$11$	−5.59543			−1.68709			−0.843543	−	0.537061i	$-0.819534\pi$
$11$	−5.59543			−1.68709			−0.843543	+	0.537061i	$0.819534\pi$
$12$	0.267657	+	0.267657i	0.0772659	+	0.0772659i
$13$	−2.99477	+	2.99477i	−0.830600	+	0.830600i	−0.987599	−	0.156999i	$-0.949818\pi$
$13$	−2.99477	+	2.99477i	−0.830600	+	0.830600i	0.156999	+	0.987599i	$0.449818\pi$
$14$	−1.00385			−0.268289
$15$		0			0
$16$	−1.00000			−0.250000
$17$	2.20326	−	2.20326i	0.534369	−	0.534369i	−0.387501	−	0.921869i	$-0.626662\pi$
$17$	2.20326	−	2.20326i	0.534369	−	0.534369i	0.921869	+	0.387501i	$0.126662\pi$
$18$	−2.02001	+	2.02001i	−0.476120	+	0.476120i
$19$	3.84194	+	2.05900i	0.881402	+	0.472368i
$19$	3.84194	+	2.05900i	0.881402	+	0.472368i
$20$		0			0
$21$			0.379980i			0.0829185i
$22$	−3.95657	−	3.95657i	−0.843543	−	0.843543i
$23$	−5.89692	−	5.89692i	−1.22959	−	1.22959i	−0.964118	−	0.265475i	$-0.914471\pi$
$23$	−5.89692	−	5.89692i	−1.22959	−	1.22959i	−0.265475	−	0.964118i	$-0.585529\pi$
$24$			0.378524i			0.0772659i
$25$		0			0
$26$	−4.23524			−0.830600
$27$	1.56759	+	1.56759i	0.301683	+	0.301683i
$28$	−0.709827	−	0.709827i	−0.134145	−	0.134145i
$29$	−9.34335			−1.73502			−0.867508	−	0.497423i	$-0.834280\pi$
$29$	−9.34335			−1.73502			−0.867508	+	0.497423i	$0.834280\pi$
$30$		0			0
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−1.49766	+	1.49766i	−0.260709	+	0.260709i
$34$	3.11588			0.534369
$35$		0			0
$36$	−2.85672			−0.476120
$37$	6.61320	+	6.61320i	1.08720	+	1.08720i	0.995815	+	0.0913885i	$0.0291305\pi$
$37$	6.61320	+	6.61320i	1.08720	+	1.08720i	0.0913885	+	0.995815i	$0.470869\pi$
$38$	1.26073	+	4.17260i	0.204517	+	0.676885i
$39$			1.60314i			0.256708i
$40$		0			0
$41$			9.14029i			1.42747i	0.700414	+	0.713737i	$0.252999\pi$
$41$			9.14029i			1.42747i	−0.700414	+	0.713737i	$0.747001\pi$
$42$	−0.268687	+	0.268687i	−0.0414592	+	0.0414592i
$43$	0.927191	+	0.927191i	0.141395	+	0.141395i	0.774261	−	0.632866i	$-0.218122\pi$
$43$	0.927191	+	0.927191i	0.141395	+	0.141395i	−0.632866	+	0.774261i	$0.718122\pi$
$44$		−	5.59543i		−	0.843543i
$45$		0			0
$46$		−	8.33950i		−	1.22959i
$47$	4.20858	−	4.20858i	0.613884	−	0.613884i	−0.330072	−	0.943956i	$-0.607073\pi$
$47$	4.20858	−	4.20858i	0.613884	−	0.613884i	0.943956	+	0.330072i	$0.107073\pi$
$48$	−0.267657	+	0.267657i	−0.0386329	+	0.0386329i
$49$			5.99229i			0.856042i
$50$		0			0
$51$		−	1.17943i		−	0.165154i
$52$	−2.99477	−	2.99477i	−0.415300	−	0.415300i
$53$	2.44104	−	2.44104i	0.335303	−	0.335303i	−0.519293	−	0.854596i	$-0.673805\pi$
$53$	2.44104	−	2.44104i	0.335303	−	0.335303i	0.854596	+	0.519293i	$0.173805\pi$
$54$			2.21691i			0.301683i
$55$		0			0
$56$		−	1.00385i		−	0.134145i
$57$	1.57943	−	0.477216i	0.209200	−	0.0632087i
$58$	−6.60675	−	6.60675i	−0.867508	−	0.867508i
$59$	12.5001			1.62737			0.813684	−	0.581307i	$-0.197459\pi$
$59$	12.5001			1.62737			0.813684	+	0.581307i	$0.197459\pi$
$60$		0			0
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$	−2.44949	+	2.44949i	−0.311086	+	0.311086i
$63$	−2.02778	−	2.02778i	−0.255476	−	0.255476i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	−2.11801			−0.260709
$67$	−5.72134	−	5.72134i	−0.698973	−	0.698973i	0.265216	−	0.964189i	$-0.414557\pi$
$67$	−5.72134	−	5.72134i	−0.698973	−	0.698973i	−0.964189	+	0.265216i	$0.914557\pi$
$68$	2.20326	+	2.20326i	0.267184	+	0.267184i
$69$	−3.15670			−0.380022
$70$		0			0
$71$			13.9114i			1.65097i	0.564421	+	0.825487i	$0.309099\pi$
$71$			13.9114i			1.65097i	−0.564421	+	0.825487i	$0.690901\pi$
$72$	−2.02001	−	2.02001i	−0.238060	−	0.238060i
$73$	−4.33274	−	4.33274i	−0.507109	−	0.507109i	0.406529	−	0.913638i	$-0.366739\pi$
$73$	−4.33274	−	4.33274i	−0.507109	−	0.507109i	−0.913638	+	0.406529i	$0.866739\pi$
$74$			9.35248i			1.08720i
$75$		0			0
$76$	−2.05900	+	3.84194i	−0.236184	+	0.440701i
$77$	3.97179	−	3.97179i	0.452627	−	0.452627i
$78$	−1.13359	+	1.13359i	−0.128354	+	0.128354i
$79$	−5.47180			−0.615625			−0.307813	−	0.951447i	$-0.599597\pi$
$79$	−5.47180			−0.615625			−0.307813	+	0.951447i	$0.599597\pi$
$80$		0			0
$81$	−7.73101			−0.859001
$82$	−6.46316	+	6.46316i	−0.713737	+	0.713737i
$83$	−5.53597	−	5.53597i	−0.607652	−	0.607652i	0.334680	−	0.942332i	$-0.391372\pi$
$83$	−5.53597	−	5.53597i	−0.607652	−	0.607652i	−0.942332	+	0.334680i	$0.891372\pi$
$84$	−0.379980			−0.0414592
$85$		0			0
$86$			1.31125i			0.141395i
$87$	−2.50081	+	2.50081i	−0.268115	+	0.268115i
$88$	3.95657	−	3.95657i	0.421772	−	0.421772i
$89$	8.99513			0.953482			0.476741	−	0.879044i	$-0.341818\pi$
$89$	8.99513			0.953482			0.476741	+	0.879044i	$0.341818\pi$
$90$		0			0
$91$		−	4.25154i		−	0.445682i
$92$	5.89692	−	5.89692i	0.614796	−	0.614796i
$93$	0.927191	+	0.927191i	0.0961452	+	0.0961452i
$94$	5.95183			0.613884
$95$		0			0
$96$	−0.378524			−0.0386329
$97$	9.16155	+	9.16155i	0.930215	+	0.930215i	0.997719	−	0.0675043i	$-0.0215036\pi$
$97$	9.16155	+	9.16155i	0.930215	+	0.930215i	−0.0675043	+	0.997719i	$0.521504\pi$
$98$	−4.23719	+	4.23719i	−0.428021	+	0.428021i
$99$		−	15.9846i		−	1.60651i
$100$		0			0
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$	0.833986	−	0.833986i	0.0825769	−	0.0825769i
$103$	4.91891	−	4.91891i	0.484675	−	0.484675i	−0.421946	−	0.906621i	$-0.638653\pi$
$103$	4.91891	−	4.91891i	0.484675	−	0.484675i	0.906621	+	0.421946i	$0.138653\pi$
$104$		−	4.23524i		−	0.415300i
$105$		0			0
$106$	3.45215			0.335303
$107$	−2.21021	−	2.21021i	−0.213669	−	0.213669i	0.592155	−	0.805824i	$-0.298277\pi$
$107$	−2.21021	−	2.21021i	−0.213669	−	0.213669i	−0.805824	+	0.592155i	$0.798277\pi$
$108$	−1.56759	+	1.56759i	−0.150842	+	0.150842i
$109$	−0.858684			−0.0822471			−0.0411235	−	0.999154i	$-0.513094\pi$
$109$	−0.858684			−0.0822471			−0.0411235	+	0.999154i	$0.513094\pi$
$110$		0			0
$111$	3.54014			0.336015
$112$	0.709827	−	0.709827i	0.0670723	−	0.0670723i
$113$	8.19921	−	8.19921i	0.771317	−	0.771317i	−0.207020	−	0.978337i	$-0.566377\pi$
$113$	8.19921	−	8.19921i	0.771317	−	0.771317i	0.978337	+	0.207020i	$0.0663765\pi$
$114$	1.45427	+	0.779382i	0.136205	+	0.0729958i
$115$		0			0
$116$		−	9.34335i		−	0.867508i
$117$	−8.55522	−	8.55522i	−0.790930	−	0.790930i
$118$	8.83887	+	8.83887i	0.813684	+	0.813684i
$119$			3.12786i			0.286731i
$120$		0			0
$121$	20.3089			1.84626
$122$	−1.41421	−	1.41421i	−0.128037	−	0.128037i
$123$	2.44646	+	2.44646i	0.220590	+	0.220590i
$124$	−3.46410			−0.311086
$125$		0			0
$126$		−	2.86771i		−	0.255476i
$127$	2.85436	+	2.85436i	0.253283	+	0.253283i	0.822315	−	0.569032i	$-0.192682\pi$
$127$	2.85436	+	2.85436i	0.253283	+	0.253283i	−0.569032	+	0.822315i	$0.692682\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	0.496338			0.0437001
$130$		0			0
$131$	13.7134			1.19815			0.599074	−	0.800693i	$-0.295535\pi$
$131$	13.7134			1.19815			0.599074	+	0.800693i	$0.295535\pi$
$132$	−1.49766	−	1.49766i	−0.130354	−	0.130354i
$133$	−4.18865	+	1.26558i	−0.363202	+	0.109739i
$134$		−	8.09119i		−	0.698973i
$135$		0			0
$136$			3.11588i			0.267184i
$137$	−12.3591	+	12.3591i	−1.05591	+	1.05591i	−0.0575711	+	0.998341i	$0.518336\pi$
$137$	−12.3591	+	12.3591i	−1.05591	+	1.05591i	−0.998341	+	0.0575711i	$0.981664\pi$
$138$	−2.23213	−	2.23213i	−0.190011	−	0.190011i
$139$			11.0729i			0.939188i	0.882883	+	0.469594i	$0.155600\pi$
$139$			11.0729i			0.939188i	−0.882883	+	0.469594i	$0.844400\pi$
$140$		0			0
$141$		−	2.25291i		−	0.189729i
$142$	−9.83681	+	9.83681i	−0.825487	+	0.825487i
$143$	16.7570	−	16.7570i	1.40129	−	1.40129i
$144$		−	2.85672i		−	0.238060i
$145$		0			0
$146$		−	6.12742i		−	0.507109i
$147$	1.60388	+	1.60388i	0.132286	+	0.132286i
$148$	−6.61320	+	6.61320i	−0.543602	+	0.543602i
$149$		−	5.19087i		−	0.425252i	−0.977134	−	0.212626i	$-0.931798\pi$
$149$		−	5.19087i		−	0.425252i	0.977134	−	0.212626i	$-0.0682017\pi$
$150$		0			0
$151$		−	6.37692i		−	0.518946i	−0.965750	−	0.259473i	$-0.916451\pi$
$151$		−	6.37692i		−	0.518946i	0.965750	−	0.259473i	$-0.0835489\pi$
$152$	−4.17260	+	1.26073i	−0.338442	+	0.102258i
$153$	6.29409	+	6.29409i	0.508847	+	0.508847i
$154$	5.61696			0.452627
$155$		0			0
$156$	−1.60314			−0.128354
$157$	4.30387	−	4.30387i	0.343486	−	0.343486i	−0.514190	−	0.857676i	$-0.671907\pi$
$157$	4.30387	−	4.30387i	0.343486	−	0.343486i	0.857676	+	0.514190i	$0.171907\pi$
$158$	−3.86914	−	3.86914i	−0.307813	−	0.307813i
$159$		−	1.30672i		−	0.103630i
$160$		0			0
$161$	8.37158			0.659773
$162$	−5.46665	−	5.46665i	−0.429500	−	0.429500i
$163$	9.73720	+	9.73720i	0.762676	+	0.762676i	0.976805	−	0.214129i	$-0.0686914\pi$
$163$	9.73720	+	9.73720i	0.762676	+	0.762676i	−0.214129	+	0.976805i	$0.568691\pi$
$164$	−9.14029			−0.713737
$165$		0			0
$166$		−	7.82904i		−	0.607652i
$167$	15.5454	+	15.5454i	1.20294	+	1.20294i	0.973267	+	0.229676i	$0.0737665\pi$
$167$	15.5454	+	15.5454i	1.20294	+	1.20294i	0.229676	+	0.973267i	$0.426233\pi$
$168$	−0.268687	−	0.268687i	−0.0207296	−	0.0207296i
$169$		−	4.93729i		−	0.379791i
$170$		0			0
$171$	−5.88199	+	10.9753i	−0.449807	+	0.839306i
$172$	−0.927191	+	0.927191i	−0.0706976	+	0.0706976i
$173$	−11.9265	+	11.9265i	−0.906753	+	0.906753i	−0.996009	−	0.0892559i	$-0.971551\pi$
$173$	−11.9265	+	11.9265i	−0.906753	+	0.906753i	0.0892559	+	0.996009i	$0.471551\pi$
$174$	−3.53668			−0.268115
$175$		0			0
$176$	5.59543			0.421772
$177$	3.34573	−	3.34573i	0.251480	−	0.251480i
$178$	6.36052	+	6.36052i	0.476741	+	0.476741i
$179$	−5.34131			−0.399229			−0.199614	−	0.979875i	$-0.563969\pi$
$179$	−5.34131			−0.399229			−0.199614	+	0.979875i	$0.563969\pi$
$180$		0			0
$181$		−	12.1836i		−	0.905599i	−0.891612	−	0.452799i	$-0.850425\pi$
$181$		−	12.1836i		−	0.905599i	0.891612	−	0.452799i	$-0.149575\pi$
$182$	3.00629	−	3.00629i	0.222841	−	0.222841i
$183$	−0.535314	+	0.535314i	−0.0395715	+	0.0395715i
$184$	8.33950			0.614796
$185$		0			0
$186$			1.31125i			0.0961452i
$187$	−12.3282	+	12.3282i	−0.901526	+	0.901526i
$188$	4.20858	+	4.20858i	0.306942	+	0.306942i
$189$	−2.22544			−0.161877
$190$		0			0
$191$	7.54014			0.545585			0.272793	−	0.962073i	$-0.412053\pi$
$191$	7.54014			0.545585			0.272793	+	0.962073i	$0.412053\pi$
$192$	−0.267657	−	0.267657i	−0.0193165	−	0.0193165i
$193$	−5.88017	+	5.88017i	−0.423264	+	0.423264i	−0.886326	−	0.463062i	$-0.846751\pi$
$193$	−5.88017	+	5.88017i	−0.423264	+	0.423264i	0.463062	+	0.886326i	$0.346751\pi$
$194$			12.9564i			0.930215i
$195$		0			0
$196$	−5.99229			−0.428021
$197$	12.8237	−	12.8237i	0.913649	−	0.913649i	−0.0829081	−	0.996557i	$-0.526421\pi$
$197$	12.8237	−	12.8237i	0.913649	−	0.913649i	0.996557	+	0.0829081i	$0.0264208\pi$
$198$	11.3028	−	11.3028i	0.803256	−	0.803256i
$199$		−	8.00986i		−	0.567804i	−0.958853	−	0.283902i	$-0.908371\pi$
$199$		−	8.00986i		−	0.567804i	0.958853	−	0.283902i	$-0.0916290\pi$
$200$		0			0
$201$	−3.06271			−0.216027
$202$	−4.24264	−	4.24264i	−0.298511	−	0.298511i
$203$	6.63216	−	6.63216i	0.465486	−	0.465486i
$204$	1.17943			0.0825769
$205$		0			0
$206$	6.95639			0.484675
$207$	16.8458	−	16.8458i	1.17087	−	1.17087i
$208$	2.99477	−	2.99477i	0.207650	−	0.207650i
$209$	−21.4973	−	11.5210i	−1.48700	−	0.796925i
$210$		0			0
$211$		−	9.88184i		−	0.680294i	−0.940372	−	0.340147i	$-0.889523\pi$
$211$		−	9.88184i		−	0.680294i	0.940372	−	0.340147i	$-0.110477\pi$
$212$	2.44104	+	2.44104i	0.167651	+	0.167651i
$213$	3.72347	+	3.72347i	0.255128	+	0.255128i
$214$		−	3.12571i		−	0.213669i
$215$		0			0
$216$	−2.21691			−0.150842
$217$	−2.45891	−	2.45891i	−0.166922	−	0.166922i
$218$	−0.607182	−	0.607182i	−0.0411235	−	0.0411235i
$219$	−2.31938			−0.156729
$220$		0			0
$221$			13.1965i			0.887693i
$222$	2.50326	+	2.50326i	0.168008	+	0.168008i
$223$	1.07063	−	1.07063i	0.0716945	−	0.0716945i	−0.670350	−	0.742045i	$-0.733856\pi$
$223$	1.07063	−	1.07063i	0.0716945	−	0.0716945i	0.742045	+	0.670350i	$0.233856\pi$
$224$	1.00385			0.0670723
$225$		0			0
$226$	11.5954			0.771317
$227$	−10.0734	−	10.0734i	−0.668592	−	0.668592i	0.288798	−	0.957390i	$-0.406744\pi$
$227$	−10.0734	−	10.0734i	−0.668592	−	0.668592i	−0.957390	+	0.288798i	$0.906744\pi$
$228$	0.477216	+	1.57943i	0.0316044	+	0.104600i
$229$			13.4423i			0.888292i	0.895954	+	0.444146i	$0.146493\pi$
$229$			13.4423i			0.888292i	−0.895954	+	0.444146i	$0.853507\pi$
$230$		0			0
$231$		−	2.12615i		−	0.139891i
$232$	6.60675	−	6.60675i	0.433754	−	0.433754i
$233$	10.9619	+	10.9619i	0.718141	+	0.718141i	0.968224	−	0.250084i	$-0.0804581\pi$
$233$	10.9619	+	10.9619i	0.718141	+	0.718141i	−0.250084	+	0.968224i	$0.580458\pi$
$234$		−	12.0989i		−	0.790930i
$235$		0			0
$236$			12.5001i			0.813684i
$237$	−1.46456	+	1.46456i	−0.0951336	+	0.0951336i
$238$	−2.21173	+	2.21173i	−0.143365	+	0.143365i
$239$		−	20.6959i		−	1.33870i	−0.742945	−	0.669352i	$-0.766572\pi$
$239$		−	20.6959i		−	1.33870i	0.742945	−	0.669352i	$-0.233428\pi$
$240$		0			0
$241$		−	7.82904i		−	0.504313i	−0.967686	−	0.252157i	$-0.918860\pi$
$241$		−	7.82904i		−	0.504313i	0.967686	−	0.252157i	$-0.0811398\pi$
$242$	14.3605	+	14.3605i	0.923131	+	0.923131i
$243$	−6.77203	+	6.77203i	−0.434426	+	0.434426i
$244$		−	2.00000i		−	0.128037i
$245$		0			0
$246$			3.45982i			0.220590i
$247$	−17.6720	+	5.33949i	−1.12444	+	0.339743i
$248$	−2.44949	−	2.44949i	−0.155543	−	0.155543i
$249$	−2.96348			−0.187803
$250$		0			0
$251$	3.07286			0.193957			0.0969786	−	0.995286i	$-0.469082\pi$
$251$	3.07286			0.193957			0.0969786	+	0.995286i	$0.469082\pi$
$252$	2.02778	−	2.02778i	0.127738	−	0.127738i
$253$	32.9958	+	32.9958i	2.07443	+	2.07443i
$254$			4.03667i			0.253283i
$255$		0			0
$256$	1.00000			0.0625000
$257$	11.5836	+	11.5836i	0.722567	+	0.722567i	0.969127	−	0.246560i	$-0.0793003\pi$
$257$	11.5836	+	11.5836i	0.722567	+	0.722567i	−0.246560	+	0.969127i	$0.579300\pi$
$258$	0.350964	+	0.350964i	0.0218501	+	0.0218501i
$259$	−9.38846			−0.583370
$260$		0			0
$261$		−	26.6913i		−	1.65215i
$262$	9.69687	+	9.69687i	0.599074	+	0.599074i
$263$	5.28880	+	5.28880i	0.326121	+	0.326121i	0.851109	−	0.524988i	$-0.175930\pi$
$263$	5.28880	+	5.28880i	0.326121	+	0.326121i	−0.524988	+	0.851109i	$0.675930\pi$
$264$		−	2.11801i		−	0.130354i
$265$		0			0
$266$	−3.85672	−	2.06692i	−0.236471	−	0.126731i
$267$	2.40761	−	2.40761i	0.147343	−	0.147343i
$268$	5.72134	−	5.72134i	0.349486	−	0.349486i
$269$	−18.5605			−1.13165			−0.565827	−	0.824524i	$-0.691443\pi$
$269$	−18.5605			−1.13165			−0.565827	+	0.824524i	$0.691443\pi$
$270$		0			0
$271$	13.9219			0.845693			0.422847	−	0.906201i	$-0.361031\pi$
$271$	13.9219			0.845693			0.422847	+	0.906201i	$0.361031\pi$
$272$	−2.20326	+	2.20326i	−0.133592	+	0.133592i
$273$	−1.13795	−	1.13795i	−0.0688720	−	0.0688720i
$274$	−17.4785			−1.05591
$275$		0			0
$276$		−	3.15670i		−	0.190011i
$277$	−18.3178	+	18.3178i	−1.10061	+	1.10061i	−0.106270	+	0.994337i	$0.533891\pi$
$277$	−18.3178	+	18.3178i	−1.10061	+	1.10061i	−0.994337	+	0.106270i	$0.966109\pi$
$278$	−7.82969	+	7.82969i	−0.469594	+	0.469594i
$279$	−9.89597			−0.592456
$280$		0			0
$281$		−	10.9436i		−	0.652840i	−0.945225	−	0.326420i	$-0.894158\pi$
$281$		−	10.9436i		−	0.652840i	0.945225	−	0.326420i	$-0.105842\pi$
$282$	1.59305	−	1.59305i	0.0948647	−	0.0948647i
$283$	−19.1004	−	19.1004i	−1.13540	−	1.13540i	−0.989264	−	0.146138i	$-0.953316\pi$
$283$	−19.1004	−	19.1004i	−1.13540	−	1.13540i	−0.146138	−	0.989264i	$-0.546684\pi$
$284$	−13.9114			−0.825487
$285$		0			0
$286$	23.6980			1.40129
$287$	−6.48802	−	6.48802i	−0.382976	−	0.382976i
$288$	2.02001	−	2.02001i	0.119030	−	0.119030i
$289$			7.29131i			0.428900i
$290$		0			0
$291$	4.90431			0.287495
$292$	4.33274	−	4.33274i	0.253554	−	0.253554i
$293$	−8.41216	+	8.41216i	−0.491444	+	0.491444i	−0.908761	−	0.417317i	$-0.862970\pi$
$293$	−8.41216	+	8.41216i	−0.491444	+	0.491444i	0.417317	+	0.908761i	$0.362970\pi$
$294$			2.26823i			0.132286i
$295$		0			0
$296$	−9.35248			−0.543602
$297$	−8.77135	−	8.77135i	−0.508966	−	0.508966i
$298$	3.67050	−	3.67050i	0.212626	−	0.212626i
$299$	35.3198			2.04260
$300$		0			0
$301$	−1.31629			−0.0758697
$302$	4.50916	−	4.50916i	0.259473	−	0.259473i
$303$	−1.60594	+	1.60594i	−0.0922589	+	0.0922589i
$304$	−3.84194	−	2.05900i	−0.220350	−	0.118092i
$305$		0			0
$306$			8.90119i			0.508847i
$307$	−12.9256	−	12.9256i	−0.737705	−	0.737705i	0.234428	−	0.972133i	$-0.424678\pi$
$307$	−12.9256	−	12.9256i	−0.737705	−	0.737705i	−0.972133	+	0.234428i	$0.924678\pi$
$308$	3.97179	+	3.97179i	0.226314	+	0.226314i
$309$		−	2.63316i		−	0.149795i
$310$		0			0
$311$	−11.7233			−0.664767			−0.332384	−	0.943144i	$-0.607853\pi$
$311$	−11.7233			−0.664767			−0.332384	+	0.943144i	$0.607853\pi$
$312$	−1.13359	−	1.13359i	−0.0641770	−	0.0641770i
$313$	−16.3409	−	16.3409i	−0.923643	−	0.923643i	0.0736417	−	0.997285i	$-0.476538\pi$
$313$	−16.3409	−	16.3409i	−0.923643	−	0.923643i	−0.997285	+	0.0736417i	$0.976538\pi$
$314$	6.08659			0.343486
$315$		0			0
$316$		−	5.47180i		−	0.307813i
$317$	7.39624	+	7.39624i	0.415414	+	0.415414i	0.883620	−	0.468205i	$-0.155099\pi$
$317$	7.39624	+	7.39624i	0.415414	+	0.415414i	−0.468205	+	0.883620i	$0.655099\pi$
$318$	0.923993	−	0.923993i	0.0518149	−	0.0518149i
$319$	52.2801			2.92712
$320$		0			0
$321$	−1.18316			−0.0660374
$322$	5.91960	+	5.91960i	0.329887	+	0.329887i
$323$	13.0013	−	3.92827i	0.723412	−	0.218575i
$324$		−	7.73101i		−	0.429500i
$325$		0			0
$326$			13.7705i			0.762676i
$327$	−0.229833	+	0.229833i	−0.0127098	+	0.0127098i
$328$	−6.46316	−	6.46316i	−0.356868	−	0.356868i
$329$			5.97473i			0.329397i
$330$		0			0
$331$			18.4836i			1.01595i	0.861371	+	0.507976i	$0.169606\pi$
$331$			18.4836i			1.01595i	−0.861371	+	0.507976i	$0.830394\pi$
$332$	5.53597	−	5.53597i	0.303826	−	0.303826i
$333$	−18.8921	+	18.8921i	−1.03528	+	1.03528i
$334$			21.9846i			1.20294i
$335$		0			0
$336$		−	0.379980i		−	0.0207296i
$337$	23.8856	+	23.8856i	1.30113	+	1.30113i	0.927629	+	0.373504i	$0.121844\pi$
$337$	23.8856	+	23.8856i	1.30113	+	1.30113i	0.373504	+	0.927629i	$0.378156\pi$
$338$	3.49119	−	3.49119i	0.189896	−	0.189896i
$339$		−	4.38915i		−	0.238386i
$340$		0			0
$341$		−	19.3831i		−	1.04966i
$342$	−11.9199	+	3.60154i	−0.644557	+	0.194749i
$343$	−9.22228	−	9.22228i	−0.497956	−	0.497956i
$344$	−1.31125			−0.0706976
$345$		0			0
$346$	−16.8666			−0.906753
$347$	−7.59564	+	7.59564i	−0.407755	+	0.407755i	−0.880955	−	0.473200i	$-0.843099\pi$
$347$	−7.59564	+	7.59564i	−0.407755	+	0.407755i	0.473200	+	0.880955i	$0.343099\pi$
$348$	−2.50081	−	2.50081i	−0.134058	−	0.134058i
$349$			32.0798i			1.71719i	0.512655	+	0.858595i	$0.328662\pi$
$349$			32.0798i			1.71719i	−0.512655	+	0.858595i	$0.671338\pi$
$350$		0			0
$351$	−9.38915			−0.501156
$352$	3.95657	+	3.95657i	0.210886	+	0.210886i
$353$	−1.84231	−	1.84231i	−0.0980562	−	0.0980562i	0.656377	−	0.754433i	$-0.272088\pi$
$353$	−1.84231	−	1.84231i	−0.0980562	−	0.0980562i	−0.754433	+	0.656377i	$0.772088\pi$
$354$	4.73157			0.251480
$355$		0			0
$356$			8.99513i			0.476741i
$357$	0.837194	+	0.837194i	0.0443090	+	0.0443090i
$358$	−3.77688	−	3.77688i	−0.199614	−	0.199614i
$359$			8.46972i			0.447015i	0.974702	+	0.223507i	$0.0717507\pi$
$359$			8.46972i			0.447015i	−0.974702	+	0.223507i	$0.928249\pi$
$360$		0			0
$361$	10.5210	+	15.8211i	0.553738	+	0.832691i
$362$	8.61510	−	8.61510i	0.452799	−	0.452799i
$363$	5.43581	−	5.43581i	0.285306	−	0.285306i
$364$	4.25154			0.222841
$365$		0			0
$366$	−0.757048			−0.0395715
$367$	−12.3312	+	12.3312i	−0.643684	+	0.643684i	−0.951459	−	0.307775i	$-0.900416\pi$
$367$	−12.3312	+	12.3312i	−0.643684	+	0.643684i	0.307775	+	0.951459i	$0.400416\pi$
$368$	5.89692	+	5.89692i	0.307398	+	0.307398i
$369$	−26.1112			−1.35930
$370$		0			0
$371$			3.46543i			0.179916i
$372$	−0.927191	+	0.927191i	−0.0480726	+	0.0480726i
$373$	5.47155	−	5.47155i	0.283306	−	0.283306i	−0.551120	−	0.834426i	$-0.685799\pi$
$373$	5.47155	−	5.47155i	0.283306	−	0.283306i	0.834426	+	0.551120i	$0.185799\pi$
$374$	−17.4347			−0.901526
$375$		0			0
$376$			5.95183i			0.306942i
$377$	27.9812	−	27.9812i	1.44110	−	1.44110i
$378$	−1.57362	−	1.57362i	−0.0809384	−	0.0809384i
$379$	−13.3179			−0.684095			−0.342048	−	0.939683i	$-0.611120\pi$
$379$	−13.3179			−0.684095			−0.342048	+	0.939683i	$0.611120\pi$
$380$		0			0
$381$	1.52798			0.0782806
$382$	5.33168	+	5.33168i	0.272793	+	0.272793i
$383$	14.0425	−	14.0425i	0.717541	−	0.717541i	−0.250560	−	0.968101i	$-0.580615\pi$
$383$	14.0425	−	14.0425i	0.717541	−	0.717541i	0.968101	+	0.250560i	$0.0806149\pi$
$384$		−	0.378524i		−	0.0193165i
$385$		0			0
$386$	−8.31581			−0.423264
$387$	−2.64872	+	2.64872i	−0.134642	+	0.134642i
$388$	−9.16155	+	9.16155i	−0.465107	+	0.465107i
$389$		−	12.5072i		−	0.634138i	−0.948402	−	0.317069i	$-0.897301\pi$
$389$		−	12.5072i		−	0.634138i	0.948402	−	0.317069i	$-0.102699\pi$
$390$		0			0
$391$	−25.9849			−1.31411
$392$	−4.23719	−	4.23719i	−0.214010	−	0.214010i
$393$	3.67050	−	3.67050i	0.185152	−	0.185152i
$394$	18.1354			0.913649
$395$		0			0
$396$	15.9846			0.803256
$397$	−18.2540	+	18.2540i	−0.916141	+	0.916141i	−0.996746	−	0.0806055i	$-0.974315\pi$
$397$	−18.2540	+	18.2540i	−0.916141	+	0.916141i	0.0806055	+	0.996746i	$0.474315\pi$
$398$	5.66382	−	5.66382i	0.283902	−	0.283902i
$399$	−0.782380	+	1.45986i	−0.0391680	+	0.0730845i
$400$		0			0
$401$			9.54641i			0.476725i	0.971176	+	0.238363i	$0.0766106\pi$
$401$			9.54641i			0.476725i	−0.971176	+	0.238363i	$0.923389\pi$
$402$	−2.16566	−	2.16566i	−0.108014	−	0.108014i
$403$	−10.3742	−	10.3742i	−0.516775	−	0.516775i
$404$		−	6.00000i		−	0.298511i
$405$		0			0
$406$	9.37929			0.465486
$407$	−37.0037	−	37.0037i	−1.83421	−	1.83421i
$408$	0.833986	+	0.833986i	0.0412885	+	0.0412885i
$409$	11.2029			0.553949			0.276975	−	0.960877i	$-0.410668\pi$
$409$	11.2029			0.553949			0.276975	+	0.960877i	$0.410668\pi$
$410$		0			0
$411$			6.61602i			0.326344i
$412$	4.91891	+	4.91891i	0.242337	+	0.242337i
$413$	−8.87287	+	8.87287i	−0.436606	+	0.436606i
$414$	23.8236			1.17087
$415$		0			0
$416$	4.23524			0.207650
$417$	2.96373	+	2.96373i	0.145134	+	0.145134i
$418$	−7.05431	−	23.3475i	−0.345038	−	1.14196i
$419$		−	6.91172i		−	0.337660i	−0.985645	−	0.168830i	$-0.946001\pi$
$419$		−	6.91172i		−	0.337660i	0.985645	−	0.168830i	$-0.0539988\pi$
$420$		0			0
$421$			8.98100i			0.437707i	0.975758	+	0.218854i	$0.0702317\pi$
$421$			8.98100i			0.437707i	−0.975758	+	0.218854i	$0.929768\pi$
$422$	6.98752	−	6.98752i	0.340147	−	0.340147i
$423$	12.0227	+	12.0227i	0.584565	+	0.584565i
$424$			3.45215i			0.167651i
$425$		0			0
$426$			5.26578i			0.255128i
$427$	1.41965	−	1.41965i	0.0687019	−	0.0687019i
$428$	2.21021	−	2.21021i	0.106835	−	0.106835i
$429$		−	8.97027i		−	0.433089i
$430$		0			0
$431$		−	13.5052i		−	0.650524i	−0.945624	−	0.325262i	$-0.894547\pi$
$431$		−	13.5052i		−	0.650524i	0.945624	−	0.325262i	$-0.105453\pi$
$432$	−1.56759	−	1.56759i	−0.0754208	−	0.0754208i
$433$	−16.9664	+	16.9664i	−0.815353	+	0.815353i	−0.985431	−	0.170077i	$-0.945598\pi$
$433$	−16.9664	+	16.9664i	−0.815353	+	0.815353i	0.170077	+	0.985431i	$0.445598\pi$
$434$		−	3.47743i		−	0.166922i
$435$		0			0
$436$		−	0.858684i		−	0.0411235i
$437$	−10.5138	−	34.7974i	−0.502945	−	1.66458i
$438$	−1.64005	−	1.64005i	−0.0783644	−	0.0783644i
$439$	34.2082			1.63267			0.816334	−	0.577580i	$-0.196003\pi$
$439$	34.2082			1.63267			0.816334	+	0.577580i	$0.196003\pi$
$440$		0			0
$441$	−17.1183			−0.815157
$442$	−9.33134	+	9.33134i	−0.443846	+	0.443846i
$443$	−9.98134	−	9.98134i	−0.474228	−	0.474228i	0.429052	−	0.903280i	$-0.358848\pi$
$443$	−9.98134	−	9.98134i	−0.474228	−	0.474228i	−0.903280	+	0.429052i	$0.858848\pi$
$444$			3.54014i			0.168008i
$445$		0			0
$446$	1.51410			0.0716945
$447$	−1.38937	−	1.38937i	−0.0657150	−	0.0657150i
$448$	0.709827	+	0.709827i	0.0335362	+	0.0335362i
$449$	−15.8684			−0.748875			−0.374438	−	0.927252i	$-0.622164\pi$
$449$	−15.8684			−0.748875			−0.374438	+	0.927252i	$0.622164\pi$
$450$		0			0
$451$		−	51.1439i		−	2.40827i
$452$	8.19921	+	8.19921i	0.385658	+	0.385658i
$453$	−1.70683	−	1.70683i	−0.0801937	−	0.0801937i
$454$		−	14.2459i		−	0.668592i
$455$		0			0
$456$	−0.779382	+	1.45427i	−0.0364979	+	0.0681023i
$457$	20.0286	−	20.0286i	0.936896	−	0.936896i	−0.0612274	−	0.998124i	$-0.519501\pi$
$457$	20.0286	−	20.0286i	0.936896	−	0.936896i	0.998124	+	0.0612274i	$0.0195015\pi$
$458$	−9.50514	+	9.50514i	−0.444146	+	0.444146i
$459$	6.90762			0.322420
$460$		0			0
$461$	−39.5726			−1.84308			−0.921540	−	0.388284i	$-0.873068\pi$
$461$	−39.5726			−1.84308			−0.921540	+	0.388284i	$0.873068\pi$
$462$	1.50342	−	1.50342i	0.0699453	−	0.0699453i
$463$	−8.32792	−	8.32792i	−0.387031	−	0.387031i	0.486596	−	0.873627i	$-0.338238\pi$
$463$	−8.32792	−	8.32792i	−0.387031	−	0.387031i	−0.873627	+	0.486596i	$0.838238\pi$
$464$	9.34335			0.433754
$465$		0			0
$466$			15.5025i			0.718141i
$467$	−18.6687	+	18.6687i	−0.863886	+	0.863886i	−0.991787	−	0.127901i	$-0.959176\pi$
$467$	−18.6687	+	18.6687i	−0.863886	+	0.863886i	0.127901	+	0.991787i	$0.459176\pi$
$468$	8.55522	−	8.55522i	0.395465	−	0.395465i
$469$	8.12232			0.375054
$470$		0			0
$471$		−	2.30392i		−	0.106159i
$472$	−8.83887	+	8.83887i	−0.406842	+	0.406842i
$473$	−5.18803	−	5.18803i	−0.238546	−	0.238546i
$474$	−2.07121			−0.0951336
$475$		0			0
$476$	−3.12786			−0.143365
$477$	6.97337	+	6.97337i	0.319289	+	0.319289i
$478$	14.6342	−	14.6342i	0.669352	−	0.669352i
$479$		−	14.5449i		−	0.664573i	−0.943179	−	0.332286i	$-0.892180\pi$
$479$		−	14.5449i		−	0.664573i	0.943179	−	0.332286i	$-0.107820\pi$
$480$		0			0
$481$	−39.6100			−1.80606
$482$	5.53597	−	5.53597i	0.252157	−	0.252157i
$483$	2.24071	−	2.24071i	0.101956	−	0.101956i
$484$			20.3089i			0.923131i
$485$		0			0
$486$	−9.57710			−0.434426
$487$	−22.3869	−	22.3869i	−1.01445	−	1.01445i	−0.999894	−	0.0145519i	$-0.995368\pi$
$487$	−22.3869	−	22.3869i	−1.01445	−	1.01445i	−0.0145519	−	0.999894i	$-0.504632\pi$
$488$	1.41421	−	1.41421i	0.0640184	−	0.0640184i
$489$	5.21246			0.235715
$490$		0			0
$491$	−6.90431			−0.311587			−0.155793	−	0.987790i	$-0.549793\pi$
$491$	−6.90431			−0.311587			−0.155793	+	0.987790i	$0.549793\pi$
$492$	−2.44646	+	2.44646i	−0.110295	+	0.110295i
$493$	−20.5858	+	20.5858i	−0.927138	+	0.927138i
$494$	−16.2716	−	8.72038i	−0.732092	−	0.392348i
$495$		0			0
$496$		−	3.46410i		−	0.155543i
$497$	−9.87465	−	9.87465i	−0.442939	−	0.442939i
$498$	−2.09550	−	2.09550i	−0.0939015	−	0.0939015i
$499$			27.6980i			1.23993i	0.784628	+	0.619967i	$0.212854\pi$
$499$			27.6980i			1.23993i	−0.784628	+	0.619967i	$0.787146\pi$
$500$		0			0
$501$	8.32169			0.371786
$502$	2.17284	+	2.17284i	0.0969786	+	0.0969786i
$503$	−7.10527	−	7.10527i	−0.316808	−	0.316808i	0.530732	−	0.847540i	$-0.321917\pi$
$503$	−7.10527	−	7.10527i	−0.316808	−	0.316808i	−0.847540	+	0.530732i	$0.821917\pi$
$504$	2.86771			0.127738
$505$		0			0
$506$			46.6631i			2.07443i
$507$	−1.32150	−	1.32150i	−0.0586898	−	0.0586898i
$508$	−2.85436	+	2.85436i	−0.126642	+	0.126642i
$509$	20.7950			0.921723			0.460861	−	0.887472i	$-0.347541\pi$
$509$	20.7950			0.921723			0.460861	+	0.887472i	$0.347541\pi$
$510$		0			0
$511$	6.15099			0.272104
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	2.79492	+	9.25027i	0.123399	+	0.408409i
$514$			16.3817i			0.722567i
$515$		0			0
$516$			0.496338i			0.0218501i
$517$	−23.5488	+	23.5488i	−1.03568	+	1.03568i
$518$	−6.63864	−	6.63864i	−0.291685	−	0.291685i
$519$			6.38440i			0.280244i
$520$		0			0
$521$			27.8270i			1.21912i	0.792739	+	0.609561i	$0.208654\pi$
$521$			27.8270i			1.21912i	−0.792739	+	0.609561i	$0.791346\pi$
$522$	18.8736	−	18.8736i	0.826076	−	0.826076i
$523$	−8.18242	+	8.18242i	−0.357792	+	0.357792i	−0.862999	−	0.505206i	$-0.831416\pi$
$523$	−8.18242	+	8.18242i	−0.357792	+	0.357792i	0.505206	+	0.862999i	$0.331416\pi$
$524$			13.7134i			0.599074i
$525$		0			0
$526$			7.47949i			0.326121i
$527$	7.63231	+	7.63231i	0.332469	+	0.332469i
$528$	1.49766	−	1.49766i	0.0651771	−	0.0651771i
$529$			46.5473i			2.02380i
$530$		0			0
$531$			35.7091i			1.54964i
$532$	−1.26558	−	4.18865i	−0.0548697	−	0.181601i
$533$	−27.3731	−	27.3731i	−1.18566	−	1.18566i
$534$	3.40487			0.147343
$535$		0			0
$536$	8.09119			0.349486
$537$	−1.42964	+	1.42964i	−0.0616935	+	0.0616935i
$538$	−13.1243	−	13.1243i	−0.565827	−	0.565827i
$539$		−	33.5295i		−	1.44422i
$540$		0			0
$541$	4.27114			0.183631			0.0918154	−	0.995776i	$-0.470733\pi$
$541$	4.27114			0.183631			0.0918154	+	0.995776i	$0.470733\pi$
$542$	9.84425	+	9.84425i	0.422847	+	0.422847i
$543$	−3.26102	−	3.26102i	−0.139944	−	0.139944i
$544$	−3.11588			−0.133592
$545$		0			0
$546$		−	1.60931i		−	0.0688720i
$547$	13.1550	+	13.1550i	0.562465	+	0.562465i	0.930007	−	0.367542i	$-0.119801\pi$
$547$	13.1550	+	13.1550i	0.562465	+	0.562465i	−0.367542	+	0.930007i	$0.619801\pi$
$548$	−12.3591	−	12.3591i	−0.527956	−	0.527956i
$549$		−	5.71344i		−	0.243844i
$550$		0			0
$551$	−35.8966	−	19.2380i	−1.52925	−	0.819566i
$552$	2.23213	−	2.23213i	0.0950056	−	0.0950056i
$553$	3.88403	−	3.88403i	0.165166	−	0.165166i
$554$	−25.9052			−1.10061
$555$		0			0
$556$	−11.0729			−0.469594
$557$	−11.7550	+	11.7550i	−0.498075	+	0.498075i	−0.910838	−	0.412764i	$-0.864564\pi$
$557$	−11.7550	+	11.7550i	−0.498075	+	0.498075i	0.412764	+	0.910838i	$0.364564\pi$
$558$	−6.99751	−	6.99751i	−0.296228	−	0.296228i
$559$	−5.55345			−0.234886
$560$		0			0
$561$			6.59945i			0.278629i
$562$	7.73829	−	7.73829i	0.326420	−	0.326420i
$563$	−5.14713	+	5.14713i	−0.216926	+	0.216926i	−0.807202	−	0.590276i	$-0.799019\pi$
$563$	−5.14713	+	5.14713i	−0.216926	+	0.216926i	0.590276	+	0.807202i	$0.299019\pi$
$564$	2.25291			0.0948647
$565$		0			0
$566$		−	27.0121i		−	1.13540i
$567$	5.48768	−	5.48768i	0.230461	−	0.230461i
$568$	−9.83681	−	9.83681i	−0.412743	−	0.412743i
$569$	23.4663			0.983760			0.491880	−	0.870663i	$-0.336310\pi$
$569$	23.4663			0.983760			0.491880	+	0.870663i	$0.336310\pi$
$570$		0			0
$571$	7.94945			0.332674			0.166337	−	0.986069i	$-0.446806\pi$
$571$	7.94945			0.332674			0.166337	+	0.986069i	$0.446806\pi$
$572$	16.7570	+	16.7570i	0.700647	+	0.700647i
$573$	2.01817	−	2.01817i	0.0843103	−	0.0843103i
$574$		−	9.17545i		−	0.382976i
$575$		0			0
$576$	2.85672			0.119030
$577$	18.2440	−	18.2440i	0.759507	−	0.759507i	−0.216726	−	0.976233i	$-0.569538\pi$
$577$	18.2440	−	18.2440i	0.759507	−	0.759507i	0.976233	+	0.216726i	$0.0695377\pi$
$578$	−5.15573	+	5.15573i	−0.214450	+	0.214450i
$579$			3.14773i			0.130815i
$580$		0			0
$581$	7.85916			0.326053
$582$	3.46787	+	3.46787i	0.143748	+	0.143748i
$583$	−13.6587	+	13.6587i	−0.565685	+	0.565685i
$584$	6.12742			0.253554
$585$		0			0
$586$	−11.8966			−0.491444
$587$	32.3528	−	32.3528i	1.33534	−	1.33534i	0.434829	−	0.900513i	$-0.356809\pi$
$587$	32.3528	−	32.3528i	1.33534	−	1.33534i	0.900513	−	0.434829i	$-0.143191\pi$
$588$	−1.60388	+	1.60388i	−0.0661428	+	0.0661428i
$589$	−7.13260	+	13.3089i	−0.293893	+	0.548383i
$590$		0			0
$591$		−	6.86469i		−	0.282376i
$592$	−6.61320	−	6.61320i	−0.271801	−	0.271801i
$593$	10.0317	+	10.0317i	0.411953	+	0.411953i	0.882419	−	0.470465i	$-0.155914\pi$
$593$	10.0317	+	10.0317i	0.411953	+	0.411953i	−0.470465	+	0.882419i	$0.655914\pi$
$594$		−	12.4046i		−	0.508966i
$595$		0			0
$596$	5.19087			0.212626
$597$	−2.14389	−	2.14389i	−0.0877437	−	0.0877437i
$598$	24.9749	+	24.9749i	1.02130	+	1.02130i
$599$	−9.68729			−0.395812			−0.197906	−	0.980221i	$-0.563414\pi$
$599$	−9.68729			−0.395812			−0.197906	+	0.980221i	$0.563414\pi$
$600$		0			0
$601$		−	0.610515i		−	0.0249034i	−0.999922	−	0.0124517i	$-0.996036\pi$
$601$		−	0.610515i		−	0.0249034i	0.999922	−	0.0124517i	$-0.00396361\pi$
$602$	−0.930757	−	0.930757i	−0.0379348	−	0.0379348i
$603$	16.3443	−	16.3443i	0.665590	−	0.665590i
$604$	6.37692			0.259473
$605$		0			0
$606$	−2.27114			−0.0922589
$607$	−3.31601	−	3.31601i	−0.134593	−	0.134593i	0.636601	−	0.771193i	$-0.280340\pi$
$607$	−3.31601	−	3.31601i	−0.134593	−	0.134593i	−0.771193	+	0.636601i	$0.780340\pi$
$608$	−1.26073	−	4.17260i	−0.0511292	−	0.169221i
$609$		−	3.55029i		−	0.143865i
$610$		0			0
$611$			25.2075i			1.01978i
$612$	−6.29409	+	6.29409i	−0.254424	+	0.254424i
$613$	−8.70433	−	8.70433i	−0.351565	−	0.351565i	0.509127	−	0.860691i	$-0.329968\pi$
$613$	−8.70433	−	8.70433i	−0.351565	−	0.351565i	−0.860691	+	0.509127i	$0.829968\pi$
$614$		−	18.2796i		−	0.737705i
$615$		0			0
$616$			5.61696i			0.226314i
$617$	−18.5096	+	18.5096i	−0.745170	+	0.745170i	−0.973568	−	0.228398i	$-0.926651\pi$
$617$	−18.5096	+	18.5096i	−0.745170	+	0.745170i	0.228398	+	0.973568i	$0.426651\pi$
$618$	1.86193	−	1.86193i	0.0748977	−	0.0748977i
$619$		−	24.7937i		−	0.996544i	−0.867021	−	0.498272i	$-0.833968\pi$
$619$		−	24.7937i		−	0.996544i	0.867021	−	0.498272i	$-0.166032\pi$
$620$		0			0
$621$		−	18.4879i		−	0.741895i
$622$	−8.28962	−	8.28962i	−0.332384	−	0.332384i
$623$	−6.38498	+	6.38498i	−0.255809	+	0.255809i
$624$		−	1.60314i		−	0.0641770i
$625$		0			0
$626$		−	23.1095i		−	0.923643i
$627$	−8.83759	+	2.67023i	−0.352939	+	0.106639i
$628$	4.30387	+	4.30387i	0.171743	+	0.171743i
$629$	29.1412			1.16194
$630$		0			0
$631$	25.4997			1.01513			0.507564	−	0.861614i	$-0.330546\pi$
$631$	25.4997			1.01513			0.507564	+	0.861614i	$0.330546\pi$
$632$	3.86914	−	3.86914i	0.153906	−	0.153906i
$633$	−2.64494	−	2.64494i	−0.105127	−	0.105127i
$634$			10.4599i			0.415414i
$635$		0			0
$636$	1.30672			0.0518149
$637$	−17.9455	−	17.9455i	−0.711028	−	0.711028i
$638$	36.9676	+	36.9676i	1.46356	+	1.46356i
$639$	−39.7408			−1.57212
$640$		0			0
$641$			4.36066i			0.172236i	0.996285	+	0.0861178i	$0.0274462\pi$
$641$			4.36066i			0.172236i	−0.996285	+	0.0861178i	$0.972554\pi$
$642$	−0.836619	−	0.836619i	−0.0330187	−	0.0330187i
$643$	17.0826	+	17.0826i	0.673673	+	0.673673i	0.958561	−	0.284888i	$-0.0919563\pi$
$643$	17.0826	+	17.0826i	0.673673	+	0.673673i	−0.284888	+	0.958561i	$0.591956\pi$
$644$			8.37158i			0.329887i
$645$		0			0
$646$	11.9710	+	6.41560i	0.470993	+	0.252418i
$647$	−14.0709	+	14.0709i	−0.553183	+	0.553183i	−0.927358	−	0.374175i	$-0.877926\pi$
$647$	−14.0709	+	14.0709i	−0.553183	+	0.553183i	0.374175	+	0.927358i	$0.377926\pi$
$648$	5.46665	−	5.46665i	0.214750	−	0.214750i
$649$	−69.9432			−2.74551
$650$		0			0
$651$	−1.31629			−0.0515895
$652$	−9.73720	+	9.73720i	−0.381338	+	0.381338i
$653$	3.12836	+	3.12836i	0.122422	+	0.122422i	0.765664	−	0.643241i	$-0.222411\pi$
$653$	3.12836	+	3.12836i	0.122422	+	0.122422i	−0.643241	+	0.765664i	$0.722411\pi$
$654$	−0.325033			−0.0127098
$655$		0			0
$656$		−	9.14029i		−	0.356868i
$657$	12.3774	−	12.3774i	0.482889	−	0.482889i
$658$	−4.22477	+	4.22477i	−0.164699	+	0.164699i
$659$	34.5113			1.34437			0.672185	−	0.740383i	$-0.265356\pi$
$659$	34.5113			1.34437			0.672185	+	0.740383i	$0.265356\pi$
$660$		0			0
$661$		−	1.89056i		−	0.0735344i	−0.999324	−	0.0367672i	$-0.988294\pi$
$661$		−	1.89056i		−	0.0735344i	0.999324	−	0.0367672i	$-0.0117060\pi$
$662$	−13.0699	+	13.0699i	−0.507976	+	0.507976i
$663$	3.53213	+	3.53213i	0.137177	+	0.137177i
$664$	7.82904			0.303826
$665$		0			0
$666$	−26.7174			−1.03528
$667$	55.0970	+	55.0970i	2.13336	+	2.13336i
$668$	−15.5454	+	15.5454i	−0.601471	+	0.601471i
$669$		−	0.573122i		−	0.0221582i
$670$		0			0
$671$	11.1909			0.432019
$672$	0.268687	−	0.268687i	0.0103648	−	0.0103648i
$673$	0.499570	−	0.499570i	0.0192570	−	0.0192570i	−0.697413	−	0.716670i	$-0.745666\pi$
$673$	0.499570	−	0.499570i	0.0192570	−	0.0192570i	0.716670	+	0.697413i	$0.245666\pi$
$674$			33.7794i			1.30113i
$675$		0			0
$676$	4.93729			0.189896
$677$	−24.8658	−	24.8658i	−0.955671	−	0.955671i	0.0433869	−	0.999058i	$-0.486185\pi$
$677$	−24.8658	−	24.8658i	−0.955671	−	0.955671i	−0.999058	+	0.0433869i	$0.986185\pi$
$678$	3.10360	−	3.10360i	0.119193	−	0.119193i
$679$	−13.0062			−0.499133
$680$		0			0
$681$	−5.39240			−0.206637
$682$	13.7060	−	13.7060i	0.524828	−	0.524828i
$683$	20.7651	−	20.7651i	0.794555	−	0.794555i	−0.187676	−	0.982231i	$-0.560095\pi$
$683$	20.7651	−	20.7651i	0.794555	−	0.794555i	0.982231	+	0.187676i	$0.0600954\pi$
$684$	−10.9753	−	5.88199i	−0.419653	−	0.224904i
$685$		0			0
$686$		−	13.0423i		−	0.497956i
$687$	3.59792	+	3.59792i	0.137269	+	0.137269i
$688$	−0.927191	−	0.927191i	−0.0353488	−	0.0353488i
$689$			14.6207i			0.557005i
$690$		0			0
$691$	−4.67571			−0.177872			−0.0889362	−	0.996037i	$-0.528347\pi$
$691$	−4.67571			−0.177872			−0.0889362	+	0.996037i	$0.528347\pi$
$692$	−11.9265	−	11.9265i	−0.453376	−	0.453376i
$693$	11.3463	+	11.3463i	0.431010	+	0.431010i
$694$	−10.7419			−0.407755
$695$		0			0
$696$		−	3.53668i		−	0.134058i
$697$	20.1384	+	20.1384i	0.762797	+	0.762797i
$698$	−22.6838	+	22.6838i	−0.858595	+	0.858595i
$699$	5.86808			0.221951
$700$		0			0
$701$	13.2106			0.498957			0.249478	−	0.968380i	$-0.419741\pi$
$701$	13.2106			0.498957			0.249478	+	0.968380i	$0.419741\pi$
$702$	−6.63913	−	6.63913i	−0.250578	−	0.250578i
$703$	11.7909	+	39.0241i	0.444703	+	1.47182i
$704$			5.59543i			0.210886i
$705$		0			0
$706$		−	2.60542i		−	0.0980562i
$707$	4.25896	−	4.25896i	0.160175	−	0.160175i
$708$	3.34573	+	3.34573i	0.125740	+	0.125740i
$709$		−	4.01972i		−	0.150964i	−0.997147	−	0.0754818i	$-0.975951\pi$
$709$		−	4.01972i		−	0.150964i	0.997147	−	0.0754818i	$-0.0240495\pi$
$710$		0			0
$711$		−	15.6314i		−	0.586223i
$712$	−6.36052	+	6.36052i	−0.238370	+	0.238370i
$713$	20.4275	−	20.4275i	0.765017	−	0.765017i
$714$			1.18397i			0.0443090i
$715$		0			0
$716$		−	5.34131i		−	0.199614i
$717$	−5.53939	−	5.53939i	−0.206872	−	0.206872i
$718$	−5.98900	+	5.98900i	−0.223507	+	0.223507i
$719$			7.54014i			0.281200i	0.990067	+	0.140600i	$0.0449031\pi$
$719$			7.54014i			0.281200i	−0.990067	+	0.140600i	$0.955097\pi$
$720$		0			0
$721$			6.98315i			0.260066i
$722$	−3.74775	+	18.6267i	−0.139477	+	0.693214i
$723$	−2.09550	−	2.09550i	−0.0779324	−	0.0779324i
$724$	12.1836			0.452799
$725$		0			0
$726$	7.68740			0.285306
$727$	35.6576	−	35.6576i	1.32247	−	1.32247i	0.410691	−	0.911775i	$-0.365287\pi$
$727$	35.6576	−	35.6576i	1.32247	−	1.32247i	0.911775	−	0.410691i	$-0.134713\pi$
$728$	3.00629	+	3.00629i	0.111421	+	0.111421i
$729$		−	19.5679i		−	0.724735i
$730$		0			0
$731$	4.08568			0.151114
$732$	−0.535314	−	0.535314i	−0.0197858	−	0.0197858i
$733$	−26.5296	−	26.5296i	−0.979894	−	0.979894i	0.0199075	−	0.999802i	$-0.493663\pi$
$733$	−26.5296	−	26.5296i	−0.979894	−	0.979894i	−0.999802	+	0.0199075i	$0.993663\pi$
$734$	−17.4390			−0.643684
$735$		0			0
$736$			8.33950i			0.307398i
$737$	32.0134	+	32.0134i	1.17923	+	1.17923i
$738$	−18.4634	−	18.4634i	−0.679648	−	0.679648i
$739$			38.6023i			1.42001i	0.704197	+	0.710005i	$0.251307\pi$
$739$			38.6023i			1.42001i	−0.704197	+	0.710005i	$0.748693\pi$
$740$		0			0
$741$	−3.30087	+	6.15917i	−0.121261	+	0.226263i
$742$	−2.45043	+	2.45043i	−0.0899581	+	0.0899581i
$743$	−20.8219	+	20.8219i	−0.763881	+	0.763881i	−0.977022	−	0.213141i	$-0.931631\pi$
$743$	−20.8219	+	20.8219i	−0.763881	+	0.763881i	0.213141	+	0.977022i	$0.431631\pi$
$744$	−1.31125			−0.0480726
$745$		0			0
$746$	7.73795			0.283306
$747$	15.8147	−	15.8147i	0.578630	−	0.578630i
$748$	−12.3282	−	12.3282i	−0.450763	−	0.450763i
$749$	3.13774			0.114650
$750$		0			0
$751$			35.9437i			1.31160i	0.754933	+	0.655802i	$0.227669\pi$
$751$			35.9437i			1.31160i	−0.754933	+	0.655802i	$0.772331\pi$
$752$	−4.20858	+	4.20858i	−0.153471	+	0.153471i
$753$	0.822472	−	0.822472i	0.0299726	−	0.0299726i
$754$	39.5714			1.44110
$755$		0			0
$756$		−	2.22544i		−	0.0809384i
$757$	7.77714	−	7.77714i	0.282665	−	0.282665i	−0.551506	−	0.834171i	$-0.685947\pi$
$757$	7.77714	−	7.77714i	0.282665	−	0.282665i	0.834171	+	0.551506i	$0.185947\pi$
$758$	−9.41719	−	9.41719i	−0.342048	−	0.342048i
$759$	17.6631			0.641131
$760$		0			0
$761$	34.7886			1.26109			0.630543	−	0.776154i	$-0.282832\pi$
$761$	34.7886			1.26109			0.630543	+	0.776154i	$0.282832\pi$
$762$	1.08044	+	1.08044i	0.0391403	+	0.0391403i
$763$	0.609517	−	0.609517i	0.0220660	−	0.0220660i
$764$			7.54014i			0.272793i
$765$		0			0
$766$	19.8592			0.717541
$767$	−37.4348	+	37.4348i	−1.35169	+	1.35169i
$768$	0.267657	−	0.267657i	0.00965824	−	0.00965824i
$769$		−	25.7435i		−	0.928333i	−0.885748	−	0.464166i	$-0.846354\pi$
$769$		−	25.7435i		−	0.928333i	0.885748	−	0.464166i	$-0.153646\pi$
$770$		0			0
$771$	6.20088			0.223319
$772$	−5.88017	−	5.88017i	−0.211632	−	0.211632i
$773$	1.08904	−	1.08904i	0.0391701	−	0.0391701i	−0.687250	−	0.726421i	$-0.741182\pi$
$773$	1.08904	−	1.08904i	0.0391701	−	0.0391701i	0.726421	+	0.687250i	$0.241182\pi$
$774$	−3.74586			−0.134642
$775$		0			0
$776$	−12.9564			−0.465107
$777$	−2.51289	+	2.51289i	−0.0901493	+	0.0901493i
$778$	8.84389	−	8.84389i	0.317069	−	0.317069i
$779$	−18.8199	+	35.1164i	−0.674292	+	1.25818i
$780$		0			0
$781$		−	77.8401i		−	2.78534i
$782$	−18.3741	−	18.3741i	−0.657056	−	0.657056i
$783$	−14.6466	−	14.6466i	−0.523425	−	0.523425i
$784$		−	5.99229i		−	0.214010i
$785$		0			0
$786$	5.19087			0.185152
$787$	24.4918	+	24.4918i	0.873040	+	0.873040i	0.992803	−	0.119763i	$-0.0382134\pi$
$787$	24.4918	+	24.4918i	0.873040	+	0.873040i	−0.119763	+	0.992803i	$0.538213\pi$
$788$	12.8237	+	12.8237i	0.456825	+	0.456825i
$789$	2.83117			0.100792
$790$		0			0
$791$			11.6400i			0.413872i
$792$	11.3028	+	11.3028i	0.401628	+	0.401628i
$793$	5.98954	−	5.98954i	0.212695	−	0.212695i
$794$	−25.8150			−0.916141
$795$		0			0
$796$	8.00986			0.283902
$797$	8.41216	+	8.41216i	0.297974	+	0.297974i	0.840220	−	0.542246i	$-0.182426\pi$
$797$	8.41216	+	8.41216i	0.297974	+	0.297974i	−0.542246	+	0.840220i	$0.682426\pi$
$798$	−1.58550	+	0.479051i	−0.0561262	+	0.0169582i
$799$		−	18.5452i		−	0.656081i
$800$		0			0
$801$			25.6966i			0.907943i
$802$	−6.75033	+	6.75033i	−0.238363	+	0.238363i
$803$	24.2436	+	24.2436i	0.855536	+	0.855536i
$804$		−	3.06271i		−	0.108014i
$805$		0			0
$806$		−	14.6713i		−	0.516775i
$807$	−4.96785	+	4.96785i	−0.174876	+	0.174876i
$808$	4.24264	−	4.24264i	0.149256	−	0.149256i
$809$		−	3.30643i		−	0.116248i	−0.998309	−	0.0581240i	$-0.981488\pi$
$809$		−	3.30643i		−	0.116248i	0.998309	−	0.0581240i	$-0.0185119\pi$
$810$		0			0
$811$			29.3864i			1.03190i	0.856620	+	0.515948i	$0.172560\pi$
$811$			29.3864i			1.03190i	−0.856620	+	0.515948i	$0.827440\pi$
$812$	6.63216	+	6.63216i	0.232743	+	0.232743i
$813$	3.72629	−	3.72629i	0.130687	−	0.130687i
$814$		−	52.3312i		−	1.83421i
$815$		0			0
$816$			1.17943i			0.0412885i
$817$	1.65312	+	5.47130i	0.0578355	+	0.191417i
$818$	7.92167	+	7.92167i	0.276975	+	0.276975i
$819$	12.1454			0.424396
$820$		0			0
$821$	−48.0995			−1.67868			−0.839342	−	0.543604i	$-0.817059\pi$
$821$	−48.0995			−1.67868			−0.839342	+	0.543604i	$0.817059\pi$
$822$	−4.67823	+	4.67823i	−0.163172	+	0.163172i
$823$	1.98892	+	1.98892i	0.0693295	+	0.0693295i	0.740921	−	0.671592i	$-0.234389\pi$
$823$	1.98892	+	1.98892i	0.0693295	+	0.0693295i	−0.671592	+	0.740921i	$0.734389\pi$
$824$			6.95639i			0.242337i
$825$		0			0
$826$	−12.5481			−0.436606
$827$	−36.0051	−	36.0051i	−1.25202	−	1.25202i	−0.954813	−	0.297207i	$-0.903945\pi$
$827$	−36.0051	−	36.0051i	−1.25202	−	1.25202i	−0.297207	−	0.954813i	$-0.596055\pi$
$828$	16.8458	+	16.8458i	0.585434	+	0.585434i
$829$	−49.7577			−1.72815			−0.864077	−	0.503359i	$-0.832097\pi$
$829$	−49.7577			−1.72815			−0.864077	+	0.503359i	$0.832097\pi$
$830$		0			0
$831$			9.80575i			0.340158i
$832$	2.99477	+	2.99477i	0.103825	+	0.103825i
$833$	13.2026	+	13.2026i	0.457442	+	0.457442i
$834$			4.19134i			0.145134i
$835$		0			0
$836$	11.5210	−	21.4973i	0.398463	−	0.743500i
$837$	−5.43030	+	5.43030i	−0.187698	+	0.187698i
$838$	4.88733	−	4.88733i	0.168830	−	0.168830i
$839$	−44.3918			−1.53258			−0.766288	−	0.642497i	$-0.777898\pi$
$839$	−44.3918			−1.53258			−0.766288	+	0.642497i	$0.777898\pi$
$840$		0			0
$841$	58.2982			2.01028
$842$	−6.35053	+	6.35053i	−0.218854	+	0.218854i
$843$	−2.92913	−	2.92913i	−0.100885	−	0.100885i
$844$	9.88184			0.340147
$845$		0			0
$846$			17.0027i			0.584565i
$847$	−14.4158	+	14.4158i	−0.495332	+	0.495332i
$848$	−2.44104	+	2.44104i	−0.0838257	+	0.0838257i
$849$	−10.2247			−0.350912
$850$		0			0
$851$		−	77.9951i		−	2.67364i
$852$	−3.72347	+	3.72347i	−0.127564	+	0.127564i
$853$	37.8438	+	37.8438i	1.29575	+	1.29575i	0.931175	+	0.364574i	$0.118785\pi$
$853$	37.8438	+	37.8438i	1.29575	+	1.29575i	0.364574	+	0.931175i	$0.381215\pi$
$854$	2.00769			0.0687019
$855$		0			0
$856$	3.12571			0.106835
$857$	20.1772	+	20.1772i	0.689240	+	0.689240i	0.962064	−	0.272824i	$-0.0879576\pi$
$857$	20.1772	+	20.1772i	0.689240	+	0.689240i	−0.272824	+	0.962064i	$0.587958\pi$
$858$	6.34294	−	6.34294i	0.216544	−	0.216544i
$859$		−	6.94256i		−	0.236877i	−0.992961	−	0.118438i	$-0.962211\pi$
$859$		−	6.94256i		−	0.236877i	0.992961	−	0.118438i	$-0.0377888\pi$
$860$		0			0
$861$	−3.47313			−0.118364
$862$	9.54964	−	9.54964i	0.325262	−	0.325262i
$863$	12.0170	−	12.0170i	0.409063	−	0.409063i	−0.472349	−	0.881412i	$-0.656594\pi$
$863$	12.0170	−	12.0170i	0.409063	−	0.409063i	0.881412	+	0.472349i	$0.156594\pi$
$864$		−	2.21691i		−	0.0754208i
$865$		0			0
$866$	−23.9941			−0.815353
$867$	1.95157	+	1.95157i	0.0662787	+	0.0662787i
$868$	2.45891	−	2.45891i	0.0834609	−	0.0834609i
$869$	30.6171			1.03861
$870$		0			0
$871$	34.2682			1.16113
$872$	0.607182	−	0.607182i	0.0205618	−	0.0205618i
$873$	−26.1720	+	26.1720i	−0.885787	+	0.885787i
$874$	17.1711	−	32.0399i	0.580820	−	1.08377i
$875$		0			0
$876$		−	2.31938i		−	0.0783644i
$877$	−32.4987	−	32.4987i	−1.09740	−	1.09740i	−0.994714	−	0.102689i	$-0.967255\pi$
$877$	−32.4987	−	32.4987i	−1.09740	−	1.09740i	−0.102689	−	0.994714i	$-0.532745\pi$
$878$	24.1888	+	24.1888i	0.816334	+	0.816334i
$879$			4.50315i			0.151887i
$880$		0			0
$881$	38.5449			1.29861			0.649305	−	0.760528i	$-0.275060\pi$
$881$	38.5449			1.29861			0.649305	+	0.760528i	$0.275060\pi$
$882$	−12.1045	−	12.1045i	−0.407578	−	0.407578i
$883$	2.14041	+	2.14041i	0.0720305	+	0.0720305i	0.742204	−	0.670174i	$-0.233780\pi$
$883$	2.14041	+	2.14041i	0.0720305	+	0.0720305i	−0.670174	+	0.742204i	$0.733780\pi$
$884$	−13.1965			−0.443846
$885$		0			0
$886$		−	14.1157i		−	0.474228i
$887$	−0.280827	−	0.280827i	−0.00942925	−	0.00942925i	0.702376	−	0.711806i	$-0.252122\pi$
$887$	−0.280827	−	0.280827i	−0.00942925	−	0.00942925i	−0.711806	+	0.702376i	$0.752122\pi$
$888$	−2.50326	+	2.50326i	−0.0840038	+	0.0840038i
$889$	−4.05220			−0.135906
$890$		0			0
$891$	43.2583			1.44921
$892$	1.07063	+	1.07063i	0.0358473	+	0.0358473i
$893$	24.8346	−	7.50363i	0.831058	−	0.251100i
$894$		−	1.96487i		−	0.0657150i
$895$		0			0
$896$			1.00385i			0.0335362i
$897$	9.45360	−	9.45360i	0.315646	−	0.315646i
$898$	−11.2206	−	11.2206i	−0.374438	−	0.374438i
$899$		−	32.3663i		−	1.07948i
$900$		0			0
$901$		−	10.7565i		−	0.358350i
$902$	36.1642	−	36.1642i	1.20414	−	1.20414i
$903$	−0.352314	+	0.352314i	−0.0117243	+	0.0117243i
$904$			11.5954i			0.385658i
$905$		0			0
$906$		−	2.41382i		−	0.0801937i
$907$	8.68507	+	8.68507i	0.288383	+	0.288383i	0.836441	−	0.548058i	$-0.184633\pi$
$907$	8.68507	+	8.68507i	0.288383	+	0.288383i	−0.548058	+	0.836441i	$0.684633\pi$
$908$	10.0734	−	10.0734i	0.334296	−	0.334296i
$909$		−	17.1403i		−	0.568508i
$910$		0			0
$911$		−	8.99084i		−	0.297880i	−0.988846	−	0.148940i	$-0.952414\pi$
$911$		−	8.99084i		−	0.297880i	0.988846	−	0.148940i	$-0.0475861\pi$
$912$	−1.57943	+	0.477216i	−0.0523001	+	0.0158022i
$913$	30.9761	+	30.9761i	1.02516	+	1.02516i
$914$	28.3247			0.936896
$915$		0			0
$916$	−13.4423			−0.444146
$917$	−9.73417	+	9.73417i	−0.321451	+	0.321451i
$918$	4.88442	+	4.88442i	0.161210	+	0.161210i
$919$		−	20.8360i		−	0.687317i	−0.939095	−	0.343659i	$-0.888334\pi$
$919$		−	20.8360i		−	0.687317i	0.939095	−	0.343659i	$-0.111666\pi$
$920$		0			0
$921$	−6.91928			−0.227998
$922$	−27.9821	−	27.9821i	−0.921540	−	0.921540i
$923$	−41.6613	−	41.6613i	−1.37130	−	1.37130i
$924$	2.12615			0.0699453
$925$		0			0
$926$		−	11.7775i		−	0.387031i
$927$	14.0520	+	14.0520i	0.461527	+	0.461527i
$928$	6.60675	+	6.60675i	0.216877	+	0.216877i
$929$		−	27.9065i		−	0.915581i	−0.889060	−	0.457791i	$-0.848641\pi$
$929$		−	27.9065i		−	0.915581i	0.889060	−	0.457791i	$-0.151359\pi$
$930$		0			0
$931$	−12.3381	+	23.0220i	−0.404366	+	0.754516i
$932$	−10.9619	+	10.9619i	−0.359070	+	0.359070i
$933$	−3.13782	+	3.13782i	−0.102728	+	0.102728i
$934$	−26.4016			−0.863886
$935$		0			0
$936$	12.0989			0.395465
$937$	−11.2974	+	11.2974i	−0.369070	+	0.369070i	−0.867138	−	0.498068i	$-0.834043\pi$
$937$	−11.2974	+	11.2974i	−0.369070	+	0.369070i	0.498068	+	0.867138i	$0.334043\pi$
$938$	5.74335	+	5.74335i	0.187527	+	0.187527i
$939$	−8.74752			−0.285464
$940$		0			0
$941$			4.26784i			0.139128i	0.997578	+	0.0695638i	$0.0221607\pi$
$941$			4.26784i			0.139128i	−0.997578	+	0.0695638i	$0.977839\pi$
$942$	1.62912	−	1.62912i	0.0530796	−	0.0530796i
$943$	53.8996	−	53.8996i	1.75521	−	1.75521i
$944$	−12.5001			−0.406842
$945$		0			0
$946$		−	7.33699i		−	0.238546i
$947$	12.7848	−	12.7848i	0.415451	−	0.415451i	−0.468181	−	0.883632i	$-0.655091\pi$
$947$	12.7848	−	12.7848i	0.415451	−	0.415451i	0.883632	+	0.468181i	$0.155091\pi$
$948$	−1.46456	−	1.46456i	−0.0475668	−	0.0475668i
$949$	25.9511			0.842409
$950$		0			0
$951$	3.95931			0.128389
$952$	−2.21173	−	2.21173i	−0.0716827	−	0.0716827i
$953$	37.5706	−	37.5706i	1.21703	−	1.21703i	0.248366	−	0.968666i	$-0.420106\pi$
$953$	37.5706	−	37.5706i	1.21703	−	1.21703i	0.968666	−	0.248366i	$-0.0798935\pi$
$954$			9.86183i			0.319289i
$955$		0			0
$956$	20.6959			0.669352
$957$	13.9931	−	13.9931i	0.452334	−	0.452334i
$958$	10.2848	−	10.2848i	0.332286	−	0.332286i
$959$		−	17.5457i		−	0.566580i
$960$		0			0
$961$	19.0000			0.612903
$962$	−28.0085	−	28.0085i	−0.903031	−	0.903031i
$963$	6.31396	−	6.31396i	0.203465	−	0.203465i
$964$	7.82904			0.252157
$965$		0			0
$966$	3.16885			0.101956
$967$	2.45555	−	2.45555i	0.0789650	−	0.0789650i	−0.666521	−	0.745486i	$-0.732217\pi$
$967$	2.45555	−	2.45555i	0.0789650	−	0.0789650i	0.745486	+	0.666521i	$0.232217\pi$
$968$	−14.3605	+	14.3605i	−0.461565	+	0.461565i
$969$	2.42846	−	4.53132i	0.0780134	−	0.145567i
$970$		0			0
$971$		−	3.95882i		−	0.127045i	−0.997980	−	0.0635223i	$-0.979767\pi$
$971$		−	3.95882i		−	0.127045i	0.997980	−	0.0635223i	$-0.0202334\pi$
$972$	−6.77203	−	6.77203i	−0.217213	−	0.217213i
$973$	−7.85981	−	7.85981i	−0.251974	−	0.251974i
$974$		−	31.6598i		−	1.01445i
$975$		0			0
$976$	2.00000			0.0640184
$977$	7.80485	+	7.80485i	0.249699	+	0.249699i	0.820847	−	0.571148i	$-0.193502\pi$
$977$	7.80485	+	7.80485i	0.249699	+	0.249699i	−0.571148	+	0.820847i	$0.693502\pi$
$978$	3.68576	+	3.68576i	0.117858	+	0.117858i
$979$	−50.3316			−1.60861
$980$		0			0
$981$		−	2.45302i		−	0.0783189i
$982$	−4.88208	−	4.88208i	−0.155793	−	0.155793i
$983$	−17.7520	+	17.7520i	−0.566202	+	0.566202i	−0.931062	−	0.364860i	$-0.881117\pi$
$983$	−17.7520	+	17.7520i	−0.566202	+	0.566202i	0.364860	+	0.931062i	$0.381117\pi$
$984$	−3.45982			−0.110295
$985$		0			0
$986$	−29.1127			−0.927138
$987$	1.59918	+	1.59918i	0.0509024	+	0.0509024i
$988$	−5.33949	−	17.6720i	−0.169872	−	0.562220i
$989$		−	10.9351i		−	0.347717i
$990$		0			0
$991$			23.1109i			0.734141i	0.930193	+	0.367071i	$0.119639\pi$
$991$			23.1109i			0.734141i	−0.930193	+	0.367071i	$0.880361\pi$
$992$	2.44949	−	2.44949i	0.0777714	−	0.0777714i
$993$	4.94727	+	4.94727i	0.156997	+	0.156997i
$994$		−	13.9649i		−	0.442939i
$995$		0			0
$996$		−	2.96348i		−	0.0939015i
$997$	0.574345	−	0.574345i	0.0181897	−	0.0181897i	−0.697953	−	0.716143i	$-0.745906\pi$
$997$	0.574345	−	0.574345i	0.0181897	−	0.0181897i	0.716143	+	0.697953i	$0.245906\pi$
$998$	−19.5855	+	19.5855i	−0.619967	+	0.619967i
$999$			20.7336i			0.655982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.f.d.493.13	yes	32
5.2	odd	4	inner	950.2.f.d.607.3	yes	32
5.3	odd	4	inner	950.2.f.d.607.14	yes	32
5.4	even	2	inner	950.2.f.d.493.4	yes	32
19.18	odd	2	inner	950.2.f.d.493.3	✓	32
95.18	even	4	inner	950.2.f.d.607.4	yes	32
95.37	even	4	inner	950.2.f.d.607.13	yes	32
95.94	odd	2	inner	950.2.f.d.493.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.f.d.493.3	✓	32	19.18	odd	2	inner
950.2.f.d.493.4	yes	32	5.4	even	2	inner
950.2.f.d.493.13	yes	32	1.1	even	1	trivial
950.2.f.d.493.14	yes	32	95.94	odd	2	inner
950.2.f.d.607.3	yes	32	5.2	odd	4	inner
950.2.f.d.607.4	yes	32	95.18	even	4	inner
950.2.f.d.607.13	yes	32	95.37	even	4	inner
950.2.f.d.607.14	yes	32	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.267657 - 0.267657i) q^{3} +1.00000i q^{4} +0.378524 q^{6} +(-0.709827 + 0.709827i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.85672i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.267657 - 0.267657i) q^{3} +1.00000i q^{4} +0.378524 q^{6} +(-0.709827 + 0.709827i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.85672i q^{9} -5.59543 q^{11} +(0.267657 + 0.267657i) q^{12} +(-2.99477 + 2.99477i) q^{13} -1.00385 q^{14} -1.00000 q^{16} +(2.20326 - 2.20326i) q^{17} +(-2.02001 + 2.02001i) q^{18} +(3.84194 + 2.05900i) q^{19} +0.379980i q^{21} +(-3.95657 - 3.95657i) q^{22} +(-5.89692 - 5.89692i) q^{23} +0.378524i q^{24} -4.23524 q^{26} +(1.56759 + 1.56759i) q^{27} +(-0.709827 - 0.709827i) q^{28} -9.34335 q^{29} +3.46410i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.49766 + 1.49766i) q^{33} +3.11588 q^{34} -2.85672 q^{36} +(6.61320 + 6.61320i) q^{37} +(1.26073 + 4.17260i) q^{38} +1.60314i q^{39} +9.14029i q^{41} +(-0.268687 + 0.268687i) q^{42} +(0.927191 + 0.927191i) q^{43} -5.59543i q^{44} -8.33950i q^{46} +(4.20858 - 4.20858i) q^{47} +(-0.267657 + 0.267657i) q^{48} +5.99229i q^{49} -1.17943i q^{51} +(-2.99477 - 2.99477i) q^{52} +(2.44104 - 2.44104i) q^{53} +2.21691i q^{54} -1.00385i q^{56} +(1.57943 - 0.477216i) q^{57} +(-6.60675 - 6.60675i) q^{58} +12.5001 q^{59} -2.00000 q^{61} +(-2.44949 + 2.44949i) q^{62} +(-2.02778 - 2.02778i) q^{63} -1.00000i q^{64} -2.11801 q^{66} +(-5.72134 - 5.72134i) q^{67} +(2.20326 + 2.20326i) q^{68} -3.15670 q^{69} +13.9114i q^{71} +(-2.02001 - 2.02001i) q^{72} +(-4.33274 - 4.33274i) q^{73} +9.35248i q^{74} +(-2.05900 + 3.84194i) q^{76} +(3.97179 - 3.97179i) q^{77} +(-1.13359 + 1.13359i) q^{78} -5.47180 q^{79} -7.73101 q^{81} +(-6.46316 + 6.46316i) q^{82} +(-5.53597 - 5.53597i) q^{83} -0.379980 q^{84} +1.31125i q^{86} +(-2.50081 + 2.50081i) q^{87} +(3.95657 - 3.95657i) q^{88} +8.99513 q^{89} -4.25154i q^{91} +(5.89692 - 5.89692i) q^{92} +(0.927191 + 0.927191i) q^{93} +5.95183 q^{94} -0.378524 q^{96} +(9.16155 + 9.16155i) q^{97} +(-4.23719 + 4.23719i) q^{98} -15.9846i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{6}+O(q^{10}) \) 32 * q - 8 * q^6	\( 32 q - 8 q^{6} - 24 q^{11} - 32 q^{16} + 32 q^{26} + 56 q^{36} - 64 q^{61} + 72 q^{66} + 4 q^{76} - 32 q^{81} + 8 q^{96}+O(q^{100}) \) 32 * q - 8 * q^6 - 24 * q^11 - 32 * q^16 + 32 * q^26 + 56 * q^36 - 64 * q^61 + 72 * q^66 + 4 * q^76 - 32 * q^81 + 8 * q^96

Introduction

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