LMFDB - Embedded newform 1008.2.q.k.625.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(529,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))

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

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

chi := DirichletCharacter("1008.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.q (of order $3$, 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.8
Character	$\chi$	$=$	1008.625
Dual form			1008.2.q.k.529.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13364 - 1.30952i) q^{3} +(-0.170100 - 0.294622i) q^{5} +(2.63360 + 0.253251i) q^{7} +(-0.429705 - 2.96907i) q^{9} +O(q^{10})$	\(q+(1.13364 - 1.30952i) q^{3} +(-0.170100 - 0.294622i) q^{5} +(2.63360 + 0.253251i) q^{7} +(-0.429705 - 2.96907i) q^{9} +(-0.335794 + 0.581612i) q^{11} +(1.62370 - 2.81233i) q^{13} +(-0.578647 - 0.111246i) q^{15} +(-1.10014 - 1.90550i) q^{17} +(-0.242085 + 0.419303i) q^{19} +(3.31720 - 3.16167i) q^{21} +(2.09495 + 3.62856i) q^{23} +(2.44213 - 4.22990i) q^{25} +(-4.37520 - 2.80315i) q^{27} +(0.478868 + 0.829424i) q^{29} -2.08263 q^{31} +(0.380964 + 1.09907i) q^{33} +(-0.373363 - 0.818995i) q^{35} +(4.81613 - 8.34178i) q^{37} +(-1.84212 - 5.31445i) q^{39} +(-3.90207 + 6.75858i) q^{41} +(3.66119 + 6.34136i) q^{43} +(-0.801659 + 0.631639i) q^{45} +2.69901 q^{47} +(6.87173 + 1.33392i) q^{49} +(-3.74247 - 0.719498i) q^{51} +(-6.12335 - 10.6059i) q^{53} +0.228474 q^{55} +(0.274649 + 0.792355i) q^{57} +4.94297 q^{59} -3.52119 q^{61} +(-0.379756 - 7.92816i) q^{63} -1.10477 q^{65} -12.3202 q^{67} +(7.12661 + 1.37011i) q^{69} +5.57304 q^{71} +(-3.71686 - 6.43779i) q^{73} +(-2.77064 - 7.99322i) q^{75} +(-1.03164 + 1.44669i) q^{77} +10.0127 q^{79} +(-8.63071 + 2.55165i) q^{81} +(-2.47376 - 4.28468i) q^{83} +(-0.374269 + 0.648252i) q^{85} +(1.62902 + 0.313182i) q^{87} +(-8.52177 + 14.7601i) q^{89} +(4.98840 - 6.99536i) q^{91} +(-2.36096 + 2.72725i) q^{93} +0.164714 q^{95} +(4.23657 + 7.33795i) q^{97} +(1.87114 + 0.747072i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} + 3 q^{5} + 5 q^{7} + 10 q^{9}+O(q^{10}) $ 22 * q - 2 * q^3 + 3 * q^5 + 5 * q^7 + 10 * q^9	$ 22 q - 2 q^{3} + 3 q^{5} + 5 q^{7} + 10 q^{9} + 3 q^{11} - 3 q^{13} + q^{15} + 7 q^{17} + q^{19} - 2 q^{23} - 10 q^{25} + 4 q^{27} + 9 q^{29} - 8 q^{31} + 29 q^{33} - 14 q^{35} + 2 q^{37} + 16 q^{39} + 16 q^{41} + q^{45} + 10 q^{47} + 15 q^{49} - 7 q^{51} + 11 q^{53} - 22 q^{55} + 7 q^{57} - 38 q^{59} + 26 q^{61} - 48 q^{63} - 26 q^{65} + 52 q^{67} - 4 q^{69} + 48 q^{71} - 35 q^{73} + 23 q^{75} + 17 q^{77} + 20 q^{79} - 38 q^{81} + 28 q^{83} - 20 q^{85} + 33 q^{87} + 6 q^{89} + 37 q^{91} + 19 q^{93} + 24 q^{95} - 29 q^{97} + 56 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 + 3 * q^5 + 5 * q^7 + 10 * q^9 + 3 * q^11 - 3 * q^13 + q^15 + 7 * q^17 + q^19 - 2 * q^23 - 10 * q^25 + 4 * q^27 + 9 * q^29 - 8 * q^31 + 29 * q^33 - 14 * q^35 + 2 * q^37 + 16 * q^39 + 16 * q^41 + q^45 + 10 * q^47 + 15 * q^49 - 7 * q^51 + 11 * q^53 - 22 * q^55 + 7 * q^57 - 38 * q^59 + 26 * q^61 - 48 * q^63 - 26 * q^65 + 52 * q^67 - 4 * q^69 + 48 * q^71 - 35 * q^73 + 23 * q^75 + 17 * q^77 + 20 * q^79 - 38 * q^81 + 28 * q^83 - 20 * q^85 + 33 * q^87 + 6 * q^89 + 37 * q^91 + 19 * q^93 + 24 * q^95 - 29 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	1.13364	−	1.30952i	0.654509	−	0.756054i
$3$	1.13364	−	1.30952i	0.654509	−	0.756054i
$4$		0			0
$5$	−0.170100	−	0.294622i	−0.0760711	−	0.131759i	0.825480	−	0.564431i	$-0.190904\pi$
$5$	−0.170100	−	0.294622i	−0.0760711	−	0.131759i	−0.901552	+	0.432672i	$0.857571\pi$
$6$		0			0
$7$	2.63360	+	0.253251i	0.995408	+	0.0957197i
$7$	2.63360	+	0.253251i	0.995408	+	0.0957197i
$8$		0			0
$9$	−0.429705	−	2.96907i	−0.143235	−	0.989689i
$10$		0			0
$11$	−0.335794	+	0.581612i	−0.101246	+	0.175363i	−0.912198	−	0.409749i	$-0.865616\pi$
$11$	−0.335794	+	0.581612i	−0.101246	+	0.175363i	0.810952	+	0.585112i	$0.198949\pi$
$12$		0			0
$13$	1.62370	−	2.81233i	0.450333	−	0.780000i	−0.548073	−	0.836430i	$-0.684639\pi$
$13$	1.62370	−	2.81233i	0.450333	−	0.780000i	0.998407	+	0.0564303i	$0.0179719\pi$
$14$		0			0
$15$	−0.578647	−	0.111246i	−0.149406	−	0.0287236i
$16$		0			0
$17$	−1.10014	−	1.90550i	−0.266824	−	0.462152i	0.701216	−	0.712949i	$-0.252641\pi$
$17$	−1.10014	−	1.90550i	−0.266824	−	0.462152i	−0.968040	+	0.250796i	$0.919308\pi$
$18$		0			0
$19$	−0.242085	+	0.419303i	−0.0555380	+	0.0961946i	−0.892458	−	0.451131i	$-0.851021\pi$
$19$	−0.242085	+	0.419303i	−0.0555380	+	0.0961946i	0.836920	+	0.547326i	$0.184354\pi$
$20$		0			0
$21$	3.31720	−	3.16167i	0.723873	−	0.689933i
$22$		0			0
$23$	2.09495	+	3.62856i	0.436827	+	0.756607i	0.997443	−	0.0714692i	$-0.0227688\pi$
$23$	2.09495	+	3.62856i	0.436827	+	0.756607i	−0.560616	+	0.828076i	$0.689435\pi$
$24$		0			0
$25$	2.44213	−	4.22990i	0.488426	−	0.845979i
$26$		0			0
$27$	−4.37520	−	2.80315i	−0.842007	−	0.539467i
$28$		0			0
$29$	0.478868	+	0.829424i	0.0889235	+	0.154020i	0.907056	−	0.421009i	$-0.138324\pi$
$29$	0.478868	+	0.829424i	0.0889235	+	0.154020i	−0.818133	+	0.575029i	$0.804991\pi$
$30$		0			0
$31$	−2.08263			−0.374052			−0.187026	−	0.982355i	$-0.559885\pi$
$31$	−2.08263			−0.374052			−0.187026	+	0.982355i	$0.559885\pi$
$32$		0			0
$33$	0.380964	+	1.09907i	0.0663174	+	0.191324i
$34$		0			0
$35$	−0.373363	−	0.818995i	−0.0631098	−	0.138435i
$36$		0			0
$37$	4.81613	−	8.34178i	0.791767	−	1.37138i	−0.133105	−	0.991102i	$-0.542495\pi$
$37$	4.81613	−	8.34178i	0.791767	−	1.37138i	0.924872	−	0.380278i	$-0.124172\pi$
$38$		0			0
$39$	−1.84212	−	5.31445i	−0.294975	−	0.850993i
$40$		0			0
$41$	−3.90207	+	6.75858i	−0.609400	+	1.05551i	0.381939	+	0.924188i	$0.375256\pi$
$41$	−3.90207	+	6.75858i	−0.609400	+	1.05551i	−0.991339	+	0.131325i	$0.958077\pi$
$42$		0			0
$43$	3.66119	+	6.34136i	0.558326	+	0.967048i	0.997636	+	0.0687132i	$0.0218893\pi$
$43$	3.66119	+	6.34136i	0.558326	+	0.967048i	−0.439311	+	0.898335i	$0.644777\pi$
$44$		0			0
$45$	−0.801659	+	0.631639i	−0.119504	+	0.0941592i
$46$		0			0
$47$	2.69901			0.393692			0.196846	−	0.980434i	$-0.436930\pi$
$47$	2.69901			0.393692			0.196846	+	0.980434i	$0.436930\pi$
$48$		0			0
$49$	6.87173	+	1.33392i	0.981675	+	0.190560i
$50$		0			0
$51$	−3.74247	−	0.719498i	−0.524051	−	0.100750i
$52$		0			0
$53$	−6.12335	−	10.6059i	−0.841107	−	1.45684i	−0.888960	−	0.457985i	$-0.848571\pi$
$53$	−6.12335	−	10.6059i	−0.841107	−	1.45684i	0.0478535	−	0.998854i	$-0.484762\pi$
$54$		0			0
$55$	0.228474			0.0308075
$56$		0			0
$57$	0.274649	+	0.792355i	0.0363782	+	0.104950i
$58$		0			0
$59$	4.94297			0.643520			0.321760	−	0.946821i	$-0.395726\pi$
$59$	4.94297			0.643520			0.321760	+	0.946821i	$0.395726\pi$
$60$		0			0
$61$	−3.52119			−0.450842			−0.225421	−	0.974261i	$-0.572376\pi$
$61$	−3.52119			−0.450842			−0.225421	+	0.974261i	$0.572376\pi$
$62$		0			0
$63$	−0.379756	−	7.92816i	−0.0478447	−	0.998855i
$64$		0			0
$65$	−1.10477			−0.137029
$66$		0			0
$67$	−12.3202			−1.50516			−0.752579	−	0.658502i	$-0.771190\pi$
$67$	−12.3202			−1.50516			−0.752579	+	0.658502i	$0.771190\pi$
$68$		0			0
$69$	7.12661	+	1.37011i	0.857943	+	0.164941i
$70$		0			0
$71$	5.57304			0.661398			0.330699	−	0.943736i	$-0.392715\pi$
$71$	5.57304			0.661398			0.330699	+	0.943736i	$0.392715\pi$
$72$		0			0
$73$	−3.71686	−	6.43779i	−0.435026	−	0.753487i	0.562272	−	0.826952i	$-0.309927\pi$
$73$	−3.71686	−	6.43779i	−0.435026	−	0.753487i	−0.997298	+	0.0734657i	$0.976594\pi$
$74$		0			0
$75$	−2.77064	−	7.99322i	−0.319926	−	0.922978i
$76$		0			0
$77$	−1.03164	+	1.44669i	−0.117566	+	0.164866i
$78$		0			0
$79$	10.0127			1.12652			0.563260	−	0.826279i	$-0.309547\pi$
$79$	10.0127			1.12652			0.563260	+	0.826279i	$0.309547\pi$
$80$		0			0
$81$	−8.63071	+	2.55165i	−0.958967	+	0.283516i
$82$		0			0
$83$	−2.47376	−	4.28468i	−0.271530	−	0.470305i	0.697723	−	0.716367i	$-0.254196\pi$
$83$	−2.47376	−	4.28468i	−0.271530	−	0.470305i	−0.969254	+	0.246063i	$0.920863\pi$
$84$		0			0
$85$	−0.374269	+	0.648252i	−0.0405951	+	0.0703128i
$86$		0			0
$87$	1.62902	+	0.313182i	0.174649	+	0.0335766i
$88$		0			0
$89$	−8.52177	+	14.7601i	−0.903306	+	1.56457i	−0.0801310	+	0.996784i	$0.525534\pi$
$89$	−8.52177	+	14.7601i	−0.903306	+	1.56457i	−0.823175	+	0.567788i	$0.807799\pi$
$90$		0			0
$91$	4.98840	−	6.99536i	0.522927	−	0.733313i
$92$		0			0
$93$	−2.36096	+	2.72725i	−0.244820	+	0.282803i
$94$		0			0
$95$	0.164714			0.0168993
$96$		0			0
$97$	4.23657	+	7.33795i	0.430159	+	0.745056i	0.996887	−	0.0788485i	$-0.0251243\pi$
$97$	4.23657	+	7.33795i	0.430159	+	0.745056i	−0.566728	+	0.823905i	$0.691791\pi$
$98$		0			0
$99$	1.87114	+	0.747072i	0.188056	+	0.0750836i
$100$		0			0
$101$	2.28693	−	3.96107i	0.227558	−	0.394141i	−0.729526	−	0.683953i	$-0.760259\pi$
$101$	2.28693	−	3.96107i	0.227558	−	0.394141i	0.957084	+	0.289812i	$0.0935927\pi$
$102$		0			0
$103$	−0.903563	−	1.56502i	−0.0890307	−	0.154206i	0.818071	−	0.575117i	$-0.195044\pi$
$103$	−0.903563	−	1.56502i	−0.0890307	−	0.154206i	−0.907102	+	0.420912i	$0.861710\pi$
$104$		0			0
$105$	−1.49575	−	0.439521i	−0.145971	−	0.0428928i
$106$		0			0
$107$	−3.88188	+	6.72361i	−0.375275	+	0.649996i	−0.990368	−	0.138459i	$-0.955785\pi$
$107$	−3.88188	+	6.72361i	−0.375275	+	0.649996i	0.615093	+	0.788454i	$0.289118\pi$
$108$		0			0
$109$	−1.07178	−	1.85638i	−0.102658	−	0.177809i	0.810121	−	0.586263i	$-0.199401\pi$
$109$	−1.07178	−	1.85638i	−0.102658	−	0.177809i	−0.912779	+	0.408454i	$0.866068\pi$
$110$		0			0
$111$	−5.46399	−	15.7634i	−0.518619	−	1.49620i
$112$		0			0
$113$	−7.91006	+	13.7006i	−0.744116	+	1.28885i	0.206491	+	0.978449i	$0.433796\pi$
$113$	−7.91006	+	13.7006i	−0.744116	+	1.28885i	−0.950607	+	0.310398i	$0.899538\pi$
$114$		0			0
$115$	0.712702	−	1.23444i	0.0664598	−	0.115112i
$116$		0			0
$117$	−9.04771	−	3.61240i	−0.836461	−	0.333966i
$118$		0			0
$119$	−2.41477	−	5.29695i	−0.221362	−	0.485571i
$120$		0			0
$121$	5.27449	+	9.13568i	0.479499	+	0.830516i
$122$		0			0
$123$	4.42697	+	12.7717i	0.399166	+	1.15158i
$124$		0			0
$125$	−3.36263			−0.300763
$126$		0			0
$127$	13.8820			1.23183			0.615915	−	0.787812i	$-0.288786\pi$
$127$	13.8820			1.23183			0.615915	+	0.787812i	$0.288786\pi$
$128$		0			0
$129$	12.4546	+	2.39443i	1.09657	+	0.210818i
$130$		0			0
$131$	−2.08769	−	3.61599i	−0.182402	−	0.315930i	0.760296	−	0.649577i	$-0.225054\pi$
$131$	−2.08769	−	3.61599i	−0.182402	−	0.315930i	−0.942698	+	0.333647i	$0.891721\pi$
$132$		0			0
$133$	−0.743743	+	1.04297i	−0.0644907	+	0.0904369i
$134$		0			0
$135$	−0.0816493	+	1.76585i	−0.00702725	+	0.151980i
$136$		0			0
$137$	6.38043	−	11.0512i	0.545117	−	0.944170i	−0.453483	−	0.891265i	$-0.649819\pi$
$137$	6.38043	−	11.0512i	0.545117	−	0.944170i	0.998600	−	0.0529051i	$-0.0168481\pi$
$138$		0			0
$139$	−5.95986	+	10.3228i	−0.505509	+	0.875567i	0.494471	+	0.869194i	$0.335362\pi$
$139$	−5.95986	+	10.3228i	−0.505509	+	0.875567i	−0.999980	+	0.00637264i	$0.997972\pi$
$140$		0			0
$141$	3.05972	−	3.53442i	0.257675	−	0.297652i
$142$		0			0
$143$	1.09046	+	1.88873i	0.0911885	+	0.157943i
$144$		0			0
$145$	0.162911	−	0.282170i	0.0135290	−	0.0234329i
$146$		0			0
$147$	9.53689	−	7.48650i	0.786590	−	0.617476i
$148$		0			0
$149$	5.37548	+	9.31060i	0.440376	+	0.762754i	0.997717	−	0.0675295i	$-0.0215117\pi$
$149$	5.37548	+	9.31060i	0.440376	+	0.762754i	−0.557341	+	0.830284i	$0.688178\pi$
$150$		0			0
$151$	−1.29050	+	2.23521i	−0.105019	+	0.181899i	−0.913746	−	0.406286i	$-0.866824\pi$
$151$	−1.29050	+	2.23521i	−0.105019	+	0.181899i	0.808727	+	0.588184i	$0.200157\pi$
$152$		0			0
$153$	−5.18483	+	4.08520i	−0.419168	+	0.330269i
$154$		0			0
$155$	0.354256	+	0.613589i	0.0284545	+	0.0492846i
$156$		0			0
$157$	7.99693			0.638224			0.319112	−	0.947717i	$-0.396615\pi$
$157$	7.99693			0.638224			0.319112	+	0.947717i	$0.396615\pi$
$158$		0			0
$159$	−20.8304	−	4.00469i	−1.65196	−	0.317593i
$160$		0			0
$161$	4.59833	+	10.0867i	0.362399	+	0.794946i
$162$		0			0
$163$	−4.13306	+	7.15868i	−0.323727	+	0.560711i	−0.981254	−	0.192720i	$-0.938269\pi$
$163$	−4.13306	+	7.15868i	−0.323727	+	0.560711i	0.657527	+	0.753431i	$0.271602\pi$
$164$		0			0
$165$	0.259008	−	0.299192i	0.0201638	−	0.0232921i
$166$		0			0
$167$	−8.99384	+	15.5778i	−0.695964	+	1.20544i	0.273891	+	0.961761i	$0.411689\pi$
$167$	−8.99384	+	15.5778i	−0.695964	+	1.20544i	−0.969855	+	0.243684i	$0.921644\pi$
$168$		0			0
$169$	1.22720	+	2.12557i	0.0944000	+	0.163506i
$170$		0			0
$171$	1.34896	+	0.538588i	0.103158	+	0.0411869i
$172$		0			0
$173$	−16.9983			−1.29236			−0.646179	−	0.763186i	$-0.723634\pi$
$173$	−16.9983			−1.29236			−0.646179	+	0.763186i	$0.723634\pi$
$174$		0			0
$175$	7.50283	−	10.5214i	0.567161	−	0.795343i
$176$		0			0
$177$	5.60356	−	6.47293i	0.421190	−	0.486536i
$178$		0			0
$179$	9.65073	+	16.7156i	0.721329	+	1.24938i	0.960467	+	0.278393i	$0.0898019\pi$
$179$	9.65073	+	16.7156i	0.721329	+	1.24938i	−0.239138	+	0.970986i	$0.576865\pi$
$180$		0			0
$181$	21.9640			1.63257			0.816287	−	0.577646i	$-0.196029\pi$
$181$	21.9640			1.63257			0.816287	+	0.577646i	$0.196029\pi$
$182$		0			0
$183$	−3.99177	+	4.61108i	−0.295080	+	0.340861i
$184$		0			0
$185$	−3.27690			−0.240922
$186$		0			0
$187$	1.47768			0.108059
$188$		0			0
$189$	−10.8126	−	8.49041i	−0.786503	−	0.617587i
$190$		0			0
$191$	−6.65744			−0.481716			−0.240858	−	0.970560i	$-0.577429\pi$
$191$	−6.65744			−0.481716			−0.240858	+	0.970560i	$0.577429\pi$
$192$		0			0
$193$	6.34906			0.457015			0.228508	−	0.973542i	$-0.426615\pi$
$193$	6.34906			0.457015			0.228508	+	0.973542i	$0.426615\pi$
$194$		0			0
$195$	−1.25241	+	1.44672i	−0.0896870	+	0.103602i
$196$		0			0
$197$	23.8112			1.69648			0.848239	−	0.529614i	$-0.177663\pi$
$197$	23.8112			1.69648			0.848239	+	0.529614i	$0.177663\pi$
$198$		0			0
$199$	10.4771	+	18.1468i	0.742701	+	1.28640i	0.951261	+	0.308386i	$0.0997887\pi$
$199$	10.4771	+	18.1468i	0.742701	+	1.28640i	−0.208561	+	0.978009i	$0.566878\pi$
$200$		0			0
$201$	−13.9668	+	16.1337i	−0.985140	+	1.13798i
$202$		0			0
$203$	1.05110	+	2.30565i	0.0737725	+	0.161825i
$204$		0			0
$205$	2.65497			0.185431
$206$		0			0
$207$	9.87322	−	7.77926i	0.686236	−	0.540696i
$208$		0			0
$209$	−0.162581	−	0.281599i	−0.0112460	−	0.0194786i
$210$		0			0
$211$	6.32431	−	10.9540i	0.435384	−	0.754106i	−0.561943	−	0.827176i	$-0.689946\pi$
$211$	6.32431	−	10.9540i	0.435384	−	0.754106i	0.997327	+	0.0730693i	$0.0232794\pi$
$212$		0			0
$213$	6.31784	−	7.29803i	0.432891	−	0.500053i
$214$		0			0
$215$	1.24554	−	2.15733i	0.0849448	−	0.147129i
$216$		0			0
$217$	−5.48482	−	0.527427i	−0.372334	−	0.0358041i
$218$		0			0
$219$	−12.6440	−	2.43084i	−0.854405	−	0.164261i
$220$		0			0
$221$	−7.14520			−0.480638
$222$		0			0
$223$	1.34432	+	2.32843i	0.0900225	+	0.155924i	0.907520	−	0.420008i	$-0.137973\pi$
$223$	1.34432	+	2.32843i	0.0900225	+	0.155924i	−0.817498	+	0.575932i	$0.804639\pi$
$224$		0			0
$225$	−13.6082	−	5.43324i	−0.907216	−	0.362216i
$226$		0			0
$227$	13.9942	−	24.2387i	0.928829	−	1.60878i	0.143546	−	0.989644i	$-0.454150\pi$
$227$	13.9942	−	24.2387i	0.928829	−	1.60878i	0.785284	−	0.619136i	$-0.212517\pi$
$228$		0			0
$229$	−12.2695	−	21.2514i	−0.810790	−	1.40433i	−0.912312	−	0.409497i	$-0.865704\pi$
$229$	−12.2695	−	21.2514i	−0.810790	−	1.40433i	0.101521	−	0.994833i	$-0.467629\pi$
$230$		0			0
$231$	0.724968	+	2.99099i	0.0476994	+	0.196793i
$232$		0			0
$233$	−4.61844	+	7.99938i	−0.302564	+	0.524057i	−0.976716	−	0.214536i	$-0.931176\pi$
$233$	−4.61844	+	7.99938i	−0.302564	+	0.524057i	0.674152	+	0.738593i	$0.264509\pi$
$234$		0			0
$235$	−0.459103	−	0.795189i	−0.0299486	−	0.0518724i
$236$		0			0
$237$	11.3509	−	13.1119i	0.737318	−	0.851711i
$238$		0			0
$239$	−14.0126	+	24.2706i	−0.906403	+	1.56994i	−0.0873796	+	0.996175i	$0.527849\pi$
$239$	−14.0126	+	24.2706i	−0.906403	+	1.56994i	−0.819023	+	0.573760i	$0.805484\pi$
$240$		0			0
$241$	−9.91411	+	17.1717i	−0.638624	+	1.10613i	0.347111	+	0.937824i	$0.387163\pi$
$241$	−9.91411	+	17.1717i	−0.638624	+	1.10613i	−0.985735	+	0.168305i	$0.946171\pi$
$242$		0			0
$243$	−6.44270	+	14.1948i	−0.413299	+	0.910595i
$244$		0			0
$245$	−0.775879	−	2.25146i	−0.0495691	−	0.143841i
$246$		0			0
$247$	0.786145	+	1.36164i	0.0500212	+	0.0866393i
$248$		0			0
$249$	−8.41525	−	1.61785i	−0.533295	−	0.102527i
$250$		0			0
$251$	−16.5759			−1.04626			−0.523132	−	0.852252i	$-0.675236\pi$
$251$	−16.5759			−1.04626			−0.523132	+	0.852252i	$0.675236\pi$
$252$		0			0
$253$	−2.81389			−0.176907
$254$		0			0
$255$	0.424615	+	1.22500i	0.0265904	+	0.0767125i
$256$		0			0
$257$	−3.64750	−	6.31766i	−0.227525	−	0.394085i	0.729549	−	0.683929i	$-0.239730\pi$
$257$	−3.64750	−	6.31766i	−0.227525	−	0.394085i	−0.957074	+	0.289844i	$0.906397\pi$
$258$		0			0
$259$	14.7963	−	20.7493i	0.919399	−	1.28930i
$260$		0			0
$261$	2.25684	−	1.77820i	0.139695	−	0.110068i
$262$		0			0
$263$	−13.3899	+	23.1920i	−0.825657	+	1.43008i	0.0757586	+	0.997126i	$0.475862\pi$
$263$	−13.3899	+	23.1920i	−0.825657	+	1.43008i	−0.901416	+	0.432954i	$0.857471\pi$
$264$		0			0
$265$	−2.08316	+	3.60815i	−0.127968	+	0.221647i
$266$		0			0
$267$	9.66811	+	27.8922i	0.591679	+	1.70698i
$268$		0			0
$269$	10.1791	+	17.6307i	0.620630	+	1.07496i	0.989369	+	0.145429i	$0.0464562\pi$
$269$	10.1791	+	17.6307i	0.620630	+	1.07496i	−0.368739	+	0.929533i	$0.620210\pi$
$270$		0			0
$271$	−5.45842	+	9.45427i	−0.331576	+	0.574306i	−0.982821	−	0.184561i	$-0.940914\pi$
$271$	−5.45842	+	9.45427i	−0.331576	+	0.574306i	0.651245	+	0.758867i	$0.274247\pi$
$272$		0			0
$273$	−3.50552	−	14.4627i	−0.212164	−	0.875321i
$274$		0			0
$275$	1.64011	+	2.84075i	0.0989021	+	0.171303i
$276$		0			0
$277$	−8.83689	+	15.3059i	−0.530957	+	0.919645i	0.468390	+	0.883522i	$0.344834\pi$
$277$	−8.83689	+	15.3059i	−0.530957	+	0.919645i	−0.999347	+	0.0361231i	$0.988499\pi$
$278$		0			0
$279$	0.894918	+	6.18347i	0.0535773	+	0.370195i
$280$		0			0
$281$	7.17614	+	12.4294i	0.428092	+	0.741478i	0.996704	−	0.0811286i	$-0.0258524\pi$
$281$	7.17614	+	12.4294i	0.428092	+	0.741478i	−0.568611	+	0.822606i	$0.692519\pi$
$282$		0			0
$283$	−9.72841			−0.578294			−0.289147	−	0.957285i	$-0.593372\pi$
$283$	−9.72841			−0.578294			−0.289147	+	0.957285i	$0.593372\pi$
$284$		0			0
$285$	0.186727	−	0.215697i	0.0110608	−	0.0127768i
$286$		0			0
$287$	−11.9881	+	16.8112i	−0.707636	+	0.992334i
$288$		0			0
$289$	6.07937	−	10.5298i	0.357610	−	0.619399i
$290$		0			0
$291$	14.4120	+	2.77073i	0.844846	+	0.162423i
$292$		0			0
$293$	6.26345	−	10.8486i	0.365915	−	0.633783i	−0.623008	−	0.782216i	$-0.714089\pi$
$293$	6.26345	−	10.8486i	0.365915	−	0.633783i	0.988923	+	0.148433i	$0.0474228\pi$
$294$		0			0
$295$	−0.840799	−	1.45631i	−0.0489532	−	0.0847895i
$296$		0			0
$297$	3.09951	−	1.60338i	0.179852	−	0.0930378i
$298$		0			0
$299$	13.6063			0.786871
$300$		0			0
$301$	8.03616	+	17.6278i	0.463196	+	1.01605i
$302$		0			0
$303$	−2.59456	−	7.48523i	−0.149054	−	0.430015i
$304$		0			0
$305$	0.598954	+	1.03742i	0.0342960	+	0.0594025i
$306$		0			0
$307$	−25.8747			−1.47675			−0.738375	−	0.674391i	$-0.764406\pi$
$307$	−25.8747			−1.47675			−0.738375	+	0.674391i	$0.764406\pi$
$308$		0			0
$309$	−3.07375	−	0.590934i	−0.174859	−	0.0336171i
$310$		0			0
$311$	−28.4001			−1.61042			−0.805211	−	0.592988i	$-0.797948\pi$
$311$	−28.4001			−1.61042			−0.805211	+	0.592988i	$0.797948\pi$
$312$		0			0
$313$	−12.2015			−0.689668			−0.344834	−	0.938664i	$-0.612065\pi$
$313$	−12.2015			−0.689668			−0.344834	+	0.938664i	$0.612065\pi$
$314$		0			0
$315$	−2.27121	+	1.46047i	−0.127968	+	0.0822879i
$316$		0			0
$317$	−3.95219			−0.221977			−0.110988	−	0.993822i	$-0.535402\pi$
$317$	−3.95219			−0.221977			−0.110988	+	0.993822i	$0.535402\pi$
$318$		0			0
$319$	−0.643204			−0.0360125
$320$		0			0
$321$	4.40406	+	12.7056i	0.245811	+	0.709156i
$322$		0			0
$323$	1.06531			0.0592754
$324$		0			0
$325$	−7.93058	−	13.7362i	−0.439909	−	0.761945i
$326$		0			0
$327$	−3.64600	−	0.700951i	−0.201624	−	0.0387627i
$328$		0			0
$329$	7.10813	+	0.683527i	0.391884	+	0.0376841i
$330$		0			0
$331$	8.88286			0.488246			0.244123	−	0.969744i	$-0.421500\pi$
$331$	8.88286			0.488246			0.244123	+	0.969744i	$0.421500\pi$
$332$		0			0
$333$	−26.8368	−	10.7149i	−1.47065	−	0.587173i
$334$		0			0
$335$	2.09567	+	3.62981i	0.114499	+	0.198318i
$336$		0			0
$337$	−11.9741	+	20.7397i	−0.652269	+	1.12976i	0.330302	+	0.943875i	$0.392849\pi$
$337$	−11.9741	+	20.7397i	−0.652269	+	1.12976i	−0.982571	+	0.185887i	$0.940484\pi$
$338$		0			0
$339$	8.97411	+	25.8900i	0.487407	+	1.40615i
$340$		0			0
$341$	0.699335	−	1.21128i	0.0378711	−	0.0655947i
$342$		0			0
$343$	17.7596	+	5.25329i	0.958928	+	0.283651i
$344$		0			0
$345$	−0.808574	−	2.33271i	−0.0435322	−	0.125589i
$346$		0			0
$347$	−9.49059			−0.509481			−0.254741	−	0.967009i	$-0.581990\pi$
$347$	−9.49059			−0.509481			−0.254741	+	0.967009i	$0.581990\pi$
$348$		0			0
$349$	4.26145	+	7.38104i	0.228110	+	0.395098i	0.957248	−	0.289269i	$-0.0934121\pi$
$349$	4.26145	+	7.38104i	0.228110	+	0.395098i	−0.729138	+	0.684367i	$0.760079\pi$
$350$		0			0
$351$	−14.9874	+	7.75302i	−0.799968	+	0.413825i
$352$		0			0
$353$	18.5872	−	32.1940i	0.989297	−	1.71351i	0.368279	−	0.929715i	$-0.379947\pi$
$353$	18.5872	−	32.1940i	0.989297	−	1.71351i	0.621018	−	0.783797i	$-0.286719\pi$
$354$		0			0
$355$	−0.947975	−	1.64194i	−0.0503133	−	0.0871451i
$356$		0			0
$357$	−9.67397	−	2.84265i	−0.512001	−	0.150449i
$358$		0			0
$359$	5.30964	−	9.19657i	0.280232	−	0.485376i	−0.691210	−	0.722654i	$-0.742922\pi$
$359$	5.30964	−	9.19657i	0.280232	−	0.485376i	0.971442	+	0.237278i	$0.0762552\pi$
$360$		0			0
$361$	9.38279	+	16.2515i	0.493831	+	0.855340i
$362$		0			0
$363$	17.9428	+	3.44953i	0.941751	+	0.181054i
$364$		0			0
$365$	−1.26448	+	2.19014i	−0.0661857	+	0.114637i
$366$		0			0
$367$	11.1799	−	19.3642i	0.583586	−	1.01080i	−0.411464	−	0.911426i	$-0.634982\pi$
$367$	11.1799	−	19.3642i	0.583586	−	1.01080i	0.995050	−	0.0993751i	$-0.0316844\pi$
$368$		0			0
$369$	21.7434	+	8.68130i	1.13192	+	0.451930i
$370$		0			0
$371$	−13.4405	−	29.4826i	−0.697796	−	1.53066i
$372$		0			0
$373$	8.79264	+	15.2293i	0.455266	+	0.788544i	0.998703	−	0.0509059i	$-0.0162109\pi$
$373$	8.79264	+	15.2293i	0.455266	+	0.788544i	−0.543438	+	0.839450i	$0.682878\pi$
$374$		0			0
$375$	−3.81202	+	4.40344i	−0.196852	+	0.227393i
$376$		0			0
$377$	3.11015			0.160181
$378$		0			0
$379$	−10.0443			−0.515939			−0.257969	−	0.966153i	$-0.583053\pi$
$379$	−10.0443			−0.515939			−0.257969	+	0.966153i	$0.583053\pi$
$380$		0			0
$381$	15.7373	−	18.1788i	0.806245	−	0.931330i
$382$		0			0
$383$	−3.93619	−	6.81768i	−0.201130	−	0.348367i	0.747763	−	0.663966i	$-0.231128\pi$
$383$	−3.93619	−	6.81768i	−0.201130	−	0.348367i	−0.948893	+	0.315599i	$0.897795\pi$
$384$		0			0
$385$	0.601710	+	0.0578612i	0.0306660	+	0.00294888i
$386$		0			0
$387$	17.2547	−	13.5952i	0.877105	−	0.691084i
$388$		0			0
$389$	1.82417	−	3.15956i	0.0924893	−	0.160196i	−0.816069	−	0.577955i	$-0.803851\pi$
$389$	1.82417	−	3.15956i	0.0924893	−	0.160196i	0.908558	+	0.417759i	$0.137184\pi$
$390$		0			0
$391$	4.60949	−	7.98387i	0.233112	−	0.403762i
$392$		0			0
$393$	−7.10192	−	1.36536i	−0.358244	−	0.0688732i
$394$		0			0
$395$	−1.70317	−	2.94997i	−0.0856956	−	0.148429i
$396$		0			0
$397$	6.56071	−	11.3635i	0.329272	−	0.570317i	−0.653095	−	0.757276i	$-0.726530\pi$
$397$	6.56071	−	11.3635i	0.329272	−	0.570317i	0.982368	+	0.186959i	$0.0598632\pi$
$398$		0			0
$399$	0.522653	+	2.15630i	0.0261654	+	0.107950i
$400$		0			0
$401$	−5.71872	−	9.90511i	−0.285579	−	0.494638i	0.687170	−	0.726496i	$-0.258853\pi$
$401$	−5.71872	−	9.90511i	−0.285579	−	0.494638i	−0.972749	+	0.231859i	$0.925519\pi$
$402$		0			0
$403$	−3.38157	+	5.85705i	−0.168448	+	0.291760i
$404$		0			0
$405$	2.21986	+	2.10876i	0.110305	+	0.104785i
$406$		0			0
$407$	3.23445	+	5.60224i	0.160326	+	0.277693i
$408$		0			0
$409$	−18.4821			−0.913882			−0.456941	−	0.889497i	$-0.651055\pi$
$409$	−18.4821			−0.913882			−0.456941	+	0.889497i	$0.651055\pi$
$410$		0			0
$411$	−7.23872	−	20.8835i	−0.357060	−	1.03011i
$412$		0			0
$413$	13.0178	+	1.25181i	0.640565	+	0.0615975i
$414$		0			0
$415$	−0.841574	+	1.45765i	−0.0413112	+	0.0715531i
$416$		0			0
$417$	6.76157	+	19.5069i	0.331116	+	0.955258i
$418$		0			0
$419$	10.6290	−	18.4099i	0.519260	−	0.899385i	−0.480489	−	0.877001i	$-0.659541\pi$
$419$	10.6290	−	18.4099i	0.519260	−	0.899385i	0.999749	−	0.0223843i	$-0.00712574\pi$
$420$		0			0
$421$	−8.60478	−	14.9039i	−0.419371	−	0.726373i	0.576505	−	0.817094i	$-0.304416\pi$
$421$	−8.60478	−	14.9039i	−0.419371	−	0.726373i	−0.995876	+	0.0907211i	$0.971083\pi$
$422$		0			0
$423$	−1.15978	−	8.01355i	−0.0563905	−	0.389632i
$424$		0			0
$425$	−10.7468			−0.521295
$426$		0			0
$427$	−9.27341	−	0.891743i	−0.448772	−	0.0431545i
$428$		0			0
$429$	3.70952	+	0.713163i	0.179097	+	0.0344318i
$430$		0			0
$431$	−3.02962	−	5.24745i	−0.145931	−	0.252761i	0.783789	−	0.621028i	$-0.213285\pi$
$431$	−3.02962	−	5.24745i	−0.145931	−	0.252761i	−0.929720	+	0.368267i	$0.879951\pi$
$432$		0			0
$433$	−17.6963			−0.850432			−0.425216	−	0.905092i	$-0.639802\pi$
$433$	−17.6963			−0.850432			−0.425216	+	0.905092i	$0.639802\pi$
$434$		0			0
$435$	−0.184825	−	0.533216i	−0.00886170	−	0.0255657i
$436$		0			0
$437$	−2.02862			−0.0970421
$438$		0			0
$439$	−27.3373			−1.30474			−0.652370	−	0.757901i	$-0.726225\pi$
$439$	−27.3373			−1.30474			−0.652370	+	0.757901i	$0.726225\pi$
$440$		0			0
$441$	1.00769	−	20.9758i	0.0479851	−	0.998848i
$442$		0			0
$443$	−1.91771			−0.0911132			−0.0455566	−	0.998962i	$-0.514506\pi$
$443$	−1.91771			−0.0911132			−0.0455566	+	0.998962i	$0.514506\pi$
$444$		0			0
$445$	5.79822			0.274862
$446$		0			0
$447$	18.2863	+	3.51559i	0.864914	+	0.166281i
$448$		0			0
$449$	28.3249			1.33674			0.668368	−	0.743831i	$-0.266993\pi$
$449$	28.3249			1.33674			0.668368	+	0.743831i	$0.266993\pi$
$450$		0			0
$451$	−2.62058	−	4.53898i	−0.123398	−	0.213732i
$452$		0			0
$453$	1.46409	+	4.22386i	0.0687891	+	0.198454i
$454$		0			0
$455$	−2.90951	−	0.279782i	−0.136400	−	0.0131164i
$456$		0			0
$457$	13.0085			0.608514			0.304257	−	0.952590i	$-0.401592\pi$
$457$	13.0085			0.608514			0.304257	+	0.952590i	$0.401592\pi$
$458$		0			0
$459$	−0.528076	+	11.4208i	−0.0246485	+	0.533078i
$460$		0			0
$461$	−11.8278	−	20.4863i	−0.550875	−	0.954144i	−0.998212	−	0.0597782i	$-0.980961\pi$
$461$	−11.8278	−	20.4863i	−0.550875	−	0.954144i	0.447336	−	0.894366i	$-0.352373\pi$
$462$		0			0
$463$	20.2403	−	35.0572i	0.940647	−	1.62925i	0.176406	−	0.984317i	$-0.443553\pi$
$463$	20.2403	−	35.0572i	0.940647	−	1.62925i	0.764241	−	0.644931i	$-0.223114\pi$
$464$		0			0
$465$	1.20511	+	0.231685i	0.0558856	+	0.0107441i
$466$		0			0
$467$	18.6010	−	32.2179i	0.860753	−	1.49087i	−0.0104492	−	0.999945i	$-0.503326\pi$
$467$	18.6010	−	32.2179i	0.860753	−	1.49087i	0.871203	−	0.490923i	$-0.163341\pi$
$468$		0			0
$469$	−32.4466	−	3.12011i	−1.49825	−	0.144073i
$470$		0			0
$471$	9.06566	−	10.4722i	0.417724	−	0.482532i
$472$		0			0
$473$	−4.91761			−0.226112
$474$		0			0
$475$	1.18240	+	2.04799i	0.0542525	+	0.0939680i
$476$		0			0
$477$	−28.8585	+	22.7381i	−1.32134	+	1.04110i
$478$		0			0
$479$	20.2918	−	35.1463i	0.927154	−	1.60588i	0.139094	−	0.990279i	$-0.455581\pi$
$479$	20.2918	−	35.1463i	0.927154	−	1.60588i	0.788060	−	0.615598i	$-0.211086\pi$
$480$		0			0
$481$	−15.6399	−	27.0891i	−0.713118	−	1.23516i
$482$		0			0
$483$	18.4217	+	5.41313i	0.838216	+	0.246306i
$484$		0			0
$485$	1.44128	−	2.49637i	0.0654452	−	0.113354i
$486$		0			0
$487$	−10.5255	−	18.2307i	−0.476956	−	0.826113i	0.522695	−	0.852520i	$-0.324927\pi$
$487$	−10.5255	−	18.2307i	−0.476956	−	0.826113i	−0.999651	+	0.0264072i	$0.991593\pi$
$488$		0			0
$489$	4.68904	+	13.5277i	0.212046	+	0.611745i
$490$		0			0
$491$	4.97925	−	8.62432i	0.224711	−	0.389210i	−0.731522	−	0.681818i	$-0.761190\pi$
$491$	4.97925	−	8.62432i	0.224711	−	0.389210i	0.956233	+	0.292608i	$0.0945230\pi$
$492$		0			0
$493$	1.05365	−	1.82497i	0.0474538	−	0.0821924i
$494$		0			0
$495$	−0.0981766	−	0.678355i	−0.00441271	−	0.0304898i
$496$		0			0
$497$	14.6772	+	1.41138i	0.658361	+	0.0633088i
$498$		0			0
$499$	11.3150	+	19.5982i	0.506531	+	0.877337i	0.999971	+	0.00755788i	$0.00240577\pi$
$499$	11.3150	+	19.5982i	0.506531	+	0.877337i	−0.493440	+	0.869780i	$0.664261\pi$
$500$		0			0
$501$	10.2037	+	29.4373i	0.455867	+	1.31516i
$502$		0			0
$503$	43.4520			1.93743			0.968714	−	0.248179i	$-0.0798321\pi$
$503$	43.4520			1.93743			0.968714	+	0.248179i	$0.0798321\pi$
$504$		0			0
$505$	−1.55602			−0.0692422
$506$		0			0
$507$	4.17470	+	0.802594i	0.185405	+	0.0356444i
$508$		0			0
$509$	4.77739	+	8.27468i	0.211754	+	0.366769i	0.952264	−	0.305277i	$-0.0987491\pi$
$509$	4.77739	+	8.27468i	0.211754	+	0.366769i	−0.740510	+	0.672046i	$0.765416\pi$
$510$		0			0
$511$	−8.15836	−	17.8959i	−0.360905	−	0.791667i
$512$		0			0
$513$	2.23454	−	1.15593i	0.0986572	−	0.0510356i
$514$		0			0
$515$	−0.307392	+	0.532419i	−0.0135453	+	0.0234612i
$516$		0			0
$517$	−0.906312	+	1.56978i	−0.0398596	+	0.0690388i
$518$		0			0
$519$	−19.2700	+	22.2597i	−0.845860	+	0.977092i
$520$		0			0
$521$	0.581462	+	1.00712i	0.0254743	+	0.0441228i	0.878482	−	0.477776i	$-0.158557\pi$
$521$	0.581462	+	1.00712i	0.0254743	+	0.0441228i	−0.853007	+	0.521899i	$0.825224\pi$
$522$		0			0
$523$	3.20567	−	5.55239i	0.140174	−	0.242789i	−0.787388	−	0.616458i	$-0.788567\pi$
$523$	3.20567	−	5.55239i	0.140174	−	0.242789i	0.927562	+	0.373669i	$0.121900\pi$
$524$		0			0
$525$	−5.27249	−	21.7526i	−0.230110	−	0.949363i
$526$		0			0
$527$	2.29119	+	3.96846i	0.0998059	+	0.172869i
$528$		0			0
$529$	2.72237	−	4.71528i	0.118364	−	0.205012i
$530$		0			0
$531$	−2.12402	−	14.6760i	−0.0921746	−	0.636884i
$532$		0			0
$533$	12.6716	+	21.9478i	0.548866	+	0.950665i
$534$		0			0
$535$	2.64123			0.114190
$536$		0			0
$537$	32.8299	+	6.31162i	1.41671	+	0.272366i
$538$		0			0
$539$	−3.08331	+	3.54876i	−0.132808	+	0.152856i
$540$		0			0
$541$	−7.37443	+	12.7729i	−0.317052	+	0.549150i	−0.979871	−	0.199629i	$-0.936026\pi$
$541$	−7.37443	+	12.7729i	−0.317052	+	0.549150i	0.662820	+	0.748779i	$0.269360\pi$
$542$		0			0
$543$	24.8994	−	28.7624i	1.06854	−	1.23431i
$544$		0			0
$545$	−0.364621	+	0.631542i	−0.0156187	+	0.0270523i
$546$		0			0
$547$	−6.57905	−	11.3952i	−0.281300	−	0.487226i	0.690405	−	0.723423i	$-0.257432\pi$
$547$	−6.57905	−	11.3952i	−0.281300	−	0.487226i	−0.971705	+	0.236197i	$0.924099\pi$
$548$		0			0
$549$	1.51307	+	10.4546i	0.0645764	+	0.446193i
$550$		0			0
$551$	−0.463706			−0.0197545
$552$		0			0
$553$	26.3696	+	2.53573i	1.12135	+	0.107830i
$554$		0			0
$555$	−3.71483	+	4.29117i	−0.157686	+	0.182150i
$556$		0			0
$557$	−12.1869	−	21.1083i	−0.516374	−	0.894385i	−0.999819	−	0.0190111i	$-0.993948\pi$
$557$	−12.1869	−	21.1083i	−0.516374	−	0.894385i	0.483446	−	0.875374i	$-0.339385\pi$
$558$		0			0
$559$	23.7787			1.00573
$560$		0			0
$561$	1.67517	−	1.93506i	0.0707256	−	0.0816984i
$562$		0			0
$563$	3.11965			0.131478			0.0657388	−	0.997837i	$-0.479060\pi$
$563$	3.11965			0.131478			0.0657388	+	0.997837i	$0.479060\pi$
$564$		0			0
$565$	5.38201			0.226423
$566$		0			0
$567$	−23.3761	+	4.53429i	−0.981702	+	0.190422i
$568$		0			0
$569$	−21.4769			−0.900358			−0.450179	−	0.892938i	$-0.648640\pi$
$569$	−21.4769			−0.900358			−0.450179	+	0.892938i	$0.648640\pi$
$570$		0			0
$571$	−33.0460			−1.38293			−0.691466	−	0.722409i	$-0.743035\pi$
$571$	−33.0460			−1.38293			−0.691466	+	0.722409i	$0.743035\pi$
$572$		0			0
$573$	−7.54717	+	8.71808i	−0.315287	+	0.364203i
$574$		0			0
$575$	20.4646			0.853432
$576$		0			0
$577$	0.904826	+	1.56720i	0.0376684	+	0.0652436i	0.884245	−	0.467023i	$-0.154674\pi$
$577$	0.904826	+	1.56720i	0.0376684	+	0.0652436i	−0.846577	+	0.532267i	$0.821340\pi$
$578$		0			0
$579$	7.19757	−	8.31425i	0.299121	−	0.345528i
$580$		0			0
$581$	−5.42980	−	11.9106i	−0.225266	−	0.494136i
$582$		0			0
$583$	8.22473			0.340633
$584$		0			0
$585$	0.474724	+	3.28012i	0.0196274	+	0.135616i
$586$		0			0
$587$	−1.65901	−	2.87349i	−0.0684746	−	0.118601i	0.829755	−	0.558127i	$-0.188480\pi$
$587$	−1.65901	−	2.87349i	−0.0684746	−	0.118601i	−0.898230	+	0.439526i	$0.855147\pi$
$588$		0			0
$589$	0.504173	−	0.873253i	0.0207741	−	0.0359818i
$590$		0			0
$591$	26.9934	−	31.1813i	1.11036	−	1.28263i
$592$		0			0
$593$	15.3784	−	26.6362i	0.631516	−	1.09382i	−0.355726	−	0.934590i	$-0.615766\pi$
$593$	15.3784	−	26.6362i	0.631516	−	1.09382i	0.987242	−	0.159228i	$-0.0509005\pi$
$594$		0			0
$595$	−1.14985	+	1.61246i	−0.0471391	+	0.0661042i
$596$		0			0
$597$	35.6410	+	6.85205i	1.45869	+	0.280436i
$598$		0			0
$599$	−13.9705			−0.570817			−0.285409	−	0.958406i	$-0.592129\pi$
$599$	−13.9705			−0.570817			−0.285409	+	0.958406i	$0.592129\pi$
$600$		0			0
$601$	−7.50432	−	12.9979i	−0.306108	−	0.530194i	0.671400	−	0.741096i	$-0.265693\pi$
$601$	−7.50432	−	12.9979i	−0.306108	−	0.530194i	−0.977507	+	0.210901i	$0.932360\pi$
$602$		0			0
$603$	5.29408	+	36.5796i	0.215591	+	1.48964i
$604$		0			0
$605$	1.79438	−	3.10796i	0.0729519	−	0.126356i
$606$		0			0
$607$	11.6644	+	20.2034i	0.473444	+	0.820030i	0.999538	−	0.0303969i	$-0.00967712\pi$
$607$	11.6644	+	20.2034i	0.473444	+	0.820030i	−0.526093	+	0.850427i	$0.676344\pi$
$608$		0			0
$609$	4.21087	+	1.23734i	0.170633	+	0.0501397i
$610$		0			0
$611$	4.38239	−	7.59052i	0.177292	−	0.307080i
$612$		0			0
$613$	22.3374	+	38.6895i	0.902198	+	1.56265i	0.824635	+	0.565666i	$0.191381\pi$
$613$	22.3374	+	38.6895i	0.902198	+	1.56265i	0.0775635	+	0.996987i	$0.475286\pi$
$614$		0			0
$615$	3.00979	−	3.47674i	0.121366	−	0.140196i
$616$		0			0
$617$	−1.18488	+	2.05227i	−0.0477013	+	0.0826212i	−0.888890	−	0.458120i	$-0.848523\pi$
$617$	−1.18488	+	2.05227i	−0.0477013	+	0.0826212i	0.841189	+	0.540741i	$0.181856\pi$
$618$		0			0
$619$	−11.3863	+	19.7217i	−0.457655	+	0.792682i	−0.998837	−	0.0482236i	$-0.984644\pi$
$619$	−11.3863	+	19.7217i	−0.457655	+	0.792682i	0.541181	+	0.840906i	$0.317977\pi$
$620$		0			0
$621$	1.00559	−	21.7481i	0.0403530	−	0.872722i
$622$		0			0
$623$	−26.1810	+	36.7142i	−1.04892	+	1.47092i
$624$		0			0
$625$	−11.6387	−	20.1588i	−0.465547	−	0.806351i
$626$		0			0
$627$	−0.553069	−	0.106329i	−0.0220874	−	0.00424636i
$628$		0			0
$629$	−21.1937			−0.845049
$630$		0			0
$631$	−17.8652			−0.711201			−0.355600	−	0.934638i	$-0.615724\pi$
$631$	−17.8652			−0.711201			−0.355600	+	0.934638i	$0.615724\pi$
$632$		0			0
$633$	−7.17505	−	20.6998i	−0.285183	−	0.822743i
$634$		0			0
$635$	−2.36133	−	4.08995i	−0.0937067	−	0.162305i
$636$		0			0
$637$	14.9091	−	17.1597i	0.590718	−	0.679891i
$638$		0			0
$639$	−2.39477	−	16.5467i	−0.0947355	−	0.654578i
$640$		0			0
$641$	12.7900	−	22.1529i	0.505175	−	0.874988i	−0.494808	−	0.869003i	$-0.664761\pi$
$641$	12.7900	−	22.1529i	0.505175	−	0.874988i	0.999982	−	0.00598543i	$-0.00190523\pi$
$642$		0			0
$643$	−7.99334	+	13.8449i	−0.315227	+	0.545989i	−0.979486	−	0.201514i	$-0.935414\pi$
$643$	−7.99334	+	13.8449i	−0.315227	+	0.545989i	0.664259	+	0.747503i	$0.268747\pi$
$644$		0			0
$645$	−1.41308	−	4.07670i	−0.0556401	−	0.160520i
$646$		0			0
$647$	−7.47306	−	12.9437i	−0.293796	−	0.508870i	0.680908	−	0.732369i	$-0.261585\pi$
$647$	−7.47306	−	12.9437i	−0.293796	−	0.508870i	−0.974704	+	0.223499i	$0.928252\pi$
$648$		0			0
$649$	−1.65982	+	2.87489i	−0.0651536	+	0.112849i
$650$		0			0
$651$	−6.90851	+	6.58459i	−0.270766	+	0.258070i
$652$		0			0
$653$	4.82885	+	8.36381i	0.188967	+	0.327301i	0.944906	−	0.327341i	$-0.106153\pi$
$653$	4.82885	+	8.36381i	0.188967	+	0.327301i	−0.755939	+	0.654642i	$0.772819\pi$
$654$		0			0
$655$	−0.710233	+	1.23016i	−0.0277511	+	0.0480663i
$656$		0			0
$657$	−17.5171	+	13.8020i	−0.683406	+	0.538466i
$658$		0			0
$659$	−9.80353	−	16.9802i	−0.381891	−	0.661455i	0.609441	−	0.792831i	$-0.291394\pi$
$659$	−9.80353	−	16.9802i	−0.381891	−	0.661455i	−0.991333	+	0.131376i	$0.958060\pi$
$660$		0			0
$661$	−10.2655			−0.399281			−0.199641	−	0.979869i	$-0.563977\pi$
$661$	−10.2655			−0.399281			−0.199641	+	0.979869i	$0.563977\pi$
$662$		0			0
$663$	−8.10011	+	9.35682i	−0.314582	+	0.363389i
$664$		0			0
$665$	0.433792	+	0.0417140i	0.0168217	+	0.00161760i
$666$		0			0
$667$	−2.00641	+	3.47520i	−0.0776885	+	0.134560i
$668$		0			0
$669$	4.57312	+	0.879192i	0.176807	+	0.0339915i
$670$		0			0
$671$	1.18239	−	2.04797i	0.0456458	−	0.0790608i
$672$		0			0
$673$	−17.1584	−	29.7191i	−0.661406	−	1.14559i	−0.980246	−	0.197780i	$-0.936627\pi$
$673$	−17.1584	−	29.7191i	−0.661406	−	1.14559i	0.318840	−	0.947808i	$-0.396707\pi$
$674$		0			0
$675$	−22.5419	+	11.6610i	−0.867636	+	0.448830i
$676$		0			0
$677$	7.47419			0.287256			0.143628	−	0.989632i	$-0.454123\pi$
$677$	7.47419			0.287256			0.143628	+	0.989632i	$0.454123\pi$
$678$		0			0
$679$	9.29910	+	20.3982i	0.356867	+	0.782810i
$680$		0			0
$681$	−15.8767	−	45.8038i	−0.608397	−	1.75521i
$682$		0			0
$683$	18.1577	+	31.4501i	0.694786	+	1.20340i	0.970253	+	0.242094i	$0.0778341\pi$
$683$	18.1577	+	31.4501i	0.694786	+	1.20340i	−0.275467	+	0.961310i	$0.588833\pi$
$684$		0			0
$685$	−4.34125			−0.165871
$686$		0			0
$687$	−41.7384	−	8.02429i	−1.59242	−	0.306146i
$688$		0			0
$689$	−39.7699			−1.51511
$690$		0			0
$691$	−50.9624			−1.93870			−0.969350	−	0.245684i	$-0.920987\pi$
$691$	−50.9624			−1.93870			−0.969350	+	0.245684i	$0.920987\pi$
$692$		0			0
$693$	4.73863	+	2.44136i	0.180006	+	0.0927395i
$694$		0			0
$695$	4.05509			0.153818
$696$		0			0
$697$	17.1713			0.650410
$698$		0			0
$699$	5.23971	+	15.1164i	0.198184	+	0.571755i
$700$		0			0
$701$	36.6075			1.38265			0.691324	−	0.722545i	$-0.257028\pi$
$701$	36.6075			1.38265			0.691324	+	0.722545i	$0.257028\pi$
$702$		0			0
$703$	2.33182	+	4.03883i	0.0879463	+	0.152327i
$704$		0			0
$705$	−1.56178	−	0.300255i	−0.0588199	−	0.0113083i
$706$		0			0
$707$	7.02600	−	9.85272i	0.264240	−	0.370550i
$708$		0			0
$709$	−5.87578			−0.220670			−0.110335	−	0.993894i	$-0.535192\pi$
$709$	−5.87578			−0.220670			−0.110335	+	0.993894i	$0.535192\pi$
$710$		0			0
$711$	−4.30253	−	29.7285i	−0.161357	−	1.11491i
$712$		0			0
$713$	−4.36301	−	7.55695i	−0.163396	−	0.283010i
$714$		0			0
$715$	0.370973	−	0.642545i	0.0138736	−	0.0240298i
$716$		0			0
$717$	15.8976	+	45.8641i	0.593707	+	1.71283i
$718$		0			0
$719$	8.09642	−	14.0234i	0.301945	−	0.522985i	−0.674631	−	0.738155i	$-0.735697\pi$
$719$	8.09642	−	14.0234i	0.301945	−	0.522985i	0.976577	+	0.215170i	$0.0690306\pi$
$720$		0			0
$721$	−1.98328	−	4.35046i	−0.0738614	−	0.162020i
$722$		0			0
$723$	11.2477	+	32.4494i	0.418308	+	1.20681i
$724$		0			0
$725$	4.67783			0.173730
$726$		0			0
$727$	22.8771	+	39.6243i	0.848464	+	1.46958i	0.882578	+	0.470166i	$0.155806\pi$
$727$	22.8771	+	39.6243i	0.848464	+	1.46958i	−0.0341138	+	0.999418i	$0.510861\pi$
$728$		0			0
$729$	11.2847	+	24.5287i	0.417951	+	0.908470i
$730$		0			0
$731$	8.05565	−	13.9528i	0.297949	−	0.516063i
$732$		0			0
$733$	−13.5916	−	23.5414i	−0.502019	−	0.869522i	−0.999997	−	0.00233276i	$-0.999257\pi$
$733$	−13.5916	−	23.5414i	−0.502019	−	0.869522i	0.497978	−	0.867189i	$-0.334076\pi$
$734$		0			0
$735$	−3.82791	−	1.53632i	−0.141195	−	0.0566682i
$736$		0			0
$737$	4.13706	−	7.16560i	0.152391	−	0.263948i
$738$		0			0
$739$	−12.1738	−	21.0856i	−0.447821	−	0.775648i	0.550423	−	0.834886i	$-0.314466\pi$
$739$	−12.1738	−	21.0856i	−0.447821	−	0.775648i	−0.998244	+	0.0592377i	$0.981133\pi$
$740$		0			0
$741$	2.67431	+	0.514142i	0.0982433	+	0.0188875i
$742$		0			0
$743$	0.0683178	−	0.118330i	0.00250634	−	0.00434110i	−0.864770	−	0.502169i	$-0.832536\pi$
$743$	0.0683178	−	0.118330i	0.00250634	−	0.00434110i	0.867276	+	0.497828i	$0.165869\pi$
$744$		0			0
$745$	1.82874	−	3.16747i	0.0669998	−	0.116047i
$746$		0			0
$747$	−11.6585	+	9.18591i	−0.426562	+	0.336095i
$748$		0			0
$749$	−11.9261	+	16.7242i	−0.435769	+	0.611090i
$750$		0			0
$751$	3.71446	+	6.43364i	0.135543	+	0.234767i	0.925805	−	0.378002i	$-0.123389\pi$
$751$	3.71446	+	6.43364i	0.135543	+	0.234767i	−0.790262	+	0.612769i	$0.790056\pi$
$752$		0			0
$753$	−18.7912	+	21.7066i	−0.684789	+	0.791031i
$754$		0			0
$755$	0.878055			0.0319557
$756$		0			0
$757$	−14.0794			−0.511723			−0.255861	−	0.966713i	$-0.582359\pi$
$757$	−14.0794			−0.511723			−0.255861	+	0.966713i	$0.582359\pi$
$758$		0			0
$759$	−3.18994	+	3.68485i	−0.115788	+	0.133752i
$760$		0			0
$761$	−19.3616	−	33.5353i	−0.701858	−	1.21565i	−0.967813	−	0.251669i	$-0.919021\pi$
$761$	−19.3616	−	33.5353i	−0.701858	−	1.21565i	0.265955	−	0.963985i	$-0.414313\pi$
$762$		0			0
$763$	−2.35252	−	5.16041i	−0.0851671	−	0.186819i
$764$		0			0
$765$	2.08553	+	0.832671i	0.0754025	+	0.0301053i
$766$		0			0
$767$	8.02589	−	13.9013i	0.289798	−	0.501945i
$768$		0			0
$769$	5.14295	−	8.90786i	0.185460	−	0.321226i	−0.758272	−	0.651939i	$-0.773956\pi$
$769$	5.14295	−	8.90786i	0.185460	−	0.321226i	0.943731	+	0.330713i	$0.107289\pi$
$770$		0			0
$771$	−12.4081	−	2.38548i	−0.446867	−	0.0859111i
$772$		0			0
$773$	−22.6768	−	39.2773i	−0.815627	−	1.41271i	−0.908877	−	0.417064i	$-0.863059\pi$
$773$	−22.6768	−	39.2773i	−0.815627	−	1.41271i	0.0932501	−	0.995643i	$-0.470274\pi$
$774$		0			0
$775$	−5.08606	+	8.80931i	−0.182697	+	0.316440i
$776$		0			0
$777$	−10.3979	−	42.8984i	−0.373022	−	1.53897i
$778$		0			0
$779$	−1.88926	−	3.27229i	−0.0676898	−	0.117242i
$780$		0			0
$781$	−1.87139	+	3.24135i	−0.0669637	+	0.115985i
$782$		0			0
$783$	0.229860	−	4.97123i	0.00821453	−	0.177657i
$784$		0			0
$785$	−1.36028	−	2.35607i	−0.0485504	−	0.0840917i
$786$		0			0
$787$	−26.1087			−0.930675			−0.465337	−	0.885133i	$-0.654067\pi$
$787$	−26.1087			−0.930675			−0.465337	+	0.885133i	$0.654067\pi$
$788$		0			0
$789$	15.1911	+	43.8259i	0.540818	+	1.56024i
$790$		0			0
$791$	−24.3017	+	34.0788i	−0.864067	+	1.21170i
$792$		0			0
$793$	−5.71735	+	9.90274i	−0.203029	+	0.351657i
$794$		0			0
$795$	2.36339	+	6.81830i	0.0838207	+	0.241820i
$796$		0			0
$797$	−16.1618	+	27.9931i	−0.572481	+	0.991567i	0.423829	+	0.905742i	$0.360686\pi$
$797$	−16.1618	+	27.9931i	−0.572481	+	0.991567i	−0.996310	+	0.0858244i	$0.972648\pi$
$798$		0			0
$799$	−2.96930	−	5.14298i	−0.105046	−	0.181946i
$800$		0			0
$801$	47.4857	+	18.9592i	1.67782	+	0.669890i
$802$		0			0
$803$	4.99240			0.176178
$804$		0			0
$805$	2.18960	−	3.07052i	0.0771731	−	0.108222i
$806$		0			0
$807$	34.6273	+	6.65716i	1.21894	+	0.234343i
$808$		0			0
$809$	22.4553	+	38.8938i	0.789488	+	1.36743i	0.926281	+	0.376833i	$0.122987\pi$
$809$	22.4553	+	38.8938i	0.789488	+	1.36743i	−0.136793	+	0.990600i	$0.543680\pi$
$810$		0			0
$811$	−42.8204			−1.50363			−0.751813	−	0.659376i	$-0.770820\pi$
$811$	−42.8204			−1.50363			−0.751813	+	0.659376i	$0.770820\pi$
$812$		0			0
$813$	6.19268	+	17.8657i	0.217187	+	0.626578i
$814$		0			0
$815$	2.81214			0.0985049
$816$		0			0
$817$	−3.54527			−0.124033
$818$		0			0
$819$	−22.9132	−	11.8050i	−0.800653	−	0.412499i
$820$		0			0
$821$	−32.2200			−1.12448			−0.562242	−	0.826972i	$-0.690061\pi$
$821$	−32.2200			−1.12448			−0.562242	+	0.826972i	$0.690061\pi$
$822$		0			0
$823$	−4.38841			−0.152970			−0.0764851	−	0.997071i	$-0.524370\pi$
$823$	−4.38841			−0.152970			−0.0764851	+	0.997071i	$0.524370\pi$
$824$		0			0
$825$	5.57932	+	1.07264i	0.194247	+	0.0373444i
$826$		0			0
$827$	42.0996			1.46395			0.731973	−	0.681333i	$-0.238600\pi$
$827$	42.0996			1.46395			0.731973	+	0.681333i	$0.238600\pi$
$828$		0			0
$829$	−5.55838	−	9.62739i	−0.193050	−	0.334373i	0.753209	−	0.657781i	$-0.228505\pi$
$829$	−5.55838	−	9.62739i	−0.193050	−	0.334373i	−0.946260	+	0.323408i	$0.895171\pi$
$830$		0			0
$831$	10.0256	+	28.9236i	0.347785	+	1.00335i
$832$		0			0
$833$	−5.01809	−	14.5616i	−0.173866	−	0.504530i
$834$		0			0
$835$	6.11941			0.211771
$836$		0			0
$837$	9.11192	+	5.83793i	0.314954	+	0.201788i
$838$		0			0
$839$	27.2669	+	47.2277i	0.941360	+	1.63048i	0.762881	+	0.646539i	$0.223784\pi$
$839$	27.2669	+	47.2277i	0.941360	+	1.63048i	0.178479	+	0.983944i	$0.442882\pi$
$840$		0			0
$841$	14.0414	−	24.3204i	0.484185	−	0.838633i
$842$		0			0
$843$	24.4118	+	4.69322i	0.840788	+	0.161643i
$844$		0			0
$845$	0.417494	−	0.723120i	0.0143622	−	0.0248761i
$846$		0			0
$847$	11.5773	+	25.3955i	0.397800	+	0.872600i
$848$		0			0
$849$	−11.0285	+	12.7396i	−0.378499	+	0.437221i
$850$		0			0
$851$	40.3582			1.38346
$852$		0			0
$853$	−11.3669	−	19.6880i	−0.389194	−	0.674105i	0.603147	−	0.797630i	$-0.293913\pi$
$853$	−11.3669	−	19.6880i	−0.389194	−	0.674105i	−0.992341	+	0.123526i	$0.960580\pi$
$854$		0			0
$855$	−0.0707787	−	0.489048i	−0.00242058	−	0.0167251i
$856$		0			0
$857$	−5.61928	+	9.73288i	−0.191951	+	0.332469i	−0.945897	−	0.324468i	$-0.894815\pi$
$857$	−5.61928	+	9.73288i	−0.191951	+	0.332469i	0.753946	+	0.656937i	$0.228148\pi$
$858$		0			0
$859$	25.4024	+	43.9983i	0.866720	+	1.50120i	0.865329	+	0.501204i	$0.167109\pi$
$859$	25.4024	+	43.9983i	0.866720	+	1.50120i	0.00139066	+	0.999999i	$0.499557\pi$
$860$		0			0
$861$	8.42444	+	34.7566i	0.287104	+	1.18450i
$862$		0			0
$863$	0.340985	−	0.590603i	0.0116073	−	0.0201044i	−0.860163	−	0.510018i	$-0.829639\pi$
$863$	0.340985	−	0.590603i	0.0116073	−	0.0201044i	0.871771	+	0.489914i	$0.162972\pi$
$864$		0			0
$865$	2.89141	+	5.00807i	0.0983110	+	0.170280i
$866$		0			0
$867$	−6.89716	−	19.8981i	−0.234240	−	0.675775i
$868$		0			0
$869$	−3.36222	+	5.82353i	−0.114055	+	0.197550i
$870$		0			0
$871$	−20.0044	+	34.6486i	−0.677822	+	1.17402i
$872$		0			0
$873$	19.9664	−	15.7318i	0.675760	−	0.532441i
$874$		0			0
$875$	−8.85583	−	0.851587i	−0.299382	−	0.0287889i
$876$		0			0
$877$	12.6595	+	21.9269i	0.427480	+	0.740418i	0.996648	−	0.0818035i	$-0.0260680\pi$
$877$	12.6595	+	21.9269i	0.427480	+	0.740418i	−0.569168	+	0.822221i	$0.692735\pi$
$878$		0			0
$879$	−7.10600	−	20.5006i	−0.239680	−	0.691468i
$880$		0			0
$881$	−30.9482			−1.04267			−0.521335	−	0.853352i	$-0.674566\pi$
$881$	−30.9482			−1.04267			−0.521335	+	0.853352i	$0.674566\pi$
$882$		0			0
$883$	−9.48501			−0.319196			−0.159598	−	0.987182i	$-0.551020\pi$
$883$	−9.48501			−0.319196			−0.159598	+	0.987182i	$0.551020\pi$
$884$		0			0
$885$	−2.86024	−	0.549886i	−0.0961458	−	0.0184842i
$886$		0			0
$887$	1.97469	+	3.42026i	0.0663036	+	0.114841i	0.897272	−	0.441479i	$-0.145546\pi$
$887$	1.97469	+	3.42026i	0.0663036	+	0.114841i	−0.830968	+	0.556320i	$0.812213\pi$
$888$		0			0
$889$	36.5597	+	3.51563i	1.22617	+	0.117910i
$890$		0			0
$891$	1.41407	−	5.87655i	0.0473731	−	0.196872i
$892$		0			0
$893$	−0.653390	+	1.13170i	−0.0218649	+	0.0378710i
$894$		0			0
$895$	3.28318	−	5.68663i	0.109745	−	0.190083i
$896$		0			0
$897$	15.4247	−	17.8177i	0.515015	−	0.594917i
$898$		0			0
$899$	−0.997305	−	1.72738i	−0.0332620	−	0.0576115i
$900$		0			0
$901$	−13.4731	+	23.3361i	−0.448854	+	0.777439i
$902$		0			0
$903$	32.1942	+	9.46012i	1.07136	+	0.314813i
$904$		0			0
$905$	−3.73609	−	6.47109i	−0.124192	−	0.215106i
$906$		0			0
$907$	−16.7531	+	29.0171i	−0.556276	+	0.963498i	0.441527	+	0.897248i	$0.354437\pi$
$907$	−16.7531	+	29.0171i	−0.556276	+	0.963498i	−0.997803	+	0.0662505i	$0.978896\pi$
$908$		0			0
$909$	−12.7434	−	5.08794i	−0.422671	−	0.168756i
$910$		0			0
$911$	−5.26585	−	9.12072i	−0.174465	−	0.302183i	0.765511	−	0.643423i	$-0.222486\pi$
$911$	−5.26585	−	9.12072i	−0.174465	−	0.302183i	−0.939976	+	0.341240i	$0.889153\pi$
$912$		0			0
$913$	3.32269			0.109965
$914$		0			0
$915$	2.03753	+	0.391719i	0.0673585	+	0.0129498i
$916$		0			0
$917$	−4.58240	−	10.0518i	−0.151324	−	0.331939i
$918$		0			0
$919$	−1.81600	+	3.14540i	−0.0599042	+	0.103757i	−0.894422	−	0.447224i	$-0.852413\pi$
$919$	−1.81600	+	3.14540i	−0.0599042	+	0.103757i	0.834518	+	0.550981i	$0.185746\pi$
$920$		0			0
$921$	−29.3327	+	33.8836i	−0.966546	+	1.11650i
$922$		0			0
$923$	9.04894	−	15.6732i	0.297850	−	0.515891i
$924$		0			0
$925$	−23.5232	−	40.7435i	−0.773440	−	1.33964i
$926$		0			0
$927$	−4.25837	+	3.35523i	−0.139863	+	0.110200i
$928$		0			0
$929$	13.6058			0.446392			0.223196	−	0.974774i	$-0.428351\pi$
$929$	13.6058			0.446392			0.223196	+	0.974774i	$0.428351\pi$
$930$		0			0
$931$	−2.22286	+	2.55841i	−0.0728512	+	0.0838486i
$932$		0			0
$933$	−32.1956	+	37.1906i	−1.05404	+	1.21757i
$934$		0			0
$935$	−0.251354	−	0.435358i	−0.00822016	−	0.0142377i
$936$		0			0
$937$	9.98770			0.326284			0.163142	−	0.986603i	$-0.447837\pi$
$937$	9.98770			0.326284			0.163142	+	0.986603i	$0.447837\pi$
$938$		0			0
$939$	−13.8321	+	15.9781i	−0.451394	+	0.521426i
$940$		0			0
$941$	34.6209			1.12861			0.564305	−	0.825566i	$-0.309144\pi$
$941$	34.6209			1.12861			0.564305	+	0.825566i	$0.309144\pi$
$942$		0			0
$943$	−32.6985			−1.06481
$944$		0			0
$945$	−0.662233	+	4.62986i	−0.0215424	+	0.150609i
$946$		0			0
$947$	−49.2171			−1.59934			−0.799670	−	0.600440i	$-0.794992\pi$
$947$	−49.2171			−1.59934			−0.799670	+	0.600440i	$0.794992\pi$
$948$		0			0
$949$	−24.1403			−0.783626
$950$		0			0
$951$	−4.48037	+	5.17548i	−0.145286	+	0.167827i
$952$		0			0
$953$	14.2310			0.460987			0.230494	−	0.973074i	$-0.425966\pi$
$953$	14.2310			0.460987			0.230494	+	0.973074i	$0.425966\pi$
$954$		0			0
$955$	1.13243	+	1.96143i	0.0366446	+	0.0634704i
$956$		0			0
$957$	−0.729163	+	0.842290i	−0.0235705	+	0.0272274i
$958$		0			0
$959$	19.6022	−	27.4887i	0.632990	−	0.887656i
$960$		0			0
$961$	−26.6626			−0.860085
$962$		0			0
$963$	21.6309	+	8.63638i	0.697046	+	0.278303i
$964$		0			0
$965$	−1.07998	−	1.87057i	−0.0347657	−	0.0602159i
$966$		0			0
$967$	19.4246	−	33.6443i	0.624652	−	1.08193i	−0.363956	−	0.931416i	$-0.618574\pi$
$967$	19.4246	−	33.6443i	0.624652	−	1.08193i	0.988608	−	0.150513i	$-0.0480925\pi$
$968$		0			0
$969$	1.20768	−	1.39505i	0.0387963	−	0.0448154i
$970$		0			0
$971$	4.13629	−	7.16427i	0.132740	−	0.229912i	−0.791992	−	0.610532i	$-0.790956\pi$
$971$	4.13629	−	7.16427i	0.132740	−	0.229912i	0.924732	+	0.380619i	$0.124289\pi$
$972$		0			0
$973$	−18.3102	+	25.6768i	−0.586997	+	0.823159i
$974$		0			0
$975$	−26.9783	−	5.18663i	−0.863996	−	0.166105i
$976$		0			0
$977$	7.37473			0.235938			0.117969	−	0.993017i	$-0.462362\pi$
$977$	7.37473			0.235938			0.117969	+	0.993017i	$0.462362\pi$
$978$		0			0
$979$	−5.72312	−	9.91273i	−0.182912	−	0.316812i
$980$		0			0
$981$	−5.05118	+	3.97990i	−0.161272	+	0.127068i
$982$		0			0
$983$	−2.39181	+	4.14274i	−0.0762870	+	0.132133i	−0.901645	−	0.432476i	$-0.857640\pi$
$983$	−2.39181	+	4.14274i	−0.0762870	+	0.132133i	0.825358	+	0.564609i	$0.190973\pi$
$984$		0			0
$985$	−4.05029	−	7.01530i	−0.129053	−	0.223526i
$986$		0			0
$987$	8.95318	−	8.53339i	0.284983	−	0.271621i
$988$		0			0
$989$	−15.3400	+	26.5697i	−0.487784	+	0.844866i
$990$		0			0
$991$	−18.4932	−	32.0312i	−0.587456	−	1.01750i	−0.994564	−	0.104124i	$-0.966796\pi$
$991$	−18.4932	−	32.0312i	−0.587456	−	1.01750i	0.407108	−	0.913380i	$-0.366537\pi$
$992$		0			0
$993$	10.0700	−	11.6323i	0.319562	−	0.369140i
$994$		0			0
$995$	3.56430	−	6.17356i	0.112996	−	0.195715i
$996$		0			0
$997$	−24.3285	+	42.1382i	−0.770491	+	1.33453i	0.166803	+	0.985990i	$0.446656\pi$
$997$	−24.3285	+	42.1382i	−0.770491	+	1.33453i	−0.937294	+	0.348539i	$0.886678\pi$
$998$		0			0
$999$	−44.4548	+	22.9966i	−1.40649	+	0.727579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.q.k.625.8		22
3.2	odd	2		3024.2.q.k.2305.7		22
4.3	odd	2		504.2.q.d.121.4	yes	22
7.4	even	3		1008.2.t.k.193.1		22
9.2	odd	6		3024.2.t.l.289.5		22
9.7	even	3		1008.2.t.k.961.1		22
12.11	even	2		1512.2.q.c.793.7		22
21.11	odd	6		3024.2.t.l.1873.5		22
28.11	odd	6		504.2.t.d.193.11	yes	22
36.7	odd	6		504.2.t.d.457.11	yes	22
36.11	even	6		1512.2.t.d.289.5		22
63.11	odd	6		3024.2.q.k.2881.7		22
63.25	even	3	inner	1008.2.q.k.529.8		22
84.11	even	6		1512.2.t.d.361.5		22
252.11	even	6		1512.2.q.c.1369.7		22
252.151	odd	6		504.2.q.d.25.4	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.4	✓	22	252.151	odd	6
504.2.q.d.121.4	yes	22	4.3	odd	2
504.2.t.d.193.11	yes	22	28.11	odd	6
504.2.t.d.457.11	yes	22	36.7	odd	6
1008.2.q.k.529.8		22	63.25	even	3	inner
1008.2.q.k.625.8		22	1.1	even	1	trivial
1008.2.t.k.193.1		22	7.4	even	3
1008.2.t.k.961.1		22	9.7	even	3
1512.2.q.c.793.7		22	12.11	even	2
1512.2.q.c.1369.7		22	252.11	even	6
1512.2.t.d.289.5		22	36.11	even	6
1512.2.t.d.361.5		22	84.11	even	6
3024.2.q.k.2305.7		22	3.2	odd	2
3024.2.q.k.2881.7		22	63.11	odd	6
3024.2.t.l.289.5		22	9.2	odd	6
3024.2.t.l.1873.5		22	21.11	odd	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.13364 - 1.30952i) q^{3} +(-0.170100 - 0.294622i) q^{5} +(2.63360 + 0.253251i) q^{7} +(-0.429705 - 2.96907i) q^{9} +O(q^{10})\)	\(q+(1.13364 - 1.30952i) q^{3} +(-0.170100 - 0.294622i) q^{5} +(2.63360 + 0.253251i) q^{7} +(-0.429705 - 2.96907i) q^{9} +(-0.335794 + 0.581612i) q^{11} +(1.62370 - 2.81233i) q^{13} +(-0.578647 - 0.111246i) q^{15} +(-1.10014 - 1.90550i) q^{17} +(-0.242085 + 0.419303i) q^{19} +(3.31720 - 3.16167i) q^{21} +(2.09495 + 3.62856i) q^{23} +(2.44213 - 4.22990i) q^{25} +(-4.37520 - 2.80315i) q^{27} +(0.478868 + 0.829424i) q^{29} -2.08263 q^{31} +(0.380964 + 1.09907i) q^{33} +(-0.373363 - 0.818995i) q^{35} +(4.81613 - 8.34178i) q^{37} +(-1.84212 - 5.31445i) q^{39} +(-3.90207 + 6.75858i) q^{41} +(3.66119 + 6.34136i) q^{43} +(-0.801659 + 0.631639i) q^{45} +2.69901 q^{47} +(6.87173 + 1.33392i) q^{49} +(-3.74247 - 0.719498i) q^{51} +(-6.12335 - 10.6059i) q^{53} +0.228474 q^{55} +(0.274649 + 0.792355i) q^{57} +4.94297 q^{59} -3.52119 q^{61} +(-0.379756 - 7.92816i) q^{63} -1.10477 q^{65} -12.3202 q^{67} +(7.12661 + 1.37011i) q^{69} +5.57304 q^{71} +(-3.71686 - 6.43779i) q^{73} +(-2.77064 - 7.99322i) q^{75} +(-1.03164 + 1.44669i) q^{77} +10.0127 q^{79} +(-8.63071 + 2.55165i) q^{81} +(-2.47376 - 4.28468i) q^{83} +(-0.374269 + 0.648252i) q^{85} +(1.62902 + 0.313182i) q^{87} +(-8.52177 + 14.7601i) q^{89} +(4.98840 - 6.99536i) q^{91} +(-2.36096 + 2.72725i) q^{93} +0.164714 q^{95} +(4.23657 + 7.33795i) q^{97} +(1.87114 + 0.747072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} + 3 q^{5} + 5 q^{7} + 10 q^{9}+O(q^{10}) \) 22 * q - 2 * q^3 + 3 * q^5 + 5 * q^7 + 10 * q^9	\( 22 q - 2 q^{3} + 3 q^{5} + 5 q^{7} + 10 q^{9} + 3 q^{11} - 3 q^{13} + q^{15} + 7 q^{17} + q^{19} - 2 q^{23} - 10 q^{25} + 4 q^{27} + 9 q^{29} - 8 q^{31} + 29 q^{33} - 14 q^{35} + 2 q^{37} + 16 q^{39} + 16 q^{41} + q^{45} + 10 q^{47} + 15 q^{49} - 7 q^{51} + 11 q^{53} - 22 q^{55} + 7 q^{57} - 38 q^{59} + 26 q^{61} - 48 q^{63} - 26 q^{65} + 52 q^{67} - 4 q^{69} + 48 q^{71} - 35 q^{73} + 23 q^{75} + 17 q^{77} + 20 q^{79} - 38 q^{81} + 28 q^{83} - 20 q^{85} + 33 q^{87} + 6 q^{89} + 37 q^{91} + 19 q^{93} + 24 q^{95} - 29 q^{97} + 56 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 + 3 * q^5 + 5 * q^7 + 10 * q^9 + 3 * q^11 - 3 * q^13 + q^15 + 7 * q^17 + q^19 - 2 * q^23 - 10 * q^25 + 4 * q^27 + 9 * q^29 - 8 * q^31 + 29 * q^33 - 14 * q^35 + 2 * q^37 + 16 * q^39 + 16 * q^41 + q^45 + 10 * q^47 + 15 * q^49 - 7 * q^51 + 11 * q^53 - 22 * q^55 + 7 * q^57 - 38 * q^59 + 26 * q^61 - 48 * q^63 - 26 * q^65 + 52 * q^67 - 4 * q^69 + 48 * q^71 - 35 * q^73 + 23 * q^75 + 17 * q^77 + 20 * q^79 - 38 * q^81 + 28 * q^83 - 20 * q^85 + 33 * q^87 + 6 * q^89 + 37 * q^91 + 19 * q^93 + 24 * q^95 - 29 * q^97 + 56 * q^99

Introduction

L-functions

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Database

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