LMFDB - Embedded newform 400.2.bi.b.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(47,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 17]))

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

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

chi := DirichletCharacter("400.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.bi (of order $20$, degree $8$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 806 x^{12} - 2288 x^{11} + 5530 x^{10} - 11062 x^{9} + \cdots + 521 $ x^16 - 8x^15 + 52x^14 - 224x^13 + 806x^12 - 2288x^11 + 5530x^10 - 11062x^9 + 18924x^8 - 27056x^7 + 32750x^6 - 32636x^5 + 26711x^4 - 17122x^3 + 8368x^2 - 2746*x + 521
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			127.2
Root			$0.500000 + 0.821074i$ of defining polynomial
Character	$\chi$	$=$	400.127
Dual form			400.2.bi.b.63.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.66465 - 0.848182i) q^{3} +(2.06909 - 0.847859i) q^{5} +(-1.19176 + 1.19176i) q^{7} +(0.288294 - 0.396802i) q^{9} +O(q^{10})$	\(q+(1.66465 - 0.848182i) q^{3} +(2.06909 - 0.847859i) q^{5} +(-1.19176 + 1.19176i) q^{7} +(0.288294 - 0.396802i) q^{9} +(2.95401 + 4.06585i) q^{11} +(2.88139 - 0.456367i) q^{13} +(2.72517 - 3.16635i) q^{15} +(1.64204 - 3.22268i) q^{17} +(-1.61334 - 4.96534i) q^{19} +(-0.973034 + 2.99469i) q^{21} +(-9.36975 - 1.48402i) q^{23} +(3.56227 - 3.50859i) q^{25} +(-0.733443 + 4.63078i) q^{27} +(-3.92554 - 1.27549i) q^{29} +(-3.72227 + 1.20944i) q^{31} +(8.36598 + 4.26268i) q^{33} +(-1.45541 + 3.47630i) q^{35} +(-0.633446 - 3.99942i) q^{37} +(4.40943 - 3.20363i) q^{39} +(3.59403 + 2.61121i) q^{41} +(1.34378 + 1.34378i) q^{43} +(0.260074 - 1.06545i) q^{45} +(-1.37239 - 2.69346i) q^{47} +4.15942i q^{49} -6.75739i q^{51} +(-0.699000 - 1.37186i) q^{53} +(9.55938 + 5.90802i) q^{55} +(-6.89716 - 6.89716i) q^{57} +(-0.801892 - 0.582609i) q^{59} +(-10.4845 + 7.61746i) q^{61} +(0.129316 + 0.816469i) q^{63} +(5.57492 - 3.38728i) q^{65} +(1.64697 + 0.839173i) q^{67} +(-16.8561 + 5.47687i) q^{69} +(11.6416 + 3.78259i) q^{71} +(-1.34702 + 8.50473i) q^{73} +(2.95401 - 8.86204i) q^{75} +(-8.36598 - 1.32504i) q^{77} +(-3.59104 + 11.0521i) q^{79} +(3.16151 + 9.73012i) q^{81} +(-0.472892 + 0.928104i) q^{83} +(0.665148 - 8.06024i) q^{85} +(-7.61650 + 1.20634i) q^{87} +(-9.08976 - 12.5110i) q^{89} +(-2.89004 + 3.97780i) q^{91} +(-5.17046 + 5.17046i) q^{93} +(-7.54805 - 8.90586i) q^{95} +(-1.18915 + 0.605904i) q^{97} +2.46496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 20 q^{9}+O(q^{10}) $ 16 * q - 20 * q^9	$ 16 q - 20 q^{9} + 20 q^{17} - 20 q^{21} - 20 q^{25} + 20 q^{29} + 60 q^{33} - 20 q^{37} + 28 q^{41} - 20 q^{45} + 60 q^{53} - 20 q^{57} - 12 q^{61} - 20 q^{65} - 80 q^{69} - 40 q^{73} - 60 q^{77} + 56 q^{81} - 60 q^{85} + 40 q^{97}+O(q^{100}) $ 16 * q - 20 * q^9 + 20 * q^17 - 20 * q^21 - 20 * q^25 + 20 * q^29 + 60 * q^33 - 20 * q^37 + 28 * q^41 - 20 * q^45 + 60 * q^53 - 20 * q^57 - 12 * q^61 - 20 * q^65 - 80 * q^69 - 40 * q^73 - 60 * q^77 + 56 * q^81 - 60 * q^85 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{1}{20}\right)$	$-1$

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			0
$2$		0			0
$3$	1.66465	−	0.848182i	0.961087	−	0.489698i	0.0982393	−	0.995163i	$-0.468679\pi$
$3$	1.66465	−	0.848182i	0.961087	−	0.489698i	0.862847	+	0.505465i	$0.168679\pi$
$4$		0			0
$5$	2.06909	−	0.847859i	0.925325	−	0.379174i
$5$	2.06909	−	0.847859i	0.925325	−	0.379174i
$6$		0			0
$7$	−1.19176	+	1.19176i	−0.450442	+	0.450442i	−0.895501	−	0.445059i	$-0.853183\pi$
$7$	−1.19176	+	1.19176i	−0.450442	+	0.450442i	0.445059	+	0.895501i	$0.353183\pi$
$8$		0			0
$9$	0.288294	−	0.396802i	0.0960979	−	0.132267i
$10$		0			0
$11$	2.95401	+	4.06585i	0.890668	+	1.22590i	0.973350	+	0.229324i	$0.0736514\pi$
$11$	2.95401	+	4.06585i	0.890668	+	1.22590i	−0.0826822	+	0.996576i	$0.526349\pi$
$12$		0			0
$13$	2.88139	−	0.456367i	0.799154	−	0.126574i	0.256516	−	0.966540i	$-0.417426\pi$
$13$	2.88139	−	0.456367i	0.799154	−	0.126574i	0.542638	+	0.839967i	$0.317426\pi$
$14$		0			0
$15$	2.72517	−	3.16635i	0.703637	−	0.817549i
$16$		0			0
$17$	1.64204	−	3.22268i	0.398253	−	0.781616i	−0.601599	−	0.798798i	$-0.705470\pi$
$17$	1.64204	−	3.22268i	0.398253	−	0.781616i	0.999852	+	0.0171823i	$0.00546958\pi$
$18$		0			0
$19$	−1.61334	−	4.96534i	−0.370125	−	1.13913i	−0.946709	−	0.322090i	$-0.895615\pi$
$19$	−1.61334	−	4.96534i	−0.370125	−	1.13913i	0.576584	−	0.817038i	$-0.304385\pi$
$20$		0			0
$21$	−0.973034	+	2.99469i	−0.212333	+	0.653495i
$22$		0			0
$23$	−9.36975	−	1.48402i	−1.95373	−	0.309440i	−0.999960	−	0.00889143i	$-0.997170\pi$
$23$	−9.36975	−	1.48402i	−1.95373	−	0.309440i	−0.953767	−	0.300549i	$-0.902830\pi$
$24$		0			0
$25$	3.56227	−	3.50859i	0.712454	−	0.701719i
$26$		0			0
$27$	−0.733443	+	4.63078i	−0.141151	+	0.891193i
$28$		0			0
$29$	−3.92554	−	1.27549i	−0.728955	−	0.236852i	−0.0790535	−	0.996870i	$-0.525190\pi$
$29$	−3.92554	−	1.27549i	−0.728955	−	0.236852i	−0.649901	+	0.760019i	$0.725190\pi$
$30$		0			0
$31$	−3.72227	+	1.20944i	−0.668540	+	0.217222i	−0.623571	−	0.781767i	$-0.714319\pi$
$31$	−3.72227	+	1.20944i	−0.668540	+	0.217222i	−0.0449687	+	0.998988i	$0.514319\pi$
$32$		0			0
$33$	8.36598	+	4.26268i	1.45633	+	0.742037i
$34$		0			0
$35$	−1.45541	+	3.47630i	−0.246010	+	0.587602i
$36$		0			0
$37$	−0.633446	−	3.99942i	−0.104138	−	0.657501i	−0.983440	−	0.181236i	$-0.941990\pi$
$37$	−0.633446	−	3.99942i	−0.104138	−	0.657501i	0.879302	−	0.476265i	$-0.158010\pi$
$38$		0			0
$39$	4.40943	−	3.20363i	0.706073	−	0.512992i
$40$		0			0
$41$	3.59403	+	2.61121i	0.561293	+	0.407803i	0.831932	−	0.554878i	$-0.187235\pi$
$41$	3.59403	+	2.61121i	0.561293	+	0.407803i	−0.270639	+	0.962681i	$0.587235\pi$
$42$		0			0
$43$	1.34378	+	1.34378i	0.204924	+	0.204924i	0.802106	−	0.597182i	$-0.203713\pi$
$43$	1.34378	+	1.34378i	0.204924	+	0.204924i	−0.597182	+	0.802106i	$0.703713\pi$
$44$		0			0
$45$	0.260074	−	1.06545i	0.0387695	−	0.158828i
$46$		0			0
$47$	−1.37239	−	2.69346i	−0.200183	−	0.392882i	0.768990	−	0.639260i	$-0.220759\pi$
$47$	−1.37239	−	2.69346i	−0.200183	−	0.392882i	−0.969174	+	0.246379i	$0.920759\pi$
$48$		0			0
$49$			4.15942i			0.594203i
$50$		0			0
$51$		−	6.75739i		−	0.946224i
$52$		0			0
$53$	−0.699000	−	1.37186i	−0.0960150	−	0.188440i	0.838003	−	0.545665i	$-0.183723\pi$
$53$	−0.699000	−	1.37186i	−0.0960150	−	0.188440i	−0.934018	+	0.357225i	$0.883723\pi$
$54$		0			0
$55$	9.55938	+	5.90802i	1.28899	+	0.796638i
$56$		0			0
$57$	−6.89716	−	6.89716i	−0.913551	−	0.913551i
$58$		0			0
$59$	−0.801892	−	0.582609i	−0.104397	−	0.0758492i	0.534362	−	0.845256i	$-0.320552\pi$
$59$	−0.801892	−	0.582609i	−0.104397	−	0.0758492i	−0.638759	+	0.769407i	$0.720552\pi$
$60$		0			0
$61$	−10.4845	+	7.61746i	−1.34241	+	0.975316i	−0.343055	+	0.939315i	$0.611462\pi$
$61$	−10.4845	+	7.61746i	−1.34241	+	0.975316i	−0.999352	+	0.0360002i	$0.988538\pi$
$62$		0			0
$63$	0.129316	+	0.816469i	0.0162923	+	0.102865i
$64$		0			0
$65$	5.57492	−	3.38728i	0.691484	−	0.420140i
$66$		0			0
$67$	1.64697	+	0.839173i	0.201209	+	0.102521i	0.551692	−	0.834048i	$-0.313982\pi$
$67$	1.64697	+	0.839173i	0.201209	+	0.102521i	−0.350483	+	0.936569i	$0.613982\pi$
$68$		0			0
$69$	−16.8561	+	5.47687i	−2.02923	+	0.659338i
$70$		0			0
$71$	11.6416	+	3.78259i	1.38161	+	0.448911i	0.903197	−	0.429225i	$-0.141213\pi$
$71$	11.6416	+	3.78259i	1.38161	+	0.448911i	0.478410	+	0.878137i	$0.341213\pi$
$72$		0			0
$73$	−1.34702	+	8.50473i	−0.157656	+	0.995404i	0.774296	+	0.632824i	$0.218104\pi$
$73$	−1.34702	+	8.50473i	−0.157656	+	0.995404i	−0.931953	+	0.362580i	$0.881896\pi$
$74$		0			0
$75$	2.95401	−	8.86204i	0.341100	−	1.02330i
$76$		0			0
$77$	−8.36598	−	1.32504i	−0.953392	−	0.151002i
$78$		0			0
$79$	−3.59104	+	11.0521i	−0.404023	+	1.24346i	0.517685	+	0.855571i	$0.326794\pi$
$79$	−3.59104	+	11.0521i	−0.404023	+	1.24346i	−0.921708	+	0.387884i	$0.873206\pi$
$80$		0			0
$81$	3.16151	+	9.73012i	0.351279	+	1.08112i
$82$		0			0
$83$	−0.472892	+	0.928104i	−0.0519067	+	0.101873i	−0.915503	−	0.402312i	$-0.868207\pi$
$83$	−0.472892	+	0.928104i	−0.0519067	+	0.101873i	0.863596	+	0.504184i	$0.168207\pi$
$84$		0			0
$85$	0.665148	−	8.06024i	0.0721454	−	0.874256i
$86$		0			0
$87$	−7.61650	+	1.20634i	−0.816575	+	0.129333i
$88$		0			0
$89$	−9.08976	−	12.5110i	−0.963512	−	1.32616i	−0.945257	−	0.326328i	$-0.894189\pi$
$89$	−9.08976	−	12.5110i	−0.963512	−	1.32616i	−0.0182556	−	0.999833i	$-0.505811\pi$
$90$		0			0
$91$	−2.89004	+	3.97780i	−0.302959	+	0.416987i
$92$		0			0
$93$	−5.17046	+	5.17046i	−0.536152	+	0.536152i
$94$		0			0
$95$	−7.54805	−	8.90586i	−0.774414	−	0.913722i
$96$		0			0
$97$	−1.18915	+	0.605904i	−0.120740	+	0.0615202i	−0.513317	−	0.858199i	$-0.671584\pi$
$97$	−1.18915	+	0.605904i	−0.120740	+	0.0615202i	0.392577	+	0.919719i	$0.371584\pi$
$98$		0			0
$99$	2.46496			0.247738
$100$		0			0
$101$	−6.10143			−0.607115			−0.303558	−	0.952813i	$-0.598175\pi$
$101$	−6.10143			−0.607115			−0.303558	+	0.952813i	$0.598175\pi$
$102$		0			0
$103$	7.08018	−	3.60753i	0.697631	−	0.355461i	−0.0689395	−	0.997621i	$-0.521962\pi$
$103$	7.08018	−	3.60753i	0.697631	−	0.355461i	0.766571	+	0.642160i	$0.221962\pi$
$104$		0			0
$105$	0.525779	+	7.02128i	0.0513108	+	0.685207i
$106$		0			0
$107$	7.75641	−	7.75641i	0.749840	−	0.749840i	−0.224609	−	0.974449i	$-0.572110\pi$
$107$	7.75641	−	7.75641i	0.749840	−	0.749840i	0.974449	+	0.224609i	$0.0721104\pi$
$108$		0			0
$109$	−4.97178	+	6.84307i	−0.476210	+	0.655447i	−0.977771	−	0.209675i	$-0.932759\pi$
$109$	−4.97178	+	6.84307i	−0.476210	+	0.655447i	0.501561	+	0.865122i	$0.332759\pi$
$110$		0			0
$111$	−4.44671	−	6.12037i	−0.422063	−	0.580919i
$112$		0			0
$113$	18.1812	−	2.87962i	1.71034	−	0.270892i	0.776901	−	0.629623i	$-0.216791\pi$
$113$	18.1812	−	2.87962i	1.71034	−	0.270892i	0.933441	+	0.358731i	$0.116791\pi$
$114$		0			0
$115$	−20.6451	+	4.87365i	−1.92516	+	0.454470i
$116$		0			0
$117$	0.649599	−	1.27491i	0.0600554	−	0.117865i
$118$		0			0
$119$	1.88375	+	5.79757i	0.172683	+	0.531463i
$120$		0			0
$121$	−4.40575	+	13.5595i	−0.400523	+	1.23268i
$122$		0			0
$123$	8.19759	+	1.29837i	0.739152	+	0.117070i
$124$		0			0
$125$	4.39587	−	10.2799i	0.393179	−	0.919462i
$126$		0			0
$127$	1.89157	−	11.9429i	0.167850	−	1.05976i	−0.749595	−	0.661897i	$-0.769752\pi$
$127$	1.89157	−	11.9429i	0.167850	−	1.05976i	0.917444	−	0.397864i	$-0.130248\pi$
$128$		0			0
$129$	3.37669	+	1.09715i	0.297301	+	0.0965989i
$130$		0			0
$131$	−17.1783	+	5.58158i	−1.50088	+	0.487665i	−0.940274	−	0.340418i	$-0.889431\pi$
$131$	−17.1783	+	5.58158i	−1.50088	+	0.487665i	−0.560605	+	0.828083i	$0.689431\pi$
$132$		0			0
$133$	7.84020	+	3.99478i	0.679831	+	0.346391i
$134$		0			0
$135$	2.40868	+	10.2034i	0.207307	+	0.878165i
$136$		0			0
$137$	−2.54805	−	16.0877i	−0.217694	−	1.37447i	−0.818240	−	0.574877i	$-0.805050\pi$
$137$	−2.54805	−	16.0877i	−0.217694	−	1.37447i	0.600546	−	0.799590i	$-0.294950\pi$
$138$		0			0
$139$	−9.34704	+	6.79102i	−0.792806	+	0.576007i	−0.908795	−	0.417243i	$-0.862996\pi$
$139$	−9.34704	+	6.79102i	−0.792806	+	0.576007i	0.115989	+	0.993250i	$0.462996\pi$
$140$		0			0
$141$	−4.56909	−	3.31964i	−0.384787	−	0.279564i
$142$		0			0
$143$	10.3672	+	10.3672i	0.866947	+	0.866947i
$144$		0			0
$145$	−9.20373	+	0.689209i	−0.764329	+	0.0572357i
$146$		0			0
$147$	3.52795	+	6.92399i	0.290980	+	0.571081i
$148$		0			0
$149$			9.85765i			0.807570i	0.914854	+	0.403785i	$0.132306\pi$
$149$			9.85765i			0.807570i	−0.914854	+	0.403785i	$0.867694\pi$
$150$		0			0
$151$		−	22.0626i		−	1.79543i	−0.440579	−	0.897714i	$-0.645227\pi$
$151$		−	22.0626i		−	1.79543i	0.440579	−	0.897714i	$-0.354773\pi$
$152$		0			0
$153$	−0.805379	−	1.58064i	−0.0651110	−	0.127788i
$154$		0			0
$155$	−6.67628	+	5.65840i	−0.536252	+	0.454494i
$156$		0			0
$157$	2.00145	+	2.00145i	0.159733	+	0.159733i	0.782449	−	0.622715i	$-0.213970\pi$
$157$	2.00145	+	2.00145i	0.159733	+	0.159733i	−0.622715	+	0.782449i	$0.713970\pi$
$158$		0			0
$159$	−2.32718	−	1.69080i	−0.184557	−	0.134089i
$160$		0			0
$161$	12.9351	−	9.39788i	1.01943	−	0.740656i
$162$		0			0
$163$	−2.84183	−	17.9426i	−0.222589	−	1.40537i	−0.805383	−	0.592754i	$-0.798040\pi$
$163$	−2.84183	−	17.9426i	−0.222589	−	1.40537i	0.582794	−	0.812620i	$-0.301960\pi$
$164$		0			0
$165$	20.9241	+	1.72670i	1.62894	+	0.134423i
$166$		0			0
$167$	5.80850	+	2.95958i	0.449475	+	0.229019i	0.664050	−	0.747689i	$-0.268836\pi$
$167$	5.80850	+	2.95958i	0.449475	+	0.229019i	−0.214574	+	0.976708i	$0.568836\pi$
$168$		0			0
$169$	−4.26960	+	1.38728i	−0.328431	+	0.106714i
$170$		0			0
$171$	−2.43537	−	0.791301i	−0.186238	−	0.0605123i
$172$		0			0
$173$	1.65153	−	10.4274i	0.125564	−	0.792777i	−0.841875	−	0.539672i	$-0.818548\pi$
$173$	1.65153	−	10.4274i	0.125564	−	0.792777i	0.967439	−	0.253105i	$-0.0814517\pi$
$174$		0			0
$175$	−0.0639712	+	8.42676i	−0.00483577	+	0.637003i
$176$		0			0
$177$	−1.82903	−	0.289690i	−0.137478	−	0.0217744i
$178$		0			0
$179$	5.81042	−	17.8826i	0.434291	−	1.33661i	−0.459520	−	0.888167i	$-0.651979\pi$
$179$	5.81042	−	17.8826i	0.434291	−	1.33661i	0.893811	−	0.448444i	$-0.148021\pi$
$180$		0			0
$181$	2.12480	+	6.53945i	0.157935	+	0.486074i	0.998446	−	0.0557200i	$-0.0177454\pi$
$181$	2.12480	+	6.53945i	0.157935	+	0.486074i	−0.840512	+	0.541794i	$0.817745\pi$
$182$		0			0
$183$	−10.9921	+	21.5732i	−0.812559	+	1.59474i
$184$		0			0
$185$	−4.70160	−	7.73810i	−0.345669	−	0.568916i
$186$		0			0
$187$	17.9535	−	2.84356i	1.31289	−	0.207942i
$188$		0			0
$189$	−4.64468	−	6.39285i	−0.337851	−	0.465012i
$190$		0			0
$191$	6.42666	−	8.84554i	0.465017	−	0.640041i	−0.510523	−	0.859864i	$-0.670548\pi$
$191$	6.42666	−	8.84554i	0.465017	−	0.640041i	0.975540	+	0.219823i	$0.0705481\pi$
$192$		0			0
$193$	−18.0575	+	18.0575i	−1.29981	+	1.29981i	−0.371288	+	0.928518i	$0.621084\pi$
$193$	−18.0575	+	18.0575i	−1.29981	+	1.29981i	−0.928518	+	0.371288i	$0.878916\pi$
$194$		0			0
$195$	6.40727	−	10.3672i	0.458834	−	0.742409i
$196$		0			0
$197$	10.0634	−	5.12756i	0.716988	−	0.365323i	−0.0571286	−	0.998367i	$-0.518195\pi$
$197$	10.0634	−	5.12756i	0.716988	−	0.365323i	0.774116	+	0.633043i	$0.218195\pi$
$198$		0			0
$199$	9.98407			0.707752			0.353876	−	0.935292i	$-0.384864\pi$
$199$	9.98407			0.707752			0.353876	+	0.935292i	$0.384864\pi$
$200$		0			0
$201$	3.45340			0.243584
$202$		0			0
$203$	6.19837	−	3.15823i	0.435040	−	0.221664i
$204$		0			0
$205$	9.65031	+	2.35561i	0.674007	+	0.164523i
$206$		0			0
$207$	−3.29010	+	3.29010i	−0.228678	+	0.228678i
$208$		0			0
$209$	15.4225	−	21.2273i	1.06680	−	1.46832i
$210$		0			0
$211$	14.0061	+	19.2777i	0.964219	+	1.32713i	0.944914	+	0.327320i	$0.106145\pi$
$211$	14.0061	+	19.2777i	0.964219	+	1.32713i	0.0193054	+	0.999814i	$0.493855\pi$
$212$		0			0
$213$	22.5876	−	3.57752i	1.54767	−	0.245128i
$214$		0			0
$215$	3.91973	+	1.64106i	0.267324	+	0.111920i
$216$		0			0
$217$	2.99469	−	5.87741i	0.203293	−	0.398984i
$218$		0			0
$219$	4.97125	+	15.2999i	0.335926	+	1.03387i
$220$		0			0
$221$	3.26063	−	10.0352i	0.219334	−	0.675039i
$222$		0			0
$223$	1.15256	+	0.182547i	0.0771810	+	0.0122243i	0.194906	−	0.980822i	$-0.437560\pi$
$223$	1.15256	+	0.182547i	0.0771810	+	0.0122243i	−0.117724	+	0.993046i	$0.537560\pi$
$224$		0			0
$225$	−0.365237	−	2.42502i	−0.0243492	−	0.161668i
$226$		0			0
$227$	−0.793765	+	5.01163i	−0.0526840	+	0.332634i	0.947243	+	0.320518i	$0.103857\pi$
$227$	−0.793765	+	5.01163i	−0.0526840	+	0.332634i	−0.999927	+	0.0121162i	$0.996143\pi$
$228$		0			0
$229$	19.2281	+	6.24759i	1.27063	+	0.412852i	0.865270	−	0.501306i	$-0.167147\pi$
$229$	19.2281	+	6.24759i	1.27063	+	0.412852i	0.405358	+	0.914158i	$0.367147\pi$
$230$		0			0
$231$	−15.0503	+	4.89014i	−0.990237	+	0.321748i
$232$		0			0
$233$	15.1785	+	7.73382i	0.994375	+	0.506659i	0.873925	−	0.486060i	$-0.161566\pi$
$233$	15.1785	+	7.73382i	0.994375	+	0.506659i	0.120450	+	0.992719i	$0.461566\pi$
$234$		0			0
$235$	−5.12327	−	4.40943i	−0.334205	−	0.287639i
$236$		0			0
$237$	3.39635	+	21.4437i	0.220617	+	1.39292i
$238$		0			0
$239$	−9.70185	+	7.04881i	−0.627560	+	0.455949i	−0.855554	−	0.517713i	$-0.826783\pi$
$239$	−9.70185	+	7.04881i	−0.627560	+	0.455949i	0.227994	+	0.973663i	$0.426783\pi$
$240$		0			0
$241$	10.4523	+	7.59401i	0.673289	+	0.489173i	0.871125	−	0.491062i	$-0.163391\pi$
$241$	10.4523	+	7.59401i	0.673289	+	0.489173i	−0.197836	+	0.980235i	$0.563391\pi$
$242$		0			0
$243$	3.56992	+	3.56992i	0.229010	+	0.229010i
$244$		0			0
$245$	3.52660	+	8.60623i	0.225306	+	0.549832i
$246$		0			0
$247$	−6.91468	−	13.5708i	−0.439970	−	0.863490i
$248$		0			0
$249$			1.94607i			0.123327i
$250$		0			0
$251$		−	6.08412i		−	0.384026i	−0.981392	−	0.192013i	$-0.938498\pi$
$251$		−	6.08412i		−	0.384026i	0.981392	−	0.192013i	$-0.0615016\pi$
$252$		0			0
$253$	−21.6445	−	42.4798i	−1.36078	−	2.67068i
$254$		0			0
$255$	−5.72931	−	13.9817i	−0.358784	−	0.875565i
$256$		0			0
$257$	−1.33184	−	1.33184i	−0.0830776	−	0.0830776i	0.664347	−	0.747424i	$-0.268710\pi$
$257$	−1.33184	−	1.33184i	−0.0830776	−	0.0830776i	−0.747424	+	0.664347i	$0.768710\pi$
$258$		0			0
$259$	5.52126	+	4.01143i	0.343075	+	0.249258i
$260$		0			0
$261$	−1.63782	+	1.18995i	−0.101379	+	0.0736560i
$262$		0			0
$263$	−3.48896	−	22.0284i	−0.215138	−	1.35833i	−0.824691	−	0.565584i	$-0.808651\pi$
$263$	−3.48896	−	22.0284i	−0.215138	−	1.35833i	0.609552	−	0.792746i	$-0.291349\pi$
$264$		0			0
$265$	−2.60944	−	2.24586i	−0.160297	−	0.137962i
$266$		0			0
$267$	−25.7429	−	13.1166i	−1.57544	−	0.802725i
$268$		0			0
$269$	−5.86133	+	1.90446i	−0.357372	+	0.116117i	−0.482200	−	0.876061i	$-0.660162\pi$
$269$	−5.86133	+	1.90446i	−0.357372	+	0.116117i	0.124828	+	0.992178i	$0.460162\pi$
$270$		0			0
$271$	8.10501	+	2.63348i	0.492344	+	0.159972i	0.544658	−	0.838658i	$-0.316660\pi$
$271$	8.10501	+	2.63348i	0.492344	+	0.159972i	−0.0523137	+	0.998631i	$0.516660\pi$
$272$		0			0
$273$	−1.43701	+	9.07293i	−0.0869718	+	0.549119i
$274$		0			0
$275$	24.7884	+	4.11923i	1.49480	+	0.248399i
$276$		0			0
$277$	24.9456	+	3.95100i	1.49884	+	0.237393i	0.851316	−	0.524654i	$-0.175805\pi$
$277$	24.9456	+	3.95100i	1.49884	+	0.237393i	0.647522	+	0.762047i	$0.275805\pi$
$278$		0			0
$279$	−0.593199	+	1.82568i	−0.0355139	+	0.109301i
$280$		0			0
$281$	−5.09194	−	15.6714i	−0.303760	−	0.934877i	−0.980137	−	0.198321i	$-0.936451\pi$
$281$	−5.09194	−	15.6714i	−0.303760	−	0.934877i	0.676377	−	0.736555i	$-0.263549\pi$
$282$		0			0
$283$	−2.32064	+	4.55450i	−0.137947	+	0.270737i	−0.949637	−	0.313352i	$-0.898548\pi$
$283$	−2.32064	+	4.55450i	−0.137947	+	0.270737i	0.811690	+	0.584089i	$0.198548\pi$
$284$		0			0
$285$	−20.1187	−	8.42303i	−1.19173	−	0.498937i
$286$		0			0
$287$	−7.39515	+	1.17128i	−0.436522	+	0.0691383i
$288$		0			0
$289$	2.30295	+	3.16974i	0.135468	+	0.186455i
$290$		0			0
$291$	−1.46561	+	2.01724i	−0.0859155	+	0.118252i
$292$		0			0
$293$	−11.8855	+	11.8855i	−0.694356	+	0.694356i	−0.963187	−	0.268831i	$-0.913363\pi$
$293$	−11.8855	+	11.8855i	−0.694356	+	0.694356i	0.268831	+	0.963187i	$0.413363\pi$
$294$		0			0
$295$	−2.15316	−	0.525579i	−0.125362	−	0.0306004i
$296$		0			0
$297$	−20.9946	+	10.6973i	−1.21823	+	0.620720i
$298$		0			0
$299$	−27.6751			−1.60050
$300$		0			0
$301$	−3.20292			−0.184613
$302$		0			0
$303$	−10.1568	+	5.17513i	−0.583490	+	0.297303i
$304$		0			0
$305$	−15.2349	+	24.6506i	−0.872349	+	1.41149i
$306$		0			0
$307$	−20.2344	+	20.2344i	−1.15484	+	1.15484i	−0.169271	+	0.985570i	$0.554141\pi$
$307$	−20.2344	+	20.2344i	−1.15484	+	1.15484i	−0.985570	+	0.169271i	$0.945859\pi$
$308$		0			0
$309$	8.72619	−	12.0106i	0.496415	−	0.683257i
$310$		0			0
$311$	6.85499	+	9.43509i	0.388711	+	0.535015i	0.957866	−	0.287215i	$-0.0927296\pi$
$311$	6.85499	+	9.43509i	0.388711	+	0.535015i	−0.569155	+	0.822230i	$0.692730\pi$
$312$		0			0
$313$	−15.3647	+	2.43352i	−0.868462	+	0.137551i	−0.574736	−	0.818339i	$-0.694895\pi$
$313$	−15.3647	+	2.43352i	−0.868462	+	0.137551i	−0.293726	+	0.955890i	$0.594895\pi$
$314$		0			0
$315$	0.959817	+	1.57971i	0.0540795	+	0.0890064i
$316$		0			0
$317$	−7.58814	+	14.8926i	−0.426192	+	0.836450i	0.573657	+	0.819096i	$0.305524\pi$
$317$	−7.58814	+	14.8926i	−0.426192	+	0.836450i	−0.999849	+	0.0173542i	$0.994476\pi$
$318$		0			0
$319$	−6.41017	−	19.7285i	−0.358900	−	1.10458i
$320$		0			0
$321$	6.33286	−	19.4906i	0.353466	−	1.08786i
$322$		0			0
$323$	−18.6509	−	2.95401i	−1.03776	−	0.164366i
$324$		0			0
$325$	8.66308	−	11.7353i	0.480541	−	0.650959i
$326$		0			0
$327$	−2.47211	+	15.6083i	−0.136708	+	0.863140i
$328$		0			0
$329$	4.84551	+	1.57440i	0.267142	+	0.0867996i
$330$		0			0
$331$	24.0911	−	7.82766i	1.32416	−	0.430247i	0.440241	−	0.897880i	$-0.354893\pi$
$331$	24.0911	−	7.82766i	1.32416	−	0.430247i	0.883923	+	0.467633i	$0.154893\pi$
$332$		0			0
$333$	−1.76960	−	0.901656i	−0.0969734	−	0.0494104i
$334$		0			0
$335$	4.11923	+	0.339927i	0.225058	+	0.0185722i
$336$		0			0
$337$	−0.701492	−	4.42904i	−0.0382127	−	0.241265i	0.961187	−	0.275896i	$-0.0889745\pi$
$337$	−0.701492	−	4.42904i	−0.0382127	−	0.241265i	−0.999400	+	0.0346306i	$0.988975\pi$
$338$		0			0
$339$	27.8229	−	20.2145i	1.51113	−	1.09790i
$340$		0			0
$341$	−15.9130	−	11.5615i	−0.861739	−	0.626090i
$342$		0			0
$343$	−13.2993	−	13.2993i	−0.718097	−	0.718097i
$344$		0			0
$345$	−30.2331	+	25.6237i	−1.62770	+	1.37953i
$346$		0			0
$347$	6.75030	+	13.2482i	0.362375	+	0.711201i	0.998158	−	0.0606666i	$-0.0193227\pi$
$347$	6.75030	+	13.2482i	0.362375	+	0.711201i	−0.635783	+	0.771868i	$0.719323\pi$
$348$		0			0
$349$			31.1101i			1.66529i	0.553809	+	0.832644i	$0.313174\pi$
$349$			31.1101i			1.66529i	−0.553809	+	0.832644i	$0.686826\pi$
$350$		0			0
$351$			13.6778i			0.730066i
$352$		0			0
$353$	−12.5205	−	24.5729i	−0.666399	−	1.30788i	−0.938389	−	0.345582i	$-0.887682\pi$
$353$	−12.5205	−	24.5729i	−0.666399	−	1.30788i	0.271990	−	0.962300i	$-0.412318\pi$
$354$		0			0
$355$	27.2947	−	2.04393i	1.44865	−	0.108480i
$356$		0			0
$357$	8.05318	+	8.05318i	0.426219	+	0.426219i
$358$		0			0
$359$	−7.67929	−	5.57933i	−0.405297	−	0.294466i	0.366398	−	0.930458i	$-0.380591\pi$
$359$	−7.67929	−	5.57933i	−0.405297	−	0.294466i	−0.771695	+	0.635993i	$0.780591\pi$
$360$		0			0
$361$	−6.68045	+	4.85363i	−0.351603	+	0.255454i
$362$		0			0
$363$	4.16689	+	26.3087i	0.218705	+	1.38085i
$364$		0			0
$365$	4.42371	+	18.7391i	0.231548	+	0.980852i
$366$		0			0
$367$	27.0785	+	13.7972i	1.41349	+	0.720207i	0.983208	−	0.182489i	$-0.0584153\pi$
$367$	27.0785	+	13.7972i	1.41349	+	0.720207i	0.430279	+	0.902696i	$0.358415\pi$
$368$		0			0
$369$	2.07227	−	0.673322i	0.107878	−	0.0350517i
$370$		0			0
$371$	2.46797	+	0.801892i	0.128131	+	0.0416322i
$372$		0			0
$373$	0.346615	−	2.18844i	0.0179470	−	0.113313i	−0.977088	−	0.212833i	$-0.931731\pi$
$373$	0.346615	−	2.18844i	0.0179470	−	0.113313i	0.995036	+	0.0995203i	$0.0317308\pi$
$374$		0			0
$375$	−1.40164	−	20.8409i	−0.0723802	−	1.07622i
$376$		0			0
$377$	−11.8931	−	1.88368i	−0.612526	−	0.0970146i
$378$		0			0
$379$	7.17553	−	22.0840i	0.368582	−	1.13438i	−0.579125	−	0.815239i	$-0.696606\pi$
$379$	7.17553	−	22.0840i	0.368582	−	1.13438i	0.947707	−	0.319141i	$-0.103394\pi$
$380$		0			0
$381$	−6.98095	−	21.4852i	−0.357645	−	1.10072i
$382$		0			0
$383$	11.4851	−	22.5408i	0.586863	−	1.15178i	−0.386452	−	0.922309i	$-0.626300\pi$
$383$	11.4851	−	22.5408i	0.586863	−	1.15178i	0.973315	−	0.229473i	$-0.0737004\pi$
$384$		0			0
$385$	−18.4334	+	4.35154i	−0.939454	+	0.221775i
$386$		0			0
$387$	0.920617	−	0.145811i	0.0467976	−	0.00741201i
$388$		0			0
$389$	−3.95328	−	5.44122i	−0.200439	−	0.275881i	0.696951	−	0.717119i	$-0.254539\pi$
$389$	−3.95328	−	5.44122i	−0.200439	−	0.275881i	−0.897390	+	0.441238i	$0.854539\pi$
$390$		0			0
$391$	−20.1680	+	27.7589i	−1.01994	+	1.40383i
$392$		0			0
$393$	−23.8618	+	23.8618i	−1.20367	+	1.20367i
$394$		0			0
$395$	1.94042	+	25.9124i	0.0976331	+	1.30380i
$396$		0			0
$397$	18.3705	−	9.36024i	0.921990	−	0.469777i	0.0724916	−	0.997369i	$-0.476905\pi$
$397$	18.3705	−	9.36024i	0.921990	−	0.469777i	0.849498	+	0.527592i	$0.176905\pi$
$398$		0			0
$399$	16.4395			0.823004
$400$		0			0
$401$	10.6780			0.533235			0.266617	−	0.963802i	$-0.414094\pi$
$401$	10.6780			0.533235			0.266617	+	0.963802i	$0.414094\pi$
$402$		0			0
$403$	−10.1734	+	5.18359i	−0.506772	+	0.258213i
$404$		0			0
$405$	14.7912	+	17.4520i	0.734982	+	0.867197i
$406$		0			0
$407$	14.3898	−	14.3898i	0.713278	−	0.713278i
$408$		0			0
$409$	15.8404	−	21.8025i	0.783259	−	1.07806i	−0.211655	−	0.977344i	$-0.567885\pi$
$409$	15.8404	−	21.8025i	0.783259	−	1.07806i	0.994915	−	0.100720i	$-0.0321145\pi$
$410$		0			0
$411$	−17.8869	−	24.6192i	−0.882297	−	1.21438i
$412$		0			0
$413$	1.64999	−	0.261333i	0.0811907	−	0.0128593i
$414$		0			0
$415$	−0.191556	+	2.32128i	−0.00940313	+	0.113947i
$416$		0			0
$417$	−9.79954	+	19.2327i	−0.479885	+	0.941828i
$418$		0			0
$419$	0.647616	+	1.99316i	0.0316381	+	0.0973722i	0.965629	−	0.259926i	$-0.0836981\pi$
$419$	0.647616	+	1.99316i	0.0316381	+	0.0973722i	−0.933990	+	0.357298i	$0.883698\pi$
$420$		0			0
$421$	−0.961713	+	2.95985i	−0.0468710	+	0.144254i	−0.971753	−	0.236000i	$-0.924163\pi$
$421$	−0.961713	+	2.95985i	−0.0468710	+	0.144254i	0.924882	+	0.380254i	$0.124163\pi$
$422$		0			0
$423$	−1.46442	−	0.231942i	−0.0712026	−	0.0112774i
$424$		0			0
$425$	−5.45770	−	17.2413i	−0.264737	−	0.836327i
$426$		0			0
$427$	3.41686	−	21.5732i	0.165353	−	1.04400i
$428$		0			0
$429$	26.0510	+	8.46448i	1.25775	+	0.408669i
$430$		0			0
$431$	7.80462	−	2.53587i	0.375935	−	0.122149i	−0.114954	−	0.993371i	$-0.536672\pi$
$431$	7.80462	−	2.53587i	0.375935	−	0.122149i	0.490889	+	0.871222i	$0.336672\pi$
$432$		0			0
$433$	−22.4223	−	11.4247i	−1.07755	−	0.549038i	−0.177185	−	0.984178i	$-0.556699\pi$
$433$	−22.4223	−	11.4247i	−1.07755	−	0.549038i	−0.900363	+	0.435139i	$0.856699\pi$
$434$		0			0
$435$	−14.7364	+	8.95373i	−0.706558	+	0.429299i
$436$		0			0
$437$	7.74789	+	48.9182i	0.370632	+	2.34008i
$438$		0			0
$439$	−0.0277269	+	0.0201448i	−0.00132333	+	0.000961458i	−0.588447	−	0.808536i	$-0.700260\pi$
$439$	−0.0277269	+	0.0201448i	−0.00132333	+	0.000961458i	0.587123	+	0.809497i	$0.300260\pi$
$440$		0			0
$441$	1.65047	+	1.19914i	0.0785938	+	0.0571017i
$442$		0			0
$443$	−10.5012	−	10.5012i	−0.498926	−	0.498926i	0.412177	−	0.911104i	$-0.364768\pi$
$443$	−10.5012	−	10.5012i	−0.498926	−	0.498926i	−0.911104	+	0.412177i	$0.864768\pi$
$444$		0			0
$445$	−29.4151	−	18.1795i	−1.39441	−	0.861792i
$446$		0			0
$447$	8.36108	+	16.4095i	0.395465	+	0.776145i
$448$		0			0
$449$		−	0.660520i		−	0.0311719i	−0.999879	−	0.0155859i	$-0.995039\pi$
$449$		−	0.660520i		−	0.0311719i	0.999879	−	0.0155859i	$-0.00496136\pi$
$450$		0			0
$451$			22.3263i			1.05131i
$452$		0			0
$453$	−18.7131	−	36.7265i	−0.879217	−	1.72556i
$454$		0			0
$455$	−2.60714	+	10.6808i	−0.122225	+	0.500722i
$456$		0			0
$457$	14.0516	+	14.0516i	0.657307	+	0.657307i	0.954742	−	0.297435i	$-0.0961311\pi$
$457$	14.0516	+	14.0516i	0.657307	+	0.657307i	−0.297435	+	0.954742i	$0.596131\pi$
$458$		0			0
$459$	13.7192	+	9.96757i	0.640357	+	0.465246i
$460$		0			0
$461$	13.5448	−	9.84085i	0.630843	−	0.458334i	−0.225849	−	0.974162i	$-0.572516\pi$
$461$	13.5448	−	9.84085i	0.630843	−	0.458334i	0.856692	+	0.515828i	$0.172516\pi$
$462$		0			0
$463$	4.71316	+	29.7577i	0.219039	+	1.38296i	0.814774	+	0.579778i	$0.196861\pi$
$463$	4.71316	+	29.7577i	0.219039	+	1.38296i	−0.595735	+	0.803181i	$0.703139\pi$
$464$		0			0
$465$	−6.31433	+	15.0820i	−0.292820	+	0.699409i
$466$		0			0
$467$	−12.9478	−	6.59724i	−0.599154	−	0.305284i	0.127983	−	0.991776i	$-0.459150\pi$
$467$	−12.9478	−	6.59724i	−0.599154	−	0.305284i	−0.727137	+	0.686492i	$0.759150\pi$
$468$		0			0
$469$	−2.96288	+	0.962698i	−0.136813	+	0.0444533i
$470$		0			0
$471$	5.02931	+	1.63412i	0.231739	+	0.0752964i
$472$		0			0
$473$	−1.49406	+	9.43314i	−0.0686970	+	0.433736i
$474$		0			0
$475$	−23.1685	−	12.0274i	−1.06304	−	0.551853i
$476$		0			0
$477$	−0.745876	−	0.118135i	−0.0341513	−	0.00540904i
$478$		0			0
$479$	−4.47340	+	13.7677i	−0.204395	+	0.629062i	0.795343	+	0.606160i	$0.207291\pi$
$479$	−4.47340	+	13.7677i	−0.204395	+	0.629062i	−0.999738	+	0.0229025i	$0.992709\pi$
$480$		0			0
$481$	−3.65041	−	11.2348i	−0.166444	−	0.512263i
$482$		0			0
$483$	13.5613	−	26.6155i	0.617059	−	1.21105i
$484$		0			0
$485$	−1.94674	+	2.26190i	−0.0883971	+	0.102708i
$486$		0			0
$487$	−17.1974	+	2.72380i	−0.779289	+	0.123427i	−0.533391	−	0.845869i	$-0.679083\pi$
$487$	−17.1974	+	2.72380i	−0.779289	+	0.123427i	−0.245897	+	0.969296i	$0.579083\pi$
$488$		0			0
$489$	−19.9493	−	27.4578i	−0.902137	−	1.24168i
$490$		0			0
$491$	15.7721	−	21.7084i	0.711784	−	0.979687i	−0.287973	−	0.957639i	$-0.592981\pi$
$491$	15.7721	−	21.7084i	0.711784	−	0.979687i	0.999757	−	0.0220485i	$-0.00701881\pi$
$492$		0			0
$493$	−10.5564	+	10.5564i	−0.475436	+	0.475436i
$494$		0			0
$495$	5.10023	−	2.08994i	0.229238	−	0.0939358i
$496$		0			0
$497$	−18.3819	+	9.36607i	−0.824543	+	0.420126i
$498$		0			0
$499$	−37.8610			−1.69489			−0.847446	−	0.530882i	$-0.821861\pi$
$499$	−37.8610			−1.69489			−0.847446	+	0.530882i	$0.821861\pi$
$500$		0			0
$501$	12.1794			0.544135
$502$		0			0
$503$	20.3786	−	10.3834i	0.908639	−	0.462974i	0.0637798	−	0.997964i	$-0.479684\pi$
$503$	20.3786	−	10.3834i	0.908639	−	0.462974i	0.844859	+	0.534990i	$0.179684\pi$
$504$		0			0
$505$	−12.6244	+	5.17315i	−0.561779	+	0.230202i
$506$		0			0
$507$	−5.93073	+	5.93073i	−0.263393	+	0.263393i
$508$		0			0
$509$	6.60429	−	9.09002i	0.292730	−	0.402908i	−0.637169	−	0.770724i	$-0.719894\pi$
$509$	6.60429	−	9.09002i	0.292730	−	0.402908i	0.929898	+	0.367816i	$0.119894\pi$
$510$		0			0
$511$	−8.53027	−	11.7409i	−0.377357	−	0.519387i
$512$		0			0
$513$	24.1767	−	3.82921i	1.06743	−	0.169064i
$514$		0			0
$515$	11.5909	−	13.4673i	0.510754	−	0.593440i
$516$		0			0
$517$	6.89716	−	13.5364i	0.303337	−	0.595332i
$518$		0			0
$519$	−6.09507	−	18.7587i	−0.267544	−	0.823415i
$520$		0			0
$521$	0.909768	−	2.79998i	0.0398576	−	0.122669i	−0.929148	−	0.369708i	$-0.879458\pi$
$521$	0.909768	−	2.79998i	0.0398576	−	0.122669i	0.969006	+	0.247039i	$0.0794576\pi$
$522$		0			0
$523$	−5.15154	−	0.815924i	−0.225261	−	0.0356779i	0.0427835	−	0.999084i	$-0.486377\pi$
$523$	−5.15154	−	0.815924i	−0.225261	−	0.0356779i	−0.268045	+	0.963407i	$0.586377\pi$
$524$		0			0
$525$	7.04094	+	14.0819i	0.307292	+	0.614583i
$526$		0			0
$527$	−2.21448	+	13.9817i	−0.0964641	+	0.609050i
$528$		0			0
$529$	63.7155	+	20.7024i	2.77024	+	0.900105i
$530$		0			0
$531$	−0.462361	+	0.150230i	−0.0200647	+	0.00651943i
$532$		0			0
$533$	11.5475	+	5.88373i	0.500176	+	0.254853i
$534$		0			0
$535$	9.47237	−	22.6250i	0.409526	−	0.978166i
$536$		0			0
$537$	−5.49541	−	34.6966i	−0.237144	−	1.49727i
$538$		0			0
$539$	−16.9116	+	12.2870i	−0.728434	+	0.529238i
$540$		0			0
$541$	−15.7101	−	11.4140i	−0.675429	−	0.490728i	0.196409	−	0.980522i	$-0.437072\pi$
$541$	−15.7101	−	11.4140i	−0.675429	−	0.490728i	−0.871838	+	0.489794i	$0.837072\pi$
$542$		0			0
$543$	9.08369	+	9.08369i	0.389818	+	0.389818i
$544$		0			0
$545$	−4.48511	+	18.3743i	−0.192121	+	0.787068i
$546$		0			0
$547$	−5.63944	−	11.0680i	−0.241125	−	0.473235i	0.738451	−	0.674307i	$-0.235557\pi$
$547$	−5.63944	−	11.0680i	−0.241125	−	0.473235i	−0.979576	+	0.201072i	$0.935557\pi$
$548$		0			0
$549$			6.35635i			0.271282i
$550$		0			0
$551$			21.5495i			0.918038i
$552$		0			0
$553$	−8.89176	−	17.4511i	−0.378116	−	0.742094i
$554$		0			0
$555$	−14.3898	−	8.89341i	−0.610815	−	0.377504i
$556$		0			0
$557$	16.1001	+	16.1001i	0.682185	+	0.682185i	0.960492	−	0.278307i	$-0.0897733\pi$
$557$	16.1001	+	16.1001i	0.682185	+	0.682185i	−0.278307	+	0.960492i	$0.589773\pi$
$558$		0			0
$559$	4.48521	+	3.25869i	0.189704	+	0.137828i
$560$		0			0
$561$	27.4745	−	19.9614i	1.15998	−	0.842772i
$562$		0			0
$563$	4.27229	+	26.9742i	0.180055	+	1.13682i	0.897763	+	0.440480i	$0.145192\pi$
$563$	4.27229	+	26.9742i	0.180055	+	1.13682i	−0.717707	+	0.696345i	$0.754808\pi$
$564$		0			0
$565$	35.1770	−	21.3733i	1.47991	−	0.899180i
$566$		0			0
$567$	−15.3637	−	7.82820i	−0.645215	−	0.328754i
$568$		0			0
$569$	0.135954	−	0.0441741i	0.00569948	−	0.00185187i	−0.306166	−	0.951978i	$-0.599046\pi$
$569$	0.135954	−	0.0441741i	0.00569948	−	0.00185187i	0.311865	+	0.950126i	$0.399046\pi$
$570$		0			0
$571$	−22.9829	−	7.46759i	−0.961803	−	0.312509i	−0.214300	−	0.976768i	$-0.568747\pi$
$571$	−22.9829	−	7.46759i	−0.961803	−	0.312509i	−0.747502	+	0.664259i	$0.768747\pi$
$572$		0			0
$573$	3.19552	−	20.1757i	0.133495	−	0.842852i
$574$		0			0
$575$	−38.5844	+	27.5881i	−1.60908	+	1.15050i
$576$		0			0
$577$	34.2605	+	5.42633i	1.42628	+	0.225901i	0.821373	−	0.570392i	$-0.193209\pi$
$577$	34.2605	+	5.42633i	1.42628	+	0.225901i	0.604911	+	0.796293i	$0.293209\pi$
$578$		0			0
$579$	−14.7434	+	45.3754i	−0.612714	+	1.88574i
$580$		0			0
$581$	−0.542502	−	1.66965i	−0.0225068	−	0.0692687i
$582$		0			0
$583$	3.51294	−	6.89453i	0.145491	−	0.285542i
$584$		0			0
$585$	0.263136	−	3.18867i	0.0108793	−	0.131835i
$586$		0			0
$587$	6.59292	−	1.04422i	0.272119	−	0.0430994i	−0.0188836	−	0.999822i	$-0.506011\pi$
$587$	6.59292	−	1.04422i	0.272119	−	0.0430994i	0.291003	+	0.956722i	$0.406011\pi$
$588$		0			0
$589$	12.0106	+	16.5311i	0.494887	+	0.681153i
$590$		0			0
$591$	12.4029	−	17.0712i	0.510189	−	0.702215i
$592$		0			0
$593$	−13.0877	+	13.0877i	−0.537448	+	0.537448i	−0.922779	−	0.385331i	$-0.874087\pi$
$593$	−13.0877	+	13.0877i	−0.537448	+	0.537448i	0.385331	+	0.922779i	$0.374087\pi$
$594$		0			0
$595$	8.81317	+	10.3986i	0.361305	+	0.426299i
$596$		0			0
$597$	16.6200	−	8.46831i	0.680211	−	0.346585i
$598$		0			0
$599$	27.5993			1.12768			0.563839	−	0.825885i	$-0.309324\pi$
$599$	27.5993			1.12768			0.563839	+	0.825885i	$0.309324\pi$
$600$		0			0
$601$	−7.21948			−0.294489			−0.147244	−	0.989100i	$-0.547040\pi$
$601$	−7.21948			−0.294489			−0.147244	+	0.989100i	$0.547040\pi$
$602$		0			0
$603$	0.807797	−	0.411593i	0.0328960	−	0.0167614i
$604$		0			0
$605$	2.38065	+	31.7913i	0.0967872	+	1.29250i
$606$		0			0
$607$	20.3486	−	20.3486i	0.825926	−	0.825926i	−0.161025	−	0.986950i	$-0.551480\pi$
$607$	20.3486	−	20.3486i	0.825926	−	0.825926i	0.986950	+	0.161025i	$0.0514799\pi$
$608$		0			0
$609$	7.63937	−	10.5147i	0.309563	−	0.426077i
$610$		0			0
$611$	−5.18359	−	7.13460i	−0.209706	−	0.288635i
$612$		0			0
$613$	−2.77298	+	0.439197i	−0.112000	+	0.0177390i	−0.212183	−	0.977230i	$-0.568057\pi$
$613$	−2.77298	+	0.439197i	−0.112000	+	0.0177390i	0.100183	+	0.994969i	$0.468057\pi$
$614$		0			0
$615$	18.0624	−	4.26395i	0.728346	−	0.171939i
$616$		0			0
$617$	3.98308	−	7.81723i	0.160353	−	0.314710i	−0.796825	−	0.604210i	$-0.793489\pi$
$617$	3.98308	−	7.81723i	0.160353	−	0.314710i	0.957178	+	0.289500i	$0.0934889\pi$
$618$		0			0
$619$	9.37702	+	28.8595i	0.376894	+	1.15996i	0.942192	+	0.335074i	$0.108761\pi$
$619$	9.37702	+	28.8595i	0.376894	+	1.15996i	−0.565297	+	0.824887i	$0.691239\pi$
$620$		0			0
$621$	13.7443	−	42.3007i	0.551542	−	1.69747i
$622$		0			0
$623$	25.7429	+	4.07727i	1.03137	+	0.163352i
$624$		0			0
$625$	0.379550	−	24.9971i	0.0151820	−	0.999885i
$626$		0			0
$627$	7.66851	−	48.4171i	0.306251	−	1.93359i
$628$		0			0
$629$	−13.9290	−	4.52581i	−0.555387	−	0.180456i
$630$		0			0
$631$	20.5789	−	6.68648i	0.819232	−	0.266185i	0.130729	−	0.991418i	$-0.458268\pi$
$631$	20.5789	−	6.68648i	0.819232	−	0.266185i	0.688503	+	0.725234i	$0.258268\pi$
$632$		0			0
$633$	39.6663	+	20.2110i	1.57659	+	0.803314i
$634$		0			0
$635$	−6.21206	−	26.3147i	−0.246518	−	1.04427i
$636$		0			0
$637$	1.89823	+	11.9849i	0.0752104	+	0.474860i
$638$		0			0
$639$	4.85715	−	3.52893i	0.192146	−	0.139602i
$640$		0			0
$641$	32.0885	+	23.3136i	1.26742	+	0.920833i	0.999097	−	0.0424965i	$-0.0135311\pi$
$641$	32.0885	+	23.3136i	1.26742	+	0.920833i	0.268321	+	0.963329i	$0.413531\pi$
$642$		0			0
$643$	4.12705	+	4.12705i	0.162755	+	0.162755i	0.783786	−	0.621031i	$-0.213286\pi$
$643$	4.12705	+	4.12705i	0.162755	+	0.162755i	−0.621031	+	0.783786i	$0.713286\pi$
$644$		0			0
$645$	7.91691	−	0.592847i	0.311728	−	0.0233433i
$646$		0			0
$647$	−9.93069	−	19.4901i	−0.390416	−	0.766234i	0.609226	−	0.792996i	$-0.291480\pi$
$647$	−9.93069	−	19.4901i	−0.390416	−	0.766234i	−0.999642	+	0.0267627i	$0.991480\pi$
$648$		0			0
$649$		−	4.98140i		−	0.195537i
$650$		0			0
$651$		−	12.3239i		−	0.483011i
$652$		0			0
$653$	−6.60194	−	12.9570i	−0.258354	−	0.507048i	0.725000	−	0.688749i	$-0.241840\pi$
$653$	−6.60194	−	12.9570i	−0.258354	−	0.507048i	−0.983354	+	0.181701i	$0.941840\pi$
$654$		0			0
$655$	−30.8112	+	26.1136i	−1.20389	+	1.02034i
$656$		0			0
$657$	2.98636	+	2.98636i	0.116509	+	0.116509i
$658$		0			0
$659$	27.9808	+	20.3292i	1.08998	+	0.791915i	0.979395	−	0.201952i	$-0.0647285\pi$
$659$	27.9808	+	20.3292i	1.08998	+	0.791915i	0.110582	+	0.993867i	$0.464729\pi$
$660$		0			0
$661$	−28.7386	+	20.8798i	−1.11780	+	0.812131i	−0.983874	−	0.178860i	$-0.942759\pi$
$661$	−28.7386	+	20.8798i	−1.11780	+	0.812131i	−0.133928	+	0.990991i	$0.542759\pi$
$662$		0			0
$663$	−3.08385	−	19.4707i	−0.119767	−	0.756178i
$664$		0			0
$665$	19.6091	+	1.61818i	0.760408	+	0.0627504i
$666$		0			0
$667$	34.8885	+	17.7766i	1.35089	+	0.688312i
$668$		0			0
$669$	2.07344	−	0.673702i	0.0801639	−	0.0260468i
$670$		0			0
$671$	−61.9429	−	20.1265i	−2.39128	−	0.776973i
$672$		0			0
$673$	1.31115	−	8.27825i	0.0505410	−	0.319103i	−0.949446	−	0.313931i	$-0.898354\pi$
$673$	1.31115	−	8.27825i	0.0505410	−	0.319103i	0.999987	−	0.00517176i	$-0.00164623\pi$
$674$		0			0
$675$	13.6348	+	19.0694i	0.524803	+	0.733983i
$676$		0			0
$677$	−40.7757	−	6.45823i	−1.56714	−	0.248210i	−0.688333	−	0.725395i	$-0.741657\pi$
$677$	−40.7757	−	6.45823i	−1.56714	−	0.248210i	−0.878803	+	0.477185i	$0.841657\pi$
$678$		0			0
$679$	0.695092	−	2.13927i	0.0266752	−	0.0820978i
$680$		0			0
$681$	2.92944	+	9.01588i	0.112256	+	0.345489i
$682$		0			0
$683$	−17.2369	+	33.8293i	−0.659552	+	1.29444i	0.282594	+	0.959240i	$0.408805\pi$
$683$	−17.2369	+	33.8293i	−0.659552	+	1.29444i	−0.942146	+	0.335204i	$0.891195\pi$
$684$		0			0
$685$	−18.9123	−	31.1266i	−0.722600	−	1.18929i
$686$		0			0
$687$	37.3072	−	5.90887i	1.42336	−	0.225438i
$688$		0			0
$689$	−2.64016	−	3.63388i	−0.100582	−	0.138440i
$690$		0			0
$691$	16.0217	−	22.0520i	0.609495	−	0.838897i	−0.387041	−	0.922062i	$-0.626503\pi$
$691$	16.0217	−	22.0520i	0.609495	−	0.838897i	0.996536	+	0.0831651i	$0.0265029\pi$
$692$		0			0
$693$	−2.93764	+	2.93764i	−0.111592	+	0.111592i
$694$		0			0
$695$	−13.5820	+	21.9762i	−0.515196	+	0.833605i
$696$		0			0
$697$	14.3167	−	7.29470i	0.542282	−	0.276306i
$698$		0			0
$699$	31.8265			1.20379
$700$		0			0
$701$	−9.20557			−0.347690			−0.173845	−	0.984773i	$-0.555619\pi$
$701$	−9.20557			−0.347690			−0.173845	+	0.984773i	$0.555619\pi$
$702$		0			0
$703$	−18.8365	+	9.59770i	−0.710434	+	0.361984i
$704$		0			0
$705$	−12.2684	−	2.99469i	−0.462056	−	0.112787i
$706$		0			0
$707$	7.27143	−	7.27143i	0.273470	−	0.273470i
$708$		0			0
$709$	0.928702	−	1.27825i	0.0348781	−	0.0480056i	−0.791222	−	0.611529i	$-0.790555\pi$
$709$	0.928702	−	1.27825i	0.0348781	−	0.0480056i	0.826100	+	0.563524i	$0.190555\pi$
$710$		0			0
$711$	3.35022	+	4.61118i	0.125643	+	0.172933i
$712$		0			0
$713$	36.6716	−	5.80821i	1.37336	−	0.217519i
$714$		0			0
$715$	30.2405	+	12.6607i	1.13093	+	0.473484i
$716$		0			0
$717$	−10.1715	+	19.9627i	−0.379862	+	0.745522i
$718$		0			0
$719$	−2.48979	−	7.66279i	−0.0928536	−	0.285774i	0.893835	−	0.448396i	$-0.148005\pi$
$719$	−2.48979	−	7.66279i	−0.0928536	−	0.285774i	−0.986688	+	0.162623i	$0.948005\pi$
$720$		0			0
$721$	−4.13856	+	12.7372i	−0.154128	+	0.474357i
$722$		0			0
$723$	23.8405	+	3.77596i	0.886636	+	0.140429i
$724$		0			0
$725$	−18.4590	+	9.22950i	−0.685550	+	0.342775i
$726$		0			0
$727$	−8.17212	+	51.5967i	−0.303087	+	1.91362i	0.0935010	+	0.995619i	$0.470194\pi$
$727$	−8.17212	+	51.5967i	−0.303087	+	1.91362i	−0.396588	+	0.917997i	$0.629806\pi$
$728$		0			0
$729$	−20.2198	−	6.56980i	−0.748881	−	0.243326i
$730$		0			0
$731$	6.53711	−	2.12404i	0.241784	−	0.0785603i
$732$		0			0
$733$	−18.9388	−	9.64981i	−0.699521	−	0.356424i	0.0677894	−	0.997700i	$-0.478405\pi$
$733$	−18.9388	−	9.64981i	−0.699521	−	0.356424i	−0.767310	+	0.641276i	$0.778405\pi$
$734$		0			0
$735$	13.1702	+	11.3352i	0.485790	+	0.418104i
$736$		0			0
$737$	1.45322	+	9.17526i	0.0535300	+	0.337975i
$738$		0			0
$739$	−10.2017	+	7.41195i	−0.375275	+	0.272653i	−0.759395	−	0.650630i	$-0.774505\pi$
$739$	−10.2017	+	7.41195i	−0.375275	+	0.272653i	0.384120	+	0.923283i	$0.374505\pi$
$740$		0			0
$741$	−23.0210	−	16.7258i	−0.845699	−	0.614436i
$742$		0			0
$743$	−1.17910	−	1.17910i	−0.0432570	−	0.0432570i	0.685147	−	0.728404i	$-0.259738\pi$
$743$	−1.17910	−	1.17910i	−0.0432570	−	0.0432570i	−0.728404	+	0.685147i	$0.759738\pi$
$744$		0			0
$745$	8.35789	+	20.3964i	0.306210	+	0.747265i
$746$		0			0
$747$	0.231942	+	0.455211i	0.00848630	+	0.0166553i
$748$		0			0
$749$			18.4875i			0.675520i
$750$		0			0
$751$			12.9279i			0.471745i	0.971784	+	0.235873i	$0.0757948\pi$
$751$			12.9279i			0.471745i	−0.971784	+	0.235873i	$0.924205\pi$
$752$		0			0
$753$	−5.16044	−	10.1279i	−0.188057	−	0.369083i
$754$		0			0
$755$	−18.7060	−	45.6495i	−0.680779	−	1.66135i
$756$		0			0
$757$	−31.9783	−	31.9783i	−1.16227	−	1.16227i	−0.983977	−	0.178294i	$-0.942942\pi$
$757$	−31.9783	−	31.9783i	−1.16227	−	1.16227i	−0.178294	−	0.983977i	$-0.557058\pi$
$758$		0			0
$759$	−72.0612	−	52.3555i	−2.61565	−	1.90038i
$760$		0			0
$761$	13.1358	−	9.54370i	0.476171	−	0.345959i	−0.323670	−	0.946170i	$-0.604917\pi$
$761$	13.1358	−	9.54370i	0.476171	−	0.345959i	0.799842	+	0.600211i	$0.204917\pi$
$762$		0			0
$763$	−2.23012	−	14.0804i	−0.0807359	−	0.509746i
$764$		0			0
$765$	−3.00656	−	2.58765i	−0.108703	−	0.0935567i
$766$		0			0
$767$	−2.57645	−	1.31277i	−0.0930301	−	0.0474012i
$768$		0			0
$769$	−9.41797	+	3.06008i	−0.339621	+	0.110349i	−0.473862	−	0.880599i	$-0.657140\pi$
$769$	−9.41797	+	3.06008i	−0.339621	+	0.110349i	0.134241	+	0.990949i	$0.457140\pi$
$770$		0			0
$771$	−3.34668	−	1.08740i	−0.120528	−	0.0391618i
$772$		0			0
$773$	−4.85916	+	30.6795i	−0.174772	+	1.10347i	0.731833	+	0.681484i	$0.238665\pi$
$773$	−4.85916	+	30.6795i	−0.174772	+	1.10347i	−0.906605	+	0.421981i	$0.861335\pi$
$774$		0			0
$775$	−9.01631	+	17.3683i	−0.323875	+	0.623887i
$776$		0			0
$777$	12.5934	+	1.99460i	0.451786	+	0.0715558i
$778$		0			0
$779$	7.16719	−	22.0584i	0.256791	−	0.790323i
$780$		0			0
$781$	19.0101	+	58.5069i	0.680233	+	2.09354i
$782$		0			0
$783$	8.78565	−	17.2428i	0.313974	−	0.616208i
$784$		0			0
$785$	5.83813	+	2.44424i	0.208372	+	0.0872386i
$786$		0			0
$787$	−36.8224	+	5.83209i	−1.31258	+	0.207891i	−0.773194	−	0.634170i	$-0.781342\pi$
$787$	−36.8224	+	5.83209i	−1.31258	+	0.207891i	−0.539382	+	0.842061i	$0.681342\pi$
$788$		0			0
$789$	−24.4920	−	33.7103i	−0.871938	−	1.20012i
$790$		0			0
$791$	−18.2358	+	25.0994i	−0.648389	+	0.892431i
$792$		0			0
$793$	−26.7337	+	26.7337i	−0.949340	+	0.949340i
$794$		0			0
$795$	−6.24870	−	1.52529i	−0.221619	−	0.0540964i
$796$		0			0
$797$	−9.14211	+	4.65814i	−0.323830	+	0.165000i	−0.608347	−	0.793671i	$-0.708167\pi$
$797$	−9.14211	+	4.65814i	−0.323830	+	0.165000i	0.284517	+	0.958671i	$0.408167\pi$
$798$		0			0
$799$	−10.9337			−0.386806
$800$		0			0
$801$	−7.58490			−0.267999
$802$		0			0
$803$	−38.5581	+	19.6463i	−1.36068	+	0.693303i
$804$		0			0
$805$	18.7958	−	30.4122i	0.662463	−	1.07189i
$806$		0			0
$807$	−8.14174	+	8.14174i	−0.286603	+	0.286603i
$808$		0			0
$809$	−10.0102	+	13.7779i	−0.351940	+	0.484404i	−0.947881	−	0.318624i	$-0.896779\pi$
$809$	−10.0102	+	13.7779i	−0.351940	+	0.484404i	0.595941	+	0.803028i	$0.296779\pi$
$810$		0			0
$811$	−11.2622	−	15.5010i	−0.395468	−	0.544315i	0.564131	−	0.825685i	$-0.309211\pi$
$811$	−11.2622	−	15.5010i	−0.395468	−	0.544315i	−0.959599	+	0.281370i	$0.909211\pi$
$812$		0			0
$813$	15.7257	−	2.49070i	0.551523	−	0.0873527i
$814$		0			0
$815$	−21.0928	−	34.7154i	−0.738849	−	1.21603i
$816$		0			0
$817$	4.50435	−	8.84029i	0.157587	−	0.309283i
$818$		0			0
$819$	0.745219	+	2.29355i	0.0260401	+	0.0801431i
$820$		0			0
$821$	−12.4592	+	38.3455i	−0.434829	+	1.33827i	0.458433	+	0.888729i	$0.348411\pi$
$821$	−12.4592	+	38.3455i	−0.434829	+	1.33827i	−0.893262	+	0.449537i	$0.851589\pi$
$822$		0			0
$823$	36.7832	+	5.82588i	1.28218	+	0.203077i	0.760093	−	0.649815i	$-0.225153\pi$
$823$	36.7832	+	5.82588i	1.28218	+	0.203077i	0.522087	+	0.852892i	$0.325153\pi$
$824$		0			0
$825$	44.7579	−	14.1680i	1.55827	−	0.493266i
$826$		0			0
$827$	−1.97180	+	12.4494i	−0.0685660	+	0.432909i	0.929395	+	0.369086i	$0.120329\pi$
$827$	−1.97180	+	12.4494i	−0.0685660	+	0.432909i	−0.997961	+	0.0638228i	$0.979671\pi$
$828$		0			0
$829$	−15.4362	−	5.01554i	−0.536122	−	0.174197i	0.0284272	−	0.999596i	$-0.490950\pi$
$829$	−15.4362	−	5.01554i	−0.536122	−	0.174197i	−0.564550	+	0.825399i	$0.690950\pi$
$830$		0			0
$831$	44.8769	−	14.5814i	1.55676	−	0.505823i
$832$		0			0
$833$	13.4045	+	6.82994i	0.464439	+	0.236643i
$834$		0			0
$835$	14.5276	+	1.19885i	0.502749	+	0.0414879i
$836$		0			0
$837$	−2.87057	−	18.1241i	−0.0992214	−	0.626459i
$838$		0			0
$839$	16.7761	−	12.1886i	0.579176	−	0.420796i	−0.259251	−	0.965810i	$-0.583476\pi$
$839$	16.7761	−	12.1886i	0.579176	−	0.420796i	0.838427	+	0.545014i	$0.183476\pi$
$840$		0			0
$841$	−9.67848	−	7.03182i	−0.333741	−	0.242477i
$842$		0			0
$843$	−21.7685	−	21.7685i	−0.749747	−	0.749747i
$844$		0			0
$845$	−7.65797	+	6.49042i	−0.263442	+	0.223277i
$846$		0			0
$847$	−10.9091	−	21.4102i	−0.374840	−	0.735665i
$848$		0			0
$849$			9.54998i			0.327754i
$850$		0			0
$851$			38.4136i			1.31680i
$852$		0			0
$853$	8.05976	+	15.8182i	0.275961	+	0.541604i	0.986838	−	0.161713i	$-0.0517018\pi$
$853$	8.05976	+	15.8182i	0.275961	+	0.541604i	−0.710877	+	0.703316i	$0.751702\pi$
$854$		0			0
$855$	−5.70992	+	0.427580i	−0.195275	+	0.0146229i
$856$		0			0
$857$	−10.6784	−	10.6784i	−0.364767	−	0.364767i	0.500798	−	0.865564i	$-0.333040\pi$
$857$	−10.6784	−	10.6784i	−0.364767	−	0.364767i	−0.865564	+	0.500798i	$0.833040\pi$
$858$		0			0
$859$	−4.71937	−	3.42882i	−0.161023	−	0.116990i	0.504356	−	0.863496i	$-0.331730\pi$
$859$	−4.71937	−	3.42882i	−0.161023	−	0.116990i	−0.665379	+	0.746506i	$0.731730\pi$
$860$		0			0
$861$	−11.3169	+	8.22220i	−0.385678	+	0.280212i
$862$		0			0
$863$	−0.265386	−	1.67558i	−0.00903383	−	0.0570373i	0.982760	−	0.184888i	$-0.0591922\pi$
$863$	−0.265386	−	1.67558i	−0.00903383	−	0.0570373i	−0.991793	+	0.127851i	$0.959192\pi$
$864$		0			0
$865$	−5.42376	−	22.9754i	−0.184413	−	0.781187i
$866$		0			0
$867$	6.52212	+	3.32319i	0.221503	+	0.112861i
$868$		0			0
$869$	−55.5440	+	18.0474i	−1.88420	+	0.612215i
$870$		0			0
$871$	5.12853	+	1.66636i	0.173774	+	0.0564625i
$872$		0			0
$873$	−0.102401	+	0.646537i	−0.00346576	+	0.0218820i
$874$		0			0
$875$	7.01234	+	17.4900i	0.237060	+	0.591269i
$876$		0			0
$877$	1.87695	+	0.297280i	0.0633803	+	0.0100384i	0.188044	−	0.982161i	$-0.439785\pi$
$877$	1.87695	+	0.297280i	0.0633803	+	0.0100384i	−0.124664	+	0.992199i	$0.539785\pi$
$878$		0			0
$879$	−9.70410	+	29.8662i	−0.327311	+	1.00736i
$880$		0			0
$881$	−8.03447	−	24.7276i	−0.270688	−	0.833092i	−0.990328	−	0.138745i	$-0.955693\pi$
$881$	−8.03447	−	24.7276i	−0.270688	−	0.833092i	0.719640	−	0.694347i	$-0.244307\pi$
$882$		0			0
$883$	15.6154	−	30.6470i	0.525501	−	1.03135i	−0.463864	−	0.885906i	$-0.653538\pi$
$883$	15.6154	−	30.6470i	0.525501	−	1.03135i	0.989366	−	0.145448i	$-0.0464625\pi$
$884$		0			0
$885$	−4.03004	+	0.951363i	−0.135468	+	0.0319797i
$886$		0			0
$887$	−2.05610	+	0.325654i	−0.0690370	+	0.0109344i	−0.190857	−	0.981618i	$-0.561127\pi$
$887$	−2.05610	+	0.325654i	−0.0690370	+	0.0109344i	0.121820	+	0.992552i	$0.461127\pi$
$888$		0			0
$889$	11.9788	+	16.4873i	0.401755	+	0.552968i
$890$		0			0
$891$	−30.2221	+	41.5971i	−1.01248	+	1.39356i
$892$		0			0
$893$	−11.1598	+	11.1598i	−0.373450	+	0.373450i
$894$		0			0
$895$	−3.13966	−	41.9272i	−0.104947	−	1.40147i
$896$		0			0
$897$	−46.0695	+	23.4736i	−1.53821	+	0.783759i
$898$		0			0
$899$	16.1546			0.538785
$900$		0			0
$901$	−5.56887			−0.185526
$902$		0			0
$903$	−5.33174	+	2.71666i	−0.177429	+	0.0904047i
$904$		0			0
$905$	9.94093	+	11.7292i	0.330448	+	0.389892i
$906$		0			0
$907$	−12.4489	+	12.4489i	−0.413358	+	0.413358i	−0.882907	−	0.469548i	$-0.844417\pi$
$907$	−12.4489	+	12.4489i	−0.413358	+	0.413358i	0.469548	+	0.882907i	$0.344417\pi$
$908$		0			0
$909$	−1.75901	+	2.42106i	−0.0583425	+	0.0803016i
$910$		0			0
$911$	4.73587	+	6.51836i	0.156906	+	0.215963i	0.880231	−	0.474545i	$-0.157387\pi$
$911$	4.73587	+	6.51836i	0.156906	+	0.215963i	−0.723325	+	0.690508i	$0.757387\pi$
$912$		0			0
$913$	−5.17046	+	0.818920i	−0.171117	+	0.0271023i
$914$		0			0
$915$	−4.45261	+	53.9566i	−0.147199	+	1.78375i
$916$		0			0
$917$	13.8205	−	27.1243i	0.456394	−	0.895725i
$918$		0			0
$919$	8.20122	+	25.2407i	0.270533	+	0.832615i	0.990367	+	0.138469i	$0.0442181\pi$
$919$	8.20122	+	25.2407i	0.270533	+	0.832615i	−0.719834	+	0.694147i	$0.755782\pi$
$920$		0			0
$921$	−16.5208	+	50.8458i	−0.544379	+	1.67542i
$922$		0			0
$923$	35.2703	+	5.58627i	1.16094	+	0.183874i
$924$		0			0
$925$	−16.2889	−	12.0245i	−0.535574	−	0.395364i
$926$		0			0
$927$	0.609695	−	3.84946i	0.0200250	−	0.126433i
$928$		0			0
$929$	−15.4847	−	5.03127i	−0.508035	−	0.165071i	0.0437734	−	0.999041i	$-0.486062\pi$
$929$	−15.4847	−	5.03127i	−0.508035	−	0.165071i	−0.551808	+	0.833971i	$0.686062\pi$
$930$		0			0
$931$	20.6530	−	6.71056i	0.676874	−	0.219930i
$932$		0			0
$933$	19.4138	+	9.89185i	0.635581	+	0.323845i
$934$		0			0
$935$	34.7366	−	21.1057i	1.13601	−	0.690229i
$936$		0			0
$937$	−9.45281	−	59.6827i	−0.308810	−	1.94975i	−0.312985	−	0.949758i	$-0.601329\pi$
$937$	−9.45281	−	59.6827i	−0.308810	−	1.94975i	0.00417475	−	0.999991i	$-0.498671\pi$
$938$		0			0
$939$	−23.5127	+	17.0830i	−0.767309	+	0.557483i
$940$		0			0
$941$	8.19955	+	5.95733i	0.267298	+	0.194203i	0.713358	−	0.700800i	$-0.247173\pi$
$941$	8.19955	+	5.95733i	0.267298	+	0.194203i	−0.446060	+	0.895003i	$0.647173\pi$
$942$		0			0
$943$	−29.8000	−	29.8000i	−0.970423	−	0.970423i
$944$		0			0
$945$	−15.0305	−	9.28936i	−0.488942	−	0.302183i
$946$		0			0
$947$	−1.31955	−	2.58977i	−0.0428797	−	0.0841561i	0.868573	−	0.495562i	$-0.165038\pi$
$947$	−1.31955	−	2.58977i	−0.0428797	−	0.0841561i	−0.911452	+	0.411406i	$0.865038\pi$
$948$		0			0
$949$			25.1202i			0.815436i
$950$		0			0
$951$			31.2270i			1.01261i
$952$		0			0
$953$	19.6294	+	38.5249i	0.635859	+	1.24794i	0.953974	+	0.299891i	$0.0969502\pi$
$953$	19.6294	+	38.5249i	0.635859	+	1.24794i	−0.318115	+	0.948052i	$0.603050\pi$
$954$		0			0
$955$	5.79757	−	23.7511i	0.187605	−	0.768568i
$956$		0			0
$957$	−27.4040	−	27.4040i	−0.885846	−	0.885846i
$958$		0			0
$959$	22.2093	+	16.1360i	0.717177	+	0.521060i
$960$		0			0
$961$	−12.6870	+	9.21762i	−0.409257	+	0.297342i
$962$		0			0
$963$	−0.841636	−	5.31388i	−0.0271214	−	0.171238i
$964$		0			0
$965$	−22.0524	+	52.6728i	−0.709891	+	1.69560i
$966$		0			0
$967$	−15.8999	−	8.10141i	−0.511307	−	0.260524i	0.179248	−	0.983804i	$-0.442634\pi$
$967$	−15.8999	−	8.10141i	−0.511307	−	0.260524i	−0.690555	+	0.723280i	$0.742634\pi$
$968$		0			0
$969$	−33.5528	+	10.9020i	−1.07787	+	0.350221i
$970$		0			0
$971$	50.5478	+	16.4240i	1.62216	+	0.527070i	0.972449	−	0.233115i	$-0.0748918\pi$
$971$	50.5478	+	16.4240i	1.62216	+	0.527070i	0.649706	+	0.760185i	$0.274892\pi$
$972$		0			0
$973$	3.04616	−	19.2327i	0.0976553	−	0.616571i
$974$		0			0
$975$	4.46732	−	26.8831i	0.143069	−	0.860948i
$976$		0			0
$977$	−33.5134	−	5.30799i	−1.07219	−	0.169818i	−0.404708	−	0.914446i	$-0.632627\pi$
$977$	−33.5134	−	5.30799i	−1.07219	−	0.169818i	−0.667479	+	0.744628i	$0.732627\pi$
$978$		0			0
$979$	24.0165	−	73.9152i	0.767570	−	2.36234i
$980$		0			0
$981$	1.28201	+	3.94563i	0.0409315	+	0.125974i
$982$		0			0
$983$	−11.6359	+	22.8367i	−0.371128	+	0.728379i	−0.998742	−	0.0501453i	$-0.984032\pi$
$983$	−11.6359	+	22.8367i	−0.371128	+	0.728379i	0.627614	+	0.778525i	$0.284032\pi$
$984$		0			0
$985$	16.4746	−	19.1417i	0.524926	−	0.609906i
$986$		0			0
$987$	9.40146	−	1.48904i	0.299252	−	0.0473968i
$988$		0			0
$989$	−10.5967	−	14.5851i	−0.336954	−	0.463778i
$990$		0			0
$991$	4.61343	−	6.34984i	0.146550	−	0.201709i	−0.729431	−	0.684055i	$-0.760215\pi$
$991$	4.61343	−	6.34984i	0.146550	−	0.201709i	0.875981	+	0.482345i	$0.160215\pi$
$992$		0			0
$993$	33.4639	−	33.4639i	1.06195	−	1.06195i
$994$		0			0
$995$	20.6579	−	8.46508i	0.654901	−	0.268361i
$996$		0			0
$997$	23.5713	−	12.0102i	0.746512	−	0.380367i	−0.0389790	−	0.999240i	$-0.512411\pi$
$997$	23.5713	−	12.0102i	0.746512	−	0.380367i	0.785491	+	0.618873i	$0.212411\pi$
$998$		0			0
$999$	18.9850			0.600660

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.b.127.2	yes	16
4.3	odd	2	inner	400.2.bi.b.127.1	yes	16
25.13	odd	20	inner	400.2.bi.b.63.1	✓	16
100.63	even	20	inner	400.2.bi.b.63.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.b.63.1	✓	16	25.13	odd	20	inner
400.2.bi.b.63.2	yes	16	100.63	even	20	inner
400.2.bi.b.127.1	yes	16	4.3	odd	2	inner
400.2.bi.b.127.2	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.66465 - 0.848182i) q^{3} +(2.06909 - 0.847859i) q^{5} +(-1.19176 + 1.19176i) q^{7} +(0.288294 - 0.396802i) q^{9} +O(q^{10})\)	\(q+(1.66465 - 0.848182i) q^{3} +(2.06909 - 0.847859i) q^{5} +(-1.19176 + 1.19176i) q^{7} +(0.288294 - 0.396802i) q^{9} +(2.95401 + 4.06585i) q^{11} +(2.88139 - 0.456367i) q^{13} +(2.72517 - 3.16635i) q^{15} +(1.64204 - 3.22268i) q^{17} +(-1.61334 - 4.96534i) q^{19} +(-0.973034 + 2.99469i) q^{21} +(-9.36975 - 1.48402i) q^{23} +(3.56227 - 3.50859i) q^{25} +(-0.733443 + 4.63078i) q^{27} +(-3.92554 - 1.27549i) q^{29} +(-3.72227 + 1.20944i) q^{31} +(8.36598 + 4.26268i) q^{33} +(-1.45541 + 3.47630i) q^{35} +(-0.633446 - 3.99942i) q^{37} +(4.40943 - 3.20363i) q^{39} +(3.59403 + 2.61121i) q^{41} +(1.34378 + 1.34378i) q^{43} +(0.260074 - 1.06545i) q^{45} +(-1.37239 - 2.69346i) q^{47} +4.15942i q^{49} -6.75739i q^{51} +(-0.699000 - 1.37186i) q^{53} +(9.55938 + 5.90802i) q^{55} +(-6.89716 - 6.89716i) q^{57} +(-0.801892 - 0.582609i) q^{59} +(-10.4845 + 7.61746i) q^{61} +(0.129316 + 0.816469i) q^{63} +(5.57492 - 3.38728i) q^{65} +(1.64697 + 0.839173i) q^{67} +(-16.8561 + 5.47687i) q^{69} +(11.6416 + 3.78259i) q^{71} +(-1.34702 + 8.50473i) q^{73} +(2.95401 - 8.86204i) q^{75} +(-8.36598 - 1.32504i) q^{77} +(-3.59104 + 11.0521i) q^{79} +(3.16151 + 9.73012i) q^{81} +(-0.472892 + 0.928104i) q^{83} +(0.665148 - 8.06024i) q^{85} +(-7.61650 + 1.20634i) q^{87} +(-9.08976 - 12.5110i) q^{89} +(-2.89004 + 3.97780i) q^{91} +(-5.17046 + 5.17046i) q^{93} +(-7.54805 - 8.90586i) q^{95} +(-1.18915 + 0.605904i) q^{97} +2.46496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 20 q^{9}+O(q^{10}) \) 16 * q - 20 * q^9	\( 16 q - 20 q^{9} + 20 q^{17} - 20 q^{21} - 20 q^{25} + 20 q^{29} + 60 q^{33} - 20 q^{37} + 28 q^{41} - 20 q^{45} + 60 q^{53} - 20 q^{57} - 12 q^{61} - 20 q^{65} - 80 q^{69} - 40 q^{73} - 60 q^{77} + 56 q^{81} - 60 q^{85} + 40 q^{97}+O(q^{100}) \) 16 * q - 20 * q^9 + 20 * q^17 - 20 * q^21 - 20 * q^25 + 20 * q^29 + 60 * q^33 - 20 * q^37 + 28 * q^41 - 20 * q^45 + 60 * q^53 - 20 * q^57 - 12 * q^61 - 20 * q^65 - 80 * q^69 - 40 * q^73 - 60 * q^77 + 56 * q^81 - 60 * q^85 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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