LMFDB - Embedded newform 400.2.s.e.243.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(107,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 1]))

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

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

chi := DirichletCharacter("400.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			243.2
Character	$\chi$	$=$	400.243
Dual form			400.2.s.e.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36763 - 0.359994i) q^{2} -1.86755 q^{3} +(1.74081 + 0.984676i) q^{4} +(2.55411 + 0.672307i) q^{6} +(0.719989 - 0.719989i) q^{7} +(-2.02630 - 1.97335i) q^{8} +0.487737 q^{9} +O(q^{10})$	\(q+(-1.36763 - 0.359994i) q^{2} -1.86755 q^{3} +(1.74081 + 0.984676i) q^{4} +(2.55411 + 0.672307i) q^{6} +(0.719989 - 0.719989i) q^{7} +(-2.02630 - 1.97335i) q^{8} +0.487737 q^{9} +(-0.805654 - 0.805654i) q^{11} +(-3.25104 - 1.83893i) q^{12} +5.90473i q^{13} +(-1.24387 + 0.725484i) q^{14} +(2.06082 + 3.42827i) q^{16} +(5.17145 - 5.17145i) q^{17} +(-0.667042 - 0.175583i) q^{18} +(-1.16370 - 1.16370i) q^{19} +(-1.34461 + 1.34461i) q^{21} +(0.811804 + 1.39187i) q^{22} +(-2.30177 - 2.30177i) q^{23} +(3.78421 + 3.68533i) q^{24} +(2.12567 - 8.07547i) q^{26} +4.69177 q^{27} +(1.96232 - 0.544406i) q^{28} +(3.71953 - 3.71953i) q^{29} -9.82775i q^{31} +(-1.58428 - 5.43047i) q^{32} +(1.50460 + 1.50460i) q^{33} +(-8.93430 + 5.21092i) q^{34} +(0.849056 + 0.480263i) q^{36} -1.71983i q^{37} +(1.17258 + 2.01043i) q^{38} -11.0274i q^{39} -3.93637i q^{41} +(2.32298 - 1.35488i) q^{42} -8.82362i q^{43} +(-0.609181 - 2.19580i) q^{44} +(2.31934 + 3.97659i) q^{46} +(-3.21130 - 3.21130i) q^{47} +(-3.84869 - 6.40245i) q^{48} +5.96323i q^{49} +(-9.65793 + 9.65793i) q^{51} +(-5.81425 + 10.2790i) q^{52} +8.60748 q^{53} +(-6.41660 - 1.68901i) q^{54} +(-2.87970 + 0.0381211i) q^{56} +(2.17326 + 2.17326i) q^{57} +(-6.42594 + 3.74792i) q^{58} +(5.24522 - 5.24522i) q^{59} +(1.59176 + 1.59176i) q^{61} +(-3.53793 + 13.4407i) q^{62} +(0.351165 - 0.351165i) q^{63} +(0.211769 + 7.99720i) q^{64} +(-1.51608 - 2.59938i) q^{66} +9.29532i q^{67} +(14.0947 - 3.91029i) q^{68} +(4.29867 + 4.29867i) q^{69} +9.33581 q^{71} +(-0.988300 - 0.962476i) q^{72} +(8.57821 - 8.57821i) q^{73} +(-0.619130 + 2.35209i) q^{74} +(-0.879909 - 3.17164i) q^{76} -1.16012 q^{77} +(-3.96979 + 15.0813i) q^{78} -1.70231 q^{79} -10.2253 q^{81} +(-1.41707 + 5.38349i) q^{82} -13.8974 q^{83} +(-3.66472 + 1.01671i) q^{84} +(-3.17645 + 12.0674i) q^{86} +(-6.94640 + 6.94640i) q^{87} +(0.0426568 + 3.22233i) q^{88} -4.48540 q^{89} +(4.25134 + 4.25134i) q^{91} +(-1.74044 - 6.27345i) q^{92} +18.3538i q^{93} +(3.23581 + 5.54791i) q^{94} +(2.95873 + 10.1417i) q^{96} +(4.46476 - 4.46476i) q^{97} +(2.14673 - 8.15548i) q^{98} +(-0.392947 - 0.392947i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} + 12 q^{6} + 40 q^{9}+O(q^{10}) $ 24 * q + 8 * q^4 + 12 * q^6 + 40 * q^9	$ 24 q + 8 q^{4} + 12 q^{6} + 40 q^{9} - 20 q^{11} - 44 q^{14} - 4 q^{16} + 12 q^{19} - 24 q^{24} + 32 q^{26} - 8 q^{29} - 32 q^{34} - 60 q^{36} + 44 q^{44} - 76 q^{46} + 20 q^{51} - 16 q^{54} - 28 q^{56} - 8 q^{59} - 48 q^{61} + 32 q^{64} - 8 q^{66} + 64 q^{69} - 16 q^{71} - 36 q^{74} + 40 q^{76} + 104 q^{79} + 48 q^{81} - 44 q^{84} + 84 q^{86} - 96 q^{89} + 64 q^{91} + 40 q^{94} + 212 q^{96} - 128 q^{99}+O(q^{100}) $ 24 * q + 8 * q^4 + 12 * q^6 + 40 * q^9 - 20 * q^11 - 44 * q^14 - 4 * q^16 + 12 * q^19 - 24 * q^24 + 32 * q^26 - 8 * q^29 - 32 * q^34 - 60 * q^36 + 44 * q^44 - 76 * q^46 + 20 * q^51 - 16 * q^54 - 28 * q^56 - 8 * q^59 - 48 * q^61 + 32 * q^64 - 8 * q^66 + 64 * q^69 - 16 * q^71 - 36 * q^74 + 40 * q^76 + 104 * q^79 + 48 * q^81 - 44 * q^84 + 84 * q^86 - 96 * q^89 + 64 * q^91 + 40 * q^94 + 212 * q^96 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.36763	−	0.359994i	−0.967058	−	0.254555i
$2$	−1.36763	−	0.359994i	−0.967058	−	0.254555i
$3$	−1.86755			−1.07823			−0.539115	−	0.842232i	$-0.681241\pi$
$3$	−1.86755			−1.07823			−0.539115	+	0.842232i	$0.681241\pi$
$4$	1.74081	+	0.984676i	0.870404	+	0.492338i
$5$		0			0
$5$		0			0
$6$	2.55411	+	0.672307i	1.04271	+	0.274468i
$7$	0.719989	−	0.719989i	0.272130	−	0.272130i	−0.557827	−	0.829957i	$-0.688365\pi$
$7$	0.719989	−	0.719989i	0.272130	−	0.272130i	0.829957	+	0.557827i	$0.188365\pi$
$8$	−2.02630	−	1.97335i	−0.716405	−	0.697685i
$9$	0.487737			0.162579
$10$		0			0
$11$	−0.805654	−	0.805654i	−0.242914	−	0.242914i	0.575141	−	0.818055i	$-0.304947\pi$
$11$	−0.805654	−	0.805654i	−0.242914	−	0.242914i	−0.818055	+	0.575141i	$0.804947\pi$
$12$	−3.25104	−	1.83893i	−0.938495	−	0.530854i
$13$			5.90473i			1.63768i	0.574023	+	0.818839i	$0.305382\pi$
$13$			5.90473i			1.63768i	−0.574023	+	0.818839i	$0.694618\pi$
$14$	−1.24387	+	0.725484i	−0.332438	+	0.193894i
$15$		0			0
$16$	2.06082	+	3.42827i	0.515206	+	0.857066i
$17$	5.17145	−	5.17145i	1.25426	−	1.25426i	0.300469	−	0.953792i	$-0.402857\pi$
$17$	5.17145	−	5.17145i	1.25426	−	1.25426i	0.953792	−	0.300469i	$-0.0971430\pi$
$18$	−0.667042	−	0.175583i	−0.157223	−	0.0413852i
$19$	−1.16370	−	1.16370i	−0.266971	−	0.266971i	0.560908	−	0.827878i	$-0.310452\pi$
$19$	−1.16370	−	1.16370i	−0.266971	−	0.266971i	−0.827878	+	0.560908i	$0.810452\pi$
$20$		0			0
$21$	−1.34461	+	1.34461i	−0.293419	+	0.293419i
$22$	0.811804	+	1.39187i	0.173077	+	0.296747i
$23$	−2.30177	−	2.30177i	−0.479953	−	0.479953i	0.425164	−	0.905116i	$-0.360217\pi$
$23$	−2.30177	−	2.30177i	−0.479953	−	0.479953i	−0.905116	+	0.425164i	$0.860217\pi$
$24$	3.78421	+	3.68533i	0.772449	+	0.752265i
$25$		0			0
$26$	2.12567	−	8.07547i	0.416878	−	1.58373i
$27$	4.69177			0.902932
$28$	1.96232	−	0.544406i	0.370843	−	0.102883i
$29$	3.71953	−	3.71953i	0.690699	−	0.690699i	−0.271687	−	0.962386i	$-0.587581\pi$
$29$	3.71953	−	3.71953i	0.690699	−	0.690699i	0.962386	+	0.271687i	$0.0875814\pi$
$30$		0			0
$31$		−	9.82775i		−	1.76512i	−0.470204	−	0.882558i	$-0.655820\pi$
$31$		−	9.82775i		−	1.76512i	0.470204	−	0.882558i	$-0.344180\pi$
$32$	−1.58428	−	5.43047i	−0.280064	−	0.959981i
$33$	1.50460	+	1.50460i	0.261917	+	0.261917i
$34$	−8.93430	+	5.21092i	−1.53222	+	0.893665i
$35$		0			0
$36$	0.849056	+	0.480263i	0.141509	+	0.0800438i
$37$		−	1.71983i		−	0.282739i	−0.989957	−	0.141369i	$-0.954850\pi$
$37$		−	1.71983i		−	0.282739i	0.989957	−	0.141369i	$-0.0451505\pi$
$38$	1.17258	+	2.01043i	0.190218	+	0.326135i
$39$		−	11.0274i		−	1.76579i
$40$		0			0
$41$		−	3.93637i		−	0.614758i	−0.951587	−	0.307379i	$-0.900548\pi$
$41$		−	3.93637i		−	0.614758i	0.951587	−	0.307379i	$-0.0994519\pi$
$42$	2.32298	−	1.35488i	0.358444	−	0.209062i
$43$		−	8.82362i		−	1.34559i	−0.739829	−	0.672794i	$-0.765094\pi$
$43$		−	8.82362i		−	1.34559i	0.739829	−	0.672794i	$-0.234906\pi$
$44$	−0.609181	−	2.19580i	−0.0918374	−	0.331029i
$45$		0			0
$46$	2.31934	+	3.97659i	0.341968	+	0.586317i
$47$	−3.21130	−	3.21130i	−0.468417	−	0.468417i	0.432985	−	0.901401i	$-0.357460\pi$
$47$	−3.21130	−	3.21130i	−0.468417	−	0.468417i	−0.901401	+	0.432985i	$0.857460\pi$
$48$	−3.84869	−	6.40245i	−0.555511	−	0.924114i
$49$			5.96323i			0.851890i
$50$		0			0
$51$	−9.65793	+	9.65793i	−1.35238	+	1.35238i
$52$	−5.81425	+	10.2790i	−0.806292	+	1.42544i
$53$	8.60748			1.18233			0.591164	−	0.806551i	$-0.298668\pi$
$53$	8.60748			1.18233			0.591164	+	0.806551i	$0.298668\pi$
$54$	−6.41660	−	1.68901i	−0.873188	−	0.229845i
$55$		0			0
$56$	−2.87970	+	0.0381211i	−0.384817	+	0.00509415i
$57$	2.17326	+	2.17326i	0.287856	+	0.287856i
$58$	−6.42594	+	3.74792i	−0.843767	+	0.492126i
$59$	5.24522	−	5.24522i	0.682870	−	0.682870i	−0.277776	−	0.960646i	$-0.589597\pi$
$59$	5.24522	−	5.24522i	0.682870	−	0.682870i	0.960646	+	0.277776i	$0.0895974\pi$
$60$		0			0
$61$	1.59176	+	1.59176i	0.203804	+	0.203804i	0.801628	−	0.597824i	$-0.203968\pi$
$61$	1.59176	+	1.59176i	0.203804	+	0.203804i	−0.597824	+	0.801628i	$0.703968\pi$
$62$	−3.53793	+	13.4407i	−0.449318	+	1.70697i
$63$	0.351165	−	0.351165i	0.0442426	−	0.0442426i
$64$	0.211769	+	7.99720i	0.0264711	+	0.999650i
$65$		0			0
$66$	−1.51608	−	2.59938i	−0.186617	−	0.319961i
$67$			9.29532i			1.13560i	0.823165	+	0.567802i	$0.192206\pi$
$67$			9.29532i			1.13560i	−0.823165	+	0.567802i	$0.807794\pi$
$68$	14.0947	−	3.91029i	1.70923	−	0.474193i
$69$	4.29867	+	4.29867i	0.517499	+	0.517499i
$70$		0			0
$71$	9.33581			1.10796			0.553979	−	0.832531i	$-0.313109\pi$
$71$	9.33581			1.10796			0.553979	+	0.832531i	$0.313109\pi$
$72$	−0.988300	−	0.962476i	−0.116472	−	0.113429i
$73$	8.57821	−	8.57821i	1.00400	−	1.00400i	0.00401200	−	0.999992i	$-0.498723\pi$
$73$	8.57821	−	8.57821i	1.00400	−	1.00400i	0.999992	−	0.00401200i	$-0.00127706\pi$
$74$	−0.619130	+	2.35209i	−0.0719724	+	0.273425i
$75$		0			0
$76$	−0.879909	−	3.17164i	−0.100933	−	0.363812i
$77$	−1.16012			−0.132208
$78$	−3.96979	+	15.0813i	−0.449491	+	1.70763i
$79$	−1.70231			−0.191525			−0.0957625	−	0.995404i	$-0.530529\pi$
$79$	−1.70231			−0.191525			−0.0957625	+	0.995404i	$0.530529\pi$
$80$		0			0
$81$	−10.2253			−1.13615
$82$	−1.41707	+	5.38349i	−0.156489	+	0.594507i
$83$	−13.8974			−1.52544			−0.762718	−	0.646732i	$-0.776135\pi$
$83$	−13.8974			−1.52544			−0.762718	+	0.646732i	$0.776135\pi$
$84$	−3.66472	+	1.01671i	−0.399854	+	0.110932i
$85$		0			0
$86$	−3.17645	+	12.0674i	−0.342526	+	1.30126i
$87$	−6.94640	+	6.94640i	−0.744732	+	0.744732i
$88$	0.0426568	+	3.22233i	0.00454723	+	0.343502i
$89$	−4.48540			−0.475452			−0.237726	−	0.971332i	$-0.576402\pi$
$89$	−4.48540			−0.475452			−0.237726	+	0.971332i	$0.576402\pi$
$90$		0			0
$91$	4.25134	+	4.25134i	0.445662	+	0.445662i
$92$	−1.74044	−	6.27345i	−0.181454	−	0.654052i
$93$			18.3538i			1.90320i
$94$	3.23581	+	5.54791i	0.333749	+	0.572224i
$95$		0			0
$96$	2.95873	+	10.1417i	0.301974	+	1.03508i
$97$	4.46476	−	4.46476i	0.453327	−	0.453327i	−0.443130	−	0.896457i	$-0.646132\pi$
$97$	4.46476	−	4.46476i	0.453327	−	0.453327i	0.896457	+	0.443130i	$0.146132\pi$
$98$	2.14673	−	8.15548i	0.216853	−	0.823828i
$99$	−0.392947	−	0.392947i	−0.0394927	−	0.0394927i
$100$		0			0
$101$	−9.04273	+	9.04273i	−0.899785	+	0.899785i	−0.995417	−	0.0956319i	$-0.969513\pi$
$101$	−9.04273	+	9.04273i	−0.899785	+	0.899785i	0.0956319	+	0.995417i	$0.469513\pi$
$102$	16.6852	−	9.73164i	1.65209	−	0.963576i
$103$	8.89360	+	8.89360i	0.876312	+	0.876312i	0.993151	−	0.116839i	$-0.0372760\pi$
$103$	8.89360	+	8.89360i	0.876312	+	0.876312i	−0.116839	+	0.993151i	$0.537276\pi$
$104$	11.6521	−	11.9647i	1.14258	−	1.17324i
$105$		0			0
$106$	−11.7718	−	3.09865i	−1.14338	−	0.300967i
$107$	−9.29532			−0.898612			−0.449306	−	0.893378i	$-0.648329\pi$
$107$	−9.29532			−0.898612			−0.449306	+	0.893378i	$0.648329\pi$
$108$	8.16748	+	4.61988i	0.785916	+	0.444548i
$109$	−4.10635	+	4.10635i	−0.393317	+	0.393317i	−0.875868	−	0.482551i	$-0.839710\pi$
$109$	−4.10635	+	4.10635i	−0.393317	+	0.393317i	0.482551	+	0.875868i	$0.339710\pi$
$110$		0			0
$111$			3.21187i			0.304857i
$112$	3.95208	+	0.984542i	0.373437	+	0.0930305i
$113$	−7.51147	−	7.51147i	−0.706619	−	0.706619i	0.259203	−	0.965823i	$-0.416540\pi$
$113$	−7.51147	−	7.51147i	−0.706619	−	0.706619i	−0.965823	+	0.259203i	$0.916540\pi$
$114$	−2.18985	−	3.75458i	−0.205098	−	0.351648i
$115$		0			0
$116$	10.1375	−	2.81245i	0.941245	−	0.261130i
$117$			2.87996i			0.266252i
$118$	−9.06176	+	5.28526i	−0.834202	+	0.486547i
$119$		−	7.44677i		−	0.682644i
$120$		0			0
$121$		−	9.70184i		−	0.881986i
$122$	−1.60391	−	2.74995i	−0.145211	−	0.248969i
$123$			7.35136i			0.662850i
$124$	9.67715	−	17.1082i	0.869034	−	1.53636i
$125$		0			0
$126$	−0.606680	+	0.353845i	−0.0540474	+	0.0315231i
$127$	7.66639	+	7.66639i	0.680282	+	0.680282i	0.960064	−	0.279782i	$-0.0902621\pi$
$127$	7.66639	+	7.66639i	0.680282	+	0.680282i	−0.279782	+	0.960064i	$0.590262\pi$
$128$	2.58933	−	11.0134i	0.228866	−	0.973458i
$129$			16.4785i			1.45085i
$130$		0			0
$131$	−1.70610	+	1.70610i	−0.149062	+	0.149062i	−0.777699	−	0.628637i	$-0.783613\pi$
$131$	−1.70610	+	1.70610i	−0.149062	+	0.149062i	0.628637	+	0.777699i	$0.283613\pi$
$132$	1.13767	+	4.10076i	0.0990218	+	0.356925i
$133$	−1.67570			−0.145302
$134$	3.34626	−	12.7125i	0.289073	−	1.09820i
$135$		0			0
$136$	−20.6840	+	0.273812i	−1.77364	+	0.0234792i
$137$	1.69414	+	1.69414i	0.144740	+	0.144740i	0.775764	−	0.631024i	$-0.217365\pi$
$137$	1.69414	+	1.69414i	0.144740	+	0.144740i	−0.631024	+	0.775764i	$0.717365\pi$
$138$	−4.33148	−	7.42648i	−0.368720	−	0.632184i
$139$	−2.38206	+	2.38206i	−0.202044	+	0.202044i	−0.800875	−	0.598831i	$-0.795632\pi$
$139$	−2.38206	+	2.38206i	−0.202044	+	0.202044i	0.598831	+	0.800875i	$0.295632\pi$
$140$		0			0
$141$	5.99726	+	5.99726i	0.505061	+	0.505061i
$142$	−12.7679	−	3.36084i	−1.07146	−	0.282035i
$143$	4.75717	−	4.75717i	0.397815	−	0.397815i
$144$	1.00514	+	1.67209i	0.0837617	+	0.139341i
$145$		0			0
$146$	−14.8199	+	8.64369i	−1.22650	+	0.715357i
$147$		−	11.1366i		−	0.918533i
$148$	1.69348	−	2.99390i	0.139203	−	0.246097i
$149$	2.49691	+	2.49691i	0.204555	+	0.204555i	0.801948	−	0.597393i	$-0.203797\pi$
$149$	2.49691	+	2.49691i	0.204555	+	0.204555i	−0.597393	+	0.801948i	$0.703797\pi$
$150$		0			0
$151$	16.5505			1.34686			0.673431	−	0.739250i	$-0.264820\pi$
$151$	16.5505			1.34686			0.673431	+	0.739250i	$0.264820\pi$
$152$	0.0616141	+	4.65439i	0.00499756	+	0.377521i
$153$	2.52231	−	2.52231i	0.203916	−	0.203916i
$154$	1.58662	+	0.417638i	0.127853	+	0.0336543i
$155$		0			0
$156$	10.8584	−	19.1965i	0.869367	−	1.53695i
$157$	−5.07087			−0.404699			−0.202350	−	0.979313i	$-0.564858\pi$
$157$	−5.07087			−0.404699			−0.202350	+	0.979313i	$0.564858\pi$
$158$	2.32813	+	0.612823i	0.185216	+	0.0487535i
$159$	−16.0749			−1.27482
$160$		0			0
$161$	−3.31450			−0.261219
$162$	13.9844	+	3.68106i	1.09872	+	0.289211i
$163$	−15.3065			−1.19890			−0.599450	−	0.800412i	$-0.704614\pi$
$163$	−15.3065			−1.19890			−0.599450	+	0.800412i	$0.704614\pi$
$164$	3.87605	−	6.85247i	0.302669	−	0.535088i
$165$		0			0
$166$	19.0064	+	5.00298i	1.47519	+	0.388306i
$167$	−4.78800	+	4.78800i	−0.370506	+	0.370506i	−0.867662	−	0.497155i	$-0.834378\pi$
$167$	−4.78800	+	4.78800i	−0.370506	+	0.370506i	0.497155	+	0.867662i	$0.334378\pi$
$168$	5.37799	−	0.0711930i	0.414921	−	0.00549266i
$169$	−21.8659			−1.68199
$170$		0			0
$171$	−0.567579	−	0.567579i	−0.0434038	−	0.0434038i
$172$	8.68841	−	15.3602i	0.662485	−	1.17121i
$173$		−	9.32156i		−	0.708705i	−0.935112	−	0.354353i	$-0.884701\pi$
$173$		−	9.32156i		−	0.708705i	0.935112	−	0.354353i	$-0.115299\pi$
$174$	12.0007	−	6.99942i	0.909774	−	0.530625i
$175$		0			0
$176$	1.10168	−	4.42231i	0.0830426	−	0.333344i
$177$	−9.79570	+	9.79570i	−0.736290	+	0.736290i
$178$	6.13436	+	1.61472i	0.459790	+	0.121028i
$179$	15.6273	+	15.6273i	1.16804	+	1.16804i	0.982669	+	0.185369i	$0.0593480\pi$
$179$	15.6273	+	15.6273i	1.16804	+	1.16804i	0.185369	+	0.982669i	$0.440652\pi$
$180$		0			0
$181$	17.0056	−	17.0056i	1.26401	−	1.26401i	0.314882	−	0.949131i	$-0.398035\pi$
$181$	17.0056	−	17.0056i	1.26401	−	1.26401i	0.949131	−	0.314882i	$-0.101965\pi$
$182$	−4.28379	−	7.34471i	−0.317536	−	0.544426i
$183$	−2.97268	−	2.97268i	−0.219747	−	0.219747i
$184$	0.121872	+	9.20628i	0.00898449	+	0.678696i
$185$		0			0
$186$	6.60726	−	25.1011i	0.484468	−	1.84051i
$187$	−8.33280			−0.609355
$188$	−2.42817	−	8.75235i	−0.177092	−	0.638331i
$189$	3.37802	−	3.37802i	0.245715	−	0.245715i
$190$		0			0
$191$		−	3.88531i		−	0.281131i	−0.990071	−	0.140566i	$-0.955108\pi$
$191$		−	3.88531i		−	0.281131i	0.990071	−	0.140566i	$-0.0448921\pi$
$192$	−0.395488	−	14.9352i	−0.0285419	−	1.07785i
$193$	3.68299	+	3.68299i	0.265108	+	0.265108i	0.827125	−	0.562018i	$-0.189975\pi$
$193$	3.68299	+	3.68299i	0.265108	+	0.265108i	−0.562018	+	0.827125i	$0.689975\pi$
$194$	−7.71341	+	4.49883i	−0.553790	+	0.322997i
$195$		0			0
$196$	−5.87185	+	10.3808i	−0.419418	+	0.741489i
$197$		−	12.2901i		−	0.875633i	−0.899064	−	0.437816i	$-0.855752\pi$
$197$		−	12.2901i		−	0.875633i	0.899064	−	0.437816i	$-0.144248\pi$
$198$	0.395947	+	0.678864i	0.0281387	+	0.0482448i
$199$			12.6548i			0.897075i	0.893764	+	0.448537i	$0.148055\pi$
$199$			12.6548i			0.897075i	−0.893764	+	0.448537i	$0.851945\pi$
$200$		0			0
$201$		−	17.3595i		−	1.22444i
$202$	15.6224	−	9.11175i	1.09919	−	0.641100i
$203$		−	5.35604i		−	0.375920i
$204$	−26.3225	+	7.30266i	−1.84295	+	0.511289i
$205$		0			0
$206$	−8.96148	−	15.3648i	−0.624376	−	1.07051i
$207$	−1.12266	−	1.12266i	−0.0780302	−	0.0780302i
$208$	−20.2430	+	12.1686i	−1.40360	+	0.843742i
$209$			1.87508i			0.129702i
$210$		0			0
$211$	2.57346	−	2.57346i	0.177164	−	0.177164i	−0.612954	−	0.790118i	$-0.710019\pi$
$211$	2.57346	−	2.57346i	0.177164	−	0.177164i	0.790118	+	0.612954i	$0.210019\pi$
$212$	14.9840	+	8.47559i	1.02910	+	0.582106i
$213$	−17.4351			−1.19463
$214$	12.7125	+	3.34626i	0.869011	+	0.228746i
$215$		0			0
$216$	−9.50693	−	9.25852i	−0.646865	−	0.629962i
$217$	−7.07587	−	7.07587i	−0.480341	−	0.480341i
$218$	7.09423	−	4.13770i	0.480482	−	0.280240i
$219$	−16.0202	+	16.0202i	−1.08255	+	1.08255i
$220$		0			0
$221$	30.5360	+	30.5360i	2.05407	+	2.05407i
$222$	1.15625	−	4.39264i	0.0776027	−	0.294815i
$223$	9.55375	−	9.55375i	0.639766	−	0.639766i	−0.310731	−	0.950498i	$-0.600574\pi$
$223$	9.55375	−	9.55375i	0.639766	−	0.639766i	0.950498	+	0.310731i	$0.100574\pi$
$224$	−5.05055	−	2.76921i	−0.337454	−	0.185026i
$225$		0			0
$226$	7.56880	+	12.9770i	0.503469	+	0.863215i
$227$		−	12.8481i		−	0.852759i	−0.904544	−	0.426380i	$-0.859789\pi$
$227$		−	12.8481i		−	0.852759i	0.904544	−	0.426380i	$-0.140211\pi$
$228$	1.64327	+	5.92319i	0.108828	+	0.392273i
$229$	1.96090	+	1.96090i	0.129580	+	0.129580i	0.768922	−	0.639342i	$-0.220793\pi$
$229$	1.96090	+	1.96090i	0.129580	+	0.129580i	−0.639342	+	0.768922i	$0.720793\pi$
$230$		0			0
$231$	2.16659			0.142551
$232$	−14.8768	+	0.196937i	−0.976710	+	0.0129296i
$233$	7.39089	−	7.39089i	0.484193	−	0.484193i	−0.422275	−	0.906468i	$-0.638768\pi$
$233$	7.39089	−	7.39089i	0.484193	−	0.484193i	0.906468	+	0.422275i	$0.138768\pi$
$234$	1.03677	−	3.93871i	0.0677757	−	0.257481i
$235$		0			0
$236$	14.2958	−	3.96608i	0.930575	−	0.258170i
$237$	3.17915			0.206508
$238$	−2.68080	+	10.1844i	−0.173770	+	0.660157i
$239$	10.7765			0.697074			0.348537	−	0.937295i	$-0.386679\pi$
$239$	10.7765			0.697074			0.348537	+	0.937295i	$0.386679\pi$
$240$		0			0
$241$	−14.5670			−0.938344			−0.469172	−	0.883107i	$-0.655448\pi$
$241$	−14.5670			−0.938344			−0.469172	+	0.883107i	$0.655448\pi$
$242$	−3.49261	+	13.2685i	−0.224513	+	0.852932i
$243$	5.02097			0.322095
$244$	1.20358	+	4.33831i	0.0770512	+	0.277732i
$245$		0			0
$246$	2.64645	−	10.0539i	0.168732	−	0.641015i
$247$	6.87133	−	6.87133i	0.437212	−	0.437212i
$248$	−19.3936	+	19.9139i	−1.23149	+	1.26454i
$249$	25.9540			1.64477
$250$		0			0
$251$	−12.1001	−	12.1001i	−0.763750	−	0.763750i	0.213248	−	0.976998i	$-0.431596\pi$
$251$	−12.1001	−	12.1001i	−0.763750	−	0.763750i	−0.976998	+	0.213248i	$0.931596\pi$
$252$	0.957095	−	0.265527i	0.0602913	−	0.0167266i
$253$			3.70887i			0.233174i
$254$	−7.72490	−	13.2446i	−0.484704	−	0.831041i
$255$		0			0
$256$	−7.50600	+	14.1301i	−0.469125	+	0.883132i
$257$	−17.6083	+	17.6083i	−1.09838	+	1.09838i	−0.103775	+	0.994601i	$0.533092\pi$
$257$	−17.6083	+	17.6083i	−1.09838	+	1.09838i	−0.994601	+	0.103775i	$0.966908\pi$
$258$	5.93218	−	22.5365i	0.369321	−	1.40306i
$259$	−1.23826	−	1.23826i	−0.0769417	−	0.0769417i
$260$		0			0
$261$	1.81415	−	1.81415i	0.112293	−	0.112293i
$262$	2.94749	−	1.71912i	0.182097	−	0.106208i
$263$	12.1083	+	12.1083i	0.746630	+	0.746630i	0.973845	−	0.227214i	$-0.0729618\pi$
$263$	12.1083	+	12.1083i	0.746630	+	0.746630i	−0.227214	+	0.973845i	$0.572962\pi$
$264$	−0.0796637	−	6.01787i	−0.00490296	−	0.370374i
$265$		0			0
$266$	2.29173	+	0.603243i	0.140515	+	0.0369872i
$267$	8.37671			0.512646
$268$	−9.15288	+	16.1814i	−0.559101	+	0.988434i
$269$	6.20149	−	6.20149i	0.378112	−	0.378112i	−0.492309	−	0.870421i	$-0.663847\pi$
$269$	6.20149	−	6.20149i	0.378112	−	0.378112i	0.870421	+	0.492309i	$0.163847\pi$
$270$		0			0
$271$		−	5.11166i		−	0.310511i	−0.987874	−	0.155256i	$-0.950380\pi$
$271$		−	5.11166i		−	0.310511i	0.987874	−	0.155256i	$-0.0496201\pi$
$272$	28.3865	+	7.07165i	1.72119	+	0.428781i
$273$	−7.93959	−	7.93959i	−0.480526	−	0.480526i
$274$	−1.70707	−	2.92683i	−0.103128	−	0.176816i
$275$		0			0
$276$	3.25036	+	11.7160i	0.195649	+	0.705218i
$277$			4.65720i			0.279824i	0.990164	+	0.139912i	$0.0446820\pi$
$277$			4.65720i			0.279824i	−0.990164	+	0.139912i	$0.955318\pi$
$278$	4.11530	−	2.40024i	0.246819	−	0.143957i
$279$		−	4.79335i		−	0.286971i
$280$		0			0
$281$			26.7402i			1.59519i	0.603194	+	0.797595i	$0.293895\pi$
$281$			26.7402i			1.59519i	−0.603194	+	0.797595i	$0.706105\pi$
$282$	−6.04304	−	10.3610i	−0.359858	−	0.616989i
$283$			2.12034i			0.126041i	0.998012	+	0.0630205i	$0.0200733\pi$
$283$			2.12034i			0.126041i	−0.998012	+	0.0630205i	$0.979927\pi$
$284$	16.2519	+	9.19275i	0.964370	+	0.545490i
$285$		0			0
$286$	−8.21860	+	4.79348i	−0.485976	+	0.283445i
$287$	−2.83414	−	2.83414i	−0.167294	−	0.167294i
$288$	−0.772713	−	2.64864i	−0.0455326	−	0.156073i
$289$		−	36.4877i		−	2.14634i
$290$		0			0
$291$	−8.33815	+	8.33815i	−0.488791	+	0.488791i
$292$	23.3798	−	6.48626i	1.36820	−	0.379580i
$293$	−15.7244			−0.918632			−0.459316	−	0.888273i	$-0.651905\pi$
$293$	−15.7244			−0.918632			−0.459316	+	0.888273i	$0.651905\pi$
$294$	−4.00912	+	15.2307i	−0.233817	+	0.888275i
$295$		0			0
$296$	−3.39383	+	3.48489i	−0.197262	+	0.202555i
$297$	−3.77995	−	3.77995i	−0.219335	−	0.219335i
$298$	−2.51597	−	4.31372i	−0.145746	−	0.249887i
$299$	13.5914	−	13.5914i	0.786008	−	0.786008i
$300$		0			0
$301$	−6.35291	−	6.35291i	−0.366175	−	0.366175i
$302$	−22.6350	−	5.95810i	−1.30250	−	0.342850i
$303$	16.8877	−	16.8877i	0.970175	−	0.970175i
$304$	1.59129	−	6.38765i	0.0912666	−	0.366357i
$305$		0			0
$306$	−4.35759	+	2.54156i	−0.249107	+	0.145291i
$307$		−	5.32655i		−	0.304002i	−0.988380	−	0.152001i	$-0.951428\pi$
$307$		−	5.32655i		−	0.304002i	0.988380	−	0.152001i	$-0.0485717\pi$
$308$	−2.01955	−	1.14235i	−0.115075	−	0.0650913i
$309$	−16.6092	−	16.6092i	−0.944866	−	0.944866i
$310$		0			0
$311$	−15.8269			−0.897459			−0.448730	−	0.893668i	$-0.648123\pi$
$311$	−15.8269			−0.897459			−0.448730	+	0.893668i	$0.648123\pi$
$312$	−21.7609	+	22.3447i	−1.23197	+	1.26502i
$313$	−14.4637	+	14.4637i	−0.817539	+	0.817539i	−0.985751	−	0.168212i	$-0.946201\pi$
$313$	−14.4637	+	14.4637i	−0.817539	+	0.817539i	0.168212	+	0.985751i	$0.446201\pi$
$314$	6.93505	+	1.82548i	0.391368	+	0.103018i
$315$		0			0
$316$	−2.96340	−	1.67623i	−0.166704	−	0.0942951i
$317$	5.38384			0.302387			0.151193	−	0.988504i	$-0.451688\pi$
$317$	5.38384			0.302387			0.151193	+	0.988504i	$0.451688\pi$
$318$	21.9845	+	5.78687i	1.23283	+	0.324512i
$319$	−5.99331			−0.335561
$320$		0			0
$321$	17.3595			0.968910
$322$	4.53300	+	1.19320i	0.252614	+	0.0664946i
$323$	−12.0360			−0.669702
$324$	−17.8003	−	10.0686i	−0.988907	−	0.559369i
$325$		0			0
$326$	20.9336	+	5.51027i	1.15941	+	0.305185i
$327$	7.66882	−	7.66882i	0.424086	−	0.424086i
$328$	−7.76784	+	7.97626i	−0.428907	+	0.440415i
$329$	−4.62420			−0.254941
$330$		0			0
$331$	−5.04895	−	5.04895i	−0.277516	−	0.277516i	0.554601	−	0.832116i	$-0.312871\pi$
$331$	−5.04895	−	5.04895i	−0.277516	−	0.277516i	−0.832116	+	0.554601i	$0.812871\pi$
$332$	−24.1927	−	13.6844i	−1.32775	−	0.751030i
$333$		−	0.838825i		−	0.0459673i
$334$	8.27185	−	4.82454i	0.452615	−	0.263987i
$335$		0			0
$336$	−7.38071	−	1.83868i	−0.402651	−	0.100308i
$337$	8.10233	−	8.10233i	0.441362	−	0.441362i	−0.451107	−	0.892470i	$-0.648971\pi$
$337$	8.10233	−	8.10233i	0.441362	−	0.441362i	0.892470	+	0.451107i	$0.148971\pi$
$338$	29.9044	+	7.87159i	1.62658	+	0.428158i
$339$	14.0280	+	14.0280i	0.761898	+	0.761898i
$340$		0			0
$341$	−7.91777	+	7.91777i	−0.428771	+	0.428771i
$342$	0.571911	+	0.980561i	0.0309254	+	0.0530227i
$343$	9.33338	+	9.33338i	0.503955	+	0.503955i
$344$	−17.4121	+	17.8793i	−0.938797	+	0.963986i
$345$		0			0
$346$	−3.35571	+	12.7484i	−0.180404	+	0.685359i
$347$	7.87019			0.422494			0.211247	−	0.977433i	$-0.432248\pi$
$347$	7.87019			0.422494			0.211247	+	0.977433i	$0.432248\pi$
$348$	−18.9323	+	5.25239i	−1.01488	+	0.281558i
$349$	18.7492	−	18.7492i	1.00362	−	1.00362i	0.00363019	−	0.999993i	$-0.498844\pi$
$349$	18.7492	−	18.7492i	1.00362	−	1.00362i	0.999993	−	0.00363019i	$-0.00115553\pi$
$350$		0			0
$351$			27.7037i			1.47871i
$352$	−3.09870	+	5.65147i	−0.165161	+	0.301224i
$353$	−0.0830593	−	0.0830593i	−0.00442080	−	0.00442080i	0.704893	−	0.709314i	$-0.250995\pi$
$353$	−0.0830593	−	0.0830593i	−0.00442080	−	0.00442080i	−0.709314	+	0.704893i	$0.750995\pi$
$354$	16.9233	−	9.87047i	0.899462	−	0.524610i
$355$		0			0
$356$	−7.80823	−	4.41667i	−0.413835	−	0.234083i
$357$			13.9072i			0.736047i
$358$	−15.7466	−	26.9980i	−0.832232	−	1.42689i
$359$			35.9409i			1.89689i	0.316941	+	0.948445i	$0.397344\pi$
$359$			35.9409i			1.89689i	−0.316941	+	0.948445i	$0.602656\pi$
$360$		0			0
$361$		−	16.2916i		−	0.857453i
$362$	−29.3792	+	17.1354i	−1.54413	+	0.900614i
$363$			18.1187i			0.950983i
$364$	3.21457	+	11.5870i	0.168489	+	0.607322i
$365$		0			0
$366$	2.99537	+	5.13567i	0.156571	+	0.268446i
$367$	23.6922	+	23.6922i	1.23672	+	1.23672i	0.961333	+	0.275389i	$0.0888066\pi$
$367$	23.6922	+	23.6922i	1.23672	+	1.23672i	0.275389	+	0.961333i	$0.411193\pi$
$368$	3.14754	−	12.6346i	0.164077	−	0.658626i
$369$		−	1.91991i		−	0.0999467i
$370$		0			0
$371$	6.19729	−	6.19729i	0.321747	−	0.321747i
$372$	−18.0725	+	31.9504i	−0.937018	+	1.65655i
$373$	27.8655			1.44282			0.721410	−	0.692508i	$-0.243494\pi$
$373$	27.8655			1.44282			0.721410	+	0.692508i	$0.243494\pi$
$374$	11.3962	+	2.99976i	0.589281	+	0.155114i
$375$		0			0
$376$	0.170028	+	12.8441i	0.00876853	+	0.662383i
$377$	21.9628	+	21.9628i	1.13114	+	1.13114i
$378$	−5.83595	+	3.40381i	−0.300169	+	0.175073i
$379$	−18.4005	+	18.4005i	−0.945168	+	0.945168i	−0.998573	−	0.0534045i	$-0.982993\pi$
$379$	−18.4005	+	18.4005i	−0.945168	+	0.945168i	0.0534045	+	0.998573i	$0.482993\pi$
$380$		0			0
$381$	−14.3173	−	14.3173i	−0.733500	−	0.733500i
$382$	−1.39869	+	5.31366i	−0.0715633	+	0.271870i
$383$	−27.3966	+	27.3966i	−1.39990	+	1.39990i	−0.599603	+	0.800298i	$0.704675\pi$
$383$	−27.3966	+	27.3966i	−1.39990	+	1.39990i	−0.800298	+	0.599603i	$0.795325\pi$
$384$	−4.83569	+	20.5681i	−0.246770	+	1.04961i
$385$		0			0
$386$	−3.71110	−	6.36282i	−0.188890	−	0.323859i
$387$		−	4.30360i		−	0.218764i
$388$	12.1686	−	3.37594i	0.617768	−	0.171388i
$389$	−9.05190	−	9.05190i	−0.458950	−	0.458950i	0.439361	−	0.898311i	$-0.355205\pi$
$389$	−9.05190	−	9.05190i	−0.458950	−	0.458950i	−0.898311	+	0.439361i	$0.855205\pi$
$390$		0			0
$391$	−23.8070			−1.20397
$392$	11.7676	−	12.0833i	0.594351	−	0.610298i
$393$	3.18622	−	3.18622i	0.160724	−	0.160724i
$394$	−4.42437	+	16.8083i	−0.222896	+	0.846788i
$395$		0			0
$396$	−0.297120	−	1.07097i	−0.0149308	−	0.0538184i
$397$	−11.6052			−0.582448			−0.291224	−	0.956655i	$-0.594063\pi$
$397$	−11.6052			−0.582448			−0.291224	+	0.956655i	$0.594063\pi$
$398$	4.55566	−	17.3070i	0.228354	−	0.867524i
$399$	3.12945			0.156668
$400$		0			0
$401$	−9.94759			−0.496759			−0.248379	−	0.968663i	$-0.579898\pi$
$401$	−9.94759			−0.496759			−0.248379	+	0.968663i	$0.579898\pi$
$402$	−6.24931	+	23.7413i	−0.311687	+	1.18411i
$403$	58.0302			2.89069
$404$	−24.6458	+	6.83749i	−1.22617	+	0.340178i
$405$		0			0
$406$	−1.92814	+	7.32506i	−0.0956922	+	0.363537i
$407$	−1.38559	+	1.38559i	−0.0686811	+	0.0686811i
$408$	38.6283	−	0.511356i	1.91239	−	0.0253159i
$409$	−24.7129			−1.22198			−0.610988	−	0.791640i	$-0.709228\pi$
$409$	−24.7129			−1.22198			−0.610988	+	0.791640i	$0.709228\pi$
$410$		0			0
$411$	−3.16389	−	3.16389i	−0.156063	−	0.156063i
$412$	6.72473	+	24.2394i	0.331304	+	1.19419i
$413$		−	7.55300i		−	0.371659i
$414$	1.13123	+	1.93953i	0.0555968	+	0.0953227i
$415$		0			0
$416$	32.0655	−	9.35477i	1.57214	−	0.458655i
$417$	4.44861	−	4.44861i	0.217849	−	0.217849i
$418$	0.675017	−	2.56441i	0.0330162	−	0.125429i
$419$	−12.9537	−	12.9537i	−0.632829	−	0.632829i	0.315947	−	0.948777i	$-0.397678\pi$
$419$	−12.9537	−	12.9537i	−0.632829	−	0.632829i	−0.948777	+	0.315947i	$0.897678\pi$
$420$		0			0
$421$	−8.99009	+	8.99009i	−0.438150	+	0.438150i	−0.891389	−	0.453239i	$-0.850268\pi$
$421$	−8.99009	+	8.99009i	−0.438150	+	0.438150i	0.453239	+	0.891389i	$0.350268\pi$
$422$	−4.44596	+	2.59310i	−0.216426	+	0.126230i
$423$	−1.56627	−	1.56627i	−0.0761547	−	0.0761547i
$424$	−17.4413	−	16.9856i	−0.847026	−	0.824893i
$425$		0			0
$426$	23.8447	+	6.27653i	1.15528	+	0.304099i
$427$	2.29210			0.110922
$428$	−16.1814	−	9.15288i	−0.782156	−	0.442421i
$429$	−8.88425	+	8.88425i	−0.428936	+	0.428936i
$430$		0			0
$431$		−	20.8177i		−	1.00275i	−0.865230	−	0.501376i	$-0.832828\pi$
$431$		−	20.8177i		−	1.00275i	0.865230	−	0.501376i	$-0.167172\pi$
$432$	9.66892	+	16.0846i	0.465196	+	0.773873i
$433$	−7.70002	−	7.70002i	−0.370039	−	0.370039i	0.497452	−	0.867491i	$-0.334269\pi$
$433$	−7.70002	−	7.70002i	−0.370039	−	0.370039i	−0.867491	+	0.497452i	$0.834269\pi$
$434$	7.12988	+	12.2244i	0.342245	+	0.586791i
$435$		0			0
$436$	−11.1918	+	3.10494i	−0.535990	+	0.148700i
$437$			5.35714i			0.256267i
$438$	27.6769	−	16.1425i	1.32245	−	0.771319i
$439$		−	38.4535i		−	1.83529i	−0.397407	−	0.917643i	$-0.630090\pi$
$439$		−	38.4535i		−	1.83529i	0.397407	−	0.917643i	$-0.369910\pi$
$440$		0			0
$441$			2.90849i			0.138499i
$442$	−30.7691	−	52.7547i	−1.46354	−	2.50928i
$443$			17.1242i			0.813595i	0.913518	+	0.406797i	$0.133355\pi$
$443$			17.1242i			0.813595i	−0.913518	+	0.406797i	$0.866645\pi$
$444$	−3.16265	+	5.59125i	−0.150093	+	0.265349i
$445$		0			0
$446$	−16.5053	+	9.62667i	−0.781547	+	0.455836i
$447$	−4.66310	−	4.66310i	−0.220557	−	0.220557i
$448$	5.91036	+	5.60542i	0.279238	+	0.264831i
$449$		−	12.1296i		−	0.572431i	−0.958165	−	0.286215i	$-0.907603\pi$
$449$		−	12.1296i		−	0.572431i	0.958165	−	0.286215i	$-0.0923973\pi$
$450$		0			0
$451$	−3.17135	+	3.17135i	−0.149333	+	0.149333i
$452$	−5.67966	−	20.4724i	−0.267149	−	0.962940i
$453$	−30.9089			−1.45223
$454$	−4.62525	+	17.5714i	−0.217074	+	0.824668i
$455$		0			0
$456$	−0.115067	−	8.69229i	−0.00538852	−	0.407054i
$457$	3.96532	+	3.96532i	0.185490	+	0.185490i	0.793743	−	0.608253i	$-0.208129\pi$
$457$	3.96532	+	3.96532i	0.185490	+	0.185490i	−0.608253	+	0.793743i	$0.708129\pi$
$458$	−1.97587	−	3.38769i	−0.0923261	−	0.158296i
$459$	24.2633	−	24.2633i	1.13251	−	1.13251i
$460$		0			0
$461$	−25.6620	−	25.6620i	−1.19520	−	1.19520i	−0.975587	−	0.219614i	$-0.929520\pi$
$461$	−25.6620	−	25.6620i	−1.19520	−	1.19520i	−0.219614	−	0.975587i	$-0.570480\pi$
$462$	−2.96308	−	0.779960i	−0.137855	−	0.0362870i
$463$	3.98789	−	3.98789i	0.185333	−	0.185333i	−0.608342	−	0.793675i	$-0.708165\pi$
$463$	3.98789	−	3.98789i	0.185333	−	0.185333i	0.793675	+	0.608342i	$0.208165\pi$
$464$	20.4168	+	5.08623i	0.947827	+	0.236122i
$465$		0			0
$466$	−12.7687	+	7.44730i	−0.591497	+	0.344990i
$467$			10.8576i			0.502429i	0.967931	+	0.251215i	$0.0808300\pi$
$467$			10.8576i			0.502429i	−0.967931	+	0.251215i	$0.919170\pi$
$468$	−2.83582	+	5.01345i	−0.131086	+	0.231747i
$469$	6.69253	+	6.69253i	0.309032	+	0.309032i
$470$		0			0
$471$	9.47009			0.436359
$472$	−20.9790	+	0.277718i	−0.965639	+	0.0127830i
$473$	−7.10878	+	7.10878i	−0.326862	+	0.326862i
$474$	−4.34789	−	1.14448i	−0.199705	−	0.0525675i
$475$		0			0
$476$	7.33266	−	12.9634i	0.336092	−	0.594176i
$477$	4.19819			0.192222
$478$	−14.7382	−	3.87948i	−0.674111	−	0.177443i
$479$	0.144583			0.00660618			0.00330309	−	0.999995i	$-0.498949\pi$
$479$	0.144583			0.00660618			0.00330309	+	0.999995i	$0.498949\pi$
$480$		0			0
$481$	10.1551			0.463035
$482$	19.9222	+	5.24404i	0.907433	+	0.238860i
$483$	6.18999			0.281654
$484$	9.55318	−	16.8890i	0.434235	−	0.767684i
$485$		0			0
$486$	−6.86681	−	1.80752i	−0.311485	−	0.0819908i
$487$	24.9905	−	24.9905i	1.13243	−	1.13243i	0.142655	−	0.989772i	$-0.454436\pi$
$487$	24.9905	−	24.9905i	1.13243	−	1.13243i	0.989772	−	0.142655i	$-0.0455639\pi$
$488$	−0.0842785	−	6.36647i	−0.00381511	−	0.288197i
$489$	28.5857			1.29269
$490$		0			0
$491$	16.8603	+	16.8603i	0.760893	+	0.760893i	0.976484	−	0.215591i	$-0.0691678\pi$
$491$	16.8603	+	16.8603i	0.760893	+	0.760893i	−0.215591	+	0.976484i	$0.569168\pi$
$492$	−7.23872	+	12.7973i	−0.326346	+	0.576947i
$493$		−	38.4707i		−	1.73263i
$494$	−11.8711	+	6.92378i	−0.534104	+	0.311515i
$495$		0			0
$496$	33.6921	−	20.2533i	1.51282	−	0.909399i
$497$	6.72168	−	6.72168i	0.301509	−	0.301509i
$498$	−35.4954	−	9.34331i	−1.59059	−	0.418684i
$499$	−12.2949	−	12.2949i	−0.550397	−	0.550397i	0.376159	−	0.926555i	$-0.377245\pi$
$499$	−12.2949	−	12.2949i	−0.550397	−	0.550397i	−0.926555	+	0.376159i	$0.877245\pi$
$500$		0			0
$501$	8.94182	−	8.94182i	0.399491	−	0.399491i
$502$	12.1924	+	20.9043i	0.544175	+	0.933006i
$503$	2.55961	+	2.55961i	0.114128	+	0.114128i	0.761864	−	0.647737i	$-0.224284\pi$
$503$	2.55961	+	2.55961i	0.114128	+	0.114128i	−0.647737	+	0.761864i	$0.724284\pi$
$504$	−1.40454	+	0.0185931i	−0.0625631	+	0.000828201i
$505$		0			0
$506$	1.33517	−	5.07235i	0.0593556	−	0.225493i
$507$	40.8356			1.81357
$508$	5.79680	+	20.8946i	0.257191	+	0.927049i
$509$	−6.59987	+	6.59987i	−0.292534	+	0.292534i	−0.838080	−	0.545547i	$-0.816322\pi$
$509$	−6.59987	+	6.59987i	−0.292534	+	0.292534i	0.545547	+	0.838080i	$0.316322\pi$
$510$		0			0
$511$		−	12.3524i		−	0.546440i
$512$	15.3522	−	16.6226i	0.678477	−	0.734622i
$513$	−5.45981	−	5.45981i	−0.241056	−	0.241056i
$514$	30.4205	−	17.7427i	1.34179	−	0.782597i
$515$		0			0
$516$	−16.2260	+	28.6860i	−0.714311	+	1.26283i
$517$			5.17440i			0.227570i
$518$	1.24771	+	2.13924i	0.0548213	+	0.0939930i
$519$			17.4085i			0.764147i
$520$		0			0
$521$			13.9510i			0.611204i	0.952159	+	0.305602i	$0.0988577\pi$
$521$			13.9510i			0.611204i	−0.952159	+	0.305602i	$0.901142\pi$
$522$	−3.13417	+	1.82800i	−0.137179	+	0.0800093i
$523$		−	24.6076i		−	1.07601i	−0.842941	−	0.538007i	$-0.819178\pi$
$523$		−	24.6076i		−	1.07601i	0.842941	−	0.538007i	$-0.180822\pi$
$524$	−4.64994	+	1.29003i	−0.203134	+	0.0563554i
$525$		0			0
$526$	−12.2007	−	20.9186i	−0.531977	−	0.912093i
$527$	−50.8237	−	50.8237i	−2.21391	−	2.21391i
$528$	−2.05745	+	8.25888i	−0.0895389	+	0.359421i
$529$		−	12.4037i		−	0.539291i
$530$		0			0
$531$	2.55829	−	2.55829i	0.111020	−	0.111020i
$532$	−2.91707	−	1.65002i	−0.126471	−	0.0715375i
$533$	23.2432			1.00678
$534$	−11.4562	−	3.01557i	−0.495759	−	0.130496i
$535$		0			0
$536$	18.3429	−	18.8351i	0.792294	−	0.813552i
$537$	−29.1847	−	29.1847i	−1.25941	−	1.25941i
$538$	−10.7138	+	6.24883i	−0.461906	+	0.269406i
$539$	4.80430	−	4.80430i	0.206936	−	0.206936i
$540$		0			0
$541$	−14.4785	−	14.4785i	−0.622481	−	0.622481i	0.323684	−	0.946165i	$-0.395078\pi$
$541$	−14.4785	−	14.4785i	−0.622481	−	0.622481i	−0.946165	+	0.323684i	$0.895078\pi$
$542$	−1.84017	+	6.99084i	−0.0790420	+	0.300282i
$543$	−31.7587	+	31.7587i	−1.36290	+	1.36290i
$544$	−36.2765	−	19.8904i	−1.55534	−	0.852793i
$545$		0			0
$546$	8.00019	+	13.7166i	0.342376	+	0.587016i
$547$			27.5523i			1.17805i	0.808114	+	0.589026i	$0.200488\pi$
$547$			27.5523i			1.17805i	−0.808114	+	0.589026i	$0.799512\pi$
$548$	1.28099	+	4.61735i	0.0547213	+	0.197243i
$549$	0.776359	+	0.776359i	0.0331342	+	0.0331342i
$550$		0			0
$551$	−8.65682			−0.368793
$552$	−0.227601	−	17.1932i	−0.00968734	−	0.731790i
$553$	−1.22565	+	1.22565i	−0.0521197	+	0.0521197i
$554$	1.67657	−	6.36932i	0.0712305	−	0.270606i
$555$		0			0
$556$	−6.49227	+	1.80115i	−0.275333	+	0.0763858i
$557$	23.5208			0.996608			0.498304	−	0.867002i	$-0.333956\pi$
$557$	23.5208			0.996608			0.498304	+	0.867002i	$0.333956\pi$
$558$	−1.72558	+	6.55552i	−0.0730497	+	0.277517i
$559$	52.1011			2.20364
$560$		0			0
$561$	15.5619			0.657024
$562$	9.62634	−	36.5707i	0.406063	−	1.54264i
$563$	11.3970			0.480327			0.240163	−	0.970732i	$-0.422799\pi$
$563$	11.3970			0.480327			0.240163	+	0.970732i	$0.422799\pi$
$564$	4.53472	+	16.3454i	0.190946	+	0.688267i
$565$		0			0
$566$	0.763309	−	2.89983i	0.0320843	−	0.121889i
$567$	−7.36212	+	7.36212i	−0.309180	+	0.309180i
$568$	−18.9171	−	18.4228i	−0.793746	−	0.773005i
$569$	21.2444			0.890613			0.445307	−	0.895378i	$-0.353095\pi$
$569$	21.2444			0.890613			0.445307	+	0.895378i	$0.353095\pi$
$570$		0			0
$571$	23.0980	+	23.0980i	0.966622	+	0.966622i	0.999461	−	0.0328390i	$-0.0104549\pi$
$571$	23.0980	+	23.0980i	0.966622	+	0.966622i	−0.0328390	+	0.999461i	$0.510455\pi$
$572$	12.9656	−	3.59705i	0.542119	−	0.150400i
$573$			7.25601i			0.303124i
$574$	2.85578	+	4.89633i	0.119198	+	0.204369i
$575$		0			0
$576$	0.103287	+	3.90053i	0.00430364	+	0.162522i
$577$	8.54721	−	8.54721i	0.355825	−	0.355825i	−0.506446	−	0.862271i	$-0.669041\pi$
$577$	8.54721	−	8.54721i	0.355825	−	0.355825i	0.862271	+	0.506446i	$0.169041\pi$
$578$	−13.1354	+	49.9016i	−0.546360	+	2.07563i
$579$	−6.87817	−	6.87817i	−0.285847	−	0.285847i
$580$		0			0
$581$	−10.0060	+	10.0060i	−0.415117	+	0.415117i
$582$	14.4052	−	8.40179i	0.597113	−	0.348265i
$583$	−6.93466	−	6.93466i	−0.287204	−	0.287204i
$584$	−34.3098	+	0.454189i	−1.41975	+	0.0187945i
$585$		0			0
$586$	21.5052	+	5.66071i	0.888370	+	0.233842i
$587$	−28.9980			−1.19687			−0.598437	−	0.801170i	$-0.704211\pi$
$587$	−28.9980			−1.19687			−0.598437	+	0.801170i	$0.704211\pi$
$588$	10.9660	−	19.3867i	0.452229	−	0.799495i
$589$	−11.4365	+	11.4365i	−0.471234	+	0.471234i
$590$		0			0
$591$			22.9523i			0.944133i
$592$	5.89604	−	3.54427i	0.242326	−	0.145669i
$593$	−1.73827	−	1.73827i	−0.0713822	−	0.0713822i	0.670514	−	0.741897i	$-0.266073\pi$
$593$	−1.73827	−	1.73827i	−0.0713822	−	0.0713822i	−0.741897	+	0.670514i	$0.766073\pi$
$594$	3.80880	+	6.53032i	0.156277	+	0.267942i
$595$		0			0
$596$	1.88799	+	6.80529i	0.0773352	+	0.278756i
$597$		−	23.6334i		−	0.967252i
$598$	−23.4807	+	13.6951i	−0.960198	+	0.560034i
$599$			23.3429i			0.953764i	0.878967	+	0.476882i	$0.158233\pi$
$599$			23.3429i			0.953764i	−0.878967	+	0.476882i	$0.841767\pi$
$600$		0			0
$601$			14.2850i			0.582697i	0.956617	+	0.291348i	$0.0941039\pi$
$601$			14.2850i			0.582697i	−0.956617	+	0.291348i	$0.905896\pi$
$602$	6.40140	+	10.9754i	0.260901	+	0.447325i
$603$			4.53367i			0.184625i
$604$	28.8113	+	16.2969i	1.17231	+	0.663112i
$605$		0			0
$606$	−29.1756	+	17.0166i	−1.18518	+	0.691253i
$607$	4.84325	+	4.84325i	0.196581	+	0.196581i	0.798533	−	0.601951i	$-0.205610\pi$
$607$	4.84325	+	4.84325i	0.196581	+	0.196581i	−0.601951	+	0.798533i	$0.705610\pi$
$608$	−4.47581	+	8.16306i	−0.181518	+	0.331056i
$609$			10.0027i			0.405328i
$610$		0			0
$611$	18.9619	−	18.9619i	0.767116	−	0.767116i
$612$	6.87450	−	1.90719i	0.277885	−	0.0770938i
$613$	6.37122			0.257331			0.128666	−	0.991688i	$-0.458931\pi$
$613$	6.37122			0.257331			0.128666	+	0.991688i	$0.458931\pi$
$614$	−1.91753	+	7.28473i	−0.0773852	+	0.293988i
$615$		0			0
$616$	2.35076	+	2.28933i	0.0947147	+	0.0922399i
$617$	13.7251	+	13.7251i	0.552553	+	0.552553i	0.927177	−	0.374624i	$-0.122228\pi$
$617$	13.7251	+	13.7251i	0.552553	+	0.552553i	−0.374624	+	0.927177i	$0.622228\pi$
$618$	16.7360	+	28.6945i	0.673221	+	1.15426i
$619$	−6.92352	+	6.92352i	−0.278280	+	0.278280i	−0.832422	−	0.554142i	$-0.813046\pi$
$619$	−6.92352	+	6.92352i	−0.278280	+	0.278280i	0.554142	+	0.832422i	$0.313046\pi$
$620$		0			0
$621$	−10.7994	−	10.7994i	−0.433365	−	0.433365i
$622$	21.6453	+	5.69758i	0.867895	+	0.228452i
$623$	−3.22944	+	3.22944i	−0.129385	+	0.129385i
$624$	37.8048	−	22.7255i	1.51340	−	0.909748i
$625$		0			0
$626$	24.9879	−	14.5741i	0.998716	−	0.582500i
$627$		−	3.50180i		−	0.139848i
$628$	−8.82740	−	4.99316i	−0.352252	−	0.199249i
$629$	−8.89402	−	8.89402i	−0.354628	−	0.354628i
$630$		0			0
$631$	0.299394			0.0119187			0.00595935	−	0.999982i	$-0.498103\pi$
$631$	0.299394			0.0119187			0.00595935	+	0.999982i	$0.498103\pi$
$632$	3.44939	+	3.35926i	0.137209	+	0.133624i
$633$	−4.80606	+	4.80606i	−0.191024	+	0.191024i
$634$	−7.36308	−	1.93815i	−0.292425	−	0.0769739i
$635$		0			0
$636$	−27.9833	−	15.8286i	−1.10961	−	0.627643i
$637$	−35.2113			−1.39512
$638$	8.19661	+	2.15756i	0.324507	+	0.0854185i
$639$	4.55342			0.180130
$640$		0			0
$641$	45.7708			1.80784			0.903920	−	0.427702i	$-0.140677\pi$
$641$	45.7708			1.80784			0.903920	+	0.427702i	$0.140677\pi$
$642$	−23.7413	−	6.24931i	−0.936993	−	0.246641i
$643$	−9.26732			−0.365467			−0.182734	−	0.983162i	$-0.558495\pi$
$643$	−9.26732			−0.365467			−0.182734	+	0.983162i	$0.558495\pi$
$644$	−5.76991	−	3.26371i	−0.227366	−	0.128608i
$645$		0			0
$646$	16.4608	+	4.33290i	0.647641	+	0.170476i
$647$	−0.284672	+	0.284672i	−0.0111916	+	0.0111916i	−0.712680	−	0.701489i	$-0.752519\pi$
$647$	−0.284672	+	0.284672i	−0.0111916	+	0.0111916i	0.701489	+	0.712680i	$0.252519\pi$
$648$	20.7196	+	20.1782i	0.813941	+	0.792673i
$649$	−8.45167			−0.331757
$650$		0			0
$651$	13.2145	+	13.2145i	0.517918	+	0.517918i
$652$	−26.6457	−	15.0720i	−1.04353	−	0.590264i
$653$		−	11.1970i		−	0.438173i	−0.975705	−	0.219087i	$-0.929692\pi$
$653$		−	11.1970i		−	0.438173i	0.975705	−	0.219087i	$-0.0703078\pi$
$654$	−13.2488	+	7.72735i	−0.518070	+	0.302163i
$655$		0			0
$656$	13.4949	−	8.11217i	0.526888	−	0.316727i
$657$	4.18391	−	4.18391i	0.163230	−	0.163230i
$658$	6.32419	+	1.66469i	0.246542	+	0.0648963i
$659$	−5.66498	−	5.66498i	−0.220676	−	0.220676i	0.588107	−	0.808783i	$-0.299873\pi$
$659$	−5.66498	−	5.66498i	−0.220676	−	0.220676i	−0.808783	+	0.588107i	$0.799873\pi$
$660$		0			0
$661$	23.3785	−	23.3785i	0.909320	−	0.909320i	−0.0868975	−	0.996217i	$-0.527695\pi$
$661$	23.3785	−	23.3785i	0.909320	−	0.909320i	0.996217	+	0.0868975i	$0.0276953\pi$
$662$	5.08749	+	8.72268i	0.197731	+	0.339017i
$663$	−57.0275	−	57.0275i	−2.21476	−	2.21476i
$664$	28.1602	+	27.4244i	1.09283	+	1.06427i
$665$		0			0
$666$	−0.301972	+	1.14720i	−0.0117012	+	0.0444531i
$667$	−17.1230			−0.663006
$668$	−13.0496	+	3.62036i	−0.504905	+	0.140076i
$669$	−17.8421	+	17.8421i	−0.689815	+	0.689815i
$670$		0			0
$671$		−	2.56481i		−	0.0990135i
$672$	9.43214	+	5.17164i	0.363853	+	0.199500i
$673$	26.6324	+	26.6324i	1.02660	+	1.02660i	0.999636	+	0.0269656i	$0.00858447\pi$
$673$	26.6324	+	26.6324i	1.02660	+	1.02660i	0.0269656	+	0.999636i	$0.491416\pi$
$674$	−13.9978	+	8.16418i	−0.539174	+	0.314472i
$675$		0			0
$676$	−38.0643	−	21.5308i	−1.46401	−	0.828108i
$677$			13.5539i			0.520918i	0.965485	+	0.260459i	$0.0838739\pi$
$677$			13.5539i			0.520918i	−0.965485	+	0.260459i	$0.916126\pi$
$678$	−14.1351	−	24.2351i	−0.542855	−	0.930744i
$679$		−	6.42915i		−	0.246728i
$680$		0			0
$681$			23.9945i			0.919470i
$682$	13.6789	−	7.97820i	0.523792	−	0.305501i
$683$		−	15.3467i		−	0.587225i	−0.955925	−	0.293613i	$-0.905142\pi$
$683$		−	15.3467i		−	0.587225i	0.955925	−	0.293613i	$-0.0948575\pi$
$684$	−0.429164	−	1.54693i	−0.0164095	−	0.0591482i
$685$		0			0
$686$	−9.40462	−	16.1246i	−0.359070	−	0.615638i
$687$	−3.66207	−	3.66207i	−0.139717	−	0.139717i
$688$	30.2497	−	18.1839i	1.15326	−	0.693256i
$689$			50.8249i			1.93627i
$690$		0			0
$691$	10.6170	−	10.6170i	0.403891	−	0.403891i	−0.475710	−	0.879602i	$-0.657809\pi$
$691$	10.6170	−	10.6170i	0.403891	−	0.403891i	0.879602	+	0.475710i	$0.157809\pi$
$692$	9.17872	−	16.2270i	0.348923	−	0.616860i
$693$	−0.565835			−0.0214943
$694$	−10.7635	−	2.83322i	−0.408576	−	0.107548i
$695$		0			0
$696$	27.7832	−	0.367790i	1.05312	−	0.0139410i
$697$	−20.3567	−	20.3567i	−0.771067	−	0.771067i
$698$	−32.3916	+	18.8923i	−1.22604	+	0.715086i
$699$	−13.8028	+	13.8028i	−0.522072	+	0.522072i
$700$		0			0
$701$	−5.96737	−	5.96737i	−0.225384	−	0.225384i	0.585377	−	0.810761i	$-0.300947\pi$
$701$	−5.96737	−	5.96737i	−0.225384	−	0.225384i	−0.810761	+	0.585377i	$0.800947\pi$
$702$	9.97317	−	37.8883i	0.376413	−	1.43000i
$703$	−2.00137	+	2.00137i	−0.0754829	+	0.0754829i
$704$	6.27236	−	6.61359i	0.236399	−	0.249259i
$705$		0			0
$706$	0.0836932	+	0.143495i	0.00314984	+	0.00540051i
$707$			13.0213i			0.489717i
$708$	−26.6980	+	7.40684i	−1.00337	+	0.278366i
$709$	35.3379	+	35.3379i	1.32714	+	1.32714i	0.907854	+	0.419287i	$0.137720\pi$
$709$	35.3379	+	35.3379i	1.32714	+	1.32714i	0.419287	+	0.907854i	$0.362280\pi$
$710$		0			0
$711$	−0.830280			−0.0311379
$712$	9.08876	+	8.85128i	0.340616	+	0.331716i
$713$	−22.6212	+	22.6212i	−0.847172	+	0.847172i
$714$	5.00652	−	19.0199i	0.187364	−	0.711801i
$715$		0			0
$716$	11.8163	+	42.5919i	0.441595	+	1.59173i
$717$	−20.1256			−0.751606
$718$	12.9385	−	49.1538i	0.482862	−	1.83440i
$719$	−37.8418			−1.41126			−0.705631	−	0.708580i	$-0.749336\pi$
$719$	−37.8418			−1.41126			−0.705631	+	0.708580i	$0.749336\pi$
$720$		0			0
$721$	12.8066			0.476942
$722$	−5.86489	+	22.2809i	−0.218269	+	0.829207i
$723$	27.2046			1.01175
$724$	46.3484	−	12.8584i	1.72252	−	0.477880i
$725$		0			0
$726$	6.52262	−	24.7796i	0.242077	−	0.919656i
$727$	−32.3722	+	32.3722i	−1.20062	+	1.20062i	−0.226641	+	0.973978i	$0.572774\pi$
$727$	−32.3722	+	32.3722i	−1.20062	+	1.20062i	−0.973978	+	0.226641i	$0.927226\pi$
$728$	−0.225095	−	17.0039i	−0.00834258	−	0.630206i
$729$	21.2991			0.788855
$730$		0			0
$731$	−45.6309	−	45.6309i	−1.68772	−	1.68772i
$732$	−2.24774	−	8.10200i	−0.0830789	−	0.299459i
$733$		−	1.96701i		−	0.0726532i	−0.999340	−	0.0363266i	$-0.988434\pi$
$733$		−	1.96701i		−	0.0726532i	0.999340	−	0.0363266i	$-0.0115657\pi$
$734$	−23.8730	−	40.9311i	−0.881169	−	1.51080i
$735$		0			0
$736$	−8.85306	+	16.1464i	−0.326328	+	0.595163i
$737$	7.48881	−	7.48881i	0.275854	−	0.275854i
$738$	−0.691158	+	2.62573i	−0.0254419	+	0.0966543i
$739$	−14.3605	−	14.3605i	−0.528261	−	0.528261i	0.391793	−	0.920054i	$-0.371855\pi$
$739$	−14.3605	−	14.3605i	−0.528261	−	0.528261i	−0.920054	+	0.391793i	$0.871855\pi$
$740$		0			0
$741$	−12.8325	+	12.8325i	−0.471415	+	0.471415i
$742$	−10.7066	+	6.24459i	−0.393051	+	0.229246i
$743$	−2.28846	−	2.28846i	−0.0839556	−	0.0839556i	0.663882	−	0.747837i	$-0.268908\pi$
$743$	−2.28846	−	2.28846i	−0.0839556	−	0.0839556i	−0.747837	+	0.663882i	$0.768908\pi$
$744$	36.2185	−	37.1903i	1.32783	−	1.36346i
$745$		0			0
$746$	−38.1096	−	10.0314i	−1.39529	−	0.367276i
$747$	−6.77826			−0.248004
$748$	−14.5058	−	8.20511i	−0.530385	−	0.300009i
$749$	−6.69253	+	6.69253i	−0.244540	+	0.244540i
$750$		0			0
$751$			23.7064i			0.865058i	0.901620	+	0.432529i	$0.142379\pi$
$751$			23.7064i			0.865058i	−0.901620	+	0.432529i	$0.857621\pi$
$752$	4.39126	−	17.6271i	0.160133	−	0.642795i
$753$	22.5975	+	22.5975i	0.823497	+	0.823497i
$754$	−22.1305	−	37.9434i	−0.805944	−	1.38182i
$755$		0			0
$756$	9.20675	−	2.55423i	0.334846	−	0.0928965i
$757$			30.5469i			1.11025i	0.831768	+	0.555124i	$0.187329\pi$
$757$			30.5469i			1.11025i	−0.831768	+	0.555124i	$0.812671\pi$
$758$	31.7890	−	18.5409i	1.15463	−	0.673436i
$759$		−	6.92649i		−	0.251416i
$760$		0			0
$761$			23.6988i			0.859080i	0.903048	+	0.429540i	$0.141324\pi$
$761$			23.6988i			0.859080i	−0.903048	+	0.429540i	$0.858676\pi$
$762$	14.4266	+	24.7350i	0.522622	+	0.896053i
$763$			5.91306i			0.214067i
$764$	3.82578	−	6.76358i	0.138412	−	0.244698i
$765$		0			0
$766$	47.3309	−	27.6057i	1.71014	−	0.997435i
$767$	30.9716	+	30.9716i	1.11832	+	1.11832i
$768$	14.0178	−	26.3887i	0.505825	−	0.952219i
$769$		−	2.76629i		−	0.0997548i	−0.998755	−	0.0498774i	$-0.984117\pi$
$769$		−	2.76629i		−	0.0997548i	0.998755	−	0.0498774i	$-0.0158831\pi$
$770$		0			0
$771$	32.8844	−	32.8844i	1.18430	−	1.18430i
$772$	2.78483	+	10.0379i	0.100228	+	0.361273i
$773$	36.0726			1.29744			0.648720	−	0.761027i	$-0.275304\pi$
$773$	36.0726			1.29744			0.648720	+	0.761027i	$0.275304\pi$
$774$	−1.54927	+	5.88572i	−0.0556875	+	0.211558i
$775$		0			0
$776$	−17.8575	+	0.236395i	−0.641045	+	0.00848607i
$777$	2.31251	+	2.31251i	0.0829608	+	0.0829608i
$778$	9.12099	+	15.6383i	0.327003	+	0.560659i
$779$	−4.58075	+	4.58075i	−0.164122	+	0.164122i
$780$		0			0
$781$	−7.52144	−	7.52144i	−0.269138	−	0.269138i
$782$	32.5591	+	8.57039i	1.16431	+	0.306476i
$783$	17.4512	−	17.4512i	0.623654	−	0.623654i
$784$	−20.4435	+	12.2892i	−0.730126	+	0.438899i
$785$		0			0
$786$	−5.50458	+	3.21054i	−0.196342	+	0.114516i
$787$		−	12.1024i		−	0.431402i	−0.976459	−	0.215701i	$-0.930796\pi$
$787$		−	12.1024i		−	0.431402i	0.976459	−	0.215701i	$-0.0692037\pi$
$788$	12.1018	−	21.3947i	0.431108	−	0.762154i
$789$	−22.6129	−	22.6129i	−0.805039	−	0.805039i
$790$		0			0
$791$	−10.8163			−0.384585
$792$	0.0208053	+	1.57165i	0.000739284	+	0.0558462i
$793$	−9.39890	+	9.39890i	−0.333765	+	0.333765i
$794$	15.8716	+	4.17781i	0.563261	+	0.148265i
$795$		0			0
$796$	−12.4609	+	22.0296i	−0.441664	+	0.780817i
$797$	23.6614			0.838130			0.419065	−	0.907956i	$-0.362358\pi$
$797$	23.6614			0.838130			0.419065	+	0.907956i	$0.362358\pi$
$798$	−4.27992	−	1.12658i	−0.151508	−	0.0398807i
$799$	−33.2142			−1.17503
$800$		0			0
$801$	−2.18770			−0.0772984
$802$	13.6046	+	3.58108i	0.480395	+	0.126452i
$803$	−13.8221			−0.487773
$804$	17.0934	−	30.2195i	0.602839	−	1.06576i
$805$		0			0
$806$	−79.3637	−	20.8906i	−2.79547	−	0.735839i
$807$	−11.5816	+	11.5816i	−0.407691	+	0.407691i
$808$	36.1677	−	0.478783i	1.27238	−	0.0168435i
$809$	−23.5574			−0.828235			−0.414117	−	0.910223i	$-0.635910\pi$
$809$	−23.5574			−0.828235			−0.414117	+	0.910223i	$0.635910\pi$
$810$		0			0
$811$	14.0698	+	14.0698i	0.494056	+	0.494056i	0.909581	−	0.415526i	$-0.136402\pi$
$811$	14.0698	+	14.0698i	0.494056	+	0.494056i	−0.415526	+	0.909581i	$0.636402\pi$
$812$	5.27396	−	9.32383i	0.185080	−	0.327202i
$813$			9.54627i			0.334802i
$814$	2.39377	−	1.39617i	0.0839017	−	0.0489356i
$815$		0			0
$816$	−53.0132	−	13.2066i	−1.85583	−	0.462325i
$817$	−10.2680	+	10.2680i	−0.359233	+	0.359233i
$818$	33.7981	+	8.89652i	1.18172	+	0.311060i
$819$	2.07354	+	2.07354i	0.0724552	+	0.0724552i
$820$		0			0
$821$	−28.1332	+	28.1332i	−0.981855	+	0.981855i	−0.999838	−	0.0179834i	$-0.994275\pi$
$821$	−28.1332	+	28.1332i	−0.981855	+	0.981855i	0.0179834	+	0.999838i	$0.494275\pi$
$822$	3.18803	+	5.46600i	0.111195	+	0.190649i
$823$	−27.6068	−	27.6068i	−0.962313	−	0.962313i	0.0370020	−	0.999315i	$-0.488219\pi$
$823$	−27.6068	−	27.6068i	−0.962313	−	0.962313i	−0.999315	+	0.0370020i	$0.988219\pi$
$824$	−0.470888	−	35.5713i	−0.0164041	−	1.23918i
$825$		0			0
$826$	−2.71904	+	10.3297i	−0.0946075	+	0.359416i
$827$	6.79320			0.236223			0.118111	−	0.993000i	$-0.462316\pi$
$827$	6.79320			0.236223			0.118111	+	0.993000i	$0.462316\pi$
$828$	−0.848878	−	3.05979i	−0.0295006	−	0.106335i
$829$	−25.7474	+	25.7474i	−0.894245	+	0.894245i	−0.994919	−	0.100675i	$-0.967900\pi$
$829$	−25.7474	+	25.7474i	−0.894245	+	0.894245i	0.100675	+	0.994919i	$0.467900\pi$
$830$		0			0
$831$		−	8.69755i		−	0.301715i
$832$	−47.2213	+	1.25044i	−1.63710	+	0.0433511i
$833$	30.8385	+	30.8385i	1.06849	+	1.06849i
$834$	−7.68552	+	4.48257i	−0.266128	+	0.155219i
$835$		0			0
$836$	−1.84634	+	3.26415i	−0.0638572	+	0.112893i
$837$		−	46.1096i		−	1.59378i
$838$	13.0526	+	22.3791i	0.450893	+	0.773073i
$839$			11.4280i			0.394538i	0.980349	+	0.197269i	$0.0632073\pi$
$839$			11.4280i			0.394538i	−0.980349	+	0.197269i	$0.936793\pi$
$840$		0			0
$841$			1.33022i			0.0458696i
$842$	15.5315	−	9.05871i	0.535250	−	0.312184i
$843$		−	49.9387i		−	1.71998i
$844$	7.01392	−	1.94587i	0.241429	−	0.0669797i
$845$		0			0
$846$	1.57823	+	2.70592i	0.0542605	+	0.0930315i
$847$	−6.98522	−	6.98522i	−0.240015	−	0.240015i
$848$	17.7385	+	29.5087i	0.609143	+	1.01333i
$849$		−	3.95983i		−	0.135901i
$850$		0			0
$851$	−3.95866	+	3.95866i	−0.135701	+	0.135701i
$852$	−30.3511	−	17.1679i	−1.03981	−	0.588163i
$853$	−9.67475			−0.331257			−0.165629	−	0.986188i	$-0.552965\pi$
$853$	−9.67475			−0.331257			−0.165629	+	0.986188i	$0.552965\pi$
$854$	−3.13473	−	0.825142i	−0.107268	−	0.0282358i
$855$		0			0
$856$	18.8351	+	18.3429i	0.643770	+	0.626948i
$857$	26.5831	+	26.5831i	0.908061	+	0.908061i	0.996116	−	0.0880544i	$-0.0280649\pi$
$857$	26.5831	+	26.5831i	0.908061	+	0.908061i	−0.0880544	+	0.996116i	$0.528065\pi$
$858$	15.3486	−	8.95206i	0.523993	−	0.305618i
$859$	−1.58572	+	1.58572i	−0.0541040	+	0.0541040i	−0.733641	−	0.679537i	$-0.762181\pi$
$859$	−1.58572	+	1.58572i	−0.0541040	+	0.0541040i	0.679537	+	0.733641i	$0.262181\pi$
$860$		0			0
$861$	5.29290	+	5.29290i	0.180382	+	0.180382i
$862$	−7.49424	+	28.4708i	−0.255255	+	0.969719i
$863$	−9.59115	+	9.59115i	−0.326486	+	0.326486i	−0.851249	−	0.524762i	$-0.824154\pi$
$863$	−9.59115	+	9.59115i	−0.326486	+	0.326486i	0.524762	+	0.851249i	$0.324154\pi$
$864$	−7.43310	−	25.4786i	−0.252879	−	0.866798i
$865$		0			0
$866$	7.75879	+	13.3027i	0.263654	+	0.452045i
$867$			68.1426i			2.31424i
$868$	−5.35029	−	19.2852i	−0.181601	−	0.654581i
$869$	1.37147	+	1.37147i	0.0465241	+	0.0465241i
$870$		0			0
$871$	−54.8864			−1.85975
$872$	16.4240	−	0.217418i	0.556186	−	0.00736271i
$873$	2.17763	−	2.17763i	0.0737015	−	0.0737015i
$874$	1.92854	−	7.32657i	0.0652338	−	0.247825i
$875$		0			0
$876$	−43.6629	+	12.1134i	−1.47523	+	0.409274i
$877$	32.7116			1.10459			0.552295	−	0.833649i	$-0.313752\pi$
$877$	32.7116			1.10459			0.552295	+	0.833649i	$0.313752\pi$
$878$	−13.8430	+	52.5900i	−0.467180	+	1.77483i
$879$	29.3661			0.990496
$880$		0			0
$881$	9.42337			0.317481			0.158741	−	0.987320i	$-0.449257\pi$
$881$	9.42337			0.317481			0.158741	+	0.987320i	$0.449257\pi$
$882$	1.04704	−	3.97773i	0.0352557	−	0.133937i
$883$	−13.1729			−0.443304			−0.221652	−	0.975126i	$-0.571145\pi$
$883$	−13.1729			−0.443304			−0.221652	+	0.975126i	$0.571145\pi$
$884$	23.0892	+	83.2254i	0.776575	+	2.79917i
$885$		0			0
$886$	6.16461	−	23.4195i	0.207104	−	0.786794i
$887$	7.04550	−	7.04550i	0.236565	−	0.236565i	−0.578861	−	0.815426i	$-0.696503\pi$
$887$	7.04550	−	7.04550i	0.236565	−	0.236565i	0.815426	+	0.578861i	$0.196503\pi$
$888$	6.33814	−	6.50820i	0.212694	−	0.218401i
$889$	11.0394			0.370251
$890$		0			0
$891$	8.23808	+	8.23808i	0.275986	+	0.275986i
$892$	26.0386	−	7.22389i	0.871836	−	0.241874i
$893$			7.47397i			0.250107i
$894$	4.69869	+	8.05608i	0.157148	+	0.269435i
$895$		0			0
$896$	−6.06525	−	9.79383i	−0.202626	−	0.327189i
$897$	−25.3825	+	25.3825i	−0.847497	+	0.847497i
$898$	−4.36659	+	16.5888i	−0.145715	+	0.553574i
$899$	−36.5546	−	36.5546i	−1.21916	−	1.21916i
$900$		0			0
$901$	44.5131	−	44.5131i	1.48295	−	1.48295i
$902$	5.47890	−	3.19556i	0.182427	−	0.106401i
$903$	11.8644	+	11.8644i	0.394821	+	0.394821i
$904$	0.397708	+	30.0432i	0.0132276	+	0.999223i
$905$		0			0
$906$	42.2719	+	11.1270i	1.40439	+	0.369671i
$907$	−45.4995			−1.51079			−0.755394	−	0.655271i	$-0.772554\pi$
$907$	−45.4995			−1.51079			−0.755394	+	0.655271i	$0.772554\pi$
$908$	12.6512	−	22.3661i	0.419846	−	0.742245i
$909$	−4.41047	+	4.41047i	−0.146286	+	0.146286i
$910$		0			0
$911$			41.2904i			1.36801i	0.729477	+	0.684005i	$0.239763\pi$
$911$			41.2904i			1.36801i	−0.729477	+	0.684005i	$0.760237\pi$
$912$	−2.97181	+	11.9292i	−0.0984064	+	0.395017i
$913$	11.1965	+	11.1965i	0.370549	+	0.370549i
$914$	−3.99559	−	6.85058i	−0.132162	−	0.226597i
$915$		0			0
$916$	1.48270	+	5.34440i	0.0489897	+	0.176584i
$917$			2.45674i			0.0811288i
$918$	−41.9177	+	24.4485i	−1.38349	+	0.806919i
$919$			20.1715i			0.665397i	0.943033	+	0.332698i	$0.107959\pi$
$919$			20.1715i			0.665397i	−0.943033	+	0.332698i	$0.892041\pi$
$920$		0			0
$921$			9.94759i			0.327784i
$922$	25.8579	+	44.3343i	0.851585	+	1.46007i
$923$			55.1255i			1.81448i
$924$	3.77161	+	2.13339i	0.124077	+	0.0701833i
$925$		0			0
$926$	−6.88956	+	4.01832i	−0.226405	+	0.132050i
$927$	4.33774	+	4.33774i	0.142470	+	0.142470i
$928$	−26.0916	−	14.3060i	−0.856498	−	0.469618i
$929$			8.18969i			0.268695i	0.990934	+	0.134348i	$0.0428939\pi$
$929$			8.18969i			0.268695i	−0.990934	+	0.134348i	$0.957106\pi$
$930$		0			0
$931$	6.93940	−	6.93940i	0.227430	−	0.227430i
$932$	20.1438	−	5.58849i	0.659831	−	0.183057i
$933$	29.5574			0.967667
$934$	3.90867	−	14.8491i	0.127896	−	0.485879i
$935$		0			0
$936$	5.68316	−	5.83565i	0.185760	−	0.190744i
$937$	−33.0511	−	33.0511i	−1.07973	−	1.07973i	−0.996533	−	0.0831985i	$-0.973486\pi$
$937$	−33.0511	−	33.0511i	−1.07973	−	1.07973i	−0.0831985	−	0.996533i	$-0.526514\pi$
$938$	−6.74361	−	11.5622i	−0.220187	−	0.377518i
$939$	27.0117	−	27.0117i	0.881495	−	0.881495i
$940$		0			0
$941$	26.6371	+	26.6371i	0.868345	+	0.868345i	0.992289	−	0.123944i	$-0.0395544\pi$
$941$	26.6371	+	26.6371i	0.868345	+	0.868345i	−0.123944	+	0.992289i	$0.539554\pi$
$942$	−12.9515	−	3.40918i	−0.421984	−	0.111077i
$943$	−9.06063	+	9.06063i	−0.295055	+	0.295055i
$944$	28.7915	+	7.17253i	0.937083	+	0.233446i
$945$		0			0
$946$	12.2813	−	7.16304i	0.399299	−	0.232891i
$947$		−	37.5777i		−	1.22111i	−0.791973	−	0.610556i	$-0.790946\pi$
$947$		−	37.5777i		−	1.22111i	0.791973	−	0.610556i	$-0.209054\pi$
$948$	5.53429	+	3.13043i	0.179745	+	0.101672i
$949$	50.6521	+	50.6521i	1.64424	+	1.64424i
$950$		0			0
$951$	−10.0546			−0.326042
$952$	−14.6951	+	15.0894i	−0.476271	+	0.489050i
$953$	7.96284	−	7.96284i	0.257942	−	0.257942i	−0.566275	−	0.824217i	$-0.691616\pi$
$953$	7.96284	−	7.96284i	0.257942	−	0.257942i	0.824217	+	0.566275i	$0.191616\pi$
$954$	−5.74155	−	1.51132i	−0.185890	−	0.0489309i
$955$		0			0
$956$	18.7598	+	10.6114i	0.606736	+	0.343196i
$957$	11.1928			0.361812
$958$	−0.197736	−	0.0520492i	−0.00638856	−	0.00168163i
$959$	2.43952			0.0787763
$960$		0			0
$961$	−65.5846			−2.11563
$962$	−13.8885	−	3.65580i	−0.447782	−	0.117868i
$963$	−4.53367			−0.146095
$964$	−25.3584	−	14.3438i	−0.816738	−	0.461982i
$965$		0			0
$966$	−8.46560	−	2.22836i	−0.272376	−	0.0716964i
$967$	16.6144	−	16.6144i	0.534282	−	0.534282i	−0.387562	−	0.921844i	$-0.626683\pi$
$967$	16.6144	−	16.6144i	0.534282	−	0.534282i	0.921844	+	0.387562i	$0.126683\pi$
$968$	−19.1451	+	19.6588i	−0.615348	+	0.631859i
$969$	22.4778			0.722092
$970$		0			0
$971$	−17.9269	−	17.9269i	−0.575301	−	0.575301i	0.358304	−	0.933605i	$-0.383355\pi$
$971$	−17.9269	−	17.9269i	−0.575301	−	0.575301i	−0.933605	+	0.358304i	$0.883355\pi$
$972$	8.74054	+	4.94403i	0.280353	+	0.158580i
$973$			3.43011i			0.109964i
$974$	−43.1741	+	25.1812i	−1.38339	+	0.806859i
$975$		0			0
$976$	−2.17663	+	8.73730i	−0.0696723	+	0.279674i
$977$	−35.0721	+	35.0721i	−1.12206	+	1.12206i	−0.130625	+	0.991432i	$0.541698\pi$
$977$	−35.0721	+	35.0721i	−1.12206	+	1.12206i	−0.991432	+	0.130625i	$0.958302\pi$
$978$	−39.0946	−	10.2907i	−1.25011	−	0.329060i
$979$	3.61368	+	3.61368i	0.115494	+	0.115494i
$980$		0			0
$981$	−2.00282	+	2.00282i	−0.0639451	+	0.0639451i
$982$	−16.9889	−	29.1281i	−0.542139	−	0.929517i
$983$	−24.9265	−	24.9265i	−0.795033	−	0.795033i	0.187274	−	0.982308i	$-0.440035\pi$
$983$	−24.9265	−	24.9265i	−0.795033	−	0.795033i	−0.982308	+	0.187274i	$0.940035\pi$
$984$	14.5068	−	14.8961i	0.462461	−	0.474869i
$985$		0			0
$986$	−13.8492	+	52.6136i	−0.441050	+	1.67556i
$987$	8.63592			0.274884
$988$	18.7277	−	5.19563i	0.595807	−	0.165295i
$989$	−20.3100	+	20.3100i	−0.645819	+	0.645819i
$990$		0			0
$991$			10.7686i			0.342076i	0.985264	+	0.171038i	$0.0547121\pi$
$991$			10.7686i			0.342076i	−0.985264	+	0.171038i	$0.945288\pi$
$992$	−53.3693	+	15.5699i	−1.69448	+	0.494346i
$993$	9.42916	+	9.42916i	0.299226	+	0.299226i
$994$	−11.6125	+	6.77299i	−0.368327	+	0.214826i
$995$		0			0
$996$	45.1810	+	25.5563i	1.43161	+	0.809783i
$997$			10.3858i			0.328922i	0.986384	+	0.164461i	$0.0525885\pi$
$997$			10.3858i			0.328922i	−0.986384	+	0.164461i	$0.947412\pi$
$998$	12.3888	+	21.2410i	0.392160	+	0.672372i
$999$		−	8.06906i		−	0.255294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.s.e.243.2	yes	24
4.3	odd	2		1600.2.s.e.943.9		24
5.2	odd	4		400.2.j.e.307.8	yes	24
5.3	odd	4		400.2.j.e.307.5	yes	24
5.4	even	2	inner	400.2.s.e.243.11	yes	24
16.5	even	4		1600.2.j.e.143.9		24
16.11	odd	4		400.2.j.e.43.8	yes	24
20.3	even	4		1600.2.j.e.1007.9		24
20.7	even	4		1600.2.j.e.1007.4		24
20.19	odd	2		1600.2.s.e.943.4		24
80.27	even	4	inner	400.2.s.e.107.2	yes	24
80.37	odd	4		1600.2.s.e.207.9		24
80.43	even	4	inner	400.2.s.e.107.11	yes	24
80.53	odd	4		1600.2.s.e.207.4		24
80.59	odd	4		400.2.j.e.43.5	✓	24
80.69	even	4		1600.2.j.e.143.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.j.e.43.5	✓	24	80.59	odd	4
400.2.j.e.43.8	yes	24	16.11	odd	4
400.2.j.e.307.5	yes	24	5.3	odd	4
400.2.j.e.307.8	yes	24	5.2	odd	4
400.2.s.e.107.2	yes	24	80.27	even	4	inner
400.2.s.e.107.11	yes	24	80.43	even	4	inner
400.2.s.e.243.2	yes	24	1.1	even	1	trivial
400.2.s.e.243.11	yes	24	5.4	even	2	inner
1600.2.j.e.143.4		24	80.69	even	4
1600.2.j.e.143.9		24	16.5	even	4
1600.2.j.e.1007.4		24	20.7	even	4
1600.2.j.e.1007.9		24	20.3	even	4
1600.2.s.e.207.4		24	80.53	odd	4
1600.2.s.e.207.9		24	80.37	odd	4
1600.2.s.e.943.4		24	20.19	odd	2
1600.2.s.e.943.9		24	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.36763 - 0.359994i) q^{2} -1.86755 q^{3} +(1.74081 + 0.984676i) q^{4} +(2.55411 + 0.672307i) q^{6} +(0.719989 - 0.719989i) q^{7} +(-2.02630 - 1.97335i) q^{8} +0.487737 q^{9} +O(q^{10})\)	\(q+(-1.36763 - 0.359994i) q^{2} -1.86755 q^{3} +(1.74081 + 0.984676i) q^{4} +(2.55411 + 0.672307i) q^{6} +(0.719989 - 0.719989i) q^{7} +(-2.02630 - 1.97335i) q^{8} +0.487737 q^{9} +(-0.805654 - 0.805654i) q^{11} +(-3.25104 - 1.83893i) q^{12} +5.90473i q^{13} +(-1.24387 + 0.725484i) q^{14} +(2.06082 + 3.42827i) q^{16} +(5.17145 - 5.17145i) q^{17} +(-0.667042 - 0.175583i) q^{18} +(-1.16370 - 1.16370i) q^{19} +(-1.34461 + 1.34461i) q^{21} +(0.811804 + 1.39187i) q^{22} +(-2.30177 - 2.30177i) q^{23} +(3.78421 + 3.68533i) q^{24} +(2.12567 - 8.07547i) q^{26} +4.69177 q^{27} +(1.96232 - 0.544406i) q^{28} +(3.71953 - 3.71953i) q^{29} -9.82775i q^{31} +(-1.58428 - 5.43047i) q^{32} +(1.50460 + 1.50460i) q^{33} +(-8.93430 + 5.21092i) q^{34} +(0.849056 + 0.480263i) q^{36} -1.71983i q^{37} +(1.17258 + 2.01043i) q^{38} -11.0274i q^{39} -3.93637i q^{41} +(2.32298 - 1.35488i) q^{42} -8.82362i q^{43} +(-0.609181 - 2.19580i) q^{44} +(2.31934 + 3.97659i) q^{46} +(-3.21130 - 3.21130i) q^{47} +(-3.84869 - 6.40245i) q^{48} +5.96323i q^{49} +(-9.65793 + 9.65793i) q^{51} +(-5.81425 + 10.2790i) q^{52} +8.60748 q^{53} +(-6.41660 - 1.68901i) q^{54} +(-2.87970 + 0.0381211i) q^{56} +(2.17326 + 2.17326i) q^{57} +(-6.42594 + 3.74792i) q^{58} +(5.24522 - 5.24522i) q^{59} +(1.59176 + 1.59176i) q^{61} +(-3.53793 + 13.4407i) q^{62} +(0.351165 - 0.351165i) q^{63} +(0.211769 + 7.99720i) q^{64} +(-1.51608 - 2.59938i) q^{66} +9.29532i q^{67} +(14.0947 - 3.91029i) q^{68} +(4.29867 + 4.29867i) q^{69} +9.33581 q^{71} +(-0.988300 - 0.962476i) q^{72} +(8.57821 - 8.57821i) q^{73} +(-0.619130 + 2.35209i) q^{74} +(-0.879909 - 3.17164i) q^{76} -1.16012 q^{77} +(-3.96979 + 15.0813i) q^{78} -1.70231 q^{79} -10.2253 q^{81} +(-1.41707 + 5.38349i) q^{82} -13.8974 q^{83} +(-3.66472 + 1.01671i) q^{84} +(-3.17645 + 12.0674i) q^{86} +(-6.94640 + 6.94640i) q^{87} +(0.0426568 + 3.22233i) q^{88} -4.48540 q^{89} +(4.25134 + 4.25134i) q^{91} +(-1.74044 - 6.27345i) q^{92} +18.3538i q^{93} +(3.23581 + 5.54791i) q^{94} +(2.95873 + 10.1417i) q^{96} +(4.46476 - 4.46476i) q^{97} +(2.14673 - 8.15548i) q^{98} +(-0.392947 - 0.392947i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} + 12 q^{6} + 40 q^{9}+O(q^{10}) \) 24 * q + 8 * q^4 + 12 * q^6 + 40 * q^9	\( 24 q + 8 q^{4} + 12 q^{6} + 40 q^{9} - 20 q^{11} - 44 q^{14} - 4 q^{16} + 12 q^{19} - 24 q^{24} + 32 q^{26} - 8 q^{29} - 32 q^{34} - 60 q^{36} + 44 q^{44} - 76 q^{46} + 20 q^{51} - 16 q^{54} - 28 q^{56} - 8 q^{59} - 48 q^{61} + 32 q^{64} - 8 q^{66} + 64 q^{69} - 16 q^{71} - 36 q^{74} + 40 q^{76} + 104 q^{79} + 48 q^{81} - 44 q^{84} + 84 q^{86} - 96 q^{89} + 64 q^{91} + 40 q^{94} + 212 q^{96} - 128 q^{99}+O(q^{100}) \) 24 * q + 8 * q^4 + 12 * q^6 + 40 * q^9 - 20 * q^11 - 44 * q^14 - 4 * q^16 + 12 * q^19 - 24 * q^24 + 32 * q^26 - 8 * q^29 - 32 * q^34 - 60 * q^36 + 44 * q^44 - 76 * q^46 + 20 * q^51 - 16 * q^54 - 28 * q^56 - 8 * q^59 - 48 * q^61 + 32 * q^64 - 8 * q^66 + 64 * q^69 - 16 * q^71 - 36 * q^74 + 40 * q^76 + 104 * q^79 + 48 * q^81 - 44 * q^84 + 84 * q^86 - 96 * q^89 + 64 * q^91 + 40 * q^94 + 212 * q^96 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more