LMFDB - Embedded newform 124.2.f.b.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,2,Mod(33,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("124.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	124.f (of order $5$, degree $4$, 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:	$0.990144985064$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			97.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	124.97
Dual form			124.2.f.b.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.690983 - 2.12663i) q^{3} -2.61803 q^{5} +(3.42705 - 2.48990i) q^{7} +(-1.61803 - 1.17557i) q^{9} +O(q^{10})$	\(q+(0.690983 - 2.12663i) q^{3} -2.61803 q^{5} +(3.42705 - 2.48990i) q^{7} +(-1.61803 - 1.17557i) q^{9} +(-2.61803 + 1.90211i) q^{11} +(0.736068 - 2.26538i) q^{13} +(-1.80902 + 5.56758i) q^{15} +(1.80902 + 1.31433i) q^{17} +(2.07295 + 6.37988i) q^{19} +(-2.92705 - 9.00854i) q^{21} +(5.04508 + 3.66547i) q^{23} +1.85410 q^{25} +(1.80902 - 1.31433i) q^{27} +(1.04508 + 3.21644i) q^{29} +(-5.30902 - 1.67760i) q^{31} +(2.23607 + 6.88191i) q^{33} +(-8.97214 + 6.51864i) q^{35} -8.70820 q^{37} +(-4.30902 - 3.13068i) q^{39} +(0.472136 + 1.45309i) q^{41} +(2.42705 + 7.46969i) q^{43} +(4.23607 + 3.07768i) q^{45} +(3.57295 - 10.9964i) q^{47} +(3.38197 - 10.4086i) q^{49} +(4.04508 - 2.93893i) q^{51} +(-10.6631 - 7.74721i) q^{53} +(6.85410 - 4.97980i) q^{55} +15.0000 q^{57} +(0.218847 - 0.673542i) q^{59} +2.00000 q^{61} -8.47214 q^{63} +(-1.92705 + 5.93085i) q^{65} +3.00000 q^{67} +(11.2812 - 8.19624i) q^{69} +(-1.54508 - 1.12257i) q^{71} +(-5.54508 + 4.02874i) q^{73} +(1.28115 - 3.94298i) q^{75} +(-4.23607 + 13.0373i) q^{77} +(-3.39919 - 10.4616i) q^{81} +(0.354102 + 1.08981i) q^{83} +(-4.73607 - 3.44095i) q^{85} +7.56231 q^{87} +(-10.5451 + 7.66145i) q^{89} +(-3.11803 - 9.59632i) q^{91} +(-7.23607 + 10.1311i) q^{93} +(-5.42705 - 16.7027i) q^{95} +(7.04508 - 5.11855i) q^{97} +6.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{3} - 6 q^{5} + 7 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 5 * q^3 - 6 * q^5 + 7 * q^7 - 2 * q^9	$ 4 q + 5 q^{3} - 6 q^{5} + 7 q^{7} - 2 q^{9} - 6 q^{11} - 6 q^{13} - 5 q^{15} + 5 q^{17} + 15 q^{19} - 5 q^{21} + 9 q^{23} - 6 q^{25} + 5 q^{27} - 7 q^{29} - 19 q^{31} - 18 q^{35} - 8 q^{37} - 15 q^{39} - 16 q^{41} + 3 q^{43} + 8 q^{45} + 21 q^{47} + 18 q^{49} + 5 q^{51} - 27 q^{53} + 14 q^{55} + 60 q^{57} + 21 q^{59} + 8 q^{61} - 16 q^{63} - q^{65} + 12 q^{67} + 25 q^{69} + 5 q^{71} - 11 q^{73} - 15 q^{75} - 8 q^{77} + 11 q^{81} - 12 q^{83} - 10 q^{85} - 10 q^{87} - 31 q^{89} - 8 q^{91} - 20 q^{93} - 15 q^{95} + 17 q^{97} + 8 q^{99}+O(q^{100}) $ 4 * q + 5 * q^3 - 6 * q^5 + 7 * q^7 - 2 * q^9 - 6 * q^11 - 6 * q^13 - 5 * q^15 + 5 * q^17 + 15 * q^19 - 5 * q^21 + 9 * q^23 - 6 * q^25 + 5 * q^27 - 7 * q^29 - 19 * q^31 - 18 * q^35 - 8 * q^37 - 15 * q^39 - 16 * q^41 + 3 * q^43 + 8 * q^45 + 21 * q^47 + 18 * q^49 + 5 * q^51 - 27 * q^53 + 14 * q^55 + 60 * q^57 + 21 * q^59 + 8 * q^61 - 16 * q^63 - q^65 + 12 * q^67 + 25 * q^69 + 5 * q^71 - 11 * q^73 - 15 * q^75 - 8 * q^77 + 11 * q^81 - 12 * q^83 - 10 * q^85 - 10 * q^87 - 31 * q^89 - 8 * q^91 - 20 * q^93 - 15 * q^95 + 17 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.690983	−	2.12663i	0.398939	−	1.22781i	−0.526912	−	0.849920i	$-0.676650\pi$
$3$	0.690983	−	2.12663i	0.398939	−	1.22781i	0.925851	−	0.377889i	$-0.123350\pi$
$4$		0			0
$5$	−2.61803			−1.17082			−0.585410	−	0.810737i	$-0.699067\pi$
$5$	−2.61803			−1.17082			−0.585410	+	0.810737i	$0.699067\pi$
$6$		0			0
$7$	3.42705	−	2.48990i	1.29530	−	0.941093i	0.295405	−	0.955372i	$-0.404545\pi$
$7$	3.42705	−	2.48990i	1.29530	−	0.941093i	0.999898	+	0.0142789i	$0.00454526\pi$
$8$		0			0
$9$	−1.61803	−	1.17557i	−0.539345	−	0.391857i
$10$		0			0
$11$	−2.61803	+	1.90211i	−0.789367	+	0.573509i	−0.907776	−	0.419456i	$-0.862221\pi$
$11$	−2.61803	+	1.90211i	−0.789367	+	0.573509i	0.118409	+	0.992965i	$0.462221\pi$
$12$		0			0
$13$	0.736068	−	2.26538i	0.204149	−	0.628305i	−0.795599	−	0.605824i	$-0.792844\pi$
$13$	0.736068	−	2.26538i	0.204149	−	0.628305i	0.999747	−	0.0224806i	$-0.00715641\pi$
$14$		0			0
$15$	−1.80902	+	5.56758i	−0.467086	+	1.43754i
$16$		0			0
$17$	1.80902	+	1.31433i	0.438751	+	0.318771i	0.785138	−	0.619320i	$-0.212592\pi$
$17$	1.80902	+	1.31433i	0.438751	+	0.318771i	−0.346387	+	0.938092i	$0.612592\pi$
$18$		0			0
$19$	2.07295	+	6.37988i	0.475567	+	1.46365i	0.845191	+	0.534464i	$0.179486\pi$
$19$	2.07295	+	6.37988i	0.475567	+	1.46365i	−0.369624	+	0.929181i	$0.620514\pi$
$20$		0			0
$21$	−2.92705	−	9.00854i	−0.638735	−	1.96582i
$22$		0			0
$23$	5.04508	+	3.66547i	1.05197	+	0.764303i	0.972587	−	0.232541i	$-0.0747039\pi$
$23$	5.04508	+	3.66547i	1.05197	+	0.764303i	0.0793863	+	0.996844i	$0.474704\pi$
$24$		0			0
$25$	1.85410			0.370820
$26$		0			0
$27$	1.80902	−	1.31433i	0.348145	−	0.252942i
$28$		0			0
$29$	1.04508	+	3.21644i	0.194067	+	0.597278i	0.999986	+	0.00525198i	$0.00167176\pi$
$29$	1.04508	+	3.21644i	0.194067	+	0.597278i	−0.805919	+	0.592026i	$0.798328\pi$
$30$		0			0
$31$	−5.30902	−	1.67760i	−0.953528	−	0.301306i
$31$	−5.30902	−	1.67760i	−0.953528	−	0.301306i
$32$		0			0
$33$	2.23607	+	6.88191i	0.389249	+	1.19799i
$34$		0			0
$35$	−8.97214	+	6.51864i	−1.51657	+	1.10185i
$36$		0			0
$37$	−8.70820			−1.43162			−0.715810	−	0.698295i	$-0.753942\pi$
$37$	−8.70820			−1.43162			−0.715810	+	0.698295i	$0.753942\pi$
$38$		0			0
$39$	−4.30902	−	3.13068i	−0.689995	−	0.501311i
$40$		0			0
$41$	0.472136	+	1.45309i	0.0737352	+	0.226934i	0.981131	−	0.193343i	$-0.0619330\pi$
$41$	0.472136	+	1.45309i	0.0737352	+	0.226934i	−0.907396	+	0.420277i	$0.861933\pi$
$42$		0			0
$43$	2.42705	+	7.46969i	0.370122	+	1.13912i	0.946711	+	0.322084i	$0.104383\pi$
$43$	2.42705	+	7.46969i	0.370122	+	1.13912i	−0.576589	+	0.817034i	$0.695617\pi$
$44$		0			0
$45$	4.23607	+	3.07768i	0.631476	+	0.458794i
$46$		0			0
$47$	3.57295	−	10.9964i	0.521168	−	1.60399i	−0.250603	−	0.968090i	$-0.580629\pi$
$47$	3.57295	−	10.9964i	0.521168	−	1.60399i	0.771771	−	0.635901i	$-0.219371\pi$
$48$		0			0
$49$	3.38197	−	10.4086i	0.483138	−	1.48695i
$50$		0			0
$51$	4.04508	−	2.93893i	0.566425	−	0.411532i
$52$		0			0
$53$	−10.6631	−	7.74721i	−1.46469	−	1.06416i	−0.982110	−	0.188311i	$-0.939699\pi$
$53$	−10.6631	−	7.74721i	−1.46469	−	1.06416i	−0.482582	−	0.875851i	$-0.660301\pi$
$54$		0			0
$55$	6.85410	−	4.97980i	0.924207	−	0.671476i
$56$		0			0
$57$	15.0000			1.98680
$58$		0			0
$59$	0.218847	−	0.673542i	0.0284915	−	0.0876877i	−0.935800	−	0.352532i	$-0.885321\pi$
$59$	0.218847	−	0.673542i	0.0284915	−	0.0876877i	0.964291	+	0.264845i	$0.0853207\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$		0			0
$63$	−8.47214			−1.06739
$64$		0			0
$65$	−1.92705	+	5.93085i	−0.239021	+	0.735632i
$66$		0			0
$67$	3.00000			0.366508			0.183254	−	0.983066i	$-0.441337\pi$
$67$	3.00000			0.366508			0.183254	+	0.983066i	$0.441337\pi$
$68$		0			0
$69$	11.2812	−	8.19624i	1.35809	−	0.986711i
$70$		0			0
$71$	−1.54508	−	1.12257i	−0.183368	−	0.133225i	0.492315	−	0.870417i	$-0.336151\pi$
$71$	−1.54508	−	1.12257i	−0.183368	−	0.133225i	−0.675682	+	0.737193i	$0.736151\pi$
$72$		0			0
$73$	−5.54508	+	4.02874i	−0.649003	+	0.471528i	−0.862931	−	0.505321i	$-0.831374\pi$
$73$	−5.54508	+	4.02874i	−0.649003	+	0.471528i	0.213928	+	0.976849i	$0.431374\pi$
$74$		0			0
$75$	1.28115	−	3.94298i	0.147935	−	0.455296i
$76$		0			0
$77$	−4.23607	+	13.0373i	−0.482745	+	1.48574i
$78$		0			0
$79$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$79$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$80$		0			0
$81$	−3.39919	−	10.4616i	−0.377687	−	1.16240i
$82$		0			0
$83$	0.354102	+	1.08981i	0.0388677	+	0.119623i	0.968608	−	0.248594i	$-0.0799685\pi$
$83$	0.354102	+	1.08981i	0.0388677	+	0.119623i	−0.929740	+	0.368217i	$0.879968\pi$
$84$		0			0
$85$	−4.73607	−	3.44095i	−0.513699	−	0.373224i
$86$		0			0
$87$	7.56231			0.810764
$88$		0			0
$89$	−10.5451	+	7.66145i	−1.11778	+	0.812112i	−0.983871	−	0.178882i	$-0.942752\pi$
$89$	−10.5451	+	7.66145i	−1.11778	+	0.812112i	−0.133906	+	0.990994i	$0.542752\pi$
$90$		0			0
$91$	−3.11803	−	9.59632i	−0.326859	−	1.00597i
$92$		0			0
$93$	−7.23607	+	10.1311i	−0.750345	+	1.05055i
$94$		0			0
$95$	−5.42705	−	16.7027i	−0.556804	−	1.71367i
$96$		0			0
$97$	7.04508	−	5.11855i	0.715320	−	0.519710i	−0.169566	−	0.985519i	$-0.554236\pi$
$97$	7.04508	−	5.11855i	0.715320	−	0.519710i	0.884886	+	0.465809i	$0.154236\pi$
$98$		0			0
$99$	6.47214			0.650474
$100$		0			0
$101$	3.85410	+	2.80017i	0.383497	+	0.278627i	0.762786	−	0.646651i	$-0.223831\pi$
$101$	3.85410	+	2.80017i	0.383497	+	0.278627i	−0.379288	+	0.925279i	$0.623831\pi$
$102$		0			0
$103$	4.28115	+	13.1760i	0.421835	+	1.29827i	0.905993	+	0.423293i	$0.139126\pi$
$103$	4.28115	+	13.1760i	0.421835	+	1.29827i	−0.484158	+	0.874980i	$0.660874\pi$
$104$		0			0
$105$	7.66312	+	23.5847i	0.747844	+	2.30163i
$106$		0			0
$107$	−5.73607	−	4.16750i	−0.554527	−	0.402887i	0.274925	−	0.961466i	$-0.411347\pi$
$107$	−5.73607	−	4.16750i	−0.554527	−	0.402887i	−0.829452	+	0.558578i	$0.811347\pi$
$108$		0			0
$109$	2.16312	−	6.65740i	0.207189	−	0.637663i	−0.792427	−	0.609967i	$-0.791183\pi$
$109$	2.16312	−	6.65740i	0.207189	−	0.637663i	0.999616	−	0.0276963i	$-0.00881713\pi$
$110$		0			0
$111$	−6.01722	+	18.5191i	−0.571129	+	1.75776i
$112$		0			0
$113$	−15.4443	+	11.2209i	−1.45287	+	1.05558i	−0.467726	+	0.883874i	$0.654927\pi$
$113$	−15.4443	+	11.2209i	−1.45287	+	1.05558i	−0.985149	+	0.171702i	$0.945073\pi$
$114$		0			0
$115$	−13.2082	−	9.59632i	−1.23167	−	0.894862i
$116$		0			0
$117$	−3.85410	+	2.80017i	−0.356312	+	0.258876i
$118$		0			0
$119$	9.47214			0.868309
$120$		0			0
$121$	−0.163119	+	0.502029i	−0.0148290	+	0.0456390i
$122$		0			0
$123$	3.41641			0.308047
$124$		0			0
$125$	8.23607			0.736656
$126$		0			0
$127$	−2.78115	+	8.55951i	−0.246787	+	0.759534i	0.748550	+	0.663078i	$0.230750\pi$
$127$	−2.78115	+	8.55951i	−0.246787	+	0.759534i	−0.995337	+	0.0964551i	$0.969250\pi$
$128$		0			0
$129$	17.5623			1.54627
$130$		0			0
$131$	12.1631	−	8.83702i	1.06270	−	0.772094i	0.0881112	−	0.996111i	$-0.471917\pi$
$131$	12.1631	−	8.83702i	1.06270	−	0.772094i	0.974585	+	0.224016i	$0.0719169\pi$
$132$		0			0
$133$	22.9894	+	16.7027i	1.99343	+	1.44831i
$134$		0			0
$135$	−4.73607	+	3.44095i	−0.407616	+	0.296150i
$136$		0			0
$137$	0.472136	−	1.45309i	0.0403373	−	0.124145i	−0.928860	−	0.370431i	$-0.879210\pi$
$137$	0.472136	−	1.45309i	0.0403373	−	0.124145i	0.969197	+	0.246285i	$0.0792101\pi$
$138$		0			0
$139$	0.899187	−	2.76741i	0.0762680	−	0.234729i	−0.905653	−	0.424019i	$-0.860619\pi$
$139$	0.899187	−	2.76741i	0.0762680	−	0.234729i	0.981921	+	0.189291i	$0.0606188\pi$
$140$		0			0
$141$	−20.9164	−	15.1967i	−1.76148	−	1.27979i
$142$		0			0
$143$	2.38197	+	7.33094i	0.199190	+	0.613044i
$144$		0			0
$145$	−2.73607	−	8.42075i	−0.227218	−	0.699305i
$146$		0			0
$147$	−19.7984	−	14.3844i	−1.63294	−	1.18640i
$148$		0			0
$149$	−14.5623			−1.19299			−0.596495	−	0.802617i	$-0.703441\pi$
$149$	−14.5623			−1.19299			−0.596495	+	0.802617i	$0.703441\pi$
$150$		0			0
$151$	−6.16312	+	4.47777i	−0.501548	+	0.364396i	−0.809608	−	0.586971i	$-0.800320\pi$
$151$	−6.16312	+	4.47777i	−0.501548	+	0.364396i	0.308060	+	0.951367i	$0.400320\pi$
$152$		0			0
$153$	−1.38197	−	4.25325i	−0.111725	−	0.343855i
$154$		0			0
$155$	13.8992	+	4.39201i	1.11641	+	0.352775i
$156$		0			0
$157$	1.94427	+	5.98385i	0.155170	+	0.477564i	0.998178	−	0.0603371i	$-0.0192176\pi$
$157$	1.94427	+	5.98385i	0.155170	+	0.477564i	−0.843008	+	0.537901i	$0.819218\pi$
$158$		0			0
$159$	−23.8435	+	17.3233i	−1.89091	+	1.37383i
$160$		0			0
$161$	26.4164			2.08190
$162$		0			0
$163$	−8.04508	−	5.84510i	−0.630140	−	0.457823i	0.226309	−	0.974056i	$-0.427334\pi$
$163$	−8.04508	−	5.84510i	−0.630140	−	0.457823i	−0.856449	+	0.516232i	$0.827334\pi$
$164$		0			0
$165$	−5.85410	−	18.0171i	−0.455741	−	1.40263i
$166$		0			0
$167$	−3.90983	−	12.0332i	−0.302552	−	0.931158i	−0.980579	−	0.196122i	$-0.937165\pi$
$167$	−3.90983	−	12.0332i	−0.302552	−	0.931158i	0.678028	−	0.735036i	$-0.262835\pi$
$168$		0			0
$169$	5.92705	+	4.30625i	0.455927	+	0.331250i
$170$		0			0
$171$	4.14590	−	12.7598i	0.317045	−	0.975763i
$172$		0			0
$173$	2.28115	−	7.02067i	0.173433	−	0.533771i	−0.826126	−	0.563486i	$-0.809460\pi$
$173$	2.28115	−	7.02067i	0.173433	−	0.533771i	0.999558	+	0.0297146i	$0.00945985\pi$
$174$		0			0
$175$	6.35410	−	4.61653i	0.480325	−	0.348977i
$176$		0			0
$177$	−1.28115	−	0.930812i	−0.0962974	−	0.0699641i
$178$		0			0
$179$	−7.78115	+	5.65334i	−0.581591	+	0.422550i	−0.839297	−	0.543673i	$-0.817033\pi$
$179$	−7.78115	+	5.65334i	−0.581591	+	0.422550i	0.257707	+	0.966223i	$0.417033\pi$
$180$		0			0
$181$	−10.4164			−0.774245			−0.387123	−	0.922028i	$-0.626531\pi$
$181$	−10.4164			−0.774245			−0.387123	+	0.922028i	$0.626531\pi$
$182$		0			0
$183$	1.38197	−	4.25325i	0.102158	−	0.314410i
$184$		0			0
$185$	22.7984			1.67617
$186$		0			0
$187$	−7.23607			−0.529154
$188$		0			0
$189$	2.92705	−	9.00854i	0.212912	−	0.655275i
$190$		0			0
$191$	23.6180			1.70894			0.854470	−	0.519500i	$-0.173882\pi$
$191$	23.6180			1.70894			0.854470	+	0.519500i	$0.173882\pi$
$192$		0			0
$193$	−11.0172	+	8.00448i	−0.793037	+	0.576175i	−0.908863	−	0.417094i	$-0.863048\pi$
$193$	−11.0172	+	8.00448i	−0.793037	+	0.576175i	0.115826	+	0.993269i	$0.463048\pi$
$194$		0			0
$195$	11.2812	+	8.19624i	0.807860	+	0.586945i
$196$		0			0
$197$	7.19098	−	5.22455i	0.512336	−	0.372234i	−0.301373	−	0.953506i	$-0.597445\pi$
$197$	7.19098	−	5.22455i	0.512336	−	0.372234i	0.813709	+	0.581272i	$0.197445\pi$
$198$		0			0
$199$	−1.25329	+	3.85723i	−0.0888433	+	0.273432i	−0.985600	−	0.169092i	$-0.945917\pi$
$199$	−1.25329	+	3.85723i	−0.0888433	+	0.273432i	0.896757	+	0.442523i	$0.145917\pi$
$200$		0			0
$201$	2.07295	−	6.37988i	0.146215	−	0.450002i
$202$		0			0
$203$	11.5902	+	8.42075i	0.813470	+	0.591021i
$204$		0			0
$205$	−1.23607	−	3.80423i	−0.0863307	−	0.265699i
$206$		0			0
$207$	−3.85410	−	11.8617i	−0.267879	−	0.824446i
$208$		0			0
$209$	−17.5623	−	12.7598i	−1.21481	−	0.882611i
$210$		0			0
$211$	25.8885			1.78224			0.891120	−	0.453767i	$-0.149920\pi$
$211$	25.8885			1.78224			0.891120	+	0.453767i	$0.149920\pi$
$212$		0			0
$213$	−3.45492	+	2.51014i	−0.236727	+	0.171992i
$214$		0			0
$215$	−6.35410	−	19.5559i	−0.433346	−	1.33370i
$216$		0			0
$217$	−22.3713	+	7.46969i	−1.51866	+	0.507076i
$218$		0			0
$219$	4.73607	+	14.5761i	0.320034	+	0.984963i
$220$		0			0
$221$	4.30902	−	3.13068i	0.289856	−	0.210593i
$222$		0			0
$223$	5.47214			0.366441			0.183221	−	0.983072i	$-0.441348\pi$
$223$	5.47214			0.366441			0.183221	+	0.983072i	$0.441348\pi$
$224$		0			0
$225$	−3.00000	−	2.17963i	−0.200000	−	0.145309i
$226$		0			0
$227$	−2.68034	−	8.24924i	−0.177900	−	0.547521i	0.821854	−	0.569699i	$-0.192940\pi$
$227$	−2.68034	−	8.24924i	−0.177900	−	0.547521i	−0.999754	+	0.0221775i	$0.992940\pi$
$228$		0			0
$229$	−3.29180	−	10.1311i	−0.217528	−	0.669482i	−0.998964	−	0.0454975i	$-0.985513\pi$
$229$	−3.29180	−	10.1311i	−0.217528	−	0.669482i	0.781436	−	0.623985i	$-0.214487\pi$
$230$		0			0
$231$	24.7984	+	18.0171i	1.63161	+	1.18544i
$232$		0			0
$233$	2.75329	−	8.47375i	0.180374	−	0.555134i	−0.819464	−	0.573131i	$-0.805729\pi$
$233$	2.75329	−	8.47375i	0.180374	−	0.555134i	0.999838	+	0.0179966i	$0.00572880\pi$
$234$		0			0
$235$	−9.35410	+	28.7890i	−0.610194	+	1.87799i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−12.0902	−	8.78402i	−0.782048	−	0.568191i	0.123545	−	0.992339i	$-0.460574\pi$
$239$	−12.0902	−	8.78402i	−0.782048	−	0.568191i	−0.905593	+	0.424148i	$0.860574\pi$
$240$		0			0
$241$	0.427051	−	0.310271i	0.0275088	−	0.0199863i	−0.573946	−	0.818893i	$-0.694588\pi$
$241$	0.427051	−	0.310271i	0.0275088	−	0.0199863i	0.601455	+	0.798907i	$0.294588\pi$
$242$		0			0
$243$	−17.8885			−1.14755
$244$		0			0
$245$	−8.85410	+	27.2501i	−0.565668	+	1.74095i
$246$		0			0
$247$	15.9787			1.01670
$248$		0			0
$249$	2.56231			0.162380
$250$		0			0
$251$	5.23607	−	16.1150i	0.330498	−	1.01717i	−0.638400	−	0.769705i	$-0.720403\pi$
$251$	5.23607	−	16.1150i	0.330498	−	1.01717i	0.968898	−	0.247462i	$-0.0795967\pi$
$252$		0			0
$253$	−20.1803			−1.26873
$254$		0			0
$255$	−10.5902	+	7.69421i	−0.663182	+	0.481830i
$256$		0			0
$257$	−1.14590	−	0.832544i	−0.0714792	−	0.0519326i	0.551472	−	0.834194i	$-0.314066\pi$
$257$	−1.14590	−	0.832544i	−0.0714792	−	0.0519326i	−0.622951	+	0.782261i	$0.714066\pi$
$258$		0			0
$259$	−29.8435	+	21.6825i	−1.85438	+	1.34729i
$260$		0			0
$261$	2.09017	−	6.43288i	0.129378	−	0.398185i
$262$		0			0
$263$	−4.24671	+	13.0700i	−0.261863	+	0.805933i	0.730536	+	0.682874i	$0.239270\pi$
$263$	−4.24671	+	13.0700i	−0.261863	+	0.805933i	−0.992399	+	0.123059i	$0.960730\pi$
$264$		0			0
$265$	27.9164	+	20.2825i	1.71489	+	1.24594i
$266$		0			0
$267$	9.00658	+	27.7194i	0.551194	+	1.69640i
$268$		0			0
$269$	4.51722	+	13.9026i	0.275420	+	0.847655i	0.989108	+	0.147192i	$0.0470234\pi$
$269$	4.51722	+	13.9026i	0.275420	+	0.847655i	−0.713688	+	0.700464i	$0.752977\pi$
$270$		0			0
$271$	−9.82624	−	7.13918i	−0.596901	−	0.433674i	0.247876	−	0.968792i	$-0.420267\pi$
$271$	−9.82624	−	7.13918i	−0.596901	−	0.433674i	−0.844778	+	0.535117i	$0.820267\pi$
$272$		0			0
$273$	−22.5623			−1.36553
$274$		0			0
$275$	−4.85410	+	3.52671i	−0.292713	+	0.212669i
$276$		0			0
$277$	−4.82624	−	14.8536i	−0.289981	−	0.892468i	−0.984861	−	0.173343i	$-0.944543\pi$
$277$	−4.82624	−	14.8536i	−0.289981	−	0.892468i	0.694881	−	0.719125i	$-0.255457\pi$
$278$		0			0
$279$	6.61803	+	8.95554i	0.396211	+	0.536154i
$280$		0			0
$281$	−3.35410	−	10.3229i	−0.200089	−	0.615810i	−0.999879	−	0.0155311i	$-0.995056\pi$
$281$	−3.35410	−	10.3229i	−0.200089	−	0.615810i	0.799790	−	0.600279i	$-0.204944\pi$
$282$		0			0
$283$	22.6353	−	16.4455i	1.34553	−	0.977582i	0.346305	−	0.938122i	$-0.387436\pi$
$283$	22.6353	−	16.4455i	1.34553	−	0.977582i	0.999221	−	0.0394601i	$-0.0125638\pi$
$284$		0			0
$285$	−39.2705			−2.32618
$286$		0			0
$287$	5.23607	+	3.80423i	0.309075	+	0.224556i
$288$		0			0
$289$	−3.70820	−	11.4127i	−0.218130	−	0.671334i
$290$		0			0
$291$	−6.01722	−	18.5191i	−0.352736	−	1.08561i
$292$		0			0
$293$	25.1353	+	18.2618i	1.46842	+	1.06687i	0.981069	+	0.193660i	$0.0620359\pi$
$293$	25.1353	+	18.2618i	1.46842	+	1.06687i	0.487349	+	0.873208i	$0.337964\pi$
$294$		0			0
$295$	−0.572949	+	1.76336i	−0.0333584	+	0.102667i
$296$		0			0
$297$	−2.23607	+	6.88191i	−0.129750	+	0.399329i
$298$		0			0
$299$	12.0172	−	8.73102i	0.694974	−	0.504928i
$300$		0			0
$301$	26.9164	+	19.5559i	1.55144	+	1.12718i
$302$		0			0
$303$	8.61803	−	6.26137i	0.495093	−	0.359706i
$304$		0			0
$305$	−5.23607			−0.299816
$306$		0			0
$307$	−5.91641	+	18.2088i	−0.337667	+	1.03923i	0.627726	+	0.778434i	$0.283986\pi$
$307$	−5.91641	+	18.2088i	−0.337667	+	1.03923i	−0.965393	+	0.260799i	$0.916014\pi$
$308$		0			0
$309$	30.9787			1.76232
$310$		0			0
$311$	1.05573			0.0598648			0.0299324	−	0.999552i	$-0.490471\pi$
$311$	1.05573			0.0598648			0.0299324	+	0.999552i	$0.490471\pi$
$312$		0			0
$313$	8.56231	−	26.3521i	0.483970	−	1.48951i	−0.349497	−	0.936938i	$-0.613647\pi$
$313$	8.56231	−	26.3521i	0.483970	−	1.48951i	0.833467	−	0.552569i	$-0.186353\pi$
$314$		0			0
$315$	22.1803			1.24972
$316$		0			0
$317$	10.4721	−	7.60845i	0.588174	−	0.427333i	−0.253488	−	0.967339i	$-0.581578\pi$
$317$	10.4721	−	7.60845i	0.588174	−	0.427333i	0.841662	+	0.540005i	$0.181578\pi$
$318$		0			0
$319$	−8.85410	−	6.43288i	−0.495735	−	0.360172i
$320$		0			0
$321$	−12.8262	+	9.31881i	−0.715891	+	0.520125i
$322$		0			0
$323$	−4.63525	+	14.2658i	−0.257912	+	0.793773i
$324$		0			0
$325$	1.36475	−	4.20025i	0.0757024	−	0.232988i
$326$		0			0
$327$	−12.6631	−	9.20029i	−0.700272	−	0.508777i
$328$		0			0
$329$	−15.1353	−	46.5815i	−0.834434	−	2.56812i
$330$		0			0
$331$	−6.95492	−	21.4050i	−0.382277	−	1.17653i	−0.938437	−	0.345451i	$-0.887726\pi$
$331$	−6.95492	−	21.4050i	−0.382277	−	1.17653i	0.556160	−	0.831075i	$-0.312274\pi$
$332$		0			0
$333$	14.0902	+	10.2371i	0.772137	+	0.560990i
$334$		0			0
$335$	−7.85410			−0.429115
$336$		0			0
$337$	−3.64590	+	2.64890i	−0.198605	+	0.144295i	−0.682643	−	0.730752i	$-0.739170\pi$
$337$	−3.64590	+	2.64890i	−0.198605	+	0.144295i	0.484038	+	0.875047i	$0.339170\pi$
$338$		0			0
$339$	13.1910	+	40.5977i	0.716436	+	2.20496i
$340$		0			0
$341$	17.0902	−	5.70634i	0.925485	−	0.309016i
$342$		0			0
$343$	−5.16312	−	15.8904i	−0.278782	−	0.858003i
$344$		0			0
$345$	−29.5344	+	21.4580i	−1.59008	+	1.15526i
$346$		0			0
$347$	0.527864			0.0283372			0.0141686	−	0.999900i	$-0.495490\pi$
$347$	0.527864			0.0283372			0.0141686	+	0.999900i	$0.495490\pi$
$348$		0			0
$349$	−9.13525	−	6.63715i	−0.488999	−	0.355279i	0.315800	−	0.948826i	$-0.397727\pi$
$349$	−9.13525	−	6.63715i	−0.488999	−	0.355279i	−0.804799	+	0.593547i	$0.797727\pi$
$350$		0			0
$351$	−1.64590	−	5.06555i	−0.0878515	−	0.270379i
$352$		0			0
$353$	3.59017	+	11.0494i	0.191085	+	0.588101i	1.00000		0.000174320i	$5.54877e-5\pi$
$353$	3.59017	+	11.0494i	0.191085	+	0.588101i	−0.808915	+	0.587926i	$0.799945\pi$
$354$		0			0
$355$	4.04508	+	2.93893i	0.214691	+	0.155982i
$356$		0			0
$357$	6.54508	−	20.1437i	0.346403	−	1.06612i
$358$		0			0
$359$	1.97214	−	6.06961i	0.104085	−	0.320342i	−0.885429	−	0.464774i	$-0.846136\pi$
$359$	1.97214	−	6.06961i	0.104085	−	0.320342i	0.989515	+	0.144432i	$0.0461356\pi$
$360$		0			0
$361$	−21.0344	+	15.2824i	−1.10708	+	0.804338i
$362$		0			0
$363$	0.954915	+	0.693786i	0.0501200	+	0.0364143i
$364$		0			0
$365$	14.5172	−	10.5474i	0.759866	−	0.552075i
$366$		0			0
$367$	−19.6180			−1.02405			−0.512027	−	0.858970i	$-0.671105\pi$
$367$	−19.6180			−1.02405			−0.512027	+	0.858970i	$0.671105\pi$
$368$		0			0
$369$	0.944272	−	2.90617i	0.0491568	−	0.151289i
$370$		0			0
$371$	−55.8328			−2.89870
$372$		0			0
$373$	−5.29180			−0.273999			−0.136999	−	0.990571i	$-0.543746\pi$
$373$	−5.29180			−0.273999			−0.136999	+	0.990571i	$0.543746\pi$
$374$		0			0
$375$	5.69098	−	17.5150i	0.293881	−	0.904473i
$376$		0			0
$377$	8.05573			0.414891
$378$		0			0
$379$	0.572949	−	0.416272i	0.0294304	−	0.0213824i	−0.572973	−	0.819574i	$-0.694210\pi$
$379$	0.572949	−	0.416272i	0.0294304	−	0.0213824i	0.602403	+	0.798192i	$0.294210\pi$
$380$		0			0
$381$	16.2812	+	11.8290i	0.834109	+	0.606015i
$382$		0			0
$383$	9.39919	−	6.82891i	0.480276	−	0.348941i	−0.321157	−	0.947026i	$-0.604072\pi$
$383$	9.39919	−	6.82891i	0.480276	−	0.348941i	0.801433	+	0.598085i	$0.204072\pi$
$384$		0			0
$385$	11.0902	−	34.1320i	0.565207	−	1.73953i
$386$		0			0
$387$	4.85410	−	14.9394i	0.246748	−	0.759412i
$388$		0			0
$389$	−3.89919	−	2.83293i	−0.197697	−	0.143635i	0.484533	−	0.874773i	$-0.338990\pi$
$389$	−3.89919	−	2.83293i	−0.197697	−	0.143635i	−0.682230	+	0.731138i	$0.738990\pi$
$390$		0			0
$391$	4.30902	+	13.2618i	0.217916	+	0.670678i
$392$		0			0
$393$	−10.3885	−	31.9727i	−0.524033	−	1.61281i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	5.81966			0.292080			0.146040	−	0.989279i	$-0.453347\pi$
$397$	5.81966			0.292080			0.146040	+	0.989279i	$0.453347\pi$
$398$		0			0
$399$	51.4058	−	37.3485i	2.57351	−	1.86976i
$400$		0			0
$401$	1.25329	+	3.85723i	0.0625863	+	0.192621i	0.977461	−	0.211118i	$-0.0677105\pi$
$401$	1.25329	+	3.85723i	0.0625863	+	0.192621i	−0.914874	+	0.403739i	$0.867710\pi$
$402$		0			0
$403$	−7.70820	+	10.7921i	−0.383973	+	0.537595i
$404$		0			0
$405$	8.89919	+	27.3889i	0.442204	+	1.36096i
$406$		0			0
$407$	22.7984	−	16.5640i	1.13007	−	0.821046i
$408$		0			0
$409$	9.23607			0.456694			0.228347	−	0.973580i	$-0.426668\pi$
$409$	9.23607			0.456694			0.228347	+	0.973580i	$0.426668\pi$
$410$		0			0
$411$	−2.76393	−	2.00811i	−0.136335	−	0.0990530i
$412$		0			0
$413$	−0.927051	−	2.85317i	−0.0456172	−	0.140395i
$414$		0			0
$415$	−0.927051	−	2.85317i	−0.0455071	−	0.140057i
$416$		0			0
$417$	−5.26393	−	3.82447i	−0.257776	−	0.187285i
$418$		0			0
$419$	−1.85410	+	5.70634i	−0.0905788	+	0.278773i	−0.986076	−	0.166294i	$-0.946820\pi$
$419$	−1.85410	+	5.70634i	−0.0905788	+	0.278773i	0.895497	+	0.445067i	$0.146820\pi$
$420$		0			0
$421$	−3.61803	+	11.1352i	−0.176332	+	0.542695i	−0.999692	−	0.0248253i	$-0.992097\pi$
$421$	−3.61803	+	11.1352i	−0.176332	+	0.542695i	0.823360	+	0.567520i	$0.192097\pi$
$422$		0			0
$423$	−18.7082	+	13.5923i	−0.909624	+	0.660881i
$424$		0			0
$425$	3.35410	+	2.43690i	0.162698	+	0.118207i
$426$		0			0
$427$	6.85410	−	4.97980i	0.331693	−	0.240989i
$428$		0			0
$429$	17.2361			0.832165
$430$		0			0
$431$	−6.85410	+	21.0948i	−0.330150	+	1.01610i	0.638911	+	0.769280i	$0.279385\pi$
$431$	−6.85410	+	21.0948i	−0.330150	+	1.01610i	−0.969062	+	0.246818i	$0.920615\pi$
$432$		0			0
$433$	−7.41641			−0.356410			−0.178205	−	0.983993i	$-0.557029\pi$
$433$	−7.41641			−0.356410			−0.178205	+	0.983993i	$0.557029\pi$
$434$		0			0
$435$	−19.7984			−0.949259
$436$		0			0
$437$	−12.9271	+	39.7854i	−0.618385	+	1.90319i
$438$		0			0
$439$	0.708204			0.0338007			0.0169004	−	0.999857i	$-0.494620\pi$
$439$	0.708204			0.0338007			0.0169004	+	0.999857i	$0.494620\pi$
$440$		0			0
$441$	−17.7082	+	12.8658i	−0.843248	+	0.612655i
$442$		0			0
$443$	−7.85410	−	5.70634i	−0.373160	−	0.271116i	0.385360	−	0.922766i	$-0.374077\pi$
$443$	−7.85410	−	5.70634i	−0.373160	−	0.271116i	−0.758520	+	0.651650i	$0.774077\pi$
$444$		0			0
$445$	27.6074	−	20.0579i	1.30872	−	0.950838i
$446$		0			0
$447$	−10.0623	+	30.9686i	−0.475931	+	1.46476i
$448$		0			0
$449$	−4.38197	+	13.4863i	−0.206798	+	0.636458i	0.792837	+	0.609434i	$0.208603\pi$
$449$	−4.38197	+	13.4863i	−0.206798	+	0.636458i	−0.999635	+	0.0270243i	$0.991397\pi$
$450$		0			0
$451$	−4.00000	−	2.90617i	−0.188353	−	0.136846i
$452$		0			0
$453$	5.26393	+	16.2007i	0.247321	+	0.761176i
$454$		0			0
$455$	8.16312	+	25.1235i	0.382693	+	1.17781i
$456$		0			0
$457$	24.1525	+	17.5478i	1.12981	+	0.820852i	0.985666	−	0.168706i	$-0.0539588\pi$
$457$	24.1525	+	17.5478i	1.12981	+	0.820852i	0.144139	+	0.989557i	$0.453959\pi$
$458$		0			0
$459$	5.00000			0.233380
$460$		0			0
$461$	−23.3435	+	16.9600i	−1.08721	+	0.789907i	−0.978926	−	0.204213i	$-0.934536\pi$
$461$	−23.3435	+	16.9600i	−1.08721	+	0.789907i	−0.108287	+	0.994120i	$0.534536\pi$
$462$		0			0
$463$	0.381966	+	1.17557i	0.0177515	+	0.0546334i	0.959540	−	0.281573i	$-0.0908561\pi$
$463$	0.381966	+	1.17557i	0.0177515	+	0.0546334i	−0.941788	+	0.336206i	$0.890856\pi$
$464$		0			0
$465$	18.9443	−	26.5236i	0.878520	−	1.23000i
$466$		0			0
$467$	−5.12868	−	15.7844i	−0.237327	−	0.730417i	−0.996804	−	0.0798833i	$-0.974545\pi$
$467$	−5.12868	−	15.7844i	−0.237327	−	0.730417i	0.759477	−	0.650534i	$-0.225455\pi$
$468$		0			0
$469$	10.2812	−	7.46969i	0.474740	−	0.344918i
$470$		0			0
$471$	14.0689			0.648260
$472$		0			0
$473$	−20.5623	−	14.9394i	−0.945456	−	0.686914i
$474$		0			0
$475$	3.84346	+	11.8290i	0.176350	+	0.542749i
$476$		0			0
$477$	8.14590	+	25.0705i	0.372975	+	1.14790i
$478$		0			0
$479$	−26.6525	−	19.3642i	−1.21778	−	0.884771i	−0.221869	−	0.975077i	$-0.571216\pi$
$479$	−26.6525	−	19.3642i	−1.21778	−	0.884771i	−0.995914	+	0.0903056i	$0.971216\pi$
$480$		0			0
$481$	−6.40983	+	19.7274i	−0.292263	+	0.899493i
$482$		0			0
$483$	18.2533	−	56.1778i	0.830553	−	2.55618i
$484$		0			0
$485$	−18.4443	+	13.4005i	−0.837511	+	0.608488i
$486$		0			0
$487$	−14.7812	−	10.7391i	−0.669798	−	0.486637i	0.200160	−	0.979763i	$-0.435854\pi$
$487$	−14.7812	−	10.7391i	−0.669798	−	0.486637i	−0.869958	+	0.493127i	$0.835854\pi$
$488$		0			0
$489$	−17.9894	+	13.0700i	−0.813507	+	0.591047i
$490$		0			0
$491$	22.0689			0.995955			0.497977	−	0.867190i	$-0.334076\pi$
$491$	22.0689			0.995955			0.497977	+	0.867190i	$0.334076\pi$
$492$		0			0
$493$	−2.33688	+	7.19218i	−0.105248	+	0.323920i
$494$		0			0
$495$	−16.9443			−0.761588
$496$		0			0
$497$	−8.09017			−0.362894
$498$		0			0
$499$	0.482779	−	1.48584i	0.0216122	−	0.0665154i	−0.939669	−	0.342086i	$-0.888867\pi$
$499$	0.482779	−	1.48584i	0.0216122	−	0.0665154i	0.961281	+	0.275570i	$0.0888667\pi$
$500$		0			0
$501$	−28.2918			−1.26398
$502$		0			0
$503$	20.7254	−	15.0579i	0.924101	−	0.671399i	−0.0204404	−	0.999791i	$-0.506507\pi$
$503$	20.7254	−	15.0579i	0.924101	−	0.671399i	0.944541	+	0.328392i	$0.106507\pi$
$504$		0			0
$505$	−10.0902	−	7.33094i	−0.449007	−	0.326222i
$506$		0			0
$507$	13.2533	−	9.62908i	0.588599	−	0.427642i
$508$		0			0
$509$	−12.5902	+	38.7486i	−0.558049	+	1.71750i	0.129702	+	0.991553i	$0.458598\pi$
$509$	−12.5902	+	38.7486i	−0.558049	+	1.71750i	−0.687751	+	0.725947i	$0.741402\pi$
$510$		0			0
$511$	−8.97214	+	27.6134i	−0.396904	+	1.22154i
$512$		0			0
$513$	12.1353	+	8.81678i	0.535785	+	0.389270i
$514$		0			0
$515$	−11.2082	−	34.4953i	−0.493892	−	1.52004i
$516$		0			0
$517$	11.5623	+	35.5851i	0.508510	+	1.56503i
$518$		0			0
$519$	−13.3541	−	9.70232i	−0.586180	−	0.425885i
$520$		0			0
$521$	3.65248			0.160018			0.0800089	−	0.996794i	$-0.474505\pi$
$521$	3.65248			0.160018			0.0800089	+	0.996794i	$0.474505\pi$
$522$		0			0
$523$	−16.2254	+	11.7885i	−0.709488	+	0.515473i	−0.883009	−	0.469357i	$-0.844486\pi$
$523$	−16.2254	+	11.7885i	−0.709488	+	0.515473i	0.173520	+	0.984830i	$0.444486\pi$
$524$		0			0
$525$	−5.42705	−	16.7027i	−0.236856	−	0.728968i
$526$		0			0
$527$	−7.39919	−	10.0126i	−0.322314	−	0.436155i
$528$		0			0
$529$	4.90983	+	15.1109i	0.213471	+	0.656996i
$530$		0			0
$531$	−1.14590	+	0.832544i	−0.0497277	+	0.0361293i
$532$		0			0
$533$	3.63932			0.157636
$534$		0			0
$535$	15.0172	+	10.9106i	0.649251	+	0.471709i
$536$		0			0
$537$	6.64590	+	20.4540i	0.286792	+	0.882654i
$538$		0			0
$539$	10.9443	+	33.6830i	0.471403	+	1.45083i
$540$		0			0
$541$	−33.0344	−	24.0009i	−1.42026	−	1.03188i	−0.991728	−	0.128354i	$-0.959030\pi$
$541$	−33.0344	−	24.0009i	−1.42026	−	1.03188i	−0.428533	−	0.903526i	$-0.640970\pi$
$542$		0			0
$543$	−7.19756	+	22.1518i	−0.308877	+	0.950625i
$544$		0			0
$545$	−5.66312	+	17.4293i	−0.242581	+	0.746589i
$546$		0			0
$547$	28.4164	−	20.6457i	1.21500	−	0.882748i	0.219323	−	0.975652i	$-0.429615\pi$
$547$	28.4164	−	20.6457i	1.21500	−	0.882748i	0.995675	+	0.0929047i	$0.0296152\pi$
$548$		0			0
$549$	−3.23607	−	2.35114i	−0.138112	−	0.100344i
$550$		0			0
$551$	−18.3541	+	13.3350i	−0.781911	+	0.568092i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	15.7533	−	48.4836i	0.668690	−	2.05802i
$556$		0			0
$557$	30.0000			1.27114			0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000			1.27114			0.635570	+	0.772043i	$0.280765\pi$
$558$		0			0
$559$	18.7082			0.791273
$560$		0			0
$561$	−5.00000	+	15.3884i	−0.211100	+	0.649700i
$562$		0			0
$563$	−2.38197			−0.100388			−0.0501939	−	0.998739i	$-0.515984\pi$
$563$	−2.38197			−0.100388			−0.0501939	+	0.998739i	$0.515984\pi$
$564$		0			0
$565$	40.4336	−	29.3768i	1.70106	−	1.23589i
$566$		0			0
$567$	−37.6976	−	27.3889i	−1.58315	−	1.15022i
$568$		0			0
$569$	−10.8541	+	7.88597i	−0.455028	+	0.330597i	−0.791578	−	0.611069i	$-0.790740\pi$
$569$	−10.8541	+	7.88597i	−0.455028	+	0.330597i	0.336550	+	0.941666i	$0.390740\pi$
$570$		0			0
$571$	5.34346	−	16.4455i	0.223617	−	0.688222i	−0.774812	−	0.632191i	$-0.782156\pi$
$571$	5.34346	−	16.4455i	0.223617	−	0.688222i	0.998429	−	0.0560303i	$-0.0178444\pi$
$572$		0			0
$573$	16.3197	−	50.2267i	0.681764	−	2.09825i
$574$		0			0
$575$	9.35410	+	6.79615i	0.390093	+	0.283419i
$576$		0			0
$577$	5.10081	+	15.6987i	0.212350	+	0.653545i	0.999331	+	0.0365684i	$0.0116427\pi$
$577$	5.10081	+	15.6987i	0.212350	+	0.653545i	−0.786982	+	0.616977i	$0.788357\pi$
$578$		0			0
$579$	9.40983	+	28.9605i	0.391059	+	1.20356i
$580$		0			0
$581$	3.92705	+	2.85317i	0.162922	+	0.118369i
$582$		0			0
$583$	42.6525			1.76649
$584$		0			0
$585$	10.0902	−	7.33094i	0.417177	−	0.303097i
$586$		0			0
$587$	5.54508	+	17.0660i	0.228870	+	0.704390i	0.997876	+	0.0651477i	$0.0207519\pi$
$587$	5.54508	+	17.0660i	0.228870	+	0.704390i	−0.769005	+	0.639242i	$0.779248\pi$
$588$		0			0
$589$	−0.302439	−	37.3485i	−0.0124618	−	1.53892i
$590$		0			0
$591$	−6.14183	−	18.9026i	−0.252641	−	0.777550i
$592$		0			0
$593$	21.8885	−	15.9030i	0.898855	−	0.653056i	−0.0393168	−	0.999227i	$-0.512518\pi$
$593$	21.8885	−	15.9030i	0.898855	−	0.653056i	0.938172	+	0.346171i	$0.112518\pi$
$594$		0			0
$595$	−24.7984			−1.01663
$596$		0			0
$597$	7.33688	+	5.33056i	0.300279	+	0.218165i
$598$		0			0
$599$	10.6459	+	32.7647i	0.434980	+	1.33873i	0.893108	+	0.449843i	$0.148520\pi$
$599$	10.6459	+	32.7647i	0.434980	+	1.33873i	−0.458128	+	0.888886i	$0.651480\pi$
$600$		0			0
$601$	−9.27051	−	28.5317i	−0.378152	−	1.16383i	−0.941327	−	0.337495i	$-0.890420\pi$
$601$	−9.27051	−	28.5317i	−0.378152	−	1.16383i	0.563175	−	0.826337i	$-0.309580\pi$
$602$		0			0
$603$	−4.85410	−	3.52671i	−0.197674	−	0.143619i
$604$		0			0
$605$	0.427051	−	1.31433i	0.0173621	−	0.0534350i
$606$		0			0
$607$	8.90983	−	27.4216i	0.361639	−	1.11301i	−0.590420	−	0.807096i	$-0.701038\pi$
$607$	8.90983	−	27.4216i	0.361639	−	1.11301i	0.952059	−	0.305914i	$-0.0989620\pi$
$608$		0			0
$609$	25.9164	−	18.8294i	1.05019	−	0.763005i
$610$		0			0
$611$	−22.2812	−	16.1882i	−0.901399	−	0.654905i
$612$		0			0
$613$	−3.14590	+	2.28563i	−0.127062	+	0.0923157i	−0.649501	−	0.760361i	$-0.725022\pi$
$613$	−3.14590	+	2.28563i	−0.127062	+	0.0923157i	0.522439	+	0.852676i	$0.325022\pi$
$614$		0			0
$615$	−8.94427			−0.360668
$616$		0			0
$617$	11.7812	−	36.2587i	0.474291	−	1.45972i	−0.372620	−	0.927984i	$-0.621540\pi$
$617$	11.7812	−	36.2587i	0.474291	−	1.45972i	0.846911	−	0.531735i	$-0.178460\pi$
$618$		0			0
$619$	−14.8328			−0.596181			−0.298091	−	0.954538i	$-0.596350\pi$
$619$	−14.8328			−0.596181			−0.298091	+	0.954538i	$0.596350\pi$
$620$		0			0
$621$	13.9443			0.559564
$622$		0			0
$623$	−17.0623	+	52.5124i	−0.683587	+	2.10386i
$624$		0			0
$625$	−30.8328			−1.23331
$626$		0			0
$627$	−39.2705	+	28.5317i	−1.56831	+	1.13945i
$628$		0			0
$629$	−15.7533	−	11.4454i	−0.628125	−	0.456359i
$630$		0			0
$631$	14.6803	−	10.6659i	0.584415	−	0.424602i	−0.255898	−	0.966704i	$-0.582371\pi$
$631$	14.6803	−	10.6659i	0.584415	−	0.424602i	0.840313	+	0.542101i	$0.182371\pi$
$632$		0			0
$633$	17.8885	−	55.0553i	0.711006	−	2.18825i
$634$		0			0
$635$	7.28115	−	22.4091i	0.288944	−	0.889277i
$636$		0			0
$637$	−21.0902	−	15.3229i	−0.835623	−	0.607116i
$638$		0			0
$639$	1.18034	+	3.63271i	0.0466935	+	0.143708i
$640$		0			0
$641$	7.55166	+	23.2416i	0.298273	+	0.917989i	0.982102	+	0.188347i	$0.0603131\pi$
$641$	7.55166	+	23.2416i	0.298273	+	0.917989i	−0.683830	+	0.729642i	$0.739687\pi$
$642$		0			0
$643$	27.3885	+	19.8989i	1.08010	+	0.784738i	0.977700	−	0.210006i	$-0.0673483\pi$
$643$	27.3885	+	19.8989i	1.08010	+	0.784738i	0.102399	+	0.994743i	$0.467348\pi$
$644$		0			0
$645$	−45.9787			−1.81041
$646$		0			0
$647$	17.7082	−	12.8658i	0.696181	−	0.505805i	−0.182505	−	0.983205i	$-0.558421\pi$
$647$	17.7082	−	12.8658i	0.696181	−	0.505805i	0.878686	+	0.477400i	$0.158421\pi$
$648$		0			0
$649$	0.708204	+	2.17963i	0.0277994	+	0.0855579i
$650$		0			0
$651$	0.427051	+	52.7369i	0.0167374	+	2.06692i
$652$		0			0
$653$	−4.39919	−	13.5393i	−0.172153	−	0.529834i	0.827339	−	0.561704i	$-0.189854\pi$
$653$	−4.39919	−	13.5393i	−0.172153	−	0.529834i	−0.999492	+	0.0318696i	$0.989854\pi$
$654$		0			0
$655$	−31.8435	+	23.1356i	−1.24423	+	0.903984i
$656$		0			0
$657$	13.7082			0.534808
$658$		0			0
$659$	23.9164	+	17.3763i	0.931651	+	0.676884i	0.946396	−	0.323007i	$-0.104694\pi$
$659$	23.9164	+	17.3763i	0.931651	+	0.676884i	−0.0147455	+	0.999891i	$0.504694\pi$
$660$		0			0
$661$	0.461493	+	1.42033i	0.0179500	+	0.0552444i	0.959630	−	0.281264i	$-0.0907538\pi$
$661$	0.461493	+	1.42033i	0.0179500	+	0.0552444i	−0.941680	+	0.336509i	$0.890754\pi$
$662$		0			0
$663$	−3.68034	−	11.3269i	−0.142933	−	0.439901i
$664$		0			0
$665$	−60.1869	−	43.7284i	−2.33395	−	1.69571i
$666$		0			0
$667$	−6.51722	+	20.0579i	−0.252348	+	0.776647i
$668$		0			0
$669$	3.78115	−	11.6372i	0.146188	−	0.449920i
$670$		0			0
$671$	−5.23607	+	3.80423i	−0.202136	+	0.146861i
$672$		0			0
$673$	26.2254	+	19.0539i	1.01092	+	0.734473i	0.964401	−	0.264444i	$-0.0851885\pi$
$673$	26.2254	+	19.0539i	1.01092	+	0.734473i	0.0465149	+	0.998918i	$0.485189\pi$
$674$		0			0
$675$	3.35410	−	2.43690i	0.129099	−	0.0937962i
$676$		0			0
$677$	28.0689			1.07877			0.539387	−	0.842058i	$-0.318656\pi$
$677$	28.0689			1.07877			0.539387	+	0.842058i	$0.318656\pi$
$678$		0			0
$679$	11.3992	−	35.0831i	0.437461	−	1.34637i
$680$		0			0
$681$	−19.3951			−0.743223
$682$		0			0
$683$	−12.5967			−0.482001			−0.241001	−	0.970525i	$-0.577476\pi$
$683$	−12.5967			−0.482001			−0.241001	+	0.970525i	$0.577476\pi$
$684$		0			0
$685$	−1.23607	+	3.80423i	−0.0472277	+	0.145352i
$686$		0			0
$687$	−23.8197			−0.908777
$688$		0			0
$689$	−25.3992	+	18.4536i	−0.967632	+	0.703026i
$690$		0			0
$691$	32.4615	+	23.5847i	1.23489	+	0.897203i	0.997247	−	0.0741492i	$-0.0236241\pi$
$691$	32.4615	+	23.5847i	1.23489	+	0.897203i	0.237646	+	0.971352i	$0.423624\pi$
$692$		0			0
$693$	22.1803	−	16.1150i	0.842561	−	0.612157i
$694$		0			0
$695$	−2.35410	+	7.24518i	−0.0892962	+	0.274825i
$696$		0			0
$697$	−1.05573	+	3.24920i	−0.0399886	+	0.123072i
$698$		0			0
$699$	−16.1180	−	11.7104i	−0.609640	−	0.442929i
$700$		0			0
$701$	14.1353	+	43.5038i	0.533881	+	1.64312i	0.746054	+	0.665885i	$0.231946\pi$
$701$	14.1353	+	43.5038i	0.533881	+	1.64312i	−0.212173	+	0.977232i	$0.568054\pi$
$702$		0			0
$703$	−18.0517	−	55.5573i	−0.680831	−	2.09538i
$704$		0			0
$705$	54.7599	+	39.7854i	2.06238	+	1.49840i
$706$		0			0
$707$	20.1803			0.758960
$708$		0			0
$709$	−22.7705	+	16.5437i	−0.855164	+	0.621313i	−0.926565	−	0.376134i	$-0.877253\pi$
$709$	−22.7705	+	16.5437i	−0.855164	+	0.621313i	0.0714007	+	0.997448i	$0.477253\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−20.6353	−	27.9237i	−0.772796	−	1.04575i
$714$		0			0
$715$	−6.23607	−	19.1926i	−0.233216	−	0.717764i
$716$		0			0
$717$	−27.0344	+	19.6417i	−1.00962	+	0.733532i
$718$		0			0
$719$	−14.7984			−0.551886			−0.275943	−	0.961174i	$-0.588990\pi$
$719$	−14.7984			−0.551886			−0.275943	+	0.961174i	$0.588990\pi$
$720$		0			0
$721$	47.4787	+	34.4953i	1.76820	+	1.28467i
$722$		0			0
$723$	−0.364745	−	1.12257i	−0.0135650	−	0.0417488i
$724$		0			0
$725$	1.93769	+	5.96361i	0.0719642	+	0.221483i
$726$		0			0
$727$	24.3713	+	17.7068i	0.903882	+	0.656709i	0.939460	−	0.342658i	$-0.111327\pi$
$727$	24.3713	+	17.7068i	0.903882	+	0.656709i	−0.0355779	+	0.999367i	$0.511327\pi$
$728$		0			0
$729$	−2.16312	+	6.65740i	−0.0801155	+	0.246570i
$730$		0			0
$731$	−5.42705	+	16.7027i	−0.200727	+	0.617773i
$732$		0			0
$733$	21.4615	−	15.5927i	0.792698	−	0.575929i	−0.116065	−	0.993242i	$-0.537028\pi$
$733$	21.4615	−	15.5927i	0.792698	−	0.575929i	0.908763	+	0.417313i	$0.137028\pi$
$734$		0			0
$735$	51.8328	+	37.6587i	1.91188	+	1.38906i
$736$		0			0
$737$	−7.85410	+	5.70634i	−0.289310	+	0.210196i
$738$		0			0
$739$	17.7082			0.651407			0.325703	−	0.945472i	$-0.394399\pi$
$739$	17.7082			0.651407			0.325703	+	0.945472i	$0.394399\pi$
$740$		0			0
$741$	11.0410	−	33.9808i	0.405602	−	1.24831i
$742$		0			0
$743$	−9.03444			−0.331442			−0.165721	−	0.986173i	$-0.552995\pi$
$743$	−9.03444			−0.331442			−0.165721	+	0.986173i	$0.552995\pi$
$744$		0			0
$745$	38.1246			1.39678
$746$		0			0
$747$	0.708204	−	2.17963i	0.0259118	−	0.0797484i
$748$		0			0
$749$	−30.0344			−1.09743
$750$		0			0
$751$	−18.4615	+	13.4131i	−0.673669	+	0.489449i	−0.871252	−	0.490837i	$-0.836691\pi$
$751$	−18.4615	+	13.4131i	−0.673669	+	0.489449i	0.197582	+	0.980286i	$0.436691\pi$
$752$		0			0
$753$	−30.6525	−	22.2703i	−1.11704	−	0.811576i
$754$		0			0
$755$	16.1353	−	11.7229i	0.587222	−	0.426642i
$756$		0			0
$757$	−6.27051	+	19.2986i	−0.227906	+	0.701421i	0.770078	+	0.637950i	$0.220217\pi$
$757$	−6.27051	+	19.2986i	−0.227906	+	0.701421i	−0.997984	+	0.0634715i	$0.979783\pi$
$758$		0			0
$759$	−13.9443	+	42.9161i	−0.506145	+	1.55775i
$760$		0			0
$761$	−40.1418	−	29.1647i	−1.45514	−	1.05722i	−0.984596	−	0.174845i	$-0.944058\pi$
$761$	−40.1418	−	29.1647i	−1.45514	−	1.05722i	−0.470544	−	0.882376i	$-0.655942\pi$
$762$		0			0
$763$	−9.16312	−	28.2012i	−0.331727	−	1.02095i
$764$		0			0
$765$	3.61803	+	11.1352i	0.130810	+	0.402593i
$766$		0			0
$767$	−1.36475	−	0.991545i	−0.0492781	−	0.0358026i
$768$		0			0
$769$	−44.7984			−1.61547			−0.807735	−	0.589545i	$-0.799307\pi$
$769$	−44.7984			−1.61547			−0.807735	+	0.589545i	$0.799307\pi$
$770$		0			0
$771$	−2.56231	+	1.86162i	−0.0922792	+	0.0670448i
$772$		0			0
$773$	5.04508	+	15.5272i	0.181459	+	0.558474i	0.999869	−	0.0161606i	$-0.00514431\pi$
$773$	5.04508	+	15.5272i	0.181459	+	0.558474i	−0.818410	+	0.574634i	$0.805144\pi$
$774$		0			0
$775$	−9.84346	−	3.11044i	−0.353587	−	0.111730i
$776$		0			0
$777$	25.4894	+	78.4482i	0.914426	+	2.81431i
$778$		0			0
$779$	−8.29180	+	6.02434i	−0.297084	+	0.215844i
$780$		0			0
$781$	6.18034			0.221150
$782$		0			0
$783$	6.11803	+	4.44501i	0.218641	+	0.158852i
$784$		0			0
$785$	−5.09017	−	15.6659i	−0.181676	−	0.559141i
$786$		0			0
$787$	−14.4549	−	44.4877i	−0.515262	−	1.58581i	−0.782805	−	0.622268i	$-0.786212\pi$
$787$	−14.4549	−	44.4877i	−0.515262	−	1.58581i	0.267543	−	0.963546i	$-0.413788\pi$
$788$		0			0
$789$	24.8607	+	18.0623i	0.885064	+	0.643036i
$790$		0			0
$791$	−24.9894	+	76.9093i	−0.888519	+	2.73458i
$792$		0			0
$793$	1.47214	−	4.53077i	0.0522771	−	0.160892i
$794$		0			0
$795$	62.4230	−	45.3530i	2.21392	−	1.60850i
$796$		0			0
$797$	−7.14590	−	5.19180i	−0.253121	−	0.183903i	0.453988	−	0.891008i	$-0.350001\pi$
$797$	−7.14590	−	5.19180i	−0.253121	−	0.183903i	−0.707109	+	0.707105i	$0.750001\pi$
$798$		0			0
$799$	20.9164	−	15.1967i	0.739969	−	0.537619i
$800$		0			0
$801$	26.0689			0.921099
$802$		0			0
$803$	6.85410	−	21.0948i	0.241876	−	0.744418i
$804$		0			0
$805$	−69.1591			−2.43754
$806$		0			0
$807$	32.6869			1.15063
$808$		0			0
$809$	7.22542	−	22.2376i	0.254032	−	0.781831i	−0.739986	−	0.672622i	$-0.765168\pi$
$809$	7.22542	−	22.2376i	0.254032	−	0.781831i	0.994019	−	0.109209i	$-0.0348319\pi$
$810$		0			0
$811$	−30.7082			−1.07831			−0.539155	−	0.842206i	$-0.681256\pi$
$811$	−30.7082			−1.07831			−0.539155	+	0.842206i	$0.681256\pi$
$812$		0			0
$813$	−21.9721	+	15.9637i	−0.770596	+	0.559871i
$814$		0			0
$815$	21.0623	+	15.3027i	0.737780	+	0.536029i
$816$		0			0
$817$	−42.6246	+	30.9686i	−1.49125	+	1.08345i
$818$		0			0
$819$	−6.23607	+	19.1926i	−0.217906	+	0.670645i
$820$		0			0
$821$	12.1459	−	37.3812i	0.423895	−	1.30461i	−0.480154	−	0.877184i	$-0.659419\pi$
$821$	12.1459	−	37.3812i	0.423895	−	1.30461i	0.904049	−	0.427430i	$-0.140581\pi$
$822$		0			0
$823$	22.9894	+	16.7027i	0.801359	+	0.582221i	0.911312	−	0.411716i	$-0.135070\pi$
$823$	22.9894	+	16.7027i	0.801359	+	0.582221i	−0.109954	+	0.993937i	$0.535070\pi$
$824$		0			0
$825$	4.14590	+	12.7598i	0.144342	+	0.444238i
$826$		0			0
$827$	15.5000	+	47.7041i	0.538988	+	1.65883i	0.734871	+	0.678207i	$0.237243\pi$
$827$	15.5000	+	47.7041i	0.538988	+	1.65883i	−0.195883	+	0.980627i	$0.562757\pi$
$828$		0			0
$829$	−17.5623	−	12.7598i	−0.609964	−	0.443165i	0.239438	−	0.970912i	$-0.423037\pi$
$829$	−17.5623	−	12.7598i	−0.609964	−	0.443165i	−0.849402	+	0.527747i	$0.823037\pi$
$830$		0			0
$831$	−34.9230			−1.21146
$832$		0			0
$833$	19.7984	−	14.3844i	0.685973	−	0.498389i
$834$		0			0
$835$	10.2361	+	31.5034i	0.354234	+	1.09022i
$836$		0			0
$837$	−11.8090	+	3.94298i	−0.408179	+	0.136289i
$838$		0			0
$839$	−2.12868	−	6.55139i	−0.0734901	−	0.226179i	0.907564	−	0.419914i	$-0.137940\pi$
$839$	−2.12868	−	6.55139i	−0.0734901	−	0.226179i	−0.981054	+	0.193735i	$0.937940\pi$
$840$		0			0
$841$	14.2082	−	10.3229i	0.489938	−	0.355961i
$842$		0			0
$843$	−24.2705			−0.835921
$844$		0			0
$845$	−15.5172	−	11.2739i	−0.533809	−	0.387835i
$846$		0			0
$847$	0.690983	+	2.12663i	0.0237425	+	0.0730718i
$848$		0			0
$849$	−19.3328	−	59.5003i	−0.663501	−	2.04204i
$850$		0			0
$851$	−43.9336	−	31.9196i	−1.50603	−	1.09419i
$852$		0			0
$853$	−0.291796	+	0.898056i	−0.00999091	+	0.0307489i	−0.955928	−	0.293602i	$-0.905146\pi$
$853$	−0.291796	+	0.898056i	−0.00999091	+	0.0307489i	0.945937	+	0.324351i	$0.105146\pi$
$854$		0			0
$855$	−10.8541	+	33.4055i	−0.371202	+	1.14244i
$856$		0			0
$857$	−1.09017	+	0.792055i	−0.0372395	+	0.0270561i	−0.606249	−	0.795275i	$-0.707327\pi$
$857$	−1.09017	+	0.792055i	−0.0372395	+	0.0270561i	0.569010	+	0.822331i	$0.307327\pi$
$858$		0			0
$859$	10.4271	+	7.57570i	0.355766	+	0.258479i	0.751284	−	0.659979i	$-0.229435\pi$
$859$	10.4271	+	7.57570i	0.355766	+	0.258479i	−0.395518	+	0.918458i	$0.629435\pi$
$860$		0			0
$861$	11.7082	−	8.50651i	0.399015	−	0.289901i
$862$		0			0
$863$	−38.3820			−1.30654			−0.653269	−	0.757126i	$-0.726603\pi$
$863$	−38.3820			−1.30654			−0.653269	+	0.757126i	$0.726603\pi$
$864$		0			0
$865$	−5.97214	+	18.3803i	−0.203059	+	0.624950i
$866$		0			0
$867$	−26.8328			−0.911290
$868$		0			0
$869$		0			0
$870$		0			0
$871$	2.20820	−	6.79615i	0.0748221	−	0.230279i
$872$		0			0
$873$	−17.4164			−0.589456
$874$		0			0
$875$	28.2254	−	20.5070i	0.954194	−	0.693262i
$876$		0			0
$877$	−19.1803	−	13.9353i	−0.647674	−	0.470563i	0.214804	−	0.976657i	$-0.431089\pi$
$877$	−19.1803	−	13.9353i	−0.647674	−	0.470563i	−0.862478	+	0.506094i	$0.831089\pi$
$878$		0			0
$879$	56.2041	−	40.8347i	1.89572	−	1.37732i
$880$		0			0
$881$	14.3090	−	44.0386i	0.482083	−	1.48370i	−0.354078	−	0.935216i	$-0.615205\pi$
$881$	14.3090	−	44.0386i	0.482083	−	1.48370i	0.836162	−	0.548483i	$-0.184795\pi$
$882$		0			0
$883$	−12.9058	+	39.7199i	−0.434314	+	1.33668i	0.459475	+	0.888191i	$0.348038\pi$
$883$	−12.9058	+	39.7199i	−0.434314	+	1.33668i	−0.893788	+	0.448489i	$0.851962\pi$
$884$		0			0
$885$	3.35410	+	2.43690i	0.112747	+	0.0819154i
$886$		0			0
$887$	−8.59017	−	26.4378i	−0.288430	−	0.887695i	−0.985350	−	0.170546i	$-0.945447\pi$
$887$	−8.59017	−	26.4378i	−0.288430	−	0.887695i	0.696920	−	0.717149i	$-0.254553\pi$
$888$		0			0
$889$	11.7812	+	36.2587i	0.395127	+	1.21608i
$890$		0			0
$891$	28.7984	+	20.9232i	0.964782	+	0.700955i
$892$		0			0
$893$	77.5623			2.59552
$894$		0			0
$895$	20.3713	−	14.8006i	0.680938	−	0.494731i
$896$		0			0
$897$	−10.2639	−	31.5891i	−0.342703	−	1.05473i
$898$		0			0
$899$	−0.152476	−	18.8294i	−0.00508535	−	0.627995i
$900$		0			0
$901$	−9.10739	−	28.0297i	−0.303411	−	0.933804i
$902$		0			0
$903$	60.1869	−	43.7284i	2.00290	−	1.45519i
$904$		0			0
$905$	27.2705			0.906502
$906$		0			0
$907$	−32.2877	−	23.4584i	−1.07210	−	0.778924i	−0.0958086	−	0.995400i	$-0.530544\pi$
$907$	−32.2877	−	23.4584i	−1.07210	−	0.778924i	−0.976288	+	0.216476i	$0.930544\pi$
$908$		0			0
$909$	−2.94427	−	9.06154i	−0.0976553	−	0.300552i
$910$		0			0
$911$	3.76393	+	11.5842i	0.124705	+	0.383801i	0.993847	−	0.110760i	$-0.0353286\pi$
$911$	3.76393	+	11.5842i	0.124705	+	0.383801i	−0.869143	+	0.494562i	$0.835329\pi$
$912$		0			0
$913$	−3.00000	−	2.17963i	−0.0992855	−	0.0721351i
$914$		0			0
$915$	−3.61803	+	11.1352i	−0.119609	+	0.368117i
$916$		0			0
$917$	19.6803	−	60.5699i	0.649902	−	2.00019i
$918$		0			0
$919$	0.336881	−	0.244758i	0.0111127	−	0.00807383i	−0.582215	−	0.813035i	$-0.697814\pi$
$919$	0.336881	−	0.244758i	0.0111127	−	0.00807383i	0.593328	+	0.804961i	$0.297814\pi$
$920$		0			0
$921$	34.6353	+	25.1640i	1.14127	+	0.829182i
$922$		0			0
$923$	−3.68034	+	2.67392i	−0.121140	+	0.0880133i
$924$		0			0
$925$	−16.1459			−0.530874
$926$		0			0
$927$	8.56231	−	26.3521i	0.281223	−	0.865515i
$928$		0			0
$929$	45.1803			1.48232			0.741159	−	0.671329i	$-0.234276\pi$
$929$	45.1803			1.48232			0.741159	+	0.671329i	$0.234276\pi$
$930$		0			0
$931$	73.4164			2.40613
$932$		0			0
$933$	0.729490	−	2.24514i	0.0238824	−	0.0735026i
$934$		0			0
$935$	18.9443			0.619544
$936$		0			0
$937$	−31.5172	+	22.8986i	−1.02962	+	0.748065i	−0.968233	−	0.250049i	$-0.919553\pi$
$937$	−31.5172	+	22.8986i	−1.02962	+	0.748065i	−0.0613896	+	0.998114i	$0.519553\pi$
$938$		0			0
$939$	−50.1246	−	36.4177i	−1.63575	−	1.18845i
$940$		0			0
$941$	−23.1246	+	16.8010i	−0.753841	+	0.547697i	−0.897015	−	0.442000i	$-0.854269\pi$
$941$	−23.1246	+	16.8010i	−0.753841	+	0.547697i	0.143174	+	0.989698i	$0.454269\pi$
$942$		0			0
$943$	−2.94427	+	9.06154i	−0.0958787	+	0.295084i
$944$		0			0
$945$	−7.66312	+	23.5847i	−0.249281	+	0.767209i
$946$		0			0
$947$	41.7426	+	30.3278i	1.35645	+	0.985521i	0.998662	+	0.0517201i	$0.0164704\pi$
$947$	41.7426	+	30.3278i	1.35645	+	0.985521i	0.357792	+	0.933801i	$0.383530\pi$
$948$		0			0
$949$	5.04508	+	15.5272i	0.163770	+	0.504033i
$950$		0			0
$951$	−8.94427	−	27.5276i	−0.290038	−	0.892645i
$952$		0			0
$953$	−2.73607	−	1.98787i	−0.0886299	−	0.0643934i	0.542588	−	0.839999i	$-0.317445\pi$
$953$	−2.73607	−	1.98787i	−0.0886299	−	0.0643934i	−0.631218	+	0.775606i	$0.717445\pi$
$954$		0			0
$955$	−61.8328			−2.00086
$956$		0			0
$957$	−19.7984	+	14.3844i	−0.639991	+	0.464980i
$958$		0			0
$959$	−2.00000	−	6.15537i	−0.0645834	−	0.198767i
$960$		0			0
$961$	25.3713	+	17.8128i	0.818430	+	0.574607i
$962$		0			0
$963$	4.38197	+	13.4863i	0.141207	+	0.434590i
$964$		0			0
$965$	28.8435	−	20.9560i	0.928504	−	0.674597i
$966$		0			0
$967$	−48.8885			−1.57215			−0.786075	−	0.618131i	$-0.787890\pi$
$967$	−48.8885			−1.57215			−0.786075	+	0.618131i	$0.787890\pi$
$968$		0			0
$969$	27.1353	+	19.7149i	0.871710	+	0.633334i
$970$		0			0
$971$	10.9721	+	33.7688i	0.352113	+	1.08369i	0.957665	+	0.287886i	$0.0929523\pi$
$971$	10.9721	+	33.7688i	0.352113	+	1.08369i	−0.605552	+	0.795806i	$0.707048\pi$
$972$		0			0
$973$	−3.80902	−	11.7229i	−0.122111	−	0.375820i
$974$		0			0
$975$	−7.98936	−	5.80461i	−0.255864	−	0.185896i
$976$		0			0
$977$	9.29180	−	28.5972i	0.297271	−	0.914906i	−0.685178	−	0.728375i	$-0.740276\pi$
$977$	9.29180	−	28.5972i	0.297271	−	0.914906i	0.982449	−	0.186530i	$-0.0597243\pi$
$978$		0			0
$979$	13.0344	−	40.1159i	0.416583	−	1.28211i
$980$		0			0
$981$	−11.3262	+	8.22899i	−0.361619	+	0.262732i
$982$		0			0
$983$	5.87132	+	4.26577i	0.187266	+	0.136057i	0.677468	−	0.735552i	$-0.263077\pi$
$983$	5.87132	+	4.26577i	0.187266	+	0.136057i	−0.490202	+	0.871609i	$0.663077\pi$
$984$		0			0
$985$	−18.8262	+	13.6781i	−0.599854	+	0.435819i
$986$		0			0
$987$	−109.520			−3.48605
$988$		0			0
$989$	−15.1353	+	46.5815i	−0.481273	+	1.48121i
$990$		0			0
$991$	30.9787			0.984071			0.492036	−	0.870575i	$-0.336253\pi$
$991$	30.9787			0.984071			0.492036	+	0.870575i	$0.336253\pi$
$992$		0			0
$993$	−50.3262			−1.59705
$994$		0			0
$995$	3.28115	−	10.0984i	0.104020	−	0.320139i
$996$		0			0
$997$	−7.11146			−0.225222			−0.112611	−	0.993639i	$-0.535921\pi$
$997$	−7.11146			−0.225222			−0.112611	+	0.993639i	$0.535921\pi$
$998$		0			0
$999$	−15.7533	+	11.4454i	−0.498412	+	0.362118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.2.f.b.97.1	✓	4
3.2	odd	2		1116.2.m.c.469.1		4
4.3	odd	2		496.2.n.a.97.1		4
31.8	even	5	inner	124.2.f.b.101.1	yes	4
31.15	odd	10		3844.2.a.f.1.1		2
31.16	even	5		3844.2.a.g.1.2		2
93.8	odd	10		1116.2.m.c.721.1		4
124.39	odd	10		496.2.n.a.225.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.2.f.b.97.1	✓	4	1.1	even	1	trivial
124.2.f.b.101.1	yes	4	31.8	even	5	inner
496.2.n.a.97.1		4	4.3	odd	2
496.2.n.a.225.1		4	124.39	odd	10
1116.2.m.c.469.1		4	3.2	odd	2
1116.2.m.c.721.1		4	93.8	odd	10
3844.2.a.f.1.1		2	31.15	odd	10
3844.2.a.g.1.2		2	31.16	even	5

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	124.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.690983 - 2.12663i) q^{3} -2.61803 q^{5} +(3.42705 - 2.48990i) q^{7} +(-1.61803 - 1.17557i) q^{9} +O(q^{10})\)	\(q+(0.690983 - 2.12663i) q^{3} -2.61803 q^{5} +(3.42705 - 2.48990i) q^{7} +(-1.61803 - 1.17557i) q^{9} +(-2.61803 + 1.90211i) q^{11} +(0.736068 - 2.26538i) q^{13} +(-1.80902 + 5.56758i) q^{15} +(1.80902 + 1.31433i) q^{17} +(2.07295 + 6.37988i) q^{19} +(-2.92705 - 9.00854i) q^{21} +(5.04508 + 3.66547i) q^{23} +1.85410 q^{25} +(1.80902 - 1.31433i) q^{27} +(1.04508 + 3.21644i) q^{29} +(-5.30902 - 1.67760i) q^{31} +(2.23607 + 6.88191i) q^{33} +(-8.97214 + 6.51864i) q^{35} -8.70820 q^{37} +(-4.30902 - 3.13068i) q^{39} +(0.472136 + 1.45309i) q^{41} +(2.42705 + 7.46969i) q^{43} +(4.23607 + 3.07768i) q^{45} +(3.57295 - 10.9964i) q^{47} +(3.38197 - 10.4086i) q^{49} +(4.04508 - 2.93893i) q^{51} +(-10.6631 - 7.74721i) q^{53} +(6.85410 - 4.97980i) q^{55} +15.0000 q^{57} +(0.218847 - 0.673542i) q^{59} +2.00000 q^{61} -8.47214 q^{63} +(-1.92705 + 5.93085i) q^{65} +3.00000 q^{67} +(11.2812 - 8.19624i) q^{69} +(-1.54508 - 1.12257i) q^{71} +(-5.54508 + 4.02874i) q^{73} +(1.28115 - 3.94298i) q^{75} +(-4.23607 + 13.0373i) q^{77} +(-3.39919 - 10.4616i) q^{81} +(0.354102 + 1.08981i) q^{83} +(-4.73607 - 3.44095i) q^{85} +7.56231 q^{87} +(-10.5451 + 7.66145i) q^{89} +(-3.11803 - 9.59632i) q^{91} +(-7.23607 + 10.1311i) q^{93} +(-5.42705 - 16.7027i) q^{95} +(7.04508 - 5.11855i) q^{97} +6.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{3} - 6 q^{5} + 7 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 5 * q^3 - 6 * q^5 + 7 * q^7 - 2 * q^9	\( 4 q + 5 q^{3} - 6 q^{5} + 7 q^{7} - 2 q^{9} - 6 q^{11} - 6 q^{13} - 5 q^{15} + 5 q^{17} + 15 q^{19} - 5 q^{21} + 9 q^{23} - 6 q^{25} + 5 q^{27} - 7 q^{29} - 19 q^{31} - 18 q^{35} - 8 q^{37} - 15 q^{39} - 16 q^{41} + 3 q^{43} + 8 q^{45} + 21 q^{47} + 18 q^{49} + 5 q^{51} - 27 q^{53} + 14 q^{55} + 60 q^{57} + 21 q^{59} + 8 q^{61} - 16 q^{63} - q^{65} + 12 q^{67} + 25 q^{69} + 5 q^{71} - 11 q^{73} - 15 q^{75} - 8 q^{77} + 11 q^{81} - 12 q^{83} - 10 q^{85} - 10 q^{87} - 31 q^{89} - 8 q^{91} - 20 q^{93} - 15 q^{95} + 17 q^{97} + 8 q^{99}+O(q^{100}) \) 4 * q + 5 * q^3 - 6 * q^5 + 7 * q^7 - 2 * q^9 - 6 * q^11 - 6 * q^13 - 5 * q^15 + 5 * q^17 + 15 * q^19 - 5 * q^21 + 9 * q^23 - 6 * q^25 + 5 * q^27 - 7 * q^29 - 19 * q^31 - 18 * q^35 - 8 * q^37 - 15 * q^39 - 16 * q^41 + 3 * q^43 + 8 * q^45 + 21 * q^47 + 18 * q^49 + 5 * q^51 - 27 * q^53 + 14 * q^55 + 60 * q^57 + 21 * q^59 + 8 * q^61 - 16 * q^63 - q^65 + 12 * q^67 + 25 * q^69 + 5 * q^71 - 11 * q^73 - 15 * q^75 - 8 * q^77 + 11 * q^81 - 12 * q^83 - 10 * q^85 - 10 * q^87 - 31 * q^89 - 8 * q^91 - 20 * q^93 - 15 * q^95 + 17 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

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Database

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