LMFDB - Embedded newform 1452.2.i.l.1213.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1452,2,Mod(493,1452)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1452, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("1452.493");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1452 = 2^{2} \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1452.i (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.5942783735$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 132)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1213.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	1452.1213
Dual form			1452.2.i.l.565.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{3} +(-1.61803 - 1.17557i) q^{5} +(-0.618034 + 1.90211i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	$q+(-0.309017 - 0.951057i) q^{3} +(-1.61803 - 1.17557i) q^{5} +(-0.618034 + 1.90211i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(4.85410 - 3.52671i) q^{13} +(-0.618034 + 1.90211i) q^{15} +(-3.23607 - 2.35114i) q^{17} +(0.618034 + 1.90211i) q^{19} +2.00000 q^{21} -8.00000 q^{23} +(-0.309017 - 0.951057i) q^{25} +(0.809017 + 0.587785i) q^{27} +(3.23607 - 2.35114i) q^{35} +(-1.85410 + 5.70634i) q^{37} +(-4.85410 - 3.52671i) q^{39} -10.0000 q^{43} +2.00000 q^{45} +(2.42705 + 1.76336i) q^{49} +(-1.23607 + 3.80423i) q^{51} +(-11.3262 + 8.22899i) q^{53} +(1.61803 - 1.17557i) q^{57} +(-3.70820 + 11.4127i) q^{59} +(-11.3262 - 8.22899i) q^{61} +(-0.618034 - 1.90211i) q^{63} -12.0000 q^{65} +4.00000 q^{67} +(2.47214 + 7.60845i) q^{69} +(-1.85410 + 5.70634i) q^{73} +(-0.809017 + 0.587785i) q^{75} +(1.61803 - 1.17557i) q^{79} +(0.309017 - 0.951057i) q^{81} +(12.9443 + 9.40456i) q^{83} +(2.47214 + 7.60845i) q^{85} -14.0000 q^{89} +(3.70820 + 11.4127i) q^{91} +(1.23607 - 3.80423i) q^{95} +(1.61803 - 1.17557i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 2 q^{5} + 2 q^{7} - q^{9}+O(q^{10}) $ 4 * q + q^3 - 2 * q^5 + 2 * q^7 - q^9	$ 4 q + q^{3} - 2 q^{5} + 2 q^{7} - q^{9} + 6 q^{13} + 2 q^{15} - 4 q^{17} - 2 q^{19} + 8 q^{21} - 32 q^{23} + q^{25} + q^{27} + 4 q^{35} + 6 q^{37} - 6 q^{39} - 40 q^{43} + 8 q^{45} + 3 q^{49} + 4 q^{51} - 14 q^{53} + 2 q^{57} + 12 q^{59} - 14 q^{61} + 2 q^{63} - 48 q^{65} + 16 q^{67} - 8 q^{69} + 6 q^{73} - q^{75} + 2 q^{79} - q^{81} + 16 q^{83} - 8 q^{85} - 56 q^{89} - 12 q^{91} - 4 q^{95} + 2 q^{97}+O(q^{100}) $ 4 * q + q^3 - 2 * q^5 + 2 * q^7 - q^9 + 6 * q^13 + 2 * q^15 - 4 * q^17 - 2 * q^19 + 8 * q^21 - 32 * q^23 + q^25 + q^27 + 4 * q^35 + 6 * q^37 - 6 * q^39 - 40 * q^43 + 8 * q^45 + 3 * q^49 + 4 * q^51 - 14 * q^53 + 2 * q^57 + 12 * q^59 - 14 * q^61 + 2 * q^63 - 48 * q^65 + 16 * q^67 - 8 * q^69 + 6 * q^73 - q^75 + 2 * q^79 - q^81 + 16 * q^83 - 8 * q^85 - 56 * q^89 - 12 * q^91 - 4 * q^95 + 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1452\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$1333$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$		0			0
$5$	−1.61803	−	1.17557i	−0.723607	−	0.525731i	0.163928	−	0.986472i	$-0.447584\pi$
$5$	−1.61803	−	1.17557i	−0.723607	−	0.525731i	−0.887535	+	0.460741i	$0.847584\pi$
$6$		0			0
$7$	−0.618034	+	1.90211i	−0.233595	+	0.718931i	0.763710	+	0.645560i	$0.223376\pi$
$7$	−0.618034	+	1.90211i	−0.233595	+	0.718931i	−0.997305	+	0.0733714i	$0.976624\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$		0			0
$11$		0			0
$12$		0			0
$13$	4.85410	−	3.52671i	1.34629	−	0.978134i	0.347098	−	0.937829i	$-0.387167\pi$
$13$	4.85410	−	3.52671i	1.34629	−	0.978134i	0.999187	−	0.0403050i	$-0.0128330\pi$
$14$		0			0
$15$	−0.618034	+	1.90211i	−0.159576	+	0.491123i
$16$		0			0
$17$	−3.23607	−	2.35114i	−0.784862	−	0.570235i	0.121572	−	0.992583i	$-0.461206\pi$
$17$	−3.23607	−	2.35114i	−0.784862	−	0.570235i	−0.906434	+	0.422347i	$0.861206\pi$
$18$		0			0
$19$	0.618034	+	1.90211i	0.141787	+	0.436375i	0.996584	−	0.0825877i	$-0.0263185\pi$
$19$	0.618034	+	1.90211i	0.141787	+	0.436375i	−0.854797	+	0.518962i	$0.826318\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$		0			0
$23$	−8.00000			−1.66812			−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000			−1.66812			−0.834058	+	0.551677i	$0.813988\pi$
$24$		0			0
$25$	−0.309017	−	0.951057i	−0.0618034	−	0.190211i
$26$		0			0
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$		0			0
$29$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$29$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$30$		0			0
$31$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$31$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.23607	−	2.35114i	0.546995	−	0.397415i
$36$		0			0
$37$	−1.85410	+	5.70634i	−0.304812	+	0.938116i	0.674935	+	0.737878i	$0.264172\pi$
$37$	−1.85410	+	5.70634i	−0.304812	+	0.938116i	−0.979747	+	0.200239i	$0.935828\pi$
$38$		0			0
$39$	−4.85410	−	3.52671i	−0.777278	−	0.564726i
$40$		0			0
$41$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$41$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$42$		0			0
$43$	−10.0000			−1.52499			−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000			−1.52499			−0.762493	+	0.646997i	$0.776025\pi$
$44$		0			0
$45$	2.00000			0.298142
$46$		0			0
$47$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$47$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$48$		0			0
$49$	2.42705	+	1.76336i	0.346722	+	0.251908i
$50$		0			0
$51$	−1.23607	+	3.80423i	−0.173084	+	0.532698i
$52$		0			0
$53$	−11.3262	+	8.22899i	−1.55578	+	1.13034i	−0.616412	+	0.787424i	$0.711414\pi$
$53$	−11.3262	+	8.22899i	−1.55578	+	1.13034i	−0.939366	+	0.342916i	$0.888586\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.61803	−	1.17557i	0.214314	−	0.155708i
$58$		0			0
$59$	−3.70820	+	11.4127i	−0.482767	+	1.48580i	0.352422	+	0.935841i	$0.385358\pi$
$59$	−3.70820	+	11.4127i	−0.482767	+	1.48580i	−0.835189	+	0.549963i	$0.814642\pi$
$60$		0			0
$61$	−11.3262	−	8.22899i	−1.45018	−	1.05361i	−0.985790	−	0.167982i	$-0.946275\pi$
$61$	−11.3262	−	8.22899i	−1.45018	−	1.05361i	−0.464386	−	0.885633i	$-0.653725\pi$
$62$		0			0
$63$	−0.618034	−	1.90211i	−0.0778650	−	0.239644i
$64$		0			0
$65$	−12.0000			−1.48842
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$		0			0
$69$	2.47214	+	7.60845i	0.297610	+	0.915950i
$70$		0			0
$71$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$71$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$72$		0			0
$73$	−1.85410	+	5.70634i	−0.217006	+	0.667876i	0.781999	+	0.623280i	$0.214200\pi$
$73$	−1.85410	+	5.70634i	−0.217006	+	0.667876i	−0.999005	+	0.0445966i	$0.985800\pi$
$74$		0			0
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.61803	−	1.17557i	0.182043	−	0.132262i	−0.493032	−	0.870011i	$-0.664111\pi$
$79$	1.61803	−	1.17557i	0.182043	−	0.132262i	0.675075	+	0.737749i	$0.264111\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	12.9443	+	9.40456i	1.42082	+	1.03229i	0.991636	+	0.129067i	$0.0411983\pi$
$83$	12.9443	+	9.40456i	1.42082	+	1.03229i	0.429183	+	0.903218i	$0.358802\pi$
$84$		0			0
$85$	2.47214	+	7.60845i	0.268141	+	0.825253i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−14.0000			−1.48400			−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000			−1.48400			−0.741999	+	0.670402i	$0.766122\pi$
$90$		0			0
$91$	3.70820	+	11.4127i	0.388725	+	1.19637i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.23607	−	3.80423i	0.126818	−	0.390305i
$96$		0			0
$97$	1.61803	−	1.17557i	0.164286	−	0.119361i	−0.502604	−	0.864517i	$-0.667625\pi$
$97$	1.61803	−	1.17557i	0.164286	−	0.119361i	0.666891	+	0.745155i	$0.267625\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.47214	−	4.70228i	0.644002	−	0.467895i	−0.217221	−	0.976122i	$-0.569699\pi$
$101$	6.47214	−	4.70228i	0.644002	−	0.467895i	0.861223	+	0.508228i	$0.169699\pi$
$102$		0			0
$103$	−3.70820	+	11.4127i	−0.365380	+	1.12452i	0.584362	+	0.811493i	$0.301345\pi$
$103$	−3.70820	+	11.4127i	−0.365380	+	1.12452i	−0.949743	+	0.313032i	$0.898655\pi$
$104$		0			0
$105$	−3.23607	−	2.35114i	−0.315808	−	0.229448i
$106$		0			0
$107$	−4.94427	−	15.2169i	−0.477981	−	1.47107i	−0.841895	−	0.539641i	$-0.818560\pi$
$107$	−4.94427	−	15.2169i	−0.477981	−	1.47107i	0.363914	−	0.931432i	$-0.381440\pi$
$108$		0			0
$109$	18.0000			1.72409			0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000			1.72409			0.862044	+	0.506834i	$0.169184\pi$
$110$		0			0
$111$	6.00000			0.569495
$112$		0			0
$113$	−3.09017	−	9.51057i	−0.290699	−	0.894679i	−0.984632	−	0.174640i	$-0.944124\pi$
$113$	−3.09017	−	9.51057i	−0.290699	−	0.894679i	0.693934	−	0.720039i	$-0.255876\pi$
$114$		0			0
$115$	12.9443	+	9.40456i	1.20706	+	0.876980i
$116$		0			0
$117$	−1.85410	+	5.70634i	−0.171412	+	0.527551i
$118$		0			0
$119$	6.47214	−	4.70228i	0.593300	−	0.431057i
$120$		0			0
$121$		0			0
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.70820	+	11.4127i	−0.331672	+	1.02078i
$126$		0			0
$127$	−4.85410	−	3.52671i	−0.430732	−	0.312945i	0.351210	−	0.936297i	$-0.385770\pi$
$127$	−4.85410	−	3.52671i	−0.430732	−	0.312945i	−0.781941	+	0.623352i	$0.785770\pi$
$128$		0			0
$129$	3.09017	+	9.51057i	0.272074	+	0.837359i
$130$		0			0
$131$	−4.00000			−0.349482			−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000			−0.349482			−0.174741	+	0.984614i	$0.555909\pi$
$132$		0			0
$133$	−4.00000			−0.346844
$134$		0			0
$135$	−0.618034	−	1.90211i	−0.0531919	−	0.163708i
$136$		0			0
$137$	−11.3262	−	8.22899i	−0.967666	−	0.703050i	−0.0127474	−	0.999919i	$-0.504058\pi$
$137$	−11.3262	−	8.22899i	−0.967666	−	0.703050i	−0.954918	+	0.296868i	$0.904058\pi$
$138$		0			0
$139$	−4.32624	+	13.3148i	−0.366947	+	1.12935i	0.581806	+	0.813327i	$0.302346\pi$
$139$	−4.32624	+	13.3148i	−0.366947	+	1.12935i	−0.948753	+	0.316018i	$0.897654\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.927051	−	2.85317i	0.0764619	−	0.235325i
$148$		0			0
$149$	−3.23607	−	2.35114i	−0.265109	−	0.192613i	0.447287	−	0.894390i	$-0.352390\pi$
$149$	−3.23607	−	2.35114i	−0.265109	−	0.192613i	−0.712396	+	0.701777i	$0.752390\pi$
$150$		0			0
$151$	−3.09017	−	9.51057i	−0.251474	−	0.773959i	−0.994504	−	0.104700i	$-0.966612\pi$
$151$	−3.09017	−	9.51057i	−0.251474	−	0.773959i	0.743029	−	0.669259i	$-0.233388\pi$
$152$		0			0
$153$	4.00000			0.323381
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−3.09017	−	9.51057i	−0.246622	−	0.759026i	−0.995365	−	0.0961653i	$-0.969342\pi$
$157$	−3.09017	−	9.51057i	−0.246622	−	0.759026i	0.748743	−	0.662860i	$-0.230658\pi$
$158$		0			0
$159$	11.3262	+	8.22899i	0.898229	+	0.652602i
$160$		0			0
$161$	4.94427	−	15.2169i	0.389663	−	1.19926i
$162$		0			0
$163$	−12.9443	+	9.40456i	−1.01387	+	0.736622i	−0.965018	−	0.262184i	$-0.915557\pi$
$163$	−12.9443	+	9.40456i	−1.01387	+	0.736622i	−0.0488556	+	0.998806i	$0.515557\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.70820	+	7.05342i	−0.751243	+	0.545810i	−0.896212	−	0.443626i	$-0.853692\pi$
$167$	−9.70820	+	7.05342i	−0.751243	+	0.545810i	0.144969	+	0.989436i	$0.453692\pi$
$168$		0			0
$169$	7.10739	−	21.8743i	0.546722	−	1.68264i
$170$		0			0
$171$	−1.61803	−	1.17557i	−0.123734	−	0.0898981i
$172$		0			0
$173$	−2.47214	−	7.60845i	−0.187953	−	0.578460i	0.812034	−	0.583611i	$-0.198361\pi$
$173$	−2.47214	−	7.60845i	−0.187953	−	0.578460i	−0.999987	+	0.00515062i	$0.998361\pi$
$174$		0			0
$175$	2.00000			0.151186
$176$		0			0
$177$	12.0000			0.901975
$178$		0			0
$179$	−1.23607	−	3.80423i	−0.0923881	−	0.284341i	0.894176	−	0.447715i	$-0.147762\pi$
$179$	−1.23607	−	3.80423i	−0.0923881	−	0.284341i	−0.986564	+	0.163374i	$0.947762\pi$
$180$		0			0
$181$	−17.7984	−	12.9313i	−1.32294	−	0.961174i	−0.999891	−	0.0147930i	$-0.995291\pi$
$181$	−17.7984	−	12.9313i	−1.32294	−	0.961174i	−0.323052	−	0.946381i	$-0.604709\pi$
$182$		0			0
$183$	−4.32624	+	13.3148i	−0.319805	+	0.984258i
$184$		0			0
$185$	9.70820	−	7.05342i	0.713761	−	0.518578i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−1.61803	+	1.17557i	−0.117695	+	0.0855102i
$190$		0			0
$191$	7.41641	−	22.8254i	0.536632	−	1.65158i	−0.203463	−	0.979083i	$-0.565220\pi$
$191$	7.41641	−	22.8254i	0.536632	−	1.65158i	0.740095	−	0.672502i	$-0.234780\pi$
$192$		0			0
$193$	8.09017	+	5.87785i	0.582343	+	0.423097i	0.839568	−	0.543254i	$-0.182808\pi$
$193$	8.09017	+	5.87785i	0.582343	+	0.423097i	−0.257225	+	0.966352i	$0.582808\pi$
$194$		0			0
$195$	3.70820	+	11.4127i	0.265550	+	0.817279i
$196$		0			0
$197$	−16.0000			−1.13995			−0.569976	−	0.821661i	$-0.693048\pi$
$197$	−16.0000			−1.13995			−0.569976	+	0.821661i	$0.693048\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$		0			0
$201$	−1.23607	−	3.80423i	−0.0871855	−	0.268329i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	6.47214	−	4.70228i	0.449845	−	0.326831i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−8.09017	+	5.87785i	−0.556950	+	0.404648i	−0.830342	−	0.557255i	$-0.811855\pi$
$211$	−8.09017	+	5.87785i	−0.556950	+	0.404648i	0.273391	+	0.961903i	$0.411855\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	16.1803	+	11.7557i	1.10349	+	0.801732i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	6.00000			0.405442
$220$		0			0
$221$	−24.0000			−1.61441
$222$		0			0
$223$	3.70820	+	11.4127i	0.248320	+	0.764249i	0.995073	+	0.0991480i	$0.0316117\pi$
$223$	3.70820	+	11.4127i	0.248320	+	0.764249i	−0.746753	+	0.665101i	$0.768388\pi$
$224$		0			0
$225$	0.809017	+	0.587785i	0.0539345	+	0.0391857i
$226$		0			0
$227$	7.41641	−	22.8254i	0.492244	−	1.51497i	−0.328963	−	0.944343i	$-0.606699\pi$
$227$	7.41641	−	22.8254i	0.492244	−	1.51497i	0.821208	−	0.570629i	$-0.193301\pi$
$228$		0			0
$229$	−1.61803	+	1.17557i	−0.106923	+	0.0776839i	−0.639962	−	0.768407i	$-0.721050\pi$
$229$	−1.61803	+	1.17557i	−0.106923	+	0.0776839i	0.533039	+	0.846091i	$0.321050\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.9443	−	9.40456i	0.848007	−	0.616113i	−0.0765885	−	0.997063i	$-0.524403\pi$
$233$	12.9443	−	9.40456i	0.848007	−	0.616113i	0.924596	+	0.380949i	$0.124403\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.61803	−	1.17557i	−0.105103	−	0.0763615i
$238$		0			0
$239$	1.23607	+	3.80423i	0.0799546	+	0.246075i	0.983042	−	0.183383i	$-0.0587048\pi$
$239$	1.23607	+	3.80423i	0.0799546	+	0.246075i	−0.903087	+	0.429458i	$0.858705\pi$
$240$		0			0
$241$	2.00000			0.128831			0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000			0.128831			0.0644157	+	0.997923i	$0.479482\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−1.85410	−	5.70634i	−0.118454	−	0.364565i
$246$		0			0
$247$	9.70820	+	7.05342i	0.617718	+	0.448799i
$248$		0			0
$249$	4.94427	−	15.2169i	0.313331	−	0.964332i
$250$		0			0
$251$	3.23607	−	2.35114i	0.204259	−	0.148403i	−0.480953	−	0.876746i	$-0.659709\pi$
$251$	3.23607	−	2.35114i	0.204259	−	0.148403i	0.685212	+	0.728343i	$0.259709\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	6.47214	−	4.70228i	0.405301	−	0.294468i
$256$		0			0
$257$	0.618034	−	1.90211i	0.0385519	−	0.118651i	−0.929928	−	0.367740i	$-0.880131\pi$
$257$	0.618034	−	1.90211i	0.0385519	−	0.118651i	0.968480	+	0.249090i	$0.0801315\pi$
$258$		0			0
$259$	−9.70820	−	7.05342i	−0.603238	−	0.438278i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	12.0000			0.739952			0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000			0.739952			0.369976	+	0.929041i	$0.379366\pi$
$264$		0			0
$265$	28.0000			1.72003
$266$		0			0
$267$	4.32624	+	13.3148i	0.264761	+	0.814852i
$268$		0			0
$269$	−11.3262	−	8.22899i	−0.690573	−	0.501731i	0.186275	−	0.982498i	$-0.440358\pi$
$269$	−11.3262	−	8.22899i	−0.690573	−	0.501731i	−0.876848	+	0.480767i	$0.840358\pi$
$270$		0			0
$271$	3.09017	−	9.51057i	0.187714	−	0.577726i	−0.812270	−	0.583281i	$-0.801768\pi$
$271$	3.09017	−	9.51057i	0.187714	−	0.577726i	0.999985	+	0.00555577i	$0.00176847\pi$
$272$		0			0
$273$	9.70820	−	7.05342i	0.587567	−	0.426893i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−8.09017	+	5.87785i	−0.486091	+	0.353166i	−0.803679	−	0.595063i	$-0.797127\pi$
$277$	−8.09017	+	5.87785i	−0.486091	+	0.353166i	0.317588	+	0.948229i	$0.397127\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	25.8885	+	18.8091i	1.54438	+	1.12206i	0.947512	+	0.319720i	$0.103589\pi$
$281$	25.8885	+	18.8091i	1.54438	+	1.12206i	0.596869	+	0.802339i	$0.296411\pi$
$282$		0			0
$283$	4.32624	+	13.3148i	0.257168	+	0.791482i	0.993395	+	0.114747i	$0.0366058\pi$
$283$	4.32624	+	13.3148i	0.257168	+	0.791482i	−0.736227	+	0.676735i	$0.763394\pi$
$284$		0			0
$285$	−4.00000			−0.236940
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$		0			0
$291$	−1.61803	−	1.17557i	−0.0948508	−	0.0689132i
$292$		0			0
$293$	6.18034	−	19.0211i	0.361059	−	1.11123i	−0.591353	−	0.806413i	$-0.701406\pi$
$293$	6.18034	−	19.0211i	0.361059	−	1.11123i	0.952412	−	0.304813i	$-0.0985941\pi$
$294$		0			0
$295$	19.4164	−	14.1068i	1.13047	−	0.821332i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−38.8328	+	28.2137i	−2.24576	+	1.63164i
$300$		0			0
$301$	6.18034	−	19.0211i	0.356229	−	1.09636i
$302$		0			0
$303$	−6.47214	−	4.70228i	−0.371814	−	0.270139i
$304$		0			0
$305$	8.65248	+	26.6296i	0.495439	+	1.52481i
$306$		0			0
$307$	26.0000			1.48390			0.741949	−	0.670456i	$-0.233902\pi$
$307$	26.0000			1.48390			0.741949	+	0.670456i	$0.233902\pi$
$308$		0			0
$309$	12.0000			0.682656
$310$		0			0
$311$	−2.47214	−	7.60845i	−0.140182	−	0.431436i	0.856178	−	0.516681i	$-0.172833\pi$
$311$	−2.47214	−	7.60845i	−0.140182	−	0.431436i	−0.996360	+	0.0852452i	$0.972833\pi$
$312$		0			0
$313$	−11.3262	−	8.22899i	−0.640197	−	0.465130i	0.219721	−	0.975563i	$-0.429485\pi$
$313$	−11.3262	−	8.22899i	−0.640197	−	0.465130i	−0.859918	+	0.510433i	$0.829485\pi$
$314$		0			0
$315$	−1.23607	+	3.80423i	−0.0696445	+	0.214344i
$316$		0			0
$317$	−14.5623	+	10.5801i	−0.817901	+	0.594240i	−0.916110	−	0.400926i	$-0.868688\pi$
$317$	−14.5623	+	10.5801i	−0.817901	+	0.594240i	0.0982098	+	0.995166i	$0.468688\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−12.9443	+	9.40456i	−0.722479	+	0.524912i
$322$		0			0
$323$	2.47214	−	7.60845i	0.137553	−	0.423346i
$324$		0			0
$325$	−4.85410	−	3.52671i	−0.269257	−	0.195627i
$326$		0			0
$327$	−5.56231	−	17.1190i	−0.307596	−	0.946684i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$		0			0
$333$	−1.85410	−	5.70634i	−0.101604	−	0.312705i
$334$		0			0
$335$	−6.47214	−	4.70228i	−0.353611	−	0.256913i
$336$		0			0
$337$	5.56231	−	17.1190i	0.302998	−	0.932532i	−0.677419	−	0.735598i	$-0.736901\pi$
$337$	5.56231	−	17.1190i	0.302998	−	0.932532i	0.980417	−	0.196934i	$-0.0630986\pi$
$338$		0			0
$339$	−8.09017	+	5.87785i	−0.439398	+	0.319241i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−16.1803	+	11.7557i	−0.873656	+	0.634748i
$344$		0			0
$345$	4.94427	−	15.2169i	0.266191	−	0.819251i
$346$		0			0
$347$	25.8885	+	18.8091i	1.38977	+	1.00973i	0.995891	+	0.0905647i	$0.0288672\pi$
$347$	25.8885	+	18.8091i	1.38977	+	1.00973i	0.393879	+	0.919162i	$0.371133\pi$
$348$		0			0
$349$	1.85410	+	5.70634i	0.0992478	+	0.305453i	0.988337	−	0.152280i	$-0.0486615\pi$
$349$	1.85410	+	5.70634i	0.0992478	+	0.305453i	−0.889090	+	0.457733i	$0.848662\pi$
$350$		0			0
$351$	6.00000			0.320256
$352$		0			0
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−6.47214	−	4.70228i	−0.342542	−	0.248871i
$358$		0			0
$359$	−7.41641	+	22.8254i	−0.391423	+	1.20468i	0.540289	+	0.841479i	$0.318315\pi$
$359$	−7.41641	+	22.8254i	−0.391423	+	1.20468i	−0.931712	+	0.363197i	$0.881685\pi$
$360$		0			0
$361$	12.1353	−	8.81678i	0.638698	−	0.464041i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	9.70820	−	7.05342i	0.508151	−	0.369193i
$366$		0			0
$367$	−1.23607	+	3.80423i	−0.0645222	+	0.198579i	−0.978121	−	0.208039i	$-0.933292\pi$
$367$	−1.23607	+	3.80423i	−0.0645222	+	0.198579i	0.913598	+	0.406618i	$0.133292\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−8.65248	−	26.6296i	−0.449214	−	1.38254i
$372$		0			0
$373$	−10.0000			−0.517780			−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000			−0.517780			−0.258890	+	0.965907i	$0.583357\pi$
$374$		0			0
$375$	12.0000			0.619677
$376$		0			0
$377$		0			0
$378$		0			0
$379$	12.9443	+	9.40456i	0.664903	+	0.483080i	0.868315	−	0.496013i	$-0.165203\pi$
$379$	12.9443	+	9.40456i	0.664903	+	0.483080i	−0.203412	+	0.979093i	$0.565203\pi$
$380$		0			0
$381$	−1.85410	+	5.70634i	−0.0949885	+	0.292345i
$382$		0			0
$383$	−6.47214	+	4.70228i	−0.330711	+	0.240275i	−0.740732	−	0.671801i	$-0.765521\pi$
$383$	−6.47214	+	4.70228i	−0.330711	+	0.240275i	0.410021	+	0.912076i	$0.365521\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	8.09017	−	5.87785i	0.411246	−	0.298788i
$388$		0			0
$389$	5.56231	−	17.1190i	0.282020	−	0.867969i	−0.705256	−	0.708953i	$-0.749168\pi$
$389$	5.56231	−	17.1190i	0.282020	−	0.867969i	0.987276	−	0.159016i	$-0.0508321\pi$
$390$		0			0
$391$	25.8885	+	18.8091i	1.30924	+	0.951218i
$392$		0			0
$393$	1.23607	+	3.80423i	0.0623514	+	0.191898i
$394$		0			0
$395$	−4.00000			−0.201262
$396$		0			0
$397$	−14.0000			−0.702640			−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000			−0.702640			−0.351320	+	0.936255i	$0.614267\pi$
$398$		0			0
$399$	1.23607	+	3.80423i	0.0618808	+	0.190450i
$400$		0			0
$401$	1.61803	+	1.17557i	0.0808008	+	0.0587052i	0.627452	−	0.778655i	$-0.284098\pi$
$401$	1.61803	+	1.17557i	0.0808008	+	0.0587052i	−0.546652	+	0.837360i	$0.684098\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−1.61803	+	1.17557i	−0.0804008	+	0.0584146i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	17.7984	−	12.9313i	0.880073	−	0.639410i	−0.0531978	−	0.998584i	$-0.516941\pi$
$409$	17.7984	−	12.9313i	0.880073	−	0.639410i	0.933271	+	0.359174i	$0.116941\pi$
$410$		0			0
$411$	−4.32624	+	13.3148i	−0.213398	+	0.656770i
$412$		0			0
$413$	−19.4164	−	14.1068i	−0.955419	−	0.694153i
$414$		0			0
$415$	−9.88854	−	30.4338i	−0.485410	−	1.49394i
$416$		0			0
$417$	14.0000			0.685583
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	−3.09017	−	9.51057i	−0.150606	−	0.463517i	0.847084	−	0.531460i	$-0.178356\pi$
$421$	−3.09017	−	9.51057i	−0.150606	−	0.463517i	−0.997689	+	0.0679432i	$0.978356\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.23607	+	3.80423i	−0.0599581	+	0.184532i
$426$		0			0
$427$	22.6525	−	16.4580i	1.09623	−	0.796458i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9.70820	+	7.05342i	−0.467628	+	0.339751i	−0.796516	−	0.604617i	$-0.793326\pi$
$431$	−9.70820	+	7.05342i	−0.467628	+	0.339751i	0.328888	+	0.944369i	$0.393326\pi$
$432$		0			0
$433$	4.32624	−	13.3148i	0.207906	−	0.639868i	−0.791676	−	0.610941i	$-0.790791\pi$
$433$	4.32624	−	13.3148i	0.207906	−	0.639868i	0.999582	−	0.0289266i	$-0.00920891\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.94427	−	15.2169i	−0.236517	−	0.727923i
$438$		0			0
$439$	2.00000			0.0954548			0.0477274	−	0.998860i	$-0.484802\pi$
$439$	2.00000			0.0954548			0.0477274	+	0.998860i	$0.484802\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$		0			0
$443$	1.23607	+	3.80423i	0.0587274	+	0.180744i	0.976117	−	0.217247i	$-0.0697076\pi$
$443$	1.23607	+	3.80423i	0.0587274	+	0.180744i	−0.917389	+	0.397991i	$0.869708\pi$
$444$		0			0
$445$	22.6525	+	16.4580i	1.07383	+	0.780183i
$446$		0			0
$447$	−1.23607	+	3.80423i	−0.0584640	+	0.179934i
$448$		0			0
$449$	17.7984	−	12.9313i	0.839957	−	0.610265i	−0.0824015	−	0.996599i	$-0.526259\pi$
$449$	17.7984	−	12.9313i	0.839957	−	0.610265i	0.922359	+	0.386335i	$0.126259\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−8.09017	+	5.87785i	−0.380109	+	0.276166i
$454$		0			0
$455$	7.41641	−	22.8254i	0.347687	−	1.07007i
$456$		0			0
$457$	17.7984	+	12.9313i	0.832573	+	0.604900i	0.920286	−	0.391246i	$-0.127956\pi$
$457$	17.7984	+	12.9313i	0.832573	+	0.604900i	−0.0877132	+	0.996146i	$0.527956\pi$
$458$		0			0
$459$	−1.23607	−	3.80423i	−0.0576947	−	0.177566i
$460$		0			0
$461$	28.0000			1.30409			0.652045	−	0.758180i	$-0.273911\pi$
$461$	28.0000			1.30409			0.652045	+	0.758180i	$0.273911\pi$
$462$		0			0
$463$	−12.0000			−0.557687			−0.278844	−	0.960337i	$-0.589951\pi$
$463$	−12.0000			−0.557687			−0.278844	+	0.960337i	$0.589951\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.70820	+	7.05342i	0.449242	+	0.326393i	0.789296	−	0.614012i	$-0.210445\pi$
$467$	9.70820	+	7.05342i	0.449242	+	0.326393i	−0.340054	+	0.940406i	$0.610445\pi$
$468$		0			0
$469$	−2.47214	+	7.60845i	−0.114153	+	0.351326i
$470$		0			0
$471$	−8.09017	+	5.87785i	−0.372775	+	0.270837i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	1.61803	−	1.17557i	0.0742405	−	0.0539389i
$476$		0			0
$477$	4.32624	−	13.3148i	0.198085	−	0.609642i
$478$		0			0
$479$	−9.70820	−	7.05342i	−0.443579	−	0.322279i	0.343476	−	0.939161i	$-0.388395\pi$
$479$	−9.70820	−	7.05342i	−0.443579	−	0.322279i	−0.787055	+	0.616882i	$0.788395\pi$
$480$		0			0
$481$	11.1246	+	34.2380i	0.507239	+	1.56112i
$482$		0			0
$483$	−16.0000			−0.728025
$484$		0			0
$485$	−4.00000			−0.181631
$486$		0			0
$487$	−4.94427	−	15.2169i	−0.224046	−	0.689544i	−0.998387	−	0.0567748i	$-0.981918\pi$
$487$	−4.94427	−	15.2169i	−0.224046	−	0.689544i	0.774341	−	0.632769i	$-0.218082\pi$
$488$		0			0
$489$	12.9443	+	9.40456i	0.585360	+	0.425289i
$490$		0			0
$491$	4.94427	−	15.2169i	0.223132	−	0.686729i	−0.775344	−	0.631539i	$-0.782424\pi$
$491$	4.94427	−	15.2169i	0.223132	−	0.686729i	0.998476	−	0.0551901i	$-0.0175765\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1.23607	+	3.80423i	−0.0553340	+	0.170301i	−0.974904	−	0.222626i	$-0.928537\pi$
$499$	−1.23607	+	3.80423i	−0.0553340	+	0.170301i	0.919570	+	0.392926i	$0.128537\pi$
$500$		0			0
$501$	9.70820	+	7.05342i	0.433731	+	0.315124i
$502$		0			0
$503$	−6.18034	−	19.0211i	−0.275568	−	0.848110i	−0.989069	−	0.147456i	$-0.952892\pi$
$503$	−6.18034	−	19.0211i	−0.275568	−	0.848110i	0.713501	−	0.700654i	$-0.247108\pi$
$504$		0			0
$505$	−16.0000			−0.711991
$506$		0			0
$507$	−23.0000			−1.02147
$508$		0			0
$509$	4.32624	+	13.3148i	0.191757	+	0.590168i	0.999999	+	0.00131729i	$0.000419307\pi$
$509$	4.32624	+	13.3148i	0.191757	+	0.590168i	−0.808242	+	0.588850i	$0.799581\pi$
$510$		0			0
$511$	−9.70820	−	7.05342i	−0.429466	−	0.312025i
$512$		0			0
$513$	−0.618034	+	1.90211i	−0.0272869	+	0.0839803i
$514$		0			0
$515$	19.4164	−	14.1068i	0.855589	−	0.621622i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−6.47214	+	4.70228i	−0.284095	+	0.206407i
$520$		0			0
$521$	−12.9787	+	39.9444i	−0.568608	+	1.74999i	0.0883730	+	0.996087i	$0.471833\pi$
$521$	−12.9787	+	39.9444i	−0.568608	+	1.74999i	−0.656981	+	0.753907i	$0.728167\pi$
$522$		0			0
$523$	−17.7984	−	12.9313i	−0.778269	−	0.565445i	0.126190	−	0.992006i	$-0.459725\pi$
$523$	−17.7984	−	12.9313i	−0.778269	−	0.565445i	−0.904459	+	0.426561i	$0.859725\pi$
$524$		0			0
$525$	−0.618034	−	1.90211i	−0.0269732	−	0.0830150i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	41.0000			1.78261
$530$		0			0
$531$	−3.70820	−	11.4127i	−0.160922	−	0.495268i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−9.88854	+	30.4338i	−0.427519	+	1.31577i
$536$		0			0
$537$	−3.23607	+	2.35114i	−0.139647	+	0.101459i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−21.0344	+	15.2824i	−0.904341	+	0.657042i	−0.939577	−	0.342337i	$-0.888782\pi$
$541$	−21.0344	+	15.2824i	−0.904341	+	0.657042i	0.0352361	+	0.999379i	$0.488782\pi$
$542$		0			0
$543$	−6.79837	+	20.9232i	−0.291746	+	0.897902i
$544$		0			0
$545$	−29.1246	−	21.1603i	−1.24756	−	0.906406i
$546$		0			0
$547$	6.79837	+	20.9232i	0.290677	+	0.894613i	0.984639	+	0.174601i	$0.0558637\pi$
$547$	6.79837	+	20.9232i	0.290677	+	0.894613i	−0.693962	+	0.720012i	$0.744136\pi$
$548$		0			0
$549$	14.0000			0.597505
$550$		0			0
$551$		0			0
$552$		0			0
$553$	1.23607	+	3.80423i	0.0525630	+	0.161772i
$554$		0			0
$555$	−9.70820	−	7.05342i	−0.412090	−	0.299401i
$556$		0			0
$557$	−3.70820	+	11.4127i	−0.157122	+	0.483571i	−0.998370	−	0.0570787i	$-0.981821\pi$
$557$	−3.70820	+	11.4127i	−0.157122	+	0.483571i	0.841248	+	0.540649i	$0.181821\pi$
$558$		0			0
$559$	−48.5410	+	35.2671i	−2.05307	+	1.49164i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	3.23607	−	2.35114i	0.136384	−	0.0990888i	−0.517501	−	0.855682i	$-0.673138\pi$
$563$	3.23607	−	2.35114i	0.136384	−	0.0990888i	0.653885	+	0.756594i	$0.273138\pi$
$564$		0			0
$565$	−6.18034	+	19.0211i	−0.260009	+	0.800225i
$566$		0			0
$567$	1.61803	+	1.17557i	0.0679510	+	0.0493693i
$568$		0			0
$569$	6.18034	+	19.0211i	0.259093	+	0.797407i	0.992996	+	0.118152i	$0.0376970\pi$
$569$	6.18034	+	19.0211i	0.259093	+	0.797407i	−0.733902	+	0.679255i	$0.762303\pi$
$570$		0			0
$571$	−34.0000			−1.42286			−0.711428	−	0.702759i	$-0.751951\pi$
$571$	−34.0000			−1.42286			−0.711428	+	0.702759i	$0.751951\pi$
$572$		0			0
$573$	−24.0000			−1.00261
$574$		0			0
$575$	2.47214	+	7.60845i	0.103095	+	0.317294i
$576$		0			0
$577$	−1.61803	−	1.17557i	−0.0673596	−	0.0489396i	0.553596	−	0.832785i	$-0.313255\pi$
$577$	−1.61803	−	1.17557i	−0.0673596	−	0.0489396i	−0.620956	+	0.783846i	$0.713255\pi$
$578$		0			0
$579$	3.09017	−	9.51057i	0.128423	−	0.395246i
$580$		0			0
$581$	−25.8885	+	18.8091i	−1.07404	+	0.780334i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	9.70820	−	7.05342i	0.401385	−	0.291623i
$586$		0			0
$587$	−3.70820	+	11.4127i	−0.153054	+	0.471052i	−0.997959	−	0.0638654i	$-0.979657\pi$
$587$	−3.70820	+	11.4127i	−0.153054	+	0.471052i	0.844905	+	0.534917i	$0.179657\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	4.94427	+	15.2169i	0.203380	+	0.625940i
$592$		0			0
$593$	−24.0000			−0.985562			−0.492781	−	0.870153i	$-0.664020\pi$
$593$	−24.0000			−0.985562			−0.492781	+	0.870153i	$0.664020\pi$
$594$		0			0
$595$	−16.0000			−0.655936
$596$		0			0
$597$	−2.47214	−	7.60845i	−0.101178	−	0.311393i
$598$		0			0
$599$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$599$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$600$		0			0
$601$	4.32624	−	13.3148i	0.176471	−	0.543122i	−0.823227	−	0.567713i	$-0.807828\pi$
$601$	4.32624	−	13.3148i	0.176471	−	0.543122i	0.999698	+	0.0245912i	$0.00782840\pi$
$602$		0			0
$603$	−3.23607	+	2.35114i	−0.131783	+	0.0957459i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	27.5066	−	19.9847i	1.11646	−	0.811154i	0.132789	−	0.991144i	$-0.457607\pi$
$607$	27.5066	−	19.9847i	1.11646	−	0.811154i	0.983668	+	0.179990i	$0.0576067\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−12.9787	−	39.9444i	−0.524205	−	1.61334i	−0.765882	−	0.642981i	$-0.777697\pi$
$613$	−12.9787	−	39.9444i	−0.524205	−	1.61334i	0.241677	−	0.970357i	$-0.422303\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	38.0000			1.52982			0.764911	−	0.644136i	$-0.222783\pi$
$617$	38.0000			1.52982			0.764911	+	0.644136i	$0.222783\pi$
$618$		0			0
$619$	9.88854	+	30.4338i	0.397454	+	1.22324i	0.927034	+	0.374978i	$0.122350\pi$
$619$	9.88854	+	30.4338i	0.397454	+	1.22324i	−0.529580	+	0.848260i	$0.677650\pi$
$620$		0			0
$621$	−6.47214	−	4.70228i	−0.259718	−	0.188696i
$622$		0			0
$623$	8.65248	−	26.6296i	0.346654	−	1.06689i
$624$		0			0
$625$	15.3713	−	11.1679i	0.614853	−	0.446717i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	19.4164	−	14.1068i	0.774183	−	0.562477i
$630$		0			0
$631$	−2.47214	+	7.60845i	−0.0984142	+	0.302888i	−0.988128	−	0.153630i	$-0.950904\pi$
$631$	−2.47214	+	7.60845i	−0.0984142	+	0.302888i	0.889714	+	0.456518i	$0.150904\pi$
$632$		0			0
$633$	8.09017	+	5.87785i	0.321555	+	0.233624i
$634$		0			0
$635$	3.70820	+	11.4127i	0.147156	+	0.452898i
$636$		0			0
$637$	18.0000			0.713186
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.85410	−	5.70634i	−0.0732326	−	0.225387i	0.907740	−	0.419533i	$-0.137806\pi$
$641$	−1.85410	−	5.70634i	−0.0732326	−	0.225387i	−0.980973	+	0.194147i	$0.937806\pi$
$642$		0			0
$643$	−25.8885	−	18.8091i	−1.02094	−	0.741760i	−0.0544682	−	0.998516i	$-0.517346\pi$
$643$	−25.8885	−	18.8091i	−1.02094	−	0.741760i	−0.966476	+	0.256756i	$0.917346\pi$
$644$		0			0
$645$	6.18034	−	19.0211i	0.243351	−	0.748956i
$646$		0			0
$647$	−6.47214	+	4.70228i	−0.254446	+	0.184866i	−0.707695	−	0.706518i	$-0.750265\pi$
$647$	−6.47214	+	4.70228i	−0.254446	+	0.184866i	0.453249	+	0.891384i	$0.350265\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−12.9787	+	39.9444i	−0.507896	+	1.56314i	0.287950	+	0.957645i	$0.407026\pi$
$653$	−12.9787	+	39.9444i	−0.507896	+	1.56314i	−0.795846	+	0.605499i	$0.792974\pi$
$654$		0			0
$655$	6.47214	+	4.70228i	0.252887	+	0.183733i
$656$		0			0
$657$	−1.85410	−	5.70634i	−0.0723354	−	0.222625i
$658$		0			0
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	−18.0000			−0.700119			−0.350059	−	0.936727i	$-0.613839\pi$
$661$	−18.0000			−0.700119			−0.350059	+	0.936727i	$0.613839\pi$
$662$		0			0
$663$	7.41641	+	22.8254i	0.288029	+	0.886463i
$664$		0			0
$665$	6.47214	+	4.70228i	0.250979	+	0.182347i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	9.70820	−	7.05342i	0.375341	−	0.272701i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	21.0344	−	15.2824i	0.810818	−	0.589094i	−0.103250	−	0.994655i	$-0.532924\pi$
$673$	21.0344	−	15.2824i	0.810818	−	0.589094i	0.914068	+	0.405562i	$0.132924\pi$
$674$		0			0
$675$	0.309017	−	0.951057i	0.0118941	−	0.0366062i
$676$		0			0
$677$	−25.8885	−	18.8091i	−0.994978	−	0.722894i	−0.0339721	−	0.999423i	$-0.510816\pi$
$677$	−25.8885	−	18.8091i	−0.994978	−	0.722894i	−0.961005	+	0.276529i	$0.910816\pi$
$678$		0			0
$679$	1.23607	+	3.80423i	0.0474359	+	0.145993i
$680$		0			0
$681$	−24.0000			−0.919682
$682$		0			0
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$		0			0
$685$	8.65248	+	26.6296i	0.330594	+	1.01746i
$686$		0			0
$687$	1.61803	+	1.17557i	0.0617318	+	0.0448508i
$688$		0			0
$689$	−25.9574	+	79.8887i	−0.988899	+	3.04352i
$690$		0			0
$691$	−19.4164	+	14.1068i	−0.738635	+	0.536650i	−0.892283	−	0.451476i	$-0.850898\pi$
$691$	−19.4164	+	14.1068i	−0.738635	+	0.536650i	0.153648	+	0.988126i	$0.450898\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	22.6525	−	16.4580i	0.859257	−	0.624287i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−12.9443	−	9.40456i	−0.489597	−	0.355713i
$700$		0			0
$701$	3.70820	+	11.4127i	0.140057	+	0.431051i	0.996342	−	0.0854521i	$-0.0272335\pi$
$701$	3.70820	+	11.4127i	0.140057	+	0.431051i	−0.856285	+	0.516503i	$0.827233\pi$
$702$		0			0
$703$	−12.0000			−0.452589
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.94427	+	15.2169i	0.185948	+	0.572291i
$708$		0			0
$709$	−14.5623	−	10.5801i	−0.546899	−	0.397345i	0.279742	−	0.960075i	$-0.409751\pi$
$709$	−14.5623	−	10.5801i	−0.546899	−	0.397345i	−0.826641	+	0.562730i	$0.809751\pi$
$710$		0			0
$711$	−0.618034	+	1.90211i	−0.0231781	+	0.0713348i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.23607	−	2.35114i	0.120853	−	0.0878050i
$718$		0			0
$719$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$719$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$720$		0			0
$721$	−19.4164	−	14.1068i	−0.723105	−	0.525366i
$722$		0			0
$723$	−0.618034	−	1.90211i	−0.0229849	−	0.0707403i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−48.0000			−1.78022			−0.890111	−	0.455744i	$-0.849373\pi$
$727$	−48.0000			−1.78022			−0.890111	+	0.455744i	$0.849373\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	32.3607	+	23.5114i	1.19690	+	0.869601i
$732$		0			0
$733$	10.5066	−	32.3359i	0.388069	−	1.19435i	−0.546160	−	0.837681i	$-0.683911\pi$
$733$	10.5066	−	32.3359i	0.388069	−	1.19435i	0.934229	−	0.356674i	$-0.116089\pi$
$734$		0			0
$735$	−4.85410	+	3.52671i	−0.179046	+	0.130085i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	21.0344	−	15.2824i	0.773764	−	0.562173i	−0.129337	−	0.991601i	$-0.541285\pi$
$739$	21.0344	−	15.2824i	0.773764	−	0.562173i	0.903101	+	0.429428i	$0.141285\pi$
$740$		0			0
$741$	3.70820	−	11.4127i	0.136224	−	0.419255i
$742$		0			0
$743$	−6.47214	−	4.70228i	−0.237440	−	0.172510i	0.462702	−	0.886514i	$-0.346880\pi$
$743$	−6.47214	−	4.70228i	−0.237440	−	0.172510i	−0.700142	+	0.714004i	$0.746880\pi$
$744$		0			0
$745$	2.47214	+	7.60845i	0.0905721	+	0.278752i
$746$		0			0
$747$	−16.0000			−0.585409
$748$		0			0
$749$	32.0000			1.16925
$750$		0			0
$751$	−12.3607	−	38.0423i	−0.451048	−	1.38818i	−0.875713	−	0.482832i	$-0.839608\pi$
$751$	−12.3607	−	38.0423i	−0.451048	−	1.38818i	0.424666	−	0.905350i	$-0.360392\pi$
$752$		0			0
$753$	−3.23607	−	2.35114i	−0.117929	−	0.0856803i
$754$		0			0
$755$	−6.18034	+	19.0211i	−0.224926	+	0.692250i
$756$		0			0
$757$	−30.7426	+	22.3358i	−1.11736	+	0.811810i	−0.983807	−	0.179232i	$-0.942639\pi$
$757$	−30.7426	+	22.3358i	−1.11736	+	0.811810i	−0.133554	+	0.991042i	$0.542639\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	29.1246	−	21.1603i	1.05577	−	0.767059i	0.0824659	−	0.996594i	$-0.473720\pi$
$761$	29.1246	−	21.1603i	1.05577	−	0.767059i	0.973300	+	0.229535i	$0.0737205\pi$
$762$		0			0
$763$	−11.1246	+	34.2380i	−0.402738	+	1.23950i
$764$		0			0
$765$	−6.47214	−	4.70228i	−0.234001	−	0.170011i
$766$		0			0
$767$	22.2492	+	68.4761i	0.803373	+	2.47253i
$768$		0			0
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$		0			0
$771$	−2.00000			−0.0720282
$772$		0			0
$773$	−5.56231	−	17.1190i	−0.200062	−	0.615728i	−0.999880	−	0.0154855i	$-0.995071\pi$
$773$	−5.56231	−	17.1190i	−0.200062	−	0.615728i	0.799818	−	0.600243i	$-0.204929\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−3.70820	+	11.4127i	−0.133031	+	0.409428i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−6.18034	+	19.0211i	−0.220586	+	0.678893i
$786$		0			0
$787$	−30.7426	−	22.3358i	−1.09586	−	0.796187i	−0.115478	−	0.993310i	$-0.536840\pi$
$787$	−30.7426	−	22.3358i	−1.09586	−	0.796187i	−0.980379	+	0.197123i	$0.936840\pi$
$788$		0			0
$789$	−3.70820	−	11.4127i	−0.132016	−	0.406302i
$790$		0			0
$791$	20.0000			0.711118
$792$		0			0
$793$	−84.0000			−2.98293
$794$		0			0
$795$	−8.65248	−	26.6296i	−0.306872	−	0.944454i
$796$		0			0
$797$	4.85410	+	3.52671i	0.171941	+	0.124923i	0.670428	−	0.741975i	$-0.266111\pi$
$797$	4.85410	+	3.52671i	0.171941	+	0.124923i	−0.498487	+	0.866897i	$0.666111\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	11.3262	−	8.22899i	0.400193	−	0.290757i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−25.8885	+	18.8091i	−0.912451	+	0.662935i
$806$		0			0
$807$	−4.32624	+	13.3148i	−0.152291	+	0.468703i
$808$		0			0
$809$	−35.5967	−	25.8626i	−1.25152	−	0.909279i	−0.253206	−	0.967412i	$-0.581485\pi$
$809$	−35.5967	−	25.8626i	−1.25152	−	0.909279i	−0.998309	+	0.0581335i	$0.981485\pi$
$810$		0			0
$811$	−11.7426	−	36.1401i	−0.412340	−	1.26905i	−0.914609	−	0.404340i	$-0.867501\pi$
$811$	−11.7426	−	36.1401i	−0.412340	−	1.26905i	0.502268	−	0.864712i	$-0.332499\pi$
$812$		0			0
$813$	−10.0000			−0.350715
$814$		0			0
$815$	32.0000			1.12091
$816$		0			0
$817$	−6.18034	−	19.0211i	−0.216223	−	0.665465i
$818$		0			0
$819$	−9.70820	−	7.05342i	−0.339232	−	0.246467i
$820$		0			0
$821$	−12.3607	+	38.0423i	−0.431391	+	1.32768i	0.465350	+	0.885127i	$0.345929\pi$
$821$	−12.3607	+	38.0423i	−0.431391	+	1.32768i	−0.896740	+	0.442557i	$0.854071\pi$
$822$		0			0
$823$	22.6525	−	16.4580i	0.789616	−	0.573689i	−0.118234	−	0.992986i	$-0.537723\pi$
$823$	22.6525	−	16.4580i	0.789616	−	0.573689i	0.907849	+	0.419296i	$0.137723\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.9443	+	9.40456i	−0.450116	+	0.327029i	−0.789642	−	0.613568i	$-0.789734\pi$
$827$	−12.9443	+	9.40456i	−0.450116	+	0.327029i	0.339525	+	0.940597i	$0.389734\pi$
$828$		0			0
$829$	−4.32624	+	13.3148i	−0.150256	+	0.462442i	−0.997649	−	0.0685244i	$-0.978171\pi$
$829$	−4.32624	+	13.3148i	−0.150256	+	0.462442i	0.847393	+	0.530966i	$0.178171\pi$
$830$		0			0
$831$	8.09017	+	5.87785i	0.280645	+	0.203900i
$832$		0			0
$833$	−3.70820	−	11.4127i	−0.128482	−	0.395426i
$834$		0			0
$835$	24.0000			0.830554
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7.41641	−	22.8254i	−0.256043	−	0.788019i	−0.993622	−	0.112759i	$-0.964031\pi$
$839$	−7.41641	−	22.8254i	−0.256043	−	0.788019i	0.737580	−	0.675260i	$-0.235969\pi$
$840$		0			0
$841$	23.4615	+	17.0458i	0.809017	+	0.587785i
$842$		0			0
$843$	9.88854	−	30.4338i	0.340580	−	1.04820i
$844$		0			0
$845$	−37.2148	+	27.0381i	−1.28023	+	0.930140i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	11.3262	−	8.22899i	0.388715	−	0.282418i
$850$		0			0
$851$	14.8328	−	45.6507i	0.508462	−	1.56489i
$852$		0			0
$853$	14.5623	+	10.5801i	0.498604	+	0.362257i	0.808483	−	0.588519i	$-0.200289\pi$
$853$	14.5623	+	10.5801i	0.498604	+	0.362257i	−0.309880	+	0.950776i	$0.600289\pi$
$854$		0			0
$855$	1.23607	+	3.80423i	0.0422726	+	0.130102i
$856$		0			0
$857$	−44.0000			−1.50301			−0.751506	−	0.659727i	$-0.770672\pi$
$857$	−44.0000			−1.50301			−0.751506	+	0.659727i	$0.770672\pi$
$858$		0			0
$859$	40.0000			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−6.47214	−	4.70228i	−0.220314	−	0.160068i	0.472154	−	0.881516i	$-0.343477\pi$
$863$	−6.47214	−	4.70228i	−0.220314	−	0.160068i	−0.692468	+	0.721449i	$0.743477\pi$
$864$		0			0
$865$	−4.94427	+	15.2169i	−0.168110	+	0.517390i
$866$		0			0
$867$	−0.809017	+	0.587785i	−0.0274757	+	0.0199622i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	19.4164	−	14.1068i	0.657900	−	0.477992i
$872$		0			0
$873$	−0.618034	+	1.90211i	−0.0209173	+	0.0643768i
$874$		0			0
$875$	−19.4164	−	14.1068i	−0.656394	−	0.476898i
$876$		0			0
$877$	−5.56231	−	17.1190i	−0.187826	−	0.578068i	0.812160	−	0.583435i	$-0.198292\pi$
$877$	−5.56231	−	17.1190i	−0.187826	−	0.578068i	−0.999986	+	0.00536681i	$0.998292\pi$
$878$		0			0
$879$	−20.0000			−0.674583
$880$		0			0
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$		0			0
$883$	−13.5967	−	41.8465i	−0.457567	−	1.40825i	−0.868095	−	0.496398i	$-0.834656\pi$
$883$	−13.5967	−	41.8465i	−0.457567	−	1.40825i	0.410528	−	0.911848i	$-0.365344\pi$
$884$		0			0
$885$	−19.4164	−	14.1068i	−0.652675	−	0.474196i
$886$		0			0
$887$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$887$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$888$		0			0
$889$	9.70820	−	7.05342i	0.325603	−	0.236564i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−2.47214	+	7.60845i	−0.0826344	+	0.254323i
$896$		0			0
$897$	38.8328	+	28.2137i	1.29659	+	0.942028i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	56.0000			1.86563
$902$		0			0
$903$	−20.0000			−0.665558
$904$		0			0
$905$	13.5967	+	41.8465i	0.451971	+	1.39102i
$906$		0			0
$907$	−12.9443	−	9.40456i	−0.429807	−	0.312273i	0.351764	−	0.936089i	$-0.385582\pi$
$907$	−12.9443	−	9.40456i	−0.429807	−	0.312273i	−0.781572	+	0.623815i	$0.785582\pi$
$908$		0			0
$909$	−2.47214	+	7.60845i	−0.0819956	+	0.252356i
$910$		0			0
$911$	38.8328	−	28.2137i	1.28659	−	0.934761i	0.286858	−	0.957973i	$-0.407389\pi$
$911$	38.8328	−	28.2137i	1.28659	−	0.934761i	0.999731	+	0.0232118i	$0.00738921\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	22.6525	−	16.4580i	0.748868	−	0.544084i
$916$		0			0
$917$	2.47214	−	7.60845i	0.0816371	−	0.251253i
$918$		0			0
$919$	−27.5066	−	19.9847i	−0.907358	−	0.659234i	0.0329871	−	0.999456i	$-0.489498\pi$
$919$	−27.5066	−	19.9847i	−0.907358	−	0.659234i	−0.940345	+	0.340221i	$0.889498\pi$
$920$		0			0
$921$	−8.03444	−	24.7275i	−0.264744	−	0.814798i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	6.00000			0.197279
$926$		0			0
$927$	−3.70820	−	11.4127i	−0.121793	−	0.374842i
$928$		0			0
$929$	33.9787	+	24.6870i	1.11481	+	0.809954i	0.983414	−	0.181377i	$-0.0580554\pi$
$929$	33.9787	+	24.6870i	1.11481	+	0.809954i	0.131392	+	0.991331i	$0.458055\pi$
$930$		0			0
$931$	−1.85410	+	5.70634i	−0.0607657	+	0.187018i
$932$		0			0
$933$	−6.47214	+	4.70228i	−0.211888	+	0.153946i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−30.7426	+	22.3358i	−1.00432	+	0.729680i	−0.963010	−	0.269466i	$-0.913153\pi$
$937$	−30.7426	+	22.3358i	−1.00432	+	0.729680i	−0.0413087	+	0.999146i	$0.513153\pi$
$938$		0			0
$939$	−4.32624	+	13.3148i	−0.141181	+	0.434512i
$940$		0			0
$941$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$941$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	4.00000			0.130120
$946$		0			0
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$		0			0
$949$	11.1246	+	34.2380i	0.361120	+	1.11141i
$950$		0			0
$951$	14.5623	+	10.5801i	0.472215	+	0.343084i
$952$		0			0
$953$	−3.70820	+	11.4127i	−0.120121	+	0.369693i	−0.992981	−	0.118278i	$-0.962263\pi$
$953$	−3.70820	+	11.4127i	−0.120121	+	0.369693i	0.872860	+	0.487971i	$0.162263\pi$
$954$		0			0
$955$	−38.8328	+	28.2137i	−1.25660	+	0.912974i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	22.6525	−	16.4580i	0.731487	−	0.531456i
$960$		0			0
$961$	−9.57953	+	29.4828i	−0.309017	+	0.951057i
$962$		0			0
$963$	12.9443	+	9.40456i	0.417123	+	0.303058i
$964$		0			0
$965$	−6.18034	−	19.0211i	−0.198952	−	0.612312i
$966$		0			0
$967$	−34.0000			−1.09337			−0.546683	−	0.837340i	$-0.684110\pi$
$967$	−34.0000			−1.09337			−0.546683	+	0.837340i	$0.684110\pi$
$968$		0			0
$969$	−8.00000			−0.256997
$970$		0			0
$971$	18.5410	+	57.0634i	0.595010	+	1.83125i	0.554678	+	0.832065i	$0.312841\pi$
$971$	18.5410	+	57.0634i	0.595010	+	1.83125i	0.0403315	+	0.999186i	$0.487159\pi$
$972$		0			0
$973$	−22.6525	−	16.4580i	−0.726205	−	0.527619i
$974$		0			0
$975$	−1.85410	+	5.70634i	−0.0593788	+	0.182749i
$976$		0			0
$977$	8.09017	−	5.87785i	0.258827	−	0.188049i	−0.450803	−	0.892624i	$-0.648862\pi$
$977$	8.09017	−	5.87785i	0.258827	−	0.188049i	0.709630	+	0.704575i	$0.248862\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−14.5623	+	10.5801i	−0.464939	+	0.337798i
$982$		0			0
$983$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$983$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$984$		0			0
$985$	25.8885	+	18.8091i	0.824878	+	0.599309i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	80.0000			2.54385
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$	−2.47214	−	7.60845i	−0.0784509	−	0.241447i
$994$		0			0
$995$	−12.9443	−	9.40456i	−0.410361	−	0.298145i
$996$		0			0
$997$	−3.09017	+	9.51057i	−0.0978667	+	0.301203i	−0.987990	−	0.154517i	$-0.950618\pi$
$997$	−3.09017	+	9.51057i	−0.0978667	+	0.301203i	0.890124	+	0.455719i	$0.150618\pi$
$998$		0			0
$999$	−4.85410	+	3.52671i	−0.153577	+	0.111580i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1452.2.i.l.1213.1		4
11.2	odd	10		132.2.a.a.1.1	✓	1
11.3	even	5	inner	1452.2.i.l.1237.1		4
11.4	even	5	inner	1452.2.i.l.565.1		4
11.5	even	5	inner	1452.2.i.l.493.1		4
11.6	odd	10		1452.2.i.k.493.1		4
11.7	odd	10		1452.2.i.k.565.1		4
11.8	odd	10		1452.2.i.k.1237.1		4
11.9	even	5		1452.2.a.c.1.1		1
11.10	odd	2		1452.2.i.k.1213.1		4
33.2	even	10		396.2.a.b.1.1		1
33.20	odd	10		4356.2.a.c.1.1		1
44.31	odd	10		5808.2.a.bf.1.1		1
44.35	even	10		528.2.a.h.1.1		1
55.2	even	20		3300.2.c.c.1849.2		2
55.13	even	20		3300.2.c.c.1849.1		2
55.24	odd	10		3300.2.a.k.1.1		1
77.13	even	10		6468.2.a.l.1.1		1
88.13	odd	10		2112.2.a.t.1.1		1
88.35	even	10		2112.2.a.b.1.1		1
99.2	even	30		3564.2.i.g.2377.1		2
99.13	odd	30		3564.2.i.b.1189.1		2
99.68	even	30		3564.2.i.g.1189.1		2
99.79	odd	30		3564.2.i.b.2377.1		2
132.35	odd	10		1584.2.a.c.1.1		1
165.2	odd	20		9900.2.c.k.5149.2		2
165.68	odd	20		9900.2.c.k.5149.1		2
165.134	even	10		9900.2.a.g.1.1		1
264.35	odd	10		6336.2.a.bz.1.1		1
264.101	even	10		6336.2.a.cf.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.a.a.1.1	✓	1	11.2	odd	10
396.2.a.b.1.1		1	33.2	even	10
528.2.a.h.1.1		1	44.35	even	10
1452.2.a.c.1.1		1	11.9	even	5
1452.2.i.k.493.1		4	11.6	odd	10
1452.2.i.k.565.1		4	11.7	odd	10
1452.2.i.k.1213.1		4	11.10	odd	2
1452.2.i.k.1237.1		4	11.8	odd	10
1452.2.i.l.493.1		4	11.5	even	5	inner
1452.2.i.l.565.1		4	11.4	even	5	inner
1452.2.i.l.1213.1		4	1.1	even	1	trivial
1452.2.i.l.1237.1		4	11.3	even	5	inner
1584.2.a.c.1.1		1	132.35	odd	10
2112.2.a.b.1.1		1	88.35	even	10
2112.2.a.t.1.1		1	88.13	odd	10
3300.2.a.k.1.1		1	55.24	odd	10
3300.2.c.c.1849.1		2	55.13	even	20
3300.2.c.c.1849.2		2	55.2	even	20
3564.2.i.b.1189.1		2	99.13	odd	30
3564.2.i.b.2377.1		2	99.79	odd	30
3564.2.i.g.1189.1		2	99.68	even	30
3564.2.i.g.2377.1		2	99.2	even	30
4356.2.a.c.1.1		1	33.20	odd	10
5808.2.a.bf.1.1		1	44.31	odd	10
6336.2.a.bz.1.1		1	264.35	odd	10
6336.2.a.cf.1.1		1	264.101	even	10
6468.2.a.l.1.1		1	77.13	even	10
9900.2.a.g.1.1		1	165.134	even	10
9900.2.c.k.5149.1		2	165.68	odd	20
9900.2.c.k.5149.2		2	165.2	odd	20

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:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1452.i (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{3} +(-1.61803 - 1.17557i) q^{5} +(-0.618034 + 1.90211i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{3} +(-1.61803 - 1.17557i) q^{5} +(-0.618034 + 1.90211i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(4.85410 - 3.52671i) q^{13} +(-0.618034 + 1.90211i) q^{15} +(-3.23607 - 2.35114i) q^{17} +(0.618034 + 1.90211i) q^{19} +2.00000 q^{21} -8.00000 q^{23} +(-0.309017 - 0.951057i) q^{25} +(0.809017 + 0.587785i) q^{27} +(3.23607 - 2.35114i) q^{35} +(-1.85410 + 5.70634i) q^{37} +(-4.85410 - 3.52671i) q^{39} -10.0000 q^{43} +2.00000 q^{45} +(2.42705 + 1.76336i) q^{49} +(-1.23607 + 3.80423i) q^{51} +(-11.3262 + 8.22899i) q^{53} +(1.61803 - 1.17557i) q^{57} +(-3.70820 + 11.4127i) q^{59} +(-11.3262 - 8.22899i) q^{61} +(-0.618034 - 1.90211i) q^{63} -12.0000 q^{65} +4.00000 q^{67} +(2.47214 + 7.60845i) q^{69} +(-1.85410 + 5.70634i) q^{73} +(-0.809017 + 0.587785i) q^{75} +(1.61803 - 1.17557i) q^{79} +(0.309017 - 0.951057i) q^{81} +(12.9443 + 9.40456i) q^{83} +(2.47214 + 7.60845i) q^{85} -14.0000 q^{89} +(3.70820 + 11.4127i) q^{91} +(1.23607 - 3.80423i) q^{95} +(1.61803 - 1.17557i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 2 q^{5} + 2 q^{7} - q^{9}+O(q^{10}) \) 4 * q + q^3 - 2 * q^5 + 2 * q^7 - q^9	\( 4 q + q^{3} - 2 q^{5} + 2 q^{7} - q^{9} + 6 q^{13} + 2 q^{15} - 4 q^{17} - 2 q^{19} + 8 q^{21} - 32 q^{23} + q^{25} + q^{27} + 4 q^{35} + 6 q^{37} - 6 q^{39} - 40 q^{43} + 8 q^{45} + 3 q^{49} + 4 q^{51} - 14 q^{53} + 2 q^{57} + 12 q^{59} - 14 q^{61} + 2 q^{63} - 48 q^{65} + 16 q^{67} - 8 q^{69} + 6 q^{73} - q^{75} + 2 q^{79} - q^{81} + 16 q^{83} - 8 q^{85} - 56 q^{89} - 12 q^{91} - 4 q^{95} + 2 q^{97}+O(q^{100}) \) 4 * q + q^3 - 2 * q^5 + 2 * q^7 - q^9 + 6 * q^13 + 2 * q^15 - 4 * q^17 - 2 * q^19 + 8 * q^21 - 32 * q^23 + q^25 + q^27 + 4 * q^35 + 6 * q^37 - 6 * q^39 - 40 * q^43 + 8 * q^45 + 3 * q^49 + 4 * q^51 - 14 * q^53 + 2 * q^57 + 12 * q^59 - 14 * q^61 + 2 * q^63 - 48 * q^65 + 16 * q^67 - 8 * q^69 + 6 * q^73 - q^75 + 2 * q^79 - q^81 + 16 * q^83 - 8 * q^85 - 56 * q^89 - 12 * q^91 - 4 * q^95 + 2 * q^97

Introduction

L-functions

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