LMFDB - Embedded newform 525.2.g.e.524.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(524,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("525.524");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.g (of order $2$, degree $1$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			524.4
Root			$-0.396143 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	525.524
Dual form			525.2.g.e.524.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.792287 q^{2} +(-1.26217 + 1.18614i) q^{3} -1.37228 q^{4} +(1.00000 - 0.939764i) q^{6} +(1.73205 + 2.00000i) q^{7} +2.67181 q^{8} +(0.186141 - 2.99422i) q^{9} +O(q^{10})$	\(q-0.792287 q^{2} +(-1.26217 + 1.18614i) q^{3} -1.37228 q^{4} +(1.00000 - 0.939764i) q^{6} +(1.73205 + 2.00000i) q^{7} +2.67181 q^{8} +(0.186141 - 2.99422i) q^{9} -2.52434i q^{11} +(1.73205 - 1.62772i) q^{12} +4.10891 q^{13} +(-1.37228 - 1.58457i) q^{14} +0.627719 q^{16} +4.37228i q^{17} +(-0.147477 + 2.37228i) q^{18} +3.46410i q^{19} +(-4.55842 - 0.469882i) q^{21} +2.00000i q^{22} -8.51278 q^{23} +(-3.37228 + 3.16915i) q^{24} -3.25544 q^{26} +(3.31662 + 4.00000i) q^{27} +(-2.37686 - 2.74456i) q^{28} -0.939764i q^{29} +3.46410i q^{31} -5.84096 q^{32} +(2.99422 + 3.18614i) q^{33} -3.46410i q^{34} +(-0.255437 + 4.10891i) q^{36} +6.74456i q^{37} -2.74456i q^{38} +(-5.18614 + 4.87375i) q^{39} +6.00000 q^{41} +(3.61158 + 0.372281i) q^{42} +4.74456i q^{43} +3.46410i q^{44} +6.74456 q^{46} -1.62772i q^{47} +(-0.792287 + 0.744563i) q^{48} +(-1.00000 + 6.92820i) q^{49} +(-5.18614 - 5.51856i) q^{51} -5.63858 q^{52} +1.87953 q^{53} +(-2.62772 - 3.16915i) q^{54} +(4.62772 + 5.34363i) q^{56} +(-4.10891 - 4.37228i) q^{57} +0.744563i q^{58} -8.74456 q^{59} +6.92820i q^{61} -2.74456i q^{62} +(6.31084 - 4.81386i) q^{63} +3.37228 q^{64} +(-2.37228 - 2.52434i) q^{66} -4.74456i q^{67} -6.00000i q^{68} +(10.7446 - 10.0974i) q^{69} +0.294954i q^{71} +(0.497333 - 8.00000i) q^{72} -6.92820 q^{73} -5.34363i q^{74} -4.75372i q^{76} +(5.04868 - 4.37228i) q^{77} +(4.10891 - 3.86141i) q^{78} +2.37228 q^{79} +(-8.93070 - 1.11469i) q^{81} -4.75372 q^{82} +17.4891i q^{83} +(6.25544 + 0.644810i) q^{84} -3.75906i q^{86} +(1.11469 + 1.18614i) q^{87} -6.74456i q^{88} +14.7446 q^{89} +(7.11684 + 8.21782i) q^{91} +11.6819 q^{92} +(-4.10891 - 4.37228i) q^{93} +1.28962i q^{94} +(7.37228 - 6.92820i) q^{96} -11.0371 q^{97} +(0.792287 - 5.48913i) q^{98} +(-7.55842 - 0.469882i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{4} + 8 q^{6} - 10 q^{9}+O(q^{10}) $ 8 * q + 12 * q^4 + 8 * q^6 - 10 * q^9	$ 8 q + 12 q^{4} + 8 q^{6} - 10 q^{9} + 12 q^{14} + 28 q^{16} - 2 q^{21} - 4 q^{24} - 72 q^{26} - 48 q^{36} - 30 q^{39} + 48 q^{41} + 8 q^{46} - 8 q^{49} - 30 q^{51} - 44 q^{54} + 60 q^{56} - 24 q^{59} + 4 q^{64} + 4 q^{66} + 40 q^{69} - 4 q^{79} - 14 q^{81} + 96 q^{84} + 72 q^{89} - 12 q^{91} + 36 q^{96} - 26 q^{99}+O(q^{100}) $ 8 * q + 12 * q^4 + 8 * q^6 - 10 * q^9 + 12 * q^14 + 28 * q^16 - 2 * q^21 - 4 * q^24 - 72 * q^26 - 48 * q^36 - 30 * q^39 + 48 * q^41 + 8 * q^46 - 8 * q^49 - 30 * q^51 - 44 * q^54 + 60 * q^56 - 24 * q^59 + 4 * q^64 + 4 * q^66 + 40 * q^69 - 4 * q^79 - 14 * q^81 + 96 * q^84 + 72 * q^89 - 12 * q^91 + 36 * q^96 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.792287			−0.560232			−0.280116	−	0.959966i	$-0.590373\pi$
$2$	−0.792287			−0.560232			−0.280116	+	0.959966i	$0.590373\pi$
$3$	−1.26217	+	1.18614i	−0.728714	+	0.684819i
$3$	−1.26217	+	1.18614i	−0.728714	+	0.684819i
$4$	−1.37228			−0.686141
$5$		0			0
$5$		0			0
$6$	1.00000	−	0.939764i	0.408248	−	0.383657i
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$8$	2.67181			0.944629
$9$	0.186141	−	2.99422i	0.0620469	−	0.998073i
$10$		0			0
$11$		−	2.52434i		−	0.761116i	−0.924757	−	0.380558i	$-0.875732\pi$
$11$		−	2.52434i		−	0.761116i	0.924757	−	0.380558i	$-0.124268\pi$
$12$	1.73205	−	1.62772i	0.500000	−	0.469882i
$13$	4.10891			1.13961			0.569804	−	0.821781i	$-0.307019\pi$
$13$	4.10891			1.13961			0.569804	+	0.821781i	$0.307019\pi$
$14$	−1.37228	−	1.58457i	−0.366758	−	0.423495i
$15$		0			0
$16$	0.627719			0.156930
$17$			4.37228i			1.06043i	0.847862	+	0.530217i	$0.177890\pi$
$17$			4.37228i			1.06043i	−0.847862	+	0.530217i	$0.822110\pi$
$18$	−0.147477	+	2.37228i	−0.0347606	+	0.559152i
$19$			3.46410i			0.794719i	0.917663	+	0.397360i	$0.130073\pi$
$19$			3.46410i			0.794719i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	−4.55842	−	0.469882i	−0.994729	−	0.102537i
$22$			2.00000i			0.426401i
$23$	−8.51278			−1.77504			−0.887518	−	0.460772i	$-0.847572\pi$
$23$	−8.51278			−1.77504			−0.887518	+	0.460772i	$0.847572\pi$
$24$	−3.37228	+	3.16915i	−0.688364	+	0.646900i
$25$		0			0
$26$	−3.25544			−0.638444
$27$	3.31662	+	4.00000i	0.638285	+	0.769800i
$28$	−2.37686	−	2.74456i	−0.449185	−	0.518674i
$29$		−	0.939764i		−	0.174510i	−0.996186	−	0.0872549i	$-0.972191\pi$
$29$		−	0.939764i		−	0.174510i	0.996186	−	0.0872549i	$-0.0278095\pi$
$30$		0			0
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$	−5.84096			−1.03255
$33$	2.99422	+	3.18614i	0.521227	+	0.554636i
$34$		−	3.46410i		−	0.594089i
$35$		0			0
$36$	−0.255437	+	4.10891i	−0.0425729	+	0.684819i
$37$			6.74456i			1.10880i	0.832251	+	0.554400i	$0.187052\pi$
$37$			6.74456i			1.10880i	−0.832251	+	0.554400i	$0.812948\pi$
$38$		−	2.74456i		−	0.445227i
$39$	−5.18614	+	4.87375i	−0.830447	+	0.780424i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$	3.61158	+	0.372281i	0.557279	+	0.0574443i
$43$			4.74456i			0.723539i	0.932268	+	0.361770i	$0.117827\pi$
$43$			4.74456i			0.723539i	−0.932268	+	0.361770i	$0.882173\pi$
$44$			3.46410i			0.522233i
$45$		0			0
$46$	6.74456			0.994432
$47$		−	1.62772i		−	0.237427i	−0.992929	−	0.118714i	$-0.962123\pi$
$47$		−	1.62772i		−	0.237427i	0.992929	−	0.118714i	$-0.0378770\pi$
$48$	−0.792287	+	0.744563i	−0.114357	+	0.107468i
$49$	−1.00000	+	6.92820i	−0.142857	+	0.989743i
$50$		0			0
$51$	−5.18614	−	5.51856i	−0.726205	−	0.772753i
$52$	−5.63858			−0.781931
$53$	1.87953			0.258173			0.129086	−	0.991633i	$-0.458796\pi$
$53$	1.87953			0.258173			0.129086	+	0.991633i	$0.458796\pi$
$54$	−2.62772	−	3.16915i	−0.357587	−	0.431266i
$55$		0			0
$56$	4.62772	+	5.34363i	0.618405	+	0.714072i
$57$	−4.10891	−	4.37228i	−0.544239	−	0.579123i
$58$			0.744563i			0.0977659i
$59$	−8.74456			−1.13845			−0.569223	−	0.822183i	$-0.692756\pi$
$59$	−8.74456			−1.13845			−0.569223	+	0.822183i	$0.692756\pi$
$60$		0			0
$61$			6.92820i			0.887066i	0.896258	+	0.443533i	$0.146275\pi$
$61$			6.92820i			0.887066i	−0.896258	+	0.443533i	$0.853725\pi$
$62$		−	2.74456i		−	0.348560i
$63$	6.31084	−	4.81386i	0.795092	−	0.606489i
$64$	3.37228			0.421535
$65$		0			0
$66$	−2.37228	−	2.52434i	−0.292008	−	0.310725i
$67$		−	4.74456i		−	0.579641i	−0.957081	−	0.289820i	$-0.906404\pi$
$67$		−	4.74456i		−	0.579641i	0.957081	−	0.289820i	$-0.0935955\pi$
$68$		−	6.00000i		−	0.727607i
$69$	10.7446	−	10.0974i	1.29349	−	1.21558i
$70$		0			0
$71$			0.294954i			0.0350046i	0.999847	+	0.0175023i	$0.00557143\pi$
$71$			0.294954i			0.0350046i	−0.999847	+	0.0175023i	$0.994429\pi$
$72$	0.497333	−	8.00000i	0.0586113	−	0.942809i
$73$	−6.92820			−0.810885			−0.405442	−	0.914121i	$-0.632883\pi$
$73$	−6.92820			−0.810885			−0.405442	+	0.914121i	$0.632883\pi$
$74$		−	5.34363i		−	0.621184i
$75$		0			0
$76$		−	4.75372i		−	0.545289i
$77$	5.04868	−	4.37228i	0.575350	−	0.498268i
$78$	4.10891	−	3.86141i	0.465243	−	0.437218i
$79$	2.37228			0.266903			0.133451	−	0.991055i	$-0.457394\pi$
$79$	2.37228			0.266903			0.133451	+	0.991055i	$0.457394\pi$
$80$		0			0
$81$	−8.93070	−	1.11469i	−0.992300	−	0.123855i
$82$	−4.75372			−0.524961
$83$			17.4891i			1.91968i	0.280546	+	0.959840i	$0.409484\pi$
$83$			17.4891i			1.91968i	−0.280546	+	0.959840i	$0.590516\pi$
$84$	6.25544	+	0.644810i	0.682524	+	0.0703546i
$85$		0			0
$86$		−	3.75906i		−	0.405349i
$87$	1.11469	+	1.18614i	0.119508	+	0.127168i
$88$		−	6.74456i		−	0.718973i
$89$	14.7446			1.56292			0.781460	−	0.623955i	$-0.214475\pi$
$89$	14.7446			1.56292			0.781460	+	0.623955i	$0.214475\pi$
$90$		0			0
$91$	7.11684	+	8.21782i	0.746048	+	0.861462i
$92$	11.6819			1.21792
$93$	−4.10891	−	4.37228i	−0.426074	−	0.453384i
$94$			1.28962i			0.133014i
$95$		0			0
$96$	7.37228	−	6.92820i	0.752430	−	0.707107i
$97$	−11.0371			−1.12065			−0.560325	−	0.828273i	$-0.689324\pi$
$97$	−11.0371			−1.12065			−0.560325	+	0.828273i	$0.689324\pi$
$98$	0.792287	−	5.48913i	0.0800331	−	0.554485i
$99$	−7.55842	−	0.469882i	−0.759650	−	0.0472249i
$100$		0			0
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$	4.10891	+	4.37228i	0.406843	+	0.432920i
$103$	6.28339			0.619121			0.309561	−	0.950880i	$-0.399818\pi$
$103$	6.28339			0.619121			0.309561	+	0.950880i	$0.399818\pi$
$104$	10.9783			1.07651
$105$		0			0
$106$	−1.48913			−0.144637
$107$	−6.63325			−0.641260			−0.320630	−	0.947204i	$-0.603895\pi$
$107$	−6.63325			−0.641260			−0.320630	+	0.947204i	$0.603895\pi$
$108$	−4.55134	−	5.48913i	−0.437953	−	0.528191i
$109$	17.1168			1.63950			0.819748	−	0.572724i	$-0.194113\pi$
$109$	17.1168			1.63950			0.819748	+	0.572724i	$0.194113\pi$
$110$		0			0
$111$	−8.00000	−	8.51278i	−0.759326	−	0.807997i
$112$	1.08724	+	1.25544i	0.102735	+	0.118628i
$113$	3.16915			0.298128			0.149064	−	0.988828i	$-0.452374\pi$
$113$	3.16915			0.298128			0.149064	+	0.988828i	$0.452374\pi$
$114$	3.25544	+	3.46410i	0.304900	+	0.324443i
$115$		0			0
$116$			1.28962i			0.119738i
$117$	0.764836	−	12.3030i	0.0707091	−	1.13741i
$118$	6.92820			0.637793
$119$	−8.74456	+	7.57301i	−0.801613	+	0.694217i
$120$		0			0
$121$	4.62772			0.420702
$122$		−	5.48913i		−	0.496962i
$123$	−7.57301	+	7.11684i	−0.682836	+	0.641704i
$124$		−	4.75372i		−	0.426897i
$125$		0			0
$126$	−5.00000	+	3.81396i	−0.445435	+	0.339774i
$127$			0.744563i			0.0660693i	0.999454	+	0.0330346i	$0.0105172\pi$
$127$			0.744563i			0.0660693i	−0.999454	+	0.0330346i	$0.989483\pi$
$128$	9.01011			0.796389
$129$	−5.62772	−	5.98844i	−0.495493	−	0.527253i
$130$		0			0
$131$	−5.48913			−0.479587			−0.239794	−	0.970824i	$-0.577080\pi$
$131$	−5.48913			−0.479587			−0.239794	+	0.970824i	$0.577080\pi$
$132$	−4.10891	−	4.37228i	−0.357635	−	0.380558i
$133$	−6.92820	+	6.00000i	−0.600751	+	0.520266i
$134$			3.75906i			0.324733i
$135$		0			0
$136$			11.6819i			1.00172i
$137$	13.2665			1.13343			0.566717	−	0.823913i	$-0.308213\pi$
$137$	13.2665			1.13343			0.566717	+	0.823913i	$0.308213\pi$
$138$	−8.51278	+	8.00000i	−0.724656	+	0.681005i
$139$		−	18.6101i		−	1.57849i	−0.614078	−	0.789245i	$-0.710472\pi$
$139$		−	18.6101i		−	1.57849i	0.614078	−	0.789245i	$-0.289528\pi$
$140$		0			0
$141$	1.93070	+	2.05446i	0.162595	+	0.173016i
$142$		−	0.233688i		−	0.0196107i
$143$		−	10.3723i		−	0.867374i
$144$	0.116844	−	1.87953i	0.00973700	−	0.156627i
$145$		0			0
$146$	5.48913			0.454283
$147$	−6.95565	−	9.93070i	−0.573693	−	0.819071i
$148$		−	9.25544i		−	0.760792i
$149$			3.16915i			0.259627i	0.991538	+	0.129813i	$0.0414378\pi$
$149$			3.16915i			0.259627i	−0.991538	+	0.129813i	$0.958562\pi$
$150$		0			0
$151$	−2.37228			−0.193054			−0.0965268	−	0.995330i	$-0.530773\pi$
$151$	−2.37228			−0.193054			−0.0965268	+	0.995330i	$0.530773\pi$
$152$			9.25544i			0.750715i
$153$	13.0916	+	0.813859i	1.05839	+	0.0657966i
$154$	−4.00000	+	3.46410i	−0.322329	+	0.279145i
$155$		0			0
$156$	7.11684	−	6.68815i	0.569804	−	0.535481i
$157$		0			0			−	1.00000i	$-0.5\pi$
$157$		0			0				1.00000i	$0.5\pi$
$158$	−1.87953			−0.149527
$159$	−2.37228	+	2.22938i	−0.188134	+	0.176802i
$160$		0			0
$161$	−14.7446	−	17.0256i	−1.16203	−	1.34180i
$162$	7.07568	+	0.883156i	0.555918	+	0.0693873i
$163$			8.00000i			0.626608i	0.949653	+	0.313304i	$0.101436\pi$
$163$			8.00000i			0.626608i	−0.949653	+	0.313304i	$0.898564\pi$
$164$	−8.23369			−0.642943
$165$		0			0
$166$		−	13.8564i		−	1.07547i
$167$		−	4.88316i		−	0.377870i	−0.981990	−	0.188935i	$-0.939496\pi$
$167$		−	4.88316i		−	0.377870i	0.981990	−	0.188935i	$-0.0605035\pi$
$168$	−12.1793	−	1.25544i	−0.939650	−	0.0968591i
$169$	3.88316			0.298704
$170$		0			0
$171$	10.3723	+	0.644810i	0.793188	+	0.0493099i
$172$		−	6.51087i		−	0.496450i
$173$			1.11684i			0.0849121i	0.999098	+	0.0424560i	$0.0135182\pi$
$173$			1.11684i			0.0849121i	−0.999098	+	0.0424560i	$0.986482\pi$
$174$	−0.883156	−	0.939764i	−0.0669519	−	0.0712433i
$175$		0			0
$176$		−	1.58457i		−	0.119442i
$177$	11.0371	−	10.3723i	0.829600	−	0.779628i
$178$	−11.6819			−0.875597
$179$			6.63325i			0.495792i	0.968787	+	0.247896i	$0.0797392\pi$
$179$			6.63325i			0.495792i	−0.968787	+	0.247896i	$0.920261\pi$
$180$		0			0
$181$			1.28962i			0.0958567i	0.998851	+	0.0479284i	$0.0152619\pi$
$181$			1.28962i			0.0958567i	−0.998851	+	0.0479284i	$0.984738\pi$
$182$	−5.63858	−	6.51087i	−0.417960	−	0.482618i
$183$	−8.21782	−	8.74456i	−0.607479	−	0.646417i
$184$	−22.7446			−1.67675
$185$		0			0
$186$	3.25544	+	3.46410i	0.238700	+	0.254000i
$187$	11.0371			0.807114
$188$			2.23369i			0.162908i
$189$	−2.25544	+	13.5615i	−0.164059	+	0.986451i
$190$		0			0
$191$			20.8395i			1.50789i	0.656935	+	0.753947i	$0.271853\pi$
$191$			20.8395i			1.50789i	−0.656935	+	0.753947i	$0.728147\pi$
$192$	−4.25639	+	4.00000i	−0.307178	+	0.288675i
$193$		−	12.2337i		−	0.880600i	−0.897851	−	0.440300i	$-0.854872\pi$
$193$		−	12.2337i		−	0.880600i	0.897851	−	0.440300i	$-0.145128\pi$
$194$	8.74456			0.627823
$195$		0			0
$196$	1.37228	−	9.50744i	0.0980201	−	0.679103i
$197$	−15.7359			−1.12114			−0.560569	−	0.828107i	$-0.689418\pi$
$197$	−15.7359			−1.12114			−0.560569	+	0.828107i	$0.689418\pi$
$198$	5.98844	+	0.372281i	0.425580	+	0.0264569i
$199$			26.8280i			1.90178i	0.309524	+	0.950892i	$0.399830\pi$
$199$			26.8280i			1.90178i	−0.309524	+	0.950892i	$0.600170\pi$
$200$		0			0
$201$	5.62772	+	5.98844i	0.396949	+	0.422392i
$202$	4.75372			0.334471
$203$	1.87953	−	1.62772i	0.131917	−	0.114243i
$204$	7.11684	+	7.57301i	0.498279	+	0.530217i
$205$		0			0
$206$	−4.97825			−0.346851
$207$	−1.58457	+	25.4891i	−0.110136	+	1.77162i
$208$	2.57924			0.178838
$209$	8.74456			0.604874
$210$		0			0
$211$	−11.1168			−0.765315			−0.382658	−	0.923890i	$-0.624991\pi$
$211$	−11.1168			−0.765315			−0.382658	+	0.923890i	$0.624991\pi$
$212$	−2.57924			−0.177143
$213$	−0.349857	−	0.372281i	−0.0239718	−	0.0255083i
$214$	5.25544			0.359254
$215$		0			0
$216$	8.86141	+	10.6873i	0.602942	+	0.727176i
$217$	−6.92820	+	6.00000i	−0.470317	+	0.407307i
$218$	−13.5615			−0.918497
$219$	8.74456	−	8.21782i	0.590903	−	0.555309i
$220$		0			0
$221$			17.9653i			1.20848i
$222$	6.33830	+	6.74456i	0.425399	+	0.452665i
$223$	8.86263			0.593486			0.296743	−	0.954957i	$-0.404100\pi$
$223$	8.86263			0.593486			0.296743	+	0.954957i	$0.404100\pi$
$224$	−10.1168	−	11.6819i	−0.675960	−	0.780531i
$225$		0			0
$226$	−2.51087			−0.167021
$227$			24.6060i			1.63316i	0.577235	+	0.816578i	$0.304131\pi$
$227$			24.6060i			1.63316i	−0.577235	+	0.816578i	$0.695869\pi$
$228$	5.63858	+	6.00000i	0.373424	+	0.397360i
$229$		−	15.1460i		−	1.00088i	−0.865772	−	0.500439i	$-0.833172\pi$
$229$		−	15.1460i		−	1.00088i	0.865772	−	0.500439i	$-0.166828\pi$
$230$		0			0
$231$	−1.18614	+	11.5070i	−0.0780423	+	0.757105i
$232$		−	2.51087i		−	0.164847i
$233$	17.0256			1.11538			0.557691	−	0.830049i	$-0.311688\pi$
$233$	17.0256			1.11538			0.557691	+	0.830049i	$0.311688\pi$
$234$	−0.605969	+	9.74749i	−0.0396134	+	0.637214i
$235$		0			0
$236$	12.0000			0.781133
$237$	−2.99422	+	2.81386i	−0.194495	+	0.182780i
$238$	6.92820	−	6.00000i	0.449089	−	0.388922i
$239$		−	20.8395i		−	1.34800i	−0.738733	−	0.673998i	$-0.764576\pi$
$239$		−	20.8395i		−	1.34800i	0.738733	−	0.673998i	$-0.235424\pi$
$240$		0			0
$241$		−	16.4356i		−	1.05871i	−0.848399	−	0.529357i	$-0.822433\pi$
$241$		−	16.4356i		−	1.05871i	0.848399	−	0.529357i	$-0.177567\pi$
$242$	−3.66648			−0.235690
$243$	12.5942	−	9.18614i	0.807921	−	0.589291i
$244$		−	9.50744i		−	0.608652i
$245$		0			0
$246$	6.00000	−	5.63858i	0.382546	−	0.359503i
$247$			14.2337i			0.905668i
$248$			9.25544i			0.587721i
$249$	−20.7446	−	22.0742i	−1.31463	−	1.39890i
$250$		0			0
$251$	5.48913			0.346471			0.173235	−	0.984880i	$-0.444578\pi$
$251$	5.48913			0.346471			0.173235	+	0.984880i	$0.444578\pi$
$252$	−8.66025	+	6.60597i	−0.545545	+	0.416137i
$253$			21.4891i			1.35101i
$254$		−	0.589907i		−	0.0370141i
$255$		0			0
$256$	−13.8832			−0.867697
$257$			0.510875i			0.0318675i	0.999873	+	0.0159337i	$0.00507208\pi$
$257$			0.510875i			0.0318675i	−0.999873	+	0.0159337i	$0.994928\pi$
$258$	4.45877	+	4.74456i	0.277591	+	0.295384i
$259$	−13.4891	+	11.6819i	−0.838173	+	0.725880i
$260$		0			0
$261$	−2.81386	−	0.174928i	−0.174174	−	0.0108278i
$262$	4.34896			0.268680
$263$	−0.294954			−0.0181876			−0.00909381	−	0.999959i	$-0.502895\pi$
$263$	−0.294954			−0.0181876			−0.00909381	+	0.999959i	$0.502895\pi$
$264$	8.00000	+	8.51278i	0.492366	+	0.523925i
$265$		0			0
$266$	5.48913	−	4.75372i	0.336560	−	0.291469i
$267$	−18.6101	+	17.4891i	−1.13892	+	1.07032i
$268$			6.51087i			0.397715i
$269$	2.74456			0.167339			0.0836695	−	0.996494i	$-0.473336\pi$
$269$	2.74456			0.167339			0.0836695	+	0.996494i	$0.473336\pi$
$270$		0			0
$271$		−	4.75372i		−	0.288768i	−0.989522	−	0.144384i	$-0.953880\pi$
$271$		−	4.75372i		−	0.288768i	0.989522	−	0.144384i	$-0.0461201\pi$
$272$			2.74456i			0.166414i
$273$	−18.7302	−	1.93070i	−1.13360	−	0.116851i
$274$	−10.5109			−0.634985
$275$		0			0
$276$	−14.7446	+	13.8564i	−0.887518	+	0.834058i
$277$		−	28.2337i		−	1.69640i	−0.529678	−	0.848199i	$-0.677687\pi$
$277$		−	28.2337i		−	1.69640i	0.529678	−	0.848199i	$-0.322313\pi$
$278$			14.7446i			0.884320i
$279$	10.3723	+	0.644810i	0.620972	+	0.0386038i
$280$		0			0
$281$		−	28.0627i		−	1.67408i	−0.547143	−	0.837039i	$-0.684285\pi$
$281$		−	28.0627i		−	1.67408i	0.547143	−	0.837039i	$-0.315715\pi$
$282$	−1.52967	−	1.62772i	−0.0910906	−	0.0969292i
$283$	−0.644810			−0.0383300			−0.0191650	−	0.999816i	$-0.506101\pi$
$283$	−0.644810			−0.0383300			−0.0191650	+	0.999816i	$0.506101\pi$
$284$		−	0.404759i		−	0.0240181i
$285$		0			0
$286$			8.21782i			0.485930i
$287$	10.3923	+	12.0000i	0.613438	+	0.708338i
$288$	−1.08724	+	17.4891i	−0.0640663	+	1.03056i
$289$	−2.11684			−0.124520
$290$		0			0
$291$	13.9307	−	13.0916i	0.816632	−	0.767441i
$292$	9.50744			0.556381
$293$			10.8832i			0.635801i	0.948124	+	0.317900i	$0.102978\pi$
$293$			10.8832i			0.635801i	−0.948124	+	0.317900i	$0.897022\pi$
$294$	5.51087	+	7.86797i	0.321401	+	0.458869i
$295$		0			0
$296$			18.0202i			1.04740i
$297$	10.0974	−	8.37228i	0.585908	−	0.485809i
$298$		−	2.51087i		−	0.145451i
$299$	−34.9783			−2.02284
$300$		0			0
$301$	−9.48913	+	8.21782i	−0.546944	+	0.473667i
$302$	1.87953			0.108155
$303$	7.57301	−	7.11684i	0.435058	−	0.408852i
$304$			2.17448i			0.124715i
$305$		0			0
$306$	−10.3723	−	0.644810i	−0.592944	−	0.0368613i
$307$	22.7190			1.29664			0.648322	−	0.761366i	$-0.275471\pi$
$307$	22.7190			1.29664			0.648322	+	0.761366i	$0.275471\pi$
$308$	−6.92820	+	6.00000i	−0.394771	+	0.341882i
$309$	−7.93070	+	7.45299i	−0.451162	+	0.423986i
$310$		0			0
$311$	14.2337			0.807118			0.403559	−	0.914954i	$-0.367773\pi$
$311$	14.2337			0.807118			0.403559	+	0.914954i	$0.367773\pi$
$312$	−13.8564	+	13.0217i	−0.784465	+	0.737211i
$313$	−5.39853			−0.305143			−0.152572	−	0.988292i	$-0.548755\pi$
$313$	−5.39853			−0.305143			−0.152572	+	0.988292i	$0.548755\pi$
$314$		0			0
$315$		0			0
$316$	−3.25544			−0.183133
$317$	−1.87953			−0.105565			−0.0527824	−	0.998606i	$-0.516809\pi$
$317$	−1.87953			−0.105565			−0.0527824	+	0.998606i	$0.516809\pi$
$318$	1.87953	−	1.76631i	0.105399	−	0.0990499i
$319$	−2.37228			−0.132822
$320$		0			0
$321$	8.37228	−	7.86797i	0.467295	−	0.439147i
$322$	11.6819	+	13.4891i	0.651008	+	0.751720i
$323$	−15.1460			−0.842747
$324$	12.2554	+	1.52967i	0.680858	+	0.0849817i
$325$		0			0
$326$		−	6.33830i		−	0.351046i
$327$	−21.6043	+	20.3030i	−1.19472	+	1.12276i
$328$	16.0309			0.885158
$329$	3.25544	−	2.81929i	0.179478	−	0.155433i
$330$		0			0
$331$	−4.00000			−0.219860			−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000			−0.219860			−0.109930	+	0.993939i	$0.535063\pi$
$332$		−	24.0000i		−	1.31717i
$333$	20.1947	+	1.25544i	1.10666	+	0.0687975i
$334$			3.86886i			0.211695i
$335$		0			0
$336$	−2.86141	−	0.294954i	−0.156103	−	0.0160910i
$337$		−	16.2337i		−	0.884305i	−0.896940	−	0.442153i	$-0.854215\pi$
$337$		−	16.2337i		−	0.884305i	0.896940	−	0.442153i	$-0.145785\pi$
$338$	−3.07657			−0.167344
$339$	−4.00000	+	3.75906i	−0.217250	+	0.204164i
$340$		0			0
$341$	8.74456			0.473545
$342$	−8.21782	−	0.510875i	−0.444369	−	0.0276249i
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$			12.6766i			0.683476i
$345$		0			0
$346$		−	0.884861i		−	0.0475704i
$347$	−14.8511			−0.797247			−0.398624	−	0.917115i	$-0.630512\pi$
$347$	−14.8511			−0.797247			−0.398624	+	0.917115i	$0.630512\pi$
$348$	−1.52967	−	1.62772i	−0.0819990	−	0.0872549i
$349$			15.1460i			0.810748i	0.914151	+	0.405374i	$0.132859\pi$
$349$			15.1460i			0.810748i	−0.914151	+	0.405374i	$0.867141\pi$
$350$		0			0
$351$	13.6277	+	16.4356i	0.727394	+	0.877270i
$352$			14.7446i			0.785888i
$353$		−	25.1168i		−	1.33683i	−0.743786	−	0.668417i	$-0.766972\pi$
$353$		−	25.1168i		−	1.33683i	0.743786	−	0.668417i	$-0.233028\pi$
$354$	−8.74456	+	8.21782i	−0.464768	+	0.436772i
$355$		0			0
$356$	−20.2337			−1.07238
$357$	2.05446	−	19.9307i	0.108733	−	1.05484i
$358$		−	5.25544i		−	0.277758i
$359$		−	16.7306i		−	0.883007i	−0.897259	−	0.441504i	$-0.854445\pi$
$359$		−	16.7306i		−	0.883007i	0.897259	−	0.441504i	$-0.145555\pi$
$360$		0			0
$361$	7.00000			0.368421
$362$		−	1.02175i		−	0.0537020i
$363$	−5.84096	+	5.48913i	−0.306571	+	0.288104i
$364$	−9.76631	−	11.2772i	−0.511894	−	0.591084i
$365$		0			0
$366$	6.51087	+	6.92820i	0.340329	+	0.362143i
$367$	35.2858			1.84191			0.920953	−	0.389675i	$-0.127413\pi$
$367$	35.2858			1.84191			0.920953	+	0.389675i	$0.127413\pi$
$368$	−5.34363			−0.278556
$369$	1.11684	−	17.9653i	0.0581406	−	0.935237i
$370$		0			0
$371$	3.25544	+	3.75906i	0.169014	+	0.195160i
$372$	5.63858	+	6.00000i	0.292347	+	0.311086i
$373$		−	13.2554i		−	0.686341i	−0.939273	−	0.343170i	$-0.888499\pi$
$373$		−	13.2554i		−	0.686341i	0.939273	−	0.343170i	$-0.111501\pi$
$374$	−8.74456			−0.452171
$375$		0			0
$376$		−	4.34896i		−	0.224281i
$377$		−	3.86141i		−	0.198873i
$378$	1.78695	−	10.7446i	0.0919110	−	0.552641i
$379$	21.4891			1.10382			0.551911	−	0.833903i	$-0.313899\pi$
$379$	21.4891			1.10382			0.551911	+	0.833903i	$0.313899\pi$
$380$		0			0
$381$	−0.883156	−	0.939764i	−0.0452455	−	0.0481456i
$382$		−	16.5109i		−	0.844770i
$383$		−	5.48913i		−	0.280481i	−0.990117	−	0.140241i	$-0.955212\pi$
$383$		−	5.48913i		−	0.280481i	0.990117	−	0.140241i	$-0.0447876\pi$
$384$	−11.3723	+	10.6873i	−0.580339	+	0.545382i
$385$		0			0
$386$			9.69259i			0.493340i
$387$	14.2063	+	0.883156i	0.722145	+	0.0448933i
$388$	15.1460			0.768923
$389$			29.3523i			1.48822i	0.668057	+	0.744110i	$0.267126\pi$
$389$			29.3523i			1.48822i	−0.668057	+	0.744110i	$0.732874\pi$
$390$		0			0
$391$		−	37.2203i		−	1.88231i
$392$	−2.67181	+	18.5109i	−0.134947	+	0.934940i
$393$	6.92820	−	6.51087i	0.349482	−	0.328430i
$394$	12.4674			0.628097
$395$		0			0
$396$	10.3723	+	0.644810i	0.521227	+	0.0324029i
$397$	−26.1831			−1.31409			−0.657047	−	0.753850i	$-0.728195\pi$
$397$	−26.1831			−1.31409			−0.657047	+	0.753850i	$0.728195\pi$
$398$		−	21.2554i		−	1.06544i
$399$	1.62772	−	15.7908i	0.0814879	−	0.790531i
$400$		0			0
$401$		−	5.98844i		−	0.299048i	−0.988758	−	0.149524i	$-0.952226\pi$
$401$		−	5.98844i		−	0.299048i	0.988758	−	0.149524i	$-0.0477742\pi$
$402$	−4.45877	−	4.74456i	−0.222383	−	0.236637i
$403$			14.2337i			0.709030i
$404$	8.23369			0.409641
$405$		0			0
$406$	−1.48913	+	1.28962i	−0.0739040	+	0.0640028i
$407$	17.0256			0.843925
$408$	−13.8564	−	14.7446i	−0.685994	−	0.729965i
$409$		−	24.6535i		−	1.21904i	−0.792772	−	0.609518i	$-0.791363\pi$
$409$		−	24.6535i		−	1.21904i	0.792772	−	0.609518i	$-0.208637\pi$
$410$		0			0
$411$	−16.7446	+	15.7359i	−0.825948	+	0.776196i
$412$	−8.62258			−0.424804
$413$	−15.1460	−	17.4891i	−0.745287	−	0.860584i
$414$	1.25544	−	20.1947i	0.0617014	−	0.992515i
$415$		0			0
$416$	−24.0000			−1.17670
$417$	22.0742	+	23.4891i	1.08098	+	1.15027i
$418$	−6.92820			−0.338869
$419$	8.74456			0.427200			0.213600	−	0.976921i	$-0.431481\pi$
$419$	8.74456			0.427200			0.213600	+	0.976921i	$0.431481\pi$
$420$		0			0
$421$	14.6060			0.711851			0.355926	−	0.934514i	$-0.384166\pi$
$421$	14.6060			0.711851			0.355926	+	0.934514i	$0.384166\pi$
$422$	8.80773			0.428754
$423$	−4.87375	−	0.302985i	−0.236970	−	0.0147316i
$424$	5.02175			0.243878
$425$		0			0
$426$	0.277187	+	0.294954i	0.0134297	+	0.0142906i
$427$	−13.8564	+	12.0000i	−0.670559	+	0.580721i
$428$	9.10268			0.439995
$429$	12.3030	+	13.0916i	0.593994	+	0.632067i
$430$		0			0
$431$		−	15.0911i		−	0.726914i	−0.931611	−	0.363457i	$-0.881596\pi$
$431$		−	15.0911i		−	0.726914i	0.931611	−	0.363457i	$-0.118404\pi$
$432$	2.08191	+	2.51087i	0.100166	+	0.120805i
$433$	−37.2203			−1.78869			−0.894346	−	0.447377i	$-0.852358\pi$
$433$	−37.2203			−1.78869			−0.894346	+	0.447377i	$0.852358\pi$
$434$	5.48913	−	4.75372i	0.263486	−	0.228186i
$435$		0			0
$436$	−23.4891			−1.12493
$437$		−	29.4891i		−	1.41066i
$438$	−6.92820	+	6.51087i	−0.331042	+	0.311102i
$439$			18.6101i			0.888213i	0.895974	+	0.444106i	$0.146479\pi$
$439$			18.6101i			0.888213i	−0.895974	+	0.444106i	$0.853521\pi$
$440$		0			0
$441$	20.5584	+	4.28384i	0.978972	+	0.203992i
$442$		−	14.2337i		−	0.677027i
$443$	6.63325			0.315155			0.157578	−	0.987507i	$-0.449632\pi$
$443$	6.63325			0.315155			0.157578	+	0.987507i	$0.449632\pi$
$444$	10.9783	+	11.6819i	0.521005	+	0.554400i
$445$		0			0
$446$	−7.02175			−0.332489
$447$	−3.75906	−	4.00000i	−0.177797	−	0.189194i
$448$	5.84096	+	6.74456i	0.275960	+	0.318651i
$449$			11.6270i			0.548713i	0.961628	+	0.274357i	$0.0884648\pi$
$449$			11.6270i			0.548713i	−0.961628	+	0.274357i	$0.911535\pi$
$450$		0			0
$451$		−	15.1460i		−	0.713199i
$452$	−4.34896			−0.204558
$453$	2.99422	−	2.81386i	0.140681	−	0.132207i
$454$		−	19.4950i		−	0.914945i
$455$		0			0
$456$	−10.9783	−	11.6819i	−0.514104	−	0.547056i
$457$		−	12.9783i		−	0.607097i	−0.952816	−	0.303548i	$-0.901829\pi$
$457$		−	12.9783i		−	0.607097i	0.952816	−	0.303548i	$-0.0981714\pi$
$458$			12.0000i			0.560723i
$459$	−17.4891	+	14.5012i	−0.816322	+	0.676859i
$460$		0			0
$461$	−2.74456			−0.127827			−0.0639135	−	0.997955i	$-0.520358\pi$
$461$	−2.74456			−0.127827			−0.0639135	+	0.997955i	$0.520358\pi$
$462$	0.939764	−	9.11684i	0.0437218	−	0.424154i
$463$		−	32.4674i		−	1.50889i	−0.656365	−	0.754443i	$-0.727907\pi$
$463$		−	32.4674i		−	1.50889i	0.656365	−	0.754443i	$-0.272093\pi$
$464$		−	0.589907i		−	0.0273858i
$465$		0			0
$466$	−13.4891			−0.624872
$467$		−	31.1168i		−	1.43992i	−0.694018	−	0.719958i	$-0.744161\pi$
$467$		−	31.1168i		−	1.43992i	0.694018	−	0.719958i	$-0.255839\pi$
$468$	−1.04957	+	16.8832i	−0.0485164	+	0.780424i
$469$	9.48913	−	8.21782i	0.438167	−	0.379464i
$470$		0			0
$471$		0			0
$472$	−23.3639			−1.07541
$473$	11.9769			0.550697
$474$	2.37228	−	2.22938i	0.108962	−	0.102399i
$475$		0			0
$476$	12.0000	−	10.3923i	0.550019	−	0.476331i
$477$	0.349857	−	5.62772i	0.0160188	−	0.257676i
$478$			16.5109i			0.755190i
$479$	41.4891			1.89569			0.947843	−	0.318737i	$-0.103259\pi$
$479$	41.4891			1.89569			0.947843	+	0.318737i	$0.103259\pi$
$480$		0			0
$481$			27.7128i			1.26360i
$482$			13.0217i			0.593124i
$483$	38.8048	+	4.00000i	1.76568	+	0.182006i
$484$	−6.35053			−0.288661
$485$		0			0
$486$	−9.97825	+	7.27806i	−0.452623	+	0.330139i
$487$		−	37.4891i		−	1.69879i	−0.527754	−	0.849397i	$-0.676966\pi$
$487$		−	37.4891i		−	1.69879i	0.527754	−	0.849397i	$-0.323034\pi$
$488$			18.5109i			0.837948i
$489$	−9.48913	−	10.0974i	−0.429113	−	0.456618i
$490$		0			0
$491$			5.69349i			0.256943i	0.991713	+	0.128472i	$0.0410072\pi$
$491$			5.69349i			0.256943i	−0.991713	+	0.128472i	$0.958993\pi$
$492$	10.3923	−	9.76631i	0.468521	−	0.440299i
$493$	4.10891			0.185056
$494$		−	11.2772i		−	0.507384i
$495$		0			0
$496$			2.17448i			0.0976371i
$497$	−0.589907	+	0.510875i	−0.0264610	+	0.0229159i
$498$	16.4356	+	17.4891i	0.736499	+	0.783706i
$499$	−41.3505			−1.85110			−0.925552	−	0.378620i	$-0.876399\pi$
$499$	−41.3505			−1.85110			−0.925552	+	0.378620i	$0.876399\pi$
$500$		0			0
$501$	5.79211	+	6.16337i	0.258772	+	0.275359i
$502$	−4.34896			−0.194104
$503$		−	12.6060i		−	0.562072i	−0.959697	−	0.281036i	$-0.909322\pi$
$503$		−	12.6060i		−	0.562072i	0.959697	−	0.281036i	$-0.0906781\pi$
$504$	16.8614	−	12.8617i	0.751067	−	0.572907i
$505$		0			0
$506$		−	17.0256i		−	0.756878i
$507$	−4.90120	+	4.60597i	−0.217670	+	0.204558i
$508$		−	1.02175i		−	0.0453328i
$509$	−3.76631			−0.166939			−0.0834694	−	0.996510i	$-0.526600\pi$
$509$	−3.76631			−0.166939			−0.0834694	+	0.996510i	$0.526600\pi$
$510$		0			0
$511$	−12.0000	−	13.8564i	−0.530849	−	0.612971i
$512$	−7.02078			−0.310277
$513$	−13.8564	+	11.4891i	−0.611775	+	0.507257i
$514$		−	0.404759i		−	0.0178532i
$515$		0			0
$516$	7.72281	+	8.21782i	0.339978	+	0.361770i
$517$	−4.10891			−0.180710
$518$	10.6873	−	9.25544i	0.469571	−	0.406661i
$519$	−1.32473	−	1.40965i	−0.0581494	−	0.0618766i
$520$		0			0
$521$	34.4674			1.51004			0.755022	−	0.655700i	$-0.227626\pi$
$521$	34.4674			1.51004			0.755022	+	0.655700i	$0.227626\pi$
$522$	2.22938	+	0.138593i	0.0975775	+	0.00606607i
$523$	−10.3923			−0.454424			−0.227212	−	0.973845i	$-0.572961\pi$
$523$	−10.3923			−0.454424			−0.227212	+	0.973845i	$0.572961\pi$
$524$	7.53262			0.329064
$525$		0			0
$526$	0.233688			0.0101893
$527$	−15.1460			−0.659771
$528$	1.87953	+	2.00000i	0.0817959	+	0.0870388i
$529$	49.4674			2.15076
$530$		0			0
$531$	−1.62772	+	26.1831i	−0.0706370	+	1.13625i
$532$	9.50744	−	8.23369i	0.412200	−	0.356976i
$533$	24.6535			1.06786
$534$	14.7446	−	13.8564i	0.638060	−	0.599625i
$535$		0			0
$536$		−	12.6766i		−	0.547545i
$537$	−7.86797	−	8.37228i	−0.339528	−	0.361291i
$538$	−2.17448			−0.0937485
$539$	17.4891	+	2.52434i	0.753310	+	0.108731i
$540$		0			0
$541$	24.3723			1.04785			0.523923	−	0.851766i	$-0.324468\pi$
$541$	24.3723			1.04785			0.523923	+	0.851766i	$0.324468\pi$
$542$			3.76631i			0.161777i
$543$	−1.52967	−	1.62772i	−0.0656445	−	0.0698521i
$544$		−	25.5383i		−	1.09495i
$545$		0			0
$546$	14.8397	+	1.52967i	0.635079	+	0.0654639i
$547$			2.97825i			0.127341i	0.997971	+	0.0636704i	$0.0202806\pi$
$547$			2.97825i			0.127341i	−0.997971	+	0.0636704i	$0.979719\pi$
$548$	−18.2054			−0.777695
$549$	20.7446	+	1.28962i	0.885356	+	0.0550397i
$550$		0			0
$551$	3.25544			0.138686
$552$	28.7075	−	26.9783i	1.22187	−	1.14827i
$553$	4.10891	+	4.74456i	0.174729	+	0.201759i
$554$			22.3692i			0.950376i
$555$		0			0
$556$			25.5383i			1.08307i
$557$	17.6155			0.746391			0.373196	−	0.927753i	$-0.378262\pi$
$557$	17.6155			0.746391			0.373196	+	0.927753i	$0.378262\pi$
$558$	−8.21782	−	0.510875i	−0.347888	−	0.0216271i
$559$			19.4950i			0.824550i
$560$		0			0
$561$	−13.9307	+	13.0916i	−0.588155	+	0.552727i
$562$			22.2337i			0.937872i
$563$			17.4891i			0.737079i	0.929612	+	0.368539i	$0.120142\pi$
$563$			17.4891i			0.737079i	−0.929612	+	0.368539i	$0.879858\pi$
$564$	−2.64947	−	2.81929i	−0.111563	−	0.118714i
$565$		0			0
$566$	0.510875			0.0214737
$567$	−13.2390	−	19.7921i	−0.555988	−	0.831190i
$568$			0.788061i			0.0330663i
$569$			23.9538i			1.00419i	0.864811	+	0.502097i	$0.167438\pi$
$569$			23.9538i			1.00419i	−0.864811	+	0.502097i	$0.832562\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$			14.2337i			0.595140i
$573$	−24.7186	−	26.3030i	−1.03263	−	1.09882i
$574$	−8.23369	−	9.50744i	−0.343667	−	0.396833i
$575$		0			0
$576$	0.627719	−	10.0974i	0.0261549	−	0.420723i
$577$	−2.81929			−0.117369			−0.0586843	−	0.998277i	$-0.518691\pi$
$577$	−2.81929			−0.117369			−0.0586843	+	0.998277i	$0.518691\pi$
$578$	1.67715			0.0697602
$579$	14.5109	+	15.4410i	0.603051	+	0.641705i
$580$		0			0
$581$	−34.9783	+	30.2921i	−1.45114	+	1.25673i
$582$	−11.0371	+	10.3723i	−0.457503	+	0.429945i
$583$		−	4.74456i		−	0.196500i
$584$	−18.5109			−0.765985
$585$		0			0
$586$		−	8.62258i		−	0.356196i
$587$			17.4891i			0.721853i	0.932594	+	0.360927i	$0.117540\pi$
$587$			17.4891i			0.721853i	−0.932594	+	0.360927i	$0.882460\pi$
$588$	9.54511	+	13.6277i	0.393634	+	0.561998i
$589$	−12.0000			−0.494451
$590$		0			0
$591$	19.8614	−	18.6650i	0.816989	−	0.767777i
$592$			4.23369i			0.174004i
$593$		−	4.37228i		−	0.179548i	−0.995962	−	0.0897740i	$-0.971386\pi$
$593$		−	4.37228i		−	0.179548i	0.995962	−	0.0897740i	$-0.0286145\pi$
$594$	−8.00000	+	6.63325i	−0.328244	+	0.272166i
$595$		0			0
$596$		−	4.34896i		−	0.178140i
$597$	−31.8217	−	33.8614i	−1.30238	−	1.38586i
$598$	27.7128			1.13326
$599$		−	34.6959i		−	1.41764i	−0.705391	−	0.708818i	$-0.749229\pi$
$599$		−	34.6959i		−	1.41764i	0.705391	−	0.708818i	$-0.250771\pi$
$600$		0			0
$601$			22.0742i			0.900427i	0.892921	+	0.450213i	$0.148652\pi$
$601$			22.0742i			0.900427i	−0.892921	+	0.450213i	$0.851348\pi$
$602$	7.51811	−	6.51087i	0.306415	−	0.265363i
$603$	−14.2063	−	0.883156i	−0.578524	−	0.0359649i
$604$	3.25544			0.132462
$605$		0			0
$606$	−6.00000	+	5.63858i	−0.243733	+	0.229052i
$607$	−8.86263			−0.359723			−0.179862	−	0.983692i	$-0.557565\pi$
$607$	−8.86263			−0.359723			−0.179862	+	0.983692i	$0.557565\pi$
$608$		−	20.2337i		−	0.820584i
$609$	−0.441578	+	4.28384i	−0.0178936	+	0.173590i
$610$		0			0
$611$		−	6.68815i		−	0.270574i
$612$	−17.9653	−	1.11684i	−0.726205	−	0.0451457i
$613$		−	27.4891i		−	1.11028i	−0.831758	−	0.555138i	$-0.812666\pi$
$613$		−	27.4891i		−	1.11028i	0.831758	−	0.555138i	$-0.187334\pi$
$614$	−18.0000			−0.726421
$615$		0			0
$616$	13.4891	−	11.6819i	0.543492	−	0.470678i
$617$	24.5437			0.988091			0.494045	−	0.869436i	$-0.335518\pi$
$617$	24.5437			0.988091			0.494045	+	0.869436i	$0.335518\pi$
$618$	6.28339	−	5.90491i	0.252755	−	0.237530i
$619$		−	18.6101i		−	0.748004i	−0.927428	−	0.374002i	$-0.877985\pi$
$619$		−	18.6101i		−	0.748004i	0.927428	−	0.374002i	$-0.122015\pi$
$620$		0			0
$621$	−28.2337	−	34.0511i	−1.13298	−	1.36642i
$622$	−11.2772			−0.452173
$623$	25.5383	+	29.4891i	1.02317	+	1.18146i
$624$	−3.25544	+	3.05934i	−0.130322	+	0.122472i
$625$		0			0
$626$	4.27719			0.170951
$627$	−11.0371	+	10.3723i	−0.440780	+	0.414229i
$628$		0			0
$629$	−29.4891			−1.17581
$630$		0			0
$631$	−23.1168			−0.920267			−0.460134	−	0.887850i	$-0.652198\pi$
$631$	−23.1168			−0.920267			−0.460134	+	0.887850i	$0.652198\pi$
$632$	6.33830			0.252124
$633$	14.0313	−	13.1861i	0.557695	−	0.524102i
$634$	1.48913			0.0591407
$635$		0			0
$636$	3.25544	−	3.05934i	0.129086	−	0.121311i
$637$	−4.10891	+	28.4674i	−0.162801	+	1.12792i
$638$	1.87953			0.0744112
$639$	0.883156	+	0.0549029i	0.0349371	+	0.00217192i
$640$		0			0
$641$			36.6303i			1.44681i	0.690423	+	0.723406i	$0.257424\pi$
$641$			36.6303i			1.44681i	−0.690423	+	0.723406i	$0.742576\pi$
$642$	−6.63325	+	6.23369i	−0.261793	+	0.246024i
$643$	10.1523			0.400366			0.200183	−	0.979759i	$-0.435846\pi$
$643$	10.1523			0.400366			0.200183	+	0.979759i	$0.435846\pi$
$644$	20.2337	+	23.3639i	0.797319	+	0.920665i
$645$		0			0
$646$	12.0000			0.472134
$647$			12.0000i			0.471769i	0.971781	+	0.235884i	$0.0757987\pi$
$647$			12.0000i			0.471769i	−0.971781	+	0.235884i	$0.924201\pi$
$648$	−23.8612	−	2.97825i	−0.937356	−	0.116997i
$649$			22.0742i			0.866489i
$650$		0			0
$651$	1.62772	−	15.7908i	0.0637953	−	0.618892i
$652$		−	10.9783i		−	0.429941i
$653$	−39.6897			−1.55318			−0.776589	−	0.630008i	$-0.783052\pi$
$653$	−39.6897			−1.55318			−0.776589	+	0.630008i	$0.783052\pi$
$654$	17.1168	−	16.0858i	0.669322	−	0.629004i
$655$		0			0
$656$	3.76631			0.147050
$657$	−1.28962	+	20.7446i	−0.0503129	+	0.809322i
$658$	−2.57924	+	2.23369i	−0.100549	+	0.0870782i
$659$		−	35.9855i		−	1.40180i	−0.713261	−	0.700899i	$-0.752782\pi$
$659$		−	35.9855i		−	1.40180i	0.713261	−	0.700899i	$-0.247218\pi$
$660$		0			0
$661$		−	6.92820i		−	0.269476i	−0.990881	−	0.134738i	$-0.956981\pi$
$661$		−	6.92820i		−	0.269476i	0.990881	−	0.134738i	$-0.0430193\pi$
$662$	3.16915			0.123172
$663$	−21.3094	−	22.6753i	−0.827588	−	0.880634i
$664$			46.7277i			1.81339i
$665$		0			0
$666$	−16.0000	−	0.994667i	−0.619987	−	0.0385426i
$667$			8.00000i			0.309761i
$668$			6.70106i			0.259272i
$669$	−11.1861	+	10.5123i	−0.432481	+	0.406430i
$670$		0			0
$671$	17.4891			0.675160
$672$	26.6256	+	2.74456i	1.02710	+	0.105874i
$673$		−	12.2337i		−	0.471574i	−0.971805	−	0.235787i	$-0.924233\pi$
$673$		−	12.2337i		−	0.471574i	0.971805	−	0.235787i	$-0.0757668\pi$
$674$			12.8617i			0.495416i
$675$		0			0
$676$	−5.32878			−0.204953
$677$		−	18.6060i		−	0.715085i	−0.933897	−	0.357543i	$-0.883615\pi$
$677$		−	18.6060i		−	0.715085i	0.933897	−	0.357543i	$-0.116385\pi$
$678$	3.16915	−	2.97825i	0.121710	−	0.114379i
$679$	−19.1168	−	22.0742i	−0.733637	−	0.847131i
$680$		0			0
$681$	−29.1861	−	31.0569i	−1.11842	−	1.19010i
$682$	−6.92820			−0.265295
$683$	−34.4559			−1.31842			−0.659209	−	0.751960i	$-0.729109\pi$
$683$	−34.4559			−1.31842			−0.659209	+	0.751960i	$0.729109\pi$
$684$	−14.2337	−	0.884861i	−0.544239	−	0.0338335i
$685$		0			0
$686$	12.3505	−	7.92287i	0.471545	−	0.302497i
$687$	17.9653	+	19.1168i	0.685420	+	0.729353i
$688$			2.97825i			0.113545i
$689$	7.72281			0.294216
$690$		0			0
$691$			21.1894i			0.806082i	0.915182	+	0.403041i	$0.132047\pi$
$691$			21.1894i			0.806082i	−0.915182	+	0.403041i	$0.867953\pi$
$692$		−	1.53262i		−	0.0582616i
$693$	−12.1518	−	15.9307i	−0.461609	−	0.605157i
$694$	11.7663			0.446643
$695$		0			0
$696$	2.97825	+	3.16915i	0.112890	+	0.120126i
$697$			26.2337i			0.993672i
$698$		−	12.0000i		−	0.454207i
$699$	−21.4891	+	20.1947i	−0.812793	+	0.763834i
$700$		0			0
$701$			42.5090i			1.60554i	0.596287	+	0.802771i	$0.296642\pi$
$701$			42.5090i			1.60554i	−0.596287	+	0.802771i	$0.703358\pi$
$702$	−10.7971	−	13.0217i	−0.407509	−	0.491474i
$703$	−23.3639			−0.881184
$704$		−	8.51278i		−	0.320837i
$705$		0			0
$706$			19.8997i			0.748937i
$707$	−10.3923	−	12.0000i	−0.390843	−	0.451306i
$708$	−15.1460	+	14.2337i	−0.569223	+	0.534935i
$709$	−6.88316			−0.258502			−0.129251	−	0.991612i	$-0.541257\pi$
$709$	−6.88316			−0.258502			−0.129251	+	0.991612i	$0.541257\pi$
$710$		0			0
$711$	0.441578	−	7.10313i	0.0165605	−	0.266388i
$712$	39.3947			1.47638
$713$		−	29.4891i		−	1.10438i
$714$	−1.62772	+	15.7908i	−0.0609158	+	0.590957i
$715$		0			0
$716$		−	9.10268i		−	0.340183i
$717$	24.7186	+	26.3030i	0.923133	+	0.982303i
$718$			13.2554i			0.494689i
$719$	−28.4674			−1.06165			−0.530827	−	0.847480i	$-0.678119\pi$
$719$	−28.4674			−1.06165			−0.530827	+	0.847480i	$0.678119\pi$
$720$		0			0
$721$	10.8832	+	12.5668i	0.405310	+	0.468012i
$722$	−5.54601			−0.206401
$723$	19.4950	+	20.7446i	0.725026	+	0.771499i
$724$		−	1.76972i		−	0.0657712i
$725$		0			0
$726$	4.62772	−	4.34896i	0.171751	−	0.161405i
$727$	3.46410			0.128476			0.0642382	−	0.997935i	$-0.479538\pi$
$727$	3.46410			0.128476			0.0642382	+	0.997935i	$0.479538\pi$
$728$	19.0149	+	21.9565i	0.704739	+	0.813762i
$729$	−5.00000	+	26.5330i	−0.185185	+	0.982704i
$730$		0			0
$731$	−20.7446			−0.767265
$732$	11.2772	+	12.0000i	0.416816	+	0.443533i
$733$	40.0395			1.47889			0.739447	−	0.673215i	$-0.235087\pi$
$733$	40.0395			1.47889			0.739447	+	0.673215i	$0.235087\pi$
$734$	−27.9565			−1.03189
$735$		0			0
$736$	49.7228			1.83281
$737$	−11.9769			−0.441174
$738$	−0.884861	+	14.2337i	−0.0325722	+	0.523949i
$739$	14.3723			0.528693			0.264346	−	0.964428i	$-0.414844\pi$
$739$	14.3723			0.528693			0.264346	+	0.964428i	$0.414844\pi$
$740$		0			0
$741$	−16.8832	−	17.9653i	−0.620218	−	0.659972i
$742$	−2.57924	−	2.97825i	−0.0946869	−	0.109335i
$743$	16.1407			0.592145			0.296072	−	0.955166i	$-0.404323\pi$
$743$	16.1407			0.592145			0.296072	+	0.955166i	$0.404323\pi$
$744$	−10.9783	−	11.6819i	−0.402482	−	0.428280i
$745$		0			0
$746$			10.5021i			0.384510i
$747$	52.3663	+	3.25544i	1.91598	+	0.119110i
$748$	−15.1460			−0.553794
$749$	−11.4891	−	13.2665i	−0.419804	−	0.484747i
$750$		0			0
$751$	29.3505			1.07102			0.535508	−	0.844530i	$-0.320120\pi$
$751$	29.3505			1.07102			0.535508	+	0.844530i	$0.320120\pi$
$752$		−	1.02175i		−	0.0372594i
$753$	−6.92820	+	6.51087i	−0.252478	+	0.237269i
$754$			3.05934i			0.111415i
$755$		0			0
$756$	3.09509	−	18.6101i	0.112568	−	0.676844i
$757$			19.7663i			0.718419i	0.933257	+	0.359209i	$0.116954\pi$
$757$			19.7663i			0.718419i	−0.933257	+	0.359209i	$0.883046\pi$
$758$	−17.0256			−0.618396
$759$	−25.4891	−	27.1229i	−0.925197	−	0.984499i
$760$		0			0
$761$	−8.23369			−0.298471			−0.149235	−	0.988802i	$-0.547681\pi$
$761$	−8.23369			−0.298471			−0.149235	+	0.988802i	$0.547681\pi$
$762$	0.699713	+	0.744563i	0.0253479	+	0.0269727i
$763$	29.6472	+	34.2337i	1.07330	+	1.23934i
$764$		−	28.5977i		−	1.03463i
$765$		0			0
$766$			4.34896i			0.157134i
$767$	−35.9306			−1.29738
$768$	17.5229	−	16.4674i	0.632303	−	0.594215i
$769$			38.5099i			1.38870i	0.719637	+	0.694351i	$0.244308\pi$
$769$			38.5099i			1.38870i	−0.719637	+	0.694351i	$0.755692\pi$
$770$		0			0
$771$	−0.605969	−	0.644810i	−0.0218234	−	0.0232223i
$772$			16.7881i			0.604216i
$773$			52.3723i			1.88370i	0.336034	+	0.941850i	$0.390914\pi$
$773$			52.3723i			1.88370i	−0.336034	+	0.941850i	$0.609086\pi$
$774$	−11.2554	−	0.699713i	−0.404568	−	0.0251507i
$775$		0			0
$776$	−29.4891			−1.05860
$777$	3.16915	−	30.7446i	0.113693	−	1.10296i
$778$		−	23.2554i		−	0.833748i
$779$			20.7846i			0.744686i
$780$		0			0
$781$	0.744563			0.0266425
$782$			29.4891i			1.05453i
$783$	3.75906	−	3.11684i	0.134338	−	0.111387i
$784$	−0.627719	+	4.34896i	−0.0224185	+	0.155320i
$785$		0			0
$786$	−5.48913	+	5.15848i	−0.195791	+	0.183997i
$787$	3.22405			0.114925			0.0574625	−	0.998348i	$-0.481699\pi$
$787$	3.22405			0.114925			0.0574625	+	0.998348i	$0.481699\pi$
$788$	21.5941			0.769259
$789$	0.372281	−	0.349857i	0.0132536	−	0.0124552i
$790$		0			0
$791$	5.48913	+	6.33830i	0.195171	+	0.225364i
$792$	−20.1947	−	1.25544i	−0.717588	−	0.0446100i
$793$			28.4674i			1.01091i
$794$	20.7446			0.736197
$795$		0			0
$796$		−	36.8155i		−	1.30489i
$797$		−	14.1386i		−	0.500815i	−0.968141	−	0.250407i	$-0.919435\pi$
$797$		−	14.1386i		−	0.500815i	0.968141	−	0.250407i	$-0.0805645\pi$
$798$	−1.28962	+	12.5109i	−0.0456521	+	0.442880i
$799$	7.11684			0.251776
$800$		0			0
$801$	2.74456	−	44.1485i	0.0969744	−	1.55991i
$802$			4.74456i			0.167536i
$803$			17.4891i			0.617178i
$804$	−7.72281	−	8.21782i	−0.272363	−	0.289820i
$805$		0			0
$806$		−	11.2772i		−	0.397221i
$807$	−3.46410	+	3.25544i	−0.121942	+	0.114597i
$808$	−16.0309			−0.563965
$809$		−	13.5065i		−	0.474865i	−0.971404	−	0.237433i	$-0.923694\pi$
$809$		−	13.5065i		−	0.474865i	0.971404	−	0.237433i	$-0.0763059\pi$
$810$		0			0
$811$			18.6101i			0.653490i	0.945113	+	0.326745i	$0.105952\pi$
$811$			18.6101i			0.653490i	−0.945113	+	0.326745i	$0.894048\pi$
$812$	−2.57924	+	2.23369i	−0.0905136	+	0.0783871i
$813$	5.63858	+	6.00000i	0.197754	+	0.210429i
$814$	−13.4891			−0.472794
$815$		0			0
$816$	−3.25544	−	3.46410i	−0.113963	−	0.121268i
$817$	−16.4356			−0.575011
$818$			19.5326i			0.682942i
$819$	25.9307	−	19.7797i	0.906092	−	0.691159i
$820$		0			0
$821$		−	34.9909i		−	1.22119i	−0.791943	−	0.610595i	$-0.790930\pi$
$821$		−	34.9909i		−	1.22119i	0.791943	−	0.610595i	$-0.209070\pi$
$822$	13.2665	−	12.4674i	0.462722	−	0.434850i
$823$		−	13.7663i		−	0.479863i	−0.970790	−	0.239932i	$-0.922875\pi$
$823$		−	13.7663i		−	0.479863i	0.970790	−	0.239932i	$-0.0771251\pi$
$824$	16.7881			0.584840
$825$		0			0
$826$	12.0000	+	13.8564i	0.417533	+	0.482126i
$827$	−14.8511			−0.516422			−0.258211	−	0.966088i	$-0.583133\pi$
$827$	−14.8511			−0.516422			−0.258211	+	0.966088i	$0.583133\pi$
$828$	2.17448	−	34.9783i	0.0755684	−	1.21558i
$829$		−	12.5668i		−	0.436463i	−0.975897	−	0.218231i	$-0.929971\pi$
$829$		−	12.5668i		−	0.436463i	0.975897	−	0.218231i	$-0.0700287\pi$
$830$		0			0
$831$	33.4891	+	35.6357i	1.16172	+	1.23619i
$832$	13.8564			0.480384
$833$	−30.2921	−	4.37228i	−1.04956	−	0.151491i
$834$	−17.4891	−	18.6101i	−0.605599	−	0.644416i
$835$		0			0
$836$	−12.0000			−0.415029
$837$	−13.8564	+	11.4891i	−0.478947	+	0.397122i
$838$	−6.92820			−0.239331
$839$	−30.5109			−1.05335			−0.526676	−	0.850066i	$-0.676562\pi$
$839$	−30.5109			−1.05335			−0.526676	+	0.850066i	$0.676562\pi$
$840$		0			0
$841$	28.1168			0.969546
$842$	−11.5721			−0.398802
$843$	33.2863	+	35.4198i	1.14644	+	1.21992i
$844$	15.2554			0.525114
$845$		0			0
$846$	3.86141	+	0.240051i	0.132758	+	0.00825312i
$847$	8.01544	+	9.25544i	0.275414	+	0.318021i
$848$	1.17981			0.0405150
$849$	0.813859	−	0.764836i	0.0279316	−	0.0262491i
$850$		0			0
$851$		−	57.4150i		−	1.96816i
$852$	0.480102	+	0.510875i	0.0164480	+	0.0175023i
$853$	−32.8713			−1.12549			−0.562746	−	0.826630i	$-0.690255\pi$
$853$	−32.8713			−1.12549			−0.562746	+	0.826630i	$0.690255\pi$
$854$	10.9783	−	9.50744i	0.375668	−	0.325338i
$855$		0			0
$856$	−17.7228			−0.605753
$857$			46.4674i			1.58730i	0.608378	+	0.793648i	$0.291821\pi$
$857$			46.4674i			1.58730i	−0.608378	+	0.793648i	$0.708179\pi$
$858$	−9.74749	−	10.3723i	−0.332774	−	0.354104i
$859$			14.2612i			0.486585i	0.969953	+	0.243292i	$0.0782274\pi$
$859$			14.2612i			0.486585i	−0.969953	+	0.243292i	$0.921773\pi$
$860$		0			0
$861$	−27.3505	−	2.81929i	−0.932104	−	0.0960812i
$862$			11.9565i			0.407240i
$863$	41.2743			1.40499			0.702496	−	0.711688i	$-0.252069\pi$
$863$	41.2743			1.40499			0.702496	+	0.711688i	$0.252069\pi$
$864$	−19.3723	−	23.3639i	−0.659058	−	0.794854i
$865$		0			0
$866$	29.4891			1.00208
$867$	2.67181	−	2.51087i	0.0907396	−	0.0852738i
$868$	9.50744	−	8.23369i	0.322704	−	0.279470i
$869$		−	5.98844i		−	0.203144i
$870$		0			0
$871$		−	19.4950i		−	0.660563i
$872$	45.7330			1.54872
$873$	−2.05446	+	33.0475i	−0.0695328	+	1.11849i
$874$			23.3639i			0.790294i
$875$		0			0
$876$	−12.0000	+	11.2772i	−0.405442	+	0.381020i
$877$			38.4674i			1.29895i	0.760383	+	0.649475i	$0.225011\pi$
$877$			38.4674i			1.29895i	−0.760383	+	0.649475i	$0.774989\pi$
$878$		−	14.7446i		−	0.497605i
$879$	−12.9090	−	13.7364i	−0.435408	−	0.463317i
$880$		0			0
$881$	−32.2337			−1.08598			−0.542990	−	0.839739i	$-0.682708\pi$
$881$	−32.2337			−1.08598			−0.542990	+	0.839739i	$0.682708\pi$
$882$	−16.2882	−	3.39403i	−0.548451	−	0.114283i
$883$			49.4891i			1.66544i	0.553693	+	0.832721i	$0.313218\pi$
$883$			49.4891i			1.66544i	−0.553693	+	0.832721i	$0.686782\pi$
$884$		−	24.6535i		−	0.829186i
$885$		0			0
$886$	−5.25544			−0.176560
$887$			18.5109i			0.621534i	0.950486	+	0.310767i	$0.100586\pi$
$887$			18.5109i			0.621534i	−0.950486	+	0.310767i	$0.899414\pi$
$888$	−21.3745	−	22.7446i	−0.717282	−	0.763258i
$889$	−1.48913	+	1.28962i	−0.0499437	+	0.0432525i
$890$		0			0
$891$	−2.81386	+	22.5441i	−0.0942678	+	0.755256i
$892$	−12.1620			−0.407215
$893$	5.63858			0.188688
$894$	2.97825	+	3.16915i	0.0996076	+	0.105992i
$895$		0			0
$896$	15.6060	+	18.0202i	0.521359	+	0.602013i
$897$	44.1485	−	41.4891i	1.47407	−	1.38528i
$898$		−	9.21194i		−	0.307406i
$899$	3.25544			0.108575
$900$		0			0
$901$			8.21782i			0.273775i
$902$			12.0000i			0.399556i
$903$	2.22938	−	21.6277i	0.0741893	−	0.719725i
$904$	8.46738			0.281621
$905$		0			0
$906$	−2.37228	+	2.22938i	−0.0788138	+	0.0740663i
$907$		−	8.00000i		−	0.265636i	−0.991140	−	0.132818i	$-0.957597\pi$
$907$		−	8.00000i		−	0.265636i	0.991140	−	0.132818i	$-0.0424025\pi$
$908$		−	33.7663i		−	1.12057i
$909$	−1.11684	+	17.9653i	−0.0370434	+	0.595872i
$910$		0			0
$911$			2.87419i			0.0952263i	0.998866	+	0.0476132i	$0.0151615\pi$
$911$			2.87419i			0.0952263i	−0.998866	+	0.0476132i	$0.984839\pi$
$912$	−2.57924	−	2.74456i	−0.0854072	−	0.0908816i
$913$	44.1485			1.46110
$914$			10.2825i			0.340115i
$915$		0			0
$916$			20.7846i			0.686743i
$917$	−9.50744	−	10.9783i	−0.313963	−	0.362534i
$918$	13.8564	−	11.4891i	0.457330	−	0.379198i
$919$	5.62772			0.185641			0.0928207	−	0.995683i	$-0.470412\pi$
$919$	5.62772			0.185641			0.0928207	+	0.995683i	$0.470412\pi$
$920$		0			0
$921$	−28.6753	+	26.9480i	−0.944882	+	0.887966i
$922$	2.17448			0.0716127
$923$			1.21194i			0.0398914i
$924$	1.62772	−	15.7908i	0.0535480	−	0.519480i
$925$		0			0
$926$			25.7235i			0.845326i
$927$	1.16959	−	18.8139i	0.0384145	−	0.617928i
$928$			5.48913i			0.180189i
$929$	52.9783			1.73816			0.869080	−	0.494672i	$-0.164712\pi$
$929$	52.9783			1.73816			0.869080	+	0.494672i	$0.164712\pi$
$930$		0			0
$931$	−24.0000	−	3.46410i	−0.786568	−	0.113531i
$932$	−23.3639			−0.765308
$933$	−17.9653	+	16.8832i	−0.588158	+	0.552730i
$934$			24.6535i			0.806686i
$935$		0			0
$936$	2.04350	−	32.8713i	0.0667938	−	1.07443i
$937$	−0.240051			−0.00784212			−0.00392106	−	0.999992i	$-0.501248\pi$
$937$	−0.240051			−0.00784212			−0.00392106	+	0.999992i	$0.501248\pi$
$938$	−7.51811	+	6.51087i	−0.245475	+	0.212588i
$939$	6.81386	−	6.40342i	0.222362	−	0.208968i
$940$		0			0
$941$	38.7446			1.26304			0.631518	−	0.775361i	$-0.282432\pi$
$941$	38.7446			1.26304			0.631518	+	0.775361i	$0.282432\pi$
$942$		0			0
$943$	−51.0767			−1.66329
$944$	−5.48913			−0.178656
$945$		0			0
$946$	−9.48913			−0.308518
$947$	34.9360			1.13527			0.567633	−	0.823282i	$-0.307859\pi$
$947$	34.9360			1.13527			0.567633	+	0.823282i	$0.307859\pi$
$948$	4.10891	−	3.86141i	0.133451	−	0.125413i
$949$	−28.4674			−0.924090
$950$		0			0
$951$	2.37228	−	2.22938i	0.0769265	−	0.0722927i
$952$	−23.3639	+	20.2337i	−0.757227	+	0.655778i
$953$	−7.62792			−0.247092			−0.123546	−	0.992339i	$-0.539427\pi$
$953$	−7.62792			−0.247092			−0.123546	+	0.992339i	$0.539427\pi$
$954$	−0.277187	+	4.45877i	−0.00897425	+	0.144358i
$955$		0			0
$956$			28.5977i			0.924915i
$957$	2.99422	−	2.81386i	0.0967894	−	0.0909592i
$958$	−32.8713			−1.06202
$959$	22.9783	+	26.5330i	0.742006	+	0.856795i
$960$		0			0
$961$	19.0000			0.612903
$962$		−	21.9565i		−	0.707906i
$963$	−1.23472	+	19.8614i	−0.0397882	+	0.640025i
$964$			22.5543i			0.726426i
$965$		0			0
$966$	−30.7446	−	3.16915i	−0.989190	−	0.101966i
$967$		−	10.2337i		−	0.329093i	−0.986369	−	0.164547i	$-0.947384\pi$
$967$		−	10.2337i		−	0.329093i	0.986369	−	0.164547i	$-0.0526161\pi$
$968$	12.3644			0.397407
$969$	19.1168	−	17.9653i	0.614122	−	0.577129i
$970$		0			0
$971$	−37.2119			−1.19419			−0.597094	−	0.802171i	$-0.703678\pi$
$971$	−37.2119			−1.19419			−0.597094	+	0.802171i	$0.703678\pi$
$972$	−17.2828	+	12.6060i	−0.554347	+	0.404337i
$973$	37.2203	−	32.2337i	1.19323	−	1.03336i
$974$			29.7021i			0.951718i
$975$		0			0
$976$			4.34896i			0.139207i
$977$	7.62792			0.244039			0.122019	−	0.992528i	$-0.461063\pi$
$977$	7.62792			0.244039			0.122019	+	0.992528i	$0.461063\pi$
$978$	7.51811	+	8.00000i	0.240403	+	0.255812i
$979$		−	37.2203i		−	1.18956i
$980$		0			0
$981$	3.18614	−	51.2516i	0.101726	−	1.63634i
$982$		−	4.51087i		−	0.143948i
$983$		−	39.8614i		−	1.27138i	−0.771944	−	0.635691i	$-0.780715\pi$
$983$		−	39.8614i		−	1.27138i	0.771944	−	0.635691i	$-0.219285\pi$
$984$	−20.2337	+	19.0149i	−0.645026	+	0.606172i
$985$		0			0
$986$	−3.25544			−0.103674
$987$	−0.764836	+	7.41983i	−0.0243450	+	0.236176i
$988$		−	19.5326i		−	0.621416i
$989$		−	40.3894i		−	1.28431i
$990$		0			0
$991$	25.4891			0.809689			0.404844	−	0.914386i	$-0.367326\pi$
$991$	25.4891			0.809689			0.404844	+	0.914386i	$0.367326\pi$
$992$		−	20.2337i		−	0.642420i
$993$	5.04868	−	4.74456i	0.160215	−	0.150564i
$994$	0.467376	−	0.404759i	0.0148243	−	0.0128382i
$995$		0			0
$996$	28.4674	+	30.2921i	0.902023	+	0.959840i
$997$	−31.8217			−1.00780			−0.503902	−	0.863761i	$-0.668103\pi$
$997$	−31.8217			−1.00780			−0.503902	+	0.863761i	$0.668103\pi$
$998$	32.7615			1.03705
$999$	−26.9783	+	22.3692i	−0.853554	+	0.707730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.g.e.524.4		8
3.2	odd	2		525.2.g.d.524.5		8
5.2	odd	4		105.2.b.c.41.2	✓	4
5.3	odd	4		525.2.b.g.251.3		4
5.4	even	2	inner	525.2.g.e.524.5		8
7.6	odd	2		525.2.g.d.524.3		8
15.2	even	4		105.2.b.d.41.3	yes	4
15.8	even	4		525.2.b.e.251.2		4
15.14	odd	2		525.2.g.d.524.4		8
20.7	even	4		1680.2.f.h.881.1		4
21.20	even	2	inner	525.2.g.e.524.6		8
35.2	odd	12		735.2.s.i.521.1		4
35.12	even	12		735.2.s.j.521.1		4
35.13	even	4		525.2.b.e.251.3		4
35.17	even	12		735.2.s.g.656.2		4
35.27	even	4		105.2.b.d.41.2	yes	4
35.32	odd	12		735.2.s.h.656.2		4
35.34	odd	2		525.2.g.d.524.6		8
60.47	odd	4		1680.2.f.g.881.3		4
105.2	even	12		735.2.s.g.521.2		4
105.17	odd	12		735.2.s.i.656.1		4
105.32	even	12		735.2.s.j.656.1		4
105.47	odd	12		735.2.s.h.521.2		4
105.62	odd	4		105.2.b.c.41.3	yes	4
105.83	odd	4		525.2.b.g.251.2		4
105.104	even	2	inner	525.2.g.e.524.3		8
140.27	odd	4		1680.2.f.g.881.4		4
420.167	even	4		1680.2.f.h.881.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.b.c.41.2	✓	4	5.2	odd	4
105.2.b.c.41.3	yes	4	105.62	odd	4
105.2.b.d.41.2	yes	4	35.27	even	4
105.2.b.d.41.3	yes	4	15.2	even	4
525.2.b.e.251.2		4	15.8	even	4
525.2.b.e.251.3		4	35.13	even	4
525.2.b.g.251.2		4	105.83	odd	4
525.2.b.g.251.3		4	5.3	odd	4
525.2.g.d.524.3		8	7.6	odd	2
525.2.g.d.524.4		8	15.14	odd	2
525.2.g.d.524.5		8	3.2	odd	2
525.2.g.d.524.6		8	35.34	odd	2
525.2.g.e.524.3		8	105.104	even	2	inner
525.2.g.e.524.4		8	1.1	even	1	trivial
525.2.g.e.524.5		8	5.4	even	2	inner
525.2.g.e.524.6		8	21.20	even	2	inner
735.2.s.g.521.2		4	105.2	even	12
735.2.s.g.656.2		4	35.17	even	12
735.2.s.h.521.2		4	105.47	odd	12
735.2.s.h.656.2		4	35.32	odd	12
735.2.s.i.521.1		4	35.2	odd	12
735.2.s.i.656.1		4	105.17	odd	12
735.2.s.j.521.1		4	35.12	even	12
735.2.s.j.656.1		4	105.32	even	12
1680.2.f.g.881.3		4	60.47	odd	4
1680.2.f.g.881.4		4	140.27	odd	4
1680.2.f.h.881.1		4	20.7	even	4
1680.2.f.h.881.2		4	420.167	even	4

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.g (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.792287 q^{2} +(-1.26217 + 1.18614i) q^{3} -1.37228 q^{4} +(1.00000 - 0.939764i) q^{6} +(1.73205 + 2.00000i) q^{7} +2.67181 q^{8} +(0.186141 - 2.99422i) q^{9} +O(q^{10})\)	\(q-0.792287 q^{2} +(-1.26217 + 1.18614i) q^{3} -1.37228 q^{4} +(1.00000 - 0.939764i) q^{6} +(1.73205 + 2.00000i) q^{7} +2.67181 q^{8} +(0.186141 - 2.99422i) q^{9} -2.52434i q^{11} +(1.73205 - 1.62772i) q^{12} +4.10891 q^{13} +(-1.37228 - 1.58457i) q^{14} +0.627719 q^{16} +4.37228i q^{17} +(-0.147477 + 2.37228i) q^{18} +3.46410i q^{19} +(-4.55842 - 0.469882i) q^{21} +2.00000i q^{22} -8.51278 q^{23} +(-3.37228 + 3.16915i) q^{24} -3.25544 q^{26} +(3.31662 + 4.00000i) q^{27} +(-2.37686 - 2.74456i) q^{28} -0.939764i q^{29} +3.46410i q^{31} -5.84096 q^{32} +(2.99422 + 3.18614i) q^{33} -3.46410i q^{34} +(-0.255437 + 4.10891i) q^{36} +6.74456i q^{37} -2.74456i q^{38} +(-5.18614 + 4.87375i) q^{39} +6.00000 q^{41} +(3.61158 + 0.372281i) q^{42} +4.74456i q^{43} +3.46410i q^{44} +6.74456 q^{46} -1.62772i q^{47} +(-0.792287 + 0.744563i) q^{48} +(-1.00000 + 6.92820i) q^{49} +(-5.18614 - 5.51856i) q^{51} -5.63858 q^{52} +1.87953 q^{53} +(-2.62772 - 3.16915i) q^{54} +(4.62772 + 5.34363i) q^{56} +(-4.10891 - 4.37228i) q^{57} +0.744563i q^{58} -8.74456 q^{59} +6.92820i q^{61} -2.74456i q^{62} +(6.31084 - 4.81386i) q^{63} +3.37228 q^{64} +(-2.37228 - 2.52434i) q^{66} -4.74456i q^{67} -6.00000i q^{68} +(10.7446 - 10.0974i) q^{69} +0.294954i q^{71} +(0.497333 - 8.00000i) q^{72} -6.92820 q^{73} -5.34363i q^{74} -4.75372i q^{76} +(5.04868 - 4.37228i) q^{77} +(4.10891 - 3.86141i) q^{78} +2.37228 q^{79} +(-8.93070 - 1.11469i) q^{81} -4.75372 q^{82} +17.4891i q^{83} +(6.25544 + 0.644810i) q^{84} -3.75906i q^{86} +(1.11469 + 1.18614i) q^{87} -6.74456i q^{88} +14.7446 q^{89} +(7.11684 + 8.21782i) q^{91} +11.6819 q^{92} +(-4.10891 - 4.37228i) q^{93} +1.28962i q^{94} +(7.37228 - 6.92820i) q^{96} -11.0371 q^{97} +(0.792287 - 5.48913i) q^{98} +(-7.55842 - 0.469882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{4} + 8 q^{6} - 10 q^{9}+O(q^{10}) \) 8 * q + 12 * q^4 + 8 * q^6 - 10 * q^9	\( 8 q + 12 q^{4} + 8 q^{6} - 10 q^{9} + 12 q^{14} + 28 q^{16} - 2 q^{21} - 4 q^{24} - 72 q^{26} - 48 q^{36} - 30 q^{39} + 48 q^{41} + 8 q^{46} - 8 q^{49} - 30 q^{51} - 44 q^{54} + 60 q^{56} - 24 q^{59} + 4 q^{64} + 4 q^{66} + 40 q^{69} - 4 q^{79} - 14 q^{81} + 96 q^{84} + 72 q^{89} - 12 q^{91} + 36 q^{96} - 26 q^{99}+O(q^{100}) \) 8 * q + 12 * q^4 + 8 * q^6 - 10 * q^9 + 12 * q^14 + 28 * q^16 - 2 * q^21 - 4 * q^24 - 72 * q^26 - 48 * q^36 - 30 * q^39 + 48 * q^41 + 8 * q^46 - 8 * q^49 - 30 * q^51 - 44 * q^54 + 60 * q^56 - 24 * q^59 + 4 * q^64 + 4 * q^66 + 40 * q^69 - 4 * q^79 - 14 * q^81 + 96 * q^84 + 72 * q^89 - 12 * q^91 + 36 * q^96 - 26 * q^99

Introduction

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