LMFDB - Embedded newform 525.2.b.e.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(251,525)]

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, 0, 1]))

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

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

chi := DirichletCharacter("525.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.b (of order $2$, degree $1$, 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:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.2
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	525.251
Dual form			525.2.b.e.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.792287i q^{2} +(1.18614 - 1.26217i) q^{3} +1.37228 q^{4} +(-1.00000 - 0.939764i) q^{6} +(2.00000 - 1.73205i) q^{7} -2.67181i q^{8} +(-0.186141 - 2.99422i) q^{9} +2.52434i q^{11} +(1.62772 - 1.73205i) q^{12} +4.10891i q^{13} +(-1.37228 - 1.58457i) q^{14} +0.627719 q^{16} -4.37228 q^{17} +(-2.37228 + 0.147477i) q^{18} -3.46410i q^{19} +(0.186141 - 4.57879i) q^{21} +2.00000 q^{22} +8.51278i q^{23} +(-3.37228 - 3.16915i) q^{24} +3.25544 q^{26} +(-4.00000 - 3.31662i) q^{27} +(2.74456 - 2.37686i) q^{28} -0.939764i q^{29} +3.46410i q^{31} -5.84096i q^{32} +(3.18614 + 2.99422i) q^{33} +3.46410i q^{34} +(-0.255437 - 4.10891i) q^{36} +6.74456 q^{37} -2.74456 q^{38} +(5.18614 + 4.87375i) q^{39} -6.00000 q^{41} +(-3.62772 - 0.147477i) q^{42} -4.74456 q^{43} +3.46410i q^{44} +6.74456 q^{46} +1.62772 q^{47} +(0.744563 - 0.792287i) q^{48} +(1.00000 - 6.92820i) q^{49} +(-5.18614 + 5.51856i) q^{51} +5.63858i q^{52} -1.87953i q^{53} +(-2.62772 + 3.16915i) q^{54} +(-4.62772 - 5.34363i) q^{56} +(-4.37228 - 4.10891i) q^{57} -0.744563 q^{58} -8.74456 q^{59} +6.92820i q^{61} +2.74456 q^{62} +(-5.55842 - 5.66603i) q^{63} -3.37228 q^{64} +(2.37228 - 2.52434i) q^{66} -4.74456 q^{67} -6.00000 q^{68} +(10.7446 + 10.0974i) q^{69} -0.294954i q^{71} +(-8.00000 + 0.497333i) q^{72} -6.92820i q^{73} -5.34363i q^{74} -4.75372i q^{76} +(4.37228 + 5.04868i) q^{77} +(3.86141 - 4.10891i) q^{78} -2.37228 q^{79} +(-8.93070 + 1.11469i) q^{81} +4.75372i q^{82} +17.4891 q^{83} +(0.255437 - 6.28339i) q^{84} +3.75906i q^{86} +(-1.18614 - 1.11469i) q^{87} +6.74456 q^{88} +14.7446 q^{89} +(7.11684 + 8.21782i) q^{91} +11.6819i q^{92} +(4.37228 + 4.10891i) q^{93} -1.28962i q^{94} +(-7.37228 - 6.92820i) q^{96} +11.0371i q^{97} +(-5.48913 - 0.792287i) q^{98} +(7.55842 - 0.469882i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} - 6 q^{4} - 4 q^{6} + 8 q^{7} + 5 q^{9} + 18 q^{12} + 6 q^{14} + 14 q^{16} - 6 q^{17} + 2 q^{18} - 5 q^{21} + 8 q^{22} - 2 q^{24} + 36 q^{26} - 16 q^{27} - 12 q^{28} + 7 q^{33} - 24 q^{36}+ \cdots + 13 q^{99}+O(q^{100}) $ 4 * q - q^3 - 6 * q^4 - 4 * q^6 + 8 * q^7 + 5 * q^9 + 18 * q^12 + 6 * q^14 + 14 * q^16 - 6 * q^17 + 2 * q^18 - 5 * q^21 + 8 * q^22 - 2 * q^24 + 36 * q^26 - 16 * q^27 - 12 * q^28 + 7 * q^33 - 24 * q^36 + 4 * q^37 + 12 * q^38 + 15 * q^39 - 24 * q^41 - 26 * q^42 + 4 * q^43 + 4 * q^46 + 18 * q^47 - 20 * q^48 + 4 * q^49 - 15 * q^51 - 22 * q^54 - 30 * q^56 - 6 * q^57 + 20 * q^58 - 12 * q^59 - 12 * q^62 - 5 * q^63 - 2 * q^64 - 2 * q^66 + 4 * q^67 - 24 * q^68 + 20 * q^69 - 32 * q^72 + 6 * q^77 - 42 * q^78 + 2 * q^79 - 7 * q^81 + 24 * q^83 + 24 * q^84 + q^87 + 4 * q^88 + 36 * q^89 - 6 * q^91 + 6 * q^93 - 18 * q^96 + 24 * q^98 + 13 * q^99

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 $

$2$		−	0.792287i		−	0.560232i	−0.959966	−	0.280116i	$-0.909627\pi$
$2$		−	0.792287i		−	0.560232i	0.959966	−	0.280116i	$-0.0903729\pi$
$3$	1.18614	−	1.26217i	0.684819	−	0.728714i
$3$	1.18614	−	1.26217i	0.684819	−	0.728714i
$4$	1.37228			0.686141
$5$		0			0
$5$		0			0
$6$	−1.00000	−	0.939764i	−0.408248	−	0.383657i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$		−	2.67181i		−	0.944629i
$9$	−0.186141	−	2.99422i	−0.0620469	−	0.998073i
$10$		0			0
$11$			2.52434i			0.761116i	0.924757	+	0.380558i	$0.124268\pi$
$11$			2.52434i			0.761116i	−0.924757	+	0.380558i	$0.875732\pi$
$12$	1.62772	−	1.73205i	0.469882	−	0.500000i
$13$			4.10891i			1.13961i	0.821781	+	0.569804i	$0.192981\pi$
$13$			4.10891i			1.13961i	−0.821781	+	0.569804i	$0.807019\pi$
$14$	−1.37228	−	1.58457i	−0.366758	−	0.423495i
$15$		0			0
$16$	0.627719			0.156930
$17$	−4.37228			−1.06043			−0.530217	−	0.847862i	$-0.677890\pi$
$17$	−4.37228			−1.06043			−0.530217	+	0.847862i	$0.677890\pi$
$18$	−2.37228	+	0.147477i	−0.559152	+	0.0347606i
$19$		−	3.46410i		−	0.794719i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$		−	3.46410i		−	0.794719i	0.917663	−	0.397360i	$-0.130073\pi$
$20$		0			0
$21$	0.186141	−	4.57879i	0.0406192	−	0.999175i
$22$	2.00000			0.426401
$23$			8.51278i			1.77504i	0.460772	+	0.887518i	$0.347572\pi$
$23$			8.51278i			1.77504i	−0.460772	+	0.887518i	$0.652428\pi$
$24$	−3.37228	−	3.16915i	−0.688364	−	0.646900i
$25$		0			0
$26$	3.25544			0.638444
$27$	−4.00000	−	3.31662i	−0.769800	−	0.638285i
$28$	2.74456	−	2.37686i	0.518674	−	0.449185i
$29$		−	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	$0.899307\pi$
$32$		−	5.84096i		−	1.03255i
$33$	3.18614	+	2.99422i	0.554636	+	0.521227i
$34$			3.46410i			0.594089i
$35$		0			0
$36$	−0.255437	−	4.10891i	−0.0425729	−	0.684819i
$37$	6.74456			1.10880			0.554400	−	0.832251i	$-0.312948\pi$
$37$	6.74456			1.10880			0.554400	+	0.832251i	$0.312948\pi$
$38$	−2.74456			−0.445227
$39$	5.18614	+	4.87375i	0.830447	+	0.780424i
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$	−3.62772	−	0.147477i	−0.559769	−	0.0227562i
$43$	−4.74456			−0.723539			−0.361770	−	0.932268i	$-0.617827\pi$
$43$	−4.74456			−0.723539			−0.361770	+	0.932268i	$0.617827\pi$
$44$			3.46410i			0.522233i
$45$		0			0
$46$	6.74456			0.994432
$47$	1.62772			0.237427			0.118714	−	0.992929i	$-0.462123\pi$
$47$	1.62772			0.237427			0.118714	+	0.992929i	$0.462123\pi$
$48$	0.744563	−	0.792287i	0.107468	−	0.114357i
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$	−5.18614	+	5.51856i	−0.726205	+	0.772753i
$52$			5.63858i			0.781931i
$53$		−	1.87953i		−	0.258173i	−0.991633	−	0.129086i	$-0.958796\pi$
$53$		−	1.87953i		−	0.258173i	0.991633	−	0.129086i	$-0.0412045\pi$
$54$	−2.62772	+	3.16915i	−0.357587	+	0.431266i
$55$		0			0
$56$	−4.62772	−	5.34363i	−0.618405	−	0.714072i
$57$	−4.37228	−	4.10891i	−0.579123	−	0.544239i
$58$	−0.744563			−0.0977659
$59$	−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	$0.853725\pi$
$62$	2.74456			0.348560
$63$	−5.55842	−	5.66603i	−0.700295	−	0.713853i
$64$	−3.37228			−0.421535
$65$		0			0
$66$	2.37228	−	2.52434i	0.292008	−	0.310725i
$67$	−4.74456			−0.579641			−0.289820	−	0.957081i	$-0.593596\pi$
$67$	−4.74456			−0.579641			−0.289820	+	0.957081i	$0.593596\pi$
$68$	−6.00000			−0.727607
$69$	10.7446	+	10.0974i	1.29349	+	1.21558i
$70$		0			0
$71$		−	0.294954i		−	0.0350046i	−0.999847	−	0.0175023i	$-0.994429\pi$
$71$		−	0.294954i		−	0.0350046i	0.999847	−	0.0175023i	$-0.00557143\pi$
$72$	−8.00000	+	0.497333i	−0.942809	+	0.0586113i
$73$		−	6.92820i		−	0.810885i	−0.914121	−	0.405442i	$-0.867117\pi$
$73$		−	6.92820i		−	0.810885i	0.914121	−	0.405442i	$-0.132883\pi$
$74$		−	5.34363i		−	0.621184i
$75$		0			0
$76$		−	4.75372i		−	0.545289i
$77$	4.37228	+	5.04868i	0.498268	+	0.575350i
$78$	3.86141	−	4.10891i	0.437218	−	0.465243i
$79$	−2.37228			−0.266903			−0.133451	−	0.991055i	$-0.542606\pi$
$79$	−2.37228			−0.266903			−0.133451	+	0.991055i	$0.542606\pi$
$80$		0			0
$81$	−8.93070	+	1.11469i	−0.992300	+	0.123855i
$82$			4.75372i			0.524961i
$83$	17.4891			1.91968			0.959840	−	0.280546i	$-0.0905157\pi$
$83$	17.4891			1.91968			0.959840	+	0.280546i	$0.0905157\pi$
$84$	0.255437	−	6.28339i	0.0278705	−	0.685574i
$85$		0			0
$86$			3.75906i			0.405349i
$87$	−1.18614	−	1.11469i	−0.127168	−	0.119508i
$88$	6.74456			0.718973
$89$	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
$92$			11.6819i			1.21792i
$93$	4.37228	+	4.10891i	0.453384	+	0.426074i
$94$		−	1.28962i		−	0.133014i
$95$		0			0
$96$	−7.37228	−	6.92820i	−0.752430	−	0.707107i
$97$			11.0371i			1.12065i	0.828273	+	0.560325i	$0.189324\pi$
$97$			11.0371i			1.12065i	−0.828273	+	0.560325i	$0.810676\pi$
$98$	−5.48913	−	0.792287i	−0.554485	−	0.0800331i
$99$	7.55842	−	0.469882i	0.759650	−	0.0472249i
$100$		0			0
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$	4.37228	+	4.10891i	0.432920	+	0.406843i
$103$			6.28339i			0.619121i	0.950880	+	0.309561i	$0.100182\pi$
$103$			6.28339i			0.619121i	−0.950880	+	0.309561i	$0.899818\pi$
$104$	10.9783			1.07651
$105$		0			0
$106$	−1.48913			−0.144637
$107$		−	6.63325i		−	0.641260i	−0.947204	−	0.320630i	$-0.896105\pi$
$107$		−	6.63325i		−	0.641260i	0.947204	−	0.320630i	$-0.103895\pi$
$108$	−5.48913	−	4.55134i	−0.528191	−	0.437953i
$109$	−17.1168			−1.63950			−0.819748	−	0.572724i	$-0.805887\pi$
$109$	−17.1168			−1.63950			−0.819748	+	0.572724i	$0.805887\pi$
$110$		0			0
$111$	8.00000	−	8.51278i	0.759326	−	0.807997i
$112$	1.25544	−	1.08724i	0.118628	−	0.102735i
$113$		−	3.16915i		−	0.298128i	−0.988828	−	0.149064i	$-0.952374\pi$
$113$		−	3.16915i		−	0.298128i	0.988828	−	0.149064i	$-0.0476261\pi$
$114$	−3.25544	+	3.46410i	−0.304900	+	0.324443i
$115$		0			0
$116$		−	1.28962i		−	0.119738i
$117$	12.3030	−	0.764836i	1.13741	−	0.0707091i
$118$			6.92820i			0.637793i
$119$	−8.74456	+	7.57301i	−0.801613	+	0.694217i
$120$		0			0
$121$	4.62772			0.420702
$122$	5.48913			0.496962
$123$	−7.11684	+	7.57301i	−0.641704	+	0.682836i
$124$			4.75372i			0.426897i
$125$		0			0
$126$	−4.48913	+	4.40387i	−0.399923	+	0.392328i
$127$	0.744563			0.0660693			0.0330346	−	0.999454i	$-0.489483\pi$
$127$	0.744563			0.0660693			0.0330346	+	0.999454i	$0.489483\pi$
$128$		−	9.01011i		−	0.796389i
$129$	−5.62772	+	5.98844i	−0.495493	+	0.527253i
$130$		0			0
$131$	5.48913			0.479587			0.239794	−	0.970824i	$-0.422920\pi$
$131$	5.48913			0.479587			0.239794	+	0.970824i	$0.422920\pi$
$132$	4.37228	+	4.10891i	0.380558	+	0.357635i
$133$	−6.00000	−	6.92820i	−0.520266	−	0.600751i
$134$			3.75906i			0.324733i
$135$		0			0
$136$			11.6819i			1.00172i
$137$			13.2665i			1.13343i	0.823913	+	0.566717i	$0.191787\pi$
$137$			13.2665i			1.13343i	−0.823913	+	0.566717i	$0.808213\pi$
$138$	8.00000	−	8.51278i	0.681005	−	0.724656i
$139$			18.6101i			1.57849i	0.614078	+	0.789245i	$0.289528\pi$
$139$			18.6101i			1.57849i	−0.614078	+	0.789245i	$0.710472\pi$
$140$		0			0
$141$	1.93070	−	2.05446i	0.162595	−	0.173016i
$142$	−0.233688			−0.0196107
$143$	−10.3723			−0.867374
$144$	−0.116844	−	1.87953i	−0.00973700	−	0.156627i
$145$		0			0
$146$	−5.48913			−0.454283
$147$	−7.55842	−	9.47999i	−0.623408	−	0.781897i
$148$	9.25544			0.760792
$149$			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	$0.530773\pi$
$152$	−9.25544			−0.750715
$153$	0.813859	+	13.0916i	0.0657966	+	1.05839i
$154$	4.00000	−	3.46410i	0.322329	−	0.279145i
$155$		0			0
$156$	7.11684	+	6.68815i	0.569804	+	0.535481i
$157$		0			0		1.00000			$0$
$157$		0			0		−1.00000			$\pi$
$158$			1.87953i			0.149527i
$159$	−2.37228	−	2.22938i	−0.188134	−	0.176802i
$160$		0			0
$161$	14.7446	+	17.0256i	1.16203	+	1.34180i
$162$	0.883156	+	7.07568i	0.0693873	+	0.555918i
$163$	−8.00000			−0.626608			−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000			−0.626608			−0.313304	+	0.949653i	$0.601436\pi$
$164$	−8.23369			−0.642943
$165$		0			0
$166$		−	13.8564i		−	1.07547i
$167$	4.88316			0.377870			0.188935	−	0.981990i	$-0.439496\pi$
$167$	4.88316			0.377870			0.188935	+	0.981990i	$0.439496\pi$
$168$	−12.2337	−	0.497333i	−0.943850	−	0.0383701i
$169$	−3.88316			−0.298704
$170$		0			0
$171$	−10.3723	+	0.644810i	−0.793188	+	0.0493099i
$172$	−6.51087			−0.496450
$173$	1.11684			0.0849121			0.0424560	−	0.999098i	$-0.486482\pi$
$173$	1.11684			0.0849121			0.0424560	+	0.999098i	$0.486482\pi$
$174$	−0.883156	+	0.939764i	−0.0669519	+	0.0712433i
$175$		0			0
$176$			1.58457i			0.119442i
$177$	−10.3723	+	11.0371i	−0.779628	+	0.829600i
$178$		−	11.6819i		−	0.875597i
$179$			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	$0.984738\pi$
$182$	6.51087	−	5.63858i	0.482618	−	0.417960i
$183$	8.74456	+	8.21782i	0.646417	+	0.607479i
$184$	22.7446			1.67675
$185$		0			0
$186$	3.25544	−	3.46410i	0.238700	−	0.254000i
$187$		−	11.0371i		−	0.807114i
$188$	2.23369			0.162908
$189$	−13.7446	+	0.294954i	−0.999770	+	0.0214547i
$190$		0			0
$191$		−	20.8395i		−	1.50789i	−0.656935	−	0.753947i	$-0.728147\pi$
$191$		−	20.8395i		−	1.50789i	0.656935	−	0.753947i	$-0.271853\pi$
$192$	−4.00000	+	4.25639i	−0.288675	+	0.307178i
$193$	12.2337			0.880600			0.440300	−	0.897851i	$-0.354872\pi$
$193$	12.2337			0.880600			0.440300	+	0.897851i	$0.354872\pi$
$194$	8.74456			0.627823
$195$		0			0
$196$	1.37228	−	9.50744i	0.0980201	−	0.679103i
$197$		−	15.7359i		−	1.12114i	−0.828107	−	0.560569i	$-0.810582\pi$
$197$		−	15.7359i		−	1.12114i	0.828107	−	0.560569i	$-0.189418\pi$
$198$	−0.372281	−	5.98844i	−0.0264569	−	0.425580i
$199$		−	26.8280i		−	1.90178i	−0.309524	−	0.950892i	$-0.600170\pi$
$199$		−	26.8280i		−	1.90178i	0.309524	−	0.950892i	$-0.399830\pi$
$200$		0			0
$201$	−5.62772	+	5.98844i	−0.396949	+	0.422392i
$202$		−	4.75372i		−	0.334471i
$203$	−1.62772	−	1.87953i	−0.114243	−	0.131917i
$204$	−7.11684	+	7.57301i	−0.498279	+	0.530217i
$205$		0			0
$206$	4.97825			0.346851
$207$	25.4891	−	1.58457i	1.77162	−	0.110136i
$208$			2.57924i			0.178838i
$209$	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	$0.624991\pi$
$212$		−	2.57924i		−	0.177143i
$213$	−0.372281	−	0.349857i	−0.0255083	−	0.0239718i
$214$	−5.25544			−0.359254
$215$		0			0
$216$	−8.86141	+	10.6873i	−0.602942	+	0.727176i
$217$	6.00000	+	6.92820i	0.407307	+	0.470317i
$218$			13.5615i			0.918497i
$219$	−8.74456	−	8.21782i	−0.590903	−	0.555309i
$220$		0			0
$221$		−	17.9653i		−	1.20848i
$222$	−6.74456	−	6.33830i	−0.452665	−	0.425399i
$223$			8.86263i			0.593486i	0.954957	+	0.296743i	$0.0959004\pi$
$223$			8.86263i			0.593486i	−0.954957	+	0.296743i	$0.904100\pi$
$224$	−10.1168	−	11.6819i	−0.675960	−	0.780531i
$225$		0			0
$226$	−2.51087			−0.167021
$227$	−24.6060			−1.63316			−0.816578	−	0.577235i	$-0.804131\pi$
$227$	−24.6060			−1.63316			−0.816578	+	0.577235i	$0.804131\pi$
$228$	−6.00000	−	5.63858i	−0.397360	−	0.373424i
$229$			15.1460i			1.00088i	0.865772	+	0.500439i	$0.166828\pi$
$229$			15.1460i			1.00088i	−0.865772	+	0.500439i	$0.833172\pi$
$230$		0			0
$231$	11.5584	+	0.469882i	0.760488	+	0.0309160i
$232$	−2.51087			−0.164847
$233$		−	17.0256i		−	1.11538i	−0.830049	−	0.557691i	$-0.811688\pi$
$233$		−	17.0256i		−	1.11538i	0.830049	−	0.557691i	$-0.188312\pi$
$234$	−0.605969	−	9.74749i	−0.0396134	−	0.637214i
$235$		0			0
$236$	−12.0000			−0.781133
$237$	−2.81386	+	2.99422i	−0.182780	+	0.194495i
$238$	6.00000	+	6.92820i	0.388922	+	0.449089i
$239$		−	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	$-0.177567\pi$
$242$		−	3.66648i		−	0.235690i
$243$	−9.18614	+	12.5942i	−0.589291	+	0.807921i
$244$			9.50744i			0.608652i
$245$		0			0
$246$	6.00000	+	5.63858i	0.382546	+	0.359503i
$247$	14.2337			0.905668
$248$	9.25544			0.587721
$249$	20.7446	−	22.0742i	1.31463	−	1.39890i
$250$		0			0
$251$	−5.48913			−0.346471			−0.173235	−	0.984880i	$-0.555422\pi$
$251$	−5.48913			−0.346471			−0.173235	+	0.984880i	$0.555422\pi$
$252$	−7.62772	−	7.77539i	−0.480501	−	0.489804i
$253$	−21.4891			−1.35101
$254$		−	0.589907i		−	0.0370141i
$255$		0			0
$256$	−13.8832			−0.867697
$257$	−0.510875			−0.0318675			−0.0159337	−	0.999873i	$-0.505072\pi$
$257$	−0.510875			−0.0318675			−0.0159337	+	0.999873i	$0.505072\pi$
$258$	4.74456	+	4.45877i	0.295384	+	0.277591i
$259$	13.4891	−	11.6819i	0.838173	−	0.725880i
$260$		0			0
$261$	−2.81386	+	0.174928i	−0.174174	+	0.0108278i
$262$		−	4.34896i		−	0.268680i
$263$			0.294954i			0.0181876i	0.999959	+	0.00909381i	$0.00289469\pi$
$263$			0.294954i			0.0181876i	−0.999959	+	0.00909381i	$0.997105\pi$
$264$	8.00000	−	8.51278i	0.492366	−	0.523925i
$265$		0			0
$266$	−5.48913	+	4.75372i	−0.336560	+	0.291469i
$267$	17.4891	−	18.6101i	1.07032	−	1.13892i
$268$	−6.51087			−0.397715
$269$	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	$-0.0461201\pi$
$272$	−2.74456			−0.166414
$273$	18.8139	+	0.764836i	1.13867	+	0.0462900i
$274$	10.5109			0.634985
$275$		0			0
$276$	14.7446	+	13.8564i	0.887518	+	0.834058i
$277$	−28.2337			−1.69640			−0.848199	−	0.529678i	$-0.822313\pi$
$277$	−28.2337			−1.69640			−0.848199	+	0.529678i	$0.822313\pi$
$278$	14.7446			0.884320
$279$	10.3723	−	0.644810i	0.620972	−	0.0386038i
$280$		0			0
$281$			28.0627i			1.67408i	0.547143	+	0.837039i	$0.315715\pi$
$281$			28.0627i			1.67408i	−0.547143	+	0.837039i	$0.684285\pi$
$282$	−1.62772	−	1.52967i	−0.0969292	−	0.0910906i
$283$		−	0.644810i		−	0.0383300i	−0.999816	−	0.0191650i	$-0.993899\pi$
$283$		−	0.644810i		−	0.0383300i	0.999816	−	0.0191650i	$-0.00610078\pi$
$284$		−	0.404759i		−	0.0240181i
$285$		0			0
$286$			8.21782i			0.485930i
$287$	−12.0000	+	10.3923i	−0.708338	+	0.613438i
$288$	−17.4891	+	1.08724i	−1.03056	+	0.0640663i
$289$	2.11684			0.124520
$290$		0			0
$291$	13.9307	+	13.0916i	0.816632	+	0.767441i
$292$		−	9.50744i		−	0.556381i
$293$	10.8832			0.635801			0.317900	−	0.948124i	$-0.397022\pi$
$293$	10.8832			0.635801			0.317900	+	0.948124i	$0.397022\pi$
$294$	−7.51087	+	5.98844i	−0.438043	+	0.349253i
$295$		0			0
$296$		−	18.0202i		−	1.04740i
$297$	8.37228	−	10.0974i	0.485809	−	0.585908i
$298$	2.51087			0.145451
$299$	−34.9783			−2.02284
$300$		0			0
$301$	−9.48913	+	8.21782i	−0.546944	+	0.473667i
$302$			1.87953i			0.108155i
$303$	7.11684	−	7.57301i	0.408852	−	0.435058i
$304$		−	2.17448i		−	0.124715i
$305$		0			0
$306$	10.3723	−	0.644810i	0.592944	−	0.0368613i
$307$		−	22.7190i		−	1.29664i	−0.761366	−	0.648322i	$-0.775471\pi$
$307$		−	22.7190i		−	1.29664i	0.761366	−	0.648322i	$-0.224529\pi$
$308$	6.00000	+	6.92820i	0.341882	+	0.394771i
$309$	7.93070	+	7.45299i	0.451162	+	0.423986i
$310$		0			0
$311$	−14.2337			−0.807118			−0.403559	−	0.914954i	$-0.632227\pi$
$311$	−14.2337			−0.807118			−0.403559	+	0.914954i	$0.632227\pi$
$312$	13.0217	−	13.8564i	0.737211	−	0.784465i
$313$		−	5.39853i		−	0.305143i	−0.988292	−	0.152572i	$-0.951245\pi$
$313$		−	5.39853i		−	0.305143i	0.988292	−	0.152572i	$-0.0487554\pi$
$314$		0			0
$315$		0			0
$316$	−3.25544			−0.183133
$317$		−	1.87953i		−	0.105565i	−0.998606	−	0.0527824i	$-0.983191\pi$
$317$		−	1.87953i		−	0.105565i	0.998606	−	0.0527824i	$-0.0168090\pi$
$318$	−1.76631	+	1.87953i	−0.0990499	+	0.105399i
$319$	2.37228			0.132822
$320$		0			0
$321$	−8.37228	−	7.86797i	−0.467295	−	0.439147i
$322$	13.4891	−	11.6819i	0.751720	−	0.651008i
$323$			15.1460i			0.842747i
$324$	−12.2554	+	1.52967i	−0.680858	+	0.0849817i
$325$		0			0
$326$			6.33830i			0.351046i
$327$	−20.3030	+	21.6043i	−1.12276	+	1.19472i
$328$			16.0309i			0.885158i
$329$	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	$0.535063\pi$
$332$	24.0000			1.31717
$333$	−1.25544	−	20.1947i	−0.0687975	−	1.10666i
$334$		−	3.86886i		−	0.211695i
$335$		0			0
$336$	0.116844	−	2.87419i	0.00637436	−	0.156800i
$337$	−16.2337			−0.884305			−0.442153	−	0.896940i	$-0.645785\pi$
$337$	−16.2337			−0.884305			−0.442153	+	0.896940i	$0.645785\pi$
$338$			3.07657i			0.167344i
$339$	−4.00000	−	3.75906i	−0.217250	−	0.204164i
$340$		0			0
$341$	−8.74456			−0.473545
$342$	0.510875	+	8.21782i	0.0276249	+	0.444369i
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$			12.6766i			0.683476i
$345$		0			0
$346$		−	0.884861i		−	0.0475704i
$347$		−	14.8511i		−	0.797247i	−0.917115	−	0.398624i	$-0.869488\pi$
$347$		−	14.8511i		−	0.797247i	0.917115	−	0.398624i	$-0.130512\pi$
$348$	−1.62772	−	1.52967i	−0.0872549	−	0.0819990i
$349$		−	15.1460i		−	0.810748i	−0.914151	−	0.405374i	$-0.867141\pi$
$349$		−	15.1460i		−	0.810748i	0.914151	−	0.405374i	$-0.132859\pi$
$350$		0			0
$351$	13.6277	−	16.4356i	0.727394	−	0.877270i
$352$	14.7446			0.785888
$353$	−25.1168			−1.33683			−0.668417	−	0.743786i	$-0.733028\pi$
$353$	−25.1168			−1.33683			−0.668417	+	0.743786i	$0.733028\pi$
$354$	8.74456	+	8.21782i	0.464768	+	0.436772i
$355$		0			0
$356$	20.2337			1.07238
$357$	−0.813859	+	20.0198i	−0.0430740	+	1.05956i
$358$	5.25544			0.277758
$359$		−	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
$362$	1.02175			0.0537020
$363$	5.48913	−	5.84096i	0.288104	−	0.306571i
$364$	9.76631	+	11.2772i	0.511894	+	0.591084i
$365$		0			0
$366$	6.51087	−	6.92820i	0.340329	−	0.362143i
$367$		−	35.2858i		−	1.84191i	−0.389675	−	0.920953i	$-0.627413\pi$
$367$		−	35.2858i		−	1.84191i	0.389675	−	0.920953i	$-0.372587\pi$
$368$			5.34363i			0.278556i
$369$	1.11684	+	17.9653i	0.0581406	+	0.935237i
$370$		0			0
$371$	−3.25544	−	3.75906i	−0.169014	−	0.195160i
$372$	6.00000	+	5.63858i	0.311086	+	0.292347i
$373$	13.2554			0.686341			0.343170	−	0.939273i	$-0.388499\pi$
$373$	13.2554			0.686341			0.343170	+	0.939273i	$0.388499\pi$
$374$	−8.74456			−0.452171
$375$		0			0
$376$		−	4.34896i		−	0.224281i
$377$	3.86141			0.198873
$378$	0.233688	+	10.8896i	0.0120196	+	0.560103i
$379$	−21.4891			−1.10382			−0.551911	−	0.833903i	$-0.686101\pi$
$379$	−21.4891			−1.10382			−0.551911	+	0.833903i	$0.686101\pi$
$380$		0			0
$381$	0.883156	−	0.939764i	0.0452455	−	0.0481456i
$382$	−16.5109			−0.844770
$383$	−5.48913			−0.280481			−0.140241	−	0.990117i	$-0.544788\pi$
$383$	−5.48913			−0.280481			−0.140241	+	0.990117i	$0.544788\pi$
$384$	−11.3723	−	10.6873i	−0.580339	−	0.545382i
$385$		0			0
$386$		−	9.69259i		−	0.493340i
$387$	0.883156	+	14.2063i	0.0448933	+	0.722145i
$388$			15.1460i			0.768923i
$389$			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
$392$	−18.5109	−	2.67181i	−0.934940	−	0.134947i
$393$	6.51087	−	6.92820i	0.328430	−	0.349482i
$394$	−12.4674			−0.628097
$395$		0			0
$396$	10.3723	−	0.644810i	0.521227	−	0.0324029i
$397$			26.1831i			1.31409i	0.753850	+	0.657047i	$0.228195\pi$
$397$			26.1831i			1.31409i	−0.753850	+	0.657047i	$0.771805\pi$
$398$	−21.2554			−1.06544
$399$	−15.8614	−	0.644810i	−0.794064	−	0.0322809i
$400$		0			0
$401$			5.98844i			0.299048i	0.988758	+	0.149524i	$0.0477742\pi$
$401$			5.98844i			0.299048i	−0.988758	+	0.149524i	$0.952226\pi$
$402$	4.74456	+	4.45877i	0.236637	+	0.222383i
$403$	−14.2337			−0.709030
$404$	8.23369			0.409641
$405$		0			0
$406$	−1.48913	+	1.28962i	−0.0739040	+	0.0640028i
$407$			17.0256i			0.843925i
$408$	14.7446	+	13.8564i	0.729965	+	0.685994i
$409$			24.6535i			1.21904i	0.792772	+	0.609518i	$0.208637\pi$
$409$			24.6535i			1.21904i	−0.792772	+	0.609518i	$0.791363\pi$
$410$		0			0
$411$	16.7446	+	15.7359i	0.825948	+	0.776196i
$412$			8.62258i			0.424804i
$413$	−17.4891	+	15.1460i	−0.860584	+	0.745287i
$414$	−1.25544	−	20.1947i	−0.0617014	−	0.992515i
$415$		0			0
$416$	24.0000			1.17670
$417$	23.4891	+	22.0742i	1.15027	+	1.08098i
$418$		−	6.92820i		−	0.338869i
$419$	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	$0.384166\pi$
$422$			8.80773i			0.428754i
$423$	−0.302985	−	4.87375i	−0.0147316	−	0.236970i
$424$	−5.02175			−0.243878
$425$		0			0
$426$	−0.277187	+	0.294954i	−0.0134297	+	0.0142906i
$427$	12.0000	+	13.8564i	0.580721	+	0.670559i
$428$		−	9.10268i		−	0.439995i
$429$	−12.3030	+	13.0916i	−0.593994	+	0.632067i
$430$		0			0
$431$			15.0911i			0.726914i	0.931611	+	0.363457i	$0.118404\pi$
$431$			15.0911i			0.726914i	−0.931611	+	0.363457i	$0.881596\pi$
$432$	−2.51087	−	2.08191i	−0.120805	−	0.100166i
$433$		−	37.2203i		−	1.78869i	−0.447377	−	0.894346i	$-0.647642\pi$
$433$		−	37.2203i		−	1.78869i	0.447377	−	0.894346i	$-0.352358\pi$
$434$	5.48913	−	4.75372i	0.263486	−	0.228186i
$435$		0			0
$436$	−23.4891			−1.12493
$437$	29.4891			1.41066
$438$	−6.51087	+	6.92820i	−0.311102	+	0.331042i
$439$		−	18.6101i		−	0.888213i	−0.895974	−	0.444106i	$-0.853521\pi$
$439$		−	18.6101i		−	0.888213i	0.895974	−	0.444106i	$-0.146479\pi$
$440$		0			0
$441$	−20.9307	−	1.70460i	−0.996700	−	0.0811714i
$442$	−14.2337			−0.677027
$443$		−	6.63325i		−	0.315155i	−0.987507	−	0.157578i	$-0.949632\pi$
$443$		−	6.63325i		−	0.315155i	0.987507	−	0.157578i	$-0.0503684\pi$
$444$	10.9783	−	11.6819i	0.521005	−	0.554400i
$445$		0			0
$446$	7.02175			0.332489
$447$	4.00000	+	3.75906i	0.189194	+	0.177797i
$448$	−6.74456	+	5.84096i	−0.318651	+	0.275960i
$449$			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
$452$		−	4.34896i		−	0.204558i
$453$	−2.81386	+	2.99422i	−0.132207	+	0.140681i
$454$			19.4950i			0.914945i
$455$		0			0
$456$	−10.9783	+	11.6819i	−0.514104	+	0.547056i
$457$	−12.9783			−0.607097			−0.303548	−	0.952816i	$-0.598171\pi$
$457$	−12.9783			−0.607097			−0.303548	+	0.952816i	$0.598171\pi$
$458$	12.0000			0.560723
$459$	17.4891	+	14.5012i	0.816322	+	0.676859i
$460$		0			0
$461$	2.74456			0.127827			0.0639135	−	0.997955i	$-0.479642\pi$
$461$	2.74456			0.127827			0.0639135	+	0.997955i	$0.479642\pi$
$462$	0.372281	−	9.15759i	0.0173201	−	0.426050i
$463$	32.4674			1.50889			0.754443	−	0.656365i	$-0.227907\pi$
$463$	32.4674			1.50889			0.754443	+	0.656365i	$0.227907\pi$
$464$		−	0.589907i		−	0.0273858i
$465$		0			0
$466$	−13.4891			−0.624872
$467$	31.1168			1.43992			0.719958	−	0.694018i	$-0.244161\pi$
$467$	31.1168			1.43992			0.719958	+	0.694018i	$0.244161\pi$
$468$	16.8832	−	1.04957i	0.780424	−	0.0485164i
$469$	−9.48913	+	8.21782i	−0.438167	+	0.379464i
$470$		0			0
$471$		0			0
$472$			23.3639i			1.07541i
$473$		−	11.9769i		−	0.550697i
$474$	2.37228	+	2.22938i	0.108962	+	0.102399i
$475$		0			0
$476$	−12.0000	+	10.3923i	−0.550019	+	0.476331i
$477$	−5.62772	+	0.349857i	−0.257676	+	0.0160188i
$478$	−16.5109			−0.755190
$479$	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
$482$	−13.0217			−0.593124
$483$	38.9783	+	1.58457i	1.77357	+	0.0721006i
$484$	6.35053			0.288661
$485$		0			0
$486$	9.97825	+	7.27806i	0.452623	+	0.330139i
$487$	−37.4891			−1.69879			−0.849397	−	0.527754i	$-0.823034\pi$
$487$	−37.4891			−1.69879			−0.849397	+	0.527754i	$0.823034\pi$
$488$	18.5109			0.837948
$489$	−9.48913	+	10.0974i	−0.429113	+	0.456618i
$490$		0			0
$491$		−	5.69349i		−	0.256943i	−0.991713	−	0.128472i	$-0.958993\pi$
$491$		−	5.69349i		−	0.256943i	0.991713	−	0.128472i	$-0.0410072\pi$
$492$	−9.76631	+	10.3923i	−0.440299	+	0.468521i
$493$			4.10891i			0.185056i
$494$		−	11.2772i		−	0.507384i
$495$		0			0
$496$			2.17448i			0.0976371i
$497$	−0.510875	−	0.589907i	−0.0229159	−	0.0264610i
$498$	−17.4891	−	16.4356i	−0.783706	−	0.736499i
$499$	41.3505			1.85110			0.925552	−	0.378620i	$-0.123601\pi$
$499$	41.3505			1.85110			0.925552	+	0.378620i	$0.123601\pi$
$500$		0			0
$501$	5.79211	−	6.16337i	0.258772	−	0.275359i
$502$			4.34896i			0.194104i
$503$	−12.6060			−0.562072			−0.281036	−	0.959697i	$-0.590678\pi$
$503$	−12.6060			−0.562072			−0.281036	+	0.959697i	$0.590678\pi$
$504$	−15.1386	+	14.8511i	−0.674327	+	0.661519i
$505$		0			0
$506$			17.0256i			0.756878i
$507$	−4.60597	+	4.90120i	−0.204558	+	0.217670i
$508$	1.02175			0.0453328
$509$	−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
$512$		−	7.02078i		−	0.310277i
$513$	−11.4891	+	13.8564i	−0.507257	+	0.611775i
$514$			0.404759i			0.0178532i
$515$		0			0
$516$	−7.72281	+	8.21782i	−0.339978	+	0.361770i
$517$			4.10891i			0.180710i
$518$	−9.25544	−	10.6873i	−0.406661	−	0.469571i
$519$	1.32473	−	1.40965i	0.0581494	−	0.0618766i
$520$		0			0
$521$	−34.4674			−1.51004			−0.755022	−	0.655700i	$-0.772374\pi$
$521$	−34.4674			−1.51004			−0.755022	+	0.655700i	$0.772374\pi$
$522$	0.138593	+	2.22938i	0.00606607	+	0.0975775i
$523$		−	10.3923i		−	0.454424i	−0.973845	−	0.227212i	$-0.927039\pi$
$523$		−	10.3923i		−	0.454424i	0.973845	−	0.227212i	$-0.0729610\pi$
$524$	7.53262			0.329064
$525$		0			0
$526$	0.233688			0.0101893
$527$		−	15.1460i		−	0.659771i
$528$	2.00000	+	1.87953i	0.0870388	+	0.0817959i
$529$	−49.4674			−2.15076
$530$		0			0
$531$	1.62772	+	26.1831i	0.0706370	+	1.13625i
$532$	−8.23369	−	9.50744i	−0.356976	−	0.412200i
$533$		−	24.6535i		−	1.06786i
$534$	−14.7446	−	13.8564i	−0.638060	−	0.599625i
$535$		0			0
$536$			12.6766i			0.547545i
$537$	8.37228	+	7.86797i	0.361291	+	0.339528i
$538$		−	2.17448i		−	0.0937485i
$539$	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	$0.324468\pi$
$542$	−3.76631			−0.161777
$543$	1.62772	+	1.52967i	0.0698521	+	0.0656445i
$544$			25.5383i			1.09495i
$545$		0			0
$546$	0.605969	−	14.9060i	0.0259331	−	0.637917i
$547$	2.97825			0.127341			0.0636704	−	0.997971i	$-0.479719\pi$
$547$	2.97825			0.127341			0.0636704	+	0.997971i	$0.479719\pi$
$548$			18.2054i			0.777695i
$549$	20.7446	−	1.28962i	0.885356	−	0.0550397i
$550$		0			0
$551$	−3.25544			−0.138686
$552$	26.9783	−	28.7075i	1.14827	−	1.22187i
$553$	−4.74456	+	4.10891i	−0.201759	+	0.174729i
$554$			22.3692i			0.950376i
$555$		0			0
$556$			25.5383i			1.08307i
$557$			17.6155i			0.746391i	0.927753	+	0.373196i	$0.121738\pi$
$557$			17.6155i			0.746391i	−0.927753	+	0.373196i	$0.878262\pi$
$558$	−0.510875	−	8.21782i	−0.0216271	−	0.347888i
$559$		−	19.4950i		−	0.824550i
$560$		0			0
$561$	−13.9307	−	13.0916i	−0.588155	−	0.552727i
$562$	22.2337			0.937872
$563$	17.4891			0.737079			0.368539	−	0.929612i	$-0.379858\pi$
$563$	17.4891			0.737079			0.368539	+	0.929612i	$0.379858\pi$
$564$	2.64947	−	2.81929i	0.111563	−	0.118714i
$565$		0			0
$566$	−0.510875			−0.0214737
$567$	−15.9307	+	17.6978i	−0.669027	+	0.743238i
$568$	−0.788061			−0.0330663
$569$			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	$0.526673\pi$
$572$	−14.2337			−0.595140
$573$	−26.3030	−	24.7186i	−1.09882	−	1.03263i
$574$	8.23369	+	9.50744i	0.343667	+	0.396833i
$575$		0			0
$576$	0.627719	+	10.0974i	0.0261549	+	0.420723i
$577$			2.81929i			0.117369i	0.998277	+	0.0586843i	$0.0186905\pi$
$577$			2.81929i			0.117369i	−0.998277	+	0.0586843i	$0.981309\pi$
$578$		−	1.67715i		−	0.0697602i
$579$	14.5109	−	15.4410i	0.603051	−	0.641705i
$580$		0			0
$581$	34.9783	−	30.2921i	1.45114	−	1.25673i
$582$	10.3723	−	11.0371i	0.429945	−	0.457503i
$583$	4.74456			0.196500
$584$	−18.5109			−0.765985
$585$		0			0
$586$		−	8.62258i		−	0.356196i
$587$	−17.4891			−0.721853			−0.360927	−	0.932594i	$-0.617540\pi$
$587$	−17.4891			−0.721853			−0.360927	+	0.932594i	$0.617540\pi$
$588$	−10.3723	−	13.0092i	−0.427746	−	0.536491i
$589$	12.0000			0.494451
$590$		0			0
$591$	−19.8614	−	18.6650i	−0.816989	−	0.767777i
$592$	4.23369			0.174004
$593$	−4.37228			−0.179548			−0.0897740	−	0.995962i	$-0.528614\pi$
$593$	−4.37228			−0.179548			−0.0897740	+	0.995962i	$0.528614\pi$
$594$	−8.00000	−	6.63325i	−0.328244	−	0.272166i
$595$		0			0
$596$			4.34896i			0.178140i
$597$	−33.8614	−	31.8217i	−1.38586	−	1.30238i
$598$			27.7128i			1.13326i
$599$		−	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	$0.851348\pi$
$602$	6.51087	+	7.51811i	0.265363	+	0.306415i
$603$	0.883156	+	14.2063i	0.0359649	+	0.578524i
$604$	−3.25544			−0.132462
$605$		0			0
$606$	−6.00000	−	5.63858i	−0.243733	−	0.229052i
$607$			8.86263i			0.359723i	0.983692	+	0.179862i	$0.0575650\pi$
$607$			8.86263i			0.359723i	−0.983692	+	0.179862i	$0.942435\pi$
$608$	−20.2337			−0.820584
$609$	−4.30298	−	0.174928i	−0.174366	−	0.00708845i
$610$		0			0
$611$			6.68815i			0.270574i
$612$	1.11684	+	17.9653i	0.0451457	+	0.726205i
$613$	27.4891			1.11028			0.555138	−	0.831758i	$-0.312666\pi$
$613$	27.4891			1.11028			0.555138	+	0.831758i	$0.312666\pi$
$614$	−18.0000			−0.726421
$615$		0			0
$616$	13.4891	−	11.6819i	0.543492	−	0.470678i
$617$			24.5437i			0.988091i	0.869436	+	0.494045i	$0.164482\pi$
$617$			24.5437i			0.988091i	−0.869436	+	0.494045i	$0.835518\pi$
$618$	5.90491	−	6.28339i	0.237530	−	0.252755i
$619$			18.6101i			0.748004i	0.927428	+	0.374002i	$0.122015\pi$
$619$			18.6101i			0.748004i	−0.927428	+	0.374002i	$0.877985\pi$
$620$		0			0
$621$	28.2337	−	34.0511i	1.13298	−	1.36642i
$622$			11.2772i			0.452173i
$623$	29.4891	−	25.5383i	1.18146	−	1.02317i
$624$	3.25544	+	3.05934i	0.130322	+	0.122472i
$625$		0			0
$626$	−4.27719			−0.170951
$627$	10.3723	−	11.0371i	0.414229	−	0.440780i
$628$		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	$0.652198\pi$
$632$			6.33830i			0.252124i
$633$	−13.1861	+	14.0313i	−0.524102	+	0.557695i
$634$	−1.48913			−0.0591407
$635$		0			0
$636$	−3.25544	−	3.05934i	−0.129086	−	0.121311i
$637$	28.4674	+	4.10891i	1.12792	+	0.162801i
$638$		−	1.87953i		−	0.0744112i
$639$	−0.883156	+	0.0549029i	−0.0349371	+	0.00217192i
$640$		0			0
$641$		−	36.6303i		−	1.44681i	−0.690423	−	0.723406i	$-0.742576\pi$
$641$		−	36.6303i		−	1.44681i	0.690423	−	0.723406i	$-0.257424\pi$
$642$	−6.23369	+	6.63325i	−0.246024	+	0.261793i
$643$			10.1523i			0.400366i	0.979759	+	0.200183i	$0.0641536\pi$
$643$			10.1523i			0.400366i	−0.979759	+	0.200183i	$0.935846\pi$
$644$	20.2337	+	23.3639i	0.797319	+	0.920665i
$645$		0			0
$646$	12.0000			0.472134
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$	2.97825	+	23.8612i	0.116997	+	0.937356i
$649$		−	22.0742i		−	0.866489i
$650$		0			0
$651$	15.8614	+	0.644810i	0.621658	+	0.0252721i
$652$	−10.9783			−0.429941
$653$			39.6897i			1.55318i	0.630008	+	0.776589i	$0.283052\pi$
$653$			39.6897i			1.55318i	−0.630008	+	0.776589i	$0.716948\pi$
$654$	17.1168	+	16.0858i	0.669322	+	0.629004i
$655$		0			0
$656$	−3.76631			−0.147050
$657$	−20.7446	+	1.28962i	−0.809322	+	0.0503129i
$658$	−2.23369	−	2.57924i	−0.0870782	−	0.100549i
$659$		−	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	$-0.0430193\pi$
$662$			3.16915i			0.123172i
$663$	−22.6753	−	21.3094i	−0.880634	−	0.827588i
$664$		−	46.7277i		−	1.81339i
$665$		0			0
$666$	−16.0000	+	0.994667i	−0.619987	+	0.0385426i
$667$	8.00000			0.309761
$668$	6.70106			0.259272
$669$	11.1861	+	10.5123i	0.432481	+	0.406430i
$670$		0			0
$671$	−17.4891			−0.675160
$672$	−26.7446	−	1.08724i	−1.03169	−	0.0419412i
$673$	12.2337			0.471574			0.235787	−	0.971805i	$-0.424233\pi$
$673$	12.2337			0.471574			0.235787	+	0.971805i	$0.424233\pi$
$674$			12.8617i			0.495416i
$675$		0			0
$676$	−5.32878			−0.204953
$677$	18.6060			0.715085			0.357543	−	0.933897i	$-0.383615\pi$
$677$	18.6060			0.715085			0.357543	+	0.933897i	$0.383615\pi$
$678$	−2.97825	+	3.16915i	−0.114379	+	0.121710i
$679$	19.1168	+	22.0742i	0.733637	+	0.847131i
$680$		0			0
$681$	−29.1861	+	31.0569i	−1.11842	+	1.19010i
$682$			6.92820i			0.265295i
$683$			34.4559i			1.31842i	0.751960	+	0.659209i	$0.229109\pi$
$683$			34.4559i			1.31842i	−0.751960	+	0.659209i	$0.770891\pi$
$684$	−14.2337	+	0.884861i	−0.544239	+	0.0338335i
$685$		0			0
$686$	−12.3505	+	7.92287i	−0.471545	+	0.302497i
$687$	19.1168	+	17.9653i	0.729353	+	0.685420i
$688$	−2.97825			−0.113545
$689$	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	$0.867953\pi$
$692$	1.53262			0.0582616
$693$	14.3030	−	14.0313i	0.543325	−	0.533006i
$694$	−11.7663			−0.446643
$695$		0			0
$696$	−2.97825	+	3.16915i	−0.112890	+	0.120126i
$697$	26.2337			0.993672
$698$	−12.0000			−0.454207
$699$	−21.4891	−	20.1947i	−0.812793	−	0.763834i
$700$		0			0
$701$		−	42.5090i		−	1.60554i	−0.596287	−	0.802771i	$-0.703358\pi$
$701$		−	42.5090i		−	1.60554i	0.596287	−	0.802771i	$-0.296642\pi$
$702$	−13.0217	−	10.7971i	−0.491474	−	0.407509i
$703$		−	23.3639i		−	0.881184i
$704$		−	8.51278i		−	0.320837i
$705$		0			0
$706$			19.8997i			0.748937i
$707$	12.0000	−	10.3923i	0.451306	−	0.390843i
$708$	−14.2337	+	15.1460i	−0.534935	+	0.569223i
$709$	6.88316			0.258502			0.129251	−	0.991612i	$-0.458743\pi$
$709$	6.88316			0.258502			0.129251	+	0.991612i	$0.458743\pi$
$710$		0			0
$711$	0.441578	+	7.10313i	0.0165605	+	0.266388i
$712$		−	39.3947i		−	1.47638i
$713$	−29.4891			−1.10438
$714$	15.8614	+	0.644810i	0.593598	+	0.0241314i
$715$		0			0
$716$			9.10268i			0.340183i
$717$	−26.3030	−	24.7186i	−0.982303	−	0.923133i
$718$	−13.2554			−0.494689
$719$	−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
$722$		−	5.54601i		−	0.206401i
$723$	−20.7446	−	19.4950i	−0.771499	−	0.725026i
$724$			1.76972i			0.0657712i
$725$		0			0
$726$	−4.62772	−	4.34896i	−0.171751	−	0.161405i
$727$		−	3.46410i		−	0.128476i	−0.997935	−	0.0642382i	$-0.979538\pi$
$727$		−	3.46410i		−	0.128476i	0.997935	−	0.0642382i	$-0.0204617\pi$
$728$	21.9565	−	19.0149i	0.813762	−	0.704739i
$729$	5.00000	+	26.5330i	0.185185	+	0.982704i
$730$		0			0
$731$	20.7446			0.767265
$732$	12.0000	+	11.2772i	0.443533	+	0.416816i
$733$			40.0395i			1.47889i	0.673215	+	0.739447i	$0.264913\pi$
$733$			40.0395i			1.47889i	−0.673215	+	0.739447i	$0.735087\pi$
$734$	−27.9565			−1.03189
$735$		0			0
$736$	49.7228			1.83281
$737$		−	11.9769i		−	0.441174i
$738$	14.2337	−	0.884861i	0.523949	−	0.0325722i
$739$	−14.3723			−0.528693			−0.264346	−	0.964428i	$-0.585156\pi$
$739$	−14.3723			−0.528693			−0.264346	+	0.964428i	$0.585156\pi$
$740$		0			0
$741$	16.8832	−	17.9653i	0.620218	−	0.659972i
$742$	−2.97825	+	2.57924i	−0.109335	+	0.0946869i
$743$		−	16.1407i		−	0.592145i	−0.955166	−	0.296072i	$-0.904323\pi$
$743$		−	16.1407i		−	0.592145i	0.955166	−	0.296072i	$-0.0956769\pi$
$744$	10.9783	−	11.6819i	0.402482	−	0.428280i
$745$		0			0
$746$		−	10.5021i		−	0.384510i
$747$	−3.25544	−	52.3663i	−0.119110	−	1.91598i
$748$		−	15.1460i		−	0.553794i
$749$	−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	$0.320120\pi$
$752$	1.02175			0.0372594
$753$	−6.51087	+	6.92820i	−0.237269	+	0.252478i
$754$		−	3.05934i		−	0.111415i
$755$		0			0
$756$	−18.8614	+	0.404759i	−0.685983	+	0.0147210i
$757$	19.7663			0.718419			0.359209	−	0.933257i	$-0.383046\pi$
$757$	19.7663			0.718419			0.359209	+	0.933257i	$0.383046\pi$
$758$			17.0256i			0.618396i
$759$	−25.4891	+	27.1229i	−0.925197	+	0.984499i
$760$		0			0
$761$	8.23369			0.298471			0.149235	−	0.988802i	$-0.452319\pi$
$761$	8.23369			0.298471			0.149235	+	0.988802i	$0.452319\pi$
$762$	−0.744563	−	0.699713i	−0.0269727	−	0.0253479i
$763$	−34.2337	+	29.6472i	−1.23934	+	1.07330i
$764$		−	28.5977i		−	1.03463i
$765$		0			0
$766$			4.34896i			0.157134i
$767$		−	35.9306i		−	1.29738i
$768$	−16.4674	+	17.5229i	−0.594215	+	0.632303i
$769$		−	38.5099i		−	1.38870i	−0.719637	−	0.694351i	$-0.755692\pi$
$769$		−	38.5099i		−	1.38870i	0.719637	−	0.694351i	$-0.244308\pi$
$770$		0			0
$771$	−0.605969	+	0.644810i	−0.0218234	+	0.0232223i
$772$	16.7881			0.604216
$773$	52.3723			1.88370			0.941850	−	0.336034i	$-0.109086\pi$
$773$	52.3723			1.88370			0.941850	+	0.336034i	$0.109086\pi$
$774$	11.2554	−	0.699713i	0.404568	−	0.0251507i
$775$		0			0
$776$	29.4891			1.05860
$777$	1.25544	−	30.8820i	0.0450386	−	1.10788i
$778$	23.2554			0.833748
$779$			20.7846i			0.744686i
$780$		0			0
$781$	0.744563			0.0266425
$782$	−29.4891			−1.05453
$783$	−3.11684	+	3.75906i	−0.111387	+	0.134338i
$784$	0.627719	−	4.34896i	0.0224185	−	0.155320i
$785$		0			0
$786$	−5.48913	−	5.15848i	−0.195791	−	0.183997i
$787$		−	3.22405i		−	0.114925i	−0.998348	−	0.0574625i	$-0.981699\pi$
$787$		−	3.22405i		−	0.114925i	0.998348	−	0.0574625i	$-0.0183010\pi$
$788$		−	21.5941i		−	0.769259i
$789$	0.372281	+	0.349857i	0.0132536	+	0.0124552i
$790$		0			0
$791$	−5.48913	−	6.33830i	−0.195171	−	0.225364i
$792$	−1.25544	−	20.1947i	−0.0446100	−	0.717588i
$793$	−28.4674			−1.01091
$794$	20.7446			0.736197
$795$		0			0
$796$		−	36.8155i		−	1.30489i
$797$	14.1386			0.500815			0.250407	−	0.968141i	$-0.419435\pi$
$797$	14.1386			0.500815			0.250407	+	0.968141i	$0.419435\pi$
$798$	−0.510875	+	12.5668i	−0.0180848	+	0.444859i
$799$	−7.11684			−0.251776
$800$		0			0
$801$	−2.74456	−	44.1485i	−0.0969744	−	1.55991i
$802$	4.74456			0.167536
$803$	17.4891			0.617178
$804$	−7.72281	+	8.21782i	−0.272363	+	0.289820i
$805$		0			0
$806$			11.2772i			0.397221i
$807$	3.25544	−	3.46410i	0.114597	−	0.121942i
$808$		−	16.0309i		−	0.563965i
$809$		−	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	$0.894048\pi$
$812$	−2.23369	−	2.57924i	−0.0783871	−	0.0905136i
$813$	−6.00000	−	5.63858i	−0.210429	−	0.197754i
$814$	13.4891			0.472794
$815$		0			0
$816$	−3.25544	+	3.46410i	−0.113963	+	0.121268i
$817$			16.4356i			0.575011i
$818$	19.5326			0.682942
$819$	23.2812	−	22.8391i	0.813512	−	0.798062i
$820$		0			0
$821$			34.9909i			1.22119i	0.791943	+	0.610595i	$0.209070\pi$
$821$			34.9909i			1.22119i	−0.791943	+	0.610595i	$0.790930\pi$
$822$	12.4674	−	13.2665i	0.434850	−	0.462722i
$823$	13.7663			0.479863			0.239932	−	0.970790i	$-0.422875\pi$
$823$	13.7663			0.479863			0.239932	+	0.970790i	$0.422875\pi$
$824$	16.7881			0.584840
$825$		0			0
$826$	12.0000	+	13.8564i	0.417533	+	0.482126i
$827$		−	14.8511i		−	0.516422i	−0.966088	−	0.258211i	$-0.916867\pi$
$827$		−	14.8511i		−	0.516422i	0.966088	−	0.258211i	$-0.0831330\pi$
$828$	34.9783	−	2.17448i	1.21558	−	0.0755684i
$829$			12.5668i			0.436463i	0.975897	+	0.218231i	$0.0700287\pi$
$829$			12.5668i			0.436463i	−0.975897	+	0.218231i	$0.929971\pi$
$830$		0			0
$831$	−33.4891	+	35.6357i	−1.16172	+	1.23619i
$832$		−	13.8564i		−	0.480384i
$833$	−4.37228	+	30.2921i	−0.151491	+	1.04956i
$834$	17.4891	−	18.6101i	0.605599	−	0.644416i
$835$		0			0
$836$	12.0000			0.415029
$837$	11.4891	−	13.8564i	0.397122	−	0.478947i
$838$		−	6.92820i		−	0.239331i
$839$	−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
$842$		−	11.5721i		−	0.398802i
$843$	35.4198	+	33.2863i	1.21992	+	1.14644i
$844$	−15.2554			−0.525114
$845$		0			0
$846$	−3.86141	+	0.240051i	−0.132758	+	0.00825312i
$847$	9.25544	−	8.01544i	0.318021	−	0.275414i
$848$		−	1.17981i		−	0.0405150i
$849$	−0.813859	−	0.764836i	−0.0279316	−	0.0262491i
$850$		0			0
$851$			57.4150i			1.96816i
$852$	−0.510875	−	0.480102i	−0.0175023	−	0.0164480i
$853$		−	32.8713i		−	1.12549i	−0.826630	−	0.562746i	$-0.809745\pi$
$853$		−	32.8713i		−	1.12549i	0.826630	−	0.562746i	$-0.190255\pi$
$854$	10.9783	−	9.50744i	0.375668	−	0.325338i
$855$		0			0
$856$	−17.7228			−0.605753
$857$	−46.4674			−1.58730			−0.793648	−	0.608378i	$-0.791821\pi$
$857$	−46.4674			−1.58730			−0.793648	+	0.608378i	$0.791821\pi$
$858$	10.3723	+	9.74749i	0.354104	+	0.332774i
$859$		−	14.2612i		−	0.486585i	−0.969953	−	0.243292i	$-0.921773\pi$
$859$		−	14.2612i		−	0.486585i	0.969953	−	0.243292i	$-0.0782274\pi$
$860$		0			0
$861$	−1.11684	+	27.4728i	−0.0380619	+	0.936269i
$862$	11.9565			0.407240
$863$		−	41.2743i		−	1.40499i	−0.711688	−	0.702496i	$-0.752069\pi$
$863$		−	41.2743i		−	1.40499i	0.711688	−	0.702496i	$-0.247931\pi$
$864$	−19.3723	+	23.3639i	−0.659058	+	0.794854i
$865$		0			0
$866$	−29.4891			−1.00208
$867$	2.51087	−	2.67181i	0.0852738	−	0.0907396i
$868$	8.23369	+	9.50744i	0.279470	+	0.322704i
$869$		−	5.98844i		−	0.203144i
$870$		0			0
$871$		−	19.4950i		−	0.660563i
$872$			45.7330i			1.54872i
$873$	33.0475	−	2.05446i	1.11849	−	0.0695328i
$874$		−	23.3639i		−	0.790294i
$875$		0			0
$876$	−12.0000	−	11.2772i	−0.405442	−	0.381020i
$877$	38.4674			1.29895			0.649475	−	0.760383i	$-0.274989\pi$
$877$	38.4674			1.29895			0.649475	+	0.760383i	$0.274989\pi$
$878$	−14.7446			−0.497605
$879$	12.9090	−	13.7364i	0.435408	−	0.463317i
$880$		0			0
$881$	32.2337			1.08598			0.542990	−	0.839739i	$-0.317292\pi$
$881$	32.2337			1.08598			0.542990	+	0.839739i	$0.317292\pi$
$882$	−1.35053	+	16.5831i	−0.0454748	+	0.558383i
$883$	−49.4891			−1.66544			−0.832721	−	0.553693i	$-0.813218\pi$
$883$	−49.4891			−1.66544			−0.832721	+	0.553693i	$0.813218\pi$
$884$		−	24.6535i		−	0.829186i
$885$		0			0
$886$	−5.25544			−0.176560
$887$	−18.5109			−0.621534			−0.310767	−	0.950486i	$-0.600586\pi$
$887$	−18.5109			−0.621534			−0.310767	+	0.950486i	$0.600586\pi$
$888$	−22.7446	−	21.3745i	−0.763258	−	0.717282i
$889$	1.48913	−	1.28962i	0.0499437	−	0.0432525i
$890$		0			0
$891$	−2.81386	−	22.5441i	−0.0942678	−	0.755256i
$892$			12.1620i			0.407215i
$893$		−	5.63858i		−	0.188688i
$894$	2.97825	−	3.16915i	0.0996076	−	0.105992i
$895$		0			0
$896$	−15.6060	−	18.0202i	−0.521359	−	0.602013i
$897$	−41.4891	+	44.1485i	−1.38528	+	1.47407i
$898$	9.21194			0.307406
$899$	3.25544			0.108575
$900$		0			0
$901$			8.21782i			0.273775i
$902$	−12.0000			−0.399556
$903$	−0.883156	+	21.7244i	−0.0293896	+	0.722942i
$904$	−8.46738			−0.281621
$905$		0			0
$906$	2.37228	+	2.22938i	0.0788138	+	0.0740663i
$907$	−8.00000			−0.265636			−0.132818	−	0.991140i	$-0.542403\pi$
$907$	−8.00000			−0.265636			−0.132818	+	0.991140i	$0.542403\pi$
$908$	−33.7663			−1.12057
$909$	−1.11684	−	17.9653i	−0.0370434	−	0.595872i
$910$		0			0
$911$		−	2.87419i		−	0.0952263i	−0.998866	−	0.0476132i	$-0.984839\pi$
$911$		−	2.87419i		−	0.0952263i	0.998866	−	0.0476132i	$-0.0151615\pi$
$912$	−2.74456	−	2.57924i	−0.0908816	−	0.0854072i
$913$			44.1485i			1.46110i
$914$			10.2825i			0.340115i
$915$		0			0
$916$			20.7846i			0.686743i
$917$	10.9783	−	9.50744i	0.362534	−	0.313963i
$918$	11.4891	−	13.8564i	0.379198	−	0.457330i
$919$	−5.62772			−0.185641			−0.0928207	−	0.995683i	$-0.529588\pi$
$919$	−5.62772			−0.185641			−0.0928207	+	0.995683i	$0.529588\pi$
$920$		0			0
$921$	−28.6753	−	26.9480i	−0.944882	−	0.887966i
$922$		−	2.17448i		−	0.0716127i
$923$	1.21194			0.0398914
$924$	15.8614	+	0.644810i	0.521802	+	0.0212127i
$925$		0			0
$926$		−	25.7235i		−	0.845326i
$927$	18.8139	−	1.16959i	0.617928	−	0.0384145i
$928$	−5.48913			−0.180189
$929$	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
$932$		−	23.3639i		−	0.765308i
$933$	−16.8832	+	17.9653i	−0.552730	+	0.588158i
$934$		−	24.6535i		−	0.806686i
$935$		0			0
$936$	−2.04350	−	32.8713i	−0.0667938	−	1.07443i
$937$			0.240051i			0.00784212i	0.999992	+	0.00392106i	$0.00124811\pi$
$937$			0.240051i			0.00784212i	−0.999992	+	0.00392106i	$0.998752\pi$
$938$	6.51087	+	7.51811i	0.212588	+	0.245475i
$939$	−6.81386	−	6.40342i	−0.222362	−	0.208968i
$940$		0			0
$941$	−38.7446			−1.26304			−0.631518	−	0.775361i	$-0.717568\pi$
$941$	−38.7446			−1.26304			−0.631518	+	0.775361i	$0.717568\pi$
$942$		0			0
$943$		−	51.0767i		−	1.66329i
$944$	−5.48913			−0.178656
$945$		0			0
$946$	−9.48913			−0.308518
$947$			34.9360i			1.13527i	0.823282	+	0.567633i	$0.192141\pi$
$947$			34.9360i			1.13527i	−0.823282	+	0.567633i	$0.807859\pi$
$948$	−3.86141	+	4.10891i	−0.125413	+	0.133451i
$949$	28.4674			0.924090
$950$		0			0
$951$	−2.37228	−	2.22938i	−0.0769265	−	0.0722927i
$952$	20.2337	+	23.3639i	0.655778	+	0.757227i
$953$			7.62792i			0.247092i	0.992339	+	0.123546i	$0.0394267\pi$
$953$			7.62792i			0.247092i	−0.992339	+	0.123546i	$0.960573\pi$
$954$	0.277187	+	4.45877i	0.00897425	+	0.144358i
$955$		0			0
$956$		−	28.5977i		−	0.924915i
$957$	2.81386	−	2.99422i	0.0909592	−	0.0967894i
$958$		−	32.8713i		−	1.06202i
$959$	22.9783	+	26.5330i	0.742006	+	0.856795i
$960$		0			0
$961$	19.0000			0.612903
$962$	21.9565			0.707906
$963$	−19.8614	+	1.23472i	−0.640025	+	0.0397882i
$964$		−	22.5543i		−	0.726426i
$965$		0			0
$966$	1.25544	−	30.8820i	0.0403930	−	0.993611i
$967$	−10.2337			−0.329093			−0.164547	−	0.986369i	$-0.552616\pi$
$967$	−10.2337			−0.329093			−0.164547	+	0.986369i	$0.552616\pi$
$968$		−	12.3644i		−	0.397407i
$969$	19.1168	+	17.9653i	0.614122	+	0.577129i
$970$		0			0
$971$	37.2119			1.19419			0.597094	−	0.802171i	$-0.296322\pi$
$971$	37.2119			1.19419			0.597094	+	0.802171i	$0.296322\pi$
$972$	−12.6060	+	17.2828i	−0.404337	+	0.554347i
$973$	32.2337	+	37.2203i	1.03336	+	1.19323i
$974$			29.7021i			0.951718i
$975$		0			0
$976$			4.34896i			0.139207i
$977$			7.62792i			0.244039i	0.992528	+	0.122019i	$0.0389370\pi$
$977$			7.62792i			0.244039i	−0.992528	+	0.122019i	$0.961063\pi$
$978$	8.00000	+	7.51811i	0.255812	+	0.240403i
$979$			37.2203i			1.18956i
$980$		0			0
$981$	3.18614	+	51.2516i	0.101726	+	1.63634i
$982$	−4.51087			−0.143948
$983$	−39.8614			−1.27138			−0.635691	−	0.771944i	$-0.719285\pi$
$983$	−39.8614			−1.27138			−0.635691	+	0.771944i	$0.719285\pi$
$984$	20.2337	+	19.0149i	0.645026	+	0.606172i
$985$		0			0
$986$	3.25544			0.103674
$987$	0.302985	−	7.45299i	0.00964411	−	0.237231i
$988$	19.5326			0.621416
$989$		−	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	$0.367326\pi$
$992$	20.2337			0.642420
$993$	−4.74456	+	5.04868i	−0.150564	+	0.160215i
$994$	−0.467376	+	0.404759i	−0.0148243	+	0.0128382i
$995$		0			0
$996$	28.4674	−	30.2921i	0.902023	−	0.959840i
$997$			31.8217i			1.00780i	0.863761	+	0.503902i	$0.168103\pi$
$997$			31.8217i			1.00780i	−0.863761	+	0.503902i	$0.831897\pi$
$998$		−	32.7615i		−	1.03705i
$999$	−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.b.e.251.2		4
3.2	odd	2		525.2.b.g.251.3		4
5.2	odd	4		525.2.g.d.524.5		8
5.3	odd	4		525.2.g.d.524.4		8
5.4	even	2		105.2.b.d.41.3	yes	4
7.6	odd	2		525.2.b.g.251.2		4
15.2	even	4		525.2.g.e.524.4		8
15.8	even	4		525.2.g.e.524.5		8
15.14	odd	2		105.2.b.c.41.2	✓	4
20.19	odd	2		1680.2.f.g.881.3		4
21.20	even	2	inner	525.2.b.e.251.3		4
35.4	even	6		735.2.s.j.656.1		4
35.9	even	6		735.2.s.g.521.2		4
35.13	even	4		525.2.g.e.524.3		8
35.19	odd	6		735.2.s.h.521.2		4
35.24	odd	6		735.2.s.i.656.1		4
35.27	even	4		525.2.g.e.524.6		8
35.34	odd	2		105.2.b.c.41.3	yes	4
60.59	even	2		1680.2.f.h.881.1		4
105.44	odd	6		735.2.s.i.521.1		4
105.59	even	6		735.2.s.g.656.2		4
105.62	odd	4		525.2.g.d.524.3		8
105.74	odd	6		735.2.s.h.656.2		4
105.83	odd	4		525.2.g.d.524.6		8
105.89	even	6		735.2.s.j.521.1		4
105.104	even	2		105.2.b.d.41.2	yes	4
140.139	even	2		1680.2.f.h.881.2		4
420.419	odd	2		1680.2.f.g.881.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.b.c.41.2	✓	4	15.14	odd	2
105.2.b.c.41.3	yes	4	35.34	odd	2
105.2.b.d.41.2	yes	4	105.104	even	2
105.2.b.d.41.3	yes	4	5.4	even	2
525.2.b.e.251.2		4	1.1	even	1	trivial
525.2.b.e.251.3		4	21.20	even	2	inner
525.2.b.g.251.2		4	7.6	odd	2
525.2.b.g.251.3		4	3.2	odd	2
525.2.g.d.524.3		8	105.62	odd	4
525.2.g.d.524.4		8	5.3	odd	4
525.2.g.d.524.5		8	5.2	odd	4
525.2.g.d.524.6		8	105.83	odd	4
525.2.g.e.524.3		8	35.13	even	4
525.2.g.e.524.4		8	15.2	even	4
525.2.g.e.524.5		8	15.8	even	4
525.2.g.e.524.6		8	35.27	even	4
735.2.s.g.521.2		4	35.9	even	6
735.2.s.g.656.2		4	105.59	even	6
735.2.s.h.521.2		4	35.19	odd	6
735.2.s.h.656.2		4	105.74	odd	6
735.2.s.i.521.1		4	105.44	odd	6
735.2.s.i.656.1		4	35.24	odd	6
735.2.s.j.521.1		4	105.89	even	6
735.2.s.j.656.1		4	35.4	even	6
1680.2.f.g.881.3		4	20.19	odd	2
1680.2.f.g.881.4		4	420.419	odd	2
1680.2.f.h.881.1		4	60.59	even	2
1680.2.f.h.881.2		4	140.139	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.792287i q^{2} +(1.18614 - 1.26217i) q^{3} +1.37228 q^{4} +(-1.00000 - 0.939764i) q^{6} +(2.00000 - 1.73205i) q^{7} -2.67181i q^{8} +(-0.186141 - 2.99422i) q^{9} +2.52434i q^{11} +(1.62772 - 1.73205i) q^{12} +4.10891i q^{13} +(-1.37228 - 1.58457i) q^{14} +0.627719 q^{16} -4.37228 q^{17} +(-2.37228 + 0.147477i) q^{18} -3.46410i q^{19} +(0.186141 - 4.57879i) q^{21} +2.00000 q^{22} +8.51278i q^{23} +(-3.37228 - 3.16915i) q^{24} +3.25544 q^{26} +(-4.00000 - 3.31662i) q^{27} +(2.74456 - 2.37686i) q^{28} -0.939764i q^{29} +3.46410i q^{31} -5.84096i q^{32} +(3.18614 + 2.99422i) q^{33} +3.46410i q^{34} +(-0.255437 - 4.10891i) q^{36} +6.74456 q^{37} -2.74456 q^{38} +(5.18614 + 4.87375i) q^{39} -6.00000 q^{41} +(-3.62772 - 0.147477i) q^{42} -4.74456 q^{43} +3.46410i q^{44} +6.74456 q^{46} +1.62772 q^{47} +(0.744563 - 0.792287i) q^{48} +(1.00000 - 6.92820i) q^{49} +(-5.18614 + 5.51856i) q^{51} +5.63858i q^{52} -1.87953i q^{53} +(-2.62772 + 3.16915i) q^{54} +(-4.62772 - 5.34363i) q^{56} +(-4.37228 - 4.10891i) q^{57} -0.744563 q^{58} -8.74456 q^{59} +6.92820i q^{61} +2.74456 q^{62} +(-5.55842 - 5.66603i) q^{63} -3.37228 q^{64} +(2.37228 - 2.52434i) q^{66} -4.74456 q^{67} -6.00000 q^{68} +(10.7446 + 10.0974i) q^{69} -0.294954i q^{71} +(-8.00000 + 0.497333i) q^{72} -6.92820i q^{73} -5.34363i q^{74} -4.75372i q^{76} +(4.37228 + 5.04868i) q^{77} +(3.86141 - 4.10891i) q^{78} -2.37228 q^{79} +(-8.93070 + 1.11469i) q^{81} +4.75372i q^{82} +17.4891 q^{83} +(0.255437 - 6.28339i) q^{84} +3.75906i q^{86} +(-1.18614 - 1.11469i) q^{87} +6.74456 q^{88} +14.7446 q^{89} +(7.11684 + 8.21782i) q^{91} +11.6819i q^{92} +(4.37228 + 4.10891i) q^{93} -1.28962i q^{94} +(-7.37228 - 6.92820i) q^{96} +11.0371i q^{97} +(-5.48913 - 0.792287i) q^{98} +(7.55842 - 0.469882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} - 6 q^{4} - 4 q^{6} + 8 q^{7} + 5 q^{9} + 18 q^{12} + 6 q^{14} + 14 q^{16} - 6 q^{17} + 2 q^{18} - 5 q^{21} + 8 q^{22} - 2 q^{24} + 36 q^{26} - 16 q^{27} - 12 q^{28} + 7 q^{33} - 24 q^{36}+ \cdots + 13 q^{99}+O(q^{100}) \) 4 * q - q^3 - 6 * q^4 - 4 * q^6 + 8 * q^7 + 5 * q^9 + 18 * q^12 + 6 * q^14 + 14 * q^16 - 6 * q^17 + 2 * q^18 - 5 * q^21 + 8 * q^22 - 2 * q^24 + 36 * q^26 - 16 * q^27 - 12 * q^28 + 7 * q^33 - 24 * q^36 + 4 * q^37 + 12 * q^38 + 15 * q^39 - 24 * q^41 - 26 * q^42 + 4 * q^43 + 4 * q^46 + 18 * q^47 - 20 * q^48 + 4 * q^49 - 15 * q^51 - 22 * q^54 - 30 * q^56 - 6 * q^57 + 20 * q^58 - 12 * q^59 - 12 * q^62 - 5 * q^63 - 2 * q^64 - 2 * q^66 + 4 * q^67 - 24 * q^68 + 20 * q^69 - 32 * q^72 + 6 * q^77 - 42 * q^78 + 2 * q^79 - 7 * q^81 + 24 * q^83 + 24 * q^84 + q^87 + 4 * q^88 + 36 * q^89 - 6 * q^91 + 6 * q^93 - 18 * q^96 + 24 * q^98 + 13 * q^99

Introduction

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