LMFDB - Embedded newform 525.2.b.g.251.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [525,2,Mod(251,525)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [4,0,1,-6,0,4,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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			251.3
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	525.251
Dual form			525.2.b.g.251.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.792287i q^{2} +(-1.18614 - 1.26217i) q^{3} +1.37228 q^{4} +(1.00000 - 0.939764i) q^{6} +(2.00000 - 1.73205i) q^{7} +2.67181i q^{8} +(-0.186141 + 2.99422i) q^{9} -2.52434i q^{11} +(-1.62772 - 1.73205i) q^{12} +4.10891i q^{13} +(1.37228 + 1.58457i) q^{14} +0.627719 q^{16} +4.37228 q^{17} +(-2.37228 - 0.147477i) q^{18} -3.46410i q^{19} +(-4.55842 - 0.469882i) q^{21} +2.00000 q^{22} -8.51278i q^{23} +(3.37228 - 3.16915i) q^{24} -3.25544 q^{26} +(4.00000 - 3.31662i) q^{27} +(2.74456 - 2.37686i) q^{28} +0.939764i q^{29} +3.46410i q^{31} +5.84096i q^{32} +(-3.18614 + 2.99422i) q^{33} +3.46410i q^{34} +(-0.255437 + 4.10891i) q^{36} +6.74456 q^{37} +2.74456 q^{38} +(5.18614 - 4.87375i) q^{39} +6.00000 q^{41} +(0.372281 - 3.61158i) q^{42} -4.74456 q^{43} -3.46410i q^{44} +6.74456 q^{46} -1.62772 q^{47} +(-0.744563 - 0.792287i) q^{48} +(1.00000 - 6.92820i) q^{49} +(-5.18614 - 5.51856i) q^{51} +5.63858i q^{52} +1.87953i q^{53} +(2.62772 + 3.16915i) q^{54} +(4.62772 + 5.34363i) q^{56} +(-4.37228 + 4.10891i) q^{57} -0.744563 q^{58} +8.74456 q^{59} +6.92820i q^{61} -2.74456 q^{62} +(4.81386 + 6.31084i) q^{63} -3.37228 q^{64} +(-2.37228 - 2.52434i) q^{66} -4.74456 q^{67} +6.00000 q^{68} +(-10.7446 + 10.0974i) q^{69} +0.294954i q^{71} +(-8.00000 - 0.497333i) q^{72} -6.92820i q^{73} +5.34363i q^{74} -4.75372i q^{76} +(-4.37228 - 5.04868i) q^{77} +(3.86141 + 4.10891i) q^{78} -2.37228 q^{79} +(-8.93070 - 1.11469i) q^{81} +4.75372i q^{82} -17.4891 q^{83} +(-6.25544 - 0.644810i) q^{84} -3.75906i q^{86} +(1.18614 - 1.11469i) q^{87} +6.74456 q^{88} -14.7446 q^{89} +(7.11684 + 8.21782i) q^{91} -11.6819i q^{92} +(4.37228 - 4.10891i) q^{93} -1.28962i q^{94} +(7.37228 - 6.92820i) q^{96} +11.0371i q^{97} +(5.48913 + 0.792287i) q^{98} +(7.55842 + 0.469882i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 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}+ \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 - 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 - 10 * 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 + 25 * 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 - 48 * 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	$0.0903729\pi$
$2$			0.792287i			0.560232i	−0.959966	+	0.280116i	$0.909627\pi$
$3$	−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	$-0.875732\pi$
$11$		−	2.52434i		−	0.761116i	0.924757	−	0.380558i	$-0.124268\pi$
$12$	−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	$-0.322110\pi$
$17$	4.37228			1.06043			0.530217	+	0.847862i	$0.322110\pi$
$18$	−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
$21$	−4.55842	−	0.469882i	−0.994729	−	0.102537i
$22$	2.00000			0.426401
$23$		−	8.51278i		−	1.77504i	−0.460772	−	0.887518i	$-0.652428\pi$
$23$		−	8.51278i		−	1.77504i	0.460772	−	0.887518i	$-0.347572\pi$
$24$	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	$0.0278095\pi$
$29$			0.939764i			0.174510i	−0.996186	+	0.0872549i	$0.972191\pi$
$30$		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	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$	0.372281	−	3.61158i	0.0574443	−	0.557279i
$43$	−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	$-0.537877\pi$
$47$	−1.62772			−0.237427			−0.118714	+	0.992929i	$0.537877\pi$
$48$	−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	$0.0412045\pi$
$53$			1.87953i			0.258173i	−0.991633	+	0.129086i	$0.958796\pi$
$54$	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	$-0.307244\pi$
$59$	8.74456			1.13845			0.569223	+	0.822183i	$0.307244\pi$
$60$		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
$63$	4.81386	+	6.31084i	0.606489	+	0.795092i
$64$	−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	$0.00557143\pi$
$71$			0.294954i			0.0350046i	−0.999847	+	0.0175023i	$0.994429\pi$
$72$	−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	$-0.909484\pi$
$83$	−17.4891			−1.91968			−0.959840	+	0.280546i	$0.909484\pi$
$84$	−6.25544	−	0.644810i	−0.682524	−	0.0703546i
$85$		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	$-0.785525\pi$
$89$	−14.7446			−1.56292			−0.781460	+	0.623955i	$0.785525\pi$
$90$		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	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$	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	$0.103895\pi$
$107$			6.63325i			0.641260i	−0.947204	+	0.320630i	$0.896105\pi$
$108$	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	$0.0476261\pi$
$113$			3.16915i			0.298128i	−0.988828	+	0.149064i	$0.952374\pi$
$114$	−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
$126$	−5.00000	+	3.81396i	−0.445435	+	0.339774i
$127$	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	$-0.577080\pi$
$131$	−5.48913			−0.479587			−0.239794	+	0.970824i	$0.577080\pi$
$132$	−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	$-0.808213\pi$
$137$		−	13.2665i		−	1.13343i	0.823913	−	0.566717i	$-0.191787\pi$
$138$	−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
$147$	−9.93070	+	6.95565i	−0.819071	+	0.573693i
$148$	9.25544			0.760792
$149$		−	3.16915i		−	0.259627i	−0.991538	−	0.129813i	$-0.958562\pi$
$149$		−	3.16915i		−	0.259627i	0.991538	−	0.129813i	$-0.0414378\pi$
$150$		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	$-0.560504\pi$
$167$	−4.88316			−0.377870			−0.188935	+	0.981990i	$0.560504\pi$
$168$	1.25544	−	12.1793i	0.0968591	−	0.939650i
$169$	−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	$-0.513518\pi$
$173$	−1.11684			−0.0849121			−0.0424560	+	0.999098i	$0.513518\pi$
$174$	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	$-0.920261\pi$
$179$		−	6.63325i		−	0.495792i	0.968787	−	0.247896i	$-0.0797392\pi$
$180$		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
$189$	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	$0.728147\pi$
$192$	4.00000	+	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	$0.189418\pi$
$197$			15.7359i			1.12114i	−0.828107	+	0.560569i	$0.810582\pi$
$198$	−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	$-0.195869\pi$
$227$	24.6060			1.63316			0.816578	+	0.577235i	$0.195869\pi$
$228$	−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
$231$	−1.18614	+	11.5070i	−0.0780423	+	0.757105i
$232$	−2.51087			−0.164847
$233$			17.0256i			1.11538i	0.830049	+	0.557691i	$0.188312\pi$
$233$			17.0256i			1.11538i	−0.830049	+	0.557691i	$0.811688\pi$
$234$	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	$0.235424\pi$
$239$			20.8395i			1.34800i	−0.738733	+	0.673998i	$0.764576\pi$
$240$		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	$-0.444578\pi$
$251$	5.48913			0.346471			0.173235	+	0.984880i	$0.444578\pi$
$252$	6.60597	+	8.66025i	0.416137	+	0.545545i
$253$	−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	$-0.494928\pi$
$257$	0.510875			0.0318675			0.0159337	+	0.999873i	$0.494928\pi$
$258$	−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	$-0.997105\pi$
$263$		−	0.294954i		−	0.0181876i	0.999959	−	0.00909381i	$-0.00289469\pi$
$264$	−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	$-0.526664\pi$
$269$	−2.74456			−0.167339			−0.0836695	+	0.996494i	$0.526664\pi$
$270$		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
$273$	1.93070	−	18.7302i	0.116851	−	1.13360i
$274$	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	$-0.684285\pi$
$281$		−	28.0627i		−	1.67408i	0.547143	−	0.837039i	$-0.315715\pi$
$282$	−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	$-0.602978\pi$
$293$	−10.8832			−0.635801			−0.317900	+	0.948124i	$0.602978\pi$
$294$	−5.51087	−	7.86797i	−0.321401	−	0.458869i
$295$		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	$-0.367773\pi$
$311$	14.2337			0.807118			0.403559	+	0.914954i	$0.367773\pi$
$312$	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	$0.0168090\pi$
$317$			1.87953i			0.105565i	−0.998606	+	0.0527824i	$0.983191\pi$
$318$	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
$336$	−2.86141	−	0.294954i	−0.156103	−	0.0160910i
$337$	−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	$0.130512\pi$
$347$			14.8511i			0.797247i	−0.917115	+	0.398624i	$0.869488\pi$
$348$	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	$-0.266972\pi$
$353$	25.1168			1.33683			0.668417	+	0.743786i	$0.266972\pi$
$354$	8.74456	−	8.21782i	0.464768	−	0.436772i
$355$		0			0
$356$	−20.2337			−1.07238
$357$	−19.9307	−	2.05446i	−1.05484	−	0.108733i
$358$	5.25544			0.277758
$359$			16.7306i			0.883007i	0.897259	+	0.441504i	$0.145555\pi$
$359$			16.7306i			0.883007i	−0.897259	+	0.441504i	$0.854445\pi$
$360$		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
$378$	10.7446	+	1.78695i	0.552641	+	0.0919110i
$379$	−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	$-0.455212\pi$
$383$	5.48913			0.280481			0.140241	+	0.990117i	$0.455212\pi$
$384$	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	$-0.732874\pi$
$389$		−	29.3523i		−	1.48822i	0.668057	−	0.744110i	$-0.267126\pi$
$390$		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
$399$	−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	$-0.0477742\pi$
$402$	−4.74456	+	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	$-0.568519\pi$
$419$	−8.74456			−0.427200			−0.213600	+	0.976921i	$0.568519\pi$
$420$		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	$-0.881596\pi$
$431$		−	15.0911i		−	0.726914i	0.931611	−	0.363457i	$-0.118404\pi$
$432$	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
$441$	20.5584	+	4.28384i	0.978972	+	0.203992i
$442$	−14.2337			−0.677027
$443$			6.63325i			0.315155i	0.987507	+	0.157578i	$0.0503684\pi$
$443$			6.63325i			0.315155i	−0.987507	+	0.157578i	$0.949632\pi$
$444$	−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	$-0.911535\pi$
$449$		−	11.6270i		−	0.548713i	0.961628	−	0.274357i	$-0.0884648\pi$
$450$		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	$-0.520358\pi$
$461$	−2.74456			−0.127827			−0.0639135	+	0.997955i	$0.520358\pi$
$462$	−9.11684	−	0.939764i	−0.424154	−	0.0437218i
$463$	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	$-0.755839\pi$
$467$	−31.1168			−1.43992			−0.719958	+	0.694018i	$0.755839\pi$
$468$	−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	$-0.896741\pi$
$479$	−41.4891			−1.89569			−0.947843	+	0.318737i	$0.896741\pi$
$480$		0			0
$481$			27.7128i			1.26360i
$482$	13.0217			0.593124
$483$	−4.00000	+	38.8048i	−0.182006	+	1.76568i
$484$	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	$0.0410072\pi$
$491$			5.69349i			0.256943i	−0.991713	+	0.128472i	$0.958993\pi$
$492$	−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	$-0.409322\pi$
$503$	12.6060			0.562072			0.281036	+	0.959697i	$0.409322\pi$
$504$	−16.8614	+	12.8617i	−0.751067	+	0.572907i
$505$		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	$-0.473400\pi$
$509$	3.76631			0.166939			0.0834694	+	0.996510i	$0.473400\pi$
$510$		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	$-0.227626\pi$
$521$	34.4674			1.51004			0.755022	+	0.655700i	$0.227626\pi$
$522$	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
$546$	14.8397	+	1.52967i	0.635079	+	0.0654639i
$547$	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	$-0.878262\pi$
$557$		−	17.6155i		−	0.746391i	0.927753	−	0.373196i	$-0.121738\pi$
$558$	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	$-0.620142\pi$
$563$	−17.4891			−0.737079			−0.368539	+	0.929612i	$0.620142\pi$
$564$	2.64947	+	2.81929i	0.111563	+	0.118714i
$565$		0			0
$566$	0.510875			0.0214737
$567$	−19.7921	+	13.2390i	−0.831190	+	0.555988i
$568$	−0.788061			−0.0330663
$569$		−	23.9538i		−	1.00419i	−0.864811	−	0.502097i	$-0.832562\pi$
$569$		−	23.9538i		−	1.00419i	0.864811	−	0.502097i	$-0.167438\pi$
$570$		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	$-0.382460\pi$
$587$	17.4891			0.721853			0.360927	+	0.932594i	$0.382460\pi$
$588$	−13.6277	+	9.54511i	−0.561998	+	0.393634i
$589$	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	$-0.471386\pi$
$593$	4.37228			0.179548			0.0897740	+	0.995962i	$0.471386\pi$
$594$	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	$0.250771\pi$
$599$			34.6959i			1.41764i	−0.705391	+	0.708818i	$0.749229\pi$
$600$		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
$609$	0.441578	−	4.28384i	0.0178936	−	0.173590i
$610$		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	$-0.835518\pi$
$617$		−	24.5437i		−	0.988091i	0.869436	−	0.494045i	$-0.164482\pi$
$618$	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	$0.257424\pi$
$641$			36.6303i			1.44681i	−0.690423	+	0.723406i	$0.742576\pi$
$642$	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	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$	2.97825	−	23.8612i	0.116997	−	0.937356i
$649$		−	22.0742i		−	0.866489i
$650$		0			0
$651$	1.62772	−	15.7908i	0.0637953	−	0.618892i
$652$	−10.9783			−0.429941
$653$		−	39.6897i		−	1.55318i	−0.630008	−	0.776589i	$-0.716948\pi$
$653$		−	39.6897i		−	1.55318i	0.630008	−	0.776589i	$-0.283052\pi$
$654$	−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	$0.247218\pi$
$659$			35.9855i			1.40180i	−0.713261	+	0.700899i	$0.752782\pi$
$660$		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
$672$	2.74456	−	26.6256i	0.105874	−	1.02710i
$673$	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	$-0.616385\pi$
$677$	−18.6060			−0.715085			−0.357543	+	0.933897i	$0.616385\pi$
$678$	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	$-0.770891\pi$
$683$		−	34.4559i		−	1.31842i	0.751960	−	0.659209i	$-0.229109\pi$
$684$	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
$693$	15.9307	−	12.1518i	0.605157	−	0.461609i
$694$	−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	$0.296642\pi$
$701$			42.5090i			1.60554i	−0.596287	+	0.802771i	$0.703358\pi$
$702$	−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
$714$	1.62772	−	15.7908i	0.0609158	−	0.590957i
$715$		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	$-0.321881\pi$
$719$	28.4674			1.06165			0.530827	+	0.847480i	$0.321881\pi$
$720$		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	$0.0956769\pi$
$743$			16.1407i			0.592145i	−0.955166	+	0.296072i	$0.904323\pi$
$744$	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
$756$	3.09509	−	18.6101i	0.112568	−	0.676844i
$757$	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	$-0.547681\pi$
$761$	−8.23369			−0.298471			−0.149235	+	0.988802i	$0.547681\pi$
$762$	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	$-0.890914\pi$
$773$	−52.3723			−1.88370			−0.941850	+	0.336034i	$0.890914\pi$
$774$	11.2554	+	0.699713i	0.404568	+	0.0251507i
$775$		0			0
$776$	−29.4891			−1.05860
$777$	−30.7446	−	3.16915i	−1.10296	−	0.113693i
$778$	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	$-0.580565\pi$
$797$	−14.1386			−0.500815			−0.250407	+	0.968141i	$0.580565\pi$
$798$	−12.5109	−	1.28962i	−0.442880	−	0.0456521i
$799$	−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	$0.0763059\pi$
$809$			13.5065i			0.474865i	−0.971404	+	0.237433i	$0.923694\pi$
$810$		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
$819$	−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	$-0.209070\pi$
$822$	−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	$0.0831330\pi$
$827$			14.8511i			0.516422i	−0.966088	+	0.258211i	$0.916867\pi$
$828$	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	$-0.323438\pi$
$839$	30.5109			1.05335			0.526676	+	0.850066i	$0.323438\pi$
$840$		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	$-0.208179\pi$
$857$	46.4674			1.58730			0.793648	+	0.608378i	$0.208179\pi$
$858$	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
$861$	−27.3505	−	2.81929i	−0.932104	−	0.0960812i
$862$	11.9565			0.407240
$863$			41.2743i			1.40499i	0.711688	+	0.702496i	$0.247931\pi$
$863$			41.2743i			1.40499i	−0.711688	+	0.702496i	$0.752069\pi$
$864$	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	$-0.682708\pi$
$881$	−32.2337			−1.08598			−0.542990	+	0.839739i	$0.682708\pi$
$882$	−3.39403	+	16.2882i	−0.114283	+	0.548451i
$883$	−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	$-0.399414\pi$
$887$	18.5109			0.621534			0.310767	+	0.950486i	$0.399414\pi$
$888$	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
$903$	21.6277	+	2.22938i	0.719725	+	0.0741893i
$904$	−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	$0.0151615\pi$
$911$			2.87419i			0.0952263i	−0.998866	+	0.0476132i	$0.984839\pi$
$912$	−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
$924$	−1.62772	+	15.7908i	−0.0535480	+	0.519480i
$925$		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	$-0.835288\pi$
$929$	−52.9783			−1.73816			−0.869080	+	0.494672i	$0.835288\pi$
$930$		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	$-0.282432\pi$
$941$	38.7446			1.26304			0.631518	+	0.775361i	$0.282432\pi$
$942$		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	$-0.807859\pi$
$947$		−	34.9360i		−	1.13527i	0.823282	−	0.567633i	$-0.192141\pi$
$948$	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	$-0.960573\pi$
$953$		−	7.62792i		−	0.247092i	0.992339	−	0.123546i	$-0.0394267\pi$
$954$	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
$966$	−30.7446	−	3.16915i	−0.989190	−	0.101966i
$967$	−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	$-0.703678\pi$
$971$	−37.2119			−1.19419			−0.597094	+	0.802171i	$0.703678\pi$
$972$	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	$-0.961063\pi$
$977$		−	7.62792i		−	0.244039i	0.992528	−	0.122019i	$-0.0389370\pi$
$978$	−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	$-0.280715\pi$
$983$	39.8614			1.27138			0.635691	+	0.771944i	$0.280715\pi$
$984$	20.2337	−	19.0149i	0.645026	−	0.606172i
$985$		0			0
$986$	−3.25544			−0.103674
$987$	7.41983	+	0.764836i	0.236176	+	0.0243450i
$988$	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.g.251.3		4
3.2	odd	2		525.2.b.e.251.2		4
5.2	odd	4		525.2.g.e.524.4		8
5.3	odd	4		525.2.g.e.524.5		8
5.4	even	2		105.2.b.c.41.2	✓	4
7.6	odd	2		525.2.b.e.251.3		4
15.2	even	4		525.2.g.d.524.5		8
15.8	even	4		525.2.g.d.524.4		8
15.14	odd	2		105.2.b.d.41.3	yes	4
20.19	odd	2		1680.2.f.h.881.1		4
21.20	even	2	inner	525.2.b.g.251.2		4
35.4	even	6		735.2.s.h.656.2		4
35.9	even	6		735.2.s.i.521.1		4
35.13	even	4		525.2.g.d.524.6		8
35.19	odd	6		735.2.s.j.521.1		4
35.24	odd	6		735.2.s.g.656.2		4
35.27	even	4		525.2.g.d.524.3		8
35.34	odd	2		105.2.b.d.41.2	yes	4
60.59	even	2		1680.2.f.g.881.3		4
105.44	odd	6		735.2.s.g.521.2		4
105.59	even	6		735.2.s.i.656.1		4
105.62	odd	4		525.2.g.e.524.6		8
105.74	odd	6		735.2.s.j.656.1		4
105.83	odd	4		525.2.g.e.524.3		8
105.89	even	6		735.2.s.h.521.2		4
105.104	even	2		105.2.b.c.41.3	yes	4
140.139	even	2		1680.2.f.g.881.4		4
420.419	odd	2		1680.2.f.h.881.2		4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.792287i q^{2} +(-1.18614 - 1.26217i) q^{3} +1.37228 q^{4} +(1.00000 - 0.939764i) q^{6} +(2.00000 - 1.73205i) q^{7} +2.67181i q^{8} +(-0.186141 + 2.99422i) q^{9} -2.52434i q^{11} +(-1.62772 - 1.73205i) q^{12} +4.10891i q^{13} +(1.37228 + 1.58457i) q^{14} +0.627719 q^{16} +4.37228 q^{17} +(-2.37228 - 0.147477i) q^{18} -3.46410i q^{19} +(-4.55842 - 0.469882i) q^{21} +2.00000 q^{22} -8.51278i q^{23} +(3.37228 - 3.16915i) q^{24} -3.25544 q^{26} +(4.00000 - 3.31662i) q^{27} +(2.74456 - 2.37686i) q^{28} +0.939764i q^{29} +3.46410i q^{31} +5.84096i q^{32} +(-3.18614 + 2.99422i) q^{33} +3.46410i q^{34} +(-0.255437 + 4.10891i) q^{36} +6.74456 q^{37} +2.74456 q^{38} +(5.18614 - 4.87375i) q^{39} +6.00000 q^{41} +(0.372281 - 3.61158i) q^{42} -4.74456 q^{43} -3.46410i q^{44} +6.74456 q^{46} -1.62772 q^{47} +(-0.744563 - 0.792287i) q^{48} +(1.00000 - 6.92820i) q^{49} +(-5.18614 - 5.51856i) q^{51} +5.63858i q^{52} +1.87953i q^{53} +(2.62772 + 3.16915i) q^{54} +(4.62772 + 5.34363i) q^{56} +(-4.37228 + 4.10891i) q^{57} -0.744563 q^{58} +8.74456 q^{59} +6.92820i q^{61} -2.74456 q^{62} +(4.81386 + 6.31084i) q^{63} -3.37228 q^{64} +(-2.37228 - 2.52434i) q^{66} -4.74456 q^{67} +6.00000 q^{68} +(-10.7446 + 10.0974i) q^{69} +0.294954i q^{71} +(-8.00000 - 0.497333i) q^{72} -6.92820i q^{73} +5.34363i q^{74} -4.75372i q^{76} +(-4.37228 - 5.04868i) q^{77} +(3.86141 + 4.10891i) q^{78} -2.37228 q^{79} +(-8.93070 - 1.11469i) q^{81} +4.75372i q^{82} -17.4891 q^{83} +(-6.25544 - 0.644810i) q^{84} -3.75906i q^{86} +(1.18614 - 1.11469i) q^{87} +6.74456 q^{88} -14.7446 q^{89} +(7.11684 + 8.21782i) q^{91} -11.6819i q^{92} +(4.37228 - 4.10891i) q^{93} -1.28962i q^{94} +(7.37228 - 6.92820i) q^{96} +11.0371i q^{97} +(5.48913 + 0.792287i) q^{98} +(7.55842 + 0.469882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 6 q^{4} + 4 q^{6} + 8 q^{7} + 5 q^{9} - 18 q^{12} - 6 q^{14} + 14 q^{16} + 6 q^{17} + 2 q^{18} - q^{21} + 8 q^{22} + 2 q^{24} - 36 q^{26} + 16 q^{27} - 12 q^{28} - 7 q^{33} - 24 q^{36} + 4 q^{37}+ \cdots + 13 q^{99}+O(q^{100}) \) 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 - 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 - 10 * 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 + 25 * 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 - 48 * 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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