LMFDB - Embedded newform 825.2.d.f.824.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(824,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("825.824");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			824.31
Character	$\chi$	$=$	825.824
Dual form			825.2.d.f.824.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.65141i q^{2} +(1.69650 - 0.349146i) q^{3} -5.02997 q^{4} +(0.925729 + 4.49810i) q^{6} -3.33404 q^{7} -8.03369i q^{8} +(2.75619 - 1.18465i) q^{9} +O(q^{10})$	\(q+2.65141i q^{2} +(1.69650 - 0.349146i) q^{3} -5.02997 q^{4} +(0.925729 + 4.49810i) q^{6} -3.33404 q^{7} -8.03369i q^{8} +(2.75619 - 1.18465i) q^{9} +(-2.53762 - 2.13553i) q^{11} +(-8.53332 + 1.75619i) q^{12} -4.82595 q^{13} -8.83990i q^{14} +11.2406 q^{16} +0.572368i q^{17} +(3.14099 + 7.30780i) q^{18} -2.94794i q^{19} +(-5.65618 + 1.16407i) q^{21} +(5.66217 - 6.72826i) q^{22} -7.34867 q^{23} +(-2.80493 - 13.6291i) q^{24} -12.7956i q^{26} +(4.26225 - 2.97207i) q^{27} +16.7701 q^{28} -1.45178 q^{29} -4.29651 q^{31} +13.7362i q^{32} +(-5.05067 - 2.73692i) q^{33} -1.51758 q^{34} +(-13.8636 + 5.95875i) q^{36} +9.93894i q^{37} +7.81620 q^{38} +(-8.18721 + 1.68496i) q^{39} +2.95845 q^{41} +(-3.08642 - 14.9968i) q^{42} +7.15409 q^{43} +(12.7641 + 10.7417i) q^{44} -19.4843i q^{46} +0.315386 q^{47} +(19.0697 - 3.92463i) q^{48} +4.11580 q^{49} +(0.199840 + 0.971019i) q^{51} +24.2744 q^{52} -6.64036 q^{53} +(7.88016 + 11.3010i) q^{54} +26.7846i q^{56} +(-1.02926 - 5.00117i) q^{57} -3.84926i q^{58} +1.44076i q^{59} +4.43986i q^{61} -11.3918i q^{62} +(-9.18925 + 3.94967i) q^{63} -13.9389 q^{64} +(7.25670 - 13.3914i) q^{66} -5.54236i q^{67} -2.87899i q^{68} +(-12.4670 + 2.56576i) q^{69} -4.97937i q^{71} +(-9.51710 - 22.1424i) q^{72} +2.71423 q^{73} -26.3522 q^{74} +14.8281i q^{76} +(8.46051 + 7.11994i) q^{77} +(-4.46752 - 21.7076i) q^{78} -9.83242i q^{79} +(6.19321 - 6.53025i) q^{81} +7.84406i q^{82} +10.9127i q^{83} +(28.4504 - 5.85522i) q^{84} +18.9684i q^{86} +(-2.46294 + 0.506883i) q^{87} +(-17.1562 + 20.3864i) q^{88} -13.8193i q^{89} +16.0899 q^{91} +36.9636 q^{92} +(-7.28902 + 1.50011i) q^{93} +0.836216i q^{94} +(4.79594 + 23.3034i) q^{96} +15.7582i q^{97} +10.9127i q^{98} +(-9.52402 - 2.87975i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} + 20 q^{9}+O(q^{10}) $ 32 * q - 32 * q^4 + 20 * q^9	$ 32 q - 32 q^{4} + 20 q^{9} + 64 q^{16} - 24 q^{31} - 56 q^{34} - 72 q^{36} + 56 q^{49} - 120 q^{64} - 60 q^{66} - 88 q^{69} - 52 q^{81} + 128 q^{91} - 28 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 + 20 * q^9 + 64 * q^16 - 24 * q^31 - 56 * q^34 - 72 * q^36 + 56 * q^49 - 120 * q^64 - 60 * q^66 - 88 * q^69 - 52 * q^81 + 128 * q^91 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$			2.65141i			1.87483i	0.348215	+	0.937415i	$0.386788\pi$
$2$			2.65141i			1.87483i	−0.348215	+	0.937415i	$0.613212\pi$
$3$	1.69650	−	0.349146i	0.979472	−	0.201580i
$3$	1.69650	−	0.349146i	0.979472	−	0.201580i
$4$	−5.02997			−2.51498
$5$		0			0
$5$		0			0
$6$	0.925729	+	4.49810i	0.377927	+	1.83634i
$7$	−3.33404			−1.26015			−0.630074	−	0.776535i	$-0.716975\pi$
$7$	−3.33404			−1.26015			−0.630074	+	0.776535i	$0.716975\pi$
$8$		−	8.03369i		−	2.84034i
$9$	2.75619	−	1.18465i	0.918731	−	0.394883i
$10$		0			0
$11$	−2.53762	−	2.13553i	−0.765120	−	0.643887i
$11$	−2.53762	−	2.13553i	−0.765120	−	0.643887i
$12$	−8.53332	+	1.75619i	−2.46336	+	0.506970i
$13$	−4.82595			−1.33848			−0.669239	−	0.743047i	$-0.733380\pi$
$13$	−4.82595			−1.33848			−0.669239	+	0.743047i	$0.733380\pi$
$14$		−	8.83990i		−	2.36256i
$15$		0			0
$16$	11.2406			2.81016
$17$			0.572368i			0.138820i	0.997588	+	0.0694098i	$0.0221116\pi$
$17$			0.572368i			0.138820i	−0.997588	+	0.0694098i	$0.977888\pi$
$18$	3.14099	+	7.30780i	0.740339	+	1.72246i
$19$		−	2.94794i		−	0.676305i	−0.941091	−	0.338152i	$-0.890198\pi$
$19$		−	2.94794i		−	0.676305i	0.941091	−	0.338152i	$-0.109802\pi$
$20$		0			0
$21$	−5.65618	+	1.16407i	−1.23428	+	0.254020i
$22$	5.66217	−	6.72826i	1.20718	−	1.43447i
$23$	−7.34867			−1.53230			−0.766152	−	0.642660i	$-0.777831\pi$
$23$	−7.34867			−1.53230			−0.766152	+	0.642660i	$0.777831\pi$
$24$	−2.80493	−	13.6291i	−0.572554	−	2.78203i
$25$		0			0
$26$		−	12.7956i		−	2.50942i
$27$	4.26225	−	2.97207i	0.820271	−	0.571975i
$28$	16.7701			3.16925
$29$	−1.45178			−0.269588			−0.134794	−	0.990874i	$-0.543037\pi$
$29$	−1.45178			−0.269588			−0.134794	+	0.990874i	$0.543037\pi$
$30$		0			0
$31$	−4.29651			−0.771677			−0.385838	−	0.922566i	$-0.626088\pi$
$31$	−4.29651			−0.771677			−0.385838	+	0.922566i	$0.626088\pi$
$32$			13.7362i			2.42824i
$33$	−5.05067	−	2.73692i	−0.879209	−	0.476437i
$34$	−1.51758			−0.260263
$35$		0			0
$36$	−13.8636	+	5.95875i	−2.31060	+	0.993125i
$37$			9.93894i			1.63395i	0.576672	+	0.816976i	$0.304351\pi$
$37$			9.93894i			1.63395i	−0.576672	+	0.816976i	$0.695649\pi$
$38$	7.81620			1.26796
$39$	−8.18721	+	1.68496i	−1.31100	+	0.269810i
$40$		0			0
$41$	2.95845			0.462033			0.231016	−	0.972950i	$-0.425795\pi$
$41$	2.95845			0.462033			0.231016	+	0.972950i	$0.425795\pi$
$42$	−3.08642	−	14.9968i	−0.476244	−	2.31406i
$43$	7.15409			1.09099			0.545494	−	0.838115i	$-0.316342\pi$
$43$	7.15409			1.09099			0.545494	+	0.838115i	$0.316342\pi$
$44$	12.7641	+	10.7417i	1.92427	+	1.61937i
$45$		0			0
$46$		−	19.4843i		−	2.87281i
$47$	0.315386			0.0460037			0.0230019	−	0.999735i	$-0.492678\pi$
$47$	0.315386			0.0460037			0.0230019	+	0.999735i	$0.492678\pi$
$48$	19.0697	−	3.92463i	2.75248	−	0.566471i
$49$	4.11580			0.587972
$50$		0			0
$51$	0.199840	+	0.971019i	0.0279832	+	0.135970i
$52$	24.2744			3.36625
$53$	−6.64036			−0.912124			−0.456062	−	0.889948i	$-0.650740\pi$
$53$	−6.64036			−0.912124			−0.456062	+	0.889948i	$0.650740\pi$
$54$	7.88016	+	11.3010i	1.07235	+	1.53787i
$55$		0			0
$56$			26.7846i			3.57924i
$57$	−1.02926	−	5.00117i	−0.136329	−	0.662422i
$58$		−	3.84926i		−	0.505432i
$59$			1.44076i			0.187571i	0.995592	+	0.0937856i	$0.0298968\pi$
$59$			1.44076i			0.187571i	−0.995592	+	0.0937856i	$0.970103\pi$
$60$		0			0
$61$			4.43986i			0.568466i	0.958755	+	0.284233i	$0.0917389\pi$
$61$			4.43986i			0.568466i	−0.958755	+	0.284233i	$0.908261\pi$
$62$		−	11.3918i		−	1.44676i
$63$	−9.18925	+	3.94967i	−1.15774	+	0.497611i
$64$	−13.9389			−1.74237
$65$		0			0
$66$	7.25670	−	13.3914i	0.893238	−	1.64837i
$67$		−	5.54236i		−	0.677107i	−0.940947	−	0.338553i	$-0.890062\pi$
$67$		−	5.54236i		−	0.677107i	0.940947	−	0.338553i	$-0.109938\pi$
$68$		−	2.87899i		−	0.349129i
$69$	−12.4670	+	2.56576i	−1.50085	+	0.308881i
$70$		0			0
$71$		−	4.97937i		−	0.590943i	−0.955352	−	0.295471i	$-0.904523\pi$
$71$		−	4.97937i		−	0.590943i	0.955352	−	0.295471i	$-0.0954767\pi$
$72$	−9.51710	−	22.1424i	−1.12160	−	2.60951i
$73$	2.71423			0.317676			0.158838	−	0.987305i	$-0.449225\pi$
$73$	2.71423			0.317676			0.158838	+	0.987305i	$0.449225\pi$
$74$	−26.3522			−3.06338
$75$		0			0
$76$			14.8281i			1.70090i
$77$	8.46051	+	7.11994i	0.964165	+	0.811393i
$78$	−4.46752	−	21.7076i	−0.505848	−	2.45791i
$79$		−	9.83242i		−	1.10623i	−0.833104	−	0.553117i	$-0.813438\pi$
$79$		−	9.83242i		−	1.10623i	0.833104	−	0.553117i	$-0.186562\pi$
$80$		0			0
$81$	6.19321	−	6.53025i	0.688135	−	0.725583i
$82$			7.84406i			0.866232i
$83$			10.9127i			1.19782i	0.800816	+	0.598911i	$0.204400\pi$
$83$			10.9127i			1.19782i	−0.800816	+	0.598911i	$0.795600\pi$
$84$	28.4504	−	5.85522i	3.10419	−	0.638856i
$85$		0			0
$86$			18.9684i			2.04542i
$87$	−2.46294	+	0.506883i	−0.264054	+	0.0543435i
$88$	−17.1562	+	20.3864i	−1.82886	+	2.17320i
$89$		−	13.8193i		−	1.46484i	−0.680853	−	0.732420i	$-0.738391\pi$
$89$		−	13.8193i		−	1.46484i	0.680853	−	0.732420i	$-0.261609\pi$
$90$		0			0
$91$	16.0899			1.68668
$92$	36.9636			3.85372
$93$	−7.28902	+	1.50011i	−0.755836	+	0.155554i
$94$			0.836216i			0.0862491i
$95$		0			0
$96$	4.79594	+	23.3034i	0.489483	+	2.37839i
$97$			15.7582i			1.60001i	0.599996	+	0.800003i	$0.295169\pi$
$97$			15.7582i			1.60001i	−0.599996	+	0.800003i	$0.704831\pi$
$98$			10.9127i			1.10235i
$99$	−9.52402	−	2.87975i	−0.957200	−	0.289426i
$100$		0			0
$101$	−13.4846			−1.34177			−0.670885	−	0.741561i	$-0.734086\pi$
$101$	−13.4846			−1.34177			−0.670885	+	0.741561i	$0.734086\pi$
$102$	−2.57457	+	0.529857i	−0.254920	+	0.0524637i
$103$			12.1548i			1.19765i	0.800880	+	0.598825i	$0.204365\pi$
$103$			12.1548i			1.19765i	−0.800880	+	0.598825i	$0.795635\pi$
$104$			38.7702i			3.80173i
$105$		0			0
$106$		−	17.6063i		−	1.71008i
$107$		−	10.7406i		−	1.03833i	−0.854674	−	0.519166i	$-0.826243\pi$
$107$		−	10.7406i		−	1.03833i	0.854674	−	0.519166i	$-0.173757\pi$
$108$	−21.4390	+	14.9494i	−2.06297	+	1.43851i
$109$			10.4522i			1.00114i	0.865695	+	0.500571i	$0.166877\pi$
$109$			10.4522i			1.00114i	−0.865695	+	0.500571i	$0.833123\pi$
$110$		0			0
$111$	3.47014	+	16.8614i	0.329371	+	1.60041i
$112$	−37.4767			−3.54122
$113$	−14.1412			−1.33029			−0.665145	−	0.746714i	$-0.731630\pi$
$113$	−14.1412			−1.33029			−0.665145	+	0.746714i	$0.731630\pi$
$114$	13.2602	−	2.72900i	1.24193	−	0.255594i
$115$		0			0
$116$	7.30240			0.678011
$117$	−13.3013	+	5.71706i	−1.22970	+	0.528543i
$118$	−3.82005			−0.351664
$119$		−	1.90830i		−	0.174933i
$120$		0			0
$121$	1.87900	+	10.8383i	0.170819	+	0.985303i
$122$	−11.7719			−1.06578
$123$	5.01900	−	1.03293i	0.452548	−	0.0931363i
$124$	21.6113			1.94076
$125$		0			0
$126$	−10.4722	−	24.3645i	−0.932936	−	2.17056i
$127$	8.15999			0.724082			0.362041	−	0.932162i	$-0.382080\pi$
$127$	8.15999			0.724082			0.362041	+	0.932162i	$0.382080\pi$
$128$		−	9.48546i		−	0.838405i
$129$	12.1369	−	2.49782i	1.06859	−	0.219921i
$130$		0			0
$131$	−10.9367			−0.955540			−0.477770	−	0.878485i	$-0.658555\pi$
$131$	−10.9367			−0.955540			−0.477770	+	0.878485i	$0.658555\pi$
$132$	25.4047	+	13.7666i	2.21120	+	1.19823i
$133$			9.82855i			0.852244i
$134$	14.6951			1.26946
$135$		0			0
$136$	4.59822			0.394294
$137$	−8.89036			−0.759555			−0.379777	−	0.925078i	$-0.623999\pi$
$137$	−8.89036			−0.759555			−0.379777	+	0.925078i	$0.623999\pi$
$138$	−6.80288	−	33.0551i	−0.579099	−	2.81383i
$139$		−	15.6643i		−	1.32863i	−0.747454	−	0.664313i	$-0.768724\pi$
$139$		−	15.6643i		−	1.32863i	0.747454	−	0.664313i	$-0.231276\pi$
$140$		0			0
$141$	0.535050	−	0.110116i	0.0450594	−	0.00927341i
$142$	13.2023			1.10792
$143$	12.2464	+	10.3060i	1.02410	+	0.861829i
$144$	30.9814	−	13.3162i	2.58178	−	1.10969i
$145$		0			0
$146$			7.19652i			0.595588i
$147$	6.98244	−	1.43702i	0.575902	−	0.118523i
$148$		−	49.9926i		−	4.10936i
$149$	6.34115			0.519487			0.259744	−	0.965678i	$-0.416362\pi$
$149$	6.34115			0.519487			0.259744	+	0.965678i	$0.416362\pi$
$150$		0			0
$151$		−	0.169689i		−	0.0138091i	−0.999976	−	0.00690454i	$-0.997802\pi$
$151$		−	0.169689i		−	0.0138091i	0.999976	−	0.00690454i	$-0.00219780\pi$
$152$	−23.6829			−1.92093
$153$	0.678055	+	1.57756i	0.0548175	+	0.127538i
$154$	−18.8779	+	22.4323i	−1.52122	+	1.80764i
$155$		0			0
$156$	41.1814	−	8.47531i	3.29715	−	0.678568i
$157$		−	7.11061i		−	0.567489i	−0.958900	−	0.283744i	$-0.908423\pi$
$157$		−	7.11061i		−	0.567489i	0.958900	−	0.283744i	$-0.0915767\pi$
$158$	26.0698			2.07400
$159$	−11.2653	+	2.31846i	−0.893400	+	0.183866i
$160$		0			0
$161$	24.5007			1.93093
$162$	17.3144	+	16.4207i	1.36034	+	1.29013i
$163$			5.59822i			0.438487i	0.975670	+	0.219243i	$0.0703589\pi$
$163$			5.59822i			0.438487i	−0.975670	+	0.219243i	$0.929641\pi$
$164$	−14.8809			−1.16200
$165$		0			0
$166$	−28.9340			−2.24571
$167$		−	7.95364i		−	0.615471i	−0.951472	−	0.307735i	$-0.900429\pi$
$167$		−	7.95364i		−	0.615471i	0.951472	−	0.307735i	$-0.0995712\pi$
$168$	9.35174	+	45.4400i	0.721503	+	3.50577i
$169$	10.2898			0.791525
$170$		0			0
$171$	−3.49228	−	8.12510i	−0.267061	−	0.621342i
$172$	−35.9848			−2.74382
$173$		−	20.3558i		−	1.54763i	−0.633414	−	0.773813i	$-0.718347\pi$
$173$		−	20.3558i		−	1.54763i	0.633414	−	0.773813i	$-0.281653\pi$
$174$	−1.34395	−	6.53025i	−0.101885	−	0.495057i
$175$		0			0
$176$	−28.5245	−	24.0048i	−2.15011	−	1.80943i
$177$	0.503036	+	2.44425i	0.0378105	+	0.183721i
$178$	36.6405			2.74632
$179$			4.67052i			0.349091i	0.984649	+	0.174545i	$0.0558456\pi$
$179$			4.67052i			0.349091i	−0.984649	+	0.174545i	$0.944154\pi$
$180$		0			0
$181$	0.301708			0.0224258			0.0112129	−	0.999937i	$-0.496431\pi$
$181$	0.301708			0.0224258			0.0112129	+	0.999937i	$0.496431\pi$
$182$			42.6609i			3.16224i
$183$	1.55016	+	7.53220i	0.114591	+	0.556796i
$184$			59.0369i			4.35226i
$185$		0			0
$186$	−3.97741	−	19.3262i	−0.291638	−	1.41706i
$187$	1.22231	−	1.45245i	0.0893841	−	0.106214i
$188$	−1.58638			−0.115699
$189$	−14.2105	+	9.90898i	−1.03366	+	0.720772i
$190$		0			0
$191$		−	3.81006i		−	0.275686i	−0.990454	−	0.137843i	$-0.955983\pi$
$191$		−	3.81006i		−	0.275686i	0.990454	−	0.137843i	$-0.0440170\pi$
$192$	−23.6474	+	4.86673i	−1.70660	+	0.351226i
$193$	−24.3743			−1.75450			−0.877251	−	0.480033i	$-0.840625\pi$
$193$	−24.3743			−1.75450			−0.877251	+	0.480033i	$0.840625\pi$
$194$	−41.7815			−2.99974
$195$		0			0
$196$	−20.7024			−1.47874
$197$		−	5.66476i		−	0.403597i	−0.979427	−	0.201799i	$-0.935321\pi$
$197$		−	5.66476i		−	0.403597i	0.979427	−	0.201799i	$-0.0646786\pi$
$198$	7.63541	−	25.2521i	0.542625	−	1.79459i
$199$	−2.42270			−0.171741			−0.0858705	−	0.996306i	$-0.527367\pi$
$199$	−2.42270			−0.171741			−0.0858705	+	0.996306i	$0.527367\pi$
$200$		0			0
$201$	−1.93509	−	9.40258i	−0.136491	−	0.663207i
$202$		−	35.7533i		−	2.51559i
$203$	4.84028			0.339721
$204$	−1.00519	−	4.88420i	−0.0703773	−	0.341962i
$205$		0			0
$206$	−32.2274			−2.24539
$207$	−20.2544	+	8.70560i	−1.40778	+	0.605081i
$208$	−54.2468			−3.76134
$209$	−6.29543	+	7.48075i	−0.435464	+	0.517454i
$210$		0			0
$211$			1.14171i			0.0785986i	0.999227	+	0.0392993i	$0.0125126\pi$
$211$			1.14171i			0.0785986i	−0.999227	+	0.0392993i	$0.987487\pi$
$212$	33.4008			2.29398
$213$	−1.73853	−	8.44748i	−0.119122	−	0.578812i
$214$	28.4777			1.94669
$215$		0			0
$216$	−23.8767	−	34.2416i	−1.62460	−	2.32985i
$217$	14.3247			0.972427
$218$	−27.7131			−1.87697
$219$	4.60467	−	0.947661i	0.311155	−	0.0640370i
$220$		0			0
$221$		−	2.76222i		−	0.185807i
$222$	−44.7064	+	9.20077i	−3.00050	+	0.617515i
$223$		−	20.6584i		−	1.38339i	−0.722191	−	0.691694i	$-0.756865\pi$
$223$		−	20.6584i		−	1.38339i	0.722191	−	0.691694i	$-0.243135\pi$
$224$		−	45.7969i		−	3.05994i
$225$		0			0
$226$		−	37.4941i		−	2.49407i
$227$			9.60902i			0.637773i	0.947793	+	0.318887i	$0.103309\pi$
$227$			9.60902i			0.637773i	−0.947793	+	0.318887i	$0.896691\pi$
$228$	5.17716	+	25.1557i	0.342866	+	1.66598i
$229$	8.21090			0.542592			0.271296	−	0.962496i	$-0.412548\pi$
$229$	8.21090			0.542592			0.271296	+	0.962496i	$0.412548\pi$
$230$		0			0
$231$	16.8391	+	9.12500i	1.10793	+	0.600381i
$232$			11.6631i			0.765722i
$233$		−	3.40964i		−	0.223373i	−0.993743	−	0.111687i	$-0.964375\pi$
$233$		−	3.40964i		−	0.223373i	0.993743	−	0.111687i	$-0.0356253\pi$
$234$	−15.1583	−	35.2671i	−0.990927	−	2.30548i
$235$		0			0
$236$		−	7.24699i		−	0.471739i
$237$	−3.43295	−	16.6807i	−0.222994	−	1.08353i
$238$	5.05967			0.327970
$239$	4.78535			0.309538			0.154769	−	0.987951i	$-0.450537\pi$
$239$	4.78535			0.309538			0.154769	+	0.987951i	$0.450537\pi$
$240$		0			0
$241$			6.22878i			0.401231i	0.979670	+	0.200615i	$0.0642942\pi$
$241$			6.22878i			0.401231i	−0.979670	+	0.200615i	$0.935706\pi$
$242$	−28.7368	+	4.98201i	−1.84727	+	0.320256i
$243$	8.22674	−	13.2409i	0.527746	−	0.849402i
$244$		−	22.3324i		−	1.42968i
$245$		0			0
$246$	2.73872	+	13.3074i	0.174615	+	0.848450i
$247$			14.2266i			0.905219i
$248$			34.5169i			2.19182i
$249$	3.81012	+	18.5133i	0.241456	+	1.17323i
$250$		0			0
$251$		−	8.29483i		−	0.523565i	−0.965127	−	0.261782i	$-0.915690\pi$
$251$		−	8.29483i		−	0.523565i	0.965127	−	0.261782i	$-0.0843103\pi$
$252$	46.2217	−	19.8667i	2.91169	−	1.25148i
$253$	18.6481	+	15.6933i	1.17240	+	0.986631i
$254$			21.6355i			1.35753i
$255$		0			0
$256$	−2.72804			−0.170502
$257$	−16.7578			−1.04532			−0.522661	−	0.852541i	$-0.675061\pi$
$257$	−16.7578			−1.04532			−0.522661	+	0.852541i	$0.675061\pi$
$258$	6.62274	+	32.1798i	0.412314	+	2.00343i
$259$		−	33.1368i		−	2.05902i
$260$		0			0
$261$	−4.00138	+	1.71985i	−0.247679	+	0.106456i
$262$		−	28.9975i		−	1.79147i
$263$		−	28.9110i		−	1.78273i	−0.453290	−	0.891363i	$-0.649750\pi$
$263$		−	28.9110i		−	1.78273i	0.453290	−	0.891363i	$-0.350250\pi$
$264$	−21.9876	+	40.5755i	−1.35324	+	2.49725i
$265$		0			0
$266$	−26.0595			−1.59781
$267$	−4.82494	−	23.4443i	−0.295282	−	1.43477i
$268$			27.8779i			1.70291i
$269$		−	17.1683i		−	1.04677i	−0.852096	−	0.523386i	$-0.824669\pi$
$269$		−	17.1683i		−	1.04677i	0.852096	−	0.523386i	$-0.175331\pi$
$270$		0			0
$271$			29.3341i			1.78192i	0.454084	+	0.890959i	$0.349967\pi$
$271$			29.3341i			1.78192i	−0.454084	+	0.890959i	$0.650033\pi$
$272$			6.43378i			0.390106i
$273$	27.2965	−	5.61773i	1.65206	−	0.340000i
$274$		−	23.5720i		−	1.42404i
$275$		0			0
$276$	62.7085	−	12.9057i	3.77461	−	0.776831i
$277$	−19.8345			−1.19174			−0.595871	−	0.803080i	$-0.703193\pi$
$277$	−19.8345			−1.19174			−0.595871	+	0.803080i	$0.703193\pi$
$278$	41.5324			2.49095
$279$	−11.8420	+	5.08986i	−0.708964	+	0.304722i
$280$		0			0
$281$	18.2528			1.08887			0.544436	−	0.838802i	$-0.316744\pi$
$281$	18.2528			1.08887			0.544436	+	0.838802i	$0.316744\pi$
$282$	0.291962	+	1.41864i	0.0173861	+	0.0844786i
$283$	−20.6708			−1.22875			−0.614374	−	0.789015i	$-0.710591\pi$
$283$	−20.6708			−1.22875			−0.614374	+	0.789015i	$0.710591\pi$
$284$			25.0461i			1.48621i
$285$		0			0
$286$	−27.3254	+	32.4703i	−1.61578	+	1.92001i
$287$	−9.86359			−0.582229
$288$	16.2726	+	37.8596i	0.958870	+	2.23090i
$289$	16.6724			0.980729
$290$		0			0
$291$	5.50192	+	26.7338i	0.322529	+	1.56716i
$292$	−13.6525			−0.798950
$293$		−	15.6431i		−	0.913881i	−0.889497	−	0.456941i	$-0.848945\pi$
$293$		−	15.6431i		−	0.913881i	0.889497	−	0.456941i	$-0.151055\pi$
$294$	3.81012	+	18.5133i	0.222211	+	1.07972i
$295$		0			0
$296$	79.8463			4.64097
$297$	−17.1629	−	1.56021i	−0.995893	−	0.0905328i
$298$			16.8130i			0.973949i
$299$	35.4643			2.05096
$300$		0			0
$301$	−23.8520			−1.37481
$302$	0.449914			0.0258897
$303$	−22.8766	+	4.70810i	−1.31423	+	0.270474i
$304$		−	33.1368i		−	1.90053i
$305$		0			0
$306$	−4.18275	+	1.79780i	−0.239112	+	0.102773i
$307$	3.01197			0.171902			0.0859512	−	0.996299i	$-0.472607\pi$
$307$	3.01197			0.171902			0.0859512	+	0.996299i	$0.472607\pi$
$308$	−42.5561	−	35.8131i	−2.42486	−	2.04064i
$309$	4.24381	+	20.6206i	0.241422	+	1.17306i
$310$		0			0
$311$			8.74474i			0.495869i	0.968777	+	0.247934i	$0.0797517\pi$
$311$			8.74474i			0.495869i	−0.968777	+	0.247934i	$0.920248\pi$
$312$	13.5365	+	65.7735i	0.766351	+	3.72369i
$313$			7.98577i			0.451382i	0.974199	+	0.225691i	$0.0724640\pi$
$313$			7.98577i			0.451382i	−0.974199	+	0.225691i	$0.927536\pi$
$314$	18.8531			1.06394
$315$		0			0
$316$			49.4568i			2.78216i
$317$	28.5166			1.60165			0.800826	−	0.598897i	$-0.204394\pi$
$317$	28.5166			1.60165			0.800826	+	0.598897i	$0.204394\pi$
$318$	−6.14718	−	29.8690i	−0.344717	−	1.67497i
$319$	3.68406	+	3.10032i	0.206268	+	0.173585i
$320$		0			0
$321$	−3.75003	−	18.2213i	−0.209306	−	1.01702i
$322$			64.9615i			3.62016i
$323$	1.68731			0.0938843
$324$	−31.1517	+	32.8469i	−1.73065	+	1.82483i
$325$		0			0
$326$	−14.8432			−0.822088
$327$	3.64936	+	17.7322i	0.201810	+	0.980591i
$328$		−	23.7673i		−	1.31233i
$329$	−1.05151			−0.0579715
$330$		0			0
$331$	−11.0142			−0.605397			−0.302699	−	0.953086i	$-0.597888\pi$
$331$	−11.0142			−0.605397			−0.302699	+	0.953086i	$0.597888\pi$
$332$		−	54.8904i		−	3.01250i
$333$	11.7742	+	27.3937i	0.645220	+	1.50116i
$334$	21.0883			1.15390
$335$		0			0
$336$	−63.5791	+	13.0849i	−3.46853	+	0.713838i
$337$	−8.82652			−0.480811			−0.240406	−	0.970673i	$-0.577280\pi$
$337$	−8.82652			−0.480811			−0.240406	+	0.970673i	$0.577280\pi$
$338$			27.2825i			1.48397i
$339$	−23.9905	+	4.93734i	−1.30298	+	0.268159i
$340$		0			0
$341$	10.9029	+	9.17535i	0.590426	+	0.496873i
$342$	21.5430	−	9.25946i	1.16491	−	0.500694i
$343$	9.61602			0.519216
$344$		−	57.4737i		−	3.09877i
$345$		0			0
$346$	53.9716			2.90153
$347$			20.6938i			1.11090i	0.831550	+	0.555451i	$0.187454\pi$
$347$			20.6938i			1.11090i	−0.831550	+	0.555451i	$0.812546\pi$
$348$	12.3885	−	2.54960i	0.664093	−	0.136673i
$349$		−	7.75658i		−	0.415200i	−0.978214	−	0.207600i	$-0.933435\pi$
$349$		−	7.75658i		−	0.415200i	0.978214	−	0.207600i	$-0.0665653\pi$
$350$		0			0
$351$	−20.5694	+	14.3431i	−1.09792	+	0.765576i
$352$	29.3341	−	34.8572i	1.56351	−	1.85789i
$353$	5.13152			0.273123			0.136562	−	0.990632i	$-0.456395\pi$
$353$	5.13152			0.273123			0.136562	+	0.990632i	$0.456395\pi$
$354$	−6.48069	+	1.33375i	−0.344445	+	0.0708883i
$355$		0			0
$356$			69.5105i			3.68405i
$357$	−0.666274	−	3.23741i	−0.0352630	−	0.171342i
$358$	−12.3834			−0.654485
$359$	6.97820			0.368295			0.184148	−	0.982899i	$-0.441048\pi$
$359$	6.97820			0.368295			0.184148	+	0.982899i	$0.441048\pi$
$360$		0			0
$361$	10.3096			0.542612
$362$			0.799951i			0.0420445i
$363$	6.97188	+	17.7311i	0.365929	+	0.930643i
$364$	−80.9317			−4.24198
$365$		0			0
$366$	−19.9709	+	4.11011i	−1.04390	+	0.214839i
$367$			1.25488i			0.0655044i	0.999464	+	0.0327522i	$0.0104272\pi$
$367$			1.25488i			0.0655044i	−0.999464	+	0.0327522i	$0.989573\pi$
$368$	−82.6038			−4.30602
$369$	8.15407	−	3.50473i	0.424484	−	0.182449i
$370$		0			0
$371$	22.1392			1.14941
$372$	36.6635	−	7.54551i	1.90092	−	0.391217i
$373$	25.7304			1.33227			0.666135	−	0.745831i	$-0.267947\pi$
$373$	25.7304			1.33227			0.666135	+	0.745831i	$0.267947\pi$
$374$	3.85104	+	3.24084i	0.199133	+	0.167580i
$375$		0			0
$376$		−	2.53371i		−	0.130666i
$377$	7.00621			0.360838
$378$	−26.2728	−	37.6779i	−1.35133	−	1.93794i
$379$	−3.89324			−0.199982			−0.0999911	−	0.994988i	$-0.531881\pi$
$379$	−3.89324			−0.199982			−0.0999911	+	0.994988i	$0.531881\pi$
$380$		0			0
$381$	13.8434	−	2.84903i	0.709218	−	0.145960i
$382$	10.1020			0.516865
$383$	10.7658			0.550107			0.275054	−	0.961429i	$-0.411304\pi$
$383$	10.7658			0.550107			0.275054	+	0.961429i	$0.411304\pi$
$384$	−3.31181	−	16.0920i	−0.169005	−	0.821194i
$385$		0			0
$386$		−	64.6263i		−	3.28939i
$387$	19.7180	−	8.47508i	1.00232	−	0.430813i
$388$		−	79.2634i		−	4.02399i
$389$		−	5.82384i		−	0.295281i	−0.989041	−	0.147640i	$-0.952832\pi$
$389$		−	5.82384i		−	0.295281i	0.989041	−	0.147640i	$-0.0471678\pi$
$390$		0			0
$391$		−	4.20614i		−	0.212714i
$392$		−	33.0651i		−	1.67004i
$393$	−18.5540	+	3.81849i	−0.935925	+	0.192617i
$394$	15.0196			0.756676
$395$		0			0
$396$	47.9055	+	14.4851i	2.40734	+	0.727902i
$397$			6.12077i			0.307193i	0.988134	+	0.153596i	$0.0490856\pi$
$397$			6.12077i			0.307193i	−0.988134	+	0.153596i	$0.950914\pi$
$398$		−	6.42358i		−	0.321985i
$399$	3.43160	+	16.6741i	0.171795	+	0.834749i
$400$		0			0
$401$			14.2298i			0.710603i	0.934752	+	0.355301i	$0.115622\pi$
$401$			14.2298i			0.710603i	−0.934752	+	0.355301i	$0.884378\pi$
$402$	24.9301	−	5.13072i	1.24340	−	0.255897i
$403$	20.7348			1.03287
$404$	67.8273			3.37453
$405$		0			0
$406$			12.8336i			0.636919i
$407$	21.2249	−	25.2212i	1.05208	−	1.25017i
$408$	7.80086	−	1.60545i	0.386200	−	0.0794817i
$409$			5.52636i			0.273261i	0.990622	+	0.136631i	$0.0436273\pi$
$409$			5.52636i			0.273261i	−0.990622	+	0.136631i	$0.956373\pi$
$410$		0			0
$411$	−15.0825	+	3.10403i	−0.743963	+	0.153111i
$412$		−	61.1383i		−	3.01207i
$413$		−	4.80355i		−	0.236367i
$414$	−23.0821	−	53.7026i	−1.13442	−	2.63934i
$415$		0			0
$416$		−	66.2902i		−	3.25014i
$417$	−5.46912	−	26.5744i	−0.267824	−	1.30135i
$418$	−19.8345	−	16.6918i	−0.970139	−	0.816420i
$419$		−	5.81275i		−	0.283972i	−0.989869	−	0.141986i	$-0.954651\pi$
$419$		−	5.81275i		−	0.283972i	0.989869	−	0.141986i	$-0.0453487\pi$
$420$		0			0
$421$	−5.61246			−0.273534			−0.136767	−	0.990603i	$-0.543671\pi$
$421$	−5.61246			−0.273534			−0.136767	+	0.990603i	$0.543671\pi$
$422$	−3.02714			−0.147359
$423$	0.869264	−	0.373621i	0.0422651	−	0.0181661i
$424$			53.3466i			2.59074i
$425$		0			0
$426$	22.3977	−	4.60955i	1.08517	−	0.223333i
$427$		−	14.8027i		−	0.716351i
$428$			54.0248i			2.61139i
$429$	24.3743	+	13.2083i	1.17680	+	0.637701i
$430$		0			0
$431$	−3.74761			−0.180516			−0.0902579	−	0.995918i	$-0.528769\pi$
$431$	−3.74761			−0.180516			−0.0902579	+	0.995918i	$0.528769\pi$
$432$	47.9105	−	33.4080i	2.30510	−	1.60734i
$433$		−	25.0094i		−	1.20188i	−0.799296	−	0.600938i	$-0.794794\pi$
$433$		−	25.0094i		−	1.20188i	0.799296	−	0.600938i	$-0.205206\pi$
$434$			37.9807i			1.82313i
$435$		0			0
$436$		−	52.5744i		−	2.51786i
$437$			21.6635i			1.03630i
$438$	2.51264	+	12.2089i	0.120058	+	0.583362i
$439$			27.7500i			1.32443i	0.749312	+	0.662217i	$0.230384\pi$
$439$			27.7500i			1.32443i	−0.749312	+	0.662217i	$0.769616\pi$
$440$		0			0
$441$	11.3440	−	4.87578i	0.540188	−	0.232180i
$442$	7.32377			0.348356
$443$	14.0900			0.669434			0.334717	−	0.942319i	$-0.391359\pi$
$443$	14.0900			0.669434			0.334717	+	0.942319i	$0.391359\pi$
$444$	−17.4547	−	84.8122i	−0.828364	−	4.02501i
$445$		0			0
$446$	54.7738			2.59362
$447$	10.7577	−	2.21399i	0.508823	−	0.104718i
$448$	46.4729			2.19564
$449$			13.5543i			0.639669i	0.947473	+	0.319835i	$0.103627\pi$
$449$			13.5543i			0.639669i	−0.947473	+	0.319835i	$0.896373\pi$
$450$		0			0
$451$	−7.50742	−	6.31787i	−0.353511	−	0.297497i
$452$	71.1297			3.34566
$453$	−0.0592462	−	0.287876i	−0.00278363	−	0.0135256i
$454$	−25.4774			−1.19572
$455$		0			0
$456$	−40.1779	+	8.26878i	−1.88150	+	0.387221i
$457$	−6.03744			−0.282419			−0.141210	−	0.989980i	$-0.545099\pi$
$457$	−6.03744			−0.282419			−0.141210	+	0.989980i	$0.545099\pi$
$458$			21.7705i			1.01727i
$459$	1.70112	+	2.43958i	0.0794013	+	0.113870i
$460$		0			0
$461$	−4.15570			−0.193550			−0.0967751	−	0.995306i	$-0.530853\pi$
$461$	−4.15570			−0.193550			−0.0967751	+	0.995306i	$0.530853\pi$
$462$	−24.1941	+	44.6474i	−1.12561	+	2.07718i
$463$			21.0953i			0.980380i	0.871616	+	0.490190i	$0.163073\pi$
$463$			21.0953i			0.980380i	−0.871616	+	0.490190i	$0.836927\pi$
$464$	−16.3189			−0.757587
$465$		0			0
$466$	9.04035			0.418786
$467$	−29.9238			−1.38471			−0.692353	−	0.721559i	$-0.743426\pi$
$467$	−29.9238			−1.38471			−0.692353	+	0.721559i	$0.743426\pi$
$468$	66.9049	−	28.7566i	3.09268	−	1.32928i
$469$			18.4784i			0.853254i
$470$		0			0
$471$	−2.48264	−	12.0631i	−0.114394	−	0.555839i
$472$	11.5746			0.532765
$473$	−18.1543	−	15.2778i	−0.834737	−	0.702473i
$474$	44.2273	−	9.10216i	2.03142	−	0.418076i
$475$		0			0
$476$			9.59867i			0.439954i
$477$	−18.3021	+	7.86650i	−0.837997	+	0.360182i
$478$			12.6879i			0.580331i
$479$	−15.5127			−0.708796			−0.354398	−	0.935095i	$-0.615314\pi$
$479$	−15.5127			−0.708796			−0.354398	+	0.935095i	$0.615314\pi$
$480$		0			0
$481$		−	47.9649i		−	2.18701i
$482$	−16.5150			−0.752239
$483$	41.5654	−	8.55434i	1.89129	−	0.389236i
$484$	−9.45133	−	54.5165i	−0.429606	−	2.47802i
$485$		0			0
$486$	35.1070	+	21.8125i	1.59248	+	0.989433i
$487$			14.4863i			0.656435i	0.944602	+	0.328218i	$0.106448\pi$
$487$			14.4863i			0.656435i	−0.944602	+	0.328218i	$0.893552\pi$
$488$	35.6684			1.61463
$489$	1.95460	+	9.49736i	0.0883900	+	0.429485i
$490$		0			0
$491$	−3.38270			−0.152659			−0.0763295	−	0.997083i	$-0.524320\pi$
$491$	−3.38270			−0.152659			−0.0763295	+	0.997083i	$0.524320\pi$
$492$	−25.2454	+	5.19561i	−1.13815	+	0.234236i
$493$		−	0.830951i		−	0.0374242i
$494$	−37.7206			−1.69713
$495$		0			0
$496$	−48.2956			−2.16854
$497$			16.6014i			0.744675i
$498$	−49.0864	+	10.1022i	−2.19961	+	0.452690i
$499$	−39.8979			−1.78608			−0.893038	−	0.449981i	$-0.851431\pi$
$499$	−39.8979			−1.78608			−0.893038	+	0.449981i	$0.851431\pi$
$500$		0			0
$501$	−2.77698	−	13.4933i	−0.124066	−	0.602837i
$502$	21.9930			0.981595
$503$		−	35.4512i		−	1.58069i	−0.612663	−	0.790345i	$-0.709902\pi$
$503$		−	35.4512i		−	1.58069i	0.612663	−	0.790345i	$-0.290098\pi$
$504$	31.7304	+	73.8236i	1.41338	+	3.28836i
$505$		0			0
$506$	−41.6094	+	49.4438i	−1.84976	+	2.19804i
$507$	17.4566	−	3.59265i	0.775277	−	0.159555i
$508$	−41.0445			−1.82106
$509$			36.9701i			1.63867i	0.573314	+	0.819336i	$0.305657\pi$
$509$			36.9701i			1.63867i	−0.573314	+	0.819336i	$0.694343\pi$
$510$		0			0
$511$	−9.04933			−0.400319
$512$		−	26.2041i		−	1.15807i
$513$	−8.76149	−	12.5649i	−0.386829	−	0.554753i
$514$		−	44.4317i		−	1.95980i
$515$		0			0
$516$	−61.0481	+	12.5640i	−2.68749	+	0.553098i
$517$	−0.800328	−	0.673516i	−0.0351984	−	0.0296212i
$518$	87.8592			3.86031
$519$	−7.10716	−	34.5336i	−0.311970	−	1.51586i
$520$		0			0
$521$			34.4245i			1.50817i	0.656779	+	0.754083i	$0.271918\pi$
$521$			34.4245i			1.50817i	−0.656779	+	0.754083i	$0.728082\pi$
$522$	−4.56002	−	10.6093i	−0.199587	−	0.464356i
$523$	14.1558			0.618990			0.309495	−	0.950901i	$-0.399840\pi$
$523$	14.1558			0.618990			0.309495	+	0.950901i	$0.399840\pi$
$524$	55.0110			2.40317
$525$		0			0
$526$	76.6548			3.34231
$527$		−	2.45919i		−	0.107124i
$528$	−56.7728	−	30.7648i	−2.47072	−	1.33887i
$529$	31.0030			1.34795
$530$		0			0
$531$	1.70680	+	3.97102i	0.0740687	+	0.172328i
$532$		−	49.4373i		−	2.14338i
$533$	−14.2773			−0.618421
$534$	62.1605	−	12.7929i	2.68995	−	0.553603i
$535$		0			0
$536$	−44.5256			−1.92321
$537$	1.63069	+	7.92351i	0.0703696	+	0.341925i
$538$	45.5202			1.96252
$539$	−10.4443	−	8.78943i	−0.449869	−	0.378588i
$540$		0			0
$541$		−	23.3325i		−	1.00314i	−0.865116	−	0.501572i	$-0.832755\pi$
$541$		−	23.3325i		−	1.00314i	0.865116	−	0.501572i	$-0.167245\pi$
$542$	−77.7766			−3.34079
$543$	0.511846	−	0.105340i	0.0219654	−	0.00452058i
$544$	−7.86215			−0.337087
$545$		0			0
$546$	14.8949	+	72.3741i	0.637443	+	3.09732i
$547$	36.5881			1.56439			0.782196	−	0.623032i	$-0.214099\pi$
$547$	36.5881			1.56439			0.782196	+	0.623032i	$0.214099\pi$
$548$	44.7182			1.91027
$549$	5.25968	+	12.2371i	0.224478	+	0.522267i
$550$		0			0
$551$			4.27976i			0.182324i
$552$	20.6125	+	100.156i	0.877327	+	4.26292i
$553$			32.7817i			1.39402i
$554$		−	52.5895i		−	2.23431i
$555$		0			0
$556$			78.7908i			3.34148i
$557$			37.6480i			1.59520i	0.603189	+	0.797598i	$0.293896\pi$
$557$			37.6480i			1.59520i	−0.603189	+	0.797598i	$0.706104\pi$
$558$	−13.4953	−	31.3981i	−0.571302	−	1.32919i
$559$	−34.5253			−1.46026
$560$		0			0
$561$	1.56653	−	2.89084i	0.0661388	−	0.122051i
$562$			48.3957i			2.04145i
$563$		−	6.93067i		−	0.292093i	−0.989278	−	0.146046i	$-0.953345\pi$
$563$		−	6.93067i		−	0.292093i	0.989278	−	0.146046i	$-0.0466549\pi$
$564$	−2.69129	+	0.553878i	−0.113324	+	0.0233225i
$565$		0			0
$566$		−	54.8066i		−	2.30369i
$567$	−20.6484	+	21.7721i	−0.867151	+	0.914342i
$568$	−40.0027			−1.67848
$569$	−19.2426			−0.806692			−0.403346	−	0.915047i	$-0.632153\pi$
$569$	−19.2426			−0.806692			−0.403346	+	0.915047i	$0.632153\pi$
$570$		0			0
$571$			8.19588i			0.342987i	0.985185	+	0.171493i	$0.0548592\pi$
$571$			8.19588i			0.342987i	−0.985185	+	0.171493i	$0.945141\pi$
$572$	−61.5991	−	51.8388i	−2.57559	−	2.16749i
$573$	−1.33027	−	6.46375i	−0.0555727	−	0.270027i
$574$		−	26.1524i		−	1.09158i
$575$		0			0
$576$	−38.4184	+	16.5128i	−1.60077	+	0.688032i
$577$		−	5.54710i		−	0.230929i	−0.993312	−	0.115464i	$-0.963164\pi$
$577$		−	5.54710i		−	0.230929i	0.993312	−	0.115464i	$-0.0368356\pi$
$578$			44.2053i			1.83870i
$579$	−41.3509	+	8.51020i	−1.71849	+	0.353672i
$580$		0			0
$581$		−	36.3833i		−	1.50943i
$582$	−70.8821	+	14.5879i	−2.93816	+	0.604686i
$583$	16.8507	+	14.1807i	0.697885	+	0.587305i
$584$		−	21.8052i		−	0.902307i
$585$		0			0
$586$	41.4763			1.71337
$587$	−14.1083			−0.582313			−0.291157	−	0.956675i	$-0.594040\pi$
$587$	−14.1083			−0.582313			−0.291157	+	0.956675i	$0.594040\pi$
$588$	−35.1215	+	7.22815i	−1.44838	+	0.298084i
$589$			12.6659i			0.521889i
$590$		0			0
$591$	−1.97783	−	9.61023i	−0.0813569	−	0.395312i
$592$			111.720i			4.59167i
$593$			33.2280i			1.36451i	0.731115	+	0.682255i	$0.239000\pi$
$593$			33.2280i			1.36451i	−0.731115	+	0.682255i	$0.761000\pi$
$594$	4.13677	−	45.5059i	0.169734	−	1.86713i
$595$		0			0
$596$	−31.8958			−1.30650
$597$	−4.11011	+	0.845878i	−0.168215	+	0.0346195i
$598$			94.0305i			3.84519i
$599$		−	23.7135i		−	0.968909i	−0.874817	−	0.484454i	$-0.839018\pi$
$599$		−	23.7135i		−	0.968909i	0.874817	−	0.484454i	$-0.160982\pi$
$600$		0			0
$601$			23.2762i			0.949457i	0.880132	+	0.474729i	$0.157454\pi$
$601$			23.2762i			0.949457i	−0.880132	+	0.474729i	$0.842546\pi$
$602$		−	63.2414i		−	2.57753i
$603$	−6.56575	−	15.2758i	−0.267378	−	0.622079i
$604$			0.853529i			0.0347296i
$605$		0			0
$606$	−12.4831	−	60.6552i	−0.507092	−	2.46395i
$607$	12.9968			0.527523			0.263761	−	0.964588i	$-0.415037\pi$
$607$	12.9968			0.527523			0.263761	+	0.964588i	$0.415037\pi$
$608$	40.4935			1.64223
$609$	8.21152	−	1.68997i	0.332747	−	0.0684809i
$610$		0			0
$611$	−1.52204			−0.0615750
$612$	−3.41060	−	7.93506i	−0.137865	−	0.320756i
$613$	−46.0228			−1.85884			−0.929422	−	0.369018i	$-0.879694\pi$
$613$	−46.0228			−1.85884			−0.929422	+	0.369018i	$0.879694\pi$
$614$			7.98597i			0.322288i
$615$		0			0
$616$	57.1994	−	67.9691i	2.30463	−	2.73855i
$617$	2.88152			0.116006			0.0580029	−	0.998316i	$-0.481527\pi$
$617$	2.88152			0.116006			0.0580029	+	0.998316i	$0.481527\pi$
$618$	−54.6736	+	11.2521i	−2.19930	+	0.452624i
$619$	35.3993			1.42282			0.711409	−	0.702778i	$-0.248057\pi$
$619$	35.3993			1.42282			0.711409	+	0.702778i	$0.248057\pi$
$620$		0			0
$621$	−31.3219	+	21.8407i	−1.25690	+	0.876439i
$622$	−23.1859			−0.929669
$623$			46.0739i			1.84591i
$624$	−92.0295	+	18.9401i	−3.68413	+	0.758210i
$625$		0			0
$626$	−21.1735			−0.846264
$627$	−8.06829	+	14.8891i	−0.322217	+	0.594613i
$628$			35.7662i			1.42722i
$629$	−5.68873			−0.226824
$630$		0			0
$631$	32.8831			1.30905			0.654527	−	0.756038i	$-0.272868\pi$
$631$	32.8831			1.30905			0.654527	+	0.756038i	$0.272868\pi$
$632$	−78.9906			−3.14208
$633$	0.398624	+	1.93691i	0.0158439	+	0.0769851i
$634$			75.6092i			3.00282i
$635$		0			0
$636$	56.6643	−	11.6618i	2.24689	−	0.462419i
$637$	−19.8627			−0.786988
$638$	−8.22021	+	9.76794i	−0.325441	+	0.386717i
$639$	−5.89881	−	13.7241i	−0.233353	−	0.542917i
$640$		0			0
$641$		−	34.4991i		−	1.36263i	−0.731989	−	0.681317i	$-0.761408\pi$
$641$		−	34.4991i		−	1.36263i	0.731989	−	0.681317i	$-0.238592\pi$
$642$	48.3122	−	9.94287i	1.90673	−	0.392414i
$643$		−	49.6440i		−	1.95777i	−0.204413	−	0.978885i	$-0.565528\pi$
$643$		−	49.6440i		−	1.95777i	0.204413	−	0.978885i	$-0.434472\pi$
$644$	−123.238			−4.85626
$645$		0			0
$646$			4.47374i			0.176017i
$647$	18.9443			0.744776			0.372388	−	0.928077i	$-0.378539\pi$
$647$	18.9443			0.744776			0.372388	+	0.928077i	$0.378539\pi$
$648$	−52.4620	−	49.7543i	−2.06090	−	1.95453i
$649$	3.07679	−	3.65610i	0.120775	−	0.143515i
$650$		0			0
$651$	24.3019	−	5.00143i	0.952465	−	0.196021i
$652$		−	28.1589i		−	1.10279i
$653$	−25.8385			−1.01114			−0.505568	−	0.862787i	$-0.668717\pi$
$653$	−25.8385			−1.01114			−0.505568	+	0.862787i	$0.668717\pi$
$654$	−47.0152	+	9.67594i	−1.83844	+	0.378359i
$655$		0			0
$656$	33.2549			1.29839
$657$	7.48093	−	3.21541i	0.291859	−	0.125445i
$658$		−	2.78798i		−	0.108687i
$659$	7.76200			0.302365			0.151182	−	0.988506i	$-0.451692\pi$
$659$	7.76200			0.302365			0.151182	+	0.988506i	$0.451692\pi$
$660$		0			0
$661$	12.6622			0.492504			0.246252	−	0.969206i	$-0.420801\pi$
$661$	12.6622			0.492504			0.246252	+	0.969206i	$0.420801\pi$
$662$		−	29.2032i		−	1.13502i
$663$	−0.964418	−	4.68609i	−0.0374549	−	0.181993i
$664$	87.6690			3.40222
$665$		0			0
$666$	−72.6318	+	31.2181i	−2.81442	+	1.20968i
$667$	10.6686			0.413091
$668$			40.0065i			1.54790i
$669$	−7.21279	−	35.0469i	−0.278863	−	1.35499i
$670$		0			0
$671$	9.48146	−	11.2667i	0.366028	−	0.434945i
$672$	−15.9898	−	77.6943i	−0.616821	−	2.99712i
$673$	−34.8963			−1.34515			−0.672577	−	0.740027i	$-0.734813\pi$
$673$	−34.8963			−1.34515			−0.672577	+	0.740027i	$0.734813\pi$
$674$		−	23.4027i		−	0.901439i
$675$		0			0
$676$	−51.7575			−1.99067
$677$		−	12.6332i		−	0.485532i	−0.970085	−	0.242766i	$-0.921945\pi$
$677$		−	12.6332i		−	0.485532i	0.970085	−	0.242766i	$-0.0780547\pi$
$678$	−13.0909	−	63.6085i	−0.502753	−	2.44287i
$679$		−	52.5385i		−	2.01624i
$680$		0			0
$681$	3.35495	+	16.3017i	0.128562	+	0.624681i
$682$	−24.3276	+	28.9081i	−0.931552	+	1.10695i
$683$	−29.2285			−1.11840			−0.559199	−	0.829033i	$-0.688891\pi$
$683$	−29.2285			−1.11840			−0.559199	+	0.829033i	$0.688891\pi$
$684$	17.5661	+	40.8690i	0.671655	+	1.56267i
$685$		0			0
$686$			25.4960i			0.973442i
$687$	13.9298	−	2.86680i	0.531453	−	0.109375i
$688$	80.4166			3.06585
$689$	32.0461			1.22086
$690$		0			0
$691$	−28.9094			−1.09977			−0.549883	−	0.835242i	$-0.685328\pi$
$691$	−28.9094			−1.09977			−0.549883	+	0.835242i	$0.685328\pi$
$692$			102.389i			3.89225i
$693$	31.7534	+	9.60121i	1.20621	+	0.364720i
$694$	−54.8677			−2.08275
$695$		0			0
$696$	4.07214	+	19.7864i	0.154354	+	0.750003i
$697$			1.69332i			0.0641392i
$698$	20.5659			0.778430
$699$	−1.19046	−	5.78444i	−0.0450275	−	0.218788i
$700$		0			0
$701$	−41.1039			−1.55247			−0.776237	−	0.630441i	$-0.782874\pi$
$701$	−41.1039			−1.55247			−0.776237	+	0.630441i	$0.782874\pi$
$702$	−38.0293	−	54.5380i	−1.43532	−	2.05840i
$703$	29.2994			1.10505
$704$	35.3717	+	29.7671i	1.33312	+	1.12189i
$705$		0			0
$706$			13.6058i			0.512059i
$707$	44.9582			1.69083
$708$	−2.53026	−	12.2945i	−0.0950929	−	0.462055i
$709$	10.7479			0.403646			0.201823	−	0.979422i	$-0.435313\pi$
$709$	10.7479			0.403646			0.201823	+	0.979422i	$0.435313\pi$
$710$		0			0
$711$	−11.6480	−	27.1001i	−0.436833	−	1.01633i
$712$	−111.020			−4.16064
$713$	31.5737			1.18244
$714$	8.58371	−	1.76656i	0.321237	−	0.0661120i
$715$		0			0
$716$		−	23.4925i		−	0.877958i
$717$	8.11832	−	1.67078i	0.303184	−	0.0623966i
$718$			18.5021i			0.690491i
$719$			6.54813i			0.244204i	0.992518	+	0.122102i	$0.0389635\pi$
$719$			6.54813i			0.244204i	−0.992518	+	0.122102i	$0.961036\pi$
$720$		0			0
$721$		−	40.5246i		−	1.50922i
$722$			27.3350i			1.01730i
$723$	2.17475	+	10.5671i	0.0808800	+	0.392995i
$724$	−1.51758			−0.0564004
$725$		0			0
$726$	−47.0125	+	18.4853i	−1.74480	+	0.686054i
$727$		−	48.6003i		−	1.80248i	−0.433316	−	0.901242i	$-0.642656\pi$
$727$		−	48.6003i		−	1.80248i	0.433316	−	0.901242i	$-0.357344\pi$
$728$		−	129.261i		−	4.79074i
$729$	9.33363	−	25.3354i	0.345690	−	0.938349i
$730$		0			0
$731$			4.09477i			0.151450i
$732$	−7.79725	−	37.8867i	−0.288195	−	1.40033i
$733$	25.1881			0.930345			0.465172	−	0.885220i	$-0.345992\pi$
$733$	25.1881			0.930345			0.465172	+	0.885220i	$0.345992\pi$
$734$	−3.32721			−0.122810
$735$		0			0
$736$		−	100.943i		−	3.72080i
$737$	−11.8359	+	14.0644i	−0.435980	+	0.518068i
$738$	9.29247	+	21.6198i	0.342060	+	0.795835i
$739$			23.4849i			0.863906i	0.901896	+	0.431953i	$0.142175\pi$
$739$			23.4849i			0.863906i	−0.901896	+	0.431953i	$0.857825\pi$
$740$		0			0
$741$	4.96717	+	24.1354i	0.182474	+	0.886637i
$742$			58.7001i			2.15495i
$743$		−	18.2670i		−	0.670151i	−0.942191	−	0.335076i	$-0.891238\pi$
$743$		−	18.2670i		−	0.670151i	0.942191	−	0.335076i	$-0.108762\pi$
$744$	12.0514	+	58.5577i	0.441827	+	2.14683i
$745$		0			0
$746$			68.2219i			2.49778i
$747$	12.9277	+	30.0775i	0.473000	+	1.10048i
$748$	−6.14818	+	7.30578i	−0.224800	+	0.267126i
$749$			35.8095i			1.30845i
$750$		0			0
$751$	24.1444			0.881043			0.440521	−	0.897742i	$-0.354794\pi$
$751$	24.1444			0.881043			0.440521	+	0.897742i	$0.354794\pi$
$752$	3.54514			0.129278
$753$	−2.89611	−	14.0721i	−0.105540	−	0.512817i
$754$			18.5763i			0.676510i
$755$		0			0
$756$	71.4785	−	49.8419i	2.59965	−	1.81273i
$757$			26.2443i			0.953864i	0.878940	+	0.476932i	$0.158251\pi$
$757$			26.2443i			0.953864i	−0.878940	+	0.476932i	$0.841749\pi$
$758$		−	10.3226i		−	0.374932i
$759$	37.1157	+	20.1127i	1.34721	+	0.730046i
$760$		0			0
$761$	−30.6299			−1.11033			−0.555166	−	0.831740i	$-0.687345\pi$
$761$	−30.6299			−1.11033			−0.555166	+	0.831740i	$0.687345\pi$
$762$	7.55394	+	36.7045i	0.273650	+	1.32966i
$763$		−	34.8481i		−	1.26159i
$764$			19.1645i			0.693347i
$765$		0			0
$766$			28.5446i			1.03136i
$767$		−	6.95305i		−	0.251060i
$768$	−4.62810	+	0.952484i	−0.167002	+	0.0343698i
$769$			44.6231i			1.60915i	0.593851	+	0.804575i	$0.297607\pi$
$769$			44.6231i			1.60915i	−0.593851	+	0.804575i	$0.702393\pi$
$770$		0			0
$771$	−28.4295	+	5.85091i	−1.02386	+	0.210716i
$772$	122.602			4.41254
$773$	−26.7071			−0.960587			−0.480293	−	0.877108i	$-0.659470\pi$
$773$	−26.7071			−0.960587			−0.480293	+	0.877108i	$0.659470\pi$
$774$	22.4709	+	52.2806i	0.807700	+	1.87919i
$775$		0			0
$776$	126.597			4.54456
$777$	−11.5696	−	56.2164i	−0.415057	−	2.01675i
$778$	15.4414			0.553601
$779$		−	8.72135i		−	0.312475i
$780$		0			0
$781$	−10.6336	+	12.6357i	−0.380500	+	0.452142i
$782$	11.1522			0.398802
$783$	−6.18785	+	4.31478i	−0.221136	+	0.154198i
$784$	46.2643			1.65230
$785$		0			0
$786$	−10.1244	−	49.1942i	−0.361125	−	1.75470i
$787$	45.9402			1.63759			0.818796	−	0.574085i	$-0.194642\pi$
$787$	45.9402			1.63759			0.818796	+	0.574085i	$0.194642\pi$
$788$			28.4935i			1.01504i
$789$	−10.0942	−	49.0473i	−0.359361	−	1.74613i
$790$		0			0
$791$	47.1472			1.67636
$792$	−23.1350	+	76.5130i	−0.822068	+	2.71877i
$793$		−	21.4266i		−	0.760879i
$794$	−16.2287			−0.575934
$795$		0			0
$796$	12.1861			0.431926
$797$	21.9069			0.775983			0.387991	−	0.921663i	$-0.373169\pi$
$797$	21.9069			0.775983			0.387991	+	0.921663i	$0.373169\pi$
$798$	−44.2098	+	9.09858i	−1.56501	+	0.322086i
$799$			0.180517i			0.00638622i
$800$		0			0
$801$	−16.3710	−	38.0886i	−0.578440	−	1.34579i
$802$	−37.7290			−1.33226
$803$	−6.88767	−	5.79632i	−0.243060	−	0.204548i
$804$	9.73345	+	47.2947i	0.343272	+	1.66796i
$805$		0			0
$806$			54.9764i			1.93646i
$807$	−5.99425	−	29.1260i	−0.211008	−	1.02528i
$808$			108.331i			3.81108i
$809$	4.69212			0.164966			0.0824830	−	0.996592i	$-0.473715\pi$
$809$	4.69212			0.164966			0.0824830	+	0.996592i	$0.473715\pi$
$810$		0			0
$811$		−	40.8050i		−	1.43286i	−0.697660	−	0.716429i	$-0.745775\pi$
$811$		−	40.8050i		−	1.43286i	0.697660	−	0.716429i	$-0.254225\pi$
$812$	−24.3465			−0.854394
$813$	10.2419	+	49.7651i	0.359198	+	1.74534i
$814$	66.8718	+	56.2760i	2.34386	+	1.97247i
$815$		0			0
$816$	2.24633	+	10.9149i	0.0786373	+	0.382097i
$817$		−	21.0898i		−	0.737840i
$818$	−14.6526			−0.512318
$819$	44.3469	−	19.0609i	1.54961	−	0.666042i
$820$		0			0
$821$	−35.0794			−1.22428			−0.612140	−	0.790749i	$-0.709691\pi$
$821$	−35.0794			−1.22428			−0.612140	+	0.790749i	$0.709691\pi$
$822$	−8.23006	−	39.9898i	−0.287056	−	1.39480i
$823$		−	41.3499i		−	1.44137i	−0.693264	−	0.720684i	$-0.743828\pi$
$823$		−	41.3499i		−	1.44137i	0.693264	−	0.720684i	$-0.256172\pi$
$824$	97.6480			3.40173
$825$		0			0
$826$	12.7362			0.443148
$827$		−	1.48329i		−	0.0515791i	−0.999667	−	0.0257895i	$-0.991790\pi$
$827$		−	1.48329i		−	0.0515791i	0.999667	−	0.0257895i	$-0.00820997\pi$
$828$	101.879	−	43.7889i	3.54053	−	1.52177i
$829$	−1.95468			−0.0678887			−0.0339443	−	0.999424i	$-0.510807\pi$
$829$	−1.95468			−0.0678887			−0.0339443	+	0.999424i	$0.510807\pi$
$830$		0			0
$831$	−33.6492	+	6.92515i	−1.16728	+	0.240231i
$832$	67.2687			2.33212
$833$			2.35575i			0.0816220i
$834$	70.4596	−	14.5009i	2.43981	−	0.502124i
$835$		0			0
$836$	31.6658	−	37.6280i	1.09518	−	1.30139i
$837$	−18.3128	+	12.7695i	−0.632984	+	0.441380i
$838$	15.4120			0.532398
$839$		−	49.7350i		−	1.71704i	−0.512777	−	0.858522i	$-0.671383\pi$
$839$		−	49.7350i		−	1.71704i	0.512777	−	0.858522i	$-0.328617\pi$
$840$		0			0
$841$	−26.8923			−0.927322
$842$		−	14.8809i		−	0.512830i
$843$	30.9658	−	6.37290i	1.06652	−	0.219494i
$844$		−	5.74277i		−	0.197674i
$845$		0			0
$846$	0.990623	+	2.30477i	0.0340583	+	0.0792398i
$847$	−6.26467	−	36.1354i	−0.215257	−	1.24163i
$848$	−74.6420			−2.56322
$849$	−35.0678	+	7.21711i	−1.20352	+	0.247691i
$850$		0			0
$851$		−	73.0380i		−	2.50371i
$852$	8.74474	+	42.4906i	0.299590	+	1.45570i
$853$	−45.5368			−1.55915			−0.779575	−	0.626308i	$-0.784565\pi$
$853$	−45.5368			−1.55915			−0.779575	+	0.626308i	$0.784565\pi$
$854$	39.2479			1.34304
$855$		0			0
$856$	−86.2865			−2.94921
$857$		−	32.8792i		−	1.12313i	−0.827432	−	0.561566i	$-0.810199\pi$
$857$		−	32.8792i		−	1.12313i	0.827432	−	0.561566i	$-0.189801\pi$
$858$	−35.0205	+	64.6262i	−1.19558	+	2.20630i
$859$	−10.5435			−0.359739			−0.179869	−	0.983690i	$-0.557568\pi$
$859$	−10.5435			−0.359739			−0.179869	+	0.983690i	$0.557568\pi$
$860$		0			0
$861$	−16.7335	+	3.44383i	−0.570277	+	0.117366i
$862$		−	9.93644i		−	0.338436i
$863$	−21.9115			−0.745875			−0.372938	−	0.927856i	$-0.621650\pi$
$863$	−21.9115			−0.745875			−0.372938	+	0.927856i	$0.621650\pi$
$864$	40.8249	+	58.5471i	1.38889	+	1.99181i
$865$		0			0
$866$	66.3102			2.25331
$867$	28.2846	−	5.82110i	0.960597	−	0.197695i
$868$	−72.0530			−2.44564
$869$	−20.9975	+	24.9509i	−0.712290	+	0.846402i
$870$		0			0
$871$			26.7472i			0.906293i
$872$	83.9700			2.84358
$873$	18.6680	+	43.4327i	0.631815	+	1.46998i
$874$	−57.4387			−1.94289
$875$		0			0
$876$	−23.1614	+	4.76671i	−0.782550	+	0.161052i
$877$	−38.0152			−1.28368			−0.641841	−	0.766838i	$-0.721829\pi$
$877$	−38.0152			−1.28368			−0.641841	+	0.766838i	$0.721829\pi$
$878$	−73.5765			−2.48309
$879$	−5.46174	−	26.5385i	−0.184220	−	0.895121i
$880$		0			0
$881$			19.6168i			0.660907i	0.943822	+	0.330453i	$0.107202\pi$
$881$			19.6168i			0.660907i	−0.943822	+	0.330453i	$0.892798\pi$
$882$	12.9277	+	30.0775i	0.435298	+	1.01276i
$883$		−	9.74489i		−	0.327942i	−0.986465	−	0.163971i	$-0.947570\pi$
$883$		−	9.74489i		−	0.327942i	0.986465	−	0.163971i	$-0.0524303\pi$
$884$			13.8939i			0.467302i
$885$		0			0
$886$			37.3582i			1.25507i
$887$		−	19.3598i		−	0.650039i	−0.945707	−	0.325019i	$-0.894629\pi$
$887$		−	19.3598i		−	0.650039i	0.945707	−	0.325019i	$-0.105371\pi$
$888$	135.459	−	27.8780i	4.54570	−	0.935526i
$889$	−27.2057			−0.912450
$890$		0			0
$891$	−29.6616	+	3.34547i	−0.993699	+	0.112077i
$892$			103.911i			3.47920i
$893$		−	0.929739i		−	0.0311125i
$894$	5.87018	+	28.5231i	0.196328	+	0.953956i
$895$		0			0
$896$			31.6249i			1.05651i
$897$	60.1651	−	12.3822i	2.00885	−	0.413431i
$898$	−35.9381			−1.19927
$899$	6.23759			0.208035
$900$		0			0
$901$		−	3.80073i		−	0.126621i
$902$	16.7513	−	19.9052i	0.557756	−	0.662772i
$903$	−40.4648	+	8.32783i	−1.34658	+	0.277133i
$904$			113.606i			3.77847i
$905$		0			0
$906$	0.763278	−	0.157086i	0.0253582	−	0.00521883i
$907$		−	42.0785i		−	1.39719i	−0.715516	−	0.698596i	$-0.753808\pi$
$907$		−	42.0785i		−	1.39719i	0.715516	−	0.698596i	$-0.246192\pi$
$908$		−	48.3331i		−	1.60399i
$909$	−37.1662	+	15.9746i	−1.23273	+	0.529843i
$910$		0			0
$911$		−	1.00771i		−	0.0333869i	−0.999861	−	0.0166935i	$-0.994686\pi$
$911$		−	1.00771i		−	0.0333869i	0.999861	−	0.0166935i	$-0.00531394\pi$
$912$	−11.5696	−	56.2164i	−0.383107	−	1.86151i
$913$	23.3044	−	27.6922i	0.771262	−	0.916478i
$914$		−	16.0077i		−	0.529488i
$915$		0			0
$916$	−41.3006			−1.36461
$917$	36.4632			1.20412
$918$	−6.46832	+	4.51035i	−0.213486	+	0.148864i
$919$		−	36.4434i		−	1.20216i	−0.799190	−	0.601079i	$-0.794738\pi$
$919$		−	36.4434i		−	1.20216i	0.799190	−	0.601079i	$-0.205262\pi$
$920$		0			0
$921$	5.10980	−	1.05162i	0.168374	−	0.0346520i
$922$		−	11.0185i		−	0.362874i
$923$			24.0302i			0.790964i
$924$	−84.7002	−	45.8985i	−2.78643	−	1.50995i
$925$		0			0
$926$	−55.9321			−1.83804
$927$	14.3992	+	33.5010i	0.472932	+	1.10032i
$928$		−	19.9419i		−	0.654625i
$929$		−	33.5641i		−	1.10120i	−0.834769	−	0.550601i	$-0.814399\pi$
$929$		−	33.5641i		−	1.10120i	0.834769	−	0.550601i	$-0.185601\pi$
$930$		0			0
$931$		−	12.1332i		−	0.397648i
$932$			17.1504i			0.561780i
$933$	3.05319	+	14.8354i	0.0999570	+	0.485690i
$934$		−	79.3401i		−	2.59609i
$935$		0			0
$936$	45.9291	+	106.858i	1.50124	+	3.49277i
$937$	11.5387			0.376954			0.188477	−	0.982078i	$-0.439645\pi$
$937$	11.5387			0.376954			0.188477	+	0.982078i	$0.439645\pi$
$938$	−48.9939			−1.59971
$939$	2.78820	+	13.5478i	0.0909894	+	0.442116i
$940$		0			0
$941$	37.0991			1.20940			0.604699	−	0.796454i	$-0.293294\pi$
$941$	37.0991			1.20940			0.604699	+	0.796454i	$0.293294\pi$
$942$	31.9843	−	6.58250i	1.04210	−	0.214469i
$943$	−21.7407			−0.707974
$944$			16.1951i			0.527105i
$945$		0			0
$946$	40.5076	−	48.1346i	1.31702	−	1.56499i
$947$	−52.9766			−1.72151			−0.860754	−	0.509021i	$-0.830008\pi$
$947$	−52.9766			−1.72151			−0.860754	+	0.509021i	$0.830008\pi$
$948$	17.2676	+	83.9032i	0.560827	+	2.72505i
$949$	−13.0987			−0.425203
$950$		0			0
$951$	48.3783	−	9.95646i	1.56877	−	0.322860i
$952$	−15.3306			−0.496869
$953$			39.9855i			1.29526i	0.761956	+	0.647629i	$0.224239\pi$
$953$			39.9855i			1.29526i	−0.761956	+	0.647629i	$0.775761\pi$
$954$	−20.8573	−	48.5264i	−0.675281	−	1.57110i
$955$		0			0
$956$	−24.0701			−0.778484
$957$	7.33245	+	3.97340i	0.237024	+	0.128442i
$958$		−	41.1306i		−	1.32887i
$959$	29.6408			0.957151
$960$		0			0
$961$	−12.5400			−0.404515
$962$	127.174			4.10027
$963$	−12.7238	−	29.6031i	−0.410020	−	0.953947i
$964$		−	31.3306i		−	1.00909i
$965$		0			0
$966$	22.6810	+	110.207i	0.729751	+	3.54585i
$967$	−55.8028			−1.79450			−0.897248	−	0.441526i	$-0.854437\pi$
$967$	−55.8028			−1.79450			−0.897248	+	0.441526i	$0.854437\pi$
$968$	87.0717	−	15.0953i	2.79859	−	0.485182i
$969$	2.86251	−	0.589117i	0.0919571	−	0.0189252i
$970$		0			0
$971$		−	16.1820i		−	0.519306i	−0.965702	−	0.259653i	$-0.916392\pi$
$971$		−	16.1820i		−	0.519306i	0.965702	−	0.259653i	$-0.0836082\pi$
$972$	−41.3803	+	66.6012i	−1.32727	+	2.13623i
$973$			52.2253i			1.67427i
$974$	−38.4090			−1.23070
$975$		0			0
$976$			49.9069i			1.59748i
$977$	−23.0147			−0.736305			−0.368152	−	0.929765i	$-0.620010\pi$
$977$	−23.0147			−0.736305			−0.368152	+	0.929765i	$0.620010\pi$
$978$	−25.1814	+	5.18244i	−0.805212	+	0.165716i
$979$	−29.5115	+	35.0680i	−0.943191	+	1.12078i
$980$		0			0
$981$	12.3822	+	28.8084i	0.395334	+	0.919781i
$982$		−	8.96891i		−	0.286209i
$983$	−36.0408			−1.14952			−0.574762	−	0.818321i	$-0.694905\pi$
$983$	−36.0408			−1.14952			−0.574762	+	0.818321i	$0.694905\pi$
$984$	−8.29825	−	40.3211i	−0.264539	−	1.28539i
$985$		0			0
$986$	2.20319			0.0701639
$987$	−1.78388	+	0.367130i	−0.0567814	+	0.0116859i
$988$		−	71.5595i		−	2.27661i
$989$	−52.5730			−1.67172
$990$		0			0
$991$	3.75980			0.119434			0.0597169	−	0.998215i	$-0.480980\pi$
$991$	3.75980			0.119434			0.0597169	+	0.998215i	$0.480980\pi$
$992$		−	59.0177i		−	1.87381i
$993$	−18.6856	+	3.84558i	−0.592970	+	0.122036i
$994$	−44.0171			−1.39614
$995$		0			0
$996$	−19.1648	−	93.1214i	−0.607259	−	2.95066i
$997$	19.0789			0.604235			0.302118	−	0.953271i	$-0.402306\pi$
$997$	19.0789			0.604235			0.302118	+	0.953271i	$0.402306\pi$
$998$		−	105.786i		−	3.34859i
$999$	29.5392	+	42.3623i	0.934579	+	1.34028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.d.f.824.31		32
3.2	odd	2	inner	825.2.d.f.824.1		32
5.2	odd	4		825.2.f.g.626.1	yes	16
5.3	odd	4		825.2.f.e.626.16	yes	16
5.4	even	2	inner	825.2.d.f.824.2		32
11.10	odd	2	inner	825.2.d.f.824.3		32
15.2	even	4		825.2.f.g.626.16	yes	16
15.8	even	4		825.2.f.e.626.1	✓	16
15.14	odd	2	inner	825.2.d.f.824.32		32
33.32	even	2	inner	825.2.d.f.824.29		32
55.32	even	4		825.2.f.g.626.15	yes	16
55.43	even	4		825.2.f.e.626.2	yes	16
55.54	odd	2	inner	825.2.d.f.824.30		32
165.32	odd	4		825.2.f.g.626.2	yes	16
165.98	odd	4		825.2.f.e.626.15	yes	16
165.164	even	2	inner	825.2.d.f.824.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.d.f.824.1		32	3.2	odd	2	inner
825.2.d.f.824.2		32	5.4	even	2	inner
825.2.d.f.824.3		32	11.10	odd	2	inner
825.2.d.f.824.4		32	165.164	even	2	inner
825.2.d.f.824.29		32	33.32	even	2	inner
825.2.d.f.824.30		32	55.54	odd	2	inner
825.2.d.f.824.31		32	1.1	even	1	trivial
825.2.d.f.824.32		32	15.14	odd	2	inner
825.2.f.e.626.1	✓	16	15.8	even	4
825.2.f.e.626.2	yes	16	55.43	even	4
825.2.f.e.626.15	yes	16	165.98	odd	4
825.2.f.e.626.16	yes	16	5.3	odd	4
825.2.f.g.626.1	yes	16	5.2	odd	4
825.2.f.g.626.2	yes	16	165.32	odd	4
825.2.f.g.626.15	yes	16	55.32	even	4
825.2.f.g.626.16	yes	16	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.65141i q^{2} +(1.69650 - 0.349146i) q^{3} -5.02997 q^{4} +(0.925729 + 4.49810i) q^{6} -3.33404 q^{7} -8.03369i q^{8} +(2.75619 - 1.18465i) q^{9} +O(q^{10})\)	\(q+2.65141i q^{2} +(1.69650 - 0.349146i) q^{3} -5.02997 q^{4} +(0.925729 + 4.49810i) q^{6} -3.33404 q^{7} -8.03369i q^{8} +(2.75619 - 1.18465i) q^{9} +(-2.53762 - 2.13553i) q^{11} +(-8.53332 + 1.75619i) q^{12} -4.82595 q^{13} -8.83990i q^{14} +11.2406 q^{16} +0.572368i q^{17} +(3.14099 + 7.30780i) q^{18} -2.94794i q^{19} +(-5.65618 + 1.16407i) q^{21} +(5.66217 - 6.72826i) q^{22} -7.34867 q^{23} +(-2.80493 - 13.6291i) q^{24} -12.7956i q^{26} +(4.26225 - 2.97207i) q^{27} +16.7701 q^{28} -1.45178 q^{29} -4.29651 q^{31} +13.7362i q^{32} +(-5.05067 - 2.73692i) q^{33} -1.51758 q^{34} +(-13.8636 + 5.95875i) q^{36} +9.93894i q^{37} +7.81620 q^{38} +(-8.18721 + 1.68496i) q^{39} +2.95845 q^{41} +(-3.08642 - 14.9968i) q^{42} +7.15409 q^{43} +(12.7641 + 10.7417i) q^{44} -19.4843i q^{46} +0.315386 q^{47} +(19.0697 - 3.92463i) q^{48} +4.11580 q^{49} +(0.199840 + 0.971019i) q^{51} +24.2744 q^{52} -6.64036 q^{53} +(7.88016 + 11.3010i) q^{54} +26.7846i q^{56} +(-1.02926 - 5.00117i) q^{57} -3.84926i q^{58} +1.44076i q^{59} +4.43986i q^{61} -11.3918i q^{62} +(-9.18925 + 3.94967i) q^{63} -13.9389 q^{64} +(7.25670 - 13.3914i) q^{66} -5.54236i q^{67} -2.87899i q^{68} +(-12.4670 + 2.56576i) q^{69} -4.97937i q^{71} +(-9.51710 - 22.1424i) q^{72} +2.71423 q^{73} -26.3522 q^{74} +14.8281i q^{76} +(8.46051 + 7.11994i) q^{77} +(-4.46752 - 21.7076i) q^{78} -9.83242i q^{79} +(6.19321 - 6.53025i) q^{81} +7.84406i q^{82} +10.9127i q^{83} +(28.4504 - 5.85522i) q^{84} +18.9684i q^{86} +(-2.46294 + 0.506883i) q^{87} +(-17.1562 + 20.3864i) q^{88} -13.8193i q^{89} +16.0899 q^{91} +36.9636 q^{92} +(-7.28902 + 1.50011i) q^{93} +0.836216i q^{94} +(4.79594 + 23.3034i) q^{96} +15.7582i q^{97} +10.9127i q^{98} +(-9.52402 - 2.87975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} + 20 q^{9}+O(q^{10}) \) 32 * q - 32 * q^4 + 20 * q^9	\( 32 q - 32 q^{4} + 20 q^{9} + 64 q^{16} - 24 q^{31} - 56 q^{34} - 72 q^{36} + 56 q^{49} - 120 q^{64} - 60 q^{66} - 88 q^{69} - 52 q^{81} + 128 q^{91} - 28 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 + 20 * q^9 + 64 * q^16 - 24 * q^31 - 56 * q^34 - 72 * q^36 + 56 * q^49 - 120 * q^64 - 60 * q^66 - 88 * q^69 - 52 * q^81 + 128 * q^91 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more