LMFDB - Embedded newform 825.2.f.g.626.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(626,825)]

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, 0, 1]))

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

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

chi := DirichletCharacter("825.626");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - 17 x^{14} + 26 x^{13} + 191 x^{12} - 390 x^{11} - 539 x^{10} + 1484 x^{9} + \cdots + 102940 $ x^16 - 2x^15 - 17x^14 + 26x^13 + 191x^12 - 390x^11 - 539x^10 + 1484x^9 + 1787x^8 - 704x^7 + 14278x^6 - 10982x^5 + 73951x^4 + 70936x^3 + 207288x^2 + 119752*x + 102940
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			626.15
Root			$2.30226 + 1.69650i$ of defining polynomial
Character	$\chi$	$=$	825.626
Dual form			825.2.f.g.626.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.65141 q^{2} +(-0.349146 - 1.69650i) q^{3} +5.02997 q^{4} +(-0.925729 - 4.49810i) q^{6} +3.33404i q^{7} +8.03369 q^{8} +(-2.75619 + 1.18465i) q^{9} +O(q^{10})$	\(q+2.65141 q^{2} +(-0.349146 - 1.69650i) q^{3} +5.02997 q^{4} +(-0.925729 - 4.49810i) q^{6} +3.33404i q^{7} +8.03369 q^{8} +(-2.75619 + 1.18465i) q^{9} +(2.53762 - 2.13553i) q^{11} +(-1.75619 - 8.53332i) q^{12} -4.82595i q^{13} +8.83990i q^{14} +11.2406 q^{16} +0.572368 q^{17} +(-7.30780 + 3.14099i) q^{18} -2.94794i q^{19} +(5.65618 - 1.16407i) q^{21} +(6.72826 - 5.66217i) q^{22} +7.34867i q^{23} +(-2.80493 - 13.6291i) q^{24} -12.7956i q^{26} +(2.97207 + 4.26225i) q^{27} +16.7701i q^{28} -1.45178 q^{29} -4.29651 q^{31} +13.7362 q^{32} +(-4.50892 - 3.55944i) q^{33} +1.51758 q^{34} +(-13.8636 + 5.95875i) q^{36} -9.93894 q^{37} -7.81620i q^{38} +(-8.18721 + 1.68496i) q^{39} -2.95845 q^{41} +(14.9968 - 3.08642i) q^{42} +7.15409i q^{43} +(12.7641 - 10.7417i) q^{44} +19.4843i q^{46} +0.315386i q^{47} +(-3.92463 - 19.0697i) q^{48} -4.11580 q^{49} +(-0.199840 - 0.971019i) q^{51} -24.2744i q^{52} +6.64036i q^{53} +(7.88016 + 11.3010i) q^{54} +26.7846i q^{56} +(-5.00117 + 1.02926i) q^{57} -3.84926 q^{58} -1.44076i q^{59} -4.43986i q^{61} -11.3918 q^{62} +(-3.94967 - 9.18925i) q^{63} +13.9389 q^{64} +(-11.9550 - 9.43754i) q^{66} +5.54236 q^{67} +2.87899 q^{68} +(12.4670 - 2.56576i) q^{69} -4.97937i q^{71} +(-22.1424 + 9.51710i) q^{72} +2.71423i q^{73} -26.3522 q^{74} -14.8281i q^{76} +(7.11994 + 8.46051i) q^{77} +(-21.7076 + 4.46752i) q^{78} -9.83242i q^{79} +(6.19321 - 6.53025i) q^{81} -7.84406 q^{82} -10.9127 q^{83} +(28.4504 - 5.85522i) q^{84} +18.9684i q^{86} +(0.506883 + 2.46294i) q^{87} +(20.3864 - 17.1562i) q^{88} +13.8193i q^{89} +16.0899 q^{91} +36.9636i q^{92} +(1.50011 + 7.28902i) q^{93} +0.836216i q^{94} +(-4.79594 - 23.3034i) q^{96} -15.7582 q^{97} -10.9127 q^{98} +(-4.46431 + 8.89213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} + 16 q^{4} - 10 q^{9}+O(q^{10}) $ 16 * q + 2 * q^3 + 16 * q^4 - 10 * q^9	$ 16 q + 2 q^{3} + 16 q^{4} - 10 q^{9} + 6 q^{12} + 32 q^{16} + 28 q^{22} + 2 q^{27} - 12 q^{31} - 20 q^{33} + 28 q^{34} - 36 q^{36} + 4 q^{37} + 58 q^{42} - 40 q^{48} - 28 q^{49} - 16 q^{58} + 60 q^{64} - 30 q^{66} - 44 q^{67} + 44 q^{69} - 44 q^{78} - 26 q^{81} - 8 q^{82} + 76 q^{88} + 64 q^{91} - 14 q^{93} - 108 q^{97} + 14 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 + 16 * q^4 - 10 * q^9 + 6 * q^12 + 32 * q^16 + 28 * q^22 + 2 * q^27 - 12 * q^31 - 20 * q^33 + 28 * q^34 - 36 * q^36 + 4 * q^37 + 58 * q^42 - 40 * q^48 - 28 * q^49 - 16 * q^58 + 60 * q^64 - 30 * q^66 - 44 * q^67 + 44 * q^69 - 44 * q^78 - 26 * q^81 - 8 * q^82 + 76 * q^88 + 64 * q^91 - 14 * q^93 - 108 * q^97 + 14 * 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 $

$2$	2.65141			1.87483			0.937415	−	0.348215i	$-0.113212\pi$
$2$	2.65141			1.87483			0.937415	+	0.348215i	$0.113212\pi$
$3$	−0.349146	−	1.69650i	−0.201580	−	0.979472i
$3$	−0.349146	−	1.69650i	−0.201580	−	0.979472i
$4$	5.02997			2.51498
$5$		0			0
$5$		0			0
$6$	−0.925729	−	4.49810i	−0.377927	−	1.83634i
$7$			3.33404i			1.26015i	0.776535	+	0.630074i	$0.216975\pi$
$7$			3.33404i			1.26015i	−0.776535	+	0.630074i	$0.783025\pi$
$8$	8.03369			2.84034
$9$	−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
$12$	−1.75619	−	8.53332i	−0.506970	−	2.46336i
$13$		−	4.82595i		−	1.33848i	−0.743047	−	0.669239i	$-0.766620\pi$
$13$		−	4.82595i		−	1.33848i	0.743047	−	0.669239i	$-0.233380\pi$
$14$			8.83990i			2.36256i
$15$		0			0
$16$	11.2406			2.81016
$17$	0.572368			0.138820			0.0694098	−	0.997588i	$-0.477888\pi$
$17$	0.572368			0.138820			0.0694098	+	0.997588i	$0.477888\pi$
$18$	−7.30780	+	3.14099i	−1.72246	+	0.740339i
$19$		−	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
$22$	6.72826	−	5.66217i	1.43447	−	1.20718i
$23$			7.34867i			1.53230i	0.642660	+	0.766152i	$0.277831\pi$
$23$			7.34867i			1.53230i	−0.642660	+	0.766152i	$0.722169\pi$
$24$	−2.80493	−	13.6291i	−0.572554	−	2.78203i
$25$		0			0
$26$		−	12.7956i		−	2.50942i
$27$	2.97207	+	4.26225i	0.571975	+	0.820271i
$28$			16.7701i			3.16925i
$29$	−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	$0.626088\pi$
$32$	13.7362			2.42824
$33$	−4.50892	−	3.55944i	−0.784902	−	0.619620i
$34$	1.51758			0.260263
$35$		0			0
$36$	−13.8636	+	5.95875i	−2.31060	+	0.993125i
$37$	−9.93894			−1.63395			−0.816976	−	0.576672i	$-0.804351\pi$
$37$	−9.93894			−1.63395			−0.816976	+	0.576672i	$0.804351\pi$
$38$		−	7.81620i		−	1.26796i
$39$	−8.18721	+	1.68496i	−1.31100	+	0.269810i
$40$		0			0
$41$	−2.95845			−0.462033			−0.231016	−	0.972950i	$-0.574205\pi$
$41$	−2.95845			−0.462033			−0.231016	+	0.972950i	$0.574205\pi$
$42$	14.9968	−	3.08642i	2.31406	−	0.476244i
$43$			7.15409i			1.09099i	0.838115	+	0.545494i	$0.183658\pi$
$43$			7.15409i			1.09099i	−0.838115	+	0.545494i	$0.816342\pi$
$44$	12.7641	−	10.7417i	1.92427	−	1.61937i
$45$		0			0
$46$			19.4843i			2.87281i
$47$			0.315386i			0.0460037i	0.999735	+	0.0230019i	$0.00732237\pi$
$47$			0.315386i			0.0460037i	−0.999735	+	0.0230019i	$0.992678\pi$
$48$	−3.92463	−	19.0697i	−0.566471	−	2.75248i
$49$	−4.11580			−0.587972
$50$		0			0
$51$	−0.199840	−	0.971019i	−0.0279832	−	0.135970i
$52$		−	24.2744i		−	3.36625i
$53$			6.64036i			0.912124i	0.889948	+	0.456062i	$0.150740\pi$
$53$			6.64036i			0.912124i	−0.889948	+	0.456062i	$0.849260\pi$
$54$	7.88016	+	11.3010i	1.07235	+	1.53787i
$55$		0			0
$56$			26.7846i			3.57924i
$57$	−5.00117	+	1.02926i	−0.662422	+	0.136329i
$58$	−3.84926			−0.505432
$59$		−	1.44076i		−	0.187571i	−0.995592	−	0.0937856i	$-0.970103\pi$
$59$		−	1.44076i		−	0.187571i	0.995592	−	0.0937856i	$-0.0298968\pi$
$60$		0			0
$61$		−	4.43986i		−	0.568466i	−0.958755	−	0.284233i	$-0.908261\pi$
$61$		−	4.43986i		−	0.568466i	0.958755	−	0.284233i	$-0.0917389\pi$
$62$	−11.3918			−1.44676
$63$	−3.94967	−	9.18925i	−0.497611	−	1.15774i
$64$	13.9389			1.74237
$65$		0			0
$66$	−11.9550	−	9.43754i	−1.47156	−	1.16168i
$67$	5.54236			0.677107			0.338553	−	0.940947i	$-0.390062\pi$
$67$	5.54236			0.677107			0.338553	+	0.940947i	$0.390062\pi$
$68$	2.87899			0.349129
$69$	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	$-0.0954767\pi$
$72$	−22.1424	+	9.51710i	−2.60951	+	1.12160i
$73$			2.71423i			0.317676i	0.987305	+	0.158838i	$0.0507748\pi$
$73$			2.71423i			0.317676i	−0.987305	+	0.158838i	$0.949225\pi$
$74$	−26.3522			−3.06338
$75$		0			0
$76$		−	14.8281i		−	1.70090i
$77$	7.11994	+	8.46051i	0.811393	+	0.964165i
$78$	−21.7076	+	4.46752i	−2.45791	+	0.505848i
$79$		−	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
$82$	−7.84406			−0.866232
$83$	−10.9127			−1.19782			−0.598911	−	0.800816i	$-0.704400\pi$
$83$	−10.9127			−1.19782			−0.598911	+	0.800816i	$0.704400\pi$
$84$	28.4504	−	5.85522i	3.10419	−	0.638856i
$85$		0			0
$86$			18.9684i			2.04542i
$87$	0.506883	+	2.46294i	0.0543435	+	0.264054i
$88$	20.3864	−	17.1562i	2.17320	−	1.82886i
$89$			13.8193i			1.46484i	0.680853	+	0.732420i	$0.261609\pi$
$89$			13.8193i			1.46484i	−0.680853	+	0.732420i	$0.738391\pi$
$90$		0			0
$91$	16.0899			1.68668
$92$			36.9636i			3.85372i
$93$	1.50011	+	7.28902i	0.155554	+	0.755836i
$94$			0.836216i			0.0862491i
$95$		0			0
$96$	−4.79594	−	23.3034i	−0.489483	−	2.37839i
$97$	−15.7582			−1.60001			−0.800003	−	0.599996i	$-0.795169\pi$
$97$	−15.7582			−1.60001			−0.800003	+	0.599996i	$0.795169\pi$
$98$	−10.9127			−1.10235
$99$	−4.46431	+	8.89213i	−0.448680	+	0.893693i
$100$		0			0
$101$	13.4846			1.34177			0.670885	−	0.741561i	$-0.265914\pi$
$101$	13.4846			1.34177			0.670885	+	0.741561i	$0.265914\pi$
$102$	−0.529857	−	2.57457i	−0.0524637	−	0.254920i
$103$	12.1548			1.19765			0.598825	−	0.800880i	$-0.295635\pi$
$103$	12.1548			1.19765			0.598825	+	0.800880i	$0.295635\pi$
$104$		−	38.7702i		−	3.80173i
$105$		0			0
$106$			17.6063i			1.71008i
$107$	−10.7406			−1.03833			−0.519166	−	0.854674i	$-0.673757\pi$
$107$	−10.7406			−1.03833			−0.519166	+	0.854674i	$0.673757\pi$
$108$	14.9494	+	21.4390i	1.43851	+	2.06297i
$109$			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
$112$			37.4767i			3.54122i
$113$			14.1412i			1.33029i	0.746714	+	0.665145i	$0.231630\pi$
$113$			14.1412i			1.33029i	−0.746714	+	0.665145i	$0.768370\pi$
$114$	−13.2602	+	2.72900i	−1.24193	+	0.255594i
$115$		0			0
$116$	−7.30240			−0.678011
$117$	5.71706	+	13.3013i	0.528543	+	1.22970i
$118$		−	3.82005i		−	0.351664i
$119$			1.90830i			0.174933i
$120$		0			0
$121$	1.87900	−	10.8383i	0.170819	−	0.985303i
$122$		−	11.7719i		−	1.06578i
$123$	1.03293	+	5.01900i	0.0931363	+	0.452548i
$124$	−21.6113			−1.94076
$125$		0			0
$126$	−10.4722	−	24.3645i	−0.932936	−	2.17056i
$127$		−	8.15999i		−	0.724082i	−0.932162	−	0.362041i	$-0.882080\pi$
$127$		−	8.15999i		−	0.724082i	0.932162	−	0.362041i	$-0.117920\pi$
$128$	9.48546			0.838405
$129$	12.1369	−	2.49782i	1.06859	−	0.219921i
$130$		0			0
$131$	10.9367			0.955540			0.477770	−	0.878485i	$-0.341445\pi$
$131$	10.9367			0.955540			0.477770	+	0.878485i	$0.341445\pi$
$132$	−22.6797	−	17.9039i	−1.97402	−	1.55833i
$133$	9.82855			0.852244
$134$	14.6951			1.26946
$135$		0			0
$136$	4.59822			0.394294
$137$		−	8.89036i		−	0.759555i	−0.925078	−	0.379777i	$-0.876001\pi$
$137$		−	8.89036i		−	0.759555i	0.925078	−	0.379777i	$-0.123999\pi$
$138$	33.0551	−	6.80288i	2.81383	−	0.579099i
$139$		−	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
$142$		−	13.2023i		−	1.10792i
$143$	−10.3060	−	12.2464i	−0.861829	−	1.02410i
$144$	−30.9814	+	13.3162i	−2.58178	+	1.10969i
$145$		0			0
$146$			7.19652i			0.595588i
$147$	1.43702	+	6.98244i	0.118523	+	0.575902i
$148$	−49.9926			−4.10936
$149$	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	$0.00219780\pi$
$151$			0.169689i			0.0138091i	−0.999976	+	0.00690454i	$0.997802\pi$
$152$		−	23.6829i		−	1.92093i
$153$	−1.57756	+	0.678055i	−0.127538	+	0.0548175i
$154$	18.8779	+	22.4323i	1.52122	+	1.80764i
$155$		0			0
$156$	−41.1814	+	8.47531i	−3.29715	+	0.678568i
$157$	7.11061			0.567489			0.283744	−	0.958900i	$-0.408423\pi$
$157$	7.11061			0.567489			0.283744	+	0.958900i	$0.408423\pi$
$158$		−	26.0698i		−	2.07400i
$159$	11.2653	−	2.31846i	0.893400	−	0.183866i
$160$		0			0
$161$	−24.5007			−1.93093
$162$	16.4207	−	17.3144i	1.29013	−	1.36034i
$163$	5.59822			0.438487			0.219243	−	0.975670i	$-0.429641\pi$
$163$	5.59822			0.438487			0.219243	+	0.975670i	$0.429641\pi$
$164$	−14.8809			−1.16200
$165$		0			0
$166$	−28.9340			−2.24571
$167$	−7.95364			−0.615471			−0.307735	−	0.951472i	$-0.599571\pi$
$167$	−7.95364			−0.615471			−0.307735	+	0.951472i	$0.599571\pi$
$168$	45.4400	−	9.35174i	3.50577	−	0.721503i
$169$	−10.2898			−0.791525
$170$		0			0
$171$	3.49228	+	8.12510i	0.267061	+	0.621342i
$172$			35.9848i			2.74382i
$173$	20.3558			1.54763			0.773813	−	0.633414i	$-0.218347\pi$
$173$	20.3558			1.54763			0.773813	+	0.633414i	$0.218347\pi$
$174$	1.34395	+	6.53025i	0.101885	+	0.495057i
$175$		0			0
$176$	28.5245	−	24.0048i	2.15011	−	1.80943i
$177$	−2.44425	+	0.503036i	−0.183721	+	0.0378105i
$178$			36.6405i			2.74632i
$179$		−	4.67052i		−	0.349091i	−0.984649	−	0.174545i	$-0.944154\pi$
$179$		−	4.67052i		−	0.349091i	0.984649	−	0.174545i	$-0.0558456\pi$
$180$		0			0
$181$	0.301708			0.0224258			0.0112129	−	0.999937i	$-0.496431\pi$
$181$	0.301708			0.0224258			0.0112129	+	0.999937i	$0.496431\pi$
$182$	42.6609			3.16224
$183$	−7.53220	+	1.55016i	−0.556796	+	0.114591i
$184$			59.0369i			4.35226i
$185$		0			0
$186$	3.97741	+	19.3262i	0.291638	+	1.41706i
$187$	1.45245	−	1.22231i	0.106214	−	0.0893841i
$188$			1.58638i			0.115699i
$189$	−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	$-0.0440170\pi$
$192$	−4.86673	−	23.6474i	−0.351226	−	1.70660i
$193$		−	24.3743i		−	1.75450i	−0.480033	−	0.877251i	$-0.659375\pi$
$193$		−	24.3743i		−	1.75450i	0.480033	−	0.877251i	$-0.340625\pi$
$194$	−41.7815			−2.99974
$195$		0			0
$196$	−20.7024			−1.47874
$197$	−5.66476			−0.403597			−0.201799	−	0.979427i	$-0.564679\pi$
$197$	−5.66476			−0.403597			−0.201799	+	0.979427i	$0.564679\pi$
$198$	−11.8367	+	23.5767i	−0.841198	+	1.67552i
$199$	2.42270			0.171741			0.0858705	−	0.996306i	$-0.472633\pi$
$199$	2.42270			0.171741			0.0858705	+	0.996306i	$0.472633\pi$
$200$		0			0
$201$	−1.93509	−	9.40258i	−0.136491	−	0.663207i
$202$	35.7533			2.51559
$203$		−	4.84028i		−	0.339721i
$204$	−1.00519	−	4.88420i	−0.0703773	−	0.341962i
$205$		0			0
$206$	32.2274			2.24539
$207$	−8.70560	−	20.2544i	−0.605081	−	1.40778i
$208$		−	54.2468i		−	3.76134i
$209$	−6.29543	−	7.48075i	−0.435464	−	0.517454i
$210$		0			0
$211$		−	1.14171i		−	0.0785986i	−0.999227	−	0.0392993i	$-0.987487\pi$
$211$		−	1.14171i		−	0.0785986i	0.999227	−	0.0392993i	$-0.0125126\pi$
$212$			33.4008i			2.29398i
$213$	−8.44748	+	1.73853i	−0.578812	+	0.119122i
$214$	−28.4777			−1.94669
$215$		0			0
$216$	23.8767	+	34.2416i	1.62460	+	2.32985i
$217$		−	14.3247i		−	0.972427i
$218$			27.7131i			1.87697i
$219$	4.60467	−	0.947661i	0.311155	−	0.0640370i
$220$		0			0
$221$		−	2.76222i		−	0.185807i
$222$	9.20077	+	44.7064i	0.617515	+	3.00050i
$223$	−20.6584			−1.38339			−0.691694	−	0.722191i	$-0.743135\pi$
$223$	−20.6584			−1.38339			−0.691694	+	0.722191i	$0.743135\pi$
$224$			45.7969i			3.05994i
$225$		0			0
$226$			37.4941i			2.49407i
$227$	9.60902			0.637773			0.318887	−	0.947793i	$-0.396691\pi$
$227$	9.60902			0.637773			0.318887	+	0.947793i	$0.396691\pi$
$228$	−25.1557	+	5.17716i	−1.66598	+	0.342866i
$229$	−8.21090			−0.542592			−0.271296	−	0.962496i	$-0.587452\pi$
$229$	−8.21090			−0.542592			−0.271296	+	0.962496i	$0.587452\pi$
$230$		0			0
$231$	11.8673	−	15.0329i	0.780812	−	0.989093i
$232$	−11.6631			−0.765722
$233$	3.40964			0.223373			0.111687	−	0.993743i	$-0.464375\pi$
$233$	3.40964			0.223373			0.111687	+	0.993743i	$0.464375\pi$
$234$	15.1583	+	35.2671i	0.990927	+	2.30548i
$235$		0			0
$236$		−	7.24699i		−	0.471739i
$237$	−16.6807	+	3.43295i	−1.08353	+	0.222994i
$238$			5.05967i			0.327970i
$239$	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	$-0.935706\pi$
$241$		−	6.22878i		−	0.401231i	0.979670	−	0.200615i	$-0.0642942\pi$
$242$	4.98201	−	28.7368i	0.320256	−	1.84727i
$243$	−13.2409	−	8.22674i	−0.849402	−	0.527746i
$244$		−	22.3324i		−	1.42968i
$245$		0			0
$246$	2.73872	+	13.3074i	0.174615	+	0.848450i
$247$	−14.2266			−0.905219
$248$	−34.5169			−2.19182
$249$	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	$-0.0843103\pi$
$252$	−19.8667	−	46.2217i	−1.25148	−	2.91169i
$253$	15.6933	+	18.6481i	0.986631	+	1.17240i
$254$		−	21.6355i		−	1.35753i
$255$		0			0
$256$	−2.72804			−0.170502
$257$		−	16.7578i		−	1.04532i	−0.852541	−	0.522661i	$-0.824939\pi$
$257$		−	16.7578i		−	1.04532i	0.852541	−	0.522661i	$-0.175061\pi$
$258$	32.1798	−	6.62274i	2.00343	−	0.412314i
$259$		−	33.1368i		−	2.05902i
$260$		0			0
$261$	4.00138	−	1.71985i	0.247679	−	0.106456i
$262$	28.9975			1.79147
$263$	28.9110			1.78273			0.891363	−	0.453290i	$-0.149750\pi$
$263$	28.9110			1.78273			0.891363	+	0.453290i	$0.149750\pi$
$264$	−36.2232	−	28.5955i	−2.22939	−	1.75993i
$265$		0			0
$266$	26.0595			1.59781
$267$	23.4443	−	4.82494i	1.43477	−	0.295282i
$268$	27.8779			1.70291
$269$			17.1683i			1.04677i	0.852096	+	0.523386i	$0.175331\pi$
$269$			17.1683i			1.04677i	−0.852096	+	0.523386i	$0.824669\pi$
$270$		0			0
$271$		−	29.3341i		−	1.78192i	−0.454084	−	0.890959i	$-0.650033\pi$
$271$		−	29.3341i		−	1.78192i	0.454084	−	0.890959i	$-0.349967\pi$
$272$	6.43378			0.390106
$273$	−5.61773	−	27.2965i	−0.340000	−	1.65206i
$274$		−	23.5720i		−	1.42404i
$275$		0			0
$276$	62.7085	−	12.9057i	3.77461	−	0.776831i
$277$			19.8345i			1.19174i	0.803080	+	0.595871i	$0.203193\pi$
$277$			19.8345i			1.19174i	−0.803080	+	0.595871i	$0.796807\pi$
$278$		−	41.5324i		−	2.49095i
$279$	11.8420	−	5.08986i	0.708964	−	0.304722i
$280$		0			0
$281$	−18.2528			−1.08887			−0.544436	−	0.838802i	$-0.683256\pi$
$281$	−18.2528			−1.08887			−0.544436	+	0.838802i	$0.683256\pi$
$282$	1.41864	−	0.291962i	0.0844786	−	0.0173861i
$283$		−	20.6708i		−	1.22875i	−0.789015	−	0.614374i	$-0.789409\pi$
$283$		−	20.6708i		−	1.22875i	0.789015	−	0.614374i	$-0.210591\pi$
$284$		−	25.0461i		−	1.48621i
$285$		0			0
$286$	−27.3254	−	32.4703i	−1.61578	−	1.92001i
$287$		−	9.86359i		−	0.582229i
$288$	−37.8596	+	16.2726i	−2.23090	+	0.958870i
$289$	−16.6724			−0.980729
$290$		0			0
$291$	5.50192	+	26.7338i	0.322529	+	1.56716i
$292$			13.6525i			0.798950i
$293$	15.6431			0.913881			0.456941	−	0.889497i	$-0.348945\pi$
$293$	15.6431			0.913881			0.456941	+	0.889497i	$0.348945\pi$
$294$	3.81012	+	18.5133i	0.222211	+	1.07972i
$295$		0			0
$296$	−79.8463			−4.64097
$297$	16.6442	+	4.46903i	0.965792	+	0.259319i
$298$	16.8130			0.973949
$299$	35.4643			2.05096
$300$		0			0
$301$	−23.8520			−1.37481
$302$			0.449914i			0.0258897i
$303$	−4.70810	−	22.8766i	−0.270474	−	1.31423i
$304$		−	33.1368i		−	1.90053i
$305$		0			0
$306$	−4.18275	+	1.79780i	−0.239112	+	0.102773i
$307$		−	3.01197i		−	0.171902i	−0.996299	−	0.0859512i	$-0.972607\pi$
$307$		−	3.01197i		−	0.171902i	0.996299	−	0.0859512i	$-0.0273929\pi$
$308$	35.8131	+	42.5561i	2.04064	+	2.42486i
$309$	−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	$0.920248\pi$
$312$	−65.7735	+	13.5365i	−3.72369	+	0.766351i
$313$	7.98577			0.451382			0.225691	−	0.974199i	$-0.427536\pi$
$313$	7.98577			0.451382			0.225691	+	0.974199i	$0.427536\pi$
$314$	18.8531			1.06394
$315$		0			0
$316$		−	49.4568i		−	2.78216i
$317$			28.5166i			1.60165i	0.598897	+	0.800826i	$0.295606\pi$
$317$			28.5166i			1.60165i	−0.598897	+	0.800826i	$0.704394\pi$
$318$	29.8690	−	6.14718i	1.67497	−	0.344717i
$319$	−3.68406	+	3.10032i	−0.206268	+	0.173585i
$320$		0			0
$321$	3.75003	+	18.2213i	0.209306	+	1.01702i
$322$	−64.9615			−3.62016
$323$		−	1.68731i		−	0.0938843i
$324$	31.1517	−	32.8469i	1.73065	−	1.82483i
$325$		0			0
$326$	14.8432			0.822088
$327$	17.7322	−	3.64936i	0.980591	−	0.201810i
$328$	−23.7673			−1.31233
$329$	−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	$0.597888\pi$
$332$	−54.8904			−3.01250
$333$	27.3937	−	11.7742i	1.50116	−	0.645220i
$334$	−21.0883			−1.15390
$335$		0			0
$336$	63.5791	−	13.0849i	3.46853	−	0.713838i
$337$			8.82652i			0.480811i	0.970673	+	0.240406i	$0.0772804\pi$
$337$			8.82652i			0.480811i	−0.970673	+	0.240406i	$0.922720\pi$
$338$	−27.2825			−1.48397
$339$	23.9905	−	4.93734i	1.30298	−	0.268159i
$340$		0			0
$341$	−10.9029	+	9.17535i	−0.590426	+	0.496873i
$342$	9.25946	+	21.5430i	0.500694	+	1.16491i
$343$			9.61602i			0.519216i
$344$			57.4737i			3.09877i
$345$		0			0
$346$	53.9716			2.90153
$347$	20.6938			1.11090			0.555451	−	0.831550i	$-0.312546\pi$
$347$	20.6938			1.11090			0.555451	+	0.831550i	$0.312546\pi$
$348$	2.54960	+	12.3885i	0.136673	+	0.664093i
$349$		−	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
$352$	34.8572	−	29.3341i	1.85789	−	1.56351i
$353$		−	5.13152i		−	0.273123i	−0.990632	−	0.136562i	$-0.956395\pi$
$353$		−	5.13152i		−	0.273123i	0.990632	−	0.136562i	$-0.0436052\pi$
$354$	−6.48069	+	1.33375i	−0.344445	+	0.0708883i
$355$		0			0
$356$			69.5105i			3.68405i
$357$	3.23741	−	0.666274i	0.171342	−	0.0352630i
$358$		−	12.3834i		−	0.654485i
$359$	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
$362$	0.799951			0.0420445
$363$	−19.0432	+	0.596439i	−0.999510	+	0.0313049i
$364$	80.9317			4.24198
$365$		0			0
$366$	−19.9709	+	4.11011i	−1.04390	+	0.214839i
$367$	−1.25488			−0.0655044			−0.0327522	−	0.999464i	$-0.510427\pi$
$367$	−1.25488			−0.0655044			−0.0327522	+	0.999464i	$0.510427\pi$
$368$			82.6038i			4.30602i
$369$	8.15407	−	3.50473i	0.424484	−	0.182449i
$370$		0			0
$371$	−22.1392			−1.14941
$372$	7.54551	+	36.6635i	0.391217	+	1.90092i
$373$			25.7304i			1.33227i	0.745831	+	0.666135i	$0.232053\pi$
$373$			25.7304i			1.33227i	−0.745831	+	0.666135i	$0.767947\pi$
$374$	3.85104	−	3.24084i	0.199133	−	0.167580i
$375$		0			0
$376$			2.53371i			0.130666i
$377$			7.00621i			0.360838i
$378$	−37.6779	+	26.2728i	−1.93794	+	1.35133i
$379$	3.89324			0.199982			0.0999911	−	0.994988i	$-0.468119\pi$
$379$	3.89324			0.199982			0.0999911	+	0.994988i	$0.468119\pi$
$380$		0			0
$381$	−13.8434	+	2.84903i	−0.709218	+	0.145960i
$382$		−	10.1020i		−	0.516865i
$383$		−	10.7658i		−	0.550107i	−0.961429	−	0.275054i	$-0.911304\pi$
$383$		−	10.7658i		−	0.550107i	0.961429	−	0.275054i	$-0.0886956\pi$
$384$	−3.31181	−	16.0920i	−0.169005	−	0.821194i
$385$		0			0
$386$		−	64.6263i		−	3.28939i
$387$	−8.47508	−	19.7180i	−0.430813	−	1.00232i
$388$	−79.2634			−4.02399
$389$			5.82384i			0.295281i	0.989041	+	0.147640i	$0.0471678\pi$
$389$			5.82384i			0.295281i	−0.989041	+	0.147640i	$0.952832\pi$
$390$		0			0
$391$			4.20614i			0.212714i
$392$	−33.0651			−1.67004
$393$	−3.81849	−	18.5540i	−0.192617	−	0.935925i
$394$	−15.0196			−0.756676
$395$		0			0
$396$	−22.4553	+	44.7271i	−1.12842	+	2.24762i
$397$	−6.12077			−0.307193			−0.153596	−	0.988134i	$-0.549086\pi$
$397$	−6.12077			−0.307193			−0.153596	+	0.988134i	$0.549086\pi$
$398$	6.42358			0.321985
$399$	−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	$0.884378\pi$
$402$	−5.13072	−	24.9301i	−0.255897	−	1.24340i
$403$			20.7348i			1.03287i
$404$	67.8273			3.37453
$405$		0			0
$406$		−	12.8336i		−	0.636919i
$407$	−25.2212	+	21.2249i	−1.25017	+	1.05208i
$408$	−1.60545	−	7.80086i	−0.0794817	−	0.386200i
$409$			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
$412$	61.1383			3.01207
$413$	4.80355			0.236367
$414$	−23.0821	−	53.7026i	−1.13442	−	2.63934i
$415$		0			0
$416$		−	66.2902i		−	3.25014i
$417$	−26.5744	+	5.46912i	−1.30135	+	0.267824i
$418$	−16.6918	−	19.8345i	−0.816420	−	0.970139i
$419$			5.81275i			0.283972i	0.989869	+	0.141986i	$0.0453487\pi$
$419$			5.81275i			0.283972i	−0.989869	+	0.141986i	$0.954651\pi$
$420$		0			0
$421$	−5.61246			−0.273534			−0.136767	−	0.990603i	$-0.543671\pi$
$421$	−5.61246			−0.273534			−0.136767	+	0.990603i	$0.543671\pi$
$422$		−	3.02714i		−	0.147359i
$423$	−0.373621	−	0.869264i	−0.0181661	−	0.0422651i
$424$			53.3466i			2.59074i
$425$		0			0
$426$	−22.3977	+	4.60955i	−1.08517	+	0.223333i
$427$	14.8027			0.716351
$428$	−54.0248			−2.61139
$429$	−17.1777	+	21.7598i	−0.829348	+	1.05057i
$430$		0			0
$431$	3.74761			0.180516			0.0902579	−	0.995918i	$-0.471231\pi$
$431$	3.74761			0.180516			0.0902579	+	0.995918i	$0.471231\pi$
$432$	33.4080	+	47.9105i	1.60734	+	2.30510i
$433$	−25.0094			−1.20188			−0.600938	−	0.799296i	$-0.705206\pi$
$433$	−25.0094			−1.20188			−0.600938	+	0.799296i	$0.705206\pi$
$434$		−	37.9807i		−	1.82313i
$435$		0			0
$436$			52.5744i			2.51786i
$437$	21.6635			1.03630
$438$	12.2089	−	2.51264i	0.583362	−	0.120058i
$439$			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
$442$		−	7.32377i		−	0.348356i
$443$		−	14.0900i		−	0.669434i	−0.942319	−	0.334717i	$-0.891359\pi$
$443$		−	14.0900i		−	0.669434i	0.942319	−	0.334717i	$-0.108641\pi$
$444$	17.4547	+	84.8122i	0.828364	+	4.02501i
$445$		0			0
$446$	−54.7738			−2.59362
$447$	−2.21399	−	10.7577i	−0.104718	−	0.508823i
$448$			46.4729i			2.19564i
$449$		−	13.5543i		−	0.639669i	−0.947473	−	0.319835i	$-0.896373\pi$
$449$		−	13.5543i		−	0.639669i	0.947473	−	0.319835i	$-0.103627\pi$
$450$		0			0
$451$	−7.50742	+	6.31787i	−0.353511	+	0.297497i
$452$			71.1297i			3.34566i
$453$	0.287876	−	0.0592462i	0.0135256	−	0.00278363i
$454$	25.4774			1.19572
$455$		0			0
$456$	−40.1779	+	8.26878i	−1.88150	+	0.387221i
$457$			6.03744i			0.282419i	0.989980	+	0.141210i	$0.0450992\pi$
$457$			6.03744i			0.282419i	−0.989980	+	0.141210i	$0.954901\pi$
$458$	−21.7705			−1.01727
$459$	1.70112	+	2.43958i	0.0794013	+	0.113870i
$460$		0			0
$461$	4.15570			0.193550			0.0967751	−	0.995306i	$-0.469147\pi$
$461$	4.15570			0.193550			0.0967751	+	0.995306i	$0.469147\pi$
$462$	31.4651	−	39.8584i	1.46389	−	1.85438i
$463$	21.0953			0.980380			0.490190	−	0.871616i	$-0.336927\pi$
$463$	21.0953			0.980380			0.490190	+	0.871616i	$0.336927\pi$
$464$	−16.3189			−0.757587
$465$		0			0
$466$	9.04035			0.418786
$467$		−	29.9238i		−	1.38471i	−0.721559	−	0.692353i	$-0.756574\pi$
$467$		−	29.9238i		−	1.38471i	0.721559	−	0.692353i	$-0.243426\pi$
$468$	28.7566	+	66.9049i	1.32928	+	3.09268i
$469$			18.4784i			0.853254i
$470$		0			0
$471$	−2.48264	−	12.0631i	−0.114394	−	0.555839i
$472$		−	11.5746i		−	0.532765i
$473$	15.2778	+	18.1543i	0.702473	+	0.834737i
$474$	−44.2273	+	9.10216i	−2.03142	+	0.418076i
$475$		0			0
$476$			9.59867i			0.439954i
$477$	−7.86650	−	18.3021i	−0.360182	−	0.837997i
$478$	12.6879			0.580331
$479$	−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
$482$		−	16.5150i		−	0.752239i
$483$	8.55434	+	41.5654i	0.389236	+	1.89129i
$484$	9.45133	−	54.5165i	0.429606	−	2.47802i
$485$		0			0
$486$	−35.1070	−	21.8125i	−1.59248	−	0.989433i
$487$	−14.4863			−0.656435			−0.328218	−	0.944602i	$-0.606448\pi$
$487$	−14.4863			−0.656435			−0.328218	+	0.944602i	$0.606448\pi$
$488$		−	35.6684i		−	1.61463i
$489$	−1.95460	−	9.49736i	−0.0883900	−	0.429485i
$490$		0			0
$491$	3.38270			0.152659			0.0763295	−	0.997083i	$-0.475680\pi$
$491$	3.38270			0.152659			0.0763295	+	0.997083i	$0.475680\pi$
$492$	5.19561	+	25.2454i	0.234236	+	1.13815i
$493$	−0.830951			−0.0374242
$494$	−37.7206			−1.69713
$495$		0			0
$496$	−48.2956			−2.16854
$497$	16.6014			0.744675
$498$	10.1022	+	49.0864i	0.452690	+	2.19961i
$499$	39.8979			1.78608			0.893038	−	0.449981i	$-0.148569\pi$
$499$	39.8979			1.78608			0.893038	+	0.449981i	$0.148569\pi$
$500$		0			0
$501$	2.77698	+	13.4933i	0.124066	+	0.602837i
$502$		−	21.9930i		−	0.981595i
$503$	35.4512			1.58069			0.790345	−	0.612663i	$-0.209902\pi$
$503$	35.4512			1.58069			0.790345	+	0.612663i	$0.209902\pi$
$504$	−31.7304	−	73.8236i	−1.41338	−	3.28836i
$505$		0			0
$506$	41.6094	+	49.4438i	1.84976	+	2.19804i
$507$	3.59265	+	17.4566i	0.159555	+	0.775277i
$508$		−	41.0445i		−	1.82106i
$509$		−	36.9701i		−	1.63867i	−0.573314	−	0.819336i	$-0.694343\pi$
$509$		−	36.9701i		−	1.63867i	0.573314	−	0.819336i	$-0.305657\pi$
$510$		0			0
$511$	−9.04933			−0.400319
$512$	−26.2041			−1.15807
$513$	12.5649	−	8.76149i	0.554753	−	0.386829i
$514$		−	44.4317i		−	1.95980i
$515$		0			0
$516$	61.0481	−	12.5640i	2.68749	−	0.553098i
$517$	0.673516	+	0.800328i	0.0296212	+	0.0351984i
$518$		−	87.8592i		−	3.86031i
$519$	−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	$0.728082\pi$
$522$	10.6093	−	4.56002i	0.464356	−	0.199587i
$523$			14.1558i			0.618990i	0.950901	+	0.309495i	$0.100160\pi$
$523$			14.1558i			0.618990i	−0.950901	+	0.309495i	$0.899840\pi$
$524$	55.0110			2.40317
$525$		0			0
$526$	76.6548			3.34231
$527$	−2.45919			−0.107124
$528$	−50.6832	−	40.0105i	−2.20570	−	1.74123i
$529$	−31.0030			−1.34795
$530$		0			0
$531$	1.70680	+	3.97102i	0.0740687	+	0.172328i
$532$	49.4373			2.14338
$533$			14.2773i			0.618421i
$534$	62.1605	−	12.7929i	2.68995	−	0.553603i
$535$		0			0
$536$	44.5256			1.92321
$537$	−7.92351	+	1.63069i	−0.341925	+	0.0703696i
$538$			45.5202i			1.96252i
$539$	−10.4443	+	8.78943i	−0.449869	+	0.378588i
$540$		0			0
$541$			23.3325i			1.00314i	0.865116	+	0.501572i	$0.167245\pi$
$541$			23.3325i			1.00314i	−0.865116	+	0.501572i	$0.832755\pi$
$542$		−	77.7766i		−	3.34079i
$543$	−0.105340	−	0.511846i	−0.00452058	−	0.0219654i
$544$	7.86215			0.337087
$545$		0			0
$546$	−14.8949	−	72.3741i	−0.637443	−	3.09732i
$547$		−	36.5881i		−	1.56439i	−0.623032	−	0.782196i	$-0.714099\pi$
$547$		−	36.5881i		−	1.56439i	0.623032	−	0.782196i	$-0.285901\pi$
$548$		−	44.7182i		−	1.91027i
$549$	5.25968	+	12.2371i	0.224478	+	0.522267i
$550$		0			0
$551$			4.27976i			0.182324i
$552$	100.156	−	20.6125i	4.26292	−	0.877327i
$553$	32.7817			1.39402
$554$			52.5895i			2.23431i
$555$		0			0
$556$		−	78.7908i		−	3.34148i
$557$	37.6480			1.59520			0.797598	−	0.603189i	$-0.206104\pi$
$557$	37.6480			1.59520			0.797598	+	0.603189i	$0.206104\pi$
$558$	31.3981	−	13.4953i	1.32919	−	0.571302i
$559$	34.5253			1.46026
$560$		0			0
$561$	−2.58076	−	2.03731i	−0.108960	−	0.0860153i
$562$	−48.3957			−2.04145
$563$	6.93067			0.292093			0.146046	−	0.989278i	$-0.453345\pi$
$563$	6.93067			0.292093			0.146046	+	0.989278i	$0.453345\pi$
$564$	2.69129	−	0.553878i	0.113324	−	0.0233225i
$565$		0			0
$566$		−	54.8066i		−	2.30369i
$567$	21.7721	+	20.6484i	0.914342	+	0.867151i
$568$		−	40.0027i		−	1.67848i
$569$	−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	$-0.945141\pi$
$571$		−	8.19588i		−	0.342987i	0.985185	−	0.171493i	$-0.0548592\pi$
$572$	−51.8388	−	61.5991i	−2.16749	−	2.57559i
$573$	−6.46375	+	1.33027i	−0.270027	+	0.0555727i
$574$		−	26.1524i		−	1.09158i
$575$		0			0
$576$	−38.4184	+	16.5128i	−1.60077	+	0.688032i
$577$	5.54710			0.230929			0.115464	−	0.993312i	$-0.463164\pi$
$577$	5.54710			0.230929			0.115464	+	0.993312i	$0.463164\pi$
$578$	−44.2053			−1.83870
$579$	−41.3509	+	8.51020i	−1.71849	+	0.353672i
$580$		0			0
$581$		−	36.3833i		−	1.50943i
$582$	14.5879	+	70.8821i	0.604686	+	2.93816i
$583$	14.1807	+	16.8507i	0.587305	+	0.697885i
$584$			21.8052i			0.902307i
$585$		0			0
$586$	41.4763			1.71337
$587$		−	14.1083i		−	0.582313i	−0.956675	−	0.291157i	$-0.905960\pi$
$587$		−	14.1083i		−	0.582313i	0.956675	−	0.291157i	$-0.0940401\pi$
$588$	7.22815	+	35.1215i	0.298084	+	1.44838i
$589$			12.6659i			0.521889i
$590$		0			0
$591$	1.97783	+	9.61023i	0.0813569	+	0.395312i
$592$	−111.720			−4.59167
$593$	−33.2280			−1.36451			−0.682255	−	0.731115i	$-0.739000\pi$
$593$	−33.2280			−1.36451			−0.682255	+	0.731115i	$0.739000\pi$
$594$	44.1305	+	11.8492i	1.81069	+	0.486179i
$595$		0			0
$596$	31.8958			1.30650
$597$	−0.845878	−	4.11011i	−0.0346195	−	0.168215i
$598$	94.0305			3.84519
$599$			23.7135i			0.968909i	0.874817	+	0.484454i	$0.160982\pi$
$599$			23.7135i			0.968909i	−0.874817	+	0.484454i	$0.839018\pi$
$600$		0			0
$601$		−	23.2762i		−	0.949457i	−0.880132	−	0.474729i	$-0.842546\pi$
$601$		−	23.2762i		−	0.949457i	0.880132	−	0.474729i	$-0.157454\pi$
$602$	−63.2414			−2.57753
$603$	−15.2758	+	6.56575i	−0.622079	+	0.267378i
$604$			0.853529i			0.0347296i
$605$		0			0
$606$	−12.4831	−	60.6552i	−0.507092	−	2.46395i
$607$		−	12.9968i		−	0.527523i	−0.964588	−	0.263761i	$-0.915037\pi$
$607$		−	12.9968i		−	0.527523i	0.964588	−	0.263761i	$-0.0849631\pi$
$608$		−	40.4935i		−	1.64223i
$609$	−8.21152	+	1.68997i	−0.332747	+	0.0684809i
$610$		0			0
$611$	1.52204			0.0615750
$612$	−7.93506	+	3.41060i	−0.320756	+	0.137865i
$613$		−	46.0228i		−	1.85884i	−0.369018	−	0.929422i	$-0.620306\pi$
$613$		−	46.0228i		−	1.85884i	0.369018	−	0.929422i	$-0.379694\pi$
$614$		−	7.98597i		−	0.322288i
$615$		0			0
$616$	57.1994	+	67.9691i	2.30463	+	2.73855i
$617$			2.88152i			0.116006i	0.998316	+	0.0580029i	$0.0184733\pi$
$617$			2.88152i			0.116006i	−0.998316	+	0.0580029i	$0.981527\pi$
$618$	−11.2521	−	54.6736i	−0.452624	−	2.19930i
$619$	−35.3993			−1.42282			−0.711409	−	0.702778i	$-0.751943\pi$
$619$	−35.3993			−1.42282			−0.711409	+	0.702778i	$0.751943\pi$
$620$		0			0
$621$	−31.3219	+	21.8407i	−1.25690	+	0.876439i
$622$			23.1859i			0.929669i
$623$	−46.0739			−1.84591
$624$	−92.0295	+	18.9401i	−3.68413	+	0.758210i
$625$		0			0
$626$	21.1735			0.846264
$627$	−10.4930	+	13.2920i	−0.419052	+	0.530833i
$628$	35.7662			1.42722
$629$	−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	$0.272868\pi$
$632$		−	78.9906i		−	3.14208i
$633$	−1.93691	+	0.398624i	−0.0769851	+	0.0158439i
$634$			75.6092i			3.00282i
$635$		0			0
$636$	56.6643	−	11.6618i	2.24689	−	0.462419i
$637$			19.8627i			0.786988i
$638$	−9.76794	+	8.22021i	−0.386717	+	0.325441i
$639$	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	$-0.238592\pi$
$642$	9.94287	+	48.3122i	0.392414	+	1.90673i
$643$	−49.6440			−1.95777			−0.978885	−	0.204413i	$-0.934472\pi$
$643$	−49.6440			−1.95777			−0.978885	+	0.204413i	$0.934472\pi$
$644$	−123.238			−4.85626
$645$		0			0
$646$		−	4.47374i		−	0.176017i
$647$			18.9443i			0.744776i	0.928077	+	0.372388i	$0.121461\pi$
$647$			18.9443i			0.744776i	−0.928077	+	0.372388i	$0.878539\pi$
$648$	49.7543	−	52.4620i	1.95453	−	2.06090i
$649$	−3.07679	−	3.65610i	−0.120775	−	0.143515i
$650$		0			0
$651$	−24.3019	+	5.00143i	−0.952465	+	0.196021i
$652$	28.1589			1.10279
$653$			25.8385i			1.01114i	0.862787	+	0.505568i	$0.168717\pi$
$653$			25.8385i			1.01114i	−0.862787	+	0.505568i	$0.831283\pi$
$654$	47.0152	−	9.67594i	1.83844	−	0.378359i
$655$		0			0
$656$	−33.2549			−1.29839
$657$	−3.21541	−	7.48093i	−0.125445	−	0.291859i
$658$	−2.78798			−0.108687
$659$	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	$0.420801\pi$
$662$	−29.2032			−1.13502
$663$	−4.68609	+	0.964418i	−0.181993	+	0.0374549i
$664$	−87.6690			−3.40222
$665$		0			0
$666$	72.6318	−	31.2181i	2.81442	−	1.20968i
$667$		−	10.6686i		−	0.413091i
$668$	−40.0065			−1.54790
$669$	7.21279	+	35.0469i	0.278863	+	1.35499i
$670$		0			0
$671$	−9.48146	−	11.2667i	−0.366028	−	0.434945i
$672$	77.6943	−	15.9898i	2.99712	−	0.616821i
$673$		−	34.8963i		−	1.34515i	−0.740027	−	0.672577i	$-0.765187\pi$
$673$		−	34.8963i		−	1.34515i	0.740027	−	0.672577i	$-0.234813\pi$
$674$			23.4027i			0.901439i
$675$		0			0
$676$	−51.7575			−1.99067
$677$	−12.6332			−0.485532			−0.242766	−	0.970085i	$-0.578055\pi$
$677$	−12.6332			−0.485532			−0.242766	+	0.970085i	$0.578055\pi$
$678$	63.6085	−	13.0909i	2.44287	−	0.502753i
$679$		−	52.5385i		−	2.01624i
$680$		0			0
$681$	−3.35495	−	16.3017i	−0.128562	−	0.624681i
$682$	−28.9081	+	24.3276i	−1.10695	+	0.931552i
$683$			29.2285i			1.11840i	0.829033	+	0.559199i	$0.188891\pi$
$683$			29.2285i			1.11840i	−0.829033	+	0.559199i	$0.811109\pi$
$684$	17.5661	+	40.8690i	0.671655	+	1.56267i
$685$		0			0
$686$			25.4960i			0.973442i
$687$	2.86680	+	13.9298i	0.109375	+	0.531453i
$688$			80.4166i			3.06585i
$689$	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	$0.685328\pi$
$692$	102.389			3.89225
$693$	−29.6467	−	14.8842i	−1.12618	−	0.565403i
$694$	54.8677			2.08275
$695$		0			0
$696$	4.07214	+	19.7864i	0.154354	+	0.750003i
$697$	−1.69332			−0.0641392
$698$		−	20.5659i		−	0.778430i
$699$	−1.19046	−	5.78444i	−0.0450275	−	0.218788i
$700$		0			0
$701$	41.1039			1.55247			0.776237	−	0.630441i	$-0.217126\pi$
$701$	41.1039			1.55247			0.776237	+	0.630441i	$0.217126\pi$
$702$	54.5380	−	38.0293i	2.05840	−	1.43532i
$703$			29.2994i			1.10505i
$704$	35.3717	−	29.7671i	1.33312	−	1.12189i
$705$		0			0
$706$		−	13.6058i		−	0.512059i
$707$			44.9582i			1.69083i
$708$	−12.2945	+	2.53026i	−0.462055	+	0.0950929i
$709$	−10.7479			−0.403646			−0.201823	−	0.979422i	$-0.564687\pi$
$709$	−10.7479			−0.403646			−0.201823	+	0.979422i	$0.564687\pi$
$710$		0			0
$711$	11.6480	+	27.1001i	0.436833	+	1.01633i
$712$			111.020i			4.16064i
$713$		−	31.5737i		−	1.18244i
$714$	8.58371	−	1.76656i	0.321237	−	0.0661120i
$715$		0			0
$716$		−	23.4925i		−	0.877958i
$717$	−1.67078	−	8.11832i	−0.0623966	−	0.303184i
$718$	18.5021			0.690491
$719$		−	6.54813i		−	0.244204i	−0.992518	−	0.122102i	$-0.961036\pi$
$719$		−	6.54813i		−	0.244204i	0.992518	−	0.122102i	$-0.0389635\pi$
$720$		0			0
$721$			40.5246i			1.50922i
$722$	27.3350			1.01730
$723$	−10.5671	+	2.17475i	−0.392995	+	0.0808800i
$724$	1.51758			0.0564004
$725$		0			0
$726$	−50.4914	+	1.58140i	−1.87391	+	0.0586914i
$727$	48.6003			1.80248			0.901242	−	0.433316i	$-0.142656\pi$
$727$	48.6003			1.80248			0.901242	+	0.433316i	$0.142656\pi$
$728$	129.261			4.79074
$729$	−9.33363	+	25.3354i	−0.345690	+	0.938349i
$730$		0			0
$731$			4.09477i			0.151450i
$732$	−37.8867	+	7.79725i	−1.40033	+	0.288195i
$733$			25.1881i			0.930345i	0.885220	+	0.465172i	$0.154008\pi$
$733$			25.1881i			0.930345i	−0.885220	+	0.465172i	$0.845992\pi$
$734$	−3.32721			−0.122810
$735$		0			0
$736$			100.943i			3.72080i
$737$	14.0644	−	11.8359i	0.518068	−	0.435980i
$738$	21.6198	−	9.29247i	0.795835	−	0.342060i
$739$			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
$742$	−58.7001			−2.15495
$743$	18.2670			0.670151			0.335076	−	0.942191i	$-0.391238\pi$
$743$	18.2670			0.670151			0.335076	+	0.942191i	$0.391238\pi$
$744$	12.0514	+	58.5577i	0.441827	+	2.14683i
$745$		0			0
$746$			68.2219i			2.49778i
$747$	30.0775	−	12.9277i	1.10048	−	0.473000i
$748$	7.30578	−	6.14818i	0.267126	−	0.224800i
$749$		−	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	$0.354794\pi$
$752$			3.54514i			0.129278i
$753$	−14.0721	+	2.89611i	−0.512817	+	0.105540i
$754$			18.5763i			0.676510i
$755$		0			0
$756$	−71.4785	+	49.8419i	−2.59965	+	1.81273i
$757$	−26.2443			−0.953864			−0.476932	−	0.878940i	$-0.658251\pi$
$757$	−26.2443			−0.953864			−0.476932	+	0.878940i	$0.658251\pi$
$758$	10.3226			0.374932
$759$	26.1572	−	33.1346i	0.949445	−	1.20271i
$760$		0			0
$761$	30.6299			1.11033			0.555166	−	0.831740i	$-0.312655\pi$
$761$	30.6299			1.11033			0.555166	+	0.831740i	$0.312655\pi$
$762$	−36.7045	+	7.55394i	−1.32966	+	0.273650i
$763$	−34.8481			−1.26159
$764$		−	19.1645i		−	0.693347i
$765$		0			0
$766$		−	28.5446i		−	1.03136i
$767$	−6.95305			−0.251060
$768$	0.952484	+	4.62810i	0.0343698	+	0.167002i
$769$			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
$772$		−	122.602i		−	4.41254i
$773$			26.7071i			0.960587i	0.877108	+	0.480293i	$0.159470\pi$
$773$			26.7071i			0.960587i	−0.877108	+	0.480293i	$0.840530\pi$
$774$	−22.4709	−	52.2806i	−0.807700	−	1.87919i
$775$		0			0
$776$	−126.597			−4.54456
$777$	−56.2164	+	11.5696i	−2.01675	+	0.415057i
$778$			15.4414i			0.553601i
$779$			8.72135i			0.312475i
$780$		0			0
$781$	−10.6336	−	12.6357i	−0.380500	−	0.452142i
$782$			11.1522i			0.398802i
$783$	−4.31478	−	6.18785i	−0.154198	−	0.221136i
$784$	−46.2643			−1.65230
$785$		0			0
$786$	−10.1244	−	49.1942i	−0.361125	−	1.75470i
$787$		−	45.9402i		−	1.63759i	−0.574085	−	0.818796i	$-0.694642\pi$
$787$		−	45.9402i		−	1.63759i	0.574085	−	0.818796i	$-0.305358\pi$
$788$	−28.4935			−1.01504
$789$	−10.0942	−	49.0473i	−0.359361	−	1.74613i
$790$		0			0
$791$	−47.1472			−1.67636
$792$	−35.8649	+	71.4366i	−1.27440	+	2.53839i
$793$	−21.4266			−0.760879
$794$	−16.2287			−0.575934
$795$		0			0
$796$	12.1861			0.431926
$797$			21.9069i			0.775983i	0.921663	+	0.387991i	$0.126831\pi$
$797$			21.9069i			0.775983i	−0.921663	+	0.387991i	$0.873169\pi$
$798$	−9.09858	−	44.2098i	−0.322086	−	1.56501i
$799$			0.180517i			0.00638622i
$800$		0			0
$801$	−16.3710	−	38.0886i	−0.578440	−	1.34579i
$802$			37.7290i			1.33226i
$803$	5.79632	+	6.88767i	0.204548	+	0.243060i
$804$	−9.73345	−	47.2947i	−0.343272	−	1.66796i
$805$		0			0
$806$			54.9764i			1.93646i
$807$	29.1260	−	5.99425i	1.02528	−	0.211008i
$808$	108.331			3.81108
$809$	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	$0.254225\pi$
$811$			40.8050i			1.43286i	−0.697660	+	0.716429i	$0.745775\pi$
$812$		−	24.3465i		−	0.854394i
$813$	−49.7651	+	10.2419i	−1.74534	+	0.359198i
$814$	−66.8718	+	56.2760i	−2.34386	+	1.97247i
$815$		0			0
$816$	−2.24633	−	10.9149i	−0.0786373	−	0.382097i
$817$	21.0898			0.737840
$818$			14.6526i			0.512318i
$819$	−44.3469	+	19.0609i	−1.54961	+	0.666042i
$820$		0			0
$821$	35.0794			1.22428			0.612140	−	0.790749i	$-0.290309\pi$
$821$	35.0794			1.22428			0.612140	+	0.790749i	$0.290309\pi$
$822$	−39.9898	+	8.23006i	−1.39480	+	0.287056i
$823$	−41.3499			−1.44137			−0.720684	−	0.693264i	$-0.756172\pi$
$823$	−41.3499			−1.44137			−0.720684	+	0.693264i	$0.756172\pi$
$824$	97.6480			3.40173
$825$		0			0
$826$	12.7362			0.443148
$827$	−1.48329			−0.0515791			−0.0257895	−	0.999667i	$-0.508210\pi$
$827$	−1.48329			−0.0515791			−0.0257895	+	0.999667i	$0.508210\pi$
$828$	−43.7889	−	101.879i	−1.52177	−	3.54053i
$829$	1.95468			0.0678887			0.0339443	−	0.999424i	$-0.489193\pi$
$829$	1.95468			0.0678887			0.0339443	+	0.999424i	$0.489193\pi$
$830$		0			0
$831$	33.6492	−	6.92515i	1.16728	−	0.240231i
$832$		−	67.2687i		−	2.33212i
$833$	−2.35575			−0.0816220
$834$	−70.4596	+	14.5009i	−2.43981	+	0.502124i
$835$		0			0
$836$	−31.6658	−	37.6280i	−1.09518	−	1.30139i
$837$	−12.7695	−	18.3128i	−0.441380	−	0.632984i
$838$			15.4120i			0.532398i
$839$			49.7350i			1.71704i	0.512777	+	0.858522i	$0.328617\pi$
$839$			49.7350i			1.71704i	−0.512777	+	0.858522i	$0.671383\pi$
$840$		0			0
$841$	−26.8923			−0.927322
$842$	−14.8809			−0.512830
$843$	6.37290	+	30.9658i	0.219494	+	1.06652i
$844$		−	5.74277i		−	0.197674i
$845$		0			0
$846$	−0.990623	−	2.30477i	−0.0340583	−	0.0792398i
$847$	36.1354	+	6.26467i	1.24163	+	0.215257i
$848$			74.6420i			2.56322i
$849$	−35.0678	+	7.21711i	−1.20352	+	0.247691i
$850$		0			0
$851$		−	73.0380i		−	2.50371i
$852$	−42.4906	+	8.74474i	−1.45570	+	0.299590i
$853$		−	45.5368i		−	1.55915i	−0.626308	−	0.779575i	$-0.715435\pi$
$853$		−	45.5368i		−	1.55915i	0.626308	−	0.779575i	$-0.284565\pi$
$854$	39.2479			1.34304
$855$		0			0
$856$	−86.2865			−2.94921
$857$	−32.8792			−1.12313			−0.561566	−	0.827432i	$-0.689801\pi$
$857$	−32.8792			−1.12313			−0.561566	+	0.827432i	$0.689801\pi$
$858$	−45.5451	+	57.6942i	−1.55488	+	1.96965i
$859$	10.5435			0.359739			0.179869	−	0.983690i	$-0.442432\pi$
$859$	10.5435			0.359739			0.179869	+	0.983690i	$0.442432\pi$
$860$		0			0
$861$	−16.7335	+	3.44383i	−0.570277	+	0.117366i
$862$	9.93644			0.338436
$863$			21.9115i			0.745875i	0.927856	+	0.372938i	$0.121650\pi$
$863$			21.9115i			0.745875i	−0.927856	+	0.372938i	$0.878350\pi$
$864$	40.8249	+	58.5471i	1.38889	+	1.99181i
$865$		0			0
$866$	−66.3102			−2.25331
$867$	5.82110	+	28.2846i	0.197695	+	0.960597i
$868$		−	72.0530i		−	2.44564i
$869$	−20.9975	−	24.9509i	−0.712290	−	0.846402i
$870$		0			0
$871$		−	26.7472i		−	0.906293i
$872$			83.9700i			2.84358i
$873$	43.4327	−	18.6680i	1.46998	−	0.631815i
$874$	57.4387			1.94289
$875$		0			0
$876$	23.1614	−	4.76671i	0.782550	−	0.161052i
$877$			38.0152i			1.28368i	0.766838	+	0.641841i	$0.221829\pi$
$877$			38.0152i			1.28368i	−0.766838	+	0.641841i	$0.778171\pi$
$878$			73.5765i			2.48309i
$879$	−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	$0.892798\pi$
$882$	30.0775	−	12.9277i	1.01276	−	0.435298i
$883$	−9.74489			−0.327942			−0.163971	−	0.986465i	$-0.552430\pi$
$883$	−9.74489			−0.327942			−0.163971	+	0.986465i	$0.552430\pi$
$884$		−	13.8939i		−	0.467302i
$885$		0			0
$886$		−	37.3582i		−	1.25507i
$887$	−19.3598			−0.650039			−0.325019	−	0.945707i	$-0.605371\pi$
$887$	−19.3598			−0.650039			−0.325019	+	0.945707i	$0.605371\pi$
$888$	27.8780	+	135.459i	0.935526	+	4.54570i
$889$	27.2057			0.912450
$890$		0			0
$891$	1.77044	−	29.7971i	0.0593121	−	0.998239i
$892$	−103.911			−3.47920
$893$	0.929739			0.0311125
$894$	−5.87018	−	28.5231i	−0.196328	−	0.953956i
$895$		0			0
$896$			31.6249i			1.05651i
$897$	−12.3822	−	60.1651i	−0.413431	−	2.00885i
$898$		−	35.9381i		−	1.19927i
$899$	6.23759			0.208035
$900$		0			0
$901$			3.80073i			0.126621i
$902$	−19.9052	+	16.7513i	−0.662772	+	0.557756i
$903$	8.32783	+	40.4648i	0.277133	+	1.34658i
$904$			113.606i			3.77847i
$905$		0			0
$906$	0.763278	−	0.157086i	0.0253582	−	0.00521883i
$907$	42.0785			1.39719			0.698596	−	0.715516i	$-0.253808\pi$
$907$	42.0785			1.39719			0.698596	+	0.715516i	$0.253808\pi$
$908$	48.3331			1.60399
$909$	−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	$-0.00531394\pi$
$912$	−56.2164	+	11.5696i	−1.86151	+	0.383107i
$913$	−27.6922	+	23.3044i	−0.916478	+	0.771262i
$914$			16.0077i			0.529488i
$915$		0			0
$916$	−41.3006			−1.36461
$917$			36.4632i			1.20412i
$918$	4.51035	+	6.46832i	0.148864	+	0.213486i
$919$		−	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
$922$	11.0185			0.362874
$923$	−24.0302			−0.790964
$924$	59.6922	−	75.6151i	1.96373	−	2.48755i
$925$		0			0
$926$	55.9321			1.83804
$927$	−33.5010	+	14.3992i	−1.10032	+	0.472932i
$928$	−19.9419			−0.654625
$929$			33.5641i			1.10120i	0.834769	+	0.550601i	$0.185601\pi$
$929$			33.5641i			1.10120i	−0.834769	+	0.550601i	$0.814399\pi$
$930$		0			0
$931$			12.1332i			0.397648i
$932$	17.1504			0.561780
$933$	14.8354	−	3.05319i	0.485690	−	0.0999570i
$934$		−	79.3401i		−	2.59609i
$935$		0			0
$936$	45.9291	+	106.858i	1.50124	+	3.49277i
$937$		−	11.5387i		−	0.376954i	−0.982078	−	0.188477i	$-0.939645\pi$
$937$		−	11.5387i		−	0.376954i	0.982078	−	0.188477i	$-0.0603551\pi$
$938$			48.9939i			1.59971i
$939$	−2.78820	−	13.5478i	−0.0909894	−	0.442116i
$940$		0			0
$941$	−37.0991			−1.20940			−0.604699	−	0.796454i	$-0.706706\pi$
$941$	−37.0991			−1.20940			−0.604699	+	0.796454i	$0.706706\pi$
$942$	−6.58250	−	31.9843i	−0.214469	−	1.04210i
$943$		−	21.7407i		−	0.707974i
$944$		−	16.1951i		−	0.527105i
$945$		0			0
$946$	40.5076	+	48.1346i	1.31702	+	1.56499i
$947$		−	52.9766i		−	1.72151i	−0.509021	−	0.860754i	$-0.669992\pi$
$947$		−	52.9766i		−	1.72151i	0.509021	−	0.860754i	$-0.330008\pi$
$948$	−83.9032	+	17.2676i	−2.72505	+	0.560827i
$949$	13.0987			0.425203
$950$		0			0
$951$	48.3783	−	9.95646i	1.56877	−	0.322860i
$952$			15.3306i			0.496869i
$953$	−39.9855			−1.29526			−0.647629	−	0.761956i	$-0.724239\pi$
$953$	−39.9855			−1.29526			−0.647629	+	0.761956i	$0.724239\pi$
$954$	−20.8573	−	48.5264i	−0.675281	−	1.57110i
$955$		0			0
$956$	24.0701			0.778484
$957$	6.54595	+	5.16752i	0.211601	+	0.167042i
$958$	−41.1306			−1.32887
$959$	29.6408			0.957151
$960$		0			0
$961$	−12.5400			−0.404515
$962$			127.174i			4.10027i
$963$	29.6031	−	12.7238i	0.953947	−	0.410020i
$964$		−	31.3306i		−	1.00909i
$965$		0			0
$966$	22.6810	+	110.207i	0.729751	+	3.54585i
$967$			55.8028i			1.79450i	0.441526	+	0.897248i	$0.354437\pi$
$967$			55.8028i			1.79450i	−0.441526	+	0.897248i	$0.645563\pi$
$968$	15.0953	−	87.0717i	0.485182	−	2.79859i
$969$	−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	$-0.0836082\pi$
$972$	−66.6012	−	41.3803i	−2.13623	−	1.32727i
$973$	52.2253			1.67427
$974$	−38.4090			−1.23070
$975$		0			0
$976$		−	49.9069i		−	1.59748i
$977$		−	23.0147i		−	0.736305i	−0.929765	−	0.368152i	$-0.879990\pi$
$977$		−	23.0147i		−	0.736305i	0.929765	−	0.368152i	$-0.120010\pi$
$978$	−5.18244	−	25.1814i	−0.165716	−	0.805212i
$979$	29.5115	+	35.0680i	0.943191	+	1.12078i
$980$		0			0
$981$	−12.3822	−	28.8084i	−0.395334	−	0.919781i
$982$	8.96891			0.286209
$983$			36.0408i			1.14952i	0.818321	+	0.574762i	$0.194905\pi$
$983$			36.0408i			1.14952i	−0.818321	+	0.574762i	$0.805095\pi$
$984$	8.29825	+	40.3211i	0.264539	+	1.28539i
$985$		0			0
$986$	−2.20319			−0.0701639
$987$	0.367130	+	1.78388i	0.0116859	+	0.0567814i
$988$	−71.5595			−2.27661
$989$	−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	$0.480980\pi$
$992$	−59.0177			−1.87381
$993$	3.84558	+	18.6856i	0.122036	+	0.592970i
$994$	44.0171			1.39614
$995$		0			0
$996$	19.1648	+	93.1214i	0.607259	+	2.95066i
$997$		−	19.0789i		−	0.604235i	−0.953271	−	0.302118i	$-0.902306\pi$
$997$		−	19.0789i		−	0.604235i	0.953271	−	0.302118i	$-0.0976936\pi$
$998$	105.786			3.34859
$999$	−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.f.g.626.15	yes	16
3.2	odd	2	inner	825.2.f.g.626.2	yes	16
5.2	odd	4		825.2.d.f.824.30		32
5.3	odd	4		825.2.d.f.824.3		32
5.4	even	2		825.2.f.e.626.2	yes	16
11.10	odd	2	inner	825.2.f.g.626.1	yes	16
15.2	even	4		825.2.d.f.824.4		32
15.8	even	4		825.2.d.f.824.29		32
15.14	odd	2		825.2.f.e.626.15	yes	16
33.32	even	2	inner	825.2.f.g.626.16	yes	16
55.32	even	4		825.2.d.f.824.2		32
55.43	even	4		825.2.d.f.824.31		32
55.54	odd	2		825.2.f.e.626.16	yes	16
165.32	odd	4		825.2.d.f.824.32		32
165.98	odd	4		825.2.d.f.824.1		32
165.164	even	2		825.2.f.e.626.1	✓	16

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

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.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.65141 q^{2} +(-0.349146 - 1.69650i) q^{3} +5.02997 q^{4} +(-0.925729 - 4.49810i) q^{6} +3.33404i q^{7} +8.03369 q^{8} +(-2.75619 + 1.18465i) q^{9} +O(q^{10})\)	\(q+2.65141 q^{2} +(-0.349146 - 1.69650i) q^{3} +5.02997 q^{4} +(-0.925729 - 4.49810i) q^{6} +3.33404i q^{7} +8.03369 q^{8} +(-2.75619 + 1.18465i) q^{9} +(2.53762 - 2.13553i) q^{11} +(-1.75619 - 8.53332i) q^{12} -4.82595i q^{13} +8.83990i q^{14} +11.2406 q^{16} +0.572368 q^{17} +(-7.30780 + 3.14099i) q^{18} -2.94794i q^{19} +(5.65618 - 1.16407i) q^{21} +(6.72826 - 5.66217i) q^{22} +7.34867i q^{23} +(-2.80493 - 13.6291i) q^{24} -12.7956i q^{26} +(2.97207 + 4.26225i) q^{27} +16.7701i q^{28} -1.45178 q^{29} -4.29651 q^{31} +13.7362 q^{32} +(-4.50892 - 3.55944i) q^{33} +1.51758 q^{34} +(-13.8636 + 5.95875i) q^{36} -9.93894 q^{37} -7.81620i q^{38} +(-8.18721 + 1.68496i) q^{39} -2.95845 q^{41} +(14.9968 - 3.08642i) q^{42} +7.15409i q^{43} +(12.7641 - 10.7417i) q^{44} +19.4843i q^{46} +0.315386i q^{47} +(-3.92463 - 19.0697i) q^{48} -4.11580 q^{49} +(-0.199840 - 0.971019i) q^{51} -24.2744i q^{52} +6.64036i q^{53} +(7.88016 + 11.3010i) q^{54} +26.7846i q^{56} +(-5.00117 + 1.02926i) q^{57} -3.84926 q^{58} -1.44076i q^{59} -4.43986i q^{61} -11.3918 q^{62} +(-3.94967 - 9.18925i) q^{63} +13.9389 q^{64} +(-11.9550 - 9.43754i) q^{66} +5.54236 q^{67} +2.87899 q^{68} +(12.4670 - 2.56576i) q^{69} -4.97937i q^{71} +(-22.1424 + 9.51710i) q^{72} +2.71423i q^{73} -26.3522 q^{74} -14.8281i q^{76} +(7.11994 + 8.46051i) q^{77} +(-21.7076 + 4.46752i) q^{78} -9.83242i q^{79} +(6.19321 - 6.53025i) q^{81} -7.84406 q^{82} -10.9127 q^{83} +(28.4504 - 5.85522i) q^{84} +18.9684i q^{86} +(0.506883 + 2.46294i) q^{87} +(20.3864 - 17.1562i) q^{88} +13.8193i q^{89} +16.0899 q^{91} +36.9636i q^{92} +(1.50011 + 7.28902i) q^{93} +0.836216i q^{94} +(-4.79594 - 23.3034i) q^{96} -15.7582 q^{97} -10.9127 q^{98} +(-4.46431 + 8.89213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} + 16 q^{4} - 10 q^{9}+O(q^{10}) \) 16 * q + 2 * q^3 + 16 * q^4 - 10 * q^9	\( 16 q + 2 q^{3} + 16 q^{4} - 10 q^{9} + 6 q^{12} + 32 q^{16} + 28 q^{22} + 2 q^{27} - 12 q^{31} - 20 q^{33} + 28 q^{34} - 36 q^{36} + 4 q^{37} + 58 q^{42} - 40 q^{48} - 28 q^{49} - 16 q^{58} + 60 q^{64} - 30 q^{66} - 44 q^{67} + 44 q^{69} - 44 q^{78} - 26 q^{81} - 8 q^{82} + 76 q^{88} + 64 q^{91} - 14 q^{93} - 108 q^{97} + 14 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 + 16 * q^4 - 10 * q^9 + 6 * q^12 + 32 * q^16 + 28 * q^22 + 2 * q^27 - 12 * q^31 - 20 * q^33 + 28 * q^34 - 36 * q^36 + 4 * q^37 + 58 * q^42 - 40 * q^48 - 28 * q^49 - 16 * q^58 + 60 * q^64 - 30 * q^66 - 44 * q^67 + 44 * q^69 - 44 * q^78 - 26 * q^81 - 8 * q^82 + 76 * q^88 + 64 * q^91 - 14 * q^93 - 108 * q^97 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more