LMFDB - Embedded newform 825.2.bi.b.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(101,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 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("825.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bi (of order $10$, degree $4$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.2
Root			$0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	825.101
Dual form			825.2.bi.b.776.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 1.80902i) q^{2} +(1.67229 - 0.451057i) q^{3} +(-1.30902 - 0.951057i) q^{4} +(0.166977 - 3.29032i) q^{6} +(-0.427051 + 0.587785i) q^{7} +(0.587785 - 0.427051i) q^{8} +(2.59310 - 1.50859i) q^{9} +O(q^{10})$	\(q+(0.587785 - 1.80902i) q^{2} +(1.67229 - 0.451057i) q^{3} +(-1.30902 - 0.951057i) q^{4} +(0.166977 - 3.29032i) q^{6} +(-0.427051 + 0.587785i) q^{7} +(0.587785 - 0.427051i) q^{8} +(2.59310 - 1.50859i) q^{9} +(-2.12663 - 2.54508i) q^{11} +(-2.61803 - 1.00000i) q^{12} +(2.92705 + 0.951057i) q^{13} +(0.812299 + 1.11803i) q^{14} +(-1.42705 - 4.39201i) q^{16} +(-0.812299 - 2.50000i) q^{17} +(-1.20489 - 5.57768i) q^{18} +(2.50000 + 3.44095i) q^{19} +(-0.449028 + 1.17557i) q^{21} +(-5.85410 + 2.35114i) q^{22} +1.76393i q^{23} +(0.790322 - 0.979277i) q^{24} +(3.44095 - 4.73607i) q^{26} +(3.65594 - 3.69244i) q^{27} +(1.11803 - 0.363271i) q^{28} +(-3.07768 - 2.23607i) q^{29} +(-0.263932 + 0.812299i) q^{31} -7.33094 q^{32} +(-4.70431 - 3.29689i) q^{33} -5.00000 q^{34} +(-4.82916 - 0.491407i) q^{36} +(2.42705 + 1.76336i) q^{37} +(7.69421 - 2.50000i) q^{38} +(5.32385 + 0.270175i) q^{39} +(-2.48990 + 1.80902i) q^{41} +(1.86269 + 1.50328i) q^{42} +1.62460i q^{43} +(0.363271 + 5.35410i) q^{44} +(3.19098 + 1.03681i) q^{46} +(-4.30625 - 5.92705i) q^{47} +(-4.36749 - 6.70103i) q^{48} +(2.00000 + 6.15537i) q^{49} +(-2.48604 - 3.81433i) q^{51} +(-2.92705 - 4.02874i) q^{52} +(-4.61653 - 1.50000i) q^{53} +(-4.53077 - 8.78402i) q^{54} +0.527864i q^{56} +(5.73279 + 4.62663i) q^{57} +(-5.85410 + 4.25325i) q^{58} +(-1.53884 + 2.11803i) q^{59} +(-4.04508 + 1.31433i) q^{61} +(1.31433 + 0.954915i) q^{62} +(-0.220655 + 2.16843i) q^{63} +(-1.45492 + 4.47777i) q^{64} +(-8.72925 + 6.57232i) q^{66} +8.32624 q^{67} +(-1.31433 + 4.04508i) q^{68} +(0.795633 + 2.94980i) q^{69} +(9.82084 - 3.19098i) q^{71} +(0.879937 - 1.99411i) q^{72} +(-8.94427 + 12.3107i) q^{73} +(4.61653 - 3.35410i) q^{74} -6.88191i q^{76} +(2.40414 - 0.163119i) q^{77} +(3.61803 - 9.47214i) q^{78} +(10.1631 + 3.30220i) q^{79} +(4.44829 - 7.82385i) q^{81} +(1.80902 + 5.56758i) q^{82} +(4.47777 + 13.7812i) q^{83} +(1.70582 - 1.11179i) q^{84} +(2.93893 + 0.954915i) q^{86} +(-6.15537 - 2.35114i) q^{87} +(-2.33688 - 0.587785i) q^{88} +9.47214i q^{89} +(-1.80902 + 1.31433i) q^{91} +(1.67760 - 2.30902i) q^{92} +(-0.0749776 + 1.47745i) q^{93} +(-13.2533 + 4.30625i) q^{94} +(-12.2594 + 3.30667i) q^{96} +(2.04508 - 6.29412i) q^{97} +12.3107 q^{98} +(-9.35405 - 3.39144i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} - 6 q^{4} + 10 q^{7} + 10 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 - 6 * q^4 + 10 * q^7 + 10 * q^9	$ 8 q + 6 q^{3} - 6 q^{4} + 10 q^{7} + 10 q^{9} - 12 q^{12} + 10 q^{13} + 2 q^{16} + 20 q^{19} - 20 q^{22} - 10 q^{24} + 12 q^{27} - 20 q^{31} + 4 q^{33} - 40 q^{34} - 10 q^{36} + 6 q^{37} + 20 q^{39} - 20 q^{42} + 30 q^{46} - 26 q^{48} + 16 q^{49} + 30 q^{51} - 10 q^{52} + 30 q^{57} - 20 q^{58} - 10 q^{61} + 30 q^{63} - 34 q^{64} - 30 q^{66} + 4 q^{67} - 16 q^{69} + 20 q^{72} + 20 q^{78} + 50 q^{79} - 2 q^{81} + 10 q^{82} - 50 q^{88} - 10 q^{91} - 10 q^{93} - 30 q^{94} + 10 q^{96} - 6 q^{97} + 16 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 - 6 * q^4 + 10 * q^7 + 10 * q^9 - 12 * q^12 + 10 * q^13 + 2 * q^16 + 20 * q^19 - 20 * q^22 - 10 * q^24 + 12 * q^27 - 20 * q^31 + 4 * q^33 - 40 * q^34 - 10 * q^36 + 6 * q^37 + 20 * q^39 - 20 * q^42 + 30 * q^46 - 26 * q^48 + 16 * q^49 + 30 * q^51 - 10 * q^52 + 30 * q^57 - 20 * q^58 - 10 * q^61 + 30 * q^63 - 34 * q^64 - 30 * q^66 + 4 * q^67 - 16 * q^69 + 20 * q^72 + 20 * q^78 + 50 * q^79 - 2 * q^81 + 10 * q^82 - 50 * q^88 - 10 * q^91 - 10 * q^93 - 30 * q^94 + 10 * q^96 - 6 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.587785	−	1.80902i	0.415627	−	1.27917i	−0.496062	−	0.868287i	$-0.665221\pi$
$2$	0.587785	−	1.80902i	0.415627	−	1.27917i	0.911689	−	0.410881i	$-0.134779\pi$
$3$	1.67229	−	0.451057i	0.965496	−	0.260418i
$3$	1.67229	−	0.451057i	0.965496	−	0.260418i
$4$	−1.30902	−	0.951057i	−0.654508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	0.166977	−	3.29032i	0.0681683	−	1.34327i
$7$	−0.427051	+	0.587785i	−0.161410	+	0.222162i	−0.882060	−	0.471137i	$-0.843844\pi$
$7$	−0.427051	+	0.587785i	−0.161410	+	0.222162i	0.720650	+	0.693299i	$0.243844\pi$
$8$	0.587785	−	0.427051i	0.207813	−	0.150985i
$9$	2.59310	−	1.50859i	0.864365	−	0.502864i
$10$		0			0
$11$	−2.12663	−	2.54508i	−0.641202	−	0.767372i
$11$	−2.12663	−	2.54508i	−0.641202	−	0.767372i
$12$	−2.61803	−	1.00000i	−0.755761	−	0.288675i
$13$	2.92705	+	0.951057i	0.811818	+	0.263776i	0.685368	−	0.728197i	$-0.259642\pi$
$13$	2.92705	+	0.951057i	0.811818	+	0.263776i	0.126450	+	0.991973i	$0.459642\pi$
$14$	0.812299	+	1.11803i	0.217096	+	0.298807i
$15$		0			0
$16$	−1.42705	−	4.39201i	−0.356763	−	1.09800i
$17$	−0.812299	−	2.50000i	−0.197012	−	0.606339i	−0.999947	−	0.0102734i	$-0.996730\pi$
$17$	−0.812299	−	2.50000i	−0.197012	−	0.606339i	0.802936	−	0.596066i	$-0.203270\pi$
$18$	−1.20489	−	5.57768i	−0.283995	−	1.31467i
$19$	2.50000	+	3.44095i	0.573539	+	0.789409i	0.992968	−	0.118379i	$-0.0377697\pi$
$19$	2.50000	+	3.44095i	0.573539	+	0.789409i	−0.419429	+	0.907788i	$0.637770\pi$
$20$		0			0
$21$	−0.449028	+	1.17557i	−0.0979859	+	0.256531i
$22$	−5.85410	+	2.35114i	−1.24810	+	0.501265i
$23$			1.76393i			0.367805i	0.982944	+	0.183903i	$0.0588731\pi$
$23$			1.76393i			0.367805i	−0.982944	+	0.183903i	$0.941127\pi$
$24$	0.790322	−	0.979277i	0.161324	−	0.199894i
$25$		0			0
$26$	3.44095	−	4.73607i	0.674827	−	0.928819i
$27$	3.65594	−	3.69244i	0.703587	−	0.710610i
$28$	1.11803	−	0.363271i	0.211289	−	0.0686518i
$29$	−3.07768	−	2.23607i	−0.571511	−	0.415227i	0.264142	−	0.964484i	$-0.414911\pi$
$29$	−3.07768	−	2.23607i	−0.571511	−	0.415227i	−0.835654	+	0.549256i	$0.814911\pi$
$30$		0			0
$31$	−0.263932	+	0.812299i	−0.0474036	+	0.145893i	−0.971957	−	0.235160i	$-0.924439\pi$
$31$	−0.263932	+	0.812299i	−0.0474036	+	0.145893i	0.924553	+	0.381053i	$0.124439\pi$
$32$	−7.33094			−1.29594
$33$	−4.70431	−	3.29689i	−0.818915	−	0.573914i
$34$	−5.00000			−0.857493
$35$		0			0
$36$	−4.82916	−	0.491407i	−0.804861	−	0.0819012i
$37$	2.42705	+	1.76336i	0.399005	+	0.289894i	0.769135	−	0.639086i	$-0.220687\pi$
$37$	2.42705	+	1.76336i	0.399005	+	0.289894i	−0.370131	+	0.928980i	$0.620687\pi$
$38$	7.69421	−	2.50000i	1.24817	−	0.405554i
$39$	5.32385	+	0.270175i	0.852499	+	0.0432627i
$40$		0			0
$41$	−2.48990	+	1.80902i	−0.388857	+	0.282521i	−0.764987	−	0.644046i	$-0.777255\pi$
$41$	−2.48990	+	1.80902i	−0.388857	+	0.282521i	0.376130	+	0.926567i	$0.377255\pi$
$42$	1.86269	+	1.50328i	0.287420	+	0.231961i
$43$			1.62460i			0.247749i	0.992298	+	0.123874i	$0.0395320\pi$
$43$			1.62460i			0.247749i	−0.992298	+	0.123874i	$0.960468\pi$
$44$	0.363271	+	5.35410i	0.0547652	+	0.807161i
$45$		0			0
$46$	3.19098	+	1.03681i	0.470485	+	0.152870i
$47$	−4.30625	−	5.92705i	−0.628132	−	0.864549i	0.369781	−	0.929119i	$-0.379433\pi$
$47$	−4.30625	−	5.92705i	−0.628132	−	0.864549i	−0.997913	+	0.0645695i	$0.979433\pi$
$48$	−4.36749	−	6.70103i	−0.630392	−	0.967210i
$49$	2.00000	+	6.15537i	0.285714	+	0.879338i
$50$		0			0
$51$	−2.48604	−	3.81433i	−0.348115	−	0.534113i
$52$	−2.92705	−	4.02874i	−0.405909	−	0.558686i
$53$	−4.61653	−	1.50000i	−0.634129	−	0.206041i	−0.0257255	−	0.999669i	$-0.508190\pi$
$53$	−4.61653	−	1.50000i	−0.634129	−	0.206041i	−0.608403	+	0.793628i	$0.708190\pi$
$54$	−4.53077	−	8.78402i	−0.616560	−	1.19535i
$55$		0			0
$56$			0.527864i			0.0705388i
$57$	5.73279	+	4.62663i	0.759326	+	0.612812i
$58$	−5.85410	+	4.25325i	−0.768681	+	0.558480i
$59$	−1.53884	+	2.11803i	−0.200340	+	0.275745i	−0.897352	−	0.441315i	$-0.854512\pi$
$59$	−1.53884	+	2.11803i	−0.200340	+	0.275745i	0.697012	+	0.717059i	$0.254512\pi$
$60$		0			0
$61$	−4.04508	+	1.31433i	−0.517920	+	0.168282i	−0.556301	−	0.830981i	$-0.687780\pi$
$61$	−4.04508	+	1.31433i	−0.517920	+	0.168282i	0.0383811	+	0.999263i	$0.487780\pi$
$62$	1.31433	+	0.954915i	0.166920	+	0.121274i
$63$	−0.220655	+	2.16843i	−0.0278000	+	0.273196i
$64$	−1.45492	+	4.47777i	−0.181864	+	0.559721i
$65$		0			0
$66$	−8.72925	+	6.57232i	−1.07450	+	0.808996i
$67$	8.32624			1.01721			0.508606	−	0.860999i	$-0.330161\pi$
$67$	8.32624			1.01721			0.508606	+	0.860999i	$0.330161\pi$
$68$	−1.31433	+	4.04508i	−0.159386	+	0.490539i
$69$	0.795633	+	2.94980i	0.0957830	+	0.355115i
$70$		0			0
$71$	9.82084	−	3.19098i	1.16552	−	0.378700i	0.338550	−	0.940948i	$-0.390063\pi$
$71$	9.82084	−	3.19098i	1.16552	−	0.378700i	0.826968	+	0.562248i	$0.190063\pi$
$72$	0.879937	−	1.99411i	0.103702	−	0.235008i
$73$	−8.94427	+	12.3107i	−1.04685	+	1.44086i	−0.155338	+	0.987861i	$0.549647\pi$
$73$	−8.94427	+	12.3107i	−1.04685	+	1.44086i	−0.891510	+	0.453001i	$0.850353\pi$
$74$	4.61653	−	3.35410i	0.536660	−	0.389906i
$75$		0			0
$76$		−	6.88191i		−	0.789409i
$77$	2.40414	−	0.163119i	0.273977	−	0.0185891i
$78$	3.61803	−	9.47214i	0.409662	−	1.07251i
$79$	10.1631	+	3.30220i	1.14344	+	0.371526i	0.818669	−	0.574266i	$-0.194713\pi$
$79$	10.1631	+	3.30220i	1.14344	+	0.371526i	0.324772	+	0.945792i	$0.394713\pi$
$80$		0			0
$81$	4.44829	−	7.82385i	0.494255	−	0.869317i
$82$	1.80902	+	5.56758i	0.199773	+	0.614837i
$83$	4.47777	+	13.7812i	0.491499	+	1.51268i	0.822343	+	0.568993i	$0.192667\pi$
$83$	4.47777	+	13.7812i	0.491499	+	1.51268i	−0.330844	+	0.943686i	$0.607333\pi$
$84$	1.70582	−	1.11179i	0.186120	−	0.121306i
$85$		0			0
$86$	2.93893	+	0.954915i	0.316913	+	0.102971i
$87$	−6.15537	−	2.35114i	−0.659925	−	0.252069i
$88$	−2.33688	−	0.587785i	−0.249112	−	0.0626581i
$89$			9.47214i			1.00404i	0.864855	+	0.502022i	$0.167410\pi$
$89$			9.47214i			1.00404i	−0.864855	+	0.502022i	$0.832590\pi$
$90$		0			0
$91$	−1.80902	+	1.31433i	−0.189637	+	0.137779i
$92$	1.67760	−	2.30902i	0.174902	−	0.240732i
$93$	−0.0749776	+	1.47745i	−0.00777481	+	0.153204i
$94$	−13.2533	+	4.30625i	−1.36697	+	0.444156i
$95$		0			0
$96$	−12.2594	+	3.30667i	−1.25122	+	0.337485i
$97$	2.04508	−	6.29412i	0.207647	−	0.639072i	−0.791947	−	0.610589i	$-0.790933\pi$
$97$	2.04508	−	6.29412i	0.207647	−	0.639072i	0.999594	−	0.0284822i	$-0.00906738\pi$
$98$	12.3107			1.24357
$99$	−9.35405	−	3.39144i	−0.940117	−	0.340852i
$100$		0			0
$101$	−3.85723	+	11.8713i	−0.383808	+	1.18124i	0.553533	+	0.832827i	$0.313279\pi$
$101$	−3.85723	+	11.8713i	−0.383808	+	1.18124i	−0.937341	+	0.348413i	$0.886721\pi$
$102$	−8.36144	+	2.25528i	−0.827906	+	0.223306i
$103$	−5.47214	−	3.97574i	−0.539186	−	0.391741i	0.284597	−	0.958647i	$-0.408140\pi$
$103$	−5.47214	−	3.97574i	−0.539186	−	0.391741i	−0.823782	+	0.566906i	$0.808140\pi$
$104$	2.12663	−	0.690983i	0.208533	−	0.0677565i
$105$		0			0
$106$	−5.42705	+	7.46969i	−0.527122	+	0.725521i
$107$	0.138757	−	0.100813i	0.0134142	−	0.00974597i	−0.581058	−	0.813862i	$-0.697361\pi$
$107$	0.138757	−	0.100813i	0.0134142	−	0.00974597i	0.594472	+	0.804116i	$0.297361\pi$
$108$	−8.29741	+	1.35645i	−0.798418	+	0.130525i
$109$		−	7.60845i		−	0.728758i	−0.931251	−	0.364379i	$-0.881281\pi$
$109$		−	7.60845i		−	0.728758i	0.931251	−	0.364379i	$-0.118719\pi$
$110$		0			0
$111$	4.85410	+	1.85410i	0.460731	+	0.175984i
$112$	3.19098	+	1.03681i	0.301520	+	0.0979696i
$113$	11.7229	+	16.1353i	1.10280	+	1.51788i	0.831617	+	0.555350i	$0.187416\pi$
$113$	11.7229	+	16.1353i	1.10280	+	1.51788i	0.271186	+	0.962527i	$0.412584\pi$
$114$	11.7393	−	7.65124i	1.09949	−	0.716605i
$115$		0			0
$116$	1.90211	+	5.85410i	0.176607	+	0.543540i
$117$	9.02488	−	1.94955i	0.834351	−	0.180236i
$118$	2.92705	+	4.02874i	0.269457	+	0.370876i
$119$	1.81636	+	0.590170i	0.166505	+	0.0541008i
$120$		0			0
$121$	−1.95492	+	10.8249i	−0.177720	+	0.984081i
$122$			8.09017i			0.732450i
$123$	−3.34786	+	4.14828i	−0.301866	+	0.374038i
$124$	1.11803	−	0.812299i	0.100402	−	0.0729466i
$125$		0			0
$126$	3.79303	+	1.67374i	0.337910	+	0.149109i
$127$	−12.5623	+	4.08174i	−1.11472	+	0.362196i	−0.807752	−	0.589522i	$-0.799316\pi$
$127$	−12.5623	+	4.08174i	−1.11472	+	0.362196i	−0.306972	+	0.951718i	$0.599316\pi$
$128$	−4.61653	−	3.35410i	−0.408047	−	0.296464i
$129$	0.732786	+	2.71680i	0.0645182	+	0.239201i
$130$		0			0
$131$	4.08174			0.356623			0.178312	−	0.983974i	$-0.442936\pi$
$131$	4.08174			0.356623			0.178312	+	0.983974i	$0.442936\pi$
$132$	3.02250	+	8.78975i	0.263075	+	0.765049i
$133$	−3.09017			−0.267952
$134$	4.89404	−	15.0623i	0.422781	−	1.30119i
$135$		0			0
$136$	−1.54508	−	1.12257i	−0.132490	−	0.0962596i
$137$	8.28199	−	2.69098i	0.707579	−	0.229906i	0.0669491	−	0.997756i	$-0.478673\pi$
$137$	8.28199	−	2.69098i	0.707579	−	0.229906i	0.640629	+	0.767850i	$0.278673\pi$
$138$	5.80390	+	0.294537i	0.494061	+	0.0250726i
$139$	−1.01722	+	1.40008i	−0.0862796	+	0.118754i	−0.849975	−	0.526823i	$-0.823383\pi$
$139$	−1.01722	+	1.40008i	−0.0862796	+	0.118754i	0.763695	+	0.645577i	$0.223383\pi$
$140$		0			0
$141$	−9.87473	−	7.96937i	−0.831603	−	0.671142i
$142$		−	19.6417i		−	1.64829i
$143$	−3.80423	−	9.47214i	−0.318125	−	0.792100i
$144$	−10.3262	−	9.23607i	−0.860520	−	0.769672i
$145$		0			0
$146$	17.0130	+	23.4164i	1.40801	+	1.93796i
$147$	6.12099	+	9.39144i	0.504851	+	0.774593i
$148$	−1.50000	−	4.61653i	−0.123299	−	0.379476i
$149$	−0.0530006	−	0.163119i	−0.00434198	−	0.0133632i	0.948862	−	0.315691i	$-0.102236\pi$
$149$	−0.0530006	−	0.163119i	−0.00434198	−	0.0133632i	−0.953204	+	0.302328i	$0.902236\pi$
$150$		0			0
$151$	−10.3262	−	14.2128i	−0.840337	−	1.15663i	−0.985910	−	0.167278i	$-0.946502\pi$
$151$	−10.3262	−	14.2128i	−0.840337	−	1.15663i	0.145573	−	0.989348i	$-0.453498\pi$
$152$	2.93893	+	0.954915i	0.238378	+	0.0774538i
$153$	−5.87785	−	5.25731i	−0.475196	−	0.425028i
$154$	1.11803	−	4.44501i	0.0900937	−	0.358189i
$155$		0			0
$156$	−6.71206	−	5.41695i	−0.537395	−	0.433703i
$157$	−3.00000	+	2.17963i	−0.239426	+	0.173953i	−0.701028	−	0.713134i	$-0.747275\pi$
$157$	−3.00000	+	2.17963i	−0.239426	+	0.173953i	0.461601	+	0.887087i	$0.347275\pi$
$158$	11.9475	−	16.4443i	0.950489	−	1.30824i
$159$	−8.39675	−	0.426119i	−0.665905	−	0.0337934i
$160$		0			0
$161$	−1.03681	−	0.753289i	−0.0817123	−	0.0593675i
$162$	−11.5388	−	12.6458i	−0.906577	−	0.993547i
$163$	3.82624	−	11.7759i	0.299694	−	0.922364i	−0.681910	−	0.731436i	$-0.738850\pi$
$163$	3.82624	−	11.7759i	0.299694	−	0.922364i	0.981604	−	0.190928i	$-0.0611495\pi$
$164$	4.97980			0.388857
$165$		0			0
$166$	27.5623			2.13925
$167$	0.0327561	−	0.100813i	0.00253475	−	0.00780115i	−0.949781	−	0.312915i	$-0.898695\pi$
$167$	0.0327561	−	0.100813i	0.00253475	−	0.00780115i	0.952316	+	0.305114i	$0.0986945\pi$
$168$	0.238097	+	0.882741i	0.0183695	+	0.0681049i
$169$	−2.85410	−	2.07363i	−0.219546	−	0.159510i
$170$		0			0
$171$	11.6737	+	5.15124i	0.892713	+	0.393925i
$172$	1.54508	−	2.12663i	0.117812	−	0.162154i
$173$	−17.9313	+	13.0279i	−1.36329	+	0.990490i	−0.365065	+	0.930982i	$0.618953\pi$
$173$	−17.9313	+	13.0279i	−1.36329	+	0.990490i	−0.998228	+	0.0595081i	$0.981047\pi$
$174$	−7.87129	+	9.75320i	−0.596721	+	0.739388i
$175$		0			0
$176$	−8.14324	+	12.9721i	−0.613820	+	0.977812i
$177$	−1.61803	+	4.23607i	−0.121619	+	0.318402i
$178$	17.1353	+	5.56758i	1.28434	+	0.417308i
$179$	−2.31838	−	3.19098i	−0.173284	−	0.238505i	0.713537	−	0.700617i	$-0.247092\pi$
$179$	−2.31838	−	3.19098i	−0.173284	−	0.238505i	−0.886822	+	0.462112i	$0.847092\pi$
$180$		0			0
$181$	3.78115	+	11.6372i	0.281051	+	0.864986i	0.987555	+	0.157276i	$0.0502713\pi$
$181$	3.78115	+	11.6372i	0.281051	+	0.864986i	−0.706504	+	0.707709i	$0.749729\pi$
$182$	1.31433	+	4.04508i	0.0974245	+	0.299842i
$183$	−6.17171	+	4.02250i	−0.456226	+	0.297352i
$184$	0.753289	+	1.03681i	0.0555332	+	0.0764349i
$185$		0			0
$186$	2.62866	+	1.00406i	0.192742	+	0.0736210i
$187$	−4.63525	+	7.38394i	−0.338963	+	0.539967i
$188$			11.8541i			0.864549i
$189$	0.609085	+	3.72577i	0.0443044	+	0.271010i
$190$		0			0
$191$	11.6169	−	15.9894i	0.840573	−	1.15695i	−0.145289	−	0.989389i	$-0.546411\pi$
$191$	11.6169	−	15.9894i	0.840573	−	1.15695i	0.985862	−	0.167560i	$-0.0535888\pi$
$192$	−0.413311	+	8.14437i	−0.0298281	+	0.587769i
$193$	19.2082	−	6.24112i	1.38264	−	0.449246i	0.479101	−	0.877760i	$-0.340963\pi$
$193$	19.2082	−	6.24112i	1.38264	−	0.449246i	0.903535	+	0.428514i	$0.140963\pi$
$194$	−10.1841	−	7.39919i	−0.731176	−	0.531231i
$195$		0			0
$196$	3.23607	−	9.95959i	0.231148	−	0.711400i
$197$	−15.8374			−1.12837			−0.564186	−	0.825648i	$-0.690810\pi$
$197$	−15.8374			−1.12837			−0.564186	+	0.825648i	$0.690810\pi$
$198$	−11.6333	+	14.9282i	−0.826745	+	1.06090i
$199$	−2.23607			−0.158511			−0.0792553	−	0.996854i	$-0.525254\pi$
$199$	−2.23607			−0.158511			−0.0792553	+	0.996854i	$0.525254\pi$
$200$		0			0
$201$	13.9239	−	3.75560i	0.982114	−	0.264900i
$202$	19.2082	+	13.9556i	1.35148	+	0.981911i
$203$	2.62866	−	0.854102i	0.184495	−	0.0599462i
$204$	−0.373373	+	7.35738i	−0.0261413	+	0.515120i
$205$		0			0
$206$	−10.4086	+	7.56231i	−0.725203	+	0.526891i
$207$	2.66106	+	4.57405i	0.184956	+	0.317918i
$208$		−	14.2128i		−	0.985484i
$209$	3.44095	−	13.6803i	0.238016	−	0.946289i
$210$		0			0
$211$	6.44427	+	2.09387i	0.443642	+	0.144148i	0.522315	−	0.852752i	$-0.325068\pi$
$211$	6.44427	+	2.09387i	0.443642	+	0.144148i	−0.0786733	+	0.996900i	$0.525068\pi$
$212$	4.61653	+	6.35410i	0.317064	+	0.436402i
$213$	14.9840	−	9.76600i	1.02668	−	0.669155i
$214$	−0.100813	−	0.310271i	−0.00689144	−	0.0212097i
$215$		0			0
$216$	0.572051	−	3.73163i	0.0389232	−	0.253905i
$217$	−0.364745	−	0.502029i	−0.0247605	−	0.0340799i
$218$	−13.7638	−	4.47214i	−0.932203	−	0.302891i
$219$	−9.40456	+	24.6215i	−0.635502	+	1.66376i
$220$		0			0
$221$		−	8.09017i		−	0.544204i
$222$	6.20727	−	7.69134i	0.416605	−	0.516209i
$223$	5.04508	−	3.66547i	0.337844	−	0.245458i	−0.405908	−	0.913914i	$-0.633045\pi$
$223$	5.04508	−	3.66547i	0.337844	−	0.245458i	0.743752	+	0.668456i	$0.233045\pi$
$224$	3.13068	−	4.30902i	0.209178	−	0.287908i
$225$		0			0
$226$	36.0795	−	11.7229i	2.39997	−	0.779799i
$227$	5.11855	+	3.71885i	0.339730	+	0.246829i	0.744548	−	0.667569i	$-0.232665\pi$
$227$	5.11855	+	3.71885i	0.339730	+	0.246829i	−0.404818	+	0.914397i	$0.632665\pi$
$228$	−3.10413	−	11.5085i	−0.205576	−	0.762171i
$229$	7.76393	−	23.8949i	0.513055	−	1.57902i	−0.273738	−	0.961804i	$-0.588260\pi$
$229$	7.76393	−	23.8949i	0.513055	−	1.57902i	0.786793	−	0.617217i	$-0.211740\pi$
$230$		0			0
$231$	3.94684	−	1.35719i	0.259683	−	0.0892963i
$232$	−2.76393			−0.181461
$233$	2.21238	−	6.80902i	0.144938	−	0.446074i	−0.852065	−	0.523436i	$-0.824650\pi$
$233$	2.21238	−	6.80902i	0.144938	−	0.446074i	0.997003	+	0.0773625i	$0.0246499\pi$
$234$	1.77793	−	17.4721i	0.116227	−	1.14219i
$235$		0			0
$236$	4.02874	−	1.30902i	0.262249	−	0.0852097i
$237$	18.4851	+	0.938085i	1.20074	+	0.0609352i
$238$	2.13525	−	2.93893i	0.138408	−	0.190502i
$239$	−20.8702	+	15.1631i	−1.34998	+	0.980821i	−0.350971	+	0.936386i	$0.614149\pi$
$239$	−20.8702	+	15.1631i	−1.34998	+	0.980821i	−0.999012	+	0.0444345i	$0.985851\pi$
$240$		0			0
$241$		−	19.5762i		−	1.26101i	−0.776185	−	0.630506i	$-0.782848\pi$
$241$		−	19.5762i		−	1.26101i	0.776185	−	0.630506i	$-0.217152\pi$
$242$	18.4333	+	9.89919i	1.18494	+	0.636344i
$243$	3.90983	−	15.0902i	0.250816	−	0.968035i
$244$	6.54508	+	2.12663i	0.419006	+	0.136143i
$245$		0			0
$246$	5.53649	+	8.49463i	0.352994	+	0.541598i
$247$	4.04508	+	12.4495i	0.257383	+	0.792142i
$248$	0.191758	+	0.590170i	0.0121766	+	0.0374758i
$249$	13.7042	+	21.0263i	0.868468	+	1.33249i
$250$		0			0
$251$	−4.44501	−	1.44427i	−0.280567	−	0.0911616i	0.165354	−	0.986234i	$-0.447123\pi$
$251$	−4.44501	−	1.44427i	−0.280567	−	0.0911616i	−0.445920	+	0.895073i	$0.647123\pi$
$252$	2.35114	−	2.62866i	0.148108	−	0.165590i
$253$	4.48936	−	3.75123i	0.282243	−	0.235838i
$254$			25.1246i			1.57646i
$255$		0			0
$256$	−16.3992	+	11.9147i	−1.02495	+	0.744669i
$257$	−6.62464	+	9.11803i	−0.413234	+	0.568767i	−0.964003	−	0.265890i	$-0.914334\pi$
$257$	−6.62464	+	9.11803i	−0.413234	+	0.568767i	0.550770	+	0.834657i	$0.314334\pi$
$258$	5.34545	+	0.271271i	0.332793	+	0.0168886i
$259$	−2.07295	+	0.673542i	−0.128807	+	0.0418519i
$260$		0			0
$261$	−11.3540	−	1.15537i	−0.702798	−	0.0715154i
$262$	2.39919	−	7.38394i	0.148222	−	0.456181i
$263$	23.2744			1.43516			0.717580	−	0.696476i	$-0.245250\pi$
$263$	23.2744			1.43516			0.717580	+	0.696476i	$0.245250\pi$
$264$	−4.17306	+	0.0711190i	−0.256834	+	0.00437707i
$265$		0			0
$266$	−1.81636	+	5.59017i	−0.111368	+	0.342755i
$267$	4.27247	+	15.8401i	0.261471	+	0.969401i
$268$	−10.8992	−	7.91872i	−0.665774	−	0.483713i
$269$	22.0988	−	7.18034i	1.34739	−	0.437793i	0.455575	−	0.890197i	$-0.349434\pi$
$269$	22.0988	−	7.18034i	1.34739	−	0.437793i	0.891813	+	0.452404i	$0.149434\pi$
$270$		0			0
$271$	−13.8820	+	19.1069i	−0.843269	+	1.16066i	0.142036	+	0.989861i	$0.454635\pi$
$271$	−13.8820	+	19.1069i	−0.843269	+	1.16066i	−0.985306	+	0.170799i	$0.945365\pi$
$272$	−9.82084	+	7.13525i	−0.595476	+	0.432638i
$273$	−2.43236	+	3.01390i	−0.147213	+	0.182410i
$274$		−	16.5640i		−	1.00067i
$275$		0			0
$276$	1.76393	−	4.61803i	0.106176	−	0.277973i
$277$	−19.5344	−	6.34712i	−1.17371	−	0.381362i	−0.343684	−	0.939085i	$-0.611675\pi$
$277$	−19.5344	−	6.34712i	−1.17371	−	0.381362i	−0.830027	+	0.557724i	$0.811675\pi$
$278$	1.93487	+	2.66312i	0.116046	+	0.159723i
$279$	0.541028	+	2.50454i	0.0323905	+	0.149943i
$280$		0			0
$281$	5.08580	+	15.6525i	0.303393	+	0.933748i	0.980272	+	0.197654i	$0.0633322\pi$
$281$	5.08580	+	15.6525i	0.303393	+	0.933748i	−0.676879	+	0.736095i	$0.736668\pi$
$282$	−20.2210	+	13.1793i	−1.20414	+	0.784815i
$283$	4.67376	+	6.43288i	0.277826	+	0.382395i	0.925012	−	0.379937i	$-0.124054\pi$
$283$	4.67376	+	6.43288i	0.277826	+	0.382395i	−0.647186	+	0.762332i	$0.724054\pi$
$284$	−15.8904	−	5.16312i	−0.942925	−	0.306375i
$285$		0			0
$286$	−19.3713	+	1.31433i	−1.14545	+	0.0777178i
$287$		−	2.23607i		−	0.131991i
$288$	−19.0098	+	11.0594i	−1.12016	+	0.651681i
$289$	8.16312	−	5.93085i	0.480183	−	0.348874i
$290$		0			0
$291$	0.580966	−	11.4480i	0.0340568	−	0.671096i
$292$	23.4164	−	7.60845i	1.37034	−	0.445251i
$293$	−7.91872	−	5.75329i	−0.462617	−	0.336111i	0.331940	−	0.943300i	$-0.392297\pi$
$293$	−7.91872	−	5.75329i	−0.462617	−	0.336111i	−0.794557	+	0.607190i	$0.792297\pi$
$294$	20.5871	−	5.55284i	1.20066	−	0.323848i
$295$		0			0
$296$	2.17963			0.126688
$297$	−17.1724	−	1.45225i	−0.996443	−	0.0842683i
$298$	−0.326238			−0.0188985
$299$	−1.67760	+	5.16312i	−0.0970181	+	0.298591i
$300$		0			0
$301$	−0.954915	−	0.693786i	−0.0550404	−	0.0399892i
$302$	−31.7809	+	10.3262i	−1.82878	+	0.594208i
$303$	−1.09576	+	21.5921i	−0.0629496	+	1.24043i
$304$	11.5451	−	15.8904i	0.662156	−	0.911380i
$305$		0			0
$306$	−12.9655	+	7.54297i	−0.741187	+	0.431203i
$307$		−	5.87785i		−	0.335467i	−0.985832	−	0.167733i	$-0.946355\pi$
$307$		−	5.87785i		−	0.335467i	0.985832	−	0.167733i	$-0.0536448\pi$
$308$	−3.30220	−	2.07295i	−0.188160	−	0.118117i
$309$	−10.9443	−	4.18034i	−0.622598	−	0.237811i
$310$		0			0
$311$	−2.93893	−	4.04508i	−0.166651	−	0.229376i	0.717521	−	0.696537i	$-0.245277\pi$
$311$	−2.93893	−	4.04508i	−0.166651	−	0.229376i	−0.884172	+	0.467161i	$0.845277\pi$
$312$	3.24466	−	2.11475i	0.183693	−	0.119724i
$313$	−3.39919	−	10.4616i	−0.192133	−	0.591326i	−0.999998	−	0.00195780i	$-0.999377\pi$
$313$	−3.39919	−	10.4616i	−0.192133	−	0.591326i	0.807865	−	0.589368i	$-0.200623\pi$
$314$	2.17963	+	6.70820i	0.123004	+	0.378566i
$315$		0			0
$316$	−10.1631	−	13.9883i	−0.571720	−	0.786905i
$317$	0.224514	+	0.0729490i	0.0126100	+	0.00409722i	0.315315	−	0.948987i	$-0.397890\pi$
$317$	0.224514	+	0.0729490i	0.0126100	+	0.00409722i	−0.302705	+	0.953084i	$0.597890\pi$
$318$	−5.70634	+	14.9394i	−0.319996	+	0.837759i
$319$	0.854102	+	12.5882i	0.0478205	+	0.704807i
$320$		0			0
$321$	0.186570	−	0.231176i	0.0104133	−	0.0129030i
$322$	−1.97214	+	1.43284i	−0.109903	+	0.0798491i
$323$	6.57164	−	9.04508i	0.365656	−	0.503282i
$324$	−13.2638	+	6.01098i	−0.736879	+	0.333943i
$325$		0			0
$326$	−19.0539	−	13.8435i	−1.05530	−	0.766718i
$327$	−3.43184	−	12.7235i	−0.189781	−	0.703613i
$328$	−0.690983	+	2.12663i	−0.0381532	+	0.117423i
$329$	5.32282			0.293457
$330$		0			0
$331$	−22.8885			−1.25807			−0.629034	−	0.777378i	$-0.716549\pi$
$331$	−22.8885			−1.25807			−0.629034	+	0.777378i	$0.716549\pi$
$332$	7.24518	−	22.2984i	0.397631	−	1.22378i
$333$	8.95376	+	0.911119i	0.490663	+	0.0499290i
$334$	−0.163119	−	0.118513i	−0.00892547	−	0.00648474i
$335$		0			0
$336$	5.80390	+	0.294537i	0.316629	+	0.0160683i
$337$	−6.05573	+	8.33499i	−0.329877	+	0.454036i	−0.941451	−	0.337151i	$-0.890537\pi$
$337$	−6.05573	+	8.33499i	−0.329877	+	0.454036i	0.611574	+	0.791187i	$0.290537\pi$
$338$	−5.42882	+	3.94427i	−0.295289	+	0.214540i
$339$	26.8821	+	21.6951i	1.46003	+	1.17832i
$340$		0			0
$341$	2.62866	−	1.05573i	0.142350	−	0.0571709i
$342$	16.1803	−	18.0902i	0.874933	−	0.978204i
$343$	−9.30902	−	3.02468i	−0.502640	−	0.163318i
$344$	0.693786	+	0.954915i	0.0374065	+	0.0514856i
$345$		0			0
$346$	13.0279	+	40.0956i	0.700382	+	2.15556i
$347$	−9.51057	−	29.2705i	−0.510554	−	1.57132i	−0.791229	−	0.611520i	$-0.790558\pi$
$347$	−9.51057	−	29.2705i	−0.510554	−	1.57132i	0.280675	−	0.959803i	$-0.409442\pi$
$348$	5.82141	+	8.93179i	0.312060	+	0.478794i
$349$	9.57295	+	13.1760i	0.512428	+	0.705297i	0.984326	−	0.176356i	$-0.0564310\pi$
$349$	9.57295	+	13.1760i	0.512428	+	0.705297i	−0.471898	+	0.881653i	$0.656431\pi$
$350$		0			0
$351$	14.2128	−	7.33094i	0.758626	−	0.391297i
$352$	15.5902	+	18.6579i	0.830959	+	0.994467i
$353$			15.5967i			0.830131i	0.909792	+	0.415066i	$0.136241\pi$
$353$			15.5967i			0.830131i	−0.909792	+	0.415066i	$0.863759\pi$
$354$	6.71206	+	5.41695i	0.356742	+	0.287908i
$355$		0			0
$356$	9.00854	−	12.3992i	0.477451	−	0.657156i
$357$	3.30367	+	0.167655i	0.174849	+	0.00887324i
$358$	−7.13525	+	2.31838i	−0.377110	+	0.122530i
$359$	−20.1967	−	14.6738i	−1.06594	−	0.774452i	−0.0907628	−	0.995873i	$-0.528931\pi$
$359$	−20.1967	−	14.6738i	−1.06594	−	0.774452i	−0.975178	+	0.221421i	$0.928931\pi$
$360$		0			0
$361$	0.281153	−	0.865300i	0.0147975	−	0.0455421i
$362$	23.2744			1.22327
$363$	1.61346	+	18.9841i	0.0846845	+	0.996408i
$364$	3.61803			0.189637
$365$		0			0
$366$	3.64912	+	13.5291i	0.190743	+	0.707177i
$367$	−18.5902	−	13.5065i	−0.970399	−	0.705036i	−0.0148565	−	0.999890i	$-0.504729\pi$
$367$	−18.5902	−	13.5065i	−0.970399	−	0.705036i	−0.955542	+	0.294854i	$0.904729\pi$
$368$	7.74721	−	2.51722i	0.403851	−	0.131219i
$369$	−3.72747	+	8.44720i	−0.194045	+	0.439744i
$370$		0			0
$371$	2.85317	−	2.07295i	0.148129	−	0.107622i
$372$	1.50328	−	1.86269i	0.0779416	−	0.0965762i
$373$			19.5357i			1.01152i	0.862675	+	0.505759i	$0.168788\pi$
$373$			19.5357i			1.01152i	−0.862675	+	0.505759i	$0.831212\pi$
$374$	10.6331	+	12.7254i	0.549826	+	0.658016i
$375$		0			0
$376$	−5.06231	−	1.64484i	−0.261068	−	0.0848263i
$377$	−6.88191	−	9.47214i	−0.354436	−	0.487840i
$378$	7.09799	+	1.08811i	0.365081	+	0.0559662i
$379$	−10.1631	−	31.2789i	−0.522044	−	1.60669i	−0.770087	−	0.637938i	$-0.779787\pi$
$379$	−10.1631	−	31.2789i	−0.522044	−	1.60669i	0.248043	−	0.968749i	$-0.420213\pi$
$380$		0			0
$381$	−19.1667	+	12.4922i	−0.981940	+	0.639993i
$382$	−22.0967	−	30.4136i	−1.13057	−	1.55609i
$383$	−13.7108	−	4.45492i	−0.700590	−	0.227636i	−0.0630025	−	0.998013i	$-0.520068\pi$
$383$	−13.7108	−	4.45492i	−0.700590	−	0.227636i	−0.637588	+	0.770378i	$0.720068\pi$
$384$	−9.23305	−	3.52671i	−0.471172	−	0.179972i
$385$		0			0
$386$		−	38.4164i		−	1.95534i
$387$	2.45086	+	4.21274i	0.124584	+	0.214146i
$388$	−8.66312	+	6.29412i	−0.439803	+	0.319536i
$389$	−5.65334	+	7.78115i	−0.286636	+	0.394520i	−0.927918	−	0.372785i	$-0.878403\pi$
$389$	−5.65334	+	7.78115i	−0.286636	+	0.394520i	0.641282	+	0.767305i	$0.278403\pi$
$390$		0			0
$391$	4.40983	−	1.43284i	0.223015	−	0.0724619i
$392$	3.80423	+	2.76393i	0.192142	+	0.139600i
$393$	6.82585	−	1.84110i	0.344318	−	0.0928710i
$394$	−9.30902	+	28.6502i	−0.468982	+	1.44338i
$395$		0			0
$396$	9.01916	+	13.3357i	0.453230	+	0.670143i
$397$	23.0000			1.15434			0.577168	−	0.816625i	$-0.304158\pi$
$397$	23.0000			1.15434			0.577168	+	0.816625i	$0.304158\pi$
$398$	−1.31433	+	4.04508i	−0.0658813	+	0.202762i
$399$	−5.16765	+	1.39384i	−0.258706	+	0.0697793i
$400$		0			0
$401$	−20.1109	+	6.53444i	−1.00429	+	0.326314i	−0.764580	−	0.644529i	$-0.777053\pi$
$401$	−20.1109	+	6.53444i	−1.00429	+	0.326314i	−0.239713	+	0.970844i	$0.577053\pi$
$402$	1.39029	−	27.3960i	0.0693416	−	1.36639i
$403$	−1.54508	+	2.12663i	−0.0769662	+	0.105935i
$404$	16.3395	−	11.8713i	0.812919	−	0.590620i
$405$		0			0
$406$		−	5.25731i		−	0.260916i
$407$	−0.673542	−	9.92705i	−0.0333862	−	0.492066i
$408$	−3.09017	−	1.18034i	−0.152986	−	0.0584355i
$409$	−32.5623	−	10.5801i	−1.61010	−	0.523154i	−0.640525	−	0.767938i	$-0.721283\pi$
$409$	−32.5623	−	10.5801i	−1.61010	−	0.523154i	−0.969578	+	0.244784i	$0.921283\pi$
$410$		0			0
$411$	12.6361	−	8.23575i	0.623293	−	0.406239i
$412$	3.38197	+	10.4086i	0.166618	+	0.512796i
$413$	−0.587785	−	1.80902i	−0.0289230	−	0.0890159i
$414$	9.83865	−	2.12534i	0.483543	−	0.104455i
$415$		0			0
$416$	−21.4580	−	6.97214i	−1.05207	−	0.341837i
$417$	−1.06957	+	2.80017i	−0.0523770	+	0.137125i
$418$	−22.7254	−	14.2658i	−1.11154	−	0.697765i
$419$			5.85410i			0.285992i	0.989723	+	0.142996i	$0.0456735\pi$
$419$			5.85410i			0.285992i	−0.989723	+	0.142996i	$0.954326\pi$
$420$		0			0
$421$	−20.9164	+	15.1967i	−1.01940	+	0.740640i	−0.966160	−	0.257942i	$-0.916956\pi$
$421$	−20.9164	+	15.1967i	−1.01940	+	0.740640i	−0.0532429	+	0.998582i	$0.516956\pi$
$422$	7.57570	−	10.4271i	0.368779	−	0.507581i
$423$	−20.1080	−	8.87303i	−0.977686	−	0.431421i
$424$	−3.35410	+	1.08981i	−0.162890	+	0.0529260i
$425$		0			0
$426$	−8.85950	−	32.8465i	−0.429244	−	1.59142i
$427$	0.954915	−	2.93893i	0.0462116	−	0.142225i
$428$	−0.277515			−0.0134142
$429$	−10.6342	−	14.1242i	−0.513426	−	0.681924i
$430$		0			0
$431$	6.96767	−	21.4443i	0.335621	−	1.03293i	−0.630795	−	0.775950i	$-0.717271\pi$
$431$	6.96767	−	21.4443i	0.335621	−	1.03293i	0.966416	−	0.256985i	$-0.0827290\pi$
$432$	−21.4344	−	10.7877i	−1.03126	−	0.519021i
$433$	−4.85410	−	3.52671i	−0.233273	−	0.169483i	0.465008	−	0.885307i	$-0.346051\pi$
$433$	−4.85410	−	3.52671i	−0.233273	−	0.169483i	−0.698281	+	0.715824i	$0.746051\pi$
$434$	−1.12257	+	0.364745i	−0.0538851	+	0.0175083i
$435$		0			0
$436$	−7.23607	+	9.95959i	−0.346545	+	0.476978i
$437$	−6.06961	+	4.40983i	−0.290349	+	0.210951i
$438$	39.0128	+	31.4852i	1.86410	+	1.50442i
$439$			25.3480i			1.20979i	0.796304	+	0.604897i	$0.206786\pi$
$439$			25.3480i			1.20979i	−0.796304	+	0.604897i	$0.793214\pi$
$440$		0			0
$441$	14.4721	+	12.9443i	0.689149	+	0.616394i
$442$	−14.6353	−	4.75528i	−0.696128	−	0.226186i
$443$	−6.15537	−	8.47214i	−0.292450	−	0.402523i	0.637358	−	0.770568i	$-0.280027\pi$
$443$	−6.15537	−	8.47214i	−0.292450	−	0.402523i	−0.929808	+	0.368045i	$0.880027\pi$
$444$	−4.59075	−	7.04358i	−0.217867	−	0.334273i
$445$		0			0
$446$	−3.66547	−	11.2812i	−0.173565	−	0.534178i
$447$	−0.162208	−	0.248876i	−0.00767218	−	0.0117714i
$448$	−2.01064	−	2.76741i	−0.0949940	−	0.130748i
$449$	−7.50245	−	2.43769i	−0.354063	−	0.115042i	0.126585	−	0.991956i	$-0.459598\pi$
$449$	−7.50245	−	2.43769i	−0.354063	−	0.115042i	−0.480648	+	0.876914i	$0.659598\pi$
$450$		0			0
$451$	9.89919	+	2.48990i	0.466135	+	0.117245i
$452$		−	32.2705i		−	1.51788i
$453$	−23.6792	−	19.1103i	−1.11255	−	0.897878i
$454$	9.73607	−	7.07367i	0.456936	−	0.331984i
$455$		0			0
$456$	5.34545	+	0.271271i	0.250324	+	0.0127034i
$457$	−10.2639	+	3.33495i	−0.480126	+	0.156003i	−0.539074	−	0.842259i	$-0.681226\pi$
$457$	−10.2639	+	3.33495i	−0.480126	+	0.156003i	0.0589473	+	0.998261i	$0.481226\pi$
$458$	−38.6628	−	28.0902i	−1.80659	−	1.31257i
$459$	−12.2008	−	6.14050i	−0.569485	−	0.286614i
$460$		0			0
$461$	−26.8666			−1.25130			−0.625651	−	0.780103i	$-0.715167\pi$
$461$	−26.8666			−1.25130			−0.625651	+	0.780103i	$0.715167\pi$
$462$	−0.135276	−	7.93764i	−0.00629363	−	0.369292i
$463$	0.270510			0.0125717			0.00628583	−	0.999980i	$-0.497999\pi$
$463$	0.270510			0.0125717			0.00628583	+	0.999980i	$0.497999\pi$
$464$	−5.42882	+	16.7082i	−0.252027	+	0.775659i
$465$		0			0
$466$	−11.0172	−	8.00448i	−0.510363	−	0.370800i
$467$	22.4948	−	7.30902i	1.04094	−	0.338221i	0.261831	−	0.965114i	$-0.415674\pi$
$467$	22.4948	−	7.30902i	1.04094	−	0.338221i	0.779106	+	0.626893i	$0.215674\pi$
$468$	−13.6679	−	6.03118i	−0.631797	−	0.278791i
$469$	−3.55573	+	4.89404i	−0.164188	+	0.225986i
$470$		0			0
$471$	−4.03373	+	4.99814i	−0.185864	+	0.230302i
$472$			1.90211i			0.0875518i
$473$	4.13474	−	3.45492i	0.190116	−	0.158857i
$474$	12.5623	−	32.8885i	0.577006	−	1.51062i
$475$		0			0
$476$	−1.81636	−	2.50000i	−0.0832526	−	0.114587i
$477$	−14.2340	+	3.07481i	−0.651729	+	0.140786i
$478$	15.1631	+	46.6673i	0.693545	+	2.13451i
$479$	−7.07367	−	21.7705i	−0.323204	−	0.994720i	−0.972245	−	0.233966i	$-0.924829\pi$
$479$	−7.07367	−	21.7705i	−0.323204	−	0.994720i	0.649041	−	0.760754i	$-0.275171\pi$
$480$		0			0
$481$	5.42705	+	7.46969i	0.247452	+	0.340589i
$482$	−35.4136	−	11.5066i	−1.61305	−	0.524110i
$483$	−2.07363	−	0.792055i	−0.0943533	−	0.0360397i
$484$	12.8541	−	12.3107i	0.584277	−	0.559579i
$485$		0			0
$486$	−25.0002	−	15.9427i	−1.13403	−	0.723177i
$487$	−6.04508	+	4.39201i	−0.273929	+	0.199021i	−0.716265	−	0.697828i	$-0.754150\pi$
$487$	−6.04508	+	4.39201i	−0.273929	+	0.199021i	0.442336	+	0.896849i	$0.354150\pi$
$488$	−1.81636	+	2.50000i	−0.0822226	+	0.113170i
$489$	1.08695	−	21.4186i	0.0491538	−	0.968584i
$490$		0			0
$491$	21.5968	+	15.6910i	0.974649	+	0.708124i	0.956506	−	0.291711i	$-0.0942246\pi$
$491$	21.5968	+	15.6910i	0.974649	+	0.708124i	0.0181429	+	0.999835i	$0.494225\pi$
$492$	8.32766	−	2.24617i	0.375440	−	0.101265i
$493$	−3.09017	+	9.51057i	−0.139174	+	0.428334i
$494$	24.8990			1.12026
$495$		0			0
$496$	3.94427			0.177103
$497$	−2.31838	+	7.13525i	−0.103994	+	0.320060i
$498$	46.0921	−	12.4322i	2.06544	−	0.557098i
$499$	−8.88197	−	6.45313i	−0.397611	−	0.288882i	0.370956	−	0.928650i	$-0.379030\pi$
$499$	−8.88197	−	6.45313i	−0.397611	−	0.288882i	−0.768567	+	0.639769i	$0.779030\pi$
$500$		0			0
$501$	0.00930534	−	0.183363i	0.000415732	−	0.00819207i
$502$	−5.22542	+	7.19218i	−0.233222	+	0.321003i
$503$	−4.25325	+	3.09017i	−0.189643	+	0.137784i	−0.678556	−	0.734549i	$-0.737394\pi$
$503$	−4.25325	+	3.09017i	−0.189643	+	0.137784i	0.488912	+	0.872333i	$0.337394\pi$
$504$	0.796332	+	1.36880i	0.0354714	+	0.0609713i
$505$		0			0
$506$	−4.14725	−	10.3262i	−0.184368	−	0.459057i
$507$	−5.70820	−	2.18034i	−0.253510	−	0.0968323i
$508$	20.3262	+	6.60440i	0.901831	+	0.293023i
$509$	−0.159002	−	0.218847i	−0.00704763	−	0.00970022i	0.805479	−	0.592625i	$-0.201908\pi$
$509$	−0.159002	−	0.218847i	−0.00704763	−	0.00970022i	−0.812526	+	0.582925i	$0.801908\pi$
$510$		0			0
$511$	−3.41641	−	10.5146i	−0.151133	−	0.465140i
$512$	8.38800	+	25.8156i	0.370701	+	1.14090i
$513$	21.8454	+	3.34885i	0.964496	+	0.147855i
$514$	12.6008	+	17.3435i	0.555798	+	0.764990i
$515$		0			0
$516$	1.62460	−	4.25325i	0.0715190	−	0.187239i
$517$	−5.92705	+	23.5644i	−0.260671	+	1.03636i
$518$			4.14590i			0.182160i
$519$	−24.1100	+	29.8744i	−1.05831	+	1.31134i
$520$		0			0
$521$	−11.9272	+	16.4164i	−0.522541	+	0.719216i	−0.985971	−	0.166918i	$-0.946619\pi$
$521$	−11.9272	+	16.4164i	−0.522541	+	0.719216i	0.463430	+	0.886134i	$0.346619\pi$
$522$	−8.76382	+	19.8606i	−0.383582	+	0.869273i
$523$	3.02786	−	0.983813i	0.132399	−	0.0430191i	−0.242068	−	0.970259i	$-0.577826\pi$
$523$	3.02786	−	0.983813i	0.132399	−	0.0430191i	0.374467	+	0.927240i	$0.377826\pi$
$524$	−5.34307	−	3.88197i	−0.233413	−	0.169584i
$525$		0			0
$526$	13.6803	−	42.1038i	0.596491	−	1.83581i
$527$	2.24514			0.0977998
$528$	−7.76667	+	25.3662i	−0.338001	+	1.10392i
$529$	19.8885			0.864719
$530$		0			0
$531$	−0.795113	+	7.81375i	−0.0345050	+	0.339088i
$532$	4.04508	+	2.93893i	0.175377	+	0.127419i
$533$	−9.00854	+	2.92705i	−0.390203	+	0.126785i
$534$	31.1664	+	1.58163i	1.34870	+	0.0684440i
$535$		0			0
$536$	4.89404	−	3.55573i	0.211390	−	0.153584i
$537$	−5.31632	−	4.29052i	−0.229416	−	0.185150i
$538$		−	44.1976i		−	1.90550i
$539$	11.4127	−	18.1803i	0.491579	−	0.783083i
$540$		0			0
$541$	23.5172	+	7.64121i	1.01108	+	0.328521i	0.767286	−	0.641305i	$-0.221607\pi$
$541$	23.5172	+	7.64121i	1.01108	+	0.328521i	0.243798	+	0.969826i	$0.421607\pi$
$542$	26.4051	+	36.3435i	1.13419	+	1.56109i
$543$	11.5722	+	17.7552i	0.496611	+	0.761950i
$544$	5.95492	+	18.3273i	0.255315	+	0.785778i
$545$		0			0
$546$	4.02250	+	6.17171i	0.172147	+	0.264125i
$547$	−18.0517	−	24.8460i	−0.771833	−	1.06234i	−0.996137	−	0.0878181i	$-0.972011\pi$
$547$	−18.0517	−	24.8460i	−0.771833	−	1.06234i	0.224303	−	0.974519i	$-0.427989\pi$
$548$	−13.4005	−	4.35410i	−0.572443	−	0.185998i
$549$	−8.50651	+	9.51057i	−0.363049	+	0.405901i
$550$		0			0
$551$		−	16.1803i		−	0.689306i
$552$	1.72738	+	1.39407i	0.0735221	+	0.0593358i
$553$	−6.28115	+	4.56352i	−0.267102	+	0.194061i
$554$	−22.9641	+	31.6074i	−0.975652	+	1.34287i
$555$		0			0
$556$	2.66312	−	0.865300i	0.112941	−	0.0366969i
$557$	6.51864	+	4.73607i	0.276204	+	0.200674i	0.717260	−	0.696806i	$-0.245396\pi$
$557$	6.51864	+	4.73607i	0.276204	+	0.200674i	−0.441056	+	0.897479i	$0.645396\pi$
$558$	4.84876	+	0.493401i	0.205264	+	0.0208873i
$559$	−1.54508	+	4.75528i	−0.0653501	+	0.201127i
$560$		0			0
$561$	−4.42091	+	14.4388i	−0.186651	+	0.609608i
$562$	31.3050			1.32052
$563$	7.10642	−	21.8713i	0.299500	−	0.921766i	−0.682173	−	0.731191i	$-0.738965\pi$
$563$	7.10642	−	21.8713i	0.299500	−	0.921766i	0.981673	−	0.190575i	$-0.0610353\pi$
$564$	5.34687	+	19.8235i	0.225144	+	0.834719i
$565$		0			0
$566$	14.3844	−	4.67376i	0.604620	−	0.196453i
$567$	2.69910	+	5.95583i	0.113351	+	0.250121i
$568$	4.40983	−	6.06961i	0.185032	−	0.254675i
$569$	6.60440	−	4.79837i	0.276871	−	0.201158i	−0.440681	−	0.897664i	$-0.645263\pi$
$569$	6.60440	−	4.79837i	0.276871	−	0.201158i	0.717551	+	0.696506i	$0.245263\pi$
$570$		0			0
$571$		−	6.04937i		−	0.253158i	−0.991957	−	0.126579i	$-0.959600\pi$
$571$		−	6.04937i		−	0.253158i	0.991957	−	0.126579i	$-0.0403997\pi$
$572$	−4.02874	+	16.0172i	−0.168450	+	0.669714i
$573$	12.2148	−	31.9787i	0.510280	−	1.33593i
$574$	−4.04508	−	1.31433i	−0.168839	−	0.0548590i
$575$		0			0
$576$	2.98240	+	13.8062i	0.124266	+	0.575257i
$577$	2.47214	+	7.60845i	0.102916	+	0.316744i	0.989236	−	0.146330i	$-0.0467463\pi$
$577$	2.47214	+	7.60845i	0.102916	+	0.316744i	−0.886319	+	0.463074i	$0.846746\pi$
$578$	−5.93085	−	18.2533i	−0.246691	−	0.759237i
$579$	29.3066	−	19.1009i	1.21794	−	0.793808i
$580$		0			0
$581$	−10.0126	−	3.25329i	−0.415392	−	0.134969i
$582$	−20.3682	−	7.77997i	−0.844290	−	0.322490i
$583$	6.00000	+	14.9394i	0.248495	+	0.618726i
$584$			11.0557i			0.457489i
$585$		0			0
$586$	−15.0623	+	10.9434i	−0.622218	+	0.452068i
$587$	3.49396	−	4.80902i	0.144211	−	0.198489i	−0.730801	−	0.682590i	$-0.760853\pi$
$587$	3.49396	−	4.80902i	0.144211	−	0.198489i	0.875012	+	0.484101i	$0.160853\pi$
$588$	0.919299	−	18.1150i	0.0379113	−	0.747048i
$589$	−3.45492	+	1.12257i	−0.142357	+	0.0462547i
$590$		0			0
$591$	−26.4848	+	7.14358i	−1.08944	+	0.293848i
$592$	4.28115	−	13.1760i	0.175954	−	0.541532i
$593$	3.35520			0.137781			0.0688907	−	0.997624i	$-0.478054\pi$
$593$	3.35520			0.137781			0.0688907	+	0.997624i	$0.478054\pi$
$594$	−12.7208	+	30.2115i	−0.521942	+	1.23959i
$595$		0			0
$596$	−0.0857567	+	0.263932i	−0.00351273	+	0.0108111i
$597$	−3.73935	+	1.00859i	−0.153041	+	0.0412790i
$598$	8.35410	+	6.06961i	0.341625	+	0.248205i
$599$	7.88597	−	2.56231i	0.322212	−	0.104693i	−0.143445	−	0.989658i	$-0.545818\pi$
$599$	7.88597	−	2.56231i	0.322212	−	0.104693i	0.465657	+	0.884965i	$0.345818\pi$
$600$		0			0
$601$	10.2254	−	14.0741i	0.417104	−	0.574094i	−0.547829	−	0.836590i	$-0.684546\pi$
$601$	10.2254	−	14.0741i	0.417104	−	0.574094i	0.964933	+	0.262496i	$0.0845457\pi$
$602$	−1.81636	+	1.31966i	−0.0740292	+	0.0537853i
$603$	21.5907	−	12.5609i	0.879243	−	0.511520i
$604$			28.4257i			1.15663i
$605$		0			0
$606$	38.4164	+	14.6738i	1.56056	+	0.596081i
$607$	11.7705	+	3.82447i	0.477750	+	0.155230i	0.537986	−	0.842954i	$-0.319185\pi$
$607$	11.7705	+	3.82447i	0.477750	+	0.155230i	−0.0602359	+	0.998184i	$0.519185\pi$
$608$	−18.3273	−	25.2254i	−0.743272	−	1.02303i
$609$	4.01062	−	2.61398i	0.162519	−	0.105924i
$610$		0			0
$611$	−6.96767	−	21.4443i	−0.281882	−	0.867542i
$612$	2.69421	+	12.4721i	0.108907	+	0.504154i
$613$	−13.8197	−	19.0211i	−0.558171	−	0.768256i	0.432922	−	0.901432i	$-0.357483\pi$
$613$	−13.8197	−	19.0211i	−0.558171	−	0.768256i	−0.991092	+	0.133175i	$0.957483\pi$
$614$	−10.6331	−	3.45492i	−0.429118	−	0.139429i
$615$		0			0
$616$	1.34346	−	1.12257i	0.0541295	−	0.0452296i
$617$			20.2361i			0.814673i	0.913278	+	0.407337i	$0.133542\pi$
$617$			20.2361i			0.814673i	−0.913278	+	0.407337i	$0.866458\pi$
$618$	−13.9952	+	17.3412i	−0.562969	+	0.697567i
$619$	−10.0451	+	7.29818i	−0.403746	+	0.293339i	−0.771065	−	0.636756i	$-0.780276\pi$
$619$	−10.0451	+	7.29818i	−0.403746	+	0.293339i	0.367319	+	0.930095i	$0.380276\pi$
$620$		0			0
$621$	6.51320	+	6.44884i	0.261366	+	0.258783i
$622$	−9.04508	+	2.93893i	−0.362675	+	0.117840i
$623$	−5.56758	−	4.04508i	−0.223060	−	0.162063i
$624$	−6.41080	−	23.7680i	−0.256637	−	0.951481i
$625$		0			0
$626$	−20.9232			−0.836261
$627$	−0.416338	−	24.4295i	−0.0166269	−	0.975622i
$628$	6.00000			0.239426
$629$	2.43690	−	7.50000i	0.0971655	−	0.299045i
$630$		0			0
$631$	10.0729	+	7.31843i	0.400998	+	0.291342i	0.769947	−	0.638108i	$-0.220282\pi$
$631$	10.0729	+	7.31843i	0.400998	+	0.291342i	−0.368950	+	0.929449i	$0.620282\pi$
$632$	7.38394	−	2.39919i	0.293717	−	0.0954345i
$633$	11.7211	+	0.594825i	0.465873	+	0.0236422i
$634$	0.263932	−	0.363271i	0.0104821	−	0.0144273i
$635$		0			0
$636$	10.5862	+	8.54358i	0.419771	+	0.338775i
$637$			19.9192i			0.789227i
$638$	23.2744	+	5.85410i	0.921442	+	0.231766i
$639$	20.6525	−	23.0902i	0.816999	−	0.913433i
$640$		0			0
$641$	−10.4944	−	14.4443i	−0.414503	−	0.570514i	0.549806	−	0.835292i	$-0.314701\pi$
$641$	−10.4944	−	14.4443i	−0.414503	−	0.570514i	−0.964310	+	0.264778i	$0.914701\pi$
$642$	−0.308538	−	0.473390i	−0.0121770	−	0.0186832i
$643$	−2.44427	−	7.52270i	−0.0963927	−	0.296666i	0.891221	−	0.453568i	$-0.149849\pi$
$643$	−2.44427	−	7.52270i	−0.0963927	−	0.296666i	−0.987614	+	0.156902i	$0.949849\pi$
$644$	0.640786	+	1.97214i	0.0252505	+	0.0777130i
$645$		0			0
$646$	−12.5000	−	17.2048i	−0.491806	−	0.676913i
$647$	41.9978	+	13.6459i	1.65110	+	0.536476i	0.978979	−	0.203963i	$-0.0653823\pi$
$647$	41.9978	+	13.6459i	1.65110	+	0.536476i	0.672124	+	0.740439i	$0.265382\pi$
$648$	−0.726543	−	6.49839i	−0.0285413	−	0.255281i
$649$	8.66312	−	0.587785i	0.340057	−	0.0230726i
$650$		0			0
$651$	−0.836402	−	0.675016i	−0.0327812	−	0.0264560i
$652$	−16.2082	+	11.7759i	−0.634762	+	0.461182i
$653$	−20.6582	+	28.4336i	−0.808419	+	1.11269i	0.183146	+	0.983086i	$0.441372\pi$
$653$	−20.6582	+	28.4336i	−0.808419	+	1.11269i	−0.991565	+	0.129608i	$0.958628\pi$
$654$	−25.0343	−	1.27044i	−0.978917	−	0.0496781i
$655$		0			0
$656$	11.4984	+	8.35410i	0.448938	+	0.326173i
$657$	−4.62147	+	45.4162i	−0.180301	+	1.77185i
$658$	3.12868	−	9.62908i	0.121969	−	0.375381i
$659$	39.8384			1.55188			0.775941	−	0.630805i	$-0.217275\pi$
$659$	39.8384			1.55188			0.775941	+	0.630805i	$0.217275\pi$
$660$		0			0
$661$	32.4508			1.26219			0.631096	−	0.775705i	$-0.282605\pi$
$661$	32.4508			1.26219			0.631096	+	0.775705i	$0.282605\pi$
$662$	−13.4535	+	41.4058i	−0.522887	+	1.60928i
$663$	−3.64912	−	13.5291i	−0.141720	−	0.525427i
$664$	8.51722	+	6.18812i	0.330532	+	0.240146i
$665$		0			0
$666$	6.91112	−	15.6620i	0.267800	−	0.606889i
$667$	3.94427	−	5.42882i	0.152723	−	0.210205i
$668$	−0.138757	+	0.100813i	−0.00536868	+	0.00390057i
$669$	6.78350	−	8.40534i	0.262265	−	0.324969i
$670$		0			0
$671$	11.9475	+	7.50000i	0.461227	+	0.289534i
$672$	3.29180	−	8.61803i	0.126984	−	0.332448i
$673$	28.5795	+	9.28605i	1.10166	+	0.357951i	0.802741	−	0.596328i	$-0.203374\pi$
$673$	28.5795	+	9.28605i	1.10166	+	0.357951i	0.298919	+	0.954279i	$0.403374\pi$
$674$	11.5187	+	15.8541i	0.443683	+	0.610677i
$675$		0			0
$676$	1.76393	+	5.42882i	0.0678435	+	0.208801i
$677$	−12.2047	−	37.5623i	−0.469066	−	1.44364i	−0.853796	−	0.520608i	$-0.825705\pi$
$677$	−12.2047	−	37.5623i	−0.469066	−	1.44364i	0.384730	−	0.923029i	$-0.374295\pi$
$678$	55.0477	−	35.8781i	2.11409	−	1.37789i
$679$	2.82624	+	3.88998i	0.108461	+	0.149284i
$680$		0			0
$681$	10.2371	+	3.91023i	0.392287	+	0.149840i
$682$	−0.364745	−	5.37582i	−0.0139668	−	0.205851i
$683$			9.00000i			0.344375i	0.985064	+	0.172188i	$0.0550836\pi$
$683$			9.00000i			0.344375i	−0.985064	+	0.172188i	$0.944916\pi$
$684$	−10.3820	−	17.8455i	−0.396966	−	0.682338i
$685$		0			0
$686$	−10.9434	+	15.0623i	−0.417821	+	0.575082i
$687$	2.20557	−	43.4612i	0.0841478	−	1.65815i
$688$	7.13525	−	2.31838i	0.272029	−	0.0883876i
$689$	−12.0862	−	8.78115i	−0.460448	−	0.334535i
$690$		0			0
$691$	10.6180	−	32.6789i	0.403929	−	1.24317i	−0.517857	−	0.855467i	$-0.673270\pi$
$691$	10.6180	−	32.6789i	0.403929	−	1.24317i	0.921786	−	0.387699i	$-0.126730\pi$
$692$	35.8626			1.36329
$693$	5.98809	−	4.04985i	0.227469	−	0.153841i
$694$	−58.5410			−2.22219
$695$		0			0
$696$	−4.62209	+	1.24669i	−0.175200	+	0.0472556i
$697$	6.54508	+	4.75528i	0.247913	+	0.180119i
$698$	29.4625	−	9.57295i	1.11517	−	0.362341i
$699$	0.628492	−	12.3845i	0.0237717	−	0.468427i
$700$		0			0
$701$	−14.1271	+	10.2639i	−0.533573	+	0.387663i	−0.821693	−	0.569931i	$-0.806970\pi$
$701$	−14.1271	+	10.2639i	−0.533573	+	0.387663i	0.288120	+	0.957594i	$0.406970\pi$
$702$	−4.90769	−	30.0203i	−0.185229	−	1.13304i
$703$			12.7598i			0.481244i
$704$	14.4904	−	5.81966i	0.546126	−	0.219337i
$705$		0			0
$706$	28.2148	+	9.16754i	1.06188	+	0.345025i
$707$	−5.33056	−	7.33688i	−0.200476	−	0.275932i
$708$	6.14677	−	4.00624i	0.231010	−	0.150564i
$709$	5.40983	+	16.6497i	0.203170	+	0.625294i	0.999784	+	0.0208048i	$0.00662286\pi$
$709$	5.40983	+	16.6497i	0.203170	+	0.625294i	−0.796613	+	0.604489i	$0.793377\pi$
$710$		0			0
$711$	31.3356	−	6.76910i	1.17518	−	0.253861i
$712$	4.04508	+	5.56758i	0.151596	+	0.208654i
$713$	−1.43284	−	0.465558i	−0.0536603	−	0.0174353i
$714$	2.24514	−	5.87785i	0.0840222	−	0.219973i
$715$		0			0
$716$			6.38197i			0.238505i
$717$	−28.0616	+	34.7708i	−1.04798	+	1.29854i
$718$	−38.4164	+	27.9112i	−1.43369	+	1.04164i
$719$	5.95110	−	8.19098i	0.221938	−	0.305472i	−0.683499	−	0.729951i	$-0.739543\pi$
$719$	5.95110	−	8.19098i	0.221938	−	0.305472i	0.905438	+	0.424479i	$0.139543\pi$
$720$		0			0
$721$	4.67376	−	1.51860i	0.174060	−	0.0565555i
$722$	−1.40008	−	1.01722i	−0.0521057	−	0.0378570i
$723$	−8.82995	−	32.7370i	−0.328390	−	1.21750i
$724$	6.11803	−	18.8294i	0.227375	−	0.699788i
$725$		0			0
$726$	35.2910	+	8.23981i	1.30977	+	0.305808i
$727$	21.1459			0.784258			0.392129	−	0.919910i	$-0.371739\pi$
$727$	21.1459			0.784258			0.392129	+	0.919910i	$0.371739\pi$
$728$	−0.502029	+	1.54508i	−0.0186064	+	0.0572647i
$729$	−0.268157	−	26.9987i	−0.00993173	−	0.999951i
$730$		0			0
$731$	4.06150	−	1.31966i	0.150220	−	0.0488094i
$732$	11.9045	+	0.604130i	0.440003	+	0.0223293i
$733$	−20.2016	+	27.8052i	−0.746164	+	1.02701i	0.252076	+	0.967707i	$0.418887\pi$
$733$	−20.2016	+	27.8052i	−0.746164	+	1.02701i	−0.998240	+	0.0592994i	$0.981113\pi$
$734$	−35.3606	+	25.6910i	−1.30518	+	0.948271i
$735$		0			0
$736$		−	12.9313i		−	0.476653i
$737$	−17.7068	−	21.1910i	−0.652238	−	0.780580i
$738$	13.0902	+	11.7082i	0.481856	+	0.430985i
$739$	−15.4894	−	5.03280i	−0.569785	−	0.185134i	0.00993415	−	0.999951i	$-0.496838\pi$
$739$	−15.4894	−	5.03280i	−0.569785	−	0.185134i	−0.579719	+	0.814816i	$0.696838\pi$
$740$		0			0
$741$	12.3800	+	18.9946i	0.454790	+	0.697783i
$742$	−2.07295	−	6.37988i	−0.0761004	−	0.234213i
$743$	−12.9188	−	39.7599i	−0.473943	−	1.45865i	−0.847377	−	0.530991i	$-0.821820\pi$
$743$	−12.9188	−	39.7599i	−0.473943	−	1.45865i	0.373434	−	0.927657i	$-0.378180\pi$
$744$	0.586874	+	0.900441i	0.0215159	+	0.0330118i
$745$		0			0
$746$	35.3404	+	11.4828i	1.29390	+	0.420414i
$747$	32.4014	+	28.9807i	1.18551	+	1.06035i
$748$	13.0902	−	5.25731i	0.478624	−	0.192226i
$749$			0.124612i			0.00455322i
$750$		0			0
$751$	−4.50000	+	3.26944i	−0.164207	+	0.119304i	−0.666854	−	0.745188i	$-0.732360\pi$
$751$	−4.50000	+	3.26944i	−0.164207	+	0.119304i	0.502647	+	0.864492i	$0.332360\pi$
$752$	−19.8864	+	27.3713i	−0.725183	+	0.998129i
$753$	−8.08479	−	0.410287i	−0.294626	−	0.0149517i
$754$	−21.1803	+	6.88191i	−0.771342	+	0.250624i
$755$		0			0
$756$	2.74611	−	5.45637i	0.0998752	−	0.198446i
$757$	7.69098	−	23.6704i	0.279534	−	0.860316i	−0.708451	−	0.705760i	$-0.750606\pi$
$757$	7.69098	−	23.6704i	0.279534	−	0.860316i	0.987984	−	0.154555i	$-0.0493945\pi$
$758$	−62.5577			−2.27220
$759$	5.81548	−	8.29808i	0.211089	−	0.301201i
$760$		0			0
$761$	−13.6453	+	41.9959i	−0.494642	+	1.52235i	0.322872	+	0.946443i	$0.395352\pi$
$761$	−13.6453	+	41.9959i	−0.494642	+	1.52235i	−0.817514	+	0.575909i	$0.804648\pi$
$762$	11.3326	+	42.0156i	0.410538	+	1.52206i
$763$	4.47214	+	3.24920i	0.161902	+	0.117629i
$764$	−30.4136	+	9.88197i	−1.10032	+	0.357517i
$765$		0			0
$766$	−16.1180	+	22.1846i	−0.582368	+	0.801561i
$767$	−6.51864	+	4.73607i	−0.235374	+	0.171010i
$768$	−22.0500	+	27.3218i	−0.795659	+	0.985890i
$769$			26.8666i			0.968835i	0.874837	+	0.484417i	$0.160968\pi$
$769$			26.8666i			0.968835i	−0.874837	+	0.484417i	$0.839032\pi$
$770$		0			0
$771$	−6.96556	+	18.2361i	−0.250858	+	0.656756i
$772$	−31.0795	−	10.0984i	−1.11858	−	0.363448i
$773$	−4.60401	−	6.33688i	−0.165595	−	0.227922i	0.718153	−	0.695885i	$-0.244988\pi$
$773$	−4.60401	−	6.33688i	−0.165595	−	0.227922i	−0.883748	+	0.467964i	$0.844988\pi$
$774$	9.06150	−	1.95746i	0.325709	−	0.0703593i
$775$		0			0
$776$	−1.48584	−	4.57295i	−0.0533386	−	0.164159i
$777$	−3.16276	+	2.06137i	−0.113463	+	0.0739514i
$778$	10.7533	+	14.8006i	0.385524	+	0.530628i
$779$	−12.4495	−	4.04508i	−0.446049	−	0.144930i
$780$		0			0
$781$	−29.0066	−	18.2088i	−1.03794	−	0.651563i
$782$		−	8.81966i		−	0.315390i
$783$	−19.5084	+	3.18921i	−0.697172	+	0.113973i
$784$	24.1803	−	17.5680i	0.863584	−	0.627430i
$785$		0			0
$786$	0.681559	−	13.4302i	0.0243104	−	0.479041i
$787$	51.8328	−	16.8415i	1.84764	−	0.600335i	0.850396	−	0.526143i	$-0.176362\pi$
$787$	51.8328	−	16.8415i	1.84764	−	0.600335i	0.997244	−	0.0741922i	$-0.0236378\pi$
$788$	20.7315	+	15.0623i	0.738529	+	0.536572i
$789$	38.9215	−	10.4981i	1.38564	−	0.373741i
$790$		0			0
$791$	−14.4904			−0.515218
$792$	−6.94649	+	2.00122i	−0.246833	+	0.0711102i
$793$	−13.0902			−0.464846
$794$	13.5191	−	41.6074i	0.479774	−	1.47659i
$795$		0			0
$796$	2.92705	+	2.12663i	0.103747	+	0.0753763i
$797$	20.9888	−	6.81966i	0.743460	−	0.241565i	0.0872952	−	0.996182i	$-0.472178\pi$
$797$	20.9888	−	6.81966i	0.743460	−	0.241565i	0.656165	+	0.754618i	$0.272178\pi$
$798$	−0.515989	+	10.1677i	−0.0182658	+	0.359931i
$799$	−11.3197	+	15.5802i	−0.400461	+	0.551187i
$800$		0			0
$801$	14.2896	+	24.5622i	0.504898	+	0.867861i
$802$			40.2219i			1.42028i
$803$	50.3530	−	3.41641i	1.77692	−	0.120562i
$804$	−21.7984	−	8.32624i	−0.768769	−	0.293644i
$805$		0			0
$806$	2.93893	+	4.04508i	0.103519	+	0.142482i
$807$	33.7168	−	21.9754i	1.18689	−	0.773571i
$808$	2.80244	+	8.62502i	0.0985895	+	0.303427i
$809$	−8.09024	−	24.8992i	−0.284438	−	0.875409i	−0.986567	−	0.163359i	$-0.947767\pi$
$809$	−8.09024	−	24.8992i	−0.284438	−	0.875409i	0.702129	−	0.712050i	$-0.252233\pi$
$810$		0			0
$811$	−7.60081	−	10.4616i	−0.266901	−	0.367357i	0.654440	−	0.756114i	$-0.272905\pi$
$811$	−7.60081	−	10.4616i	−0.266901	−	0.367357i	−0.921340	+	0.388757i	$0.872905\pi$
$812$	−4.25325	−	1.38197i	−0.149260	−	0.0484975i
$813$	−14.5964	+	38.2138i	−0.511917	+	1.34022i
$814$	−18.3541	−	4.61653i	−0.643311	−	0.161809i
$815$		0			0
$816$	−13.2049	+	16.3620i	−0.462263	+	0.572783i
$817$	−5.59017	+	4.06150i	−0.195575	+	0.142094i
$818$	−38.2793	+	52.6869i	−1.33840	+	1.84215i
$819$	−2.70817	+	6.13725i	−0.0946311	+	0.214453i
$820$		0			0
$821$	29.9115	+	21.7320i	1.04392	+	0.758452i	0.971047	−	0.238889i	$-0.0767832\pi$
$821$	29.9115	+	21.7320i	1.04392	+	0.758452i	0.0728729	+	0.997341i	$0.476783\pi$
$822$	−7.47129	−	27.6998i	−0.260591	−	0.966140i
$823$	4.36475	−	13.4333i	0.152145	−	0.468256i	−0.845715	−	0.533635i	$-0.820826\pi$
$823$	4.36475	−	13.4333i	0.152145	−	0.468256i	0.997860	+	0.0653792i	$0.0208257\pi$
$824$	−4.91428			−0.171197
$825$		0			0
$826$	−3.61803			−0.125888
$827$	0.106001	−	0.326238i	0.00368602	−	0.0113444i	−0.949197	−	0.314684i	$-0.898102\pi$
$827$	0.106001	−	0.326238i	0.00368602	−	0.0113444i	0.952883	+	0.303339i	$0.0981016\pi$
$828$	0.866808	−	8.51832i	0.0301237	−	0.296032i
$829$	−22.8713	−	16.6170i	−0.794354	−	0.577132i	0.114898	−	0.993377i	$-0.463346\pi$
$829$	−22.8713	−	16.6170i	−0.794354	−	0.577132i	−0.909252	+	0.416245i	$0.863346\pi$
$830$		0			0
$831$	−35.5301	−	1.80309i	−1.23253	−	0.0625483i
$832$	−8.51722	+	11.7229i	−0.295282	+	0.406420i
$833$	13.7638	−	10.0000i	0.476888	−	0.346479i
$834$	4.43688	+	3.58077i	0.153636	+	0.123992i
$835$		0			0
$836$	−17.5150	+	14.6353i	−0.605770	+	0.506171i
$837$	2.03444	+	3.94427i	0.0703206	+	0.136334i
$838$	10.5902	+	3.44095i	0.365831	+	0.118866i
$839$	−17.4293	−	23.9894i	−0.601726	−	0.828205i	0.394139	−	0.919051i	$-0.371043\pi$
$839$	−17.4293	−	23.9894i	−0.601726	−	0.828205i	−0.995865	+	0.0908462i	$0.971043\pi$
$840$		0			0
$841$	−4.48936	−	13.8168i	−0.154805	−	0.476442i
$842$	15.1967	+	46.7705i	0.523711	+	1.61182i
$843$	15.5651	+	23.8815i	0.536090	+	0.822521i
$844$	−6.44427	−	8.86978i	−0.221821	−	0.305310i
$845$		0			0
$846$	−27.8707	+	31.1604i	−0.958213	+	1.07131i
$847$	−5.52786	−	5.77185i	−0.189940	−	0.198323i
$848$			22.4164i			0.769783i
$849$	10.7175	+	8.64950i	0.367823	+	0.296850i
$850$		0			0
$851$	−3.11044	+	4.28115i	−0.106624	+	0.146756i
$852$	−28.9023	−	1.46673i	−0.990175	−	0.0502495i
$853$	−43.0517	+	13.9883i	−1.47406	+	0.478951i	−0.932332	−	0.361602i	$-0.882230\pi$
$853$	−43.0517	+	13.9883i	−1.47406	+	0.478951i	−0.541728	+	0.840554i	$0.682230\pi$
$854$	−4.75528	−	3.45492i	−0.162722	−	0.118225i
$855$		0			0
$856$	0.0385072	−	0.118513i	0.00131615	−	0.00405069i
$857$	−24.2380			−0.827953			−0.413976	−	0.910288i	$-0.635860\pi$
$857$	−24.2380			−0.827953			−0.413976	+	0.910288i	$0.635860\pi$
$858$	−31.8016	+	10.9355i	−1.08569	+	0.373332i
$859$	34.5279			1.17808			0.589038	−	0.808106i	$-0.299507\pi$
$859$	34.5279			1.17808			0.589038	+	0.808106i	$0.299507\pi$
$860$		0			0
$861$	−1.00859	−	3.73935i	−0.0343728	−	0.127437i
$862$	−34.6976	−	25.2093i	−1.18180	−	0.858631i
$863$	−37.2097	+	12.0902i	−1.26663	+	0.411554i	−0.863854	−	0.503743i	$-0.831956\pi$
$863$	−37.2097	+	12.0902i	−1.26663	+	0.411554i	−0.402780	+	0.915297i	$0.631956\pi$
$864$	−26.8015	+	27.0690i	−0.911805	+	0.920907i
$865$		0			0
$866$	−9.23305	+	6.70820i	−0.313752	+	0.227954i
$867$	10.9759	−	13.6001i	0.372762	−	0.461884i
$868$			1.00406i			0.0340799i
$869$	−13.2088	−	32.8885i	−0.448078	−	1.11567i
$870$		0			0
$871$	24.3713	+	7.91872i	0.825791	+	0.268316i
$872$	−3.24920	−	4.47214i	−0.110032	−	0.151446i
$873$	−4.19217	−	19.4065i	−0.141883	−	0.656809i
$874$	4.40983	+	13.5721i	0.149165	+	0.459082i
$875$		0			0
$876$	35.7271	−	23.2856i	1.20711	−	0.786749i
$877$	4.77458	+	6.57164i	0.161226	+	0.221908i	0.881985	−	0.471277i	$-0.156207\pi$
$877$	4.77458	+	6.57164i	0.161226	+	0.221908i	−0.720759	+	0.693185i	$0.756207\pi$
$878$	45.8550	+	14.8992i	1.54753	+	0.502823i
$879$	−15.8374	−	6.04937i	−0.534184	−	0.204040i
$880$		0			0
$881$			34.9230i			1.17659i	0.808648	+	0.588293i	$0.200200\pi$
$881$			34.9230i			1.17659i	−0.808648	+	0.588293i	$0.799800\pi$
$882$	31.9229	−	18.5719i	1.07490	−	0.625348i
$883$	−14.4164	+	10.4741i	−0.485151	+	0.352483i	−0.803316	−	0.595552i	$-0.796933\pi$
$883$	−14.4164	+	10.4741i	−0.485151	+	0.352483i	0.318166	+	0.948035i	$0.396933\pi$
$884$	−7.69421	+	10.5902i	−0.258784	+	0.356186i
$885$		0			0
$886$	−18.9443	+	6.15537i	−0.636445	+	0.206794i
$887$	7.91872	+	5.75329i	0.265885	+	0.193177i	0.712737	−	0.701431i	$-0.247455\pi$
$887$	7.91872	+	5.75329i	0.265885	+	0.193177i	−0.446853	+	0.894608i	$0.647455\pi$
$888$	3.64497	−	0.983135i	0.122317	−	0.0329919i
$889$	2.96556	−	9.12705i	0.0994616	−	0.306111i
$890$		0			0
$891$	−29.3722	+	5.31713i	−0.984007	+	0.178131i
$892$	−10.0902			−0.337844
$893$	9.62908	−	29.6353i	0.322225	−	0.991706i
$894$	−0.545564	+	0.147152i	−0.0182464	+	0.00492149i
$895$		0			0
$896$	3.94298	−	1.28115i	0.131726	−	0.0428003i
$897$	−0.476571	+	9.39092i	−0.0159122	+	0.313554i
$898$	−8.81966	+	12.1392i	−0.294316	+	0.405091i
$899$	2.62866	−	1.90983i	0.0876706	−	0.0636964i
$900$		0			0
$901$			12.7598i			0.425089i
$902$	10.3229	−	16.4443i	0.343714	−	0.547534i
$903$	−1.90983	−	0.729490i	−0.0635552	−	0.0242759i
$904$	13.7812	+	4.47777i	0.458354	+	0.148928i
$905$		0			0
$906$	−48.4891	+	31.6034i	−1.61094	+	1.04995i
$907$	−13.1008	−	40.3202i	−0.435005	−	1.33881i	−0.893081	−	0.449896i	$-0.851461\pi$
$907$	−13.1008	−	40.3202i	−0.435005	−	1.33881i	0.458076	−	0.888913i	$-0.348539\pi$
$908$	−3.16344	−	9.73607i	−0.104982	−	0.323103i
$909$	7.90684	+	36.6025i	0.262253	+	1.21403i
$910$		0			0
$911$	54.8963	+	17.8369i	1.81879	+	0.590962i	0.999854	+	0.0170841i	$0.00543829\pi$
$911$	54.8963	+	17.8369i	1.81879	+	0.590962i	0.818941	+	0.573878i	$0.194562\pi$
$912$	12.1392	−	31.7809i	0.401970	−	1.05237i
$913$	25.5517	−	40.7037i	0.845637	−	1.34709i
$914$			20.5279i			0.679001i
$915$		0			0
$916$	−32.8885	+	23.8949i	−1.08667	+	0.789511i
$917$	−1.74311	+	2.39919i	−0.0575626	+	0.0792281i
$918$	−18.2797	+	18.4622i	−0.603321	+	0.609343i
$919$	29.7599	−	9.66957i	0.981687	−	0.318970i	0.226163	−	0.974090i	$-0.427382\pi$
$919$	29.7599	−	9.66957i	0.981687	−	0.318970i	0.755525	+	0.655120i	$0.227382\pi$
$920$		0			0
$921$	−2.65124	−	9.82946i	−0.0873614	−	0.323892i
$922$	−15.7918	+	48.6022i	−0.520075	+	1.60063i
$923$	31.7809			1.04608
$924$	−6.45724	−	1.97709i	−0.212428	−	0.0650415i
$925$		0			0
$926$	0.159002	−	0.489357i	0.00522512	−	0.0160813i
$927$	−20.1875	−	2.05425i	−0.663046	−	0.0674704i
$928$	22.5623	+	16.3925i	0.740644	+	0.538109i
$929$	28.8217	−	9.36475i	0.945610	−	0.307247i	0.204680	−	0.978829i	$-0.434385\pi$
$929$	28.8217	−	9.36475i	0.945610	−	0.307247i	0.740930	+	0.671582i	$0.234385\pi$
$930$		0			0
$931$	−16.1803	+	22.2703i	−0.530289	+	0.729880i
$932$	−9.37181	+	6.80902i	−0.306984	+	0.223037i
$933$	−6.73929	−	5.43893i	−0.220635	−	0.178062i
$934$		−	44.9897i		−	1.47211i
$935$		0			0
$936$	4.47214	−	5.00000i	0.146176	−	0.163430i
$937$	36.0172	+	11.7027i	1.17663	+	0.382311i	0.831114	−	0.556102i	$-0.187704\pi$
$937$	36.0172	+	11.7027i	1.17663	+	0.382311i	0.345517	+	0.938412i	$0.387704\pi$
$938$	6.76340	+	9.30902i	0.220833	+	0.303950i
$939$	−10.4032	−	15.9616i	−0.339496	−	0.520888i
$940$		0			0
$941$	−14.9596	−	46.0410i	−0.487670	−	1.50089i	−0.828076	−	0.560616i	$-0.810564\pi$
$941$	−14.9596	−	46.0410i	−0.487670	−	1.50089i	0.340406	−	0.940279i	$-0.389436\pi$
$942$	6.67074	+	10.2349i	0.217345	+	0.333472i
$943$	−3.19098	−	4.39201i	−0.103913	−	0.143024i
$944$	11.4984	+	3.73607i	0.374242	+	0.121599i
$945$		0			0
$946$	−3.81966	−	9.51057i	−0.124188	−	0.309215i
$947$			23.8541i			0.775154i	0.921837	+	0.387577i	$0.126688\pi$
$947$			23.8541i			0.775154i	−0.921837	+	0.387577i	$0.873312\pi$
$948$	−23.3052	−	18.8084i	−0.756917	−	0.610868i
$949$	−37.8885	+	27.5276i	−1.22991	+	0.893585i
$950$		0			0
$951$	0.408356	+	0.0207233i	0.0132419	+	0.000671999i
$952$	1.31966	−	0.428784i	0.0427704	−	0.0138970i
$953$	36.0341	+	26.1803i	1.16726	+	0.848064i	0.990678	−	0.136222i	$-0.0434959\pi$
$953$	36.0341	+	26.1803i	1.16726	+	0.848064i	0.176582	+	0.984286i	$0.443496\pi$
$954$	−2.80413	+	27.5568i	−0.0907872	+	0.892186i
$955$		0			0
$956$	41.7405			1.34998
$957$	7.10632	+	20.6659i	0.229715	+	0.668035i
$958$	−43.5410			−1.40675
$959$	−1.95511	+	6.01722i	−0.0631339	+	0.194306i
$960$		0			0
$961$	24.4894	+	17.7926i	0.789979	+	0.573954i
$962$	16.7027	−	5.42705i	0.538518	−	0.174975i
$963$	0.207725	−	0.470746i	0.00669385	−	0.0151696i
$964$	−18.6180	+	25.6255i	−0.599646	+	0.825343i
$965$		0			0
$966$	−2.65169	+	3.28567i	−0.0853167	+	0.105715i
$967$		−	20.9232i		−	0.672846i	−0.941711	−	0.336423i	$-0.890783\pi$
$967$		−	20.9232i		−	0.672846i	0.941711	−	0.336423i	$-0.109217\pi$
$968$	3.47371	+	7.19756i	0.111649	+	0.231338i
$969$	6.90983	−	18.0902i	0.221976	−	0.581140i
$970$		0			0
$971$	−8.33499	−	11.4721i	−0.267483	−	0.368158i	0.654055	−	0.756447i	$-0.273066\pi$
$971$	−8.33499	−	11.4721i	−0.267483	−	0.368158i	−0.921538	+	0.388288i	$0.873066\pi$
$972$	−19.4696	+	16.0348i	−0.624489	+	0.514317i
$973$	−0.388544	−	1.19581i	−0.0124561	−	0.0383361i
$974$	4.39201	+	13.5172i	0.140729	+	0.433120i
$975$		0			0
$976$	11.5451	+	15.8904i	0.369549	+	0.508641i
$977$	−49.4019	−	16.0517i	−1.58051	−	0.513538i	−0.618320	−	0.785926i	$-0.712187\pi$
$977$	−49.4019	−	16.0517i	−1.58051	−	0.513538i	−0.962188	+	0.272388i	$0.912187\pi$
$978$	−38.1078	−	14.5559i	−1.21855	−	0.465446i
$979$	24.1074	−	20.1437i	0.770476	−	0.643795i
$980$		0			0
$981$	−11.4781	−	19.7294i	−0.366466	−	0.629913i
$982$	41.0795	−	29.8460i	1.31090	−	0.952425i
$983$	−3.11817	+	4.29180i	−0.0994543	+	0.136887i	−0.855844	−	0.517234i	$-0.826962\pi$
$983$	−3.11817	+	4.29180i	−0.0994543	+	0.136887i	0.756389	+	0.654122i	$0.226962\pi$
$984$	−0.196294	+	3.86801i	−0.00625762	+	0.123308i
$985$		0			0
$986$	15.3884	+	11.1803i	0.490067	+	0.356055i
$987$	8.90130	−	2.40089i	0.283331	−	0.0764213i
$988$	6.54508	−	20.1437i	0.208227	−	0.640856i
$989$	−2.86568			−0.0911234
$990$		0			0
$991$	7.56231			0.240225			0.120112	−	0.992760i	$-0.461675\pi$
$991$	7.56231			0.240225			0.120112	+	0.992760i	$0.461675\pi$
$992$	1.93487	−	5.95492i	0.0614322	−	0.189069i
$993$	−38.2762	+	10.3240i	−1.21466	+	0.327623i
$994$	11.5451	+	8.38800i	0.366188	+	0.266051i
$995$		0			0
$996$	2.05820	−	40.5573i	0.0652167	−	1.28511i
$997$	24.0066	−	33.0422i	0.760296	−	1.04646i	−0.236893	−	0.971536i	$-0.576129\pi$
$997$	24.0066	−	33.0422i	0.760296	−	1.04646i	0.997189	−	0.0749220i	$-0.0238708\pi$
$998$	−16.8945	+	12.2746i	−0.534786	+	0.388545i
$999$	15.3842	−	2.51500i	0.486736	−	0.0795711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bi.b.101.2		8
3.2	odd	2	inner	825.2.bi.b.101.1		8
5.2	odd	4		825.2.bs.d.299.1		8
5.3	odd	4		825.2.bs.a.299.2		8
5.4	even	2		33.2.f.a.2.1	✓	8
11.6	odd	10	inner	825.2.bi.b.776.1		8
15.2	even	4		825.2.bs.a.299.1		8
15.8	even	4		825.2.bs.d.299.2		8
15.14	odd	2		33.2.f.a.2.2	yes	8
20.19	odd	2		528.2.bn.c.497.2		8
33.17	even	10	inner	825.2.bi.b.776.2		8
45.4	even	6		891.2.u.a.431.1		16
45.14	odd	6		891.2.u.a.431.2		16
45.29	odd	6		891.2.u.a.134.1		16
45.34	even	6		891.2.u.a.134.2		16
55.4	even	10		363.2.d.f.362.2		8
55.9	even	10		363.2.f.d.239.2		8
55.14	even	10		363.2.f.e.161.2		8
55.17	even	20		825.2.bs.d.149.2		8
55.19	odd	10		363.2.f.d.161.1		8
55.24	odd	10		363.2.f.e.239.1		8
55.28	even	20		825.2.bs.a.149.1		8
55.29	odd	10		363.2.d.f.362.8		8
55.39	odd	10		33.2.f.a.17.2	yes	8
55.49	even	10		363.2.f.b.215.1		8
55.54	odd	2		363.2.f.b.233.2		8
60.59	even	2		528.2.bn.c.497.1		8
165.14	odd	10		363.2.f.e.161.1		8
165.17	odd	20		825.2.bs.a.149.2		8
165.29	even	10		363.2.d.f.362.1		8
165.59	odd	10		363.2.d.f.362.7		8
165.74	even	10		363.2.f.d.161.2		8
165.83	odd	20		825.2.bs.d.149.1		8
165.104	odd	10		363.2.f.b.215.2		8
165.119	odd	10		363.2.f.d.239.1		8
165.134	even	10		363.2.f.e.239.2		8
165.149	even	10		33.2.f.a.17.1	yes	8
165.164	even	2		363.2.f.b.233.1		8
220.39	even	10		528.2.bn.c.17.1		8
495.94	odd	30		891.2.u.a.512.1		16
495.149	even	30		891.2.u.a.512.2		16
495.259	odd	30		891.2.u.a.215.2		16
495.479	even	30		891.2.u.a.215.1		16
660.479	odd	10		528.2.bn.c.17.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.f.a.2.1	✓	8	5.4	even	2
33.2.f.a.2.2	yes	8	15.14	odd	2
33.2.f.a.17.1	yes	8	165.149	even	10
33.2.f.a.17.2	yes	8	55.39	odd	10
363.2.d.f.362.1		8	165.29	even	10
363.2.d.f.362.2		8	55.4	even	10
363.2.d.f.362.7		8	165.59	odd	10
363.2.d.f.362.8		8	55.29	odd	10
363.2.f.b.215.1		8	55.49	even	10
363.2.f.b.215.2		8	165.104	odd	10
363.2.f.b.233.1		8	165.164	even	2
363.2.f.b.233.2		8	55.54	odd	2
363.2.f.d.161.1		8	55.19	odd	10
363.2.f.d.161.2		8	165.74	even	10
363.2.f.d.239.1		8	165.119	odd	10
363.2.f.d.239.2		8	55.9	even	10
363.2.f.e.161.1		8	165.14	odd	10
363.2.f.e.161.2		8	55.14	even	10
363.2.f.e.239.1		8	55.24	odd	10
363.2.f.e.239.2		8	165.134	even	10
528.2.bn.c.17.1		8	220.39	even	10
528.2.bn.c.17.2		8	660.479	odd	10
528.2.bn.c.497.1		8	60.59	even	2
528.2.bn.c.497.2		8	20.19	odd	2
825.2.bi.b.101.1		8	3.2	odd	2	inner
825.2.bi.b.101.2		8	1.1	even	1	trivial
825.2.bi.b.776.1		8	11.6	odd	10	inner
825.2.bi.b.776.2		8	33.17	even	10	inner
825.2.bs.a.149.1		8	55.28	even	20
825.2.bs.a.149.2		8	165.17	odd	20
825.2.bs.a.299.1		8	15.2	even	4
825.2.bs.a.299.2		8	5.3	odd	4
825.2.bs.d.149.1		8	165.83	odd	20
825.2.bs.d.149.2		8	55.17	even	20
825.2.bs.d.299.1		8	5.2	odd	4
825.2.bs.d.299.2		8	15.8	even	4
891.2.u.a.134.1		16	45.29	odd	6
891.2.u.a.134.2		16	45.34	even	6
891.2.u.a.215.1		16	495.479	even	30
891.2.u.a.215.2		16	495.259	odd	30
891.2.u.a.431.1		16	45.4	even	6
891.2.u.a.431.2		16	45.14	odd	6
891.2.u.a.512.1		16	495.94	odd	30
891.2.u.a.512.2		16	495.149	even	30

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.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 1.80902i) q^{2} +(1.67229 - 0.451057i) q^{3} +(-1.30902 - 0.951057i) q^{4} +(0.166977 - 3.29032i) q^{6} +(-0.427051 + 0.587785i) q^{7} +(0.587785 - 0.427051i) q^{8} +(2.59310 - 1.50859i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 1.80902i) q^{2} +(1.67229 - 0.451057i) q^{3} +(-1.30902 - 0.951057i) q^{4} +(0.166977 - 3.29032i) q^{6} +(-0.427051 + 0.587785i) q^{7} +(0.587785 - 0.427051i) q^{8} +(2.59310 - 1.50859i) q^{9} +(-2.12663 - 2.54508i) q^{11} +(-2.61803 - 1.00000i) q^{12} +(2.92705 + 0.951057i) q^{13} +(0.812299 + 1.11803i) q^{14} +(-1.42705 - 4.39201i) q^{16} +(-0.812299 - 2.50000i) q^{17} +(-1.20489 - 5.57768i) q^{18} +(2.50000 + 3.44095i) q^{19} +(-0.449028 + 1.17557i) q^{21} +(-5.85410 + 2.35114i) q^{22} +1.76393i q^{23} +(0.790322 - 0.979277i) q^{24} +(3.44095 - 4.73607i) q^{26} +(3.65594 - 3.69244i) q^{27} +(1.11803 - 0.363271i) q^{28} +(-3.07768 - 2.23607i) q^{29} +(-0.263932 + 0.812299i) q^{31} -7.33094 q^{32} +(-4.70431 - 3.29689i) q^{33} -5.00000 q^{34} +(-4.82916 - 0.491407i) q^{36} +(2.42705 + 1.76336i) q^{37} +(7.69421 - 2.50000i) q^{38} +(5.32385 + 0.270175i) q^{39} +(-2.48990 + 1.80902i) q^{41} +(1.86269 + 1.50328i) q^{42} +1.62460i q^{43} +(0.363271 + 5.35410i) q^{44} +(3.19098 + 1.03681i) q^{46} +(-4.30625 - 5.92705i) q^{47} +(-4.36749 - 6.70103i) q^{48} +(2.00000 + 6.15537i) q^{49} +(-2.48604 - 3.81433i) q^{51} +(-2.92705 - 4.02874i) q^{52} +(-4.61653 - 1.50000i) q^{53} +(-4.53077 - 8.78402i) q^{54} +0.527864i q^{56} +(5.73279 + 4.62663i) q^{57} +(-5.85410 + 4.25325i) q^{58} +(-1.53884 + 2.11803i) q^{59} +(-4.04508 + 1.31433i) q^{61} +(1.31433 + 0.954915i) q^{62} +(-0.220655 + 2.16843i) q^{63} +(-1.45492 + 4.47777i) q^{64} +(-8.72925 + 6.57232i) q^{66} +8.32624 q^{67} +(-1.31433 + 4.04508i) q^{68} +(0.795633 + 2.94980i) q^{69} +(9.82084 - 3.19098i) q^{71} +(0.879937 - 1.99411i) q^{72} +(-8.94427 + 12.3107i) q^{73} +(4.61653 - 3.35410i) q^{74} -6.88191i q^{76} +(2.40414 - 0.163119i) q^{77} +(3.61803 - 9.47214i) q^{78} +(10.1631 + 3.30220i) q^{79} +(4.44829 - 7.82385i) q^{81} +(1.80902 + 5.56758i) q^{82} +(4.47777 + 13.7812i) q^{83} +(1.70582 - 1.11179i) q^{84} +(2.93893 + 0.954915i) q^{86} +(-6.15537 - 2.35114i) q^{87} +(-2.33688 - 0.587785i) q^{88} +9.47214i q^{89} +(-1.80902 + 1.31433i) q^{91} +(1.67760 - 2.30902i) q^{92} +(-0.0749776 + 1.47745i) q^{93} +(-13.2533 + 4.30625i) q^{94} +(-12.2594 + 3.30667i) q^{96} +(2.04508 - 6.29412i) q^{97} +12.3107 q^{98} +(-9.35405 - 3.39144i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} - 6 q^{4} + 10 q^{7} + 10 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 - 6 * q^4 + 10 * q^7 + 10 * q^9	\( 8 q + 6 q^{3} - 6 q^{4} + 10 q^{7} + 10 q^{9} - 12 q^{12} + 10 q^{13} + 2 q^{16} + 20 q^{19} - 20 q^{22} - 10 q^{24} + 12 q^{27} - 20 q^{31} + 4 q^{33} - 40 q^{34} - 10 q^{36} + 6 q^{37} + 20 q^{39} - 20 q^{42} + 30 q^{46} - 26 q^{48} + 16 q^{49} + 30 q^{51} - 10 q^{52} + 30 q^{57} - 20 q^{58} - 10 q^{61} + 30 q^{63} - 34 q^{64} - 30 q^{66} + 4 q^{67} - 16 q^{69} + 20 q^{72} + 20 q^{78} + 50 q^{79} - 2 q^{81} + 10 q^{82} - 50 q^{88} - 10 q^{91} - 10 q^{93} - 30 q^{94} + 10 q^{96} - 6 q^{97} + 16 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 - 6 * q^4 + 10 * q^7 + 10 * q^9 - 12 * q^12 + 10 * q^13 + 2 * q^16 + 20 * q^19 - 20 * q^22 - 10 * q^24 + 12 * q^27 - 20 * q^31 + 4 * q^33 - 40 * q^34 - 10 * q^36 + 6 * q^37 + 20 * q^39 - 20 * q^42 + 30 * q^46 - 26 * q^48 + 16 * q^49 + 30 * q^51 - 10 * q^52 + 30 * q^57 - 20 * q^58 - 10 * q^61 + 30 * q^63 - 34 * q^64 - 30 * q^66 + 4 * q^67 - 16 * q^69 + 20 * q^72 + 20 * q^78 + 50 * q^79 - 2 * q^81 + 10 * q^82 - 50 * q^88 - 10 * q^91 - 10 * q^93 - 30 * q^94 + 10 * q^96 - 6 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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