LMFDB - Embedded newform 950.2.l.g.651.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1511x^{6} + 4812x^{4} - 7788x^{2} + 5329 $ x^12 - 24x^10 + 264x^8 - 1511x^6 + 4812x^4 - 7788*x^2 + 5329
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			651.2
Root			$1.34865 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	950.651
Dual form			950.2.l.g.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(0.0710139 - 0.402740i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.0710139 - 0.402740i) q^{6} +(-1.15033 - 1.99244i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.66192 + 0.968860i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(0.0710139 - 0.402740i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.0710139 - 0.402740i) q^{6} +(-1.15033 - 1.99244i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.66192 + 0.968860i) q^{9} +(1.32398 - 2.29321i) q^{11} +(-0.204476 - 0.354164i) q^{12} +(-0.885551 - 5.02221i) q^{13} +(-1.76241 - 1.47884i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-2.62576 + 0.955698i) q^{17} +2.83276 q^{18} +(-1.11951 + 4.21268i) q^{19} +(-0.884124 + 0.321795i) q^{21} +(0.459814 - 2.60774i) q^{22} +(-0.896091 + 0.751910i) q^{23} +(-0.313276 - 0.262870i) q^{24} +(-2.54984 - 4.41645i) q^{26} +(1.19266 - 2.06575i) q^{27} +(-2.16192 - 0.786875i) q^{28} +(4.18479 + 1.52314i) q^{29} +(-4.11588 - 7.12891i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-0.829544 - 0.696070i) q^{33} +(-2.14054 + 1.79613i) q^{34} +(2.66192 - 0.968860i) q^{36} +2.99954 q^{37} +(0.388831 + 4.34152i) q^{38} -2.08553 q^{39} +(1.97511 - 11.2014i) q^{41} +(-0.720744 + 0.604776i) q^{42} +(1.18061 + 0.990646i) q^{43} +(-0.459814 - 2.60774i) q^{44} +(-0.584882 + 1.01305i) q^{46} +(9.92304 + 3.61169i) q^{47} +(-0.384290 - 0.139870i) q^{48} +(0.853462 - 1.47824i) q^{49} +(0.198432 + 1.12537i) q^{51} +(-3.90658 - 3.27801i) q^{52} +(3.24667 - 2.72428i) q^{53} +(0.414207 - 2.34908i) q^{54} -2.30067 q^{56} +(1.61712 + 0.750029i) q^{57} +4.45336 q^{58} +(-10.5415 + 3.83681i) q^{59} +(2.53595 - 2.12792i) q^{61} +(-6.30589 - 5.29127i) q^{62} +(-1.13171 - 6.41823i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.01759 - 0.370371i) q^{66} +(-7.91593 - 2.88116i) q^{67} +(-1.39714 + 2.41991i) q^{68} +(0.239189 + 0.414288i) q^{69} +(-0.239189 - 0.200703i) q^{71} +(2.17002 - 1.82086i) q^{72} +(-2.66528 + 15.1155i) q^{73} +(2.81865 - 1.02590i) q^{74} +(1.85027 + 3.94671i) q^{76} -6.09209 q^{77} +(-1.95976 + 0.713293i) q^{78} +(-1.52957 + 8.67461i) q^{79} +(5.76279 + 4.83556i) q^{81} +(-1.97511 - 11.2014i) q^{82} +(-0.887706 - 1.53755i) q^{83} +(-0.470432 + 0.814813i) q^{84} +(1.44823 + 0.527112i) q^{86} +(0.910608 - 1.57722i) q^{87} +(-1.32398 - 2.29321i) q^{88} +(1.12686 + 6.39074i) q^{89} +(-8.98775 + 7.54162i) q^{91} +(-0.203127 + 1.15199i) q^{92} +(-3.16338 + 1.15138i) q^{93} +10.5599 q^{94} -0.408953 q^{96} +(2.46256 - 0.896300i) q^{97} +(0.296404 - 1.68099i) q^{98} +(5.74613 - 4.82158i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9	$ 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9} - 6 q^{11} + 18 q^{13} - 6 q^{14} - 12 q^{17} - 24 q^{18} + 6 q^{19} - 36 q^{21} + 9 q^{22} - 3 q^{23} + 3 q^{24} - 3 q^{26} - 15 q^{27} - 3 q^{28} + 36 q^{29} - 24 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{36} - 24 q^{37} - 15 q^{38} - 12 q^{39} - 12 q^{41} - 18 q^{42} + 12 q^{43} - 9 q^{44} - 18 q^{46} + 6 q^{48} - 27 q^{51} - 18 q^{52} + 36 q^{53} + 9 q^{54} + 12 q^{56} + 42 q^{57} - 27 q^{59} + 54 q^{61} + 24 q^{62} + 3 q^{63} - 6 q^{64} - 39 q^{66} - 39 q^{67} + 15 q^{68} - 24 q^{69} + 24 q^{71} + 18 q^{72} + 15 q^{74} + 9 q^{76} - 78 q^{77} + 6 q^{78} - 36 q^{79} - 9 q^{81} + 12 q^{82} + 12 q^{84} + 24 q^{86} - 18 q^{87} + 6 q^{88} + 18 q^{89} + 12 q^{91} - 12 q^{92} - 54 q^{93} + 18 q^{94} + 27 q^{97} + 18 q^{98} + 18 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9 - 6 * q^11 + 18 * q^13 - 6 * q^14 - 12 * q^17 - 24 * q^18 + 6 * q^19 - 36 * q^21 + 9 * q^22 - 3 * q^23 + 3 * q^24 - 3 * q^26 - 15 * q^27 - 3 * q^28 + 36 * q^29 - 24 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^36 - 24 * q^37 - 15 * q^38 - 12 * q^39 - 12 * q^41 - 18 * q^42 + 12 * q^43 - 9 * q^44 - 18 * q^46 + 6 * q^48 - 27 * q^51 - 18 * q^52 + 36 * q^53 + 9 * q^54 + 12 * q^56 + 42 * q^57 - 27 * q^59 + 54 * q^61 + 24 * q^62 + 3 * q^63 - 6 * q^64 - 39 * q^66 - 39 * q^67 + 15 * q^68 - 24 * q^69 + 24 * q^71 + 18 * q^72 + 15 * q^74 + 9 * q^76 - 78 * q^77 + 6 * q^78 - 36 * q^79 - 9 * q^81 + 12 * q^82 + 12 * q^84 + 24 * q^86 - 18 * q^87 + 6 * q^88 + 18 * q^89 + 12 * q^91 - 12 * q^92 - 54 * q^93 + 18 * q^94 + 27 * q^97 + 18 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	0.0710139	−	0.402740i	0.0409999	−	0.232522i	−0.957421	−	0.288695i	$-0.906779\pi$
$3$	0.0710139	−	0.402740i	0.0409999	−	0.232522i	0.998421	+	0.0561729i	$0.0178898\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$		0			0
$5$		0			0
$6$	−0.0710139	−	0.402740i	−0.0289913	−	0.164418i
$7$	−1.15033	−	1.99244i	−0.434786	−	0.753071i	0.562493	−	0.826802i	$-0.309842\pi$
$7$	−1.15033	−	1.99244i	−0.434786	−	0.753071i	−0.997278	+	0.0737317i	$0.976509\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	2.66192	+	0.968860i	0.887307	+	0.322953i
$10$		0			0
$11$	1.32398	−	2.29321i	0.399196	−	0.691427i	−0.594431	−	0.804147i	$-0.702623\pi$
$11$	1.32398	−	2.29321i	0.399196	−	0.691427i	0.993627	+	0.112719i	$0.0359561\pi$
$12$	−0.204476	−	0.354164i	−0.0590273	−	0.102238i
$13$	−0.885551	−	5.02221i	−0.245608	−	1.39291i	−0.819077	−	0.573683i	$-0.805514\pi$
$13$	−0.885551	−	5.02221i	−0.245608	−	1.39291i	0.573470	−	0.819227i	$-0.305597\pi$
$14$	−1.76241	−	1.47884i	−0.471025	−	0.395237i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−2.62576	+	0.955698i	−0.636840	+	0.231791i	−0.640206	−	0.768203i	$-0.721151\pi$
$17$	−2.62576	+	0.955698i	−0.636840	+	0.231791i	0.00336552	+	0.999994i	$0.498929\pi$
$18$	2.83276			0.667687
$19$	−1.11951	+	4.21268i	−0.256832	+	0.966456i
$19$	−1.11951	+	4.21268i	−0.256832	+	0.966456i
$20$		0			0
$21$	−0.884124	+	0.321795i	−0.192932	+	0.0702214i
$22$	0.459814	−	2.60774i	0.0980327	−	0.555971i
$23$	−0.896091	+	0.751910i	−0.186848	+	0.156784i	−0.731413	−	0.681934i	$-0.761139\pi$
$23$	−0.896091	+	0.751910i	−0.186848	+	0.156784i	0.544566	+	0.838718i	$0.316695\pi$
$24$	−0.313276	−	0.262870i	−0.0639472	−	0.0536581i
$25$		0			0
$26$	−2.54984	−	4.41645i	−0.500065	−	0.866138i
$27$	1.19266	−	2.06575i	0.229528	−	0.397554i
$28$	−2.16192	−	0.786875i	−0.408565	−	0.148705i
$29$	4.18479	+	1.52314i	0.777096	+	0.282840i	0.699961	−	0.714181i	$-0.253201\pi$
$29$	4.18479	+	1.52314i	0.777096	+	0.282840i	0.0771351	+	0.997021i	$0.475423\pi$
$30$		0			0
$31$	−4.11588	−	7.12891i	−0.739233	−	1.28039i	−0.952841	−	0.303470i	$-0.901855\pi$
$31$	−4.11588	−	7.12891i	−0.739233	−	1.28039i	0.213608	−	0.976919i	$-0.431479\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	−0.829544	−	0.696070i	−0.144405	−	0.121170i
$34$	−2.14054	+	1.79613i	−0.367099	+	0.308033i
$35$		0			0
$36$	2.66192	−	0.968860i	0.443654	−	0.161477i
$37$	2.99954			0.493122			0.246561	−	0.969127i	$-0.420699\pi$
$37$	2.99954			0.493122			0.246561	+	0.969127i	$0.420699\pi$
$38$	0.388831	+	4.34152i	0.0630767	+	0.704288i
$39$	−2.08553			−0.333952
$40$		0			0
$41$	1.97511	−	11.2014i	0.308460	−	1.74936i	−0.298293	−	0.954474i	$-0.596417\pi$
$41$	1.97511	−	11.2014i	0.308460	−	1.74936i	0.606753	−	0.794890i	$-0.292472\pi$
$42$	−0.720744	+	0.604776i	−0.111213	+	0.0933190i
$43$	1.18061	+	0.990646i	0.180041	+	0.151072i	0.728354	−	0.685201i	$-0.240286\pi$
$43$	1.18061	+	0.990646i	0.180041	+	0.151072i	−0.548314	+	0.836273i	$0.684730\pi$
$44$	−0.459814	−	2.60774i	−0.0693196	−	0.393131i
$45$		0			0
$46$	−0.584882	+	1.01305i	−0.0862361	+	0.149365i
$47$	9.92304	+	3.61169i	1.44742	+	0.526819i	0.941871	−	0.335976i	$-0.109066\pi$
$47$	9.92304	+	3.61169i	1.44742	+	0.526819i	0.505553	+	0.862795i	$0.331288\pi$
$48$	−0.384290	−	0.139870i	−0.0554675	−	0.0201885i
$49$	0.853462	−	1.47824i	0.121923	−	0.211177i
$50$		0			0
$51$	0.198432	+	1.12537i	0.0277861	+	0.157583i
$52$	−3.90658	−	3.27801i	−0.541746	−	0.454579i
$53$	3.24667	−	2.72428i	0.445964	−	0.374208i	−0.391972	−	0.919977i	$-0.628207\pi$
$53$	3.24667	−	2.72428i	0.445964	−	0.374208i	0.837936	+	0.545769i	$0.183762\pi$
$54$	0.414207	−	2.34908i	0.0563664	−	0.319670i
$55$		0			0
$56$	−2.30067			−0.307440
$57$	1.61712	+	0.750029i	0.214192	+	0.0993438i
$58$	4.45336			0.584755
$59$	−10.5415	+	3.83681i	−1.37239	+	0.499510i	−0.919863	−	0.392239i	$-0.871700\pi$
$59$	−10.5415	+	3.83681i	−1.37239	+	0.499510i	−0.452529	+	0.891749i	$0.649478\pi$
$60$		0			0
$61$	2.53595	−	2.12792i	0.324695	−	0.272452i	−0.465839	−	0.884870i	$-0.654247\pi$
$61$	2.53595	−	2.12792i	0.324695	−	0.272452i	0.790534	+	0.612418i	$0.209803\pi$
$62$	−6.30589	−	5.29127i	−0.800849	−	0.671992i
$63$	−1.13171	−	6.41823i	−0.142582	−	0.808620i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	−1.01759	−	0.370371i	−0.125256	−	0.0455895i
$67$	−7.91593	−	2.88116i	−0.967084	−	0.351990i	−0.190279	−	0.981730i	$-0.560939\pi$
$67$	−7.91593	−	2.88116i	−0.967084	−	0.351990i	−0.776806	+	0.629740i	$0.783161\pi$
$68$	−1.39714	+	2.41991i	−0.169428	+	0.293458i
$69$	0.239189	+	0.414288i	0.0287950	+	0.0498744i
$70$		0			0
$71$	−0.239189	−	0.200703i	−0.0283865	−	0.0238191i	0.628484	−	0.777823i	$-0.283676\pi$
$71$	−0.239189	−	0.200703i	−0.0283865	−	0.0238191i	−0.656871	+	0.754003i	$0.728120\pi$
$72$	2.17002	−	1.82086i	0.255739	−	0.214591i
$73$	−2.66528	+	15.1155i	−0.311947	+	1.76914i	0.276904	+	0.960898i	$0.410692\pi$
$73$	−2.66528	+	15.1155i	−0.311947	+	1.76914i	−0.588851	+	0.808242i	$0.700419\pi$
$74$	2.81865	−	1.02590i	0.327661	−	0.119259i
$75$		0			0
$76$	1.85027	+	3.94671i	0.212240	+	0.452718i
$77$	−6.09209			−0.694258
$78$	−1.95976	+	0.713293i	−0.221899	+	0.0807645i
$79$	−1.52957	+	8.67461i	−0.172090	+	0.975970i	0.769360	+	0.638816i	$0.220575\pi$
$79$	−1.52957	+	8.67461i	−0.172090	+	0.975970i	−0.941450	+	0.337154i	$0.890536\pi$
$80$		0			0
$81$	5.76279	+	4.83556i	0.640310	+	0.537284i
$82$	−1.97511	−	11.2014i	−0.218114	−	1.23699i
$83$	−0.887706	−	1.53755i	−0.0974384	−	0.168768i	0.813185	−	0.582005i	$-0.197732\pi$
$83$	−0.887706	−	1.53755i	−0.0974384	−	0.168768i	−0.910624	+	0.413237i	$0.864398\pi$
$84$	−0.470432	+	0.814813i	−0.0513284	+	0.0889034i
$85$		0			0
$86$	1.44823	+	0.527112i	0.156166	+	0.0568399i
$87$	0.910608	−	1.57722i	0.0976274	−	0.169096i
$88$	−1.32398	−	2.29321i	−0.141137	−	0.244456i
$89$	1.12686	+	6.39074i	0.119447	+	0.677417i	0.984452	+	0.175654i	$0.0562039\pi$
$89$	1.12686	+	6.39074i	0.119447	+	0.677417i	−0.865005	+	0.501763i	$0.832685\pi$
$90$		0			0
$91$	−8.98775	+	7.54162i	−0.942173	+	0.790577i
$92$	−0.203127	+	1.15199i	−0.0211775	+	0.120104i
$93$	−3.16338	+	1.15138i	−0.328027	+	0.119392i
$94$	10.5599			1.08917
$95$		0			0
$96$	−0.408953			−0.0417386
$97$	2.46256	−	0.896300i	0.250035	−	0.0910055i	−0.213962	−	0.976842i	$-0.568637\pi$
$97$	2.46256	−	0.896300i	0.250035	−	0.0910055i	0.463997	+	0.885837i	$0.346415\pi$
$98$	0.296404	−	1.68099i	0.0299413	−	0.169806i
$99$	5.74613	−	4.82158i	0.577508	−	0.484587i
$100$		0			0
$101$	1.69635	+	9.62050i	0.168794	+	0.957276i	0.945066	+	0.326879i	$0.105997\pi$
$101$	1.69635	+	9.62050i	0.168794	+	0.957276i	−0.776273	+	0.630397i	$0.782892\pi$
$102$	0.571363	+	0.989630i	0.0565734	+	0.0979880i
$103$	0.248809	−	0.430950i	0.0245159	−	0.0424628i	−0.853507	−	0.521081i	$-0.825529\pi$
$103$	0.248809	−	0.430950i	0.0245159	−	0.0424628i	0.878023	+	0.478618i	$0.158862\pi$
$104$	−4.79213	−	1.74419i	−0.469907	−	0.171032i
$105$		0			0
$106$	2.11911	−	3.67041i	0.205826	−	0.356502i
$107$	9.62904	+	16.6780i	0.930874	+	1.61232i	0.781831	+	0.623491i	$0.214286\pi$
$107$	9.62904	+	16.6780i	0.930874	+	1.61232i	0.149044	+	0.988831i	$0.452380\pi$
$108$	−0.414207	−	2.34908i	−0.0398571	−	0.226041i
$109$	8.91741	+	7.48260i	0.854133	+	0.716703i	0.960696	−	0.277603i	$-0.0895400\pi$
$109$	8.91741	+	7.48260i	0.854133	+	0.716703i	−0.106563	+	0.994306i	$0.533984\pi$
$110$		0			0
$111$	0.213009	−	1.20804i	0.0202180	−	0.114662i
$112$	−2.16192	+	0.786875i	−0.204282	+	0.0743527i
$113$	9.87717			0.929166			0.464583	−	0.885530i	$-0.346204\pi$
$113$	9.87717			0.929166			0.464583	+	0.885530i	$0.346204\pi$
$114$	1.77612	+	0.151711i	0.166349	+	0.0142090i
$115$		0			0
$116$	4.18479	−	1.52314i	0.388548	−	0.141420i
$117$	2.50855	−	14.2267i	0.231916	−	1.31526i
$118$	−8.59355	+	7.21084i	−0.791100	+	0.663812i
$119$	4.92467	+	4.13229i	0.451444	+	0.378806i
$120$		0			0
$121$	1.99414	+	3.45395i	0.181285	+	0.313996i
$122$	1.65522	−	2.86693i	0.149857	−	0.259560i
$123$	−4.37099	−	1.59091i	−0.394119	−	0.143448i
$124$	−7.73532	−	2.81543i	−0.694652	−	0.252833i
$125$		0			0
$126$	−3.25862	−	5.64409i	−0.290301	−	0.502816i
$127$	1.46191	+	8.29089i	0.129723	+	0.735697i	0.978390	+	0.206769i	$0.0662948\pi$
$127$	1.46191	+	8.29089i	0.129723	+	0.735697i	−0.848667	+	0.528928i	$0.822594\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	0.482812	−	0.405127i	0.0425092	−	0.0356695i
$130$		0			0
$131$	−16.0131	+	5.82829i	−1.39907	+	0.509220i	−0.927903	−	0.372823i	$-0.878390\pi$
$131$	−16.0131	+	5.82829i	−1.39907	+	0.509220i	−0.471169	+	0.882043i	$0.656168\pi$
$132$	−1.08289			−0.0942537
$133$	9.68132	−	2.61545i	0.839477	−	0.226788i
$134$	−8.42395			−0.727719
$135$		0			0
$136$	−0.485221	+	2.75182i	−0.0416073	+	0.235967i
$137$	−8.98562	+	7.53983i	−0.767694	+	0.644171i	−0.940117	−	0.340851i	$-0.889285\pi$
$137$	−8.98562	+	7.53983i	−0.767694	+	0.644171i	0.172424	+	0.985023i	$0.444840\pi$
$138$	0.366459	+	0.307496i	0.0311951	+	0.0261758i
$139$	−2.24940	−	12.7570i	−0.190792	−	1.08203i	−0.918286	−	0.395919i	$-0.870426\pi$
$139$	−2.24940	−	12.7570i	−0.190792	−	1.08203i	0.727494	−	0.686114i	$-0.240685\pi$
$140$		0			0
$141$	2.15925	−	3.73992i	0.181841	−	0.314958i
$142$	−0.293409	−	0.106792i	−0.0246223	−	0.00896179i
$143$	−12.6894	−	4.61857i	−1.06114	−	0.386224i
$144$	1.41638	−	2.45324i	0.118032	−	0.204437i
$145$		0			0
$146$	2.66528	+	15.1155i	0.220580	+	1.25097i
$147$	−0.534738	−	0.448699i	−0.0441045	−	0.0370080i
$148$	2.29778	−	1.92807i	0.188877	−	0.158486i
$149$	2.84467	−	16.1329i	0.233044	−	1.32166i	−0.613649	−	0.789579i	$-0.710299\pi$
$149$	2.84467	−	16.1329i	0.233044	−	1.32166i	0.846693	−	0.532081i	$-0.178590\pi$
$150$		0			0
$151$	3.71278			0.302141			0.151071	−	0.988523i	$-0.451728\pi$
$151$	3.71278			0.302141			0.151071	+	0.988523i	$0.451728\pi$
$152$	3.08854	+	3.07586i	0.250514	+	0.249485i
$153$	−7.91550			−0.639931
$154$	−5.72469	+	2.08362i	−0.461309	+	0.167903i
$155$		0			0
$156$	−1.59761	+	1.34055i	−0.127911	+	0.107330i
$157$	3.78981	+	3.18002i	0.302459	+	0.253794i	0.781367	−	0.624072i	$-0.214523\pi$
$157$	3.78981	+	3.18002i	0.302459	+	0.253794i	−0.478908	+	0.877865i	$0.658967\pi$
$158$	1.52957	+	8.67461i	0.121686	+	0.690115i
$159$	−0.866617	−	1.50102i	−0.0687272	−	0.119039i
$160$		0			0
$161$	2.52894	+	0.920458i	0.199308	+	0.0725422i
$162$	7.06911	+	2.57295i	0.555402	+	0.202150i
$163$	−4.02997	+	6.98012i	−0.315652	+	0.546725i	−0.979576	−	0.201075i	$-0.935557\pi$
$163$	−4.02997	+	6.98012i	−0.315652	+	0.546725i	0.663924	+	0.747800i	$0.268890\pi$
$164$	−5.68710	−	9.85035i	−0.444088	−	0.769183i
$165$		0			0
$166$	−1.36004	−	1.14121i	−0.105560	−	0.0885753i
$167$	1.38408	−	1.16138i	0.107104	−	0.0898705i	−0.587663	−	0.809106i	$-0.699952\pi$
$167$	1.38408	−	1.16138i	0.107104	−	0.0898705i	0.694767	+	0.719235i	$0.255508\pi$
$168$	−0.163379	+	0.926571i	−0.0126050	+	0.0714865i
$169$	−12.2224	+	4.44857i	−0.940181	+	0.342198i
$170$		0			0
$171$	−7.06154	+	10.1292i	−0.540009	+	0.774598i
$172$	1.54117			0.117513
$173$	19.3270	−	7.03447i	1.46941	−	0.534820i	0.521468	−	0.853271i	$-0.325385\pi$
$173$	19.3270	−	7.03447i	1.46941	−	0.534820i	0.947939	+	0.318451i	$0.103162\pi$
$174$	0.316251	−	1.79355i	0.0239749	−	0.135968i
$175$		0			0
$176$	−2.02846	−	1.70208i	−0.152901	−	0.128299i
$177$	0.796640	+	4.51797i	0.0598791	+	0.339591i
$178$	3.24466	+	5.61992i	0.243198	+	0.421231i
$179$	7.78778	−	13.4888i	0.582086	−	1.00820i	−0.413146	−	0.910665i	$-0.635570\pi$
$179$	7.78778	−	13.4888i	0.582086	−	1.00820i	0.995232	−	0.0975373i	$-0.0310965\pi$
$180$		0			0
$181$	6.41314	+	2.33419i	0.476685	+	0.173499i	0.569178	−	0.822214i	$-0.307261\pi$
$181$	6.41314	+	2.33419i	0.476685	+	0.173499i	−0.0924934	+	0.995713i	$0.529484\pi$
$182$	−5.86634	+	10.1608i	−0.434842	+	0.753169i
$183$	−0.676909	−	1.17244i	−0.0500385	−	0.0866693i
$184$	0.203127	+	1.15199i	0.0149747	+	0.0849260i
$185$		0			0
$186$	−2.57881	+	2.16388i	−0.189088	+	0.158663i
$187$	−1.28485	+	7.28673i	−0.0939574	+	0.532859i
$188$	9.92304	−	3.61169i	0.723712	−	0.263410i
$189$	−5.48784			−0.399181
$190$		0			0
$191$	−3.27667			−0.237091			−0.118546	−	0.992949i	$-0.537823\pi$
$191$	−3.27667			−0.237091			−0.118546	+	0.992949i	$0.537823\pi$
$192$	−0.384290	+	0.139870i	−0.0277337	+	0.0100943i
$193$	−4.11035	+	23.3109i	−0.295869	+	1.67796i	0.367779	+	0.929913i	$0.380118\pi$
$193$	−4.11035	+	23.3109i	−0.295869	+	1.67796i	−0.663648	+	0.748045i	$0.730993\pi$
$194$	2.00750	−	1.68449i	0.144130	−	0.120940i
$195$		0			0
$196$	−0.296404	−	1.68099i	−0.0211717	−	0.120071i
$197$	3.44232	+	5.96227i	0.245255	+	0.424794i	0.962203	−	0.272332i	$-0.0877950\pi$
$197$	3.44232	+	5.96227i	0.245255	+	0.424794i	−0.716948	+	0.697126i	$0.754462\pi$
$198$	3.75052	−	6.49609i	0.266538	−	0.461657i
$199$	17.8456	+	6.49525i	1.26504	+	0.460436i	0.885456	−	0.464722i	$-0.153846\pi$
$199$	17.8456	+	6.49525i	1.26504	+	0.460436i	0.379581	+	0.925158i	$0.376068\pi$
$200$		0			0
$201$	−1.72250	+	2.98346i	−0.121496	+	0.210437i
$202$	4.88446	+	8.46013i	0.343669	+	0.595252i
$203$	−1.77915	−	10.0901i	−0.124872	−	0.708183i
$204$	0.875379	+	0.734531i	0.0612888	+	0.0514274i
$205$		0			0
$206$	0.0864105	−	0.490058i	0.00602050	−	0.0341440i
$207$	−3.11382	+	1.13334i	−0.216425	+	0.0787724i
$208$	−5.09968			−0.353599
$209$	8.17834	+	8.14478i	0.565708	+	0.563386i
$210$		0			0
$211$	11.5977	−	4.22122i	0.798419	−	0.290601i	0.0895880	−	0.995979i	$-0.471445\pi$
$211$	11.5977	−	4.22122i	0.798419	−	0.290601i	0.708831	+	0.705378i	$0.249223\pi$
$212$	0.735960	−	4.17384i	0.0505459	−	0.286660i
$213$	−0.0978170	+	0.0820782i	−0.00670231	+	0.00562391i
$214$	14.7525	+	12.3789i	1.00846	+	0.846201i
$215$		0			0
$216$	−1.19266	−	2.06575i	−0.0811503	−	0.140556i
$217$	−9.46927	+	16.4013i	−0.642816	+	1.11339i
$218$	10.9388	+	3.98141i	0.740871	+	0.269655i
$219$	5.89836	+	2.14683i	0.398574	+	0.145069i
$220$		0			0
$221$	7.12496	+	12.3408i	0.479277	+	0.830131i
$222$	−0.213009	−	1.20804i	−0.0142963	−	0.0810781i
$223$	−3.66897	−	3.07863i	−0.245693	−	0.206161i	0.511622	−	0.859210i	$-0.329045\pi$
$223$	−3.66897	−	3.07863i	−0.245693	−	0.206161i	−0.757315	+	0.653050i	$0.773489\pi$
$224$	−1.76241	+	1.47884i	−0.117756	+	0.0988092i
$225$		0			0
$226$	9.28150	−	3.37819i	0.617396	−	0.224714i
$227$	4.24421			0.281698			0.140849	−	0.990031i	$-0.455017\pi$
$227$	4.24421			0.281698			0.140849	+	0.990031i	$0.455017\pi$
$228$	1.72089	−	0.464906i	0.113969	−	0.0307892i
$229$	−28.8958			−1.90949			−0.954745	−	0.297425i	$-0.903872\pi$
$229$	−28.8958			−1.90949			−0.954745	+	0.297425i	$0.903872\pi$
$230$		0			0
$231$	−0.432623	+	2.45353i	−0.0284645	+	0.161430i
$232$	3.41147	−	2.86257i	0.223974	−	0.187937i
$233$	−10.4396	−	8.75986i	−0.683920	−	0.573877i	0.233229	−	0.972422i	$-0.425071\pi$
$233$	−10.4396	−	8.75986i	−0.683920	−	0.573877i	−0.917149	+	0.398545i	$0.869515\pi$
$234$	−2.50855	−	14.2267i	−0.163989	−	0.930028i
$235$		0			0
$236$	−5.60904	+	9.71514i	−0.365117	+	0.632402i
$237$	3.38499	+	1.23204i	0.219879	+	0.0800293i
$238$	6.04100	+	2.19875i	0.391580	+	0.142524i
$239$	−7.44355	+	12.8926i	−0.481483	+	0.833954i	−0.999774	−	0.0212507i	$-0.993235\pi$
$239$	−7.44355	+	12.8926i	−0.481483	+	0.833954i	0.518291	+	0.855205i	$0.326569\pi$
$240$		0			0
$241$	2.01439	+	11.4242i	0.129759	+	0.735897i	0.978367	+	0.206876i	$0.0663297\pi$
$241$	2.01439	+	11.4242i	0.129759	+	0.735897i	−0.848609	+	0.529021i	$0.822559\pi$
$242$	3.05520	+	2.56362i	0.196396	+	0.164796i
$243$	7.83850	−	6.57728i	0.502840	−	0.421933i
$244$	0.574854	−	3.26016i	0.0368012	−	0.208710i
$245$		0			0
$246$	−4.65151			−0.296569
$247$	22.1483	+	1.89185i	1.40927	+	0.120375i
$248$	−8.23175			−0.522717
$249$	−0.682273	+	0.248327i	−0.0432373	+	0.0157371i
$250$		0			0
$251$	16.1409	−	13.5438i	1.01880	−	0.854879i	0.0293281	−	0.999570i	$-0.490663\pi$
$251$	16.1409	−	13.5438i	1.01880	−	0.854879i	0.989477	+	0.144691i	$0.0462188\pi$
$252$	−4.99249	−	4.18920i	−0.314498	−	0.263895i
$253$	0.537874	+	3.05044i	0.0338159	+	0.191779i
$254$	4.20939	+	7.29088i	0.264121	+	0.457471i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−26.0439	−	9.47920i	−1.62457	−	0.591296i	−0.640327	−	0.768102i	$-0.721201\pi$
$257$	−26.0439	−	9.47920i	−1.62457	−	0.591296i	−0.984246	+	0.176806i	$0.943423\pi$
$258$	0.315133	−	0.545827i	0.0196193	−	0.0339817i
$259$	−3.45048	−	5.97640i	−0.214402	−	0.371356i
$260$		0			0
$261$	9.66388	+	8.10896i	0.598179	+	0.501932i
$262$	−13.0540	+	10.9536i	−0.806479	+	0.676716i
$263$	1.56375	−	8.86847i	0.0964250	−	0.546853i	−0.897876	−	0.440248i	$-0.854891\pi$
$263$	1.56375	−	8.86847i	0.0964250	−	0.546853i	0.994301	−	0.106606i	$-0.0339983\pi$
$264$	−1.01759	+	0.370371i	−0.0626281	+	0.0227948i
$265$		0			0
$266$	8.20293	−	5.76892i	0.502954	−	0.353715i
$267$	2.65383			0.162412
$268$	−7.91593	+	2.88116i	−0.483542	+	0.175995i
$269$	1.29149	−	7.32442i	0.0787437	−	0.446578i	−0.919788	−	0.392415i	$-0.871640\pi$
$269$	1.29149	−	7.32442i	0.0787437	−	0.446578i	0.998532	−	0.0541630i	$-0.0172490\pi$
$270$		0			0
$271$	−14.3191	−	12.0152i	−0.869824	−	0.729869i	0.0942373	−	0.995550i	$-0.469959\pi$
$271$	−14.3191	−	12.0152i	−0.869824	−	0.729869i	−0.964061	+	0.265681i	$0.914403\pi$
$272$	0.485221	+	2.75182i	0.0294208	+	0.166854i
$273$	2.39906	+	4.15529i	0.145197	+	0.251489i
$274$	−5.86495	+	10.1584i	−0.354315	+	0.613691i
$275$		0			0
$276$	0.449528	+	0.163615i	0.0270584	+	0.00984846i
$277$	1.94884	−	3.37548i	0.117094	−	0.202813i	−0.801521	−	0.597967i	$-0.795975\pi$
$277$	1.94884	−	3.37548i	0.117094	−	0.202813i	0.918615	+	0.395154i	$0.129309\pi$
$278$	−6.47689	−	11.2183i	−0.388458	−	0.672829i
$279$	−4.04923	−	22.9643i	−0.242421	−	1.37484i
$280$		0			0
$281$	−4.50354	+	3.77891i	−0.268658	+	0.225431i	−0.767157	−	0.641459i	$-0.778329\pi$
$281$	−4.50354	+	3.77891i	−0.268658	+	0.225431i	0.498499	+	0.866890i	$0.333885\pi$
$282$	0.749898	−	4.25288i	0.0446558	−	0.253256i
$283$	−17.5543	+	6.38923i	−1.04349	+	0.379800i	−0.806203	−	0.591639i	$-0.798481\pi$
$283$	−17.5543	+	6.38923i	−1.04349	+	0.379800i	−0.237289	+	0.971439i	$0.576259\pi$
$284$	−0.312239			−0.0185280
$285$		0			0
$286$	−13.5038			−0.798495
$287$	−24.5901	+	8.95007i	−1.45151	+	0.528306i
$288$	0.491903	−	2.78972i	0.0289857	−	0.164386i
$289$	−7.04150	+	5.90852i	−0.414206	+	0.347560i
$290$		0			0
$291$	−0.186099	−	1.05542i	−0.0109093	−	0.0618700i
$292$	7.67436	+	13.2924i	0.449108	+	0.777877i
$293$	5.29506	−	9.17131i	0.309341	−	0.535794i	−0.668878	−	0.743373i	$-0.733225\pi$
$293$	5.29506	−	9.17131i	0.309341	−	0.535794i	0.978218	+	0.207579i	$0.0665583\pi$
$294$	−0.655953	−	0.238748i	−0.0382560	−	0.0139240i
$295$		0			0
$296$	1.49977	−	2.59768i	0.0871725	−	0.150987i
$297$	−3.15813	−	5.47003i	−0.183253	−	0.317404i
$298$	−2.84467	−	16.1329i	−0.164787	−	0.934555i
$299$	4.56978	+	3.83450i	0.264277	+	0.221755i
$300$		0			0
$301$	0.615709	−	3.49186i	0.0354889	−	0.201267i
$302$	3.48887	−	1.26984i	0.200762	−	0.0730713i
$303$	3.99502			0.229508
$304$	3.95428	+	1.83402i	0.226794	+	0.105188i
$305$		0			0
$306$	−7.43814	+	2.70726i	−0.425210	+	0.154764i
$307$	0.816611	−	4.63123i	0.0466065	−	0.264318i	−0.952596	−	0.304237i	$-0.901599\pi$
$307$	0.816611	−	4.63123i	0.0466065	−	0.264318i	0.999203	+	0.0399183i	$0.0127098\pi$
$308$	−4.66681	+	3.91592i	−0.265916	+	0.223130i
$309$	−0.155892	−	0.130809i	−0.00886838	−	0.00744145i
$310$		0			0
$311$	6.81200	+	11.7987i	0.386273	+	0.669045i	0.991945	−	0.126670i	$-0.0404289\pi$
$311$	6.81200	+	11.7987i	0.386273	+	0.669045i	−0.605672	+	0.795715i	$0.707096\pi$
$312$	−1.04276	+	1.80612i	−0.0590349	+	0.102251i
$313$	29.0431	+	10.5708i	1.64161	+	0.597498i	0.987320	−	0.158744i	$-0.0507445\pi$
$313$	29.0431	+	10.5708i	1.64161	+	0.597498i	0.654292	+	0.756242i	$0.272967\pi$
$314$	4.64889	+	1.69206i	0.262352	+	0.0954882i
$315$		0			0
$316$	4.40421	+	7.62832i	0.247756	+	0.429127i
$317$	−1.41507	−	8.02529i	−0.0794785	−	0.450745i	−0.998412	−	0.0563326i	$-0.982059\pi$
$317$	−1.41507	−	8.02529i	−0.0794785	−	0.450745i	0.918934	−	0.394412i	$-0.129052\pi$
$318$	−1.32773	−	1.11410i	−0.0744556	−	0.0624757i
$319$	9.03346	−	7.57998i	0.505777	−	0.424397i
$320$		0			0
$321$	7.40069	−	2.69363i	0.413066	−	0.150344i
$322$	2.69124			0.149977
$323$	−1.08650	−	12.1314i	−0.0604545	−	0.675010i
$324$	7.52279			0.417933
$325$		0			0
$326$	−1.39960	+	7.93750i	−0.0775164	+	0.439617i
$327$	3.64680	−	3.06003i	0.201669	−	0.169220i
$328$	−8.71314	−	7.31119i	−0.481103	−	0.403693i
$329$	−4.21874	−	23.9257i	−0.232587	−	1.31907i
$330$		0			0
$331$	−0.314743	+	0.545150i	−0.0172998	+	0.0299642i	−0.874546	−	0.484943i	$-0.838840\pi$
$331$	−0.314743	+	0.545150i	−0.0172998	+	0.0299642i	0.857246	+	0.514907i	$0.172174\pi$
$332$	−1.66834	−	0.607227i	−0.0915621	−	0.0333259i
$333$	7.98455	+	2.90614i	0.437551	+	0.159255i
$334$	0.903396	−	1.56473i	0.0494316	−	0.0856181i
$335$		0			0
$336$	0.163379	+	0.926571i	0.00891308	+	0.0505486i
$337$	11.8130	+	9.91232i	0.643497	+	0.539958i	0.905090	−	0.425220i	$-0.139803\pi$
$337$	11.8130	+	9.91232i	0.643497	+	0.539958i	−0.261593	+	0.965178i	$0.584248\pi$
$338$	−9.96376	+	8.36059i	−0.541957	+	0.454756i
$339$	0.701416	−	3.97793i	0.0380957	−	0.216051i
$340$		0			0
$341$	−21.7974			−1.18040
$342$	−3.17129	+	11.9335i	−0.171484	+	0.645290i
$343$	−20.0317			−1.08161
$344$	1.44823	−	0.527112i	0.0780832	−	0.0284200i
$345$		0			0
$346$	15.7555	−	13.2205i	0.847023	−	0.710737i
$347$	−11.7701	−	9.87631i	−0.631854	−	0.530188i	0.269651	−	0.962958i	$-0.413092\pi$
$347$	−11.7701	−	9.87631i	−0.631854	−	0.530188i	−0.901504	+	0.432770i	$0.857536\pi$
$348$	−0.316251	−	1.79355i	−0.0169528	−	0.0961442i
$349$	17.7797	+	30.7954i	0.951727	+	1.64844i	0.741686	+	0.670747i	$0.234026\pi$
$349$	17.7797	+	30.7954i	0.951727	+	1.64844i	0.210041	+	0.977693i	$0.432640\pi$
$350$		0			0
$351$	−11.4308	−	4.16047i	−0.610130	−	0.222069i
$352$	−2.48827	−	0.905657i	−0.132625	−	0.0482717i
$353$	9.82488	−	17.0172i	0.522926	−	0.905734i	−0.476718	−	0.879056i	$-0.658174\pi$
$353$	9.82488	−	17.0172i	0.522926	−	0.905734i	0.999644	−	0.0266780i	$-0.00849287\pi$
$354$	2.29383	+	3.97303i	0.121916	+	0.211164i
$355$		0			0
$356$	4.97111	+	4.17126i	0.263468	+	0.221076i
$357$	2.01396	−	1.68991i	0.106590	−	0.0894396i
$358$	2.70467	−	15.3389i	0.142946	−	0.810687i
$359$	−18.3084	+	6.66371i	−0.966280	+	0.351697i	−0.776491	−	0.630128i	$-0.783002\pi$
$359$	−18.3084	+	6.66371i	−0.966280	+	0.351697i	−0.189789	+	0.981825i	$0.560780\pi$
$360$		0			0
$361$	−16.4934	−	9.43225i	−0.868074	−	0.496434i
$362$	6.82472			0.358699
$363$	1.53266	−	0.557841i	0.0804436	−	0.0292791i
$364$	−2.03736	+	11.5544i	−0.106787	+	0.605617i
$365$		0			0
$366$	−1.03708	−	0.870217i	−0.0542093	−	0.0454870i
$367$	−3.71888	−	21.0908i	−0.194124	−	1.10093i	−0.913661	−	0.406477i	$-0.866757\pi$
$367$	−3.71888	−	21.0908i	−0.194124	−	1.10093i	0.719537	−	0.694454i	$-0.244354\pi$
$368$	0.584882	+	1.01305i	0.0304891	+	0.0528086i
$369$	16.1102	−	27.9036i	0.838662	−	1.45261i
$370$		0			0
$371$	−9.16271	−	3.33495i	−0.475704	−	0.173142i
$372$	−1.68320	+	2.91539i	−0.0872698	+	0.151156i
$373$	7.21408	+	12.4952i	0.373531	+	0.646975i	0.990106	−	0.140321i	$-0.0448136\pi$
$373$	7.21408	+	12.4952i	0.373531	+	0.646975i	−0.616575	+	0.787296i	$0.711480\pi$
$374$	1.28485	+	7.28673i	0.0664379	+	0.376788i
$375$		0			0
$376$	8.08934	−	6.78776i	0.417176	−	0.350052i
$377$	3.94368	−	22.3657i	0.203110	−	1.15189i
$378$	−5.15688	+	1.87695i	−0.265241	+	0.0965399i
$379$	−8.16356			−0.419334			−0.209667	−	0.977773i	$-0.567238\pi$
$379$	−8.16356			−0.419334			−0.209667	+	0.977773i	$0.567238\pi$
$380$		0			0
$381$	3.44289			0.176384
$382$	−3.07906	+	1.12069i	−0.157538	+	0.0573393i
$383$	−4.76545	+	27.0262i	−0.243503	+	1.38098i	0.580440	+	0.814303i	$0.302881\pi$
$383$	−4.76545	+	27.0262i	−0.243503	+	1.38098i	−0.823943	+	0.566673i	$0.808230\pi$
$384$	−0.313276	+	0.262870i	−0.0159868	+	0.0134145i
$385$		0			0
$386$	4.11035	+	23.3109i	0.209211	+	1.18650i
$387$	2.18288	+	3.78086i	0.110962	+	0.192192i
$388$	1.31030	−	2.26951i	0.0665205	−	0.115217i
$389$	14.8341	+	5.39919i	0.752121	+	0.273750i	0.689498	−	0.724288i	$-0.257831\pi$
$389$	14.8341	+	5.39919i	0.752121	+	0.273750i	0.0626229	+	0.998037i	$0.480053\pi$
$390$		0			0
$391$	1.63432	−	2.83073i	0.0826512	−	0.143156i
$392$	−0.853462	−	1.47824i	−0.0431063	−	0.0746623i
$393$	1.21013	+	6.86300i	0.0610431	+	0.346193i
$394$	5.27393	+	4.42536i	0.265697	+	0.222946i
$395$		0			0
$396$	1.30254	−	7.38709i	0.0654552	−	0.371215i
$397$	35.8815	−	13.0598i	1.80084	−	0.655452i	0.802575	−	0.596551i	$-0.203463\pi$
$397$	35.8815	−	13.0598i	1.80084	−	0.655452i	0.998264	−	0.0589010i	$-0.0187596\pi$
$398$	18.9908			0.951925
$399$	−0.365838	−	4.08479i	−0.0183148	−	0.204495i
$400$		0			0
$401$	15.1995	−	5.53217i	0.759028	−	0.276264i	0.0666283	−	0.997778i	$-0.478776\pi$
$401$	15.1995	−	5.53217i	0.759028	−	0.276264i	0.692399	+	0.721514i	$0.256554\pi$
$402$	−0.598218	+	3.39266i	−0.0298364	+	0.169211i
$403$	−32.1580	+	26.9838i	−1.60191	+	1.34416i
$404$	7.48342	+	6.27934i	0.372314	+	0.312409i
$405$		0			0
$406$	−5.12286	−	8.87305i	−0.254243	−	0.440362i
$407$	3.97134	−	6.87857i	0.196852	−	0.340958i
$408$	1.07381	+	0.390836i	0.0531616	+	0.0193492i
$409$	−29.6569	−	10.7942i	−1.46644	−	0.533740i	−0.519307	−	0.854587i	$-0.673810\pi$
$409$	−29.6569	−	10.7942i	−1.46644	−	0.533740i	−0.947131	+	0.320848i	$0.896032\pi$
$410$		0			0
$411$	2.39849	+	4.15430i	0.118309	+	0.204917i
$412$	−0.0864105	−	0.490058i	−0.00425714	−	0.0241434i
$413$	19.7709	+	16.5898i	0.972863	+	0.816329i
$414$	−2.53841	+	2.12998i	−0.124756	+	0.104683i
$415$		0			0
$416$	−4.79213	+	1.74419i	−0.234954	+	0.0855162i
$417$	−5.29748			−0.259419
$418$	10.4708	+	4.85643i	0.512144	+	0.237536i
$419$	−15.0026			−0.732925			−0.366463	−	0.930433i	$-0.619431\pi$
$419$	−15.0026			−0.732925			−0.366463	+	0.930433i	$0.619431\pi$
$420$		0			0
$421$	−0.407466	+	2.31085i	−0.0198587	+	0.112624i	−0.993126	−	0.117052i	$-0.962656\pi$
$421$	−0.407466	+	2.31085i	−0.0198587	+	0.112624i	0.973267	+	0.229676i	$0.0737667\pi$
$422$	9.45454	−	7.93330i	0.460240	−	0.386187i
$423$	22.9151	+	19.2281i	1.11417	+	0.934901i
$424$	−0.735960	−	4.17384i	−0.0357414	−	0.202699i
$425$		0			0
$426$	−0.0638455	+	0.110584i	−0.00309333	+	0.00535780i
$427$	−7.15693	−	2.60491i	−0.346348	−	0.126060i
$428$	18.0967	+	6.58665i	0.874736	+	0.318378i
$429$	−2.76120	+	4.78255i	−0.133312	+	0.230904i
$430$		0			0
$431$	−6.04701	−	34.2943i	−0.291274	−	1.65190i	−0.681971	−	0.731379i	$-0.738877\pi$
$431$	−6.04701	−	34.2943i	−0.291274	−	1.65190i	0.390697	−	0.920519i	$-0.372234\pi$
$432$	−1.82726	−	1.53326i	−0.0879142	−	0.0737688i
$433$	−3.37149	+	2.82901i	−0.162023	+	0.135954i	−0.720195	−	0.693772i	$-0.755948\pi$
$433$	−3.37149	+	2.82901i	−0.162023	+	0.135954i	0.558171	+	0.829726i	$0.311503\pi$
$434$	−3.28864	+	18.6508i	−0.157860	+	0.895268i
$435$		0			0
$436$	11.6409			0.557496
$437$	−2.16438	−	4.61672i	−0.103536	−	0.220847i
$438$	6.27690			0.299922
$439$	−2.39398	+	0.871336i	−0.114258	+	0.0415866i	−0.398517	−	0.917161i	$-0.630475\pi$
$439$	−2.39398	+	0.871336i	−0.114258	+	0.0415866i	0.284258	+	0.958748i	$0.408253\pi$
$440$		0			0
$441$	3.70405	−	3.10807i	0.176384	−	0.148003i
$442$	10.9161	+	9.15967i	0.519224	+	0.435681i
$443$	−6.93673	−	39.3402i	−0.329574	−	1.86911i	−0.475361	−	0.879791i	$-0.657682\pi$
$443$	−6.93673	−	39.3402i	−0.329574	−	1.86911i	0.145787	−	0.989316i	$-0.453429\pi$
$444$	−0.613336	−	1.06233i	−0.0291076	−	0.0504159i
$445$		0			0
$446$	−4.50066	−	1.63811i	−0.213112	−	0.0775666i
$447$	−6.29536	−	2.29132i	−0.297760	−	0.108376i
$448$	−1.15033	+	1.99244i	−0.0543482	+	0.0941338i
$449$	−12.4299	−	21.5293i	−0.586605	−	1.01603i	−0.994673	−	0.103079i	$-0.967131\pi$
$449$	−12.4299	−	21.5293i	−0.586605	−	1.01603i	0.408068	−	0.912952i	$-0.366203\pi$
$450$		0			0
$451$	−23.0721	−	19.3598i	−1.08642	−	0.911617i
$452$	7.56635	−	6.34892i	0.355891	−	0.298628i
$453$	0.263659	−	1.49528i	0.0123878	−	0.0702545i
$454$	3.98825	−	1.45160i	0.187178	−	0.0681272i
$455$		0			0
$456$	1.45810	−	1.02545i	0.0682819	−	0.0480210i
$457$	−37.9539			−1.77541			−0.887703	−	0.460416i	$-0.847700\pi$
$457$	−37.9539			−1.77541			−0.887703	+	0.460416i	$0.847700\pi$
$458$	−27.1532	+	9.88296i	−1.26879	+	0.461800i
$459$	−1.15741	+	6.56399i	−0.0540232	+	0.306381i
$460$		0			0
$461$	1.29024	+	1.08264i	0.0600927	+	0.0504238i	0.672339	−	0.740243i	$-0.265290\pi$
$461$	1.29024	+	1.08264i	0.0600927	+	0.0504238i	−0.612247	+	0.790667i	$0.709734\pi$
$462$	0.432623	+	2.45353i	0.0201275	+	0.114148i
$463$	4.38825	+	7.60068i	0.203939	+	0.353233i	0.949794	−	0.312875i	$-0.101292\pi$
$463$	4.38825	+	7.60068i	0.203939	+	0.353233i	−0.745855	+	0.666108i	$0.767959\pi$
$464$	2.22668	−	3.85673i	0.103371	−	0.179044i
$465$		0			0
$466$	−12.8061	−	4.66102i	−0.593229	−	0.215918i
$467$	0.261302	−	0.452589i	0.0120916	−	0.0209433i	−0.859916	−	0.510435i	$-0.829484\pi$
$467$	0.261302	−	0.452589i	0.0120916	−	0.0209433i	0.872008	+	0.489492i	$0.162818\pi$
$468$	−7.22308	−	12.5107i	−0.333887	−	0.578309i
$469$	3.36543	+	19.0863i	0.155401	+	0.881323i
$470$		0			0
$471$	1.54985	−	1.30048i	0.0714134	−	0.0599230i
$472$	−1.94800	+	11.0477i	−0.0896639	+	0.508509i
$473$	3.83486	−	1.39577i	0.176327	−	0.0641777i
$474$	3.60223			0.165456
$475$		0			0
$476$	6.42870			0.294659
$477$	11.2818	−	4.10625i	0.516559	−	0.188012i
$478$	−2.58512	+	14.6609i	−0.118241	+	0.670576i
$479$	−5.31590	+	4.46057i	−0.242890	+	0.203809i	−0.756103	−	0.654452i	$-0.772899\pi$
$479$	−5.31590	+	4.46057i	−0.242890	+	0.203809i	0.513214	+	0.858261i	$0.328455\pi$
$480$		0			0
$481$	−2.65625	−	15.0643i	−0.121114	−	0.686874i
$482$	5.80022	+	10.0463i	0.264193	+	0.457595i
$483$	0.550295	−	0.953139i	0.0250393	−	0.0433693i
$484$	3.74776	+	1.36407i	0.170353	+	0.0620033i
$485$		0			0
$486$	5.11622	−	8.86155i	0.232076	−	0.401968i
$487$	−20.5947	−	35.6711i	−0.933236	−	1.61641i	−0.777750	−	0.628574i	$-0.783639\pi$
$487$	−20.5947	−	35.6711i	−0.933236	−	1.61641i	−0.155486	−	0.987838i	$-0.549694\pi$
$488$	−0.574854	−	3.26016i	−0.0260224	−	0.147580i
$489$	2.52499	+	2.11872i	0.114184	+	0.0958117i
$490$		0			0
$491$	−3.65055	+	20.7033i	−0.164747	+	0.934327i	0.784578	+	0.620030i	$0.212880\pi$
$491$	−3.65055	+	20.7033i	−0.164747	+	0.934327i	−0.949325	+	0.314297i	$0.898231\pi$
$492$	−4.37099	+	1.59091i	−0.197059	+	0.0717238i
$493$	−12.4439			−0.560446
$494$	21.4597	−	5.79743i	0.965517	−	0.260839i
$495$		0			0
$496$	−7.73532	+	2.81543i	−0.347326	+	0.126416i
$497$	−0.124742	+	0.707445i	−0.00559543	+	0.0317333i
$498$	−0.556194	+	0.466702i	−0.0249236	+	0.0209134i
$499$	17.9199	+	15.0366i	0.802203	+	0.673128i	0.948733	−	0.316078i	$-0.102366\pi$
$499$	17.9199	+	15.0366i	0.802203	+	0.673128i	−0.146530	+	0.989206i	$0.546810\pi$
$500$		0			0
$501$	−0.369446	−	0.639900i	−0.0165056	−	0.0285886i
$502$	10.5352	−	18.2476i	0.470210	−	0.814428i
$503$	−22.1615	−	8.06613i	−0.988132	−	0.359651i	−0.203136	−	0.979151i	$-0.565113\pi$
$503$	−22.1615	−	8.06613i	−0.988132	−	0.359651i	−0.784997	+	0.619500i	$0.787335\pi$
$504$	−6.12420	−	2.22903i	−0.272794	−	0.0992887i
$505$		0			0
$506$	1.54875	+	2.68251i	0.0688502	+	0.119252i
$507$	0.923661	+	5.23834i	0.0410212	+	0.232643i
$508$	6.44916	+	5.41149i	0.286135	+	0.240096i
$509$	−2.07742	+	1.74316i	−0.0920801	+	0.0772644i	−0.687666	−	0.726027i	$-0.741365\pi$
$509$	−2.07742	+	1.74316i	−0.0920801	+	0.0772644i	0.595586	+	0.803292i	$0.296920\pi$
$510$		0			0
$511$	33.1827	−	12.0775i	1.46792	−	0.534278i
$512$	−1.00000			−0.0441942
$513$	7.36716	+	7.33692i	0.325268	+	0.323933i
$514$	−27.7153			−1.22247
$515$		0			0
$516$	0.109445	−	0.620691i	0.00481803	−	0.0273244i
$517$	21.4203	−	17.9737i	0.942063	−	0.790485i
$518$	−5.28644	−	4.43585i	−0.232273	−	0.194900i
$519$	−1.46057	−	8.28331i	−0.0641120	−	0.363597i
$520$		0			0
$521$	8.92779	−	15.4634i	0.391134	−	0.677464i	−0.601466	−	0.798899i	$-0.705416\pi$
$521$	8.92779	−	15.4634i	0.391134	−	0.677464i	0.992599	+	0.121435i	$0.0387496\pi$
$522$	11.8545	+	4.31469i	0.518857	+	0.188849i
$523$	9.91759	+	3.60971i	0.433666	+	0.157841i	0.549623	−	0.835413i	$-0.314771\pi$
$523$	9.91759	+	3.60971i	0.433666	+	0.157841i	−0.115957	+	0.993254i	$0.536994\pi$
$524$	−8.52039	+	14.7578i	−0.372215	+	0.644695i
$525$		0			0
$526$	−1.56375	−	8.86847i	−0.0681828	−	0.386684i
$527$	17.6204	+	14.7853i	0.767556	+	0.644056i
$528$	−0.829544	+	0.696070i	−0.0361013	+	0.0302926i
$529$	−3.75630	+	21.3030i	−0.163317	+	0.926218i
$530$		0			0
$531$	−31.7781			−1.37905
$532$	5.73514	−	8.22658i	0.248650	−	0.356667i
$533$	−58.0048			−2.51247
$534$	2.49378	−	0.907662i	0.107916	−	0.0392784i
$535$		0			0
$536$	−6.45312	+	5.41481i	−0.278732	+	0.233884i
$537$	−4.87945	−	4.09434i	−0.210564	−	0.176684i
$538$	−1.29149	−	7.32442i	−0.0556802	−	0.315778i
$539$	−2.25994	−	3.91433i	−0.0973424	−	0.168602i
$540$		0			0
$541$	3.45906	+	1.25899i	0.148717	+	0.0541284i	0.415306	−	0.909682i	$-0.363675\pi$
$541$	3.45906	+	1.25899i	0.148717	+	0.0541284i	−0.266589	+	0.963810i	$0.585897\pi$
$542$	−17.5650	−	6.39313i	−0.754481	−	0.274608i
$543$	1.39549	−	2.41707i	0.0598864	−	0.103726i
$544$	1.39714	+	2.41991i	0.0599018	+	0.103753i
$545$		0			0
$546$	3.67557	+	3.08417i	0.157300	+	0.131990i
$547$	4.23706	−	3.55531i	0.181164	−	0.152014i	−0.547696	−	0.836677i	$-0.684495\pi$
$547$	4.23706	−	3.55531i	0.181164	−	0.152014i	0.728860	+	0.684663i	$0.240051\pi$
$548$	−2.03688	+	11.5517i	−0.0870110	+	0.493464i
$549$	8.81216	−	3.20736i	0.376094	−	0.136887i
$550$		0			0
$551$	−11.1014	+	15.9240i	−0.472936	+	0.678387i
$552$	0.478378			0.0203611
$553$	19.0431	−	6.93113i	0.809796	−	0.294742i
$554$	0.676824	−	3.83846i	0.0287555	−	0.163080i
$555$		0			0
$556$	−9.92317	−	8.32653i	−0.420836	−	0.353123i
$557$	−1.69098	−	9.59001i	−0.0716490	−	0.406342i	−0.999447	−	0.0332583i	$-0.989412\pi$
$557$	−1.69098	−	9.59001i	−0.0716490	−	0.406342i	0.927798	−	0.373084i	$-0.121700\pi$
$558$	−11.6593	−	20.1945i	−0.493577	−	0.854900i
$559$	3.92974	−	6.80651i	0.166210	−	0.287885i
$560$		0			0
$561$	2.84342	+	1.03492i	0.120049	+	0.0436943i
$562$	−2.93947	+	5.09132i	−0.123994	+	0.214764i
$563$	−17.0631	−	29.5542i	−0.719125	−	1.24556i	−0.961347	−	0.275340i	$-0.911210\pi$
$563$	−17.0631	−	29.5542i	−0.719125	−	1.24556i	0.242223	−	0.970221i	$-0.422124\pi$
$564$	−0.749898	−	4.25288i	−0.0315764	−	0.179079i
$565$		0			0
$566$	−14.3104	+	12.0078i	−0.601509	+	0.504726i
$567$	3.00541	−	17.0445i	0.126215	−	0.715802i
$568$	−0.293409	+	0.106792i	−0.0123112	+	0.00448090i
$569$	31.8304			1.33440			0.667199	−	0.744880i	$-0.267493\pi$
$569$	31.8304			1.33440			0.667199	+	0.744880i	$0.267493\pi$
$570$		0			0
$571$	27.6840			1.15854			0.579270	−	0.815136i	$-0.303338\pi$
$571$	27.6840			1.15854			0.579270	+	0.815136i	$0.303338\pi$
$572$	−12.6894	+	4.61857i	−0.530571	+	0.193112i
$573$	−0.232689	+	1.31964i	−0.00972071	+	0.0551289i
$574$	−20.0461	+	16.8206i	−0.836706	+	0.702080i
$575$		0			0
$576$	−0.491903	−	2.78972i	−0.0204960	−	0.116238i
$577$	−17.8008	−	30.8319i	−0.741057	−	1.28355i	−0.952014	−	0.306053i	$-0.900991\pi$
$577$	−17.8008	−	30.8319i	−0.741057	−	1.28355i	0.210957	−	0.977495i	$-0.432342\pi$
$578$	−4.59601	+	7.96053i	−0.191169	+	0.331114i
$579$	9.09635	+	3.31080i	0.378031	+	0.137592i
$580$		0			0
$581$	−2.04232	+	3.53740i	−0.0847296	+	0.146756i
$582$	−0.535852	−	0.928123i	−0.0222118	−	0.0384719i
$583$	−1.94880	−	11.0522i	−0.0807109	−	0.457734i
$584$	11.7578	+	9.86596i	0.486541	+	0.408256i
$585$		0			0
$586$	1.83896	−	10.4292i	0.0759665	−	0.430828i
$587$	0.785714	−	0.285977i	0.0324299	−	0.0118035i	−0.325754	−	0.945454i	$-0.605618\pi$
$587$	0.785714	−	0.285977i	0.0324299	−	0.0118035i	0.358184	+	0.933651i	$0.383396\pi$
$588$	−0.698051			−0.0287871
$589$	34.6396	−	9.35803i	1.42730	−	0.385591i
$590$		0			0
$591$	2.64569	−	0.962954i	0.108829	−	0.0396106i
$592$	0.520865	−	2.95397i	0.0214074	−	0.121408i
$593$	13.2512	−	11.1190i	0.544160	−	0.456604i	−0.328798	−	0.944400i	$-0.606643\pi$
$593$	13.2512	−	11.1190i	0.544160	−	0.456604i	0.872958	+	0.487796i	$0.162199\pi$
$594$	−4.83853	−	4.06001i	−0.198527	−	0.166584i
$595$		0			0
$596$	−8.19090	−	14.1871i	−0.335512	−	0.581124i
$597$	3.88318	−	6.72586i	0.158928	−	0.275271i
$598$	5.60566	+	2.04030i	0.229233	+	0.0834339i
$599$	0.980251	+	0.356782i	0.0400520	+	0.0145777i	0.361968	−	0.932190i	$-0.382105\pi$
$599$	0.980251	+	0.356782i	0.0400520	+	0.0145777i	−0.321916	+	0.946768i	$0.604327\pi$
$600$		0			0
$601$	21.9915	+	38.0903i	0.897051	+	1.55374i	0.831246	+	0.555905i	$0.187628\pi$
$601$	21.9915	+	38.0903i	0.897051	+	1.55374i	0.0658048	+	0.997833i	$0.479039\pi$
$602$	−0.615709	−	3.49186i	−0.0250944	−	0.142317i
$603$	−18.2801	−	15.3389i	−0.744425	−	0.624646i
$604$	2.84415	−	2.38653i	0.115727	−	0.0971064i
$605$		0			0
$606$	3.75409	−	1.36638i	0.152500	−	0.0555053i
$607$	−35.1548			−1.42689			−0.713445	−	0.700711i	$-0.752866\pi$
$607$	−35.1548			−1.42689			−0.713445	+	0.700711i	$0.752866\pi$
$608$	4.34308	+	0.370973i	0.176135	+	0.0150450i
$609$	−4.19001			−0.169788
$610$		0			0
$611$	9.35131	−	53.0339i	0.378313	−	2.14552i
$612$	−6.06363	+	5.08799i	−0.245108	+	0.205670i
$613$	34.0263	+	28.5514i	1.37431	+	1.15318i	0.971265	+	0.238001i	$0.0764922\pi$
$613$	34.0263	+	28.5514i	1.37431	+	1.15318i	0.403044	+	0.915181i	$0.367952\pi$
$614$	−0.816611	−	4.63123i	−0.0329557	−	0.186901i
$615$		0			0
$616$	−3.04605	+	5.27591i	−0.122729	+	0.212572i
$617$	−3.89348	−	1.41711i	−0.156746	−	0.0570508i	0.262456	−	0.964944i	$-0.415468\pi$
$617$	−3.89348	−	1.41711i	−0.156746	−	0.0570508i	−0.419201	+	0.907893i	$0.637690\pi$
$618$	−0.191230	−	0.0696019i	−0.00769238	−	0.00279980i
$619$	−22.9770	+	39.7973i	−0.923523	+	1.59959i	−0.129603	+	0.991566i	$0.541370\pi$
$619$	−22.9770	+	39.7973i	−0.923523	+	1.59959i	−0.793920	+	0.608022i	$0.791963\pi$
$620$		0			0
$621$	0.484524	+	2.74787i	0.0194433	+	0.110268i
$622$	10.4366	+	8.75734i	0.418469	+	0.351137i
$623$	11.4369	−	9.59668i	0.458209	−	0.384483i
$624$	−0.362148	+	2.05385i	−0.0144975	+	0.0822196i
$625$		0			0
$626$	30.9070			1.23529
$627$	3.86100	−	2.71535i	0.154194	−	0.108441i
$628$	4.94724			0.197416
$629$	−7.87608	+	2.86666i	−0.314040	+	0.114301i
$630$		0			0
$631$	−13.6051	+	11.4160i	−0.541609	+	0.454464i	−0.872088	−	0.489350i	$-0.837234\pi$
$631$	−13.6051	+	11.4160i	−0.541609	+	0.454464i	0.330479	+	0.943813i	$0.392790\pi$
$632$	6.74765	+	5.66195i	0.268407	+	0.225220i
$633$	−0.876455	−	4.97063i	−0.0348360	−	0.197565i
$634$	−4.07454	−	7.05732i	−0.161821	−	0.280282i
$635$		0			0
$636$	−1.62871	−	0.592801i	−0.0645824	−	0.0235061i
$637$	−8.17981	−	2.97721i	−0.324096	−	0.117961i
$638$	5.89618	−	10.2125i	0.233432	−	0.404316i
$639$	−0.442249	−	0.765998i	−0.0174951	−	0.0303024i
$640$		0			0
$641$	−2.62235	−	2.20041i	−0.103577	−	0.0869110i	0.589529	−	0.807747i	$-0.299313\pi$
$641$	−2.62235	−	2.20041i	−0.103577	−	0.0869110i	−0.693105	+	0.720836i	$0.743758\pi$
$642$	6.03309	−	5.06237i	0.238107	−	0.199796i
$643$	−7.09985	+	40.2653i	−0.279991	+	1.58791i	0.442657	+	0.896691i	$0.354036\pi$
$643$	−7.09985	+	40.2653i	−0.279991	+	1.58791i	−0.722648	+	0.691216i	$0.757075\pi$
$644$	2.52894	−	0.920458i	0.0996541	−	0.0362711i
$645$		0			0
$646$	−5.17016	−	11.0282i	−0.203417	−	0.433898i
$647$	27.9797			1.10000			0.549998	−	0.835166i	$-0.314629\pi$
$647$	27.9797			1.10000			0.549998	+	0.835166i	$0.314629\pi$
$648$	7.06911	−	2.57295i	0.277701	−	0.101075i
$649$	−5.15823	+	29.2538i	−0.202478	+	1.14831i
$650$		0			0
$651$	5.93299	+	4.97837i	0.232532	+	0.195118i
$652$	1.39960	+	7.93750i	0.0548124	+	0.310856i
$653$	7.67760	+	13.2980i	0.300448	+	0.520391i	0.976237	−	0.216704i	$-0.0695305\pi$
$653$	7.67760	+	13.2980i	0.300448	+	0.520391i	−0.675790	+	0.737095i	$0.736197\pi$
$654$	2.38028	−	4.12277i	0.0930763	−	0.161213i
$655$		0			0
$656$	−10.6883	−	3.89021i	−0.417306	−	0.151887i
$657$	−21.7396	+	37.6541i	−0.848142	+	1.46903i
$658$	−12.1474	−	21.0399i	−0.473555	−	0.820221i
$659$	−8.57081	−	48.6075i	−0.333871	−	1.89348i	−0.438101	−	0.898926i	$-0.644349\pi$
$659$	−8.57081	−	48.6075i	−0.333871	−	1.89348i	0.104229	−	0.994553i	$-0.466762\pi$
$660$		0			0
$661$	30.0511	−	25.2159i	1.16885	−	0.980785i	0.168865	−	0.985639i	$-0.445990\pi$
$661$	30.0511	−	25.2159i	1.16885	−	0.980785i	0.999988	+	0.00485448i	$0.00154524\pi$
$662$	−0.109309	+	0.619922i	−0.00424841	+	0.0240940i
$663$	5.47610	−	1.99314i	0.212674	−	0.0774070i
$664$	−1.77541			−0.0688993
$665$		0			0
$666$	8.49698			0.329251
$667$	−4.89522	+	1.78171i	−0.189544	+	0.0689882i
$668$	0.313746	−	1.77934i	0.0121392	−	0.0688448i
$669$	−1.50044	+	1.25902i	−0.0580102	+	0.0486764i
$670$		0			0
$671$	−1.52219	−	8.63278i	−0.0587636	−	0.333265i
$672$	0.470432	+	0.814813i	0.0181473	+	0.0314321i
$673$	21.4246	−	37.1086i	0.825859	−	1.43043i	−0.0754013	−	0.997153i	$-0.524024\pi$
$673$	21.4246	−	37.1086i	0.825859	−	1.43043i	0.901261	−	0.433277i	$-0.142643\pi$
$674$	14.4908	+	5.27423i	0.558166	+	0.203156i
$675$		0			0
$676$	−6.50338	+	11.2642i	−0.250130	+	0.433238i
$677$	0.513040	+	0.888611i	0.0197177	+	0.0341521i	0.875716	−	0.482827i	$-0.160390\pi$
$677$	0.513040	+	0.888611i	0.0197177	+	0.0341521i	−0.855998	+	0.516979i	$0.827057\pi$
$678$	−0.701416	−	3.97793i	−0.0269377	−	0.152771i
$679$	−4.61859	−	3.87546i	−0.177245	−	0.148727i
$680$		0			0
$681$	0.301398	−	1.70931i	0.0115496	−	0.0655010i
$682$	−20.4828	+	7.45515i	−0.784329	+	0.285472i
$683$	44.8988			1.71800			0.859002	−	0.511972i	$-0.171085\pi$
$683$	44.8988			1.71800			0.859002	+	0.511972i	$0.171085\pi$
$684$	1.10146	+	12.2985i	0.0421155	+	0.470244i
$685$		0			0
$686$	−18.8237	+	6.85126i	−0.718692	+	0.261582i
$687$	−2.05201	+	11.6375i	−0.0782889	+	0.443998i
$688$	1.18061	−	0.990646i	0.0450102	−	0.0377680i
$689$	−16.5570	−	13.8930i	−0.630771	−	0.529279i
$690$		0			0
$691$	0.745705	+	1.29160i	0.0283680	+	0.0491348i	0.879861	−	0.475231i	$-0.157636\pi$
$691$	0.745705	+	1.29160i	0.0283680	+	0.0491348i	−0.851493	+	0.524366i	$0.824302\pi$
$692$	10.2837	−	17.8119i	0.390928	−	0.677107i
$693$	−16.2167	−	5.90238i	−0.616020	−	0.224213i
$694$	−14.4382	−	5.25508i	−0.548067	−	0.199480i
$695$		0			0
$696$	−0.910608	−	1.57722i	−0.0345165	−	0.0597843i
$697$	5.51900	+	31.2998i	0.209047	+	1.18556i
$698$	27.2401	+	22.8572i	1.03105	+	0.865157i
$699$	−4.26930	+	3.58237i	−0.161480	+	0.135498i
$700$		0			0
$701$	−16.7716	+	6.10435i	−0.633453	+	0.230558i	−0.638734	−	0.769428i	$-0.720541\pi$
$701$	−16.7716	+	6.10435i	−0.633453	+	0.230558i	0.00528040	+	0.999986i	$0.498319\pi$
$702$	−12.1644			−0.459115
$703$	−3.35801	+	12.6361i	−0.126650	+	0.476581i
$704$	−2.64797			−0.0997989
$705$		0			0
$706$	3.41215	−	19.3512i	0.128418	−	0.728294i
$707$	17.2169	−	14.4467i	0.647507	−	0.543323i
$708$	3.51436	+	2.94889i	0.132078	+	0.110826i
$709$	−4.94285	−	28.0323i	−0.185632	−	1.05277i	−0.925140	−	0.379626i	$-0.876053\pi$
$709$	−4.94285	−	28.0323i	−0.185632	−	1.05277i	0.739508	−	0.673148i	$-0.235058\pi$
$710$		0			0
$711$	−12.4761	+	21.6092i	−0.467889	+	0.810408i
$712$	6.09797	+	2.21948i	0.228531	+	0.0831785i
$713$	9.04849	+	3.29338i	0.338869	+	0.123338i
$714$	1.31452	−	2.27681i	0.0491946	−	0.0852075i
$715$		0			0
$716$	−2.70467	−	15.3389i	−0.101078	−	0.573243i
$717$	4.66377	+	3.91337i	0.174172	+	0.146148i
$718$	−14.9251	+	12.5237i	−0.557001	+	0.467379i
$719$	−0.0102041	+	0.0578704i	−0.000380549	+	0.00215820i	−0.984997	−	0.172569i	$-0.944793\pi$
$719$	−0.0102041	+	0.0578704i	−0.000380549	+	0.00215820i	0.984617	+	0.174727i	$0.0559043\pi$
$720$		0			0
$721$	−1.14485			−0.0426366
$722$	−18.7248	−	3.22234i	−0.696863	−	0.119923i
$723$	4.74403			0.176432
$724$	6.41314	−	2.33419i	0.238342	−	0.0867495i
$725$		0			0
$726$	1.24943	−	1.04840i	0.0463708	−	0.0389097i
$727$	23.7254	+	19.9079i	0.879925	+	0.738345i	0.966164	−	0.257930i	$-0.0830403\pi$
$727$	23.7254	+	19.9079i	0.879925	+	0.738345i	−0.0862385	+	0.996275i	$0.527485\pi$
$728$	2.03736	+	11.5544i	0.0755095	+	0.428236i
$729$	9.19189	+	15.9208i	0.340440	+	0.589660i
$730$		0			0
$731$	−4.04675	−	1.47289i	−0.149674	−	0.0544770i
$732$	−1.27217	−	0.463033i	−0.0470209	−	0.0171142i
$733$	−6.78551	+	11.7529i	−0.250629	+	0.434102i	−0.963699	−	0.266991i	$-0.913971\pi$
$733$	−6.78551	+	11.7529i	−0.250629	+	0.434102i	0.713070	+	0.701092i	$0.247304\pi$
$734$	−10.7081	−	18.5470i	−0.395243	−	0.684580i
$735$		0			0
$736$	0.896091	+	0.751910i	0.0330304	+	0.0277158i
$737$	−17.0876	+	14.3382i	−0.629431	+	0.528156i
$738$	5.59501	−	31.7309i	0.205955	−	1.16803i
$739$	15.2620	−	5.55490i	0.561420	−	0.204340i	−0.0456930	−	0.998956i	$-0.514550\pi$
$739$	15.2620	−	5.55490i	0.561420	−	0.204340i	0.607113	+	0.794615i	$0.292327\pi$
$740$		0			0
$741$	2.33476	−	8.78568i	0.0857697	−	0.322750i
$742$	−9.75075			−0.357961
$743$	−28.8433	+	10.4981i	−1.05816	+	0.385138i	−0.811736	−	0.584024i	$-0.801477\pi$
$743$	−28.8433	+	10.4981i	−1.05816	+	0.385138i	−0.246422	+	0.969163i	$0.579255\pi$
$744$	−0.584569	+	3.31525i	−0.0214313	+	0.121543i
$745$		0			0
$746$	11.0526	+	9.27425i	0.404665	+	0.339554i
$747$	−0.873331	−	4.95290i	−0.0319535	−	0.181217i
$748$	3.69957	+	6.40785i	0.135270	+	0.234294i
$749$	22.1532	−	38.3705i	0.809461	−	1.40203i
$750$		0			0
$751$	−32.6013	−	11.8659i	−1.18964	−	0.432992i	−0.330041	−	0.943967i	$-0.607063\pi$
$751$	−32.6013	−	11.8659i	−1.18964	−	0.432992i	−0.859596	+	0.510974i	$0.829285\pi$
$752$	5.27994	−	9.14512i	0.192540	−	0.333488i
$753$	−4.30841	−	7.46239i	−0.157007	−	0.271944i
$754$	−3.94368	−	22.3657i	−0.143620	−	0.814511i
$755$		0			0
$756$	−4.20393	+	3.52751i	−0.152895	+	0.128294i
$757$	−2.72475	+	15.4528i	−0.0990326	+	0.561642i	0.894404	+	0.447259i	$0.147600\pi$
$757$	−2.72475	+	15.4528i	−0.0990326	+	0.561642i	−0.993437	+	0.114382i	$0.963511\pi$
$758$	−7.67124	+	2.79210i	−0.278632	+	0.101414i
$759$	1.26673			0.0459793
$760$		0			0
$761$	19.4434			0.704822			0.352411	−	0.935845i	$-0.385362\pi$
$761$	19.4434			0.704822			0.352411	+	0.935845i	$0.385362\pi$
$762$	3.23525	−	1.17754i	0.117201	−	0.0426576i
$763$	4.65060	−	26.3749i	0.168363	−	0.954835i
$764$	−2.51007	+	2.10620i	−0.0908112	+	0.0761996i
$765$		0			0
$766$	4.76545	+	27.0262i	0.172183	+	0.976497i
$767$	28.6043	+	49.5441i	1.03284	+	1.78894i
$768$	−0.204476	+	0.354164i	−0.00737841	+	0.0127798i
$769$	−37.7602	−	13.7436i	−1.36167	−	0.495607i	−0.445098	−	0.895482i	$-0.646831\pi$
$769$	−37.7602	−	13.7436i	−1.36167	−	0.495607i	−0.916570	+	0.399875i	$0.869054\pi$
$770$		0			0
$771$	−5.66713	+	9.81576i	−0.204097	+	0.353506i
$772$	11.8353	+	20.4993i	0.425961	+	0.737786i
$773$	−5.36365	−	30.4187i	−0.192917	−	1.09409i	−0.915354	−	0.402650i	$-0.868089\pi$
$773$	−5.36365	−	30.4187i	−0.192917	−	1.09409i	0.722437	−	0.691436i	$-0.243022\pi$
$774$	3.34437	+	2.80626i	0.120211	+	0.100869i
$775$		0			0
$776$	0.455063	−	2.58079i	0.0163358	−	0.0926451i
$777$	−2.65197	+	0.965237i	−0.0951388	+	0.0346277i
$778$	15.7862			0.565961
$779$	44.9768	+	20.8605i	1.61146	+	0.747407i
$780$		0			0
$781$	−0.776936	+	0.282782i	−0.0278010	+	0.0101187i
$782$	0.567594	−	3.21898i	0.0202971	−	0.115111i
$783$	8.13747	−	6.82814i	0.290809	−	0.244018i
$784$	−1.30758	−	1.09719i	−0.0466993	−	0.0391853i
$785$		0			0
$786$	3.48444	+	6.03522i	0.124286	+	0.215269i
$787$	−11.5669	+	20.0345i	−0.412317	+	0.714154i	−0.995143	−	0.0984430i	$-0.968614\pi$
$787$	−11.5669	+	20.0345i	−0.412317	+	0.714154i	0.582825	+	0.812597i	$0.301947\pi$
$788$	6.46944	+	2.35468i	0.230464	+	0.0838821i
$789$	−3.46064	−	1.25957i	−0.123202	−	0.0448419i
$790$		0			0
$791$	−11.3620	−	19.6796i	−0.403988	−	0.699727i
$792$	−1.30254	−	7.38709i	−0.0462838	−	0.262489i
$793$	−12.9325	−	10.8517i	−0.459248	−	0.385355i
$794$	29.2508	−	24.5444i	1.03807	−	0.871047i
$795$		0			0
$796$	17.8456	−	6.49525i	0.632519	−	0.230218i
$797$	12.1286			0.429618			0.214809	−	0.976656i	$-0.431087\pi$
$797$	12.1286			0.429618			0.214809	+	0.976656i	$0.431087\pi$
$798$	−1.74085	−	3.71332i	−0.0616256	−	0.131450i
$799$	−29.5072			−1.04389
$800$		0			0
$801$	−3.19212	+	18.1034i	−0.112788	+	0.639652i
$802$	12.3908	−	10.3971i	0.437533	−	0.367134i
$803$	31.1342	+	26.1247i	1.09870	+	0.921922i
$804$	0.598218	+	3.39266i	0.0210975	+	0.119650i
$805$		0			0
$806$	−20.9897	+	36.3552i	−0.739329	+	1.28056i
$807$	−2.85812	−	1.04027i	−0.100611	−	0.0366193i
$808$	9.17977	+	3.34116i	0.322943	+	0.117542i
$809$	2.77035	−	4.79839i	0.0974005	−	0.168703i	−0.813207	−	0.581974i	$-0.802281\pi$
$809$	2.77035	−	4.79839i	0.0974005	−	0.168703i	0.910608	+	0.413271i	$0.135614\pi$
$810$		0			0
$811$	3.82958	+	21.7186i	0.134475	+	0.762644i	0.975224	+	0.221219i	$0.0710036\pi$
$811$	3.82958	+	21.7186i	0.134475	+	0.762644i	−0.840749	+	0.541424i	$0.817885\pi$
$812$	−7.84867	−	6.58582i	−0.275434	−	0.231117i
$813$	−5.85584	+	4.91363i	−0.205373	+	0.172329i
$814$	1.37923	−	7.82202i	0.0483421	−	0.274162i
$815$		0			0
$816$	1.14273			0.0400034
$817$	−5.49497	+	3.86448i	−0.192245	+	0.135201i
$818$	−31.5602			−1.10348
$819$	−31.2315	+	11.3673i	−1.09132	+	0.397207i
$820$		0			0
$821$	−27.6363	+	23.1896i	−0.964512	+	0.809322i	−0.981681	−	0.190531i	$-0.938979\pi$
$821$	−27.6363	+	23.1896i	−0.964512	+	0.809322i	0.0171690	+	0.999853i	$0.494535\pi$
$822$	3.67470	+	3.08344i	0.128170	+	0.107547i
$823$	−6.45824	−	36.6265i	−0.225120	−	1.27672i	−0.862456	−	0.506133i	$-0.831075\pi$
$823$	−6.45824	−	36.6265i	−0.225120	−	1.27672i	0.637336	−	0.770586i	$-0.280037\pi$
$824$	−0.248809	−	0.430950i	−0.00866767	−	0.0150129i
$825$		0			0
$826$	24.2526	+	8.82723i	0.843856	+	0.307139i
$827$	46.8534	+	17.0533i	1.62925	+	0.593000i	0.985113	−	0.171908i	$-0.0549932\pi$
$827$	46.8534	+	17.0533i	1.62925	+	0.593000i	0.644140	+	0.764908i	$0.277215\pi$
$828$	−1.65683	+	2.86971i	−0.0575788	+	0.0997294i
$829$	−2.41813	−	4.18832i	−0.0839851	−	0.145466i	0.820973	−	0.570967i	$-0.193431\pi$
$829$	−2.41813	−	4.18832i	−0.0839851	−	0.145466i	−0.904958	+	0.425500i	$0.860098\pi$
$830$		0			0
$831$	−1.22105	−	1.02458i	−0.0423577	−	0.0355423i
$832$	−3.90658	+	3.27801i	−0.135436	+	0.113645i
$833$	−0.828235	+	4.69715i	−0.0286966	+	0.162747i
$834$	−4.97800	+	1.81185i	−0.172374	+	0.0627391i
$835$		0			0
$836$	11.5003	+	0.982325i	0.397747	+	0.0339744i
$837$	−19.6354			−0.678698
$838$	−14.0978	+	5.13119i	−0.487002	+	0.177254i
$839$	−1.26744	+	7.18802i	−0.0437570	+	0.248158i	−0.998838	−	0.0481853i	$-0.984656\pi$
$839$	−1.26744	+	7.18802i	−0.0437570	+	0.248158i	0.955081	+	0.296343i	$0.0957673\pi$
$840$		0			0
$841$	−7.02276	−	5.89279i	−0.242164	−	0.203200i
$842$	0.407466	+	2.31085i	0.0140422	+	0.0796372i
$843$	1.20211	+	2.08211i	0.0414027	+	0.0717116i
$844$	6.17101	−	10.6885i	0.212415	−	0.367914i
$845$		0			0
$846$	28.1096	+	10.2310i	0.966427	+	0.351751i
$847$	4.58786	−	7.94640i	0.157641	−	0.273042i
$848$	−2.11911	−	3.67041i	−0.0727706	−	0.126042i
$849$	1.32660	+	7.52352i	0.0455288	+	0.258207i
$850$		0			0
$851$	−2.68786	+	2.25539i	−0.0921388	+	0.0773136i
$852$	−0.0221733	+	0.125751i	−0.000759646	+	0.00430816i
$853$	−32.3257	+	11.7656i	−1.10681	+	0.402846i	−0.829823	−	0.558027i	$-0.811559\pi$
$853$	−32.3257	+	11.7656i	−1.10681	+	0.402846i	−0.276989	+	0.960873i	$0.589336\pi$
$854$	−7.61625			−0.260623
$855$		0			0
$856$	19.2581			0.658228
$857$	−24.8832	+	9.05674i	−0.849993	+	0.309372i	−0.730038	−	0.683407i	$-0.760498\pi$
$857$	−24.8832	+	9.05674i	−0.849993	+	0.309372i	−0.119956	+	0.992779i	$0.538275\pi$
$858$	−0.958956	+	5.43851i	−0.0327382	+	0.185668i
$859$	−21.2971	+	17.8704i	−0.726649	+	0.609731i	−0.929216	−	0.369538i	$-0.879516\pi$
$859$	−21.2971	+	17.8704i	−0.726649	+	0.609731i	0.202567	+	0.979268i	$0.435072\pi$
$860$		0			0
$861$	1.85831	+	10.5390i	0.0633311	+	0.359168i
$862$	−17.4117	−	30.1579i	−0.593044	−	1.02718i
$863$	21.6805	−	37.5517i	0.738012	−	1.27827i	−0.215378	−	0.976531i	$-0.569098\pi$
$863$	21.6805	−	37.5517i	0.738012	−	1.27827i	0.953389	−	0.301743i	$-0.0975684\pi$
$864$	−2.24147	−	0.815828i	−0.0762564	−	0.0277550i
$865$		0			0
$866$	−2.20058	+	3.81152i	−0.0747788	+	0.129521i
$867$	1.87955	+	3.25548i	0.0638329	+	0.110562i
$868$	3.28864	+	18.6508i	0.111624	+	0.633050i
$869$	17.8675	+	14.9926i	0.606115	+	0.508591i
$870$		0			0
$871$	−7.45984	+	42.3068i	−0.252767	+	1.43351i
$872$	10.9388	−	3.98141i	0.370435	−	0.134827i
$873$	7.42354			0.251249
$874$	−3.61286	−	3.59803i	−0.122207	−	0.121705i
$875$		0			0
$876$	5.89836	−	2.14683i	0.199287	−	0.0725345i
$877$	−3.24789	+	18.4197i	−0.109673	+	0.621988i	0.879577	+	0.475757i	$0.157826\pi$
$877$	−3.24789	+	18.4197i	−0.109673	+	0.621988i	−0.989250	+	0.146232i	$0.953285\pi$
$878$	−1.95159	+	1.63758i	−0.0658629	+	0.0552655i
$879$	−3.31763	−	2.78382i	−0.111901	−	0.0938960i
$880$		0			0
$881$	−6.40305	−	11.0904i	−0.215724	−	0.373646i	0.737772	−	0.675050i	$-0.235878\pi$
$881$	−6.40305	−	11.0904i	−0.215724	−	0.373646i	−0.953496	+	0.301404i	$0.902545\pi$
$882$	2.41765	−	4.18749i	0.0814065	−	0.141000i
$883$	−21.3201	−	7.75990i	−0.717480	−	0.261141i	−0.0426245	−	0.999091i	$-0.513572\pi$
$883$	−21.3201	−	7.75990i	−0.717480	−	0.261141i	−0.674856	+	0.737950i	$0.735794\pi$
$884$	13.3905	+	4.87376i	0.450373	+	0.163922i
$885$		0			0
$886$	−19.9735	−	34.5951i	−0.671023	−	1.16225i
$887$	0.143867	+	0.815912i	0.00483059	+	0.0273956i	0.987128	−	0.159934i	$-0.0511280\pi$
$887$	0.143867	+	0.815912i	0.00483059	+	0.0273956i	−0.982297	+	0.187329i	$0.940017\pi$
$888$	−0.939685	−	0.788489i	−0.0315338	−	0.0264600i
$889$	14.8374	−	12.4501i	0.497630	−	0.417561i
$890$		0			0
$891$	18.7188	−	6.81307i	0.627102	−	0.228246i
$892$	−4.78950			−0.160364
$893$	−26.3238	+	37.7593i	−0.880893	+	1.26357i
$894$	−6.69938			−0.224061
$895$		0			0
$896$	−0.399507	+	2.26572i	−0.0133466	+	0.0756923i
$897$	1.86882	−	1.56813i	0.0623982	−	0.0523583i
$898$	−19.0438	−	15.9796i	−0.635499	−	0.533247i
$899$	−6.36577	−	36.1021i	−0.212310	−	1.20407i
$900$		0			0
$901$	−5.92138	+	10.2561i	−0.197270	+	0.341681i
$902$	−28.3021	−	10.3011i	−0.942357	−	0.342990i
$903$	−1.36259	−	0.495941i	−0.0453440	−	0.0165039i
$904$	4.93858	−	8.55388i	0.164255	−	0.284498i
$905$		0			0
$906$	−0.263659	−	1.49528i	−0.00875947	−	0.0496774i
$907$	5.18644	+	4.35194i	0.172213	+	0.144504i	0.724820	−	0.688938i	$-0.241923\pi$
$907$	5.18644	+	4.35194i	0.172213	+	0.144504i	−0.552608	+	0.833442i	$0.686367\pi$
$908$	3.25125	−	2.72812i	0.107897	−	0.0905360i
$909$	−4.80536	+	27.2525i	−0.159384	+	0.903910i
$910$		0			0
$911$	26.0838			0.864196			0.432098	−	0.901827i	$-0.357773\pi$
$911$	26.0838			0.864196			0.432098	+	0.901827i	$0.357773\pi$
$912$	1.01944	−	1.46231i	0.0337571	−	0.0484218i
$913$	−4.70123			−0.155588
$914$	−35.6650	+	12.9810i	−1.17969	+	0.429373i
$915$		0			0
$916$	−22.1355	+	18.5739i	−0.731377	+	0.613698i
$917$	30.0329	+	25.2006i	0.991775	+	0.832198i
$918$	1.15741	+	6.56399i	0.0382002	+	0.216644i
$919$	29.5834	+	51.2400i	0.975867	+	1.69025i	0.677044	+	0.735942i	$0.263261\pi$
$919$	29.5834	+	51.2400i	0.975867	+	1.69025i	0.298823	+	0.954309i	$0.403406\pi$
$920$		0			0
$921$	−1.80719	−	0.657764i	−0.0595490	−	0.0216741i
$922$	1.58272	+	0.576063i	0.0521241	+	0.0189716i
$923$	−0.796160	+	1.37899i	−0.0262059	+	0.0453900i
$924$	1.24569	+	2.15760i	0.0409801	+	0.0709797i
$925$		0			0
$926$	6.72319	+	5.64143i	0.220938	+	0.185389i
$927$	1.07984	−	0.906094i	0.0354666	−	0.0297600i
$928$	0.773318	−	4.38571i	0.0253854	−	0.143968i
$929$	−35.9741	+	13.0935i	−1.18027	+	0.429583i	−0.856297	−	0.516483i	$-0.827241\pi$
$929$	−35.9741	+	13.0935i	−1.18027	+	0.429583i	−0.323973	+	0.946066i	$0.605019\pi$
$930$		0			0
$931$	5.27190	+	5.25026i	0.172779	+	0.172070i
$932$	−13.6279			−0.446397
$933$	5.23557	−	1.90559i	0.171405	−	0.0623862i
$934$	0.0907494	−	0.514665i	0.00296941	−	0.0168404i
$935$		0			0
$936$	−11.0664	−	9.28582i	−0.361717	−	0.303516i
$937$	0.677711	+	3.84349i	0.0221398	+	0.125561i	0.993875	−	0.110514i	$-0.0352498\pi$
$937$	0.677711	+	3.84349i	0.0221398	+	0.125561i	−0.971735	+	0.236076i	$0.924139\pi$
$938$	9.69036	+	16.7842i	0.316402	+	0.548024i
$939$	6.31975	−	10.9461i	0.206237	−	0.357213i
$940$		0			0
$941$	23.6727	+	8.61616i	0.771708	+	0.280879i	0.697711	−	0.716380i	$-0.254202\pi$
$941$	23.6727	+	8.61616i	0.771708	+	0.280879i	0.0739975	+	0.997258i	$0.476424\pi$
$942$	1.01159	−	1.75213i	0.0329595	−	0.0570875i
$943$	6.65256	+	11.5226i	0.216637	+	0.375227i
$944$	1.94800	+	11.0477i	0.0634020	+	0.359570i
$945$		0			0
$946$	3.12620	−	2.62320i	0.101642	−	0.0852874i
$947$	3.57460	−	20.2726i	0.116159	−	0.658770i	−0.870011	−	0.493032i	$-0.835888\pi$
$947$	3.57460	−	20.2726i	0.116159	−	0.658770i	0.986170	−	0.165738i	$-0.0530005\pi$
$948$	3.38499	−	1.23204i	0.109939	−	0.0400147i
$949$	78.2736			2.54087
$950$		0			0
$951$	−3.33259			−0.108067
$952$	6.04100	−	2.19875i	0.195790	−	0.0712618i
$953$	−6.96122	+	39.4790i	−0.225496	+	1.27885i	0.636239	+	0.771492i	$0.280489\pi$
$953$	−6.96122	+	39.4790i	−0.225496	+	1.27885i	−0.861735	+	0.507359i	$0.830622\pi$
$954$	9.19702	−	7.71722i	0.297765	−	0.249854i
$955$		0			0
$956$	2.58512	+	14.6609i	0.0836087	+	0.474169i
$957$	−2.41126	−	4.17642i	−0.0779449	−	0.135004i
$958$	−3.46971	+	6.00971i	−0.112101	+	0.194165i
$959$	25.3591	+	9.22996i	0.818889	+	0.298051i
$960$		0			0
$961$	−18.3809	+	31.8366i	−0.592931	+	1.02699i
$962$	−7.64836	−	13.2473i	−0.246593	−	0.427112i
$963$	9.47311	+	53.7247i	0.305267	+	1.73125i
$964$	8.88645	+	7.45662i	0.286213	+	0.240161i
$965$		0			0
$966$	0.191115	−	1.08387i	0.00614904	−	0.0348729i
$967$	−57.9491	+	21.0917i	−1.86352	+	0.678264i	−0.887406	+	0.460989i	$0.847495\pi$
$967$	−57.9491	+	21.0917i	−1.86352	+	0.678264i	−0.976110	+	0.217275i	$0.930283\pi$
$968$	3.98828			0.128188
$969$	−4.96296	−	0.423921i	−0.159433	−	0.0136183i
$970$		0			0
$971$	19.4401	−	7.07561i	0.623862	−	0.227067i	−0.0106954	−	0.999943i	$-0.503405\pi$
$971$	19.4401	−	7.07561i	0.623862	−	0.227067i	0.634558	+	0.772876i	$0.281182\pi$
$972$	1.77684	−	10.0770i	0.0569923	−	0.323219i
$973$	−22.8299	+	19.1566i	−0.731894	+	0.614132i
$974$	−31.5529	−	26.4761i	−1.01102	−	0.848348i
$975$		0			0
$976$	−1.65522	−	2.86693i	−0.0529825	−	0.0917683i
$977$	−5.27426	+	9.13528i	−0.168738	+	0.292264i	−0.937977	−	0.346699i	$-0.887303\pi$
$977$	−5.27426	+	9.13528i	−0.168738	+	0.292264i	0.769238	+	0.638962i	$0.220636\pi$
$978$	3.09736	+	1.12735i	0.0990426	+	0.0360485i
$979$	16.1472	+	5.87710i	0.516067	+	0.187833i
$980$		0			0
$981$	16.4879	+	28.5578i	0.526417	+	0.911781i
$982$	3.65055	+	20.7033i	0.116494	+	0.660669i
$983$	18.5072	+	15.5294i	0.590290	+	0.495312i	0.888308	−	0.459248i	$-0.151881\pi$
$983$	18.5072	+	15.5294i	0.590290	+	0.495312i	−0.298018	+	0.954560i	$0.596326\pi$
$984$	−3.56326	+	2.98993i	−0.113593	+	0.0953156i
$985$		0			0
$986$	−11.6935	+	4.25607i	−0.372396	+	0.135541i
$987$	−9.93542			−0.316248
$988$	18.1827	−	12.7874i	0.578468	−	0.406823i
$989$	−1.80281			−0.0573259
$990$		0			0
$991$	−5.95262	+	33.7590i	−0.189091	+	1.07239i	0.731494	+	0.681848i	$0.238824\pi$
$991$	−5.95262	+	33.7590i	−0.189091	+	1.07239i	−0.920585	+	0.390542i	$0.872288\pi$
$992$	−6.30589	+	5.29127i	−0.200212	+	0.167998i
$993$	0.197203	+	0.165473i	0.00625804	+	0.00525112i
$994$	0.124742	+	0.707445i	0.00395657	+	0.0224388i
$995$		0			0
$996$	−0.363030	+	0.628786i	−0.0115030	+	0.0199238i
$997$	39.7067	+	14.4521i	1.25752	+	0.457701i	0.882938	−	0.469490i	$-0.155562\pi$
$997$	39.7067	+	14.4521i	1.25752	+	0.457701i	0.374587	+	0.927192i	$0.377785\pi$
$998$	21.9820	+	8.00078i	0.695827	+	0.253260i
$999$	3.57744	−	6.19631i	0.113185	−	0.196042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.g.651.2		12
5.2	odd	4		950.2.u.f.499.3		24
5.3	odd	4		950.2.u.f.499.2		24
5.4	even	2		190.2.k.c.81.1	yes	12
19.4	even	9	inner	950.2.l.g.251.2		12
95.4	even	18		190.2.k.c.61.1	✓	12
95.23	odd	36		950.2.u.f.99.3		24
95.42	odd	36		950.2.u.f.99.2		24
95.59	odd	18		3610.2.a.bd.1.4		6
95.74	even	18		3610.2.a.bf.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.c.61.1	✓	12	95.4	even	18
190.2.k.c.81.1	yes	12	5.4	even	2
950.2.l.g.251.2		12	19.4	even	9	inner
950.2.l.g.651.2		12	1.1	even	1	trivial
950.2.u.f.99.2		24	95.42	odd	36
950.2.u.f.99.3		24	95.23	odd	36
950.2.u.f.499.2		24	5.3	odd	4
950.2.u.f.499.3		24	5.2	odd	4
3610.2.a.bd.1.4		6	95.59	odd	18
3610.2.a.bf.1.3		6	95.74	even	18

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.0710139 - 0.402740i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.0710139 - 0.402740i) q^{6} +(-1.15033 - 1.99244i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.66192 + 0.968860i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.0710139 - 0.402740i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.0710139 - 0.402740i) q^{6} +(-1.15033 - 1.99244i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.66192 + 0.968860i) q^{9} +(1.32398 - 2.29321i) q^{11} +(-0.204476 - 0.354164i) q^{12} +(-0.885551 - 5.02221i) q^{13} +(-1.76241 - 1.47884i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-2.62576 + 0.955698i) q^{17} +2.83276 q^{18} +(-1.11951 + 4.21268i) q^{19} +(-0.884124 + 0.321795i) q^{21} +(0.459814 - 2.60774i) q^{22} +(-0.896091 + 0.751910i) q^{23} +(-0.313276 - 0.262870i) q^{24} +(-2.54984 - 4.41645i) q^{26} +(1.19266 - 2.06575i) q^{27} +(-2.16192 - 0.786875i) q^{28} +(4.18479 + 1.52314i) q^{29} +(-4.11588 - 7.12891i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(-0.829544 - 0.696070i) q^{33} +(-2.14054 + 1.79613i) q^{34} +(2.66192 - 0.968860i) q^{36} +2.99954 q^{37} +(0.388831 + 4.34152i) q^{38} -2.08553 q^{39} +(1.97511 - 11.2014i) q^{41} +(-0.720744 + 0.604776i) q^{42} +(1.18061 + 0.990646i) q^{43} +(-0.459814 - 2.60774i) q^{44} +(-0.584882 + 1.01305i) q^{46} +(9.92304 + 3.61169i) q^{47} +(-0.384290 - 0.139870i) q^{48} +(0.853462 - 1.47824i) q^{49} +(0.198432 + 1.12537i) q^{51} +(-3.90658 - 3.27801i) q^{52} +(3.24667 - 2.72428i) q^{53} +(0.414207 - 2.34908i) q^{54} -2.30067 q^{56} +(1.61712 + 0.750029i) q^{57} +4.45336 q^{58} +(-10.5415 + 3.83681i) q^{59} +(2.53595 - 2.12792i) q^{61} +(-6.30589 - 5.29127i) q^{62} +(-1.13171 - 6.41823i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.01759 - 0.370371i) q^{66} +(-7.91593 - 2.88116i) q^{67} +(-1.39714 + 2.41991i) q^{68} +(0.239189 + 0.414288i) q^{69} +(-0.239189 - 0.200703i) q^{71} +(2.17002 - 1.82086i) q^{72} +(-2.66528 + 15.1155i) q^{73} +(2.81865 - 1.02590i) q^{74} +(1.85027 + 3.94671i) q^{76} -6.09209 q^{77} +(-1.95976 + 0.713293i) q^{78} +(-1.52957 + 8.67461i) q^{79} +(5.76279 + 4.83556i) q^{81} +(-1.97511 - 11.2014i) q^{82} +(-0.887706 - 1.53755i) q^{83} +(-0.470432 + 0.814813i) q^{84} +(1.44823 + 0.527112i) q^{86} +(0.910608 - 1.57722i) q^{87} +(-1.32398 - 2.29321i) q^{88} +(1.12686 + 6.39074i) q^{89} +(-8.98775 + 7.54162i) q^{91} +(-0.203127 + 1.15199i) q^{92} +(-3.16338 + 1.15138i) q^{93} +10.5599 q^{94} -0.408953 q^{96} +(2.46256 - 0.896300i) q^{97} +(0.296404 - 1.68099i) q^{98} +(5.74613 - 4.82158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9	\( 12 q - 3 q^{3} + 3 q^{6} + 6 q^{7} + 6 q^{8} + 9 q^{9} - 6 q^{11} + 18 q^{13} - 6 q^{14} - 12 q^{17} - 24 q^{18} + 6 q^{19} - 36 q^{21} + 9 q^{22} - 3 q^{23} + 3 q^{24} - 3 q^{26} - 15 q^{27} - 3 q^{28} + 36 q^{29} - 24 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{36} - 24 q^{37} - 15 q^{38} - 12 q^{39} - 12 q^{41} - 18 q^{42} + 12 q^{43} - 9 q^{44} - 18 q^{46} + 6 q^{48} - 27 q^{51} - 18 q^{52} + 36 q^{53} + 9 q^{54} + 12 q^{56} + 42 q^{57} - 27 q^{59} + 54 q^{61} + 24 q^{62} + 3 q^{63} - 6 q^{64} - 39 q^{66} - 39 q^{67} + 15 q^{68} - 24 q^{69} + 24 q^{71} + 18 q^{72} + 15 q^{74} + 9 q^{76} - 78 q^{77} + 6 q^{78} - 36 q^{79} - 9 q^{81} + 12 q^{82} + 12 q^{84} + 24 q^{86} - 18 q^{87} + 6 q^{88} + 18 q^{89} + 12 q^{91} - 12 q^{92} - 54 q^{93} + 18 q^{94} + 27 q^{97} + 18 q^{98} + 18 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 + 3 * q^6 + 6 * q^7 + 6 * q^8 + 9 * q^9 - 6 * q^11 + 18 * q^13 - 6 * q^14 - 12 * q^17 - 24 * q^18 + 6 * q^19 - 36 * q^21 + 9 * q^22 - 3 * q^23 + 3 * q^24 - 3 * q^26 - 15 * q^27 - 3 * q^28 + 36 * q^29 - 24 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^36 - 24 * q^37 - 15 * q^38 - 12 * q^39 - 12 * q^41 - 18 * q^42 + 12 * q^43 - 9 * q^44 - 18 * q^46 + 6 * q^48 - 27 * q^51 - 18 * q^52 + 36 * q^53 + 9 * q^54 + 12 * q^56 + 42 * q^57 - 27 * q^59 + 54 * q^61 + 24 * q^62 + 3 * q^63 - 6 * q^64 - 39 * q^66 - 39 * q^67 + 15 * q^68 - 24 * q^69 + 24 * q^71 + 18 * q^72 + 15 * q^74 + 9 * q^76 - 78 * q^77 + 6 * q^78 - 36 * q^79 - 9 * q^81 + 12 * q^82 + 12 * q^84 + 24 * q^86 - 18 * q^87 + 6 * q^88 + 18 * q^89 + 12 * q^91 - 12 * q^92 - 54 * q^93 + 18 * q^94 + 27 * q^97 + 18 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more