LMFDB - Embedded newform 975.2.bp.f.899.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(149,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 5]))

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

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

chi := DirichletCharacter("975.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bp (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			899.1
Root			$0.500000 - 2.19293i$ of defining polynomial
Character	$\chi$	$=$	975.899
Dual form			975.2.bp.f.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.31259 - 0.619657i) q^{2} +(-0.529480 - 1.64914i) q^{3} +(3.23205 + 1.86603i) q^{4} +(0.202571 + 4.14187i) q^{6} +(-0.366025 - 1.36603i) q^{7} +(-2.93225 - 2.93225i) q^{8} +(-2.43930 + 1.74637i) q^{9} +O(q^{10})$	\(q+(-2.31259 - 0.619657i) q^{2} +(-0.529480 - 1.64914i) q^{3} +(3.23205 + 1.86603i) q^{4} +(0.202571 + 4.14187i) q^{6} +(-0.366025 - 1.36603i) q^{7} +(-2.93225 - 2.93225i) q^{8} +(-2.43930 + 1.74637i) q^{9} +(1.69293 + 0.453620i) q^{11} +(1.36603 - 6.31812i) q^{12} +(3.23205 + 1.59808i) q^{13} +3.38587i q^{14} +(1.23205 + 2.13397i) q^{16} +(-1.85897 - 1.07328i) q^{17} +(6.72326 - 2.52711i) q^{18} +(0.267949 + 1.00000i) q^{19} +(-2.05896 + 1.32691i) q^{21} +(-3.63397 - 2.09808i) q^{22} +(-3.28311 + 6.38824i) q^{24} +(-6.48415 - 5.69846i) q^{26} +(4.17156 + 3.09808i) q^{27} +(1.36603 - 5.09808i) q^{28} +(4.79122 - 2.76621i) q^{29} +(4.46410 - 4.46410i) q^{31} +(0.619657 + 2.31259i) q^{32} +(-0.148292 - 3.03206i) q^{33} +(3.63397 + 3.63397i) q^{34} +(-11.1427 + 1.09255i) q^{36} +(-6.59808 - 1.76795i) q^{37} -2.47863i q^{38} +(0.924141 - 6.17624i) q^{39} +(0.166037 - 0.619657i) q^{41} +(5.58376 - 1.79275i) q^{42} +(4.09808 - 7.09808i) q^{43} +(4.62518 + 4.62518i) q^{44} +(6.77174 + 6.77174i) q^{47} +(2.86687 - 3.16172i) q^{48} +(4.33013 - 2.50000i) q^{49} +(-0.785693 + 3.63397i) q^{51} +(7.46410 + 11.1962i) q^{52} +4.62518 q^{53} +(-7.72737 - 9.74952i) q^{54} +(-2.93225 + 5.07880i) q^{56} +(1.50726 - 0.971364i) q^{57} +(-12.7942 + 3.42820i) q^{58} +(1.23931 + 4.62518i) q^{59} +(3.50000 - 6.06218i) q^{61} +(-13.0899 + 7.55743i) q^{62} +(3.27843 + 2.69293i) q^{63} -10.6603i q^{64} +(-1.53590 + 7.10381i) q^{66} +(2.26795 - 8.46410i) q^{67} +(-4.00552 - 6.93777i) q^{68} +(-4.62518 + 1.23931i) q^{71} +(12.2734 + 2.03185i) q^{72} +(-6.09808 + 6.09808i) q^{73} +(14.1631 + 8.17709i) q^{74} +(-1.00000 + 3.73205i) q^{76} -2.47863i q^{77} +(-5.96431 + 13.7105i) q^{78} -2.00000 q^{79} +(2.90039 - 8.51984i) q^{81} +(-0.767949 + 1.33013i) q^{82} +(1.23931 - 1.23931i) q^{83} +(-9.13071 + 0.446565i) q^{84} +(-13.8755 + 13.8755i) q^{86} +(-7.09871 - 6.43672i) q^{87} +(-3.63397 - 6.29423i) q^{88} +(-9.70398 - 2.60017i) q^{89} +(1.00000 - 5.00000i) q^{91} +(-9.72556 - 4.99826i) q^{93} +(-11.4641 - 19.8564i) q^{94} +(3.48568 - 2.24637i) q^{96} +(-12.5622 + 3.36603i) q^{97} +(-11.5630 + 3.09828i) q^{98} +(-4.92177 + 1.84997i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 12 q^{4} - 2 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 + 12 * q^4 - 2 * q^6 + 4 * q^7 - 4 * q^9	$ 8 q + 6 q^{3} + 12 q^{4} - 2 q^{6} + 4 q^{7} - 4 q^{9} + 4 q^{12} + 12 q^{13} - 4 q^{16} - 4 q^{18} + 16 q^{19} + 4 q^{21} - 36 q^{22} - 18 q^{24} + 4 q^{28} + 8 q^{31} - 20 q^{33} + 36 q^{34} - 36 q^{36} - 32 q^{37} + 14 q^{39} + 12 q^{42} + 12 q^{43} - 18 q^{48} + 32 q^{52} - 46 q^{54} + 16 q^{57} - 40 q^{58} + 28 q^{61} + 16 q^{63} - 40 q^{66} + 32 q^{67} - 24 q^{72} - 28 q^{73} - 8 q^{76} - 16 q^{78} - 16 q^{79} + 4 q^{81} - 20 q^{82} - 4 q^{84} - 6 q^{87} - 36 q^{88} + 8 q^{91} - 16 q^{93} - 64 q^{94} + 16 q^{96} - 52 q^{97} - 40 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 + 12 * q^4 - 2 * q^6 + 4 * q^7 - 4 * q^9 + 4 * q^12 + 12 * q^13 - 4 * q^16 - 4 * q^18 + 16 * q^19 + 4 * q^21 - 36 * q^22 - 18 * q^24 + 4 * q^28 + 8 * q^31 - 20 * q^33 + 36 * q^34 - 36 * q^36 - 32 * q^37 + 14 * q^39 + 12 * q^42 + 12 * q^43 - 18 * q^48 + 32 * q^52 - 46 * q^54 + 16 * q^57 - 40 * q^58 + 28 * q^61 + 16 * q^63 - 40 * q^66 + 32 * q^67 - 24 * q^72 - 28 * q^73 - 8 * q^76 - 16 * q^78 - 16 * q^79 + 4 * q^81 - 20 * q^82 - 4 * q^84 - 6 * q^87 - 36 * q^88 + 8 * q^91 - 16 * q^93 - 64 * q^94 + 16 * q^96 - 52 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$-1$	$-1$

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 $

$2$	−2.31259	−	0.619657i	−1.63525	−	0.438164i	−0.679818	−	0.733380i	$-0.737941\pi$
$2$	−2.31259	−	0.619657i	−1.63525	−	0.438164i	−0.955430	+	0.295217i	$0.904608\pi$
$3$	−0.529480	−	1.64914i	−0.305695	−	0.952129i
$3$	−0.529480	−	1.64914i	−0.305695	−	0.952129i
$4$	3.23205	+	1.86603i	1.61603	+	0.933013i
$5$		0			0
$5$		0			0
$6$	0.202571	+	4.14187i	0.0826993	+	1.69091i
$7$	−0.366025	−	1.36603i	−0.138345	−	0.516309i	−0.999962	−	0.00875026i	$-0.997215\pi$
$7$	−0.366025	−	1.36603i	−0.138345	−	0.516309i	0.861617	−	0.507559i	$-0.169452\pi$
$8$	−2.93225	−	2.93225i	−1.03671	−	1.03671i
$9$	−2.43930	+	1.74637i	−0.813101	+	0.582123i
$10$		0			0
$11$	1.69293	+	0.453620i	0.510439	+	0.136772i	0.504840	−	0.863213i	$-0.331551\pi$
$11$	1.69293	+	0.453620i	0.510439	+	0.136772i	0.00559833	+	0.999984i	$0.498218\pi$
$12$	1.36603	−	6.31812i	0.394338	−	1.82388i
$13$	3.23205	+	1.59808i	0.896410	+	0.443227i
$13$	3.23205	+	1.59808i	0.896410	+	0.443227i
$14$			3.38587i			0.904911i
$15$		0			0
$16$	1.23205	+	2.13397i	0.308013	+	0.533494i
$17$	−1.85897	−	1.07328i	−0.450867	−	0.260308i	0.257330	−	0.966324i	$-0.417157\pi$
$17$	−1.85897	−	1.07328i	−0.450867	−	0.260308i	−0.708196	+	0.706016i	$0.750491\pi$
$18$	6.72326	−	2.52711i	1.58469	−	0.595644i
$19$	0.267949	+	1.00000i	0.0614718	+	0.229416i	0.989826	−	0.142280i	$-0.0454432\pi$
$19$	0.267949	+	1.00000i	0.0614718	+	0.229416i	−0.928355	+	0.371695i	$0.878777\pi$
$20$		0			0
$21$	−2.05896	+	1.32691i	−0.449302	+	0.289555i
$22$	−3.63397	−	2.09808i	−0.774766	−	0.447311i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	−3.28311	+	6.38824i	−0.670162	+	1.30399i
$25$		0			0
$26$	−6.48415	−	5.69846i	−1.27165	−	1.11756i
$27$	4.17156	+	3.09808i	0.802817	+	0.596225i
$28$	1.36603	−	5.09808i	0.258155	−	0.963446i
$29$	4.79122	−	2.76621i	0.889707	−	0.513673i	0.0158603	−	0.999874i	$-0.494951\pi$
$29$	4.79122	−	2.76621i	0.889707	−	0.513673i	0.873847	+	0.486202i	$0.161618\pi$
$30$		0			0
$31$	4.46410	−	4.46410i	0.801776	−	0.801776i	−0.181597	−	0.983373i	$-0.558127\pi$
$31$	4.46410	−	4.46410i	0.801776	−	0.801776i	0.983373	+	0.181597i	$0.0581266\pi$
$32$	0.619657	+	2.31259i	0.109541	+	0.408812i
$33$	−0.148292	−	3.03206i	−0.0258144	−	0.527814i
$34$	3.63397	+	3.63397i	0.623222	+	0.623222i
$35$		0			0
$36$	−11.1427	+	1.09255i	−1.85712	+	0.182092i
$37$	−6.59808	−	1.76795i	−1.08472	−	0.290649i	−0.328190	−	0.944612i	$-0.606439\pi$
$37$	−6.59808	−	1.76795i	−1.08472	−	0.290649i	−0.756527	+	0.653963i	$0.773105\pi$
$38$		−	2.47863i		−	0.402086i
$39$	0.924141	−	6.17624i	0.147981	−	0.988990i
$40$		0			0
$41$	0.166037	−	0.619657i	0.0259306	−	0.0967741i	−0.951748	−	0.306881i	$-0.900715\pi$
$41$	0.166037	−	0.619657i	0.0259306	−	0.0967741i	0.977678	+	0.210107i	$0.0673812\pi$
$42$	5.58376	−	1.79275i	0.861593	−	0.276627i
$43$	4.09808	−	7.09808i	0.624951	−	1.08245i	−0.363600	−	0.931555i	$-0.618452\pi$
$43$	4.09808	−	7.09808i	0.624951	−	1.08245i	0.988550	−	0.150891i	$-0.0482143\pi$
$44$	4.62518	+	4.62518i	0.697272	+	0.697272i
$45$		0			0
$46$		0			0
$47$	6.77174	+	6.77174i	0.987759	+	0.987759i	0.999926	−	0.0121668i	$-0.00387290\pi$
$47$	6.77174	+	6.77174i	0.987759	+	0.987759i	−0.0121668	+	0.999926i	$0.503873\pi$
$48$	2.86687	−	3.16172i	0.413797	−	0.456354i
$49$	4.33013	−	2.50000i	0.618590	−	0.357143i
$50$		0			0
$51$	−0.785693	+	3.63397i	−0.110019	+	0.508858i
$52$	7.46410	+	11.1962i	1.03508	+	1.55263i
$53$	4.62518			0.635318			0.317659	−	0.948205i	$-0.397103\pi$
$53$	4.62518			0.635318			0.317659	+	0.948205i	$0.397103\pi$
$54$	−7.72737	−	9.74952i	−1.05156	−	1.32674i
$55$		0			0
$56$	−2.93225	+	5.07880i	−0.391838	+	0.678683i
$57$	1.50726	−	0.971364i	0.199642	−	0.128660i
$58$	−12.7942	+	3.42820i	−1.67996	+	0.450145i
$59$	1.23931	+	4.62518i	0.161345	+	0.602147i	0.998478	+	0.0551484i	$0.0175632\pi$
$59$	1.23931	+	4.62518i	0.161345	+	0.602147i	−0.837133	+	0.546999i	$0.815770\pi$
$60$		0			0
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$	−13.0899	+	7.55743i	−1.66241	+	0.959794i
$63$	3.27843	+	2.69293i	0.413043	+	0.339278i
$64$		−	10.6603i		−	1.33253i
$65$		0			0
$66$	−1.53590	+	7.10381i	−0.189056	+	0.874418i
$67$	2.26795	−	8.46410i	0.277074	−	1.03405i	−0.677365	−	0.735647i	$-0.736878\pi$
$67$	2.26795	−	8.46410i	0.277074	−	1.03405i	0.954439	−	0.298407i	$-0.0964553\pi$
$68$	−4.00552	−	6.93777i	−0.485741	−	0.841328i
$69$		0			0
$70$		0			0
$71$	−4.62518	+	1.23931i	−0.548908	+	0.147079i	−0.522606	−	0.852575i	$-0.675040\pi$
$71$	−4.62518	+	1.23931i	−0.548908	+	0.147079i	−0.0263025	+	0.999654i	$0.508373\pi$
$72$	12.2734	+	2.03185i	1.44644	+	0.239456i
$73$	−6.09808	+	6.09808i	−0.713726	+	0.713726i	−0.967313	−	0.253587i	$-0.918390\pi$
$73$	−6.09808	+	6.09808i	−0.713726	+	0.713726i	0.253587	+	0.967313i	$0.418390\pi$
$74$	14.1631	+	8.17709i	1.64643	+	0.950567i
$75$		0			0
$76$	−1.00000	+	3.73205i	−0.114708	+	0.428096i
$77$		−	2.47863i		−	0.282466i
$78$	−5.96431	+	13.7105i	−0.675325	+	1.55241i
$79$	−2.00000			−0.225018			−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000			−0.225018			−0.112509	+	0.993651i	$0.535889\pi$
$80$		0			0
$81$	2.90039	−	8.51984i	0.322266	−	0.946649i
$82$	−0.767949	+	1.33013i	−0.0848058	+	0.146888i
$83$	1.23931	−	1.23931i	0.136032	−	0.136032i	−0.635812	−	0.771844i	$-0.719335\pi$
$83$	1.23931	−	1.23931i	0.136032	−	0.136032i	0.771844	+	0.635812i	$0.219335\pi$
$84$	−9.13071	+	0.446565i	−0.996242	+	0.0487243i
$85$		0			0
$86$	−13.8755	+	13.8755i	−1.49624	+	1.49624i
$87$	−7.09871	−	6.43672i	−0.761062	−	0.690089i
$88$	−3.63397	−	6.29423i	−0.387383	−	0.670967i
$89$	−9.70398	−	2.60017i	−1.02862	−	0.275618i	−0.295230	−	0.955426i	$-0.595396\pi$
$89$	−9.70398	−	2.60017i	−1.02862	−	0.275618i	−0.733390	+	0.679808i	$0.762063\pi$
$90$		0			0
$91$	1.00000	−	5.00000i	0.104828	−	0.524142i
$92$		0			0
$93$	−9.72556	−	4.99826i	−1.00849	−	0.518296i
$94$	−11.4641	−	19.8564i	−1.18243	−	2.04803i
$95$		0			0
$96$	3.48568	−	2.24637i	0.355756	−	0.229269i
$97$	−12.5622	+	3.36603i	−1.27550	+	0.341768i	−0.832134	−	0.554575i	$-0.812881\pi$
$97$	−12.5622	+	3.36603i	−1.27550	+	0.341768i	−0.443362	+	0.896343i	$0.646214\pi$
$98$	−11.5630	+	3.09828i	−1.16803	+	0.312974i
$99$	−4.92177	+	1.84997i	−0.494656	+	0.185929i
$100$		0			0
$101$	−9.87002	−	17.0954i	−0.982104	−	1.70105i	−0.654160	−	0.756356i	$-0.726978\pi$
$101$	−9.87002	−	17.0954i	−0.982104	−	1.70105i	−0.327944	−	0.944697i	$-0.606356\pi$
$102$	4.06880	−	7.91704i	0.402872	−	0.783903i
$103$	−6.92820			−0.682656			−0.341328	−	0.939944i	$-0.610877\pi$
$103$	−6.92820			−0.682656			−0.341328	+	0.939944i	$0.610877\pi$
$104$	−4.79122	−	14.1631i	−0.469818	−	1.38881i
$105$		0			0
$106$	−10.6962	−	2.86603i	−1.03890	−	0.278373i
$107$	−8.34312	−	14.4507i	−0.806560	−	1.39700i	−0.915233	−	0.402925i	$-0.867993\pi$
$107$	−8.34312	−	14.4507i	−0.806560	−	1.39700i	0.108673	−	0.994078i	$-0.465340\pi$
$108$	7.70161	+	17.7974i	0.741088	+	1.71255i
$109$	2.80385	−	2.80385i	0.268560	−	0.268560i	−0.559960	−	0.828520i	$-0.689183\pi$
$109$	2.80385	−	2.80385i	0.268560	−	0.268560i	0.828520	+	0.559960i	$0.189183\pi$
$110$		0			0
$111$	0.577958	+	11.8172i	0.0548573	+	1.12164i
$112$	2.46410	−	2.46410i	0.232836	−	0.232836i
$113$	6.48415	−	11.2309i	0.609978	−	1.05651i	−0.381266	−	0.924465i	$-0.624512\pi$
$113$	6.48415	−	11.2309i	0.609978	−	1.05651i	0.991243	−	0.132047i	$-0.0421550\pi$
$114$	−4.08759	+	1.31238i	−0.382838	+	0.122916i
$115$		0			0
$116$	20.6473			1.91705
$117$	−10.6748	+	1.74616i	−0.986884	+	0.161433i
$118$		−	11.4641i		−	1.05536i
$119$	−0.785693	+	2.93225i	−0.0720244	+	0.268799i
$120$		0			0
$121$	−6.86603	−	3.96410i	−0.624184	−	0.360373i
$122$	−11.8505	+	11.8505i	−1.07290	+	1.07290i
$123$	−1.10981	+	0.0542788i	−0.100068	+	0.00489415i
$124$	22.7583	−	6.09808i	2.04376	−	0.547623i
$125$		0			0
$126$	−5.91297	−	8.25916i	−0.526770	−	0.735784i
$127$	7.56218	+	13.0981i	0.671035	+	1.16227i	0.977611	+	0.210420i	$0.0674832\pi$
$127$	7.56218	+	13.0981i	0.671035	+	1.16227i	−0.306576	+	0.951846i	$0.599183\pi$
$128$	−5.36639	+	20.0276i	−0.474326	+	1.77021i
$129$	−13.8755	−	3.00000i	−1.22167	−	0.264135i
$130$		0			0
$131$			0.907241i			0.0792660i	0.999214	+	0.0396330i	$0.0126189\pi$
$131$			0.907241i			0.0792660i	−0.999214	+	0.0396330i	$0.987381\pi$
$132$	5.17862	−	10.0765i	0.450741	−	0.877046i
$133$	1.26795	−	0.732051i	0.109945	−	0.0634769i
$134$	−10.4897	+	18.1687i	−0.906170	+	1.56953i
$135$		0			0
$136$	2.30385	+	8.59808i	0.197553	+	0.737279i
$137$	5.69846	−	1.52690i	0.486852	−	0.130452i	−0.00703925	−	0.999975i	$-0.502241\pi$
$137$	5.69846	−	1.52690i	0.486852	−	0.130452i	0.493891	+	0.869524i	$0.335574\pi$
$138$		0			0
$139$	−1.19615	+	2.07180i	−0.101456	+	0.175728i	−0.912285	−	0.409556i	$-0.865684\pi$
$139$	−1.19615	+	2.07180i	−0.101456	+	0.175728i	0.810829	+	0.585284i	$0.199017\pi$
$140$		0			0
$141$	7.58202	−	14.7530i	0.638521	−	1.24243i
$142$	11.4641			0.962046
$143$	4.74673	+	4.17156i	0.396941	+	0.348843i
$144$	−6.73205	−	3.05379i	−0.561004	−	0.254483i
$145$		0			0
$146$	17.8811	−	10.3236i	1.47985	−	0.854391i
$147$	−6.41556	−	5.81727i	−0.529146	−	0.479800i
$148$	−18.0263	−	18.0263i	−1.48175	−	1.48175i
$149$	−5.24484	+	1.40535i	−0.429674	+	0.115131i	−0.467173	−	0.884166i	$-0.654728\pi$
$149$	−5.24484	+	1.40535i	−0.429674	+	0.115131i	0.0374992	+	0.999297i	$0.488061\pi$
$150$		0			0
$151$	7.46410	+	7.46410i	0.607420	+	0.607420i	0.942271	−	0.334851i	$-0.108686\pi$
$151$	7.46410	+	7.46410i	0.607420	+	0.607420i	−0.334851	+	0.942271i	$0.608686\pi$
$152$	2.14655	−	3.71794i	0.174109	−	0.301565i
$153$	6.40893	−	0.628400i	0.518131	−	0.0508031i
$154$	−1.53590	+	5.73205i	−0.123766	+	0.461902i
$155$		0			0
$156$	14.5119	−	18.2375i	1.16188	−	1.46017i
$157$		−	15.1962i		−	1.21278i	−0.795165	−	0.606392i	$-0.792616\pi$
$157$		−	15.1962i		−	1.21278i	0.795165	−	0.606392i	$-0.207384\pi$
$158$	4.62518	+	1.23931i	0.367960	+	0.0985945i
$159$	−2.44894	−	7.62756i	−0.194214	−	0.604905i
$160$		0			0
$161$		0			0
$162$	−11.9868	+	17.9057i	−0.941772	+	1.40680i
$163$	4.00000	+	14.9282i	0.313304	+	1.16927i	0.925558	+	0.378606i	$0.123596\pi$
$163$	4.00000	+	14.9282i	0.313304	+	1.16927i	−0.612254	+	0.790661i	$0.709737\pi$
$164$	1.69293	−	1.69293i	0.132196	−	0.132196i
$165$		0			0
$166$	−3.63397	+	2.09808i	−0.282051	+	0.162842i
$167$	3.05379	−	11.3969i	0.236310	−	0.881920i	−0.741244	−	0.671235i	$-0.765764\pi$
$167$	3.05379	−	11.3969i	0.236310	−	0.881920i	0.977554	−	0.210685i	$-0.0675693\pi$
$168$	9.92820	+	2.14655i	0.765978	+	0.165610i
$169$	7.89230	+	10.3301i	0.607100	+	0.794625i
$170$		0			0
$171$	−2.39998	−	1.97136i	−0.183531	−	0.150754i
$172$	26.4904	−	15.2942i	2.01987	−	1.16617i
$173$	6.43966	+	3.71794i	0.489598	+	0.282670i	0.724408	−	0.689372i	$-0.242113\pi$
$173$	6.43966	+	3.71794i	0.489598	+	0.282670i	−0.234809	+	0.972041i	$0.575447\pi$
$174$	12.4279	+	19.2843i	0.942154	+	1.46194i
$175$		0			0
$176$	1.11777	+	4.17156i	0.0842548	+	0.314443i
$177$	6.97136	−	4.49274i	0.524000	−	0.337695i
$178$	20.8301	+	12.0263i	1.56128	+	0.901408i
$179$	−9.37191	−	16.2326i	−0.700489	−	1.21328i	−0.968295	−	0.249810i	$-0.919632\pi$
$179$	−9.37191	−	16.2326i	−0.700489	−	1.21328i	0.267805	−	0.963473i	$-0.413702\pi$
$180$		0			0
$181$			3.00000i			0.222988i	0.993765	+	0.111494i	$0.0355636\pi$
$181$			3.00000i			0.222988i	−0.993765	+	0.111494i	$0.964436\pi$
$182$	−5.41087	+	10.9433i	−0.401081	+	0.811171i
$183$	−11.8505	−	2.56218i	−0.876017	−	0.189402i
$184$		0			0
$185$		0			0
$186$	19.3940	+	17.5854i	1.42204	+	1.28943i
$187$	−2.66025	−	2.66025i	−0.194537	−	0.194537i
$188$	9.25036	+	34.5228i	0.674652	+	2.51784i
$189$	2.70515	−	6.83243i	0.196771	−	0.496986i
$190$		0			0
$191$	16.8078	+	9.70398i	1.21617	+	0.702156i	0.964096	−	0.265553i	$-0.0855544\pi$
$191$	16.8078	+	9.70398i	1.21617	+	0.702156i	0.252073	+	0.967708i	$0.418888\pi$
$192$	−17.5802	+	5.64439i	−1.26874	+	0.407349i
$193$	−6.96410	−	1.86603i	−0.501287	−	0.134319i	−0.000689767	−	1.00000i	$-0.500220\pi$
$193$	−6.96410	−	1.86603i	−0.501287	−	0.134319i	−0.500597	+	0.865680i	$0.666886\pi$
$194$	31.1370			2.23550
$195$		0			0
$196$	18.6603			1.33288
$197$	1.69293	+	0.453620i	0.120617	+	0.0323191i	0.318622	−	0.947882i	$-0.396780\pi$
$197$	1.69293	+	0.453620i	0.120617	+	0.0323191i	−0.198006	+	0.980201i	$0.563446\pi$
$198$	12.5284	−	1.22842i	0.890353	−	0.0872998i
$199$	−0.803848	−	0.464102i	−0.0569832	−	0.0328993i	0.471238	−	0.882006i	$-0.343807\pi$
$199$	−0.803848	−	0.464102i	−0.0569832	−	0.0328993i	−0.528221	+	0.849107i	$0.677141\pi$
$200$		0			0
$201$	−15.1593	+	0.741412i	−1.06925	+	0.0522952i
$202$	12.2321	+	45.6506i	0.860644	+	3.21197i
$203$	−5.53242	−	5.53242i	−0.388300	−	0.388300i
$204$	−9.32049	+	10.2791i	−0.652565	+	0.719679i
$205$		0			0
$206$	16.0221	+	4.29311i	1.11631	+	0.299115i
$207$		0			0
$208$	0.571797	+	8.86603i	0.0396470	+	0.614748i
$209$			1.81448i			0.125510i
$210$		0			0
$211$	6.09808	+	10.5622i	0.419809	+	0.727130i	0.995920	−	0.0902411i	$-0.0287638\pi$
$211$	6.09808	+	10.5622i	0.419809	+	0.727130i	−0.576111	+	0.817371i	$0.695430\pi$
$212$	14.9488	+	8.63071i	1.02669	+	0.592759i
$213$	4.49274	+	6.97136i	0.307837	+	0.477670i
$214$	10.3397	+	38.5885i	0.706810	+	2.63785i
$215$		0			0
$216$	−3.14772	−	21.3164i	−0.214176	−	1.45040i
$217$	−7.73205	−	4.46410i	−0.524886	−	0.303043i
$218$	−8.22158	+	4.74673i	−0.556835	+	0.321489i
$219$	13.2854	+	6.82775i	0.897742	+	0.461377i
$220$		0			0
$221$	−4.29311	−	6.43966i	−0.288786	−	0.433179i
$222$	5.98604	−	27.6865i	0.401757	−	1.85820i
$223$	5.97372	−	22.2942i	0.400030	−	1.49293i	−0.413011	−	0.910726i	$-0.635523\pi$
$223$	5.97372	−	22.2942i	0.400030	−	1.49293i	0.813041	−	0.582206i	$-0.197810\pi$
$224$	2.93225	−	1.69293i	0.195919	−	0.113114i
$225$		0			0
$226$	−21.9545	+	21.9545i	−1.46039	+	1.46039i
$227$	4.05001	+	15.1149i	0.268809	+	1.00321i	0.959878	+	0.280419i	$0.0904735\pi$
$227$	4.05001	+	15.1149i	0.268809	+	1.00321i	−0.691069	+	0.722789i	$0.742860\pi$
$228$	6.68414	−	0.326909i	0.442668	−	0.0216500i
$229$	−10.1244	−	10.1244i	−0.669036	−	0.669036i	0.288457	−	0.957493i	$-0.406858\pi$
$229$	−10.1244	−	10.1244i	−0.669036	−	0.669036i	−0.957493	+	0.288457i	$0.906858\pi$
$230$		0			0
$231$	−4.08759	+	1.31238i	−0.268944	+	0.0863485i
$232$	−22.1603	−	5.93782i	−1.45489	−	0.389837i
$233$		−	7.43588i		−	0.487141i	−0.969883	−	0.243570i	$-0.921681\pi$
$233$		−	7.43588i		−	0.487141i	0.969883	−	0.243570i	$-0.0783187\pi$
$234$	25.7684	+	2.57655i	1.68453	+	0.168434i
$235$		0			0
$236$	−4.62518	+	17.2614i	−0.301074	+	1.12362i
$237$	1.05896	+	3.29827i	0.0687868	+	0.214246i
$238$	3.63397	−	6.29423i	0.235556	−	0.407994i
$239$	−7.10381	−	7.10381i	−0.459507	−	0.459507i	0.438986	−	0.898494i	$-0.355338\pi$
$239$	−7.10381	−	7.10381i	−0.459507	−	0.459507i	−0.898494	+	0.438986i	$0.855338\pi$
$240$		0			0
$241$	7.23205	−	1.93782i	0.465857	−	0.124826i	−0.0182524	−	0.999833i	$-0.505810\pi$
$241$	7.23205	−	1.93782i	0.465857	−	0.124826i	0.484110	+	0.875007i	$0.339144\pi$
$242$	13.4219	+	13.4219i	0.862794	+	0.862794i
$243$	−15.5861	−	0.272062i	−0.999848	−	0.0174528i
$244$	22.6244	−	13.0622i	1.44838	−	0.836220i
$245$		0			0
$246$	2.60017	+	0.562178i	0.165781	+	0.0358431i
$247$	−0.732051	+	3.66025i	−0.0465793	+	0.232896i
$248$	−26.1797			−1.66241
$249$	−2.69999	−	1.38761i	−0.171105	−	0.0879360i
$250$		0			0
$251$	10.9433	−	18.9543i	0.690735	−	1.19639i	−0.280863	−	0.959748i	$-0.590621\pi$
$251$	10.9433	−	18.9543i	0.690735	−	1.19639i	0.971597	−	0.236640i	$-0.0760461\pi$
$252$	5.57097	+	14.8213i	0.350938	+	0.933656i
$253$		0			0
$254$	−9.37191	−	34.9764i	−0.588046	−	2.19462i
$255$		0			0
$256$	14.1603	−	24.5263i	0.885016	−	1.53289i
$257$	14.3737	−	8.29863i	0.896604	−	0.517655i	0.0205071	−	0.999790i	$-0.493472\pi$
$257$	14.3737	−	8.29863i	0.896604	−	0.517655i	0.876097	+	0.482135i	$0.160139\pi$
$258$	30.2295	+	15.5358i	1.88201	+	0.967220i
$259$			9.66025i			0.600259i
$260$		0			0
$261$	−6.85641	+	15.1149i	−0.424401	+	0.935586i
$262$	0.562178	−	2.09808i	0.0347315	−	0.129620i
$263$	5.98604	+	10.3681i	0.369115	+	0.639326i	0.989427	−	0.145029i	$-0.0463274\pi$
$263$	5.98604	+	10.3681i	0.369115	+	0.639326i	−0.620312	+	0.784355i	$0.712994\pi$
$264$	−8.45593	+	9.32559i	−0.520426	+	0.573950i
$265$		0			0
$266$	−3.38587	+	0.907241i	−0.207601	+	0.0556265i
$267$	0.850019	+	17.3799i	0.0520203	+	1.06363i
$268$	23.1244	−	23.1244i	1.41254	−	1.41254i
$269$	9.58244	+	5.53242i	0.584251	+	0.337318i	0.762821	−	0.646610i	$-0.223814\pi$
$269$	9.58244	+	5.53242i	0.584251	+	0.337318i	−0.178570	+	0.983927i	$0.557147\pi$
$270$		0			0
$271$	0.535898	−	2.00000i	0.0325535	−	0.121491i	−0.947737	−	0.319052i	$-0.896635\pi$
$271$	0.535898	−	2.00000i	0.0325535	−	0.121491i	0.980291	+	0.197561i	$0.0633021\pi$
$272$		−	5.28933i		−	0.320713i
$273$	−8.77516	+	0.998262i	−0.531097	+	0.0604176i
$274$	−14.1244			−0.853284
$275$		0			0
$276$		0			0
$277$	−1.79423	+	3.10770i	−0.107805	+	0.186723i	−0.914881	−	0.403724i	$-0.867715\pi$
$277$	−1.79423	+	3.10770i	−0.107805	+	0.186723i	0.807076	+	0.590448i	$0.201049\pi$
$278$	4.05001	−	4.05001i	0.242904	−	0.242904i
$279$	−3.09333	+	18.6853i	−0.185193	+	1.11866i
$280$		0			0
$281$	−15.9006	+	15.9006i	−0.948547	+	0.948547i	−0.998740	−	0.0501922i	$-0.984017\pi$
$281$	−15.9006	+	15.9006i	−0.948547	+	0.948547i	0.0501922	+	0.998740i	$0.484017\pi$
$282$	−26.6759	+	29.4194i	−1.58853	+	1.75190i
$283$	12.2942	+	21.2942i	0.730816	+	1.26581i	0.956535	+	0.291618i	$0.0941936\pi$
$283$	12.2942	+	21.2942i	0.730816	+	1.26581i	−0.225719	+	0.974192i	$0.572473\pi$
$284$	−17.2614	−	4.62518i	−1.02428	−	0.274454i
$285$		0			0
$286$	−8.39230	−	12.5885i	−0.496247	−	0.744371i
$287$	−0.907241			−0.0535527
$288$	−5.55017	−	4.55896i	−0.327047	−	0.268639i
$289$	−6.19615	−	10.7321i	−0.364480	−	0.631297i
$290$		0			0
$291$	12.2025	+	18.9345i	0.715320	+	1.10996i
$292$	−31.0885	+	8.33013i	−1.81931	+	0.487484i
$293$	21.2669	−	5.69846i	1.24243	−	0.332908i	0.423021	−	0.906120i	$-0.360970\pi$
$293$	21.2669	−	5.69846i	1.24243	−	0.332908i	0.819407	+	0.573212i	$0.194303\pi$
$294$	11.2318	+	17.4284i	0.655054	+	1.01645i
$295$		0			0
$296$	14.1631	+	24.5313i	0.823215	+	1.42585i
$297$	5.65683	+	7.13714i	0.328242	+	0.414139i
$298$	13.0000			0.753070
$299$		0			0
$300$		0			0
$301$	−11.1962	−	3.00000i	−0.645335	−	0.172917i
$302$	−12.6362	−	21.8866i	−0.727133	−	1.25943i
$303$	−22.9666	+	25.3287i	−1.31940	+	1.45509i
$304$	−1.80385	+	1.80385i	−0.103458	+	0.103458i
$305$		0			0
$306$	−15.2106	−	2.51810i	−0.869533	−	0.143950i
$307$	12.3923	−	12.3923i	0.707266	−	0.707266i	−0.258693	−	0.965960i	$-0.583292\pi$
$307$	12.3923	−	12.3923i	0.707266	−	0.707266i	0.965960	+	0.258693i	$0.0832919\pi$
$308$	4.62518	−	8.01105i	0.263544	−	0.456472i
$309$	3.66834	+	11.4256i	0.208685	+	0.649977i
$310$		0			0
$311$	−4.29311			−0.243440			−0.121720	−	0.992564i	$-0.538841\pi$
$311$	−4.29311			−0.243440			−0.121720	+	0.992564i	$0.538841\pi$
$312$	−20.8201	+	15.4005i	−1.17870	+	0.871879i
$313$		−	2.00000i		−	0.113047i	−0.998401	−	0.0565233i	$-0.981998\pi$
$313$		−	2.00000i		−	0.113047i	0.998401	−	0.0565233i	$-0.0180015\pi$
$314$	−9.41640	+	35.1425i	−0.531398	+	1.98321i
$315$		0			0
$316$	−6.46410	−	3.73205i	−0.363634	−	0.209944i
$317$	11.2754	−	11.2754i	0.633288	−	0.633288i	−0.315603	−	0.948891i	$-0.602207\pi$
$317$	11.2754	−	11.2754i	0.633288	−	0.633288i	0.948891	+	0.315603i	$0.102207\pi$
$318$	0.936928	+	19.1569i	0.0525403	+	1.07427i
$319$	9.36603	−	2.50962i	0.524397	−	0.140512i
$320$		0			0
$321$	−19.4137	+	21.4103i	−1.08357	+	1.19501i
$322$		0			0
$323$	0.575167	−	2.14655i	0.0320032	−	0.119437i
$324$	25.2725	−	22.1244i	1.40403	−	1.22913i
$325$		0			0
$326$		−	37.0015i		−	2.04932i
$327$	−6.10851	−	3.13935i	−0.337801	−	0.173606i
$328$	−2.30385	+	1.33013i	−0.127209	+	0.0734440i
$329$	6.77174	−	11.7290i	0.373338	−	0.646640i
$330$		0			0
$331$	5.05256	+	18.8564i	0.277714	+	1.03644i	0.954001	+	0.299804i	$0.0969212\pi$
$331$	5.05256	+	18.8564i	0.277714	+	1.03644i	−0.676287	+	0.736638i	$0.736412\pi$
$332$	6.31812	−	1.69293i	0.346752	−	0.0929118i
$333$	19.1822	−	7.21011i	1.05118	−	0.395112i
$334$	−14.1244	+	24.4641i	−0.772850	+	1.33862i
$335$		0			0
$336$	−5.36833	−	2.75895i	−0.292867	−	0.150513i
$337$	11.5359			0.628400			0.314200	−	0.949357i	$-0.398264\pi$
$337$	11.5359			0.628400			0.314200	+	0.949357i	$0.398264\pi$
$338$	−11.8505	−	28.7799i	−0.644584	−	1.56542i
$339$	−21.9545	−	4.74673i	−1.19240	−	0.257807i
$340$		0			0
$341$	9.58244	−	5.53242i	0.518918	−	0.299597i
$342$	4.32860	+	6.04612i	0.234064	+	0.326937i
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	−32.8299	+	8.79674i	−1.77007	+	0.474289i
$345$		0			0
$346$	−12.5885	−	12.5885i	−0.676760	−	0.676760i
$347$	12.9683	−	22.4618i	0.696175	−	1.20581i	−0.273608	−	0.961841i	$-0.588217\pi$
$347$	12.9683	−	22.4618i	0.696175	−	1.20581i	0.969783	−	0.243969i	$-0.0784496\pi$
$348$	−10.9323	−	34.0502i	−0.586034	−	1.82528i
$349$	−1.50962	+	5.63397i	−0.0808080	+	0.301580i	−0.994487	−	0.104856i	$-0.966562\pi$
$349$	−1.50962	+	5.63397i	−0.0808080	+	0.301580i	0.913679	+	0.406436i	$0.133228\pi$
$350$		0			0
$351$	8.53174	+	16.6796i	0.455390	+	0.890292i
$352$			4.19615i			0.223656i
$353$	26.3457	+	7.05932i	1.40224	+	0.375730i	0.879149	−	0.476546i	$-0.158111\pi$
$353$	26.3457	+	7.05932i	1.40224	+	0.375730i	0.523093	+	0.852276i	$0.324778\pi$
$354$	−18.9059	+	6.07001i	−1.00484	+	0.322617i
$355$		0			0
$356$	−26.5118	−	26.5118i	−1.40512	−	1.40512i
$357$	5.25169	−	0.256850i	0.277949	−	0.0135939i
$358$	11.6147	+	43.3468i	0.613858	+	2.29095i
$359$	−12.0611	+	12.0611i	−0.636559	+	0.636559i	−0.949705	−	0.313146i	$-0.898617\pi$
$359$	−12.0611	+	12.0611i	−0.636559	+	0.636559i	0.313146	+	0.949705i	$0.398617\pi$
$360$		0			0
$361$	15.5263	−	8.96410i	0.817173	−	0.471795i
$362$	1.85897	−	6.93777i	0.0977053	−	0.364641i
$363$	−2.90192	+	13.4219i	−0.152311	+	0.704468i
$364$	12.5622	−	14.2942i	0.658437	−	0.749221i
$365$		0			0
$366$	25.8178	+	13.2685i	1.34952	+	0.693557i
$367$	8.32051	−	4.80385i	0.434327	−	0.250759i	−0.266861	−	0.963735i	$-0.585987\pi$
$367$	8.32051	−	4.80385i	0.434327	−	0.250759i	0.701188	+	0.712976i	$0.252653\pi$
$368$		0			0
$369$	0.677136	+	1.80149i	0.0352503	+	0.0937819i
$370$		0			0
$371$	−1.69293	−	6.31812i	−0.0878928	−	0.328020i
$372$	−22.1066	−	34.3028i	−1.14618	−	1.77852i
$373$	−16.9641	−	9.79423i	−0.878368	−	0.507126i	−0.00824796	−	0.999966i	$-0.502625\pi$
$373$	−16.9641	−	9.79423i	−0.878368	−	0.507126i	−0.870120	+	0.492840i	$0.835959\pi$
$374$	4.50363	+	7.80052i	0.232877	+	0.403355i
$375$		0			0
$376$		−	39.7128i		−	2.04803i
$377$	19.9061	−	1.28380i	1.02522	−	0.0661192i
$378$	−10.4897	+	14.1244i	−0.539531	+	0.726478i
$379$	4.83013	+	1.29423i	0.248107	+	0.0664801i	0.380729	−	0.924687i	$-0.375673\pi$
$379$	4.83013	+	1.29423i	0.248107	+	0.0664801i	−0.132622	+	0.991167i	$0.542340\pi$
$380$		0			0
$381$	17.5965	−	19.4062i	0.901496	−	0.994211i
$382$	−32.8564	−	32.8564i	−1.68108	−	1.68108i
$383$	−3.62896	−	13.5435i	−0.185431	−	0.692039i	−0.994538	−	0.104377i	$-0.966715\pi$
$383$	−3.62896	−	13.5435i	−0.185431	−	0.692039i	0.809106	−	0.587662i	$-0.199952\pi$
$384$	35.8697	−	1.75432i	1.83047	−	0.0895246i
$385$		0			0
$386$	14.9488	+	8.63071i	0.760875	+	0.439291i
$387$	2.39941	+	24.4711i	0.121969	+	1.24394i
$388$	−46.8827	−	12.5622i	−2.38011	−	0.637748i
$389$	−5.28933			−0.268180			−0.134090	−	0.990969i	$-0.542811\pi$
$389$	−5.28933			−0.268180			−0.134090	+	0.990969i	$0.542811\pi$
$390$		0			0
$391$		0			0
$392$	−20.0276	−	5.36639i	−1.01155	−	0.271043i
$393$	1.49616	−	0.480365i	0.0754715	−	0.0242312i
$394$	−3.63397	−	2.09808i	−0.183077	−	0.105700i
$395$		0			0
$396$	−19.3595	−	3.20495i	−0.972851	−	0.161055i
$397$	2.29423	+	8.56218i	0.115144	+	0.429723i	0.999298	−	0.0374729i	$-0.0119308\pi$
$397$	2.29423	+	8.56218i	0.115144	+	0.429723i	−0.884154	+	0.467196i	$0.845264\pi$
$398$	1.57139	+	1.57139i	0.0787665	+	0.0787665i
$399$	−1.87861	−	1.70342i	−0.0940479	−	0.0852774i
$400$		0			0
$401$	−27.1314	−	7.26985i	−1.35488	−	0.363039i	−0.492946	−	0.870060i	$-0.664080\pi$
$401$	−27.1314	−	7.26985i	−1.35488	−	0.363039i	−0.861933	+	0.507021i	$0.830747\pi$
$402$	35.5167	+	7.67898i	1.77141	+	0.382993i
$403$	21.5622	−	7.29423i	1.07409	−	0.363351i
$404$		−	73.6708i		−	3.66526i
$405$		0			0
$406$	9.36603	+	16.2224i	0.464828	+	0.805106i
$407$	−10.3681	−	5.98604i	−0.513929	−	0.296717i
$408$	12.9596	−	8.35187i	0.641594	−	0.413479i
$409$	−3.00962	−	11.2321i	−0.148816	−	0.555389i	−0.999556	−	0.0298020i	$-0.990512\pi$
$409$	−3.00962	−	11.2321i	−0.148816	−	0.555389i	0.850740	−	0.525587i	$-0.176154\pi$
$410$		0			0
$411$	−5.53528	−	8.58908i	−0.273035	−	0.423668i
$412$	−22.3923	−	12.9282i	−1.10319	−	0.636927i
$413$	5.86450	−	3.38587i	0.288573	−	0.166608i
$414$		0			0
$415$		0			0
$416$	−1.69293	+	8.46467i	−0.0830029	+	0.415015i
$417$	4.05001	+	0.875644i	0.198330	+	0.0428805i
$418$	1.12436	−	4.19615i	0.0549940	−	0.205241i
$419$	−7.22536	+	4.17156i	−0.352982	+	0.203794i	−0.665998	−	0.745954i	$-0.731994\pi$
$419$	−7.22536	+	4.17156i	−0.352982	+	0.203794i	0.313016	+	0.949748i	$0.398661\pi$
$420$		0			0
$421$	0.830127	−	0.830127i	0.0404579	−	0.0404579i	−0.686588	−	0.727046i	$-0.740893\pi$
$421$	0.830127	−	0.830127i	0.0404579	−	0.0404579i	0.727046	+	0.686588i	$0.240893\pi$
$422$	−7.55743	−	28.2047i	−0.367890	−	1.37298i
$423$	−28.3443	−	4.69237i	−1.37815	−	0.228151i
$424$	−13.5622	−	13.5622i	−0.658638	−	0.658638i
$425$		0			0
$426$	−6.07001	−	18.9059i	−0.294093	−	0.915992i
$427$	−9.56218	−	2.56218i	−0.462746	−	0.123992i
$428$		−	62.2739i		−	3.01012i
$429$	4.36618	−	10.0368i	0.210801	−	0.484579i
$430$		0			0
$431$	−0.542599	+	2.02501i	−0.0261361	+	0.0975412i	−0.977762	−	0.209718i	$-0.932745\pi$
$431$	−0.542599	+	2.02501i	−0.0261361	+	0.0975412i	0.951626	+	0.307260i	$0.0994120\pi$
$432$	−1.47164	+	12.7190i	−0.0708043	+	0.611943i
$433$	−3.52628	+	6.10770i	−0.169462	+	0.293517i	−0.938231	−	0.346010i	$-0.887536\pi$
$433$	−3.52628	+	6.10770i	−0.169462	+	0.293517i	0.768769	+	0.639527i	$0.220870\pi$
$434$	15.1149	+	15.1149i	0.725536	+	0.725536i
$435$		0			0
$436$	14.2942	−	3.83013i	0.684569	−	0.183430i
$437$		0			0
$438$	−26.4928	−	24.0222i	−1.26587	−	1.14782i
$439$	4.09808	−	2.36603i	0.195591	−	0.112924i	−0.399007	−	0.916948i	$-0.630645\pi$
$439$	4.09808	−	2.36603i	0.195591	−	0.112924i	0.594597	+	0.804024i	$0.297312\pi$
$440$		0			0
$441$	−6.19657	+	13.6603i	−0.295075	+	0.650488i
$442$	5.93782	+	17.5526i	0.282433	+	0.834890i
$443$	−29.5656			−1.40470			−0.702351	−	0.711830i	$-0.747866\pi$
$443$	−29.5656			−1.40470			−0.702351	+	0.711830i	$0.747866\pi$
$444$	−20.1832	+	39.2723i	−0.957855	+	1.86378i
$445$		0			0
$446$	−27.6295	+	47.8558i	−1.30830	+	2.26604i
$447$	5.09465	+	7.90535i	0.240969	+	0.373910i
$448$	−14.5622	+	3.90192i	−0.687998	+	0.184349i
$449$	−2.26810	−	8.46467i	−0.107038	−	0.399472i	0.891530	−	0.452961i	$-0.149632\pi$
$449$	−2.26810	−	8.46467i	−0.107038	−	0.399472i	−0.998568	+	0.0534890i	$0.982966\pi$
$450$		0			0
$451$	0.562178	−	0.973721i	0.0264719	−	0.0458507i
$452$	41.9142	−	24.1992i	1.97148	−	1.13823i
$453$	8.35723	−	16.2614i	0.392657	−	0.764028i
$454$		−	37.4641i		−	1.75828i
$455$		0			0
$456$	−7.26795	−	1.57139i	−0.340353	−	0.0735869i
$457$	7.23205	−	26.9904i	0.338301	−	1.26256i	−0.561945	−	0.827175i	$-0.689947\pi$
$457$	7.23205	−	26.9904i	0.338301	−	1.26256i	0.900246	−	0.435382i	$-0.143387\pi$
$458$	17.1399	+	29.6871i	0.800893	+	1.38719i
$459$	−4.42972	−	10.2365i	−0.206761	−	0.477798i
$460$		0			0
$461$	23.4135	−	6.27363i	1.09048	−	0.292192i	0.331595	−	0.943422i	$-0.392413\pi$
$461$	23.4135	−	6.27363i	1.09048	−	0.292192i	0.758880	+	0.651230i	$0.225747\pi$
$462$	10.2662	−	0.502098i	0.477625	−	0.0233597i
$463$	−15.0526	+	15.0526i	−0.699552	+	0.699552i	−0.964314	−	0.264762i	$-0.914707\pi$
$463$	−15.0526	+	15.0526i	−0.699552	+	0.699552i	0.264762	+	0.964314i	$0.414707\pi$
$464$	11.8060	+	6.81623i	0.548082	+	0.316435i
$465$		0			0
$466$	−4.60770	+	17.1962i	−0.213447	+	0.796596i
$467$			30.4728i			1.41011i	0.709151	+	0.705057i	$0.249079\pi$
$467$			30.4728i			1.41011i	−0.709151	+	0.705057i	$0.750921\pi$
$468$	−37.7598	−	14.2757i	−1.74545	−	0.659896i
$469$	−12.3923			−0.572223
$470$		0			0
$471$	−25.0605	+	8.04605i	−1.15473	+	0.370743i
$472$	9.92820	−	17.1962i	0.456983	−	0.791517i
$473$	10.1576	−	10.1576i	0.467047	−	0.467047i
$474$	−0.405142	−	8.28375i	−0.0186088	−	0.380485i
$475$		0			0
$476$	−8.01105	+	8.01105i	−0.367186	+	0.367186i
$477$	−11.2822	+	8.07727i	−0.516577	+	0.369833i
$478$	12.0263	+	20.8301i	0.550069	+	0.952748i
$479$	8.46467	+	2.26810i	0.386761	+	0.103632i	0.446959	−	0.894554i	$-0.352507\pi$
$479$	8.46467	+	2.26810i	0.386761	+	0.103632i	−0.0601988	+	0.998186i	$0.519173\pi$
$480$		0			0
$481$	−18.5000	−	16.2583i	−0.843527	−	0.741316i
$482$	−17.9256			−0.816487
$483$		0			0
$484$	−14.7942	−	25.6244i	−0.672465	−	1.16474i
$485$		0			0
$486$	35.8756	+	10.2872i	1.62735	+	0.466636i
$487$	24.4904	−	6.56218i	1.10977	−	0.297361i	0.343030	−	0.939324i	$-0.388547\pi$
$487$	24.4904	−	6.56218i	1.10977	−	0.297361i	0.766735	+	0.641964i	$0.221880\pi$
$488$	−28.0387	+	7.51294i	−1.26925	+	0.340095i
$489$	22.5007	−	14.5007i	1.01752	−	0.655746i
$490$		0			0
$491$	12.5147	+	21.6761i	0.564780	+	0.978227i	0.997070	+	0.0764928i	$0.0243722\pi$
$491$	12.5147	+	21.6761i	0.564780	+	0.978227i	−0.432290	+	0.901734i	$0.642294\pi$
$492$	−3.68825	−	1.89551i	−0.166279	−	0.0854560i
$493$	−11.8756			−0.534852
$494$	3.96104	−	8.01105i	0.178215	−	0.360434i
$495$		0			0
$496$	15.0263	+	4.02628i	0.674700	+	0.180785i
$497$	3.38587	+	5.86450i	0.151877	+	0.263059i
$498$	5.38413	+	4.88203i	0.241269	+	0.218769i
$499$	−4.46410	+	4.46410i	−0.199841	+	0.199841i	−0.799932	−	0.600091i	$-0.795131\pi$
$499$	−4.46410	+	4.46410i	−0.199841	+	0.199841i	0.600091	+	0.799932i	$0.295131\pi$
$500$		0			0
$501$	−20.4120	+	0.998312i	−0.911941	+	0.0446013i
$502$	−37.0526	+	37.0526i	−1.65374	+	1.65374i
$503$	−14.3292	+	24.8188i	−0.638906	+	1.10662i	0.346767	+	0.937951i	$0.387279\pi$
$503$	−14.3292	+	24.8188i	−0.638906	+	1.10662i	−0.985673	+	0.168666i	$0.946054\pi$
$504$	−1.71682	−	17.5095i	−0.0764733	−	0.779936i
$505$		0			0
$506$		0			0
$507$	12.8570	−	18.4851i	0.570998	−	0.820951i
$508$			56.4449i			2.50434i
$509$	−3.88398	+	14.4952i	−0.172154	+	0.642489i	0.824865	+	0.565330i	$0.191251\pi$
$509$	−3.88398	+	14.4952i	−0.172154	+	0.642489i	−0.997019	+	0.0771582i	$0.975415\pi$
$510$		0			0
$511$	10.5622	+	6.09808i	0.467243	+	0.269763i
$512$	−18.6223	+	18.6223i	−0.822996	+	0.822996i
$513$	−1.98031	+	5.00169i	−0.0874328	+	0.220830i
$514$	−38.3827	+	10.2846i	−1.69299	+	0.453635i
$515$		0			0
$516$	−39.2484	−	35.5883i	−1.72781	−	1.56669i
$517$	8.39230	+	14.5359i	0.369093	+	0.639288i
$518$	5.98604	−	22.3402i	0.263012	−	0.981573i
$519$	2.72172	−	12.5885i	0.119470	−	0.552572i
$520$		0			0
$521$		−	33.2835i		−	1.45818i	−0.684419	−	0.729089i	$-0.739944\pi$
$521$		−	33.2835i		−	1.45818i	0.684419	−	0.729089i	$-0.260056\pi$
$522$	25.2221	−	30.7059i	1.10394	−	1.34396i
$523$	−11.2417	+	6.49038i	−0.491564	+	0.283805i	−0.725223	−	0.688514i	$-0.758263\pi$
$523$	−11.2417	+	6.49038i	−0.491564	+	0.283805i	0.233659	+	0.972319i	$0.424930\pi$
$524$	−1.69293	+	2.93225i	−0.0739562	+	0.128096i
$525$		0			0
$526$	−7.41858	−	27.6865i	−0.323466	−	1.20719i
$527$	−13.0899	+	3.50742i	−0.570203	+	0.152785i
$528$	6.28764	−	4.05211i	0.273634	−	0.176345i
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$		0			0
$531$	−11.1003	−	9.11792i	−0.481713	−	0.395684i
$532$	5.46410			0.236899
$533$	1.52690	−	1.73742i	0.0661373	−	0.0752562i
$534$	8.80385	−	40.7194i	0.380980	−	1.76210i
$535$		0			0
$536$	−31.4690	+	18.1687i	−1.35926	+	0.784766i
$537$	−21.8076	+	24.0504i	−0.941066	+	1.03785i
$538$	−18.7321	−	18.7321i	−0.807596	−	0.807596i
$539$	8.46467	−	2.26810i	0.364599	−	0.0976940i
$540$		0			0
$541$	23.6865	+	23.6865i	1.01836	+	1.01836i	0.999828	+	0.0185354i	$0.00590034\pi$
$541$	23.6865	+	23.6865i	1.01836	+	1.01836i	0.0185354	+	0.999828i	$0.494100\pi$
$542$	−2.47863	+	4.29311i	−0.106466	+	0.184405i
$543$	4.94741	−	1.58844i	0.212314	−	0.0681664i
$544$	1.33013	−	4.96410i	0.0570287	−	0.212834i
$545$		0			0
$546$	20.9119	+	3.12902i	0.894948	+	0.133910i
$547$			2.00000i			0.0855138i	0.999086	+	0.0427569i	$0.0136141\pi$
$547$			2.00000i			0.0855138i	−0.999086	+	0.0427569i	$0.986386\pi$
$548$	21.2669	+	5.69846i	0.908479	+	0.243426i
$549$	2.04924	+	20.8998i	0.0874593	+	0.891981i
$550$		0			0
$551$	4.05001	+	4.05001i	0.172536	+	0.172536i
$552$		0			0
$553$	0.732051	+	2.73205i	0.0311300	+	0.116179i
$554$	6.07502	−	6.07502i	0.258103	−	0.258103i
$555$		0			0
$556$	−7.73205	+	4.46410i	−0.327912	+	0.189320i
$557$	−10.5342	+	39.3140i	−0.446347	+	1.66579i	0.266009	+	0.963971i	$0.414295\pi$
$557$	−10.5342	+	39.3140i	−0.446347	+	1.66579i	−0.712355	+	0.701819i	$0.752372\pi$
$558$	18.7321	−	41.2946i	0.792991	−	1.74814i
$559$	24.5885	−	16.3923i	1.03998	−	0.693321i
$560$		0			0
$561$	−2.97857	+	5.79567i	−0.125755	+	0.244693i
$562$	46.6244	−	26.9186i	1.96673	−	1.13549i
$563$	3.71794	+	2.14655i	0.156693	+	0.0904665i	0.576296	−	0.817241i	$-0.304498\pi$
$563$	3.71794	+	2.14655i	0.156693	+	0.0904665i	−0.419603	+	0.907708i	$0.637831\pi$
$564$	52.0350	−	33.5342i	2.19107	−	1.41205i
$565$		0			0
$566$	−15.2364	−	56.8630i	−0.640434	−	2.39013i
$567$	−12.6999	−	0.843533i	−0.533347	−	0.0354250i
$568$	17.1962	+	9.92820i	0.721535	+	0.416578i
$569$	8.01105	+	13.8755i	0.335841	+	0.581693i	0.983646	−	0.180113i	$-0.0576463\pi$
$569$	8.01105	+	13.8755i	0.335841	+	0.581693i	−0.647805	+	0.761806i	$0.724313\pi$
$570$		0			0
$571$			40.0526i			1.67615i	0.545557	+	0.838074i	$0.316318\pi$
$571$			40.0526i			1.67615i	−0.545557	+	0.838074i	$0.683682\pi$
$572$	7.55743	+	22.3402i	0.315992	+	0.934091i
$573$	7.10381	−	32.8564i	0.296766	−	1.37260i
$574$	2.09808	+	0.562178i	0.0875720	+	0.0234648i
$575$		0			0
$576$	18.6167	+	26.0036i	0.775697	+	1.08348i
$577$	3.49038	+	3.49038i	0.145306	+	0.145306i	0.776018	−	0.630711i	$-0.217237\pi$
$577$	3.49038	+	3.49038i	0.145306	+	0.145306i	−0.630711	+	0.776018i	$0.717237\pi$
$578$	7.67898	+	28.6583i	0.319403	+	1.19203i
$579$	0.610020	+	12.4728i	0.0253516	+	0.518351i
$580$		0			0
$581$	−2.14655	−	1.23931i	−0.0890541	−	0.0514154i
$582$	−16.4864	−	51.3491i	−0.683383	−	2.12849i
$583$	7.83013	+	2.09808i	0.324291	+	0.0868934i
$584$	35.7621			1.47985
$585$		0			0
$586$	−52.7128			−2.17755
$587$	−19.4080	−	5.20035i	−0.801053	−	0.214641i	−0.165006	−	0.986292i	$-0.552765\pi$
$587$	−19.4080	−	5.20035i	−0.801053	−	0.214641i	−0.636046	+	0.771651i	$0.719431\pi$
$588$	−9.88023	−	30.7733i	−0.407454	−	1.26907i
$589$	5.66025	+	3.26795i	0.233227	+	0.134654i
$590$		0			0
$591$	−0.148292	−	3.03206i	−0.00609993	−	0.124722i
$592$	−4.35641	−	16.2583i	−0.179047	−	0.668213i
$593$	10.6112	+	10.6112i	0.435751	+	0.435751i	0.890579	−	0.454828i	$-0.150299\pi$
$593$	10.6112	+	10.6112i	0.435751	+	0.435751i	−0.454828	+	0.890579i	$0.650299\pi$
$594$	−8.65935	−	20.0106i	−0.355297	−	0.821044i
$595$		0			0
$596$	−19.5740	−	5.24484i	−0.801782	−	0.214837i
$597$	−0.339746	+	1.57139i	−0.0139049	+	0.0643126i
$598$		0			0
$599$		−	21.2224i		−	0.867126i	−0.901123	−	0.433563i	$-0.857256\pi$
$599$		−	21.2224i		−	0.867126i	0.901123	−	0.433563i	$-0.142744\pi$
$600$		0			0
$601$	3.79423	+	6.57180i	0.154770	+	0.268069i	0.932975	−	0.359941i	$-0.117203\pi$
$601$	3.79423	+	6.57180i	0.154770	+	0.268069i	−0.778205	+	0.628010i	$0.783870\pi$
$602$	24.0331	+	13.8755i	0.979518	+	0.565525i
$603$	9.24923	+	24.6072i	0.376658	+	1.00208i
$604$	10.1962	+	38.0526i	0.414876	+	1.54834i
$605$		0			0
$606$	68.8075	−	44.3434i	2.79511	−	1.80133i
$607$	−8.83013	−	5.09808i	−0.358404	−	0.206925i	0.309977	−	0.950744i	$-0.399679\pi$
$607$	−8.83013	−	5.09808i	−0.358404	−	0.206925i	−0.668380	+	0.743820i	$0.733012\pi$
$608$	−2.14655	+	1.23931i	−0.0870543	+	0.0502608i
$609$	−6.19441	+	12.0530i	−0.251010	+	0.488413i
$610$		0			0
$611$	11.0648	+	32.7083i	0.447636	+	1.32324i
$612$	21.8866	+	9.92820i	0.884713	+	0.401324i
$613$	4.38269	−	16.3564i	0.177015	−	0.660629i	−0.819185	−	0.573530i	$-0.805574\pi$
$613$	4.38269	−	16.3564i	0.177015	−	0.660629i	0.996200	−	0.0870991i	$-0.0277597\pi$
$614$	−36.3373	+	20.9794i	−1.46645	+	0.846658i
$615$		0			0
$616$	−7.26795	+	7.26795i	−0.292834	+	0.292834i
$617$	−9.74847	−	36.3818i	−0.392459	−	1.46468i	−0.826066	−	0.563574i	$-0.809426\pi$
$617$	−9.74847	−	36.3818i	−0.392459	−	1.46468i	0.433607	−	0.901102i	$-0.357241\pi$
$618$	−1.40345	−	28.6957i	−0.0564552	−	1.15431i
$619$	14.3397	+	14.3397i	0.576363	+	0.576363i	0.933899	−	0.357536i	$-0.116383\pi$
$619$	14.3397	+	14.3397i	0.576363	+	0.576363i	−0.357536	+	0.933899i	$0.616383\pi$
$620$		0			0
$621$		0			0
$622$	9.92820	+	2.66025i	0.398085	+	0.106666i
$623$			14.2076i			0.569216i
$624$	14.3185	−	5.63735i	0.573200	−	0.225675i
$625$		0			0
$626$	−1.23931	+	4.62518i	−0.0495329	+	0.184859i
$627$	2.99233	−	0.960731i	0.119502	−	0.0383679i
$628$	28.3564	−	49.1147i	1.13154	−	1.95989i
$629$	10.3681	+	10.3681i	0.413404	+	0.413404i
$630$		0			0
$631$	2.26795	−	0.607695i	0.0902856	−	0.0241920i	−0.213393	−	0.976966i	$-0.568452\pi$
$631$	2.26795	−	0.607695i	0.0902856	−	0.0241920i	0.303679	+	0.952774i	$0.401785\pi$
$632$	5.86450	+	5.86450i	0.233277	+	0.233277i
$633$	14.1897	−	15.6490i	0.563989	−	0.621993i
$634$	−33.0622	+	19.0885i	−1.31307	+	0.758099i
$635$		0			0
$636$	6.31812	−	29.2224i	0.250530	−	1.15874i
$637$	17.9904	−	1.16025i	0.712805	−	0.0459709i
$638$	−23.2149			−0.919086
$639$	9.11792	−	11.1003i	0.360699	−	0.439122i
$640$		0			0
$641$	9.65949	−	16.7307i	0.381527	−	0.660824i	−0.609754	−	0.792591i	$-0.708732\pi$
$641$	9.65949	−	16.7307i	0.381527	−	0.660824i	0.991281	+	0.131767i	$0.0420650\pi$
$642$	58.1629	−	37.4835i	2.29551	−	1.47935i
$643$	26.1244	−	7.00000i	1.03024	−	0.276053i	0.296179	−	0.955132i	$-0.404287\pi$
$643$	26.1244	−	7.00000i	1.03024	−	0.276053i	0.734065	+	0.679079i	$0.237621\pi$
$644$		0			0
$645$		0			0
$646$	−2.66025	+	4.60770i	−0.104666	+	0.181287i
$647$	12.5147	−	7.22536i	0.492003	−	0.284058i	−0.233402	−	0.972380i	$-0.574986\pi$
$647$	12.5147	−	7.22536i	0.492003	−	0.284058i	0.725405	+	0.688322i	$0.241652\pi$
$648$	−33.4870	+	16.4776i	−1.31549	+	0.647302i
$649$			8.39230i			0.329427i
$650$		0			0
$651$	−3.26795	+	15.1149i	−0.128081	+	0.592398i
$652$	−14.9282	+	55.7128i	−0.584634	+	2.18188i
$653$	−19.4080	−	33.6156i	−0.759492	−	1.31548i	−0.943110	−	0.332482i	$-0.892114\pi$
$653$	−19.4080	−	33.6156i	−0.759492	−	1.31548i	0.183617	−	0.982998i	$-0.441219\pi$
$654$	12.1812	+	11.0452i	0.476321	+	0.431902i
$655$		0			0
$656$	1.52690	−	0.409131i	0.0596153	−	0.0159739i
$657$	4.22556	−	25.5245i	0.164855	−	0.995807i
$658$	−22.9282	+	22.9282i	−0.893834	+	0.893834i
$659$	27.1759	+	15.6900i	1.05862	+	0.611197i	0.925051	−	0.379842i	$-0.124022\pi$
$659$	27.1759	+	15.6900i	1.05862	+	0.611197i	0.133572	+	0.991039i	$0.457355\pi$
$660$		0			0
$661$	−4.42820	+	16.5263i	−0.172237	+	0.642798i	0.824769	+	0.565470i	$0.191305\pi$
$661$	−4.42820	+	16.5263i	−0.172237	+	0.642798i	−0.997006	+	0.0773274i	$0.975361\pi$
$662$		−	46.7380i		−	1.81652i
$663$	−8.34677	+	10.4896i	−0.324162	+	0.407382i
$664$	−7.26795			−0.282051
$665$		0			0
$666$	−48.8284	+	4.78766i	−1.89206	+	0.185518i
$667$		0			0
$668$	31.1370	−	31.1370i	1.20473	−	1.20473i
$669$	−39.9292	+	1.95286i	−1.54375	+	0.0755019i
$670$		0			0
$671$	8.67520	−	8.67520i	0.334902	−	0.334902i
$672$	−4.34444	−	3.93930i	−0.167591	−	0.151962i
$673$	6.35641	+	11.0096i	0.245021	+	0.424390i	0.962138	−	0.272564i	$-0.0878717\pi$
$673$	6.35641	+	11.0096i	0.245021	+	0.424390i	−0.717116	+	0.696954i	$0.754538\pi$
$674$	−26.6778	−	7.14830i	−1.02759	−	0.275342i
$675$		0			0
$676$	6.23205	+	48.1147i	0.239694	+	1.85057i
$677$	−38.8159			−1.49182			−0.745909	−	0.666048i	$-0.767985\pi$
$677$	−38.8159			−1.49182			−0.745909	+	0.666048i	$0.767985\pi$
$678$	47.8304	+	24.5815i	1.83692	+	0.944046i
$679$	9.19615	+	15.9282i	0.352916	+	0.611268i
$680$		0			0
$681$	22.7821	−	14.6820i	0.873011	−	0.562617i
$682$	−25.5885	+	6.85641i	−0.979833	+	0.262545i
$683$	15.9006	−	4.26054i	0.608418	−	0.163025i	0.0585607	−	0.998284i	$-0.481349\pi$
$683$	15.9006	−	4.26054i	0.608418	−	0.163025i	0.549857	+	0.835259i	$0.314682\pi$
$684$	−4.07823	−	10.8500i	−0.155935	−	0.414859i
$685$		0			0
$686$	20.3152	+	35.1870i	0.775638	+	1.34344i
$687$	−11.3358	+	22.0571i	−0.432488	+	0.841530i
$688$	20.1962			0.769971
$689$	14.9488	+	7.39139i	0.569505	+	0.281590i
$690$		0			0
$691$	−41.8827	−	11.2224i	−1.59329	−	0.426921i	−0.650284	−	0.759691i	$-0.725350\pi$
$691$	−41.8827	−	11.2224i	−1.59329	−	0.426921i	−0.943008	+	0.332770i	$0.892017\pi$
$692$	13.8755	+	24.0331i	0.527469	+	0.913603i
$693$	4.32860	+	6.04612i	0.164430	+	0.229673i
$694$	−43.9090	+	43.9090i	−1.66676	+	1.66676i
$695$		0			0
$696$	1.94112	+	39.6892i	0.0735781	+	1.50442i
$697$	−0.973721	+	0.973721i	−0.0368823	+	0.0368823i
$698$	6.98226	−	12.0936i	0.264283	−	0.457751i
$699$	−12.2628	+	3.93715i	−0.463821	+	0.148917i
$700$		0			0
$701$	−20.3152			−0.767295			−0.383647	−	0.923480i	$-0.625332\pi$
$701$	−20.3152			−0.767295			−0.383647	+	0.923480i	$0.625332\pi$
$702$	−9.39478	−	43.8599i	−0.354583	−	1.65538i
$703$		−	7.07180i		−	0.266718i
$704$	4.83571	−	18.0471i	0.182253	−	0.680176i
$705$		0			0
$706$	−56.5526	−	32.6506i	−2.12838	−	1.22882i
$707$	−19.7400	+	19.7400i	−0.742401	+	0.742401i
$708$	30.9154	−	1.51201i	1.16187	−	0.0568249i
$709$	9.96410	−	2.66987i	0.374210	−	0.100269i	−0.0668121	−	0.997766i	$-0.521283\pi$
$709$	9.96410	−	2.66987i	0.374210	−	0.100269i	0.441022	+	0.897496i	$0.354616\pi$
$710$		0			0
$711$	4.87861	−	3.49274i	0.182962	−	0.130988i
$712$	20.8301	+	36.0788i	0.780642	+	1.35211i
$713$		0			0
$714$	−12.3042	−	2.66025i	−0.460472	−	0.0995575i
$715$		0			0
$716$		−	69.9529i		−	2.61426i
$717$	−7.95383	+	15.4765i	−0.297041	+	0.577979i
$718$	35.3660	−	20.4186i	1.31985	−	0.762015i
$719$	−5.86450	+	10.1576i	−0.218709	+	0.378815i	−0.954413	−	0.298488i	$-0.903518\pi$
$719$	−5.86450	+	10.1576i	−0.218709	+	0.378815i	0.735705	+	0.677302i	$0.236851\pi$
$720$		0			0
$721$	2.53590	+	9.46410i	0.0944418	+	0.352462i
$722$	−41.4606	+	11.1093i	−1.54300	+	0.413447i
$723$	−7.02496	−	10.9006i	−0.261261	−	0.405398i
$724$	−5.59808	+	9.69615i	−0.208051	+	0.360355i
$725$		0			0
$726$	15.0279	−	29.2412i	0.557740	−	1.08524i
$727$	−25.5167			−0.946361			−0.473180	−	0.880966i	$-0.656894\pi$
$727$	−25.5167			−0.946361			−0.473180	+	0.880966i	$0.656894\pi$
$728$	−17.5935	+	11.7290i	−0.652058	+	0.434705i
$729$	7.80385	+	25.8476i	0.289031	+	0.957320i
$730$		0			0
$731$	−15.2364	+	8.79674i	−0.563539	+	0.325359i
$732$	−33.5205	−	30.3945i	−1.23895	−	1.12341i
$733$	36.2224	+	36.2224i	1.33791	+	1.33791i	0.898086	+	0.439820i	$0.144958\pi$
$733$	36.2224	+	36.2224i	1.33791	+	1.33791i	0.439820	+	0.898086i	$0.355042\pi$
$734$	−22.2187	+	5.95347i	−0.820106	+	0.219747i
$735$		0			0
$736$		0			0
$737$	7.67898	−	13.3004i	0.282859	−	0.489926i
$738$	−0.449632	−	4.58570i	−0.0165512	−	0.168802i
$739$	−13.1244	+	48.9808i	−0.482787	+	1.80179i	0.107037	+	0.994255i	$0.465864\pi$
$739$	−13.1244	+	48.9808i	−0.482787	+	1.80179i	−0.589825	+	0.807531i	$0.700803\pi$
$740$		0			0
$741$	6.42386	−	0.730778i	0.235987	−	0.0268458i
$742$			15.6603i			0.574906i
$743$	−50.5449	−	13.5435i	−1.85431	−	0.496862i	−0.854566	−	0.519343i	$-0.826177\pi$
$743$	−50.5449	−	13.5435i	−1.85431	−	0.496862i	−0.999747	+	0.0224808i	$0.992844\pi$
$744$	13.8616	+	43.1739i	0.508192	+	1.58283i
$745$		0			0
$746$	33.1620	+	33.1620i	1.21415	+	1.21415i
$747$	−0.858763	+	5.18736i	−0.0314205	+	0.189796i
$748$	−3.63397	−	13.5622i	−0.132871	−	0.495882i
$749$	−16.6862	+	16.6862i	−0.609702	+	0.609702i
$750$		0			0
$751$	38.2750	−	22.0981i	1.39667	−	0.806370i	0.402632	−	0.915362i	$-0.368096\pi$
$751$	38.2750	−	22.0981i	1.39667	−	0.806370i	0.994043	+	0.108992i	$0.0347622\pi$
$752$	−6.10759	+	22.7938i	−0.222721	+	0.831206i
$753$	−37.0526	−	8.01105i	−1.35027	−	0.291939i
$754$	−46.8301	−	9.36603i	−1.70545	−	0.341091i
$755$		0			0
$756$	21.4927	−	17.0349i	0.781681	−	0.619553i
$757$	−21.4641	+	12.3923i	−0.780126	+	0.450406i	−0.836475	−	0.548005i	$-0.815387\pi$
$757$	−21.4641	+	12.3923i	−0.780126	+	0.450406i	0.0563489	+	0.998411i	$0.482054\pi$
$758$	−10.3681	−	5.98604i	−0.376587	−	0.217423i
$759$		0			0
$760$		0			0
$761$	1.11777	+	4.17156i	0.0405190	+	0.151219i	0.983222	−	0.182415i	$-0.0583916\pi$
$761$	1.11777	+	4.17156i	0.0405190	+	0.151219i	−0.942703	+	0.333634i	$0.891725\pi$
$762$	−52.7187	+	33.9749i	−1.90980	+	1.23078i
$763$	−4.85641	−	2.80385i	−0.175814	−	0.101506i
$764$	36.2158	+	62.7275i	1.31024	+	2.26940i
$765$		0			0
$766$			33.5692i			1.21291i
$767$	−3.38587	+	16.9293i	−0.122257	+	0.611283i
$768$	−47.9447	−	10.3660i	−1.73006	−	0.374052i
$769$	2.16987	+	0.581416i	0.0782476	+	0.0209664i	0.297730	−	0.954650i	$-0.403770\pi$
$769$	2.16987	+	0.581416i	0.0782476	+	0.0209664i	−0.219483	+	0.975616i	$0.570437\pi$
$770$		0			0
$771$	−21.2961	−	19.3102i	−0.766962	−	0.695438i
$772$	−19.0263	−	19.0263i	−0.684771	−	0.684771i
$773$	1.60396	+	5.98604i	0.0576903	+	0.215303i	0.988753	−	0.149555i	$-0.0477842\pi$
$773$	1.60396	+	5.98604i	0.0576903	+	0.215303i	−0.931063	+	0.364858i	$0.881117\pi$
$774$	9.61484	−	58.0785i	0.345598	−	2.08759i
$775$		0			0
$776$	46.7054	+	26.9654i	1.67663	+	0.968001i
$777$	15.9311	−	5.11491i	0.571524	−	0.183496i
$778$	12.2321	+	3.27757i	0.438540	+	0.117507i
$779$	0.664146			0.0237955
$780$		0			0
$781$	−8.39230			−0.300300
$782$		0			0
$783$	28.5568	+	3.30414i	1.02054	+	0.118080i
$784$	10.6699	+	6.16025i	0.381067	+	0.220009i
$785$		0			0
$786$	−3.75768	+	0.183781i	−0.134032	+	0.00655524i
$787$	−3.02628	−	11.2942i	−0.107875	−	0.402596i	0.890780	−	0.454434i	$-0.150159\pi$
$787$	−3.02628	−	11.2942i	−0.107875	−	0.402596i	−0.998655	+	0.0518385i	$0.983492\pi$
$788$	4.62518	+	4.62518i	0.164765	+	0.164765i
$789$	13.9290	−	15.3615i	0.495885	−	0.546884i
$790$		0			0
$791$	−17.7150	−	4.74673i	−0.629874	−	0.168774i
$792$	19.8564	+	9.00727i	0.705567	+	0.320059i
$793$	21.0000	−	14.0000i	0.745732	−	0.497155i
$794$		−	21.2224i		−	0.753157i
$795$		0			0
$796$	−1.73205	−	3.00000i	−0.0613909	−	0.106332i
$797$	−14.8718	−	8.58622i	−0.526785	−	0.304139i	0.212921	−	0.977069i	$-0.431702\pi$
$797$	−14.8718	−	8.58622i	−0.526785	−	0.304139i	−0.739706	+	0.672930i	$0.765036\pi$
$798$	3.28891	+	5.10339i	0.116426	+	0.180658i
$799$	−5.32051	−	19.8564i	−0.188226	−	0.702469i
$800$		0			0
$801$	28.2118	−	10.6041i	0.996815	−	0.374678i
$802$	58.2391	+	33.6244i	2.05649	+	1.18732i
$803$	−13.0899	+	7.55743i	−0.461931	+	0.266696i
$804$	−50.3791	−	25.8913i	−1.77673	−	0.913117i
$805$		0			0
$806$	−54.3844	+	3.50742i	−1.91561	+	0.123543i
$807$	4.05001	−	18.7321i	0.142567	−	0.659399i
$808$	−21.1865	+	79.0692i	−0.745340	+	2.78165i
$809$	17.6705	−	10.2021i	0.621263	−	0.358686i	−0.156097	−	0.987742i	$-0.549891\pi$
$809$	17.6705	−	10.2021i	0.621263	−	0.358686i	0.777361	+	0.629055i	$0.216558\pi$
$810$		0			0
$811$	19.0000	−	19.0000i	0.667180	−	0.667180i	−0.289882	−	0.957062i	$-0.593616\pi$
$811$	19.0000	−	19.0000i	0.667180	−	0.667180i	0.957062	+	0.289882i	$0.0936161\pi$
$812$	−7.55743	−	28.2047i	−0.265214	−	0.989791i
$813$	−3.58202	+	0.175190i	−0.125627	+	0.00614417i
$814$	20.2679	+	20.2679i	0.710391	+	0.710391i
$815$		0			0
$816$	−8.72282	+	2.80059i	−0.305360	+	0.0980403i
$817$	8.19615	+	2.19615i	0.286747	+	0.0768336i
$818$			27.8401i			0.973405i
$819$	6.29254	+	13.9429i	0.219879	+	0.487204i
$820$		0			0
$821$	1.60396	−	5.98604i	0.0559784	−	0.208914i	−0.932272	−	0.361758i	$-0.882177\pi$
$821$	1.60396	−	5.98604i	0.0559784	−	0.208914i	0.988250	+	0.152844i	$0.0488432\pi$
$822$	7.47856	+	23.2930i	0.260845	+	0.812436i
$823$	7.73205	−	13.3923i	0.269522	−	0.466826i	−0.699216	−	0.714910i	$-0.746468\pi$
$823$	7.73205	−	13.3923i	0.269522	−	0.466826i	0.968739	+	0.248084i	$0.0798009\pi$
$824$	20.3152	+	20.3152i	0.707714	+	0.707714i
$825$		0			0
$826$	−15.6603	+	4.19615i	−0.544890	+	0.146003i
$827$	3.62896	+	3.62896i	0.126191	+	0.126191i	0.767382	−	0.641190i	$-0.221559\pi$
$827$	3.62896	+	3.62896i	0.126191	+	0.126191i	−0.641190	+	0.767382i	$0.721559\pi$
$828$		0			0
$829$	20.6769	−	11.9378i	0.718139	−	0.414618i	−0.0959284	−	0.995388i	$-0.530582\pi$
$829$	20.6769	−	11.9378i	0.718139	−	0.414618i	0.814067	+	0.580771i	$0.197249\pi$
$830$		0			0
$831$	6.07502	+	1.31347i	0.210740	+	0.0455636i
$832$	17.0359	−	34.4545i	0.590614	−	1.19449i
$833$	−10.7328			−0.371868
$834$	−8.82343	−	4.53463i	−0.305530	−	0.157021i
$835$		0			0
$836$	−3.38587	+	5.86450i	−0.117103	+	0.202828i
$837$	32.4524	−	4.79215i	1.12172	−	0.165641i
$838$	19.2942	−	5.16987i	0.666508	−	0.178590i
$839$	2.02501	+	7.55743i	0.0699110	+	0.260911i	0.992031	−	0.125992i	$-0.0402114\pi$
$839$	2.02501	+	7.55743i	0.0699110	+	0.260911i	−0.922120	+	0.386903i	$0.873545\pi$
$840$		0			0
$841$	0.803848	−	1.39230i	0.0277189	−	0.0480105i
$842$	−2.43414	+	1.40535i	−0.0838859	+	0.0484316i
$843$	34.6412	+	17.8032i	1.19311	+	0.613173i
$844$			45.5167i			1.56675i
$845$		0			0
$846$	62.6410	+	28.4152i	2.15364	+	0.976936i
$847$	−2.90192	+	10.8301i	−0.0997113	+	0.372128i
$848$	5.69846	+	9.87002i	0.195686	+	0.338938i
$849$	28.6075	−	31.5497i	0.981808	−	1.08278i
$850$		0			0
$851$		0			0
$852$	1.51201	+	30.9154i	0.0518007	+	1.05914i
$853$	−20.6340	+	20.6340i	−0.706494	+	0.706494i	−0.965796	−	0.259302i	$-0.916507\pi$
$853$	−20.6340	+	20.6340i	−0.706494	+	0.706494i	0.259302	+	0.965796i	$0.416507\pi$
$854$	20.5257	+	11.8505i	0.702376	+	0.405517i
$855$		0			0
$856$	−17.9090	+	66.8372i	−0.612116	+	2.28445i
$857$			35.7621i			1.22161i	0.791781	+	0.610806i	$0.209154\pi$
$857$			35.7621i			1.22161i	−0.791781	+	0.610806i	$0.790846\pi$
$858$	−16.3165	+	20.5054i	−0.557037	+	0.700042i
$859$	23.1769			0.790786			0.395393	−	0.918512i	$-0.370608\pi$
$859$	23.1769			0.790786			0.395393	+	0.918512i	$0.370608\pi$
$860$		0			0
$861$	0.480365	+	1.49616i	0.0163708	+	0.0509891i
$862$	2.50962	−	4.34679i	0.0854780	−	0.148052i
$863$	−12.0611	+	12.0611i	−0.410563	+	0.410563i	−0.881935	−	0.471371i	$-0.843759\pi$
$863$	−12.0611	+	12.0611i	−0.410563	+	0.410563i	0.471371	+	0.881935i	$0.343759\pi$
$864$	−4.57965	+	11.5669i	−0.155803	+	0.393513i
$865$		0			0
$866$	11.9395	−	11.9395i	0.405721	−	0.405721i
$867$	−14.4179	+	15.9007i	−0.489657	+	0.540016i
$868$	−16.6603	−	28.8564i	−0.565486	−	0.979450i
$869$	−3.38587	−	0.907241i	−0.114858	−	0.0307760i
$870$		0			0
$871$	20.8564	−	23.7321i	0.706692	−	0.804130i
$872$	−16.4432			−0.556835
$873$	24.7646	−	30.1489i	0.838156	−	1.02039i
$874$		0			0
$875$		0			0
$876$	30.1982	+	46.8585i	1.02030	+	1.58320i
$877$	−11.2321	+	3.00962i	−0.379279	+	0.101628i	−0.443422	−	0.896313i	$-0.646236\pi$
$877$	−11.2321	+	3.00962i	−0.379279	+	0.101628i	0.0641422	+	0.997941i	$0.479569\pi$
$878$	−10.9433	+	2.93225i	−0.369318	+	0.0989586i
$879$	−20.6579	−	32.0549i	−0.696775	−	1.08118i
$880$		0			0
$881$	13.5880	+	23.5350i	0.457790	+	0.792916i	0.998844	−	0.0480724i	$-0.0153078\pi$
$881$	13.5880	+	23.5350i	0.457790	+	0.792916i	−0.541054	+	0.840988i	$0.681974\pi$
$882$	22.7948	−	27.7508i	0.767541	−	0.934419i
$883$	−39.3731			−1.32501			−0.662505	−	0.749058i	$-0.730506\pi$
$883$	−39.3731			−1.32501			−0.662505	+	0.749058i	$0.730506\pi$
$884$	−1.85897	−	28.8244i	−0.0625239	−	0.969468i
$885$		0			0
$886$	68.3731	+	18.3205i	2.29704	+	0.615490i
$887$	26.8438	+	46.4949i	0.901328	+	1.56115i	0.825772	+	0.564005i	$0.190740\pi$
$887$	26.8438	+	46.4949i	0.901328	+	1.56115i	0.0755567	+	0.997142i	$0.475927\pi$
$888$	32.9563	−	36.3457i	1.10594	−	1.21968i
$889$	15.1244	−	15.1244i	0.507255	−	0.507255i
$890$		0			0
$891$	8.77495	−	13.1079i	0.293972	−	0.439130i
$892$	60.9090	−	60.9090i	2.03938	−	2.03938i
$893$	−4.95725	+	8.58622i	−0.165888	+	0.287327i
$894$	−6.88324	−	21.4388i	−0.230210	−	0.717020i
$895$		0			0
$896$	29.3225			0.979595
$897$		0			0
$898$			20.9808i			0.700137i
$899$	9.03984	−	33.7371i	0.301495	−	1.12520i
$900$		0			0
$901$	−8.59808	−	4.96410i	−0.286443	−	0.165378i
$902$	−1.90346	+	1.90346i	−0.0633783	+	0.0633783i
$903$	0.980726	+	20.0524i	0.0326365	+	0.667303i
$904$	−51.9449	+	13.9186i	−1.72766	+	0.462925i
$905$		0			0
$906$	−29.4034	+	32.4274i	−0.976861	+	1.07733i
$907$	−8.66025	−	15.0000i	−0.287559	−	0.498067i	0.685668	−	0.727915i	$-0.259510\pi$
$907$	−8.66025	−	15.0000i	−0.287559	−	0.498067i	−0.973227	+	0.229848i	$0.926177\pi$
$908$	−15.1149	+	56.4094i	−0.501604	+	1.87201i
$909$	53.9308	+	24.4641i	1.78877	+	0.811423i
$910$		0			0
$911$		−	9.25036i		−	0.306478i	−0.988189	−	0.153239i	$-0.951030\pi$
$911$		−	9.25036i		−	0.306478i	0.988189	−	0.153239i	$-0.0489705\pi$
$912$	3.92989	+	2.01969i	0.130132	+	0.0668786i
$913$	2.66025	−	1.53590i	0.0880416	−	0.0508308i
$914$	−33.4495	+	57.9363i	−1.10641	+	1.91636i
$915$		0			0
$916$	−13.8301	−	51.6147i	−0.456960	−	1.70540i
$917$	1.23931	−	0.332073i	0.0409257	−	0.0109660i
$918$	3.90102	+	26.4177i	0.128753	+	0.871913i
$919$	22.2942	−	38.6147i	0.735419	−	1.27378i	−0.219121	−	0.975698i	$-0.570319\pi$
$919$	22.2942	−	38.6147i	0.735419	−	1.27378i	0.954539	−	0.298085i	$-0.0963478\pi$
$920$		0			0
$921$	−26.9981	−	13.8751i	−0.889617	−	0.457201i
$922$	−58.0333			−1.91123
$923$	−16.9293	−	3.38587i	−0.557236	−	0.111447i
$924$	−15.6603	−	3.38587i	−0.515185	−	0.111387i
$925$		0			0
$926$	44.1378	−	25.4830i	1.45046	−	0.837423i
$927$	16.9000	−	12.0992i	0.555068	−	0.397390i
$928$	9.36603	+	9.36603i	0.307455	+	0.307455i
$929$	47.3251	−	12.6807i	1.55269	−	0.416041i	0.622347	−	0.782742i	$-0.286179\pi$
$929$	47.3251	−	12.6807i	1.55269	−	0.416041i	0.930339	+	0.366701i	$0.119513\pi$
$930$		0			0
$931$	3.66025	+	3.66025i	0.119960	+	0.119960i
$932$	13.8755	−	24.0331i	0.454509	−	0.787232i
$933$	2.27311	+	7.07992i	0.0744184	+	0.231786i
$934$	18.8827	−	70.4711i	0.617860	−	2.30589i
$935$		0			0
$936$	36.4213	+	26.1809i	1.19047	+	0.855750i
$937$		−	37.0000i		−	1.20874i	−0.796705	−	0.604369i	$-0.793425\pi$
$937$		−	37.0000i		−	1.20874i	0.796705	−	0.604369i	$-0.206575\pi$
$938$	28.6583	+	7.67898i	0.935728	+	0.250727i
$939$	−3.29827	+	1.05896i	−0.107635	+	0.0345578i
$940$		0			0
$941$	−38.2408	−	38.2408i	−1.24661	−	1.24661i	−0.957206	−	0.289407i	$-0.906542\pi$
$941$	−38.2408	−	38.2408i	−1.24661	−	1.24661i	−0.289407	−	0.957206i	$-0.593458\pi$
$942$	62.9405	−	3.07830i	2.05071	−	0.100296i
$943$		0			0
$944$	−8.34312	+	8.34312i	−0.271546	+	0.271546i
$945$		0			0
$946$	−29.7846	+	17.1962i	−0.968381	+	0.559095i
$947$	−10.6112	+	39.6016i	−0.344818	+	1.28688i	0.548006	+	0.836475i	$0.315387\pi$
$947$	−10.6112	+	39.6016i	−0.344818	+	1.28688i	−0.892824	+	0.450405i	$0.851279\pi$
$948$	−2.73205	+	12.6362i	−0.0887329	+	0.410406i
$949$	−29.4545	+	9.96410i	−0.956133	+	0.323448i
$950$		0			0
$951$	−24.5647	−	12.6245i	−0.796565	−	0.409379i
$952$	10.9019	−	6.29423i	0.353333	−	0.203997i
$953$	37.9087	+	21.8866i	1.22798	+	0.708976i	0.966608	−	0.256261i	$-0.0824906\pi$
$953$	37.9087	+	21.8866i	1.22798	+	0.708976i	0.261375	+	0.965237i	$0.415824\pi$
$954$	31.0963	−	11.6883i	1.00678	−	0.378423i
$955$		0			0
$956$	−9.70398	−	36.2158i	−0.313849	−	1.17130i
$957$	−9.09782	−	14.1171i	−0.294091	−	0.456340i
$958$	−18.1699	−	10.4904i	−0.587042	−	0.338929i
$959$	−4.17156	−	7.22536i	−0.134707	−	0.233319i
$960$		0			0
$961$		−	8.85641i		−	0.285691i
$962$	32.7083	+	49.0625i	1.05456	+	1.58184i
$963$	45.5877	+	20.6795i	1.46904	+	0.666387i
$964$	26.9904	+	7.23205i	0.869302	+	0.232929i
$965$		0			0
$966$		0			0
$967$	−0.143594	−	0.143594i	−0.00461766	−	0.00461766i	0.704794	−	0.709412i	$-0.251039\pi$
$967$	−0.143594	−	0.143594i	−0.00461766	−	0.00461766i	−0.709412	+	0.704794i	$0.751039\pi$
$968$	8.50916	+	31.7566i	0.273495	+	1.02070i
$969$	−3.84450	+	0.188027i	−0.123503	+	0.00604030i
$970$		0			0
$971$	45.5551	+	26.3013i	1.46193	+	0.844047i	0.999101	−	0.0423987i	$-0.0135000\pi$
$971$	45.5551	+	26.3013i	1.46193	+	0.844047i	0.462832	+	0.886446i	$0.346833\pi$
$972$	−49.8673	−	29.9633i	−1.59950	−	0.961075i
$973$	3.26795	+	0.875644i	0.104766	+	0.0280719i
$974$	−60.7025			−1.94503
$975$		0			0
$976$	17.2487			0.552118
$977$	28.3707	+	7.60192i	0.907661	+	0.243207i	0.682303	−	0.731069i	$-0.260978\pi$
$977$	28.3707	+	7.60192i	0.907661	+	0.243207i	0.225357	+	0.974276i	$0.427645\pi$
$978$	−61.0204	+	19.5915i	−1.95122	+	0.626468i
$979$	−15.2487	−	8.80385i	−0.487351	−	0.281372i
$980$		0			0
$981$	−1.94288	+	11.7360i	−0.0620314	+	0.374701i
$982$	−15.5096	−	57.8827i	−0.494932	−	1.84711i
$983$	4.38209	+	4.38209i	0.139767	+	0.139767i	0.773528	−	0.633762i	$-0.218490\pi$
$983$	4.38209	+	4.38209i	0.139767	+	0.139767i	−0.633762	+	0.773528i	$0.718490\pi$
$984$	3.41340	+	3.09508i	0.108815	+	0.0986677i
$985$		0			0
$986$	27.4635	+	7.35882i	0.874616	+	0.234353i
$987$	−22.9282	−	4.95725i	−0.729813	−	0.157791i
$988$	−9.19615	+	10.4641i	−0.292569	+	0.332907i
$989$		0			0
$990$		0			0
$991$	−12.7846	−	22.1436i	−0.406117	−	0.703414i	0.588334	−	0.808618i	$-0.299784\pi$
$991$	−12.7846	−	22.1436i	−0.406117	−	0.703414i	−0.994451	+	0.105203i	$0.966451\pi$
$992$	13.0899	+	7.55743i	0.415603	+	0.239949i
$993$	28.4216	−	18.3164i	0.901931	−	0.581255i
$994$	−4.19615	−	15.6603i	−0.133094	−	0.496713i
$995$		0			0
$996$	−6.13719	−	9.52306i	−0.194464	−	0.301750i
$997$	6.06218	+	3.50000i	0.191991	+	0.110846i	0.592914	−	0.805266i	$-0.297977\pi$
$997$	6.06218	+	3.50000i	0.191991	+	0.110846i	−0.400923	+	0.916112i	$0.631311\pi$
$998$	13.0899	−	7.55743i	0.414352	−	0.239226i
$999$	−22.0470	−	27.8165i	−0.697537	−	0.880074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bp.f.899.1		8
3.2	odd	2	inner	975.2.bp.f.899.2		8
5.2	odd	4		975.2.bo.d.626.2		8
5.3	odd	4		39.2.k.b.2.1	✓	8
5.4	even	2		975.2.bp.e.899.2		8
13.7	odd	12		975.2.bp.e.449.1		8
15.2	even	4		975.2.bo.d.626.1		8
15.8	even	4		39.2.k.b.2.2	yes	8
15.14	odd	2		975.2.bp.e.899.1		8
20.3	even	4		624.2.cn.c.353.1		8
39.20	even	12		975.2.bp.e.449.2		8
60.23	odd	4		624.2.cn.c.353.2		8
65.3	odd	12		507.2.f.f.239.1		8
65.7	even	12		975.2.bo.d.176.1		8
65.8	even	4		507.2.k.e.89.1		8
65.18	even	4		507.2.k.f.89.2		8
65.23	odd	12		507.2.f.e.239.4		8
65.28	even	12		507.2.f.e.437.1		8
65.33	even	12		39.2.k.b.20.2	yes	8
65.38	odd	4		507.2.k.d.80.2		8
65.43	odd	12		507.2.k.f.188.1		8
65.48	odd	12		507.2.k.e.188.2		8
65.58	even	12		507.2.k.d.488.1		8
65.59	odd	12	inner	975.2.bp.f.449.2		8
65.63	even	12		507.2.f.f.437.4		8
195.8	odd	4		507.2.k.e.89.2		8
195.23	even	12		507.2.f.e.239.1		8
195.38	even	4		507.2.k.d.80.1		8
195.59	even	12	inner	975.2.bp.f.449.1		8
195.68	even	12		507.2.f.f.239.4		8
195.83	odd	4		507.2.k.f.89.1		8
195.98	odd	12		39.2.k.b.20.1	yes	8
195.113	even	12		507.2.k.e.188.1		8
195.128	odd	12		507.2.f.f.437.1		8
195.137	odd	12		975.2.bo.d.176.2		8
195.158	odd	12		507.2.f.e.437.4		8
195.173	even	12		507.2.k.f.188.2		8
195.188	odd	12		507.2.k.d.488.2		8
260.163	odd	12		624.2.cn.c.449.2		8
780.683	even	12		624.2.cn.c.449.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.2.1	✓	8	5.3	odd	4
39.2.k.b.2.2	yes	8	15.8	even	4
39.2.k.b.20.1	yes	8	195.98	odd	12
39.2.k.b.20.2	yes	8	65.33	even	12
507.2.f.e.239.1		8	195.23	even	12
507.2.f.e.239.4		8	65.23	odd	12
507.2.f.e.437.1		8	65.28	even	12
507.2.f.e.437.4		8	195.158	odd	12
507.2.f.f.239.1		8	65.3	odd	12
507.2.f.f.239.4		8	195.68	even	12
507.2.f.f.437.1		8	195.128	odd	12
507.2.f.f.437.4		8	65.63	even	12
507.2.k.d.80.1		8	195.38	even	4
507.2.k.d.80.2		8	65.38	odd	4
507.2.k.d.488.1		8	65.58	even	12
507.2.k.d.488.2		8	195.188	odd	12
507.2.k.e.89.1		8	65.8	even	4
507.2.k.e.89.2		8	195.8	odd	4
507.2.k.e.188.1		8	195.113	even	12
507.2.k.e.188.2		8	65.48	odd	12
507.2.k.f.89.1		8	195.83	odd	4
507.2.k.f.89.2		8	65.18	even	4
507.2.k.f.188.1		8	65.43	odd	12
507.2.k.f.188.2		8	195.173	even	12
624.2.cn.c.353.1		8	20.3	even	4
624.2.cn.c.353.2		8	60.23	odd	4
624.2.cn.c.449.1		8	780.683	even	12
624.2.cn.c.449.2		8	260.163	odd	12
975.2.bo.d.176.1		8	65.7	even	12
975.2.bo.d.176.2		8	195.137	odd	12
975.2.bo.d.626.1		8	15.2	even	4
975.2.bo.d.626.2		8	5.2	odd	4
975.2.bp.e.449.1		8	13.7	odd	12
975.2.bp.e.449.2		8	39.20	even	12
975.2.bp.e.899.1		8	15.14	odd	2
975.2.bp.e.899.2		8	5.4	even	2
975.2.bp.f.449.1		8	195.59	even	12	inner
975.2.bp.f.449.2		8	65.59	odd	12	inner
975.2.bp.f.899.1		8	1.1	even	1	trivial
975.2.bp.f.899.2		8	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bp (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.31259 - 0.619657i) q^{2} +(-0.529480 - 1.64914i) q^{3} +(3.23205 + 1.86603i) q^{4} +(0.202571 + 4.14187i) q^{6} +(-0.366025 - 1.36603i) q^{7} +(-2.93225 - 2.93225i) q^{8} +(-2.43930 + 1.74637i) q^{9} +O(q^{10})\)	\(q+(-2.31259 - 0.619657i) q^{2} +(-0.529480 - 1.64914i) q^{3} +(3.23205 + 1.86603i) q^{4} +(0.202571 + 4.14187i) q^{6} +(-0.366025 - 1.36603i) q^{7} +(-2.93225 - 2.93225i) q^{8} +(-2.43930 + 1.74637i) q^{9} +(1.69293 + 0.453620i) q^{11} +(1.36603 - 6.31812i) q^{12} +(3.23205 + 1.59808i) q^{13} +3.38587i q^{14} +(1.23205 + 2.13397i) q^{16} +(-1.85897 - 1.07328i) q^{17} +(6.72326 - 2.52711i) q^{18} +(0.267949 + 1.00000i) q^{19} +(-2.05896 + 1.32691i) q^{21} +(-3.63397 - 2.09808i) q^{22} +(-3.28311 + 6.38824i) q^{24} +(-6.48415 - 5.69846i) q^{26} +(4.17156 + 3.09808i) q^{27} +(1.36603 - 5.09808i) q^{28} +(4.79122 - 2.76621i) q^{29} +(4.46410 - 4.46410i) q^{31} +(0.619657 + 2.31259i) q^{32} +(-0.148292 - 3.03206i) q^{33} +(3.63397 + 3.63397i) q^{34} +(-11.1427 + 1.09255i) q^{36} +(-6.59808 - 1.76795i) q^{37} -2.47863i q^{38} +(0.924141 - 6.17624i) q^{39} +(0.166037 - 0.619657i) q^{41} +(5.58376 - 1.79275i) q^{42} +(4.09808 - 7.09808i) q^{43} +(4.62518 + 4.62518i) q^{44} +(6.77174 + 6.77174i) q^{47} +(2.86687 - 3.16172i) q^{48} +(4.33013 - 2.50000i) q^{49} +(-0.785693 + 3.63397i) q^{51} +(7.46410 + 11.1962i) q^{52} +4.62518 q^{53} +(-7.72737 - 9.74952i) q^{54} +(-2.93225 + 5.07880i) q^{56} +(1.50726 - 0.971364i) q^{57} +(-12.7942 + 3.42820i) q^{58} +(1.23931 + 4.62518i) q^{59} +(3.50000 - 6.06218i) q^{61} +(-13.0899 + 7.55743i) q^{62} +(3.27843 + 2.69293i) q^{63} -10.6603i q^{64} +(-1.53590 + 7.10381i) q^{66} +(2.26795 - 8.46410i) q^{67} +(-4.00552 - 6.93777i) q^{68} +(-4.62518 + 1.23931i) q^{71} +(12.2734 + 2.03185i) q^{72} +(-6.09808 + 6.09808i) q^{73} +(14.1631 + 8.17709i) q^{74} +(-1.00000 + 3.73205i) q^{76} -2.47863i q^{77} +(-5.96431 + 13.7105i) q^{78} -2.00000 q^{79} +(2.90039 - 8.51984i) q^{81} +(-0.767949 + 1.33013i) q^{82} +(1.23931 - 1.23931i) q^{83} +(-9.13071 + 0.446565i) q^{84} +(-13.8755 + 13.8755i) q^{86} +(-7.09871 - 6.43672i) q^{87} +(-3.63397 - 6.29423i) q^{88} +(-9.70398 - 2.60017i) q^{89} +(1.00000 - 5.00000i) q^{91} +(-9.72556 - 4.99826i) q^{93} +(-11.4641 - 19.8564i) q^{94} +(3.48568 - 2.24637i) q^{96} +(-12.5622 + 3.36603i) q^{97} +(-11.5630 + 3.09828i) q^{98} +(-4.92177 + 1.84997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 12 q^{4} - 2 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 + 12 * q^4 - 2 * q^6 + 4 * q^7 - 4 * q^9	\( 8 q + 6 q^{3} + 12 q^{4} - 2 q^{6} + 4 q^{7} - 4 q^{9} + 4 q^{12} + 12 q^{13} - 4 q^{16} - 4 q^{18} + 16 q^{19} + 4 q^{21} - 36 q^{22} - 18 q^{24} + 4 q^{28} + 8 q^{31} - 20 q^{33} + 36 q^{34} - 36 q^{36} - 32 q^{37} + 14 q^{39} + 12 q^{42} + 12 q^{43} - 18 q^{48} + 32 q^{52} - 46 q^{54} + 16 q^{57} - 40 q^{58} + 28 q^{61} + 16 q^{63} - 40 q^{66} + 32 q^{67} - 24 q^{72} - 28 q^{73} - 8 q^{76} - 16 q^{78} - 16 q^{79} + 4 q^{81} - 20 q^{82} - 4 q^{84} - 6 q^{87} - 36 q^{88} + 8 q^{91} - 16 q^{93} - 64 q^{94} + 16 q^{96} - 52 q^{97} - 40 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 + 12 * q^4 - 2 * q^6 + 4 * q^7 - 4 * q^9 + 4 * q^12 + 12 * q^13 - 4 * q^16 - 4 * q^18 + 16 * q^19 + 4 * q^21 - 36 * q^22 - 18 * q^24 + 4 * q^28 + 8 * q^31 - 20 * q^33 + 36 * q^34 - 36 * q^36 - 32 * q^37 + 14 * q^39 + 12 * q^42 + 12 * q^43 - 18 * q^48 + 32 * q^52 - 46 * q^54 + 16 * q^57 - 40 * q^58 + 28 * q^61 + 16 * q^63 - 40 * q^66 + 32 * q^67 - 24 * q^72 - 28 * q^73 - 8 * q^76 - 16 * q^78 - 16 * q^79 + 4 * q^81 - 20 * q^82 - 4 * q^84 - 6 * q^87 - 36 * q^88 + 8 * q^91 - 16 * q^93 - 64 * q^94 + 16 * q^96 - 52 * q^97 - 40 * q^99

Introduction

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