LMFDB - Embedded newform 975.2.bo.d.176.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(176,975)]

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, 0, 11]))

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

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

chi := DirichletCharacter("975.176");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bo (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.78541419707$
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			176.2
Root			$0.500000 - 2.19293i$ of defining polynomial
Character	$\chi$	$=$	975.176
Dual form			975.2.bo.d.626.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.619657 + 2.31259i) q^{2} +(-1.64914 - 0.529480i) q^{3} +(-3.23205 + 1.86603i) q^{4} +(0.202571 - 4.14187i) q^{6} +(1.36603 + 0.366025i) q^{7} +(-2.93225 - 2.93225i) q^{8} +(2.43930 + 1.74637i) q^{9} +O(q^{10})$	\(q+(0.619657 + 2.31259i) q^{2} +(-1.64914 - 0.529480i) q^{3} +(-3.23205 + 1.86603i) q^{4} +(0.202571 - 4.14187i) q^{6} +(1.36603 + 0.366025i) q^{7} +(-2.93225 - 2.93225i) q^{8} +(2.43930 + 1.74637i) q^{9} +(1.69293 - 0.453620i) q^{11} +(6.31812 - 1.36603i) q^{12} +(1.59808 + 3.23205i) q^{13} +3.38587i q^{14} +(1.23205 - 2.13397i) q^{16} +(1.07328 + 1.85897i) q^{17} +(-2.52711 + 6.72326i) q^{18} +(-0.267949 + 1.00000i) q^{19} +(-2.05896 - 1.32691i) q^{21} +(2.09808 + 3.63397i) q^{22} +(3.28311 + 6.38824i) q^{24} +(-6.48415 + 5.69846i) q^{26} +(-3.09808 - 4.17156i) q^{27} +(-5.09808 + 1.36603i) q^{28} +(-4.79122 - 2.76621i) q^{29} +(4.46410 + 4.46410i) q^{31} +(-2.31259 - 0.619657i) q^{32} +(-3.03206 - 0.148292i) q^{33} +(-3.63397 + 3.63397i) q^{34} +(-11.1427 - 1.09255i) q^{36} +(1.76795 + 6.59808i) q^{37} -2.47863 q^{38} +(-0.924141 - 6.17624i) q^{39} +(0.166037 + 0.619657i) q^{41} +(1.79275 - 5.58376i) q^{42} +(-7.09808 + 4.09808i) q^{43} +(-4.62518 + 4.62518i) q^{44} +(-6.77174 - 6.77174i) q^{47} +(-3.16172 + 2.86687i) q^{48} +(-4.33013 - 2.50000i) q^{49} +(-0.785693 - 3.63397i) q^{51} +(-11.1962 - 7.46410i) q^{52} +4.62518i q^{53} +(7.72737 - 9.74952i) q^{54} +(-2.93225 - 5.07880i) q^{56} +(0.971364 - 1.50726i) q^{57} +(3.42820 - 12.7942i) q^{58} +(-1.23931 + 4.62518i) q^{59} +(3.50000 + 6.06218i) q^{61} +(-7.55743 + 13.0899i) q^{62} +(2.69293 + 3.27843i) q^{63} -10.6603i q^{64} +(-1.53590 - 7.10381i) q^{66} +(8.46410 - 2.26795i) q^{67} +(-6.93777 - 4.00552i) q^{68} +(-4.62518 - 1.23931i) q^{71} +(-2.03185 - 12.2734i) q^{72} +(6.09808 - 6.09808i) q^{73} +(-14.1631 + 8.17709i) q^{74} +(-1.00000 - 3.73205i) q^{76} +2.47863 q^{77} +(13.7105 - 5.96431i) q^{78} +2.00000 q^{79} +(2.90039 + 8.51984i) q^{81} +(-1.33013 + 0.767949i) q^{82} +(-1.23931 + 1.23931i) q^{83} +(9.13071 + 0.446565i) q^{84} +(-13.8755 - 13.8755i) q^{86} +(6.43672 + 7.09871i) q^{87} +(-6.29423 - 3.63397i) q^{88} +(9.70398 - 2.60017i) q^{89} +(1.00000 + 5.00000i) q^{91} +(-4.99826 - 9.72556i) q^{93} +(11.4641 - 19.8564i) q^{94} +(3.48568 + 2.24637i) q^{96} +(-3.36603 + 12.5622i) q^{97} +(3.09828 - 11.5630i) q^{98} +(4.92177 + 1.84997i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 12 q^{4} - 2 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 - 12 * q^4 - 2 * q^6 + 4 * q^7 + 4 * q^9	$ 8 q + 2 q^{3} - 12 q^{4} - 2 q^{6} + 4 q^{7} + 4 q^{9} - 8 q^{13} - 4 q^{16} - 4 q^{18} - 16 q^{19} + 4 q^{21} - 4 q^{22} + 18 q^{24} - 4 q^{27} - 20 q^{28} + 8 q^{31} - 16 q^{33} - 36 q^{34} - 36 q^{36} + 28 q^{37} - 14 q^{39} + 16 q^{42} - 36 q^{43} + 14 q^{48} - 48 q^{52} + 46 q^{54} - 16 q^{57} - 28 q^{58} + 28 q^{61} + 8 q^{63} - 40 q^{66} + 40 q^{67} - 12 q^{72} + 28 q^{73} - 8 q^{76} + 80 q^{78} + 16 q^{79} + 4 q^{81} + 24 q^{82} + 4 q^{84} + 34 q^{87} + 12 q^{88} + 8 q^{91} - 4 q^{93} + 64 q^{94} + 16 q^{96} - 20 q^{97} + 40 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 - 12 * q^4 - 2 * q^6 + 4 * q^7 + 4 * q^9 - 8 * q^13 - 4 * q^16 - 4 * q^18 - 16 * q^19 + 4 * q^21 - 4 * q^22 + 18 * q^24 - 4 * q^27 - 20 * q^28 + 8 * q^31 - 16 * q^33 - 36 * q^34 - 36 * q^36 + 28 * q^37 - 14 * q^39 + 16 * q^42 - 36 * q^43 + 14 * q^48 - 48 * q^52 + 46 * q^54 - 16 * q^57 - 28 * q^58 + 28 * q^61 + 8 * q^63 - 40 * q^66 + 40 * q^67 - 12 * q^72 + 28 * q^73 - 8 * q^76 + 80 * q^78 + 16 * q^79 + 4 * q^81 + 24 * q^82 + 4 * q^84 + 34 * q^87 + 12 * q^88 + 8 * q^91 - 4 * q^93 + 64 * q^94 + 16 * q^96 - 20 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$-1$	$1$

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 $

$2$	0.619657	+	2.31259i	0.438164	+	1.63525i	0.733380	+	0.679818i	$0.237941\pi$
$2$	0.619657	+	2.31259i	0.438164	+	1.63525i	−0.295217	+	0.955430i	$0.595392\pi$
$3$	−1.64914	−	0.529480i	−0.952129	−	0.305695i
$3$	−1.64914	−	0.529480i	−0.952129	−	0.305695i
$4$	−3.23205	+	1.86603i	−1.61603	+	0.933013i
$5$		0			0
$5$		0			0
$6$	0.202571	−	4.14187i	0.0826993	−	1.69091i
$7$	1.36603	+	0.366025i	0.516309	+	0.138345i	0.507559	−	0.861617i	$-0.330548\pi$
$7$	1.36603	+	0.366025i	0.516309	+	0.138345i	0.00875026	+	0.999962i	$0.497215\pi$
$8$	−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	0.00559833	−	0.999984i	$-0.498218\pi$
$11$	1.69293	−	0.453620i	0.510439	−	0.136772i	0.504840	+	0.863213i	$0.331551\pi$
$12$	6.31812	−	1.36603i	1.82388	−	0.394338i
$13$	1.59808	+	3.23205i	0.443227	+	0.896410i
$13$	1.59808	+	3.23205i	0.443227	+	0.896410i
$14$			3.38587i			0.904911i
$15$		0			0
$16$	1.23205	−	2.13397i	0.308013	−	0.533494i
$17$	1.07328	+	1.85897i	0.260308	+	0.450867i	0.966324	−	0.257330i	$-0.0828426\pi$
$17$	1.07328	+	1.85897i	0.260308	+	0.450867i	−0.706016	+	0.708196i	$0.749509\pi$
$18$	−2.52711	+	6.72326i	−0.595644	+	1.58469i
$19$	−0.267949	+	1.00000i	−0.0614718	+	0.229416i	−0.989826	−	0.142280i	$-0.954557\pi$
$19$	−0.267949	+	1.00000i	−0.0614718	+	0.229416i	0.928355	+	0.371695i	$0.121223\pi$
$20$		0			0
$21$	−2.05896	−	1.32691i	−0.449302	−	0.289555i
$22$	2.09808	+	3.63397i	0.447311	+	0.774766i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	3.28311	+	6.38824i	0.670162	+	1.30399i
$25$		0			0
$26$	−6.48415	+	5.69846i	−1.27165	+	1.11756i
$27$	−3.09808	−	4.17156i	−0.596225	−	0.802817i
$28$	−5.09808	+	1.36603i	−0.963446	+	0.258155i
$29$	−4.79122	−	2.76621i	−0.889707	−	0.513673i	−0.0158603	−	0.999874i	$-0.505049\pi$
$29$	−4.79122	−	2.76621i	−0.889707	−	0.513673i	−0.873847	+	0.486202i	$0.838382\pi$
$30$		0			0
$31$	4.46410	+	4.46410i	0.801776	+	0.801776i	0.983373	−	0.181597i	$-0.0581266\pi$
$31$	4.46410	+	4.46410i	0.801776	+	0.801776i	−0.181597	+	0.983373i	$0.558127\pi$
$32$	−2.31259	−	0.619657i	−0.408812	−	0.109541i
$33$	−3.03206	−	0.148292i	−0.527814	−	0.0258144i
$34$	−3.63397	+	3.63397i	−0.623222	+	0.623222i
$35$		0			0
$36$	−11.1427	−	1.09255i	−1.85712	−	0.182092i
$37$	1.76795	+	6.59808i	0.290649	+	1.08472i	0.944612	+	0.328190i	$0.106439\pi$
$37$	1.76795	+	6.59808i	0.290649	+	1.08472i	−0.653963	+	0.756527i	$0.726895\pi$
$38$	−2.47863			−0.402086
$39$	−0.924141	−	6.17624i	−0.147981	−	0.988990i
$40$		0			0
$41$	0.166037	+	0.619657i	0.0259306	+	0.0967741i	0.977678	−	0.210107i	$-0.0673812\pi$
$41$	0.166037	+	0.619657i	0.0259306	+	0.0967741i	−0.951748	+	0.306881i	$0.900715\pi$
$42$	1.79275	−	5.58376i	0.276627	−	0.861593i
$43$	−7.09808	+	4.09808i	−1.08245	+	0.624951i	−0.931555	−	0.363600i	$-0.881548\pi$
$43$	−7.09808	+	4.09808i	−1.08245	+	0.624951i	−0.150891	+	0.988550i	$0.548214\pi$
$44$	−4.62518	+	4.62518i	−0.697272	+	0.697272i
$45$		0			0
$46$		0			0
$47$	−6.77174	−	6.77174i	−0.987759	−	0.987759i	0.0121668	−	0.999926i	$-0.496127\pi$
$47$	−6.77174	−	6.77174i	−0.987759	−	0.987759i	−0.999926	+	0.0121668i	$0.996127\pi$
$48$	−3.16172	+	2.86687i	−0.456354	+	0.413797i
$49$	−4.33013	−	2.50000i	−0.618590	−	0.357143i
$50$		0			0
$51$	−0.785693	−	3.63397i	−0.110019	−	0.508858i
$52$	−11.1962	−	7.46410i	−1.55263	−	1.03508i
$53$			4.62518i			0.635318i	0.948205	+	0.317659i	$0.102897\pi$
$53$			4.62518i			0.635318i	−0.948205	+	0.317659i	$0.897103\pi$
$54$	7.72737	−	9.74952i	1.05156	−	1.32674i
$55$		0			0
$56$	−2.93225	−	5.07880i	−0.391838	−	0.678683i
$57$	0.971364	−	1.50726i	0.128660	−	0.199642i
$58$	3.42820	−	12.7942i	0.450145	−	1.67996i
$59$	−1.23931	+	4.62518i	−0.161345	+	0.602147i	0.837133	+	0.546999i	$0.184230\pi$
$59$	−1.23931	+	4.62518i	−0.161345	+	0.602147i	−0.998478	+	0.0551484i	$0.982437\pi$
$60$		0			0
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$	−7.55743	+	13.0899i	−0.959794	+	1.66241i
$63$	2.69293	+	3.27843i	0.339278	+	0.413043i
$64$		−	10.6603i		−	1.33253i
$65$		0			0
$66$	−1.53590	−	7.10381i	−0.189056	−	0.874418i
$67$	8.46410	−	2.26795i	1.03405	−	0.277074i	0.298407	−	0.954439i	$-0.403545\pi$
$67$	8.46410	−	2.26795i	1.03405	−	0.277074i	0.735647	+	0.677365i	$0.236878\pi$
$68$	−6.93777	−	4.00552i	−0.841328	−	0.485741i
$69$		0			0
$70$		0			0
$71$	−4.62518	−	1.23931i	−0.548908	−	0.147079i	−0.0263025	−	0.999654i	$-0.508373\pi$
$71$	−4.62518	−	1.23931i	−0.548908	−	0.147079i	−0.522606	+	0.852575i	$0.675040\pi$
$72$	−2.03185	−	12.2734i	−0.239456	−	1.44644i
$73$	6.09808	−	6.09808i	0.713726	−	0.713726i	−0.253587	−	0.967313i	$-0.581610\pi$
$73$	6.09808	−	6.09808i	0.713726	−	0.713726i	0.967313	+	0.253587i	$0.0816103\pi$
$74$	−14.1631	+	8.17709i	−1.64643	+	0.950567i
$75$		0			0
$76$	−1.00000	−	3.73205i	−0.114708	−	0.428096i
$77$	2.47863			0.282466
$78$	13.7105	−	5.96431i	1.55241	−	0.675325i
$79$	2.00000			0.225018			0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000			0.225018			0.112509	+	0.993651i	$0.464111\pi$
$80$		0			0
$81$	2.90039	+	8.51984i	0.322266	+	0.946649i
$82$	−1.33013	+	0.767949i	−0.146888	+	0.0848058i
$83$	−1.23931	+	1.23931i	−0.136032	+	0.136032i	−0.771844	−	0.635812i	$-0.780665\pi$
$83$	−1.23931	+	1.23931i	−0.136032	+	0.136032i	0.635812	+	0.771844i	$0.280665\pi$
$84$	9.13071	+	0.446565i	0.996242	+	0.0487243i
$85$		0			0
$86$	−13.8755	−	13.8755i	−1.49624	−	1.49624i
$87$	6.43672	+	7.09871i	0.690089	+	0.761062i
$88$	−6.29423	−	3.63397i	−0.670967	−	0.387383i
$89$	9.70398	−	2.60017i	1.02862	−	0.275618i	0.295230	−	0.955426i	$-0.404604\pi$
$89$	9.70398	−	2.60017i	1.02862	−	0.275618i	0.733390	+	0.679808i	$0.237937\pi$
$90$		0			0
$91$	1.00000	+	5.00000i	0.104828	+	0.524142i
$92$		0			0
$93$	−4.99826	−	9.72556i	−0.518296	−	1.00849i
$94$	11.4641	−	19.8564i	1.18243	−	2.04803i
$95$		0			0
$96$	3.48568	+	2.24637i	0.355756	+	0.229269i
$97$	−3.36603	+	12.5622i	−0.341768	+	1.27550i	0.554575	+	0.832134i	$0.312881\pi$
$97$	−3.36603	+	12.5622i	−0.341768	+	1.27550i	−0.896343	+	0.443362i	$0.853786\pi$
$98$	3.09828	−	11.5630i	0.312974	−	1.16803i
$99$	4.92177	+	1.84997i	0.494656	+	0.185929i
$100$		0			0
$101$	−9.87002	+	17.0954i	−0.982104	+	1.70105i	−0.327944	+	0.944697i	$0.606356\pi$
$101$	−9.87002	+	17.0954i	−0.982104	+	1.70105i	−0.654160	+	0.756356i	$0.726978\pi$
$102$	7.91704	−	4.06880i	0.783903	−	0.402872i
$103$		−	6.92820i		−	0.682656i	−0.939944	−	0.341328i	$-0.889123\pi$
$103$		−	6.92820i		−	0.682656i	0.939944	−	0.341328i	$-0.110877\pi$
$104$	4.79122	−	14.1631i	0.469818	−	1.38881i
$105$		0			0
$106$	−10.6962	+	2.86603i	−1.03890	+	0.278373i
$107$	14.4507	+	8.34312i	1.39700	+	0.806560i	0.994078	−	0.108673i	$-0.0346600\pi$
$107$	14.4507	+	8.34312i	1.39700	+	0.806560i	0.402925	+	0.915233i	$0.367993\pi$
$108$	17.7974	+	7.70161i	1.71255	+	0.741088i
$109$	−2.80385	−	2.80385i	−0.268560	−	0.268560i	0.559960	−	0.828520i	$-0.310817\pi$
$109$	−2.80385	−	2.80385i	−0.268560	−	0.268560i	−0.828520	+	0.559960i	$0.810817\pi$
$110$		0			0
$111$	0.577958	−	11.8172i	0.0548573	−	1.12164i
$112$	2.46410	−	2.46410i	0.232836	−	0.232836i
$113$	−11.2309	+	6.48415i	−1.05651	+	0.609978i	−0.924465	−	0.381266i	$-0.875488\pi$
$113$	−11.2309	+	6.48415i	−1.05651	+	0.609978i	−0.132047	+	0.991243i	$0.542155\pi$
$114$	4.08759	+	1.31238i	0.382838	+	0.122916i
$115$		0			0
$116$	20.6473			1.91705
$117$	−1.74616	+	10.6748i	−0.161433	+	0.986884i
$118$	−11.4641			−1.05536
$119$	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
$123$	0.0542788	−	1.10981i	0.00489415	−	0.100068i
$124$	−22.7583	−	6.09808i	−2.04376	−	0.547623i
$125$		0			0
$126$	−5.91297	+	8.25916i	−0.526770	+	0.735784i
$127$	−13.0981	−	7.56218i	−1.16227	−	0.671035i	−0.210420	−	0.977611i	$-0.567483\pi$
$127$	−13.0981	−	7.56218i	−1.16227	−	0.671035i	−0.951846	+	0.306576i	$0.900817\pi$
$128$	20.0276	−	5.36639i	1.77021	−	0.474326i
$129$	13.8755	−	3.00000i	1.22167	−	0.264135i
$130$		0			0
$131$		−	0.907241i		−	0.0792660i	−0.999214	−	0.0396330i	$-0.987381\pi$
$131$		−	0.907241i		−	0.0792660i	0.999214	−	0.0396330i	$-0.0126189\pi$
$132$	10.0765	−	5.17862i	0.877046	−	0.450741i
$133$	−0.732051	+	1.26795i	−0.0634769	+	0.109945i
$134$	10.4897	+	18.1687i	0.906170	+	1.56953i
$135$		0			0
$136$	2.30385	−	8.59808i	0.197553	−	0.737279i
$137$	1.52690	−	5.69846i	0.130452	−	0.486852i	−0.869524	−	0.493891i	$-0.835574\pi$
$137$	1.52690	−	5.69846i	0.130452	−	0.486852i	0.999975	+	0.00703925i	$0.00224068\pi$
$138$		0			0
$139$	1.19615	+	2.07180i	0.101456	+	0.175728i	0.912285	−	0.409556i	$-0.134316\pi$
$139$	1.19615	+	2.07180i	0.101456	+	0.175728i	−0.810829	+	0.585284i	$0.800983\pi$
$140$		0			0
$141$	7.58202	+	14.7530i	0.638521	+	1.24243i
$142$		−	11.4641i		−	0.962046i
$143$	4.17156	+	4.74673i	0.348843	+	0.396941i
$144$	6.73205	−	3.05379i	0.561004	−	0.254483i
$145$		0			0
$146$	17.8811	+	10.3236i	1.47985	+	0.854391i
$147$	5.81727	+	6.41556i	0.479800	+	0.529146i
$148$	−18.0263	−	18.0263i	−1.48175	−	1.48175i
$149$	5.24484	+	1.40535i	0.429674	+	0.115131i	0.467173	−	0.884166i	$-0.345272\pi$
$149$	5.24484	+	1.40535i	0.429674	+	0.115131i	−0.0374992	+	0.999297i	$0.511939\pi$
$150$		0			0
$151$	7.46410	−	7.46410i	0.607420	−	0.607420i	−0.334851	−	0.942271i	$-0.608686\pi$
$151$	7.46410	−	7.46410i	0.607420	−	0.607420i	0.942271	+	0.334851i	$0.108686\pi$
$152$	3.71794	−	2.14655i	0.301565	−	0.174109i
$153$	−0.628400	+	6.40893i	−0.0508031	+	0.518131i
$154$	1.53590	+	5.73205i	0.123766	+	0.461902i
$155$		0			0
$156$	14.5119	+	18.2375i	1.16188	+	1.46017i
$157$	15.1962			1.21278			0.606392	−	0.795165i	$-0.292616\pi$
$157$	15.1962			1.21278			0.606392	+	0.795165i	$0.292616\pi$
$158$	1.23931	+	4.62518i	0.0985945	+	0.367960i
$159$	2.44894	−	7.62756i	0.194214	−	0.604905i
$160$		0			0
$161$		0			0
$162$	−17.9057	+	11.9868i	−1.40680	+	0.941772i
$163$	14.9282	+	4.00000i	1.16927	+	0.313304i	0.790661	−	0.612254i	$-0.209737\pi$
$163$	14.9282	+	4.00000i	1.16927	+	0.313304i	0.378606	+	0.925558i	$0.376404\pi$
$164$	−1.69293	−	1.69293i	−0.132196	−	0.132196i
$165$		0			0
$166$	−3.63397	−	2.09808i	−0.282051	−	0.162842i
$167$	11.3969	−	3.05379i	0.881920	−	0.236310i	0.210685	−	0.977554i	$-0.432431\pi$
$167$	11.3969	−	3.05379i	0.881920	−	0.236310i	0.671235	+	0.741244i	$0.265764\pi$
$168$	2.14655	+	9.92820i	0.165610	+	0.765978i
$169$	−7.89230	+	10.3301i	−0.607100	+	0.794625i
$170$		0			0
$171$	−2.39998	+	1.97136i	−0.183531	+	0.150754i
$172$	15.2942	−	26.4904i	1.16617	−	2.01987i
$173$	3.71794	+	6.43966i	0.282670	+	0.489598i	0.972041	−	0.234809i	$-0.0754466\pi$
$173$	3.71794	+	6.43966i	0.282670	+	0.489598i	−0.689372	+	0.724408i	$0.742113\pi$
$174$	−12.4279	+	19.2843i	−0.942154	+	1.46194i
$175$		0			0
$176$	1.11777	−	4.17156i	0.0842548	−	0.314443i
$177$	4.49274	−	6.97136i	0.337695	−	0.524000i
$178$	12.0263	+	20.8301i	0.901408	+	1.56128i
$179$	9.37191	−	16.2326i	0.700489	−	1.21328i	−0.267805	−	0.963473i	$-0.586298\pi$
$179$	9.37191	−	16.2326i	0.700489	−	1.21328i	0.968295	−	0.249810i	$-0.0803683\pi$
$180$		0			0
$181$		−	3.00000i		−	0.222988i	−0.993765	−	0.111494i	$-0.964436\pi$
$181$		−	3.00000i		−	0.222988i	0.993765	−	0.111494i	$-0.0355636\pi$
$182$	−10.9433	+	5.41087i	−0.811171	+	0.401081i
$183$	−2.56218	−	11.8505i	−0.189402	−	0.876017i
$184$		0			0
$185$		0			0
$186$	19.3940	−	17.5854i	1.42204	−	1.28943i
$187$	2.66025	+	2.66025i	0.194537	+	0.194537i
$188$	34.5228	+	9.25036i	2.51784	+	0.674652i
$189$	−2.70515	−	6.83243i	−0.196771	−	0.496986i
$190$		0			0
$191$	16.8078	−	9.70398i	1.21617	−	0.702156i	0.252073	−	0.967708i	$-0.418888\pi$
$191$	16.8078	−	9.70398i	1.21617	−	0.702156i	0.964096	+	0.265553i	$0.0855544\pi$
$192$	−5.64439	+	17.5802i	−0.407349	+	1.26874i
$193$	−1.86603	−	6.96410i	−0.134319	−	0.501287i	−1.00000		0.000689767i	$-0.999780\pi$
$193$	−1.86603	−	6.96410i	−0.134319	−	0.501287i	0.865680	−	0.500597i	$-0.166886\pi$
$194$	−31.1370			−2.23550
$195$		0			0
$196$	18.6603			1.33288
$197$	−0.453620	−	1.69293i	−0.0323191	−	0.120617i	0.947882	−	0.318622i	$-0.103220\pi$
$197$	−0.453620	−	1.69293i	−0.0323191	−	0.120617i	−0.980201	+	0.198006i	$0.936554\pi$
$198$	−1.22842	+	12.5284i	−0.0872998	+	0.890353i
$199$	0.803848	−	0.464102i	0.0569832	−	0.0328993i	−0.471238	−	0.882006i	$-0.656193\pi$
$199$	0.803848	−	0.464102i	0.0569832	−	0.0328993i	0.528221	+	0.849107i	$0.322859\pi$
$200$		0			0
$201$	−15.1593	−	0.741412i	−1.06925	−	0.0522952i
$202$	−45.6506	−	12.2321i	−3.21197	−	0.860644i
$203$	−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
$208$	8.86603	+	0.571797i	0.614748	+	0.0396470i
$209$			1.81448i			0.125510i
$210$		0			0
$211$	6.09808	−	10.5622i	0.419809	−	0.727130i	−0.576111	−	0.817371i	$-0.695430\pi$
$211$	6.09808	−	10.5622i	0.419809	−	0.727130i	0.995920	+	0.0902411i	$0.0287638\pi$
$212$	−8.63071	−	14.9488i	−0.592759	−	1.02669i
$213$	6.97136	+	4.49274i	0.477670	+	0.307837i
$214$	−10.3397	+	38.5885i	−0.706810	+	2.63785i
$215$		0			0
$216$	−3.14772	+	21.3164i	−0.214176	+	1.45040i
$217$	4.46410	+	7.73205i	0.303043	+	0.524886i
$218$	4.74673	−	8.22158i	0.321489	−	0.556835i
$219$	−13.2854	+	6.82775i	−0.897742	+	0.461377i
$220$		0			0
$221$	−4.29311	+	6.43966i	−0.288786	+	0.433179i
$222$	27.6865	−	5.98604i	1.85820	−	0.401757i
$223$	−22.2942	+	5.97372i	−1.49293	+	0.400030i	−0.910726	−	0.413011i	$-0.864477\pi$
$223$	−22.2942	+	5.97372i	−1.49293	+	0.400030i	−0.582206	+	0.813041i	$0.697810\pi$
$224$	−2.93225	−	1.69293i	−0.195919	−	0.113114i
$225$		0			0
$226$	−21.9545	−	21.9545i	−1.46039	−	1.46039i
$227$	−15.1149	−	4.05001i	−1.00321	−	0.268809i	−0.280419	−	0.959878i	$-0.590474\pi$
$227$	−15.1149	−	4.05001i	−1.00321	−	0.268809i	−0.722789	+	0.691069i	$0.757140\pi$
$228$	−0.326909	+	6.68414i	−0.0216500	+	0.442668i
$229$	10.1244	−	10.1244i	0.669036	−	0.669036i	−0.288457	−	0.957493i	$-0.593142\pi$
$229$	10.1244	−	10.1244i	0.669036	−	0.669036i	0.957493	+	0.288457i	$0.0931421\pi$
$230$		0			0
$231$	−4.08759	−	1.31238i	−0.268944	−	0.0863485i
$232$	5.93782	+	22.1603i	0.389837	+	1.45489i
$233$	−7.43588			−0.487141			−0.243570	−	0.969883i	$-0.578319\pi$
$233$	−7.43588			−0.487141			−0.243570	+	0.969883i	$0.578319\pi$
$234$	−25.7684	+	2.57655i	−1.68453	+	0.168434i
$235$		0			0
$236$	−4.62518	−	17.2614i	−0.301074	−	1.12362i
$237$	−3.29827	−	1.05896i	−0.214246	−	0.0687868i
$238$	−6.29423	+	3.63397i	−0.407994	+	0.235556i
$239$	7.10381	−	7.10381i	0.459507	−	0.459507i	−0.438986	−	0.898494i	$-0.644662\pi$
$239$	7.10381	−	7.10381i	0.459507	−	0.459507i	0.898494	+	0.438986i	$0.144662\pi$
$240$		0			0
$241$	7.23205	+	1.93782i	0.465857	+	0.124826i	0.484110	−	0.875007i	$-0.339144\pi$
$241$	7.23205	+	1.93782i	0.465857	+	0.124826i	−0.0182524	+	0.999833i	$0.505810\pi$
$242$	−13.4219	−	13.4219i	−0.862794	−	0.862794i
$243$	−0.272062	−	15.5861i	−0.0174528	−	0.999848i
$244$	−22.6244	−	13.0622i	−1.44838	−	0.836220i
$245$		0			0
$246$	2.60017	−	0.562178i	0.165781	−	0.0358431i
$247$	−3.66025	+	0.732051i	−0.232896	+	0.0465793i
$248$		−	26.1797i		−	1.66241i
$249$	2.69999	−	1.38761i	0.171105	−	0.0879360i
$250$		0			0
$251$	10.9433	+	18.9543i	0.690735	+	1.19639i	0.971597	+	0.236640i	$0.0760461\pi$
$251$	10.9433	+	18.9543i	0.690735	+	1.19639i	−0.280863	+	0.959748i	$0.590621\pi$
$252$	−14.8213	−	5.57097i	−0.933656	−	0.350938i
$253$		0			0
$254$	9.37191	−	34.9764i	0.588046	−	2.19462i
$255$		0			0
$256$	14.1603	+	24.5263i	0.885016	+	1.53289i
$257$	8.29863	−	14.3737i	0.517655	−	0.896604i	−0.482135	−	0.876097i	$-0.660139\pi$
$257$	8.29863	−	14.3737i	0.517655	−	0.896604i	0.999790	−	0.0205071i	$-0.00652807\pi$
$258$	15.5358	+	30.2295i	0.967220	+	1.88201i
$259$			9.66025i			0.600259i
$260$		0			0
$261$	−6.85641	−	15.1149i	−0.424401	−	0.935586i
$262$	2.09808	−	0.562178i	0.129620	−	0.0347315i
$263$	10.3681	+	5.98604i	0.639326	+	0.369115i	0.784355	−	0.620312i	$-0.212994\pi$
$263$	10.3681	+	5.98604i	0.639326	+	0.369115i	−0.145029	+	0.989427i	$0.546327\pi$
$264$	8.45593	+	9.32559i	0.520426	+	0.573950i
$265$		0			0
$266$	−3.38587	−	0.907241i	−0.207601	−	0.0556265i
$267$	−17.3799	−	0.850019i	−1.06363	−	0.0520203i
$268$	−23.1244	+	23.1244i	−1.41254	+	1.41254i
$269$	−9.58244	+	5.53242i	−0.584251	+	0.337318i	−0.762821	−	0.646610i	$-0.776186\pi$
$269$	−9.58244	+	5.53242i	−0.584251	+	0.337318i	0.178570	+	0.983927i	$0.442853\pi$
$270$		0			0
$271$	0.535898	+	2.00000i	0.0325535	+	0.121491i	0.980291	−	0.197561i	$-0.0633021\pi$
$271$	0.535898	+	2.00000i	0.0325535	+	0.121491i	−0.947737	+	0.319052i	$0.896635\pi$
$272$	5.28933			0.320713
$273$	0.998262	−	8.77516i	0.0604176	−	0.531097i
$274$	14.1244			0.853284
$275$		0			0
$276$		0			0
$277$	−3.10770	+	1.79423i	−0.186723	+	0.107805i	−0.590448	−	0.807076i	$-0.701049\pi$
$277$	−3.10770	+	1.79423i	−0.186723	+	0.107805i	0.403724	+	0.914881i	$0.367715\pi$
$278$	−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	0.0501922	−	0.998740i	$-0.484017\pi$
$281$	−15.9006	−	15.9006i	−0.948547	−	0.948547i	−0.998740	+	0.0501922i	$0.984017\pi$
$282$	−29.4194	+	26.6759i	−1.75190	+	1.58853i
$283$	21.2942	+	12.2942i	1.26581	+	0.730816i	0.974192	−	0.225719i	$-0.0724731\pi$
$283$	21.2942	+	12.2942i	1.26581	+	0.730816i	0.291618	+	0.956535i	$0.405806\pi$
$284$	17.2614	−	4.62518i	1.02428	−	0.274454i
$285$		0			0
$286$	−8.39230	+	12.5885i	−0.496247	+	0.744371i
$287$			0.907241i			0.0535527i
$288$	−4.55896	−	5.55017i	−0.268639	−	0.327047i
$289$	6.19615	−	10.7321i	0.364480	−	0.631297i
$290$		0			0
$291$	12.2025	−	18.9345i	0.715320	−	1.10996i
$292$	−8.33013	+	31.0885i	−0.487484	+	1.81931i
$293$	−5.69846	+	21.2669i	−0.332908	+	1.24243i	0.573212	+	0.819407i	$0.305697\pi$
$293$	−5.69846	+	21.2669i	−0.332908	+	1.24243i	−0.906120	+	0.423021i	$0.860970\pi$
$294$	−11.2318	+	17.4284i	−0.655054	+	1.01645i
$295$		0			0
$296$	14.1631	−	24.5313i	0.823215	−	1.42585i
$297$	−7.13714	−	5.65683i	−0.414139	−	0.328242i
$298$			13.0000i			0.753070i
$299$		0			0
$300$		0			0
$301$	−11.1962	+	3.00000i	−0.645335	+	0.172917i
$302$	21.8866	+	12.6362i	1.25943	+	0.727133i
$303$	25.3287	−	22.9666i	1.45509	−	1.31940i
$304$	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	$0.0832919\pi$
$308$	−8.01105	+	4.62518i	−0.456472	+	0.263544i
$309$	−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	$0.538841\pi$
$312$	−15.4005	+	20.8201i	−0.871879	+	1.17870i
$313$	−2.00000			−0.113047			−0.0565233	−	0.998401i	$-0.518002\pi$
$313$	−2.00000			−0.113047			−0.0565233	+	0.998401i	$0.518002\pi$
$314$	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	$0.102207\pi$
$318$	19.1569	+	0.936928i	1.07427	+	0.0525403i
$319$	−9.36603	−	2.50962i	−0.524397	−	0.140512i
$320$		0			0
$321$	−19.4137	−	21.4103i	−1.08357	−	1.19501i
$322$		0			0
$323$	−2.14655	+	0.575167i	−0.119437	+	0.0320032i
$324$	−25.2725	−	22.1244i	−1.40403	−	1.22913i
$325$		0			0
$326$			37.0015i			2.04932i
$327$	3.13935	+	6.10851i	0.173606	+	0.337801i
$328$	1.33013	−	2.30385i	0.0734440	−	0.127209i
$329$	−6.77174	−	11.7290i	−0.373338	−	0.646640i
$330$		0			0
$331$	5.05256	−	18.8564i	0.277714	−	1.03644i	−0.676287	−	0.736638i	$-0.736412\pi$
$331$	5.05256	−	18.8564i	0.277714	−	1.03644i	0.954001	−	0.299804i	$-0.0969212\pi$
$332$	1.69293	−	6.31812i	0.0929118	−	0.346752i
$333$	−7.21011	+	19.1822i	−0.395112	+	1.05118i
$334$	14.1244	+	24.4641i	0.772850	+	1.33862i
$335$		0			0
$336$	−5.36833	+	2.75895i	−0.292867	+	0.150513i
$337$		−	11.5359i		−	0.628400i	−0.949357	−	0.314200i	$-0.898264\pi$
$337$		−	11.5359i		−	0.628400i	0.949357	−	0.314200i	$-0.101736\pi$
$338$	−28.7799	−	11.8505i	−1.56542	−	0.644584i
$339$	21.9545	−	4.74673i	1.19240	−	0.257807i
$340$		0			0
$341$	9.58244	+	5.53242i	0.518918	+	0.299597i
$342$	−6.04612	−	4.32860i	−0.326937	−	0.234064i
$343$	−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
$347$	22.4618	−	12.9683i	1.20581	−	0.696175i	0.243969	−	0.969783i	$-0.421550\pi$
$347$	22.4618	−	12.9683i	1.20581	−	0.696175i	0.961841	+	0.273608i	$0.0882171\pi$
$348$	−34.0502	−	10.9323i	−1.82528	−	0.586034i
$349$	1.50962	+	5.63397i	0.0808080	+	0.301580i	0.994487	−	0.104856i	$-0.0334382\pi$
$349$	1.50962	+	5.63397i	0.0808080	+	0.301580i	−0.913679	+	0.406436i	$0.866772\pi$
$350$		0			0
$351$	8.53174	−	16.6796i	0.455390	−	0.890292i
$352$	−4.19615			−0.223656
$353$	7.05932	+	26.3457i	0.375730	+	1.40224i	0.852276	+	0.523093i	$0.175222\pi$
$353$	7.05932	+	26.3457i	0.375730	+	1.40224i	−0.476546	+	0.879149i	$0.658111\pi$
$354$	18.9059	+	6.07001i	1.00484	+	0.322617i
$355$		0			0
$356$	−26.5118	+	26.5118i	−1.40512	+	1.40512i
$357$	0.256850	−	5.25169i	0.0135939	−	0.277949i
$358$	43.3468	+	11.6147i	2.29095	+	0.613858i
$359$	12.0611	+	12.0611i	0.636559	+	0.636559i	0.949705	−	0.313146i	$-0.101383\pi$
$359$	12.0611	+	12.0611i	0.636559	+	0.636559i	−0.313146	+	0.949705i	$0.601383\pi$
$360$		0			0
$361$	15.5263	+	8.96410i	0.817173	+	0.471795i
$362$	6.93777	−	1.85897i	0.364641	−	0.0977053i
$363$	13.4219	−	2.90192i	0.704468	−	0.152311i
$364$	−12.5622	−	14.2942i	−0.658437	−	0.749221i
$365$		0			0
$366$	25.8178	−	13.2685i	1.34952	−	0.693557i
$367$	4.80385	−	8.32051i	0.250759	−	0.434327i	−0.712976	−	0.701188i	$-0.752653\pi$
$367$	4.80385	−	8.32051i	0.250759	−	0.434327i	0.963735	+	0.266861i	$0.0859866\pi$
$368$		0			0
$369$	−0.677136	+	1.80149i	−0.0352503	+	0.0937819i
$370$		0			0
$371$	−1.69293	+	6.31812i	−0.0878928	+	0.328020i
$372$	34.3028	+	22.1066i	1.77852	+	1.14618i
$373$	−9.79423	−	16.9641i	−0.507126	−	0.878368i	−0.999966	−	0.00824796i	$-0.997375\pi$
$373$	−9.79423	−	16.9641i	−0.507126	−	0.878368i	0.492840	−	0.870120i	$-0.335959\pi$
$374$	−4.50363	+	7.80052i	−0.232877	+	0.403355i
$375$		0			0
$376$			39.7128i			2.04803i
$377$	1.28380	−	19.9061i	0.0661192	−	1.02522i
$378$	14.1244	−	10.4897i	0.726478	−	0.539531i
$379$	−4.83013	+	1.29423i	−0.248107	+	0.0664801i	−0.380729	−	0.924687i	$-0.624327\pi$
$379$	−4.83013	+	1.29423i	−0.248107	+	0.0664801i	0.132622	+	0.991167i	$0.457660\pi$
$380$		0			0
$381$	17.5965	+	19.4062i	0.901496	+	0.994211i
$382$	32.8564	+	32.8564i	1.68108	+	1.68108i
$383$	−13.5435	−	3.62896i	−0.692039	−	0.185431i	−0.104377	−	0.994538i	$-0.533285\pi$
$383$	−13.5435	−	3.62896i	−0.692039	−	0.185431i	−0.587662	+	0.809106i	$0.699952\pi$
$384$	−35.8697	−	1.75432i	−1.83047	−	0.0895246i
$385$		0			0
$386$	14.9488	−	8.63071i	0.760875	−	0.439291i
$387$	−24.4711	−	2.39941i	−1.24394	−	0.121969i
$388$	−12.5622	−	46.8827i	−0.637748	−	2.38011i
$389$	5.28933			0.268180			0.134090	−	0.990969i	$-0.457189\pi$
$389$	5.28933			0.268180			0.134090	+	0.990969i	$0.457189\pi$
$390$		0			0
$391$		0			0
$392$	5.36639	+	20.0276i	0.271043	+	1.01155i
$393$	−0.480365	+	1.49616i	−0.0242312	+	0.0754715i
$394$	3.63397	−	2.09808i	0.183077	−	0.105700i
$395$		0			0
$396$	−19.3595	+	3.20495i	−0.972851	+	0.161055i
$397$	−8.56218	−	2.29423i	−0.429723	−	0.115144i	0.0374729	−	0.999298i	$-0.488069\pi$
$397$	−8.56218	−	2.29423i	−0.429723	−	0.115144i	−0.467196	+	0.884154i	$0.654736\pi$
$398$	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	−0.861933	−	0.507021i	$-0.830747\pi$
$401$	−27.1314	+	7.26985i	−1.35488	+	0.363039i	−0.492946	+	0.870060i	$0.664080\pi$
$402$	−7.67898	−	35.5167i	−0.382993	−	1.77141i
$403$	−7.29423	+	21.5622i	−0.363351	+	1.07409i
$404$		−	73.6708i		−	3.66526i
$405$		0			0
$406$	9.36603	−	16.2224i	0.464828	−	0.805106i
$407$	5.98604	+	10.3681i	0.296717	+	0.513929i
$408$	−8.35187	+	12.9596i	−0.413479	+	0.641594i
$409$	3.00962	−	11.2321i	0.148816	−	0.555389i	−0.850740	−	0.525587i	$-0.823846\pi$
$409$	3.00962	−	11.2321i	0.148816	−	0.555389i	0.999556	−	0.0298020i	$-0.00948767\pi$
$410$		0			0
$411$	−5.53528	+	8.58908i	−0.273035	+	0.423668i
$412$	12.9282	+	22.3923i	0.636927	+	1.10319i
$413$	−3.38587	+	5.86450i	−0.166608	+	0.288573i
$414$		0			0
$415$		0			0
$416$	−1.69293	−	8.46467i	−0.0830029	−	0.415015i
$417$	−0.875644	−	4.05001i	−0.0428805	−	0.198330i
$418$	−4.19615	+	1.12436i	−0.205241	+	0.0549940i
$419$	7.22536	+	4.17156i	0.352982	+	0.203794i	0.665998	−	0.745954i	$-0.268006\pi$
$419$	7.22536	+	4.17156i	0.352982	+	0.203794i	−0.313016	+	0.949748i	$0.601339\pi$
$420$		0			0
$421$	0.830127	+	0.830127i	0.0404579	+	0.0404579i	0.727046	−	0.686588i	$-0.240893\pi$
$421$	0.830127	+	0.830127i	0.0404579	+	0.0404579i	−0.686588	+	0.727046i	$0.740893\pi$
$422$	28.2047	+	7.55743i	1.37298	+	0.367890i
$423$	−4.69237	−	28.3443i	−0.228151	−	1.37815i
$424$	13.5622	−	13.5622i	0.658638	−	0.658638i
$425$		0			0
$426$	−6.07001	+	18.9059i	−0.294093	+	0.915992i
$427$	2.56218	+	9.56218i	0.123992	+	0.462746i
$428$	−62.2739			−3.01012
$429$	−4.36618	−	10.0368i	−0.210801	−	0.484579i
$430$		0			0
$431$	−0.542599	−	2.02501i	−0.0261361	−	0.0975412i	0.951626	−	0.307260i	$-0.0994120\pi$
$431$	−0.542599	−	2.02501i	−0.0261361	−	0.0975412i	−0.977762	+	0.209718i	$0.932745\pi$
$432$	−12.7190	+	1.47164i	−0.611943	+	0.0708043i
$433$	6.10770	−	3.52628i	0.293517	−	0.169462i	−0.346010	−	0.938231i	$-0.612464\pi$
$433$	6.10770	−	3.52628i	0.293517	−	0.169462i	0.639527	+	0.768769i	$0.279130\pi$
$434$	−15.1149	+	15.1149i	−0.725536	+	0.725536i
$435$		0			0
$436$	14.2942	+	3.83013i	0.684569	+	0.183430i
$437$		0			0
$438$	−24.0222	−	26.4928i	−1.14782	−	1.26587i
$439$	−4.09808	−	2.36603i	−0.195591	−	0.112924i	0.399007	−	0.916948i	$-0.369355\pi$
$439$	−4.09808	−	2.36603i	−0.195591	−	0.112924i	−0.594597	+	0.804024i	$0.702688\pi$
$440$		0			0
$441$	−6.19657	−	13.6603i	−0.295075	−	0.650488i
$442$	−17.5526	−	5.93782i	−0.834890	−	0.282433i
$443$		−	29.5656i		−	1.40470i	−0.711830	−	0.702351i	$-0.752134\pi$
$443$		−	29.5656i		−	1.40470i	0.711830	−	0.702351i	$-0.247866\pi$
$444$	20.1832	+	39.2723i	0.957855	+	1.86378i
$445$		0			0
$446$	−27.6295	−	47.8558i	−1.30830	−	2.26604i
$447$	−7.90535	−	5.09465i	−0.373910	−	0.240969i
$448$	3.90192	−	14.5622i	0.184349	−	0.687998i
$449$	2.26810	−	8.46467i	0.107038	−	0.399472i	−0.891530	−	0.452961i	$-0.850368\pi$
$449$	2.26810	−	8.46467i	0.107038	−	0.399472i	0.998568	+	0.0534890i	$0.0170342\pi$
$450$		0			0
$451$	0.562178	+	0.973721i	0.0264719	+	0.0458507i
$452$	24.1992	−	41.9142i	1.13823	−	1.97148i
$453$	−16.2614	+	8.35723i	−0.764028	+	0.392657i
$454$		−	37.4641i		−	1.75828i
$455$		0			0
$456$	−7.26795	+	1.57139i	−0.340353	+	0.0735869i
$457$	26.9904	−	7.23205i	1.26256	−	0.338301i	0.435382	−	0.900246i	$-0.356613\pi$
$457$	26.9904	−	7.23205i	1.26256	−	0.338301i	0.827175	+	0.561945i	$0.189947\pi$
$458$	29.6871	+	17.1399i	1.38719	+	0.800893i
$459$	4.42972	−	10.2365i	0.206761	−	0.477798i
$460$		0			0
$461$	23.4135	+	6.27363i	1.09048	+	0.292192i	0.758880	−	0.651230i	$-0.225747\pi$
$461$	23.4135	+	6.27363i	1.09048	+	0.292192i	0.331595	+	0.943422i	$0.392413\pi$
$462$	0.502098	−	10.2662i	0.0233597	−	0.477625i
$463$	15.0526	−	15.0526i	0.699552	−	0.699552i	−0.264762	−	0.964314i	$-0.585293\pi$
$463$	15.0526	−	15.0526i	0.699552	−	0.699552i	0.964314	+	0.264762i	$0.0852934\pi$
$464$	−11.8060	+	6.81623i	−0.548082	+	0.316435i
$465$		0			0
$466$	−4.60770	−	17.1962i	−0.213447	−	0.796596i
$467$	−30.4728			−1.41011			−0.705057	−	0.709151i	$-0.749079\pi$
$467$	−30.4728			−1.41011			−0.705057	+	0.709151i	$0.749079\pi$
$468$	−14.2757	−	37.7598i	−0.659896	−	1.74545i
$469$	12.3923			0.572223
$470$		0			0
$471$	−25.0605	−	8.04605i	−1.15473	−	0.370743i
$472$	17.1962	−	9.92820i	0.791517	−	0.456983i
$473$	−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
$477$	−8.07727	+	11.2822i	−0.369833	+	0.516577i
$478$	20.8301	+	12.0263i	0.952748	+	0.550069i
$479$	−8.46467	+	2.26810i	−0.386761	+	0.103632i	−0.446959	−	0.894554i	$-0.647493\pi$
$479$	−8.46467	+	2.26810i	−0.386761	+	0.103632i	0.0601988	+	0.998186i	$0.480827\pi$
$480$		0			0
$481$	−18.5000	+	16.2583i	−0.843527	+	0.741316i
$482$			17.9256i			0.816487i
$483$		0			0
$484$	14.7942	−	25.6244i	0.672465	−	1.16474i
$485$		0			0
$486$	35.8756	−	10.2872i	1.62735	−	0.466636i
$487$	6.56218	−	24.4904i	0.297361	−	1.10977i	−0.641964	−	0.766735i	$-0.721880\pi$
$487$	6.56218	−	24.4904i	0.297361	−	1.10977i	0.939324	−	0.343030i	$-0.111453\pi$
$488$	7.51294	−	28.0387i	0.340095	−	1.26925i
$489$	−22.5007	−	14.5007i	−1.01752	−	0.655746i
$490$		0			0
$491$	12.5147	−	21.6761i	0.564780	−	0.978227i	−0.432290	−	0.901734i	$-0.642294\pi$
$491$	12.5147	−	21.6761i	0.564780	−	0.978227i	0.997070	−	0.0764928i	$-0.0243722\pi$
$492$	1.89551	+	3.68825i	0.0854560	+	0.166279i
$493$		−	11.8756i		−	0.534852i
$494$	−3.96104	−	8.01105i	−0.178215	−	0.360434i
$495$		0			0
$496$	15.0263	−	4.02628i	0.674700	−	0.180785i
$497$	−5.86450	−	3.38587i	−0.263059	−	0.151877i
$498$	4.88203	+	5.38413i	0.218769	+	0.241269i
$499$	4.46410	+	4.46410i	0.199841	+	0.199841i	0.799932	−	0.600091i	$-0.204869\pi$
$499$	4.46410	+	4.46410i	0.199841	+	0.199841i	−0.600091	+	0.799932i	$0.704869\pi$
$500$		0			0
$501$	−20.4120	−	0.998312i	−0.911941	−	0.0446013i
$502$	−37.0526	+	37.0526i	−1.65374	+	1.65374i
$503$	24.8188	−	14.3292i	1.10662	−	0.638906i	0.168666	−	0.985673i	$-0.446054\pi$
$503$	24.8188	−	14.3292i	1.10662	−	0.638906i	0.937951	+	0.346767i	$0.112721\pi$
$504$	1.71682	−	17.5095i	0.0764733	−	0.779936i
$505$		0			0
$506$		0			0
$507$	18.4851	−	12.8570i	0.820951	−	0.570998i
$508$	56.4449			2.50434
$509$	3.88398	+	14.4952i	0.172154	+	0.642489i	0.997019	+	0.0771582i	$0.0245846\pi$
$509$	3.88398	+	14.4952i	0.172154	+	0.642489i	−0.824865	+	0.565330i	$0.808749\pi$
$510$		0			0
$511$	10.5622	−	6.09808i	0.467243	−	0.269763i
$512$	−18.6223	+	18.6223i	−0.822996	+	0.822996i
$513$	5.00169	−	1.98031i	0.220830	−	0.0874328i
$514$	38.3827	+	10.2846i	1.69299	+	0.453635i
$515$		0			0
$516$	−39.2484	+	35.5883i	−1.72781	+	1.56669i
$517$	−14.5359	−	8.39230i	−0.639288	−	0.369093i
$518$	−22.3402	+	5.98604i	−0.981573	+	0.263012i
$519$	−2.72172	−	12.5885i	−0.119470	−	0.552572i
$520$		0			0
$521$			33.2835i			1.45818i	0.684419	+	0.729089i	$0.260056\pi$
$521$			33.2835i			1.45818i	−0.684419	+	0.729089i	$0.739944\pi$
$522$	30.7059	−	25.2221i	1.34396	−	1.10394i
$523$	6.49038	−	11.2417i	0.283805	−	0.491564i	−0.688514	−	0.725223i	$-0.741737\pi$
$523$	6.49038	−	11.2417i	0.283805	−	0.491564i	0.972319	+	0.233659i	$0.0750700\pi$
$524$	1.69293	+	2.93225i	0.0739562	+	0.128096i
$525$		0			0
$526$	−7.41858	+	27.6865i	−0.323466	+	1.20719i
$527$	−3.50742	+	13.0899i	−0.152785	+	0.570203i
$528$	−4.05211	+	6.28764i	−0.176345	+	0.273634i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$	−11.1003	+	9.11792i	−0.481713	+	0.395684i
$532$		−	5.46410i		−	0.236899i
$533$	−1.73742	+	1.52690i	−0.0752562	+	0.0661373i
$534$	−8.80385	−	40.7194i	−0.380980	−	1.76210i
$535$		0			0
$536$	−31.4690	−	18.1687i	−1.35926	−	0.784766i
$537$	−24.0504	+	21.8076i	−1.03785	+	0.941066i
$538$	−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	0.0185354	−	0.999828i	$-0.494100\pi$
$541$	23.6865	−	23.6865i	1.01836	−	1.01836i	0.999828	−	0.0185354i	$-0.00590034\pi$
$542$	−4.29311	+	2.47863i	−0.184405	+	0.106466i
$543$	−1.58844	+	4.94741i	−0.0681664	+	0.212314i
$544$	−1.33013	−	4.96410i	−0.0570287	−	0.212834i
$545$		0			0
$546$	20.9119	−	3.12902i	0.894948	−	0.133910i
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$	5.69846	+	21.2669i	0.243426	+	0.908479i
$549$	−2.04924	+	20.8998i	−0.0874593	+	0.891981i
$550$		0			0
$551$	4.05001	−	4.05001i	0.172536	−	0.172536i
$552$		0			0
$553$	2.73205	+	0.732051i	0.116179	+	0.0311300i
$554$	−6.07502	−	6.07502i	−0.258103	−	0.258103i
$555$		0			0
$556$	−7.73205	−	4.46410i	−0.327912	−	0.189320i
$557$	−39.3140	+	10.5342i	−1.66579	+	0.446347i	−0.963971	−	0.266009i	$-0.914295\pi$
$557$	−39.3140	+	10.5342i	−1.66579	+	0.446347i	−0.701819	+	0.712355i	$0.747628\pi$
$558$	−41.2946	+	18.7321i	−1.74814	+	0.792991i
$559$	−24.5885	−	16.3923i	−1.03998	−	0.693321i
$560$		0			0
$561$	−2.97857	−	5.79567i	−0.125755	−	0.244693i
$562$	26.9186	−	46.6244i	1.13549	−	1.96673i
$563$	2.14655	+	3.71794i	0.0904665	+	0.156693i	0.907708	−	0.419603i	$-0.137831\pi$
$563$	2.14655	+	3.71794i	0.0904665	+	0.156693i	−0.817241	+	0.576296i	$0.804498\pi$
$564$	−52.0350	−	33.5342i	−2.19107	−	1.41205i
$565$		0			0
$566$	−15.2364	+	56.8630i	−0.640434	+	2.39013i
$567$	0.843533	+	12.6999i	0.0354250	+	0.533347i
$568$	9.92820	+	17.1962i	0.416578	+	0.721535i
$569$	−8.01105	+	13.8755i	−0.335841	+	0.581693i	−0.983646	−	0.180113i	$-0.942354\pi$
$569$	−8.01105	+	13.8755i	−0.335841	+	0.581693i	0.647805	+	0.761806i	$0.275687\pi$
$570$		0			0
$571$		−	40.0526i		−	1.67615i	−0.545557	−	0.838074i	$-0.683682\pi$
$571$		−	40.0526i		−	1.67615i	0.545557	−	0.838074i	$-0.316318\pi$
$572$	−22.3402	−	7.55743i	−0.934091	−	0.315992i
$573$	−32.8564	+	7.10381i	−1.37260	+	0.296766i
$574$	−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	0.630711	−	0.776018i	$-0.282763\pi$
$577$	−3.49038	−	3.49038i	−0.145306	−	0.145306i	−0.776018	+	0.630711i	$0.782763\pi$
$578$	28.6583	+	7.67898i	1.19203	+	0.319403i
$579$	−0.610020	+	12.4728i	−0.0253516	+	0.518351i
$580$		0			0
$581$	−2.14655	+	1.23931i	−0.0890541	+	0.0514154i
$582$	51.3491	+	16.4864i	2.12849	+	0.683383i
$583$	2.09808	+	7.83013i	0.0868934	+	0.324291i
$584$	−35.7621			−1.47985
$585$		0			0
$586$	−52.7128			−2.17755
$587$	5.20035	+	19.4080i	0.214641	+	0.801053i	0.986292	+	0.165006i	$0.0527645\pi$
$587$	5.20035	+	19.4080i	0.214641	+	0.801053i	−0.771651	+	0.636046i	$0.780569\pi$
$588$	−30.7733	−	9.88023i	−1.26907	−	0.407454i
$589$	−5.66025	+	3.26795i	−0.233227	+	0.134654i
$590$		0			0
$591$	−0.148292	+	3.03206i	−0.00609993	+	0.124722i
$592$	16.2583	+	4.35641i	0.668213	+	0.179047i
$593$	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
$597$	−1.57139	+	0.339746i	−0.0643126	+	0.0139049i
$598$		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	−0.778205	−	0.628010i	$-0.783870\pi$
$601$	3.79423	−	6.57180i	0.154770	−	0.268069i	0.932975	+	0.359941i	$0.117203\pi$
$602$	−13.8755	−	24.0331i	−0.565525	−	0.979518i
$603$	24.6072	+	9.24923i	1.00208	+	0.376658i
$604$	−10.1962	+	38.0526i	−0.414876	+	1.54834i
$605$		0			0
$606$	68.8075	+	44.3434i	2.79511	+	1.80133i
$607$	5.09808	+	8.83013i	0.206925	+	0.358404i	0.950744	−	0.309977i	$-0.100321\pi$
$607$	5.09808	+	8.83013i	0.206925	+	0.358404i	−0.743820	+	0.668380i	$0.766988\pi$
$608$	1.23931	−	2.14655i	0.0502608	−	0.0870543i
$609$	6.19441	+	12.0530i	0.251010	+	0.488413i
$610$		0			0
$611$	11.0648	−	32.7083i	0.447636	−	1.32324i
$612$	−9.92820	−	21.8866i	−0.401324	−	0.884713i
$613$	−16.3564	+	4.38269i	−0.660629	+	0.177015i	−0.573530	−	0.819185i	$-0.694426\pi$
$613$	−16.3564	+	4.38269i	−0.660629	+	0.177015i	−0.0870991	+	0.996200i	$0.527760\pi$
$614$	36.3373	+	20.9794i	1.46645	+	0.846658i
$615$		0			0
$616$	−7.26795	−	7.26795i	−0.292834	−	0.292834i
$617$	36.3818	+	9.74847i	1.46468	+	0.392459i	0.901102	−	0.433607i	$-0.142759\pi$
$617$	36.3818	+	9.74847i	1.46468	+	0.392459i	0.563574	+	0.826066i	$0.309426\pi$
$618$	−28.6957	−	1.40345i	−1.15431	−	0.0564552i
$619$	−14.3397	+	14.3397i	−0.576363	+	0.576363i	−0.933899	−	0.357536i	$-0.883617\pi$
$619$	−14.3397	+	14.3397i	−0.576363	+	0.576363i	0.357536	+	0.933899i	$0.383617\pi$
$620$		0			0
$621$		0			0
$622$	−2.66025	−	9.92820i	−0.106666	−	0.398085i
$623$	14.2076			0.569216
$624$	−14.3185	−	5.63735i	−0.573200	−	0.225675i
$625$		0			0
$626$	−1.23931	−	4.62518i	−0.0495329	−	0.184859i
$627$	0.960731	−	2.99233i	0.0383679	−	0.119502i
$628$	−49.1147	+	28.3564i	−1.95989	+	1.13154i
$629$	−10.3681	+	10.3681i	−0.413404	+	0.413404i
$630$		0			0
$631$	2.26795	+	0.607695i	0.0902856	+	0.0241920i	0.303679	−	0.952774i	$-0.401785\pi$
$631$	2.26795	+	0.607695i	0.0902856	+	0.0241920i	−0.213393	+	0.976966i	$0.568452\pi$
$632$	−5.86450	−	5.86450i	−0.233277	−	0.233277i
$633$	−15.6490	+	14.1897i	−0.621993	+	0.563989i
$634$	33.0622	+	19.0885i	1.31307	+	0.758099i
$635$		0			0
$636$	6.31812	+	29.2224i	0.250530	+	1.15874i
$637$	1.16025	−	17.9904i	0.0459709	−	0.712805i
$638$		−	23.2149i		−	0.919086i
$639$	−9.11792	−	11.1003i	−0.360699	−	0.439122i
$640$		0			0
$641$	9.65949	+	16.7307i	0.381527	+	0.660824i	0.991281	−	0.131767i	$-0.0420650\pi$
$641$	9.65949	+	16.7307i	0.381527	+	0.660824i	−0.609754	+	0.792591i	$0.708732\pi$
$642$	37.4835	−	58.1629i	1.47935	−	2.29551i
$643$	−7.00000	+	26.1244i	−0.276053	+	1.03024i	0.679079	+	0.734065i	$0.262379\pi$
$643$	−7.00000	+	26.1244i	−0.276053	+	1.03024i	−0.955132	+	0.296179i	$0.904287\pi$
$644$		0			0
$645$		0			0
$646$	−2.66025	−	4.60770i	−0.104666	−	0.181287i
$647$	7.22536	−	12.5147i	0.284058	−	0.492003i	−0.688322	−	0.725405i	$-0.741652\pi$
$647$	7.22536	−	12.5147i	0.284058	−	0.492003i	0.972380	+	0.233402i	$0.0749858\pi$
$648$	16.4776	−	33.4870i	0.647302	−	1.31549i
$649$			8.39230i			0.329427i
$650$		0			0
$651$	−3.26795	−	15.1149i	−0.128081	−	0.592398i
$652$	−55.7128	+	14.9282i	−2.18188	+	0.584634i
$653$	−33.6156	−	19.4080i	−1.31548	−	0.759492i	−0.332482	−	0.943110i	$-0.607886\pi$
$653$	−33.6156	−	19.4080i	−1.31548	−	0.759492i	−0.982998	+	0.183617i	$0.941219\pi$
$654$	−12.1812	+	11.0452i	−0.476321	+	0.431902i
$655$		0			0
$656$	1.52690	+	0.409131i	0.0596153	+	0.0159739i
$657$	25.5245	−	4.22556i	0.995807	−	0.164855i
$658$	22.9282	−	22.9282i	0.893834	−	0.893834i
$659$	−27.1759	+	15.6900i	−1.05862	+	0.611197i	−0.925051	−	0.379842i	$-0.875978\pi$
$659$	−27.1759	+	15.6900i	−1.05862	+	0.611197i	−0.133572	+	0.991039i	$0.542645\pi$
$660$		0			0
$661$	−4.42820	−	16.5263i	−0.172237	−	0.642798i	−0.997006	−	0.0773274i	$-0.975361\pi$
$661$	−4.42820	−	16.5263i	−0.172237	−	0.642798i	0.824769	−	0.565470i	$-0.191305\pi$
$662$	46.7380			1.81652
$663$	10.4896	−	8.34677i	0.407382	−	0.324162i
$664$	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
$672$	3.93930	+	4.34444i	0.151962	+	0.167591i
$673$	11.0096	+	6.35641i	0.424390	+	0.245021i	0.696954	−	0.717116i	$-0.254538\pi$
$673$	11.0096	+	6.35641i	0.424390	+	0.245021i	−0.272564	+	0.962138i	$0.587872\pi$
$674$	26.6778	−	7.14830i	1.02759	−	0.275342i
$675$		0			0
$676$	6.23205	−	48.1147i	0.239694	−	1.85057i
$677$			38.8159i			1.49182i	0.666048	+	0.745909i	$0.267985\pi$
$677$			38.8159i			1.49182i	−0.666048	+	0.745909i	$0.732015\pi$
$678$	24.5815	+	47.8304i	0.944046	+	1.83692i
$679$	−9.19615	+	15.9282i	−0.352916	+	0.611268i
$680$		0			0
$681$	22.7821	+	14.6820i	0.873011	+	0.562617i
$682$	−6.85641	+	25.5885i	−0.262545	+	0.979833i
$683$	−4.26054	+	15.9006i	−0.163025	+	0.608418i	0.835259	+	0.549857i	$0.185318\pi$
$683$	−4.26054	+	15.9006i	−0.163025	+	0.608418i	−0.998284	+	0.0585607i	$0.981349\pi$
$684$	4.07823	−	10.8500i	0.155935	−	0.414859i
$685$		0			0
$686$	20.3152	−	35.1870i	0.775638	−	1.34344i
$687$	−22.0571	+	11.3358i	−0.841530	+	0.432488i
$688$			20.1962i			0.769971i
$689$	−14.9488	+	7.39139i	−0.569505	+	0.281590i
$690$		0			0
$691$	−41.8827	+	11.2224i	−1.59329	+	0.426921i	−0.943008	−	0.332770i	$-0.892017\pi$
$691$	−41.8827	+	11.2224i	−1.59329	+	0.426921i	−0.650284	+	0.759691i	$0.725350\pi$
$692$	−24.0331	−	13.8755i	−0.913603	−	0.527469i
$693$	6.04612	+	4.32860i	0.229673	+	0.164430i
$694$	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
$698$	−12.0936	+	6.98226i	−0.457751	+	0.264283i
$699$	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	$0.625332\pi$
$702$	43.8599	+	9.39478i	1.65538	+	0.354583i
$703$	−7.07180			−0.266718
$704$	−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
$708$	−1.51201	+	30.9154i	−0.0568249	+	1.16187i
$709$	−9.96410	−	2.66987i	−0.374210	−	0.100269i	0.0668121	−	0.997766i	$-0.478717\pi$
$709$	−9.96410	−	2.66987i	−0.374210	−	0.100269i	−0.441022	+	0.897496i	$0.645384\pi$
$710$		0			0
$711$	4.87861	+	3.49274i	0.182962	+	0.130988i
$712$	−36.0788	−	20.8301i	−1.35211	−	0.780642i
$713$		0			0
$714$	12.3042	−	2.66025i	0.460472	−	0.0995575i
$715$		0			0
$716$			69.9529i			2.61426i
$717$	−15.4765	+	7.95383i	−0.577979	+	0.297041i
$718$	−20.4186	+	35.3660i	−0.762015	+	1.31985i
$719$	5.86450	+	10.1576i	0.218709	+	0.378815i	0.954413	−	0.298488i	$-0.0964822\pi$
$719$	5.86450	+	10.1576i	0.218709	+	0.378815i	−0.735705	+	0.677302i	$0.763149\pi$
$720$		0			0
$721$	2.53590	−	9.46410i	0.0944418	−	0.352462i
$722$	−11.1093	+	41.4606i	−0.413447	+	1.54300i
$723$	−10.9006	−	7.02496i	−0.405398	−	0.261261i
$724$	5.59808	+	9.69615i	0.208051	+	0.360355i
$725$		0			0
$726$	15.0279	+	29.2412i	0.557740	+	1.08524i
$727$			25.5167i			0.946361i	0.880966	+	0.473180i	$0.156894\pi$
$727$			25.5167i			0.946361i	−0.880966	+	0.473180i	$0.843106\pi$
$728$	11.7290	−	17.5935i	0.434705	−	0.652058i
$729$	−7.80385	+	25.8476i	−0.289031	+	0.957320i
$730$		0			0
$731$	−15.2364	−	8.79674i	−0.563539	−	0.325359i
$732$	30.3945	+	33.5205i	1.12341	+	1.23895i
$733$	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
$737$	13.3004	−	7.67898i	0.489926	−	0.282859i
$738$	−4.58570	−	0.449632i	−0.168802	−	0.0165512i
$739$	13.1244	+	48.9808i	0.482787	+	1.80179i	0.589825	+	0.807531i	$0.299197\pi$
$739$	13.1244	+	48.9808i	0.482787	+	1.80179i	−0.107037	+	0.994255i	$0.534136\pi$
$740$		0			0
$741$	6.42386	+	0.730778i	0.235987	+	0.0268458i
$742$	−15.6603			−0.574906
$743$	−13.5435	−	50.5449i	−0.496862	−	1.85431i	−0.519343	−	0.854566i	$-0.673823\pi$
$743$	−13.5435	−	50.5449i	−0.496862	−	1.85431i	0.0224808	−	0.999747i	$-0.492844\pi$
$744$	−13.8616	+	43.1739i	−0.508192	+	1.58283i
$745$		0			0
$746$	33.1620	−	33.1620i	1.21415	−	1.21415i
$747$	−5.18736	+	0.858763i	−0.189796	+	0.0314205i
$748$	−13.5622	−	3.63397i	−0.495882	−	0.132871i
$749$	16.6862	+	16.6862i	0.609702	+	0.609702i
$750$		0			0
$751$	38.2750	+	22.0981i	1.39667	+	0.806370i	0.994043	−	0.108992i	$-0.0347622\pi$
$751$	38.2750	+	22.0981i	1.39667	+	0.806370i	0.402632	+	0.915362i	$0.368096\pi$
$752$	−22.7938	+	6.10759i	−0.831206	+	0.222721i
$753$	−8.01105	−	37.0526i	−0.291939	−	1.35027i
$754$	46.8301	−	9.36603i	1.70545	−	0.341091i
$755$		0			0
$756$	21.4927	+	17.0349i	0.781681	+	0.619553i
$757$	−12.3923	+	21.4641i	−0.450406	+	0.780126i	−0.998411	−	0.0563489i	$-0.982054\pi$
$757$	−12.3923	+	21.4641i	−0.450406	+	0.780126i	0.548005	+	0.836475i	$0.315387\pi$
$758$	−5.98604	−	10.3681i	−0.217423	−	0.376587i
$759$		0			0
$760$		0			0
$761$	1.11777	−	4.17156i	0.0405190	−	0.151219i	−0.942703	−	0.333634i	$-0.891725\pi$
$761$	1.11777	−	4.17156i	0.0405190	−	0.151219i	0.983222	+	0.182415i	$0.0583916\pi$
$762$	−33.9749	+	52.7187i	−1.23078	+	1.90980i
$763$	−2.80385	−	4.85641i	−0.101506	−	0.175814i
$764$	−36.2158	+	62.7275i	−1.31024	+	2.26940i
$765$		0			0
$766$		−	33.5692i		−	1.21291i
$767$	−16.9293	+	3.38587i	−0.611283	+	0.122257i
$768$	−10.3660	−	47.9447i	−0.374052	−	1.73006i
$769$	−2.16987	+	0.581416i	−0.0782476	+	0.0209664i	−0.297730	−	0.954650i	$-0.596230\pi$
$769$	−2.16987	+	0.581416i	−0.0782476	+	0.0209664i	0.219483	+	0.975616i	$0.429563\pi$
$770$		0			0
$771$	−21.2961	+	19.3102i	−0.766962	+	0.695438i
$772$	19.0263	+	19.0263i	0.684771	+	0.684771i
$773$	5.98604	+	1.60396i	0.215303	+	0.0576903i	0.364858	−	0.931063i	$-0.381117\pi$
$773$	5.98604	+	1.60396i	0.215303	+	0.0576903i	−0.149555	+	0.988753i	$0.547784\pi$
$774$	−9.61484	−	58.0785i	−0.345598	−	2.08759i
$775$		0			0
$776$	46.7054	−	26.9654i	1.67663	−	0.968001i
$777$	5.11491	−	15.9311i	0.183496	−	0.571524i
$778$	3.27757	+	12.2321i	0.117507	+	0.438540i
$779$	−0.664146			−0.0237955
$780$		0			0
$781$	−8.39230			−0.300300
$782$		0			0
$783$	3.30414	+	28.5568i	0.118080	+	1.02054i
$784$	−10.6699	+	6.16025i	−0.381067	+	0.220009i
$785$		0			0
$786$	−3.75768	−	0.183781i	−0.134032	−	0.00655524i
$787$	11.2942	+	3.02628i	0.402596	+	0.107875i	0.454434	−	0.890780i	$-0.349841\pi$
$787$	11.2942	+	3.02628i	0.402596	+	0.107875i	−0.0518385	+	0.998655i	$0.516508\pi$
$788$	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
$792$	−9.00727	−	19.8564i	−0.320059	−	0.705567i
$793$	−14.0000	+	21.0000i	−0.497155	+	0.745732i
$794$		−	21.2224i		−	0.753157i
$795$		0			0
$796$	−1.73205	+	3.00000i	−0.0613909	+	0.106332i
$797$	8.58622	+	14.8718i	0.304139	+	0.526785i	0.977069	−	0.212921i	$-0.0682978\pi$
$797$	8.58622	+	14.8718i	0.304139	+	0.526785i	−0.672930	+	0.739706i	$0.734964\pi$
$798$	5.10339	+	3.28891i	0.180658	+	0.116426i
$799$	5.32051	−	19.8564i	0.188226	−	0.702469i
$800$		0			0
$801$	28.2118	+	10.6041i	0.996815	+	0.374678i
$802$	−33.6244	−	58.2391i	−1.18732	−	2.05649i
$803$	7.55743	−	13.0899i	0.266696	−	0.461931i
$804$	50.3791	−	25.8913i	1.77673	−	0.913117i
$805$		0			0
$806$	−54.3844	−	3.50742i	−1.91561	−	0.123543i
$807$	18.7321	−	4.05001i	0.659399	−	0.142567i
$808$	79.0692	−	21.1865i	2.78165	−	0.745340i
$809$	−17.6705	−	10.2021i	−0.621263	−	0.358686i	0.156097	−	0.987742i	$-0.450109\pi$
$809$	−17.6705	−	10.2021i	−0.621263	−	0.358686i	−0.777361	+	0.629055i	$0.783442\pi$
$810$		0			0
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	0.957062	−	0.289882i	$-0.0936161\pi$
$811$	19.0000	+	19.0000i	0.667180	+	0.667180i	−0.289882	+	0.957062i	$0.593616\pi$
$812$	28.2047	+	7.55743i	0.989791	+	0.265214i
$813$	0.175190	−	3.58202i	0.00614417	−	0.125627i
$814$	−20.2679	+	20.2679i	−0.710391	+	0.710391i
$815$		0			0
$816$	−8.72282	−	2.80059i	−0.305360	−	0.0980403i
$817$	−2.19615	−	8.19615i	−0.0768336	−	0.286747i
$818$	27.8401			0.973405
$819$	−6.29254	+	13.9429i	−0.219879	+	0.487204i
$820$		0			0
$821$	1.60396	+	5.98604i	0.0559784	+	0.208914i	0.988250	−	0.152844i	$-0.0488432\pi$
$821$	1.60396	+	5.98604i	0.0559784	+	0.208914i	−0.932272	+	0.361758i	$0.882177\pi$
$822$	−23.2930	−	7.47856i	−0.812436	−	0.260845i
$823$	−13.3923	+	7.73205i	−0.466826	+	0.269522i	−0.714910	−	0.699216i	$-0.753532\pi$
$823$	−13.3923	+	7.73205i	−0.466826	+	0.269522i	0.248084	+	0.968739i	$0.420199\pi$
$824$	−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	0.641190	−	0.767382i	$-0.278441\pi$
$827$	−3.62896	−	3.62896i	−0.126191	−	0.126191i	−0.767382	+	0.641190i	$0.778441\pi$
$828$		0			0
$829$	−20.6769	−	11.9378i	−0.718139	−	0.414618i	0.0959284	−	0.995388i	$-0.469418\pi$
$829$	−20.6769	−	11.9378i	−0.718139	−	0.414618i	−0.814067	+	0.580771i	$0.802751\pi$
$830$		0			0
$831$	6.07502	−	1.31347i	0.210740	−	0.0455636i
$832$	34.4545	−	17.0359i	1.19449	−	0.590614i
$833$		−	10.7328i		−	0.371868i
$834$	8.82343	−	4.53463i	0.305530	−	0.157021i
$835$		0			0
$836$	−3.38587	−	5.86450i	−0.117103	−	0.202828i
$837$	4.79215	−	32.4524i	0.165641	−	1.12172i
$838$	−5.16987	+	19.2942i	−0.178590	+	0.666508i
$839$	−2.02501	+	7.55743i	−0.0699110	+	0.260911i	−0.992031	−	0.125992i	$-0.959789\pi$
$839$	−2.02501	+	7.55743i	−0.0699110	+	0.260911i	0.922120	+	0.386903i	$0.126455\pi$
$840$		0			0
$841$	0.803848	+	1.39230i	0.0277189	+	0.0480105i
$842$	−1.40535	+	2.43414i	−0.0484316	+	0.0838859i
$843$	17.8032	+	34.6412i	0.613173	+	1.19311i
$844$			45.5167i			1.56675i
$845$		0			0
$846$	62.6410	−	28.4152i	2.15364	−	0.976936i
$847$	−10.8301	+	2.90192i	−0.372128	+	0.0997113i
$848$	9.87002	+	5.69846i	0.338938	+	0.195686i
$849$	−28.6075	−	31.5497i	−0.981808	−	1.08278i
$850$		0			0
$851$		0			0
$852$	−30.9154	−	1.51201i	−1.05914	−	0.0518007i
$853$	20.6340	−	20.6340i	0.706494	−	0.706494i	−0.259302	−	0.965796i	$-0.583493\pi$
$853$	20.6340	−	20.6340i	0.706494	−	0.706494i	0.965796	+	0.259302i	$0.0834926\pi$
$854$	−20.5257	+	11.8505i	−0.702376	+	0.405517i
$855$		0			0
$856$	−17.9090	−	66.8372i	−0.612116	−	2.28445i
$857$	−35.7621			−1.22161			−0.610806	−	0.791781i	$-0.709154\pi$
$857$	−35.7621			−1.22161			−0.610806	+	0.791781i	$0.709154\pi$
$858$	20.5054	−	16.3165i	0.700042	−	0.557037i
$859$	−23.1769			−0.790786			−0.395393	−	0.918512i	$-0.629392\pi$
$859$	−23.1769			−0.790786			−0.395393	+	0.918512i	$0.629392\pi$
$860$		0			0
$861$	0.480365	−	1.49616i	0.0163708	−	0.0509891i
$862$	4.34679	−	2.50962i	0.148052	−	0.0854780i
$863$	12.0611	−	12.0611i	0.410563	−	0.410563i	−0.471371	−	0.881935i	$-0.656241\pi$
$863$	12.0611	−	12.0611i	0.410563	−	0.410563i	0.881935	+	0.471371i	$0.156241\pi$
$864$	4.57965	+	11.5669i	0.155803	+	0.393513i
$865$		0			0
$866$	11.9395	+	11.9395i	0.405721	+	0.405721i
$867$	−15.9007	+	14.4179i	−0.540016	+	0.489657i
$868$	−28.8564	−	16.6603i	−0.979450	−	0.565486i
$869$	3.38587	−	0.907241i	0.114858	−	0.0307760i
$870$		0			0
$871$	20.8564	+	23.7321i	0.706692	+	0.804130i
$872$			16.4432i			0.556835i
$873$	−30.1489	+	24.7646i	−1.02039	+	0.838156i
$874$		0			0
$875$		0			0
$876$	30.1982	−	46.8585i	1.02030	−	1.58320i
$877$	−3.00962	+	11.2321i	−0.101628	+	0.379279i	−0.997941	−	0.0641422i	$-0.979569\pi$
$877$	−3.00962	+	11.2321i	−0.101628	+	0.379279i	0.896313	+	0.443422i	$0.146236\pi$
$878$	2.93225	−	10.9433i	0.0989586	−	0.369318i
$879$	20.6579	−	32.0549i	0.696775	−	1.08118i
$880$		0			0
$881$	13.5880	−	23.5350i	0.457790	−	0.792916i	−0.541054	−	0.840988i	$-0.681974\pi$
$881$	13.5880	−	23.5350i	0.457790	−	0.792916i	0.998844	+	0.0480724i	$0.0153078\pi$
$882$	27.7508	−	22.7948i	0.934419	−	0.767541i
$883$		−	39.3731i		−	1.32501i	−0.749058	−	0.662505i	$-0.769494\pi$
$883$		−	39.3731i		−	1.32501i	0.749058	−	0.662505i	$-0.230506\pi$
$884$	1.85897	−	28.8244i	0.0625239	−	0.969468i
$885$		0			0
$886$	68.3731	−	18.3205i	2.29704	−	0.615490i
$887$	−46.4949	−	26.8438i	−1.56115	−	0.901328i	−0.997142	−	0.0755567i	$-0.975927\pi$
$887$	−46.4949	−	26.8438i	−1.56115	−	0.901328i	−0.564005	−	0.825772i	$-0.690740\pi$
$888$	−36.3457	+	32.9563i	−1.21968	+	1.10594i
$889$	−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
$893$	8.58622	−	4.95725i	0.287327	−	0.165888i
$894$	6.88324	−	21.4388i	0.230210	−	0.717020i
$895$		0			0
$896$	29.3225			0.979595
$897$		0			0
$898$	20.9808			0.700137
$899$	−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
$903$	20.0524	+	0.980726i	0.667303	+	0.0326365i
$904$	51.9449	+	13.9186i	1.72766	+	0.462925i
$905$		0			0
$906$	−29.4034	−	32.4274i	−0.976861	−	1.07733i
$907$	15.0000	+	8.66025i	0.498067	+	0.287559i	0.727915	−	0.685668i	$-0.240490\pi$
$907$	15.0000	+	8.66025i	0.498067	+	0.287559i	−0.229848	+	0.973227i	$0.573823\pi$
$908$	56.4094	−	15.1149i	1.87201	−	0.501604i
$909$	−53.9308	+	24.4641i	−1.78877	+	0.811423i
$910$		0			0
$911$			9.25036i			0.306478i	0.988189	+	0.153239i	$0.0489705\pi$
$911$			9.25036i			0.306478i	−0.988189	+	0.153239i	$0.951030\pi$
$912$	−2.01969	−	3.92989i	−0.0668786	−	0.130132i
$913$	−1.53590	+	2.66025i	−0.0508308	+	0.0880416i
$914$	33.4495	+	57.9363i	1.10641	+	1.91636i
$915$		0			0
$916$	−13.8301	+	51.6147i	−0.456960	+	1.70540i
$917$	0.332073	−	1.23931i	0.0109660	−	0.0409257i
$918$	26.4177	+	3.90102i	0.871913	+	0.128753i
$919$	−22.2942	−	38.6147i	−0.735419	−	1.27378i	−0.954539	−	0.298085i	$-0.903652\pi$
$919$	−22.2942	−	38.6147i	−0.735419	−	1.27378i	0.219121	−	0.975698i	$-0.429681\pi$
$920$		0			0
$921$	−26.9981	+	13.8751i	−0.889617	+	0.457201i
$922$			58.0333i			1.91123i
$923$	−3.38587	−	16.9293i	−0.111447	−	0.557236i
$924$	15.6603	−	3.38587i	0.515185	−	0.111387i
$925$		0			0
$926$	44.1378	+	25.4830i	1.45046	+	0.837423i
$927$	12.0992	−	16.9000i	0.397390	−	0.555068i
$928$	9.36603	+	9.36603i	0.307455	+	0.307455i
$929$	−47.3251	−	12.6807i	−1.55269	−	0.416041i	−0.622347	−	0.782742i	$-0.713821\pi$
$929$	−47.3251	−	12.6807i	−1.55269	−	0.416041i	−0.930339	+	0.366701i	$0.880487\pi$
$930$		0			0
$931$	3.66025	−	3.66025i	0.119960	−	0.119960i
$932$	24.0331	−	13.8755i	0.787232	−	0.454509i
$933$	7.07992	+	2.27311i	0.231786	+	0.0744184i
$934$	−18.8827	−	70.4711i	−0.617860	−	2.30589i
$935$		0			0
$936$	36.4213	−	26.1809i	1.19047	−	0.855750i
$937$	37.0000			1.20874			0.604369	−	0.796705i	$-0.293425\pi$
$937$	37.0000			1.20874			0.604369	+	0.796705i	$0.293425\pi$
$938$	7.67898	+	28.6583i	0.250727	+	0.935728i
$939$	3.29827	+	1.05896i	0.107635	+	0.0345578i
$940$		0			0
$941$	−38.2408	+	38.2408i	−1.24661	+	1.24661i	−0.289407	+	0.957206i	$0.593458\pi$
$941$	−38.2408	+	38.2408i	−1.24661	+	1.24661i	−0.957206	+	0.289407i	$0.906542\pi$
$942$	3.07830	−	62.9405i	0.100296	−	2.05071i
$943$		0			0
$944$	8.34312	+	8.34312i	0.271546	+	0.271546i
$945$		0			0
$946$	−29.7846	−	17.1962i	−0.968381	−	0.559095i
$947$	−39.6016	+	10.6112i	−1.28688	+	0.344818i	−0.836475	−	0.548006i	$-0.815387\pi$
$947$	−39.6016	+	10.6112i	−1.28688	+	0.344818i	−0.450405	+	0.892824i	$0.648721\pi$
$948$	12.6362	−	2.73205i	0.410406	−	0.0887329i
$949$	29.4545	+	9.96410i	0.956133	+	0.323448i
$950$		0			0
$951$	−24.5647	+	12.6245i	−0.796565	+	0.409379i
$952$	6.29423	−	10.9019i	0.203997	−	0.353333i
$953$	21.8866	+	37.9087i	0.708976	+	1.22798i	0.965237	+	0.261375i	$0.0841760\pi$
$953$	21.8866	+	37.9087i	0.708976	+	1.22798i	−0.256261	+	0.966608i	$0.582491\pi$
$954$	−31.0963	−	11.6883i	−1.00678	−	0.378423i
$955$		0			0
$956$	−9.70398	+	36.2158i	−0.313849	+	1.17130i
$957$	14.1171	+	9.09782i	0.456340	+	0.294091i
$958$	−10.4904	−	18.1699i	−0.338929	−	0.587042i
$959$	4.17156	−	7.22536i	0.134707	−	0.233319i
$960$		0			0
$961$			8.85641i			0.285691i
$962$	−49.0625	−	32.7083i	−1.58184	−	1.05456i
$963$	20.6795	+	45.5877i	0.666387	+	1.46904i
$964$	−26.9904	+	7.23205i	−0.869302	+	0.232929i
$965$		0			0
$966$		0			0
$967$	0.143594	+	0.143594i	0.00461766	+	0.00461766i	0.709412	−	0.704794i	$-0.248961\pi$
$967$	0.143594	+	0.143594i	0.00461766	+	0.00461766i	−0.704794	+	0.709412i	$0.748961\pi$
$968$	31.7566	+	8.50916i	1.02070	+	0.273495i
$969$	3.84450	+	0.188027i	0.123503	+	0.00604030i
$970$		0			0
$971$	45.5551	−	26.3013i	1.46193	−	0.844047i	0.462832	−	0.886446i	$-0.346833\pi$
$971$	45.5551	−	26.3013i	1.46193	−	0.844047i	0.999101	+	0.0423987i	$0.0135000\pi$
$972$	29.9633	+	49.8673i	0.961075	+	1.59950i
$973$	0.875644	+	3.26795i	0.0280719	+	0.104766i
$974$	60.7025			1.94503
$975$		0			0
$976$	17.2487			0.552118
$977$	−7.60192	−	28.3707i	−0.243207	−	0.907661i	−0.974276	−	0.225357i	$-0.927645\pi$
$977$	−7.60192	−	28.3707i	−0.243207	−	0.907661i	0.731069	−	0.682303i	$-0.239022\pi$
$978$	19.5915	−	61.0204i	0.626468	−	1.95122i
$979$	15.2487	−	8.80385i	0.487351	−	0.281372i
$980$		0			0
$981$	−1.94288	−	11.7360i	−0.0620314	−	0.374701i
$982$	57.8827	+	15.5096i	1.84711	+	0.494932i
$983$	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
$987$	4.95725	+	22.9282i	0.157791	+	0.729813i
$988$	10.4641	−	9.19615i	0.332907	−	0.292569i
$989$		0			0
$990$		0			0
$991$	−12.7846	+	22.1436i	−0.406117	+	0.703414i	−0.994451	−	0.105203i	$-0.966451\pi$
$991$	−12.7846	+	22.1436i	−0.406117	+	0.703414i	0.588334	+	0.808618i	$0.299784\pi$
$992$	−7.55743	−	13.0899i	−0.239949	−	0.415603i
$993$	−18.3164	+	28.4216i	−0.581255	+	0.901931i
$994$	4.19615	−	15.6603i	0.133094	−	0.496713i
$995$		0			0
$996$	−6.13719	+	9.52306i	−0.194464	+	0.301750i
$997$	−3.50000	−	6.06218i	−0.110846	−	0.191991i	0.805266	−	0.592914i	$-0.202023\pi$
$997$	−3.50000	−	6.06218i	−0.110846	−	0.191991i	−0.916112	+	0.400923i	$0.868689\pi$
$998$	−7.55743	+	13.0899i	−0.239226	+	0.414352i
$999$	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.bo.d.176.2		8
3.2	odd	2	inner	975.2.bo.d.176.1		8
5.2	odd	4		975.2.bp.f.449.1		8
5.3	odd	4		975.2.bp.e.449.2		8
5.4	even	2		39.2.k.b.20.1	yes	8
13.2	odd	12	inner	975.2.bo.d.626.1		8
15.2	even	4		975.2.bp.f.449.2		8
15.8	even	4		975.2.bp.e.449.1		8
15.14	odd	2		39.2.k.b.20.2	yes	8
20.19	odd	2		624.2.cn.c.449.1		8
39.2	even	12	inner	975.2.bo.d.626.2		8
60.59	even	2		624.2.cn.c.449.2		8
65.2	even	12		975.2.bp.e.899.1		8
65.4	even	6		507.2.f.e.437.4		8
65.9	even	6		507.2.f.f.437.1		8
65.19	odd	12		507.2.f.f.239.4		8
65.24	odd	12		507.2.k.d.80.1		8
65.28	even	12		975.2.bp.f.899.2		8
65.29	even	6		507.2.k.e.89.2		8
65.34	odd	4		507.2.k.f.188.2		8
65.44	odd	4		507.2.k.e.188.1		8
65.49	even	6		507.2.k.f.89.1		8
65.54	odd	12		39.2.k.b.2.2	yes	8
65.59	odd	12		507.2.f.e.239.1		8
65.64	even	2		507.2.k.d.488.2		8
195.2	odd	12		975.2.bp.e.899.2		8
195.29	odd	6		507.2.k.e.89.1		8
195.44	even	4		507.2.k.e.188.2		8
195.59	even	12		507.2.f.e.239.4		8
195.74	odd	6		507.2.f.f.437.4		8
195.89	even	12		507.2.k.d.80.2		8
195.119	even	12		39.2.k.b.2.1	✓	8
195.134	odd	6		507.2.f.e.437.1		8
195.149	even	12		507.2.f.f.239.1		8
195.158	odd	12		975.2.bp.f.899.1		8
195.164	even	4		507.2.k.f.188.1		8
195.179	odd	6		507.2.k.f.89.2		8
195.194	odd	2		507.2.k.d.488.1		8
260.119	even	12		624.2.cn.c.353.2		8
780.119	odd	12		624.2.cn.c.353.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.k.b.2.1	✓	8	195.119	even	12
39.2.k.b.2.2	yes	8	65.54	odd	12
39.2.k.b.20.1	yes	8	5.4	even	2
39.2.k.b.20.2	yes	8	15.14	odd	2
507.2.f.e.239.1		8	65.59	odd	12
507.2.f.e.239.4		8	195.59	even	12
507.2.f.e.437.1		8	195.134	odd	6
507.2.f.e.437.4		8	65.4	even	6
507.2.f.f.239.1		8	195.149	even	12
507.2.f.f.239.4		8	65.19	odd	12
507.2.f.f.437.1		8	65.9	even	6
507.2.f.f.437.4		8	195.74	odd	6
507.2.k.d.80.1		8	65.24	odd	12
507.2.k.d.80.2		8	195.89	even	12
507.2.k.d.488.1		8	195.194	odd	2
507.2.k.d.488.2		8	65.64	even	2
507.2.k.e.89.1		8	195.29	odd	6
507.2.k.e.89.2		8	65.29	even	6
507.2.k.e.188.1		8	65.44	odd	4
507.2.k.e.188.2		8	195.44	even	4
507.2.k.f.89.1		8	65.49	even	6
507.2.k.f.89.2		8	195.179	odd	6
507.2.k.f.188.1		8	195.164	even	4
507.2.k.f.188.2		8	65.34	odd	4
624.2.cn.c.353.1		8	780.119	odd	12
624.2.cn.c.353.2		8	260.119	even	12
624.2.cn.c.449.1		8	20.19	odd	2
624.2.cn.c.449.2		8	60.59	even	2
975.2.bo.d.176.1		8	3.2	odd	2	inner
975.2.bo.d.176.2		8	1.1	even	1	trivial
975.2.bo.d.626.1		8	13.2	odd	12	inner
975.2.bo.d.626.2		8	39.2	even	12	inner
975.2.bp.e.449.1		8	15.8	even	4
975.2.bp.e.449.2		8	5.3	odd	4
975.2.bp.e.899.1		8	65.2	even	12
975.2.bp.e.899.2		8	195.2	odd	12
975.2.bp.f.449.1		8	5.2	odd	4
975.2.bp.f.449.2		8	15.2	even	4
975.2.bp.f.899.1		8	195.158	odd	12
975.2.bp.f.899.2		8	65.28	even	12

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.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.619657 + 2.31259i) q^{2} +(-1.64914 - 0.529480i) q^{3} +(-3.23205 + 1.86603i) q^{4} +(0.202571 - 4.14187i) q^{6} +(1.36603 + 0.366025i) q^{7} +(-2.93225 - 2.93225i) q^{8} +(2.43930 + 1.74637i) q^{9} +O(q^{10})\)	\(q+(0.619657 + 2.31259i) q^{2} +(-1.64914 - 0.529480i) q^{3} +(-3.23205 + 1.86603i) q^{4} +(0.202571 - 4.14187i) q^{6} +(1.36603 + 0.366025i) q^{7} +(-2.93225 - 2.93225i) q^{8} +(2.43930 + 1.74637i) q^{9} +(1.69293 - 0.453620i) q^{11} +(6.31812 - 1.36603i) q^{12} +(1.59808 + 3.23205i) q^{13} +3.38587i q^{14} +(1.23205 - 2.13397i) q^{16} +(1.07328 + 1.85897i) q^{17} +(-2.52711 + 6.72326i) q^{18} +(-0.267949 + 1.00000i) q^{19} +(-2.05896 - 1.32691i) q^{21} +(2.09808 + 3.63397i) q^{22} +(3.28311 + 6.38824i) q^{24} +(-6.48415 + 5.69846i) q^{26} +(-3.09808 - 4.17156i) q^{27} +(-5.09808 + 1.36603i) q^{28} +(-4.79122 - 2.76621i) q^{29} +(4.46410 + 4.46410i) q^{31} +(-2.31259 - 0.619657i) q^{32} +(-3.03206 - 0.148292i) q^{33} +(-3.63397 + 3.63397i) q^{34} +(-11.1427 - 1.09255i) q^{36} +(1.76795 + 6.59808i) q^{37} -2.47863 q^{38} +(-0.924141 - 6.17624i) q^{39} +(0.166037 + 0.619657i) q^{41} +(1.79275 - 5.58376i) q^{42} +(-7.09808 + 4.09808i) q^{43} +(-4.62518 + 4.62518i) q^{44} +(-6.77174 - 6.77174i) q^{47} +(-3.16172 + 2.86687i) q^{48} +(-4.33013 - 2.50000i) q^{49} +(-0.785693 - 3.63397i) q^{51} +(-11.1962 - 7.46410i) q^{52} +4.62518i q^{53} +(7.72737 - 9.74952i) q^{54} +(-2.93225 - 5.07880i) q^{56} +(0.971364 - 1.50726i) q^{57} +(3.42820 - 12.7942i) q^{58} +(-1.23931 + 4.62518i) q^{59} +(3.50000 + 6.06218i) q^{61} +(-7.55743 + 13.0899i) q^{62} +(2.69293 + 3.27843i) q^{63} -10.6603i q^{64} +(-1.53590 - 7.10381i) q^{66} +(8.46410 - 2.26795i) q^{67} +(-6.93777 - 4.00552i) q^{68} +(-4.62518 - 1.23931i) q^{71} +(-2.03185 - 12.2734i) q^{72} +(6.09808 - 6.09808i) q^{73} +(-14.1631 + 8.17709i) q^{74} +(-1.00000 - 3.73205i) q^{76} +2.47863 q^{77} +(13.7105 - 5.96431i) q^{78} +2.00000 q^{79} +(2.90039 + 8.51984i) q^{81} +(-1.33013 + 0.767949i) q^{82} +(-1.23931 + 1.23931i) q^{83} +(9.13071 + 0.446565i) q^{84} +(-13.8755 - 13.8755i) q^{86} +(6.43672 + 7.09871i) q^{87} +(-6.29423 - 3.63397i) q^{88} +(9.70398 - 2.60017i) q^{89} +(1.00000 + 5.00000i) q^{91} +(-4.99826 - 9.72556i) q^{93} +(11.4641 - 19.8564i) q^{94} +(3.48568 + 2.24637i) q^{96} +(-3.36603 + 12.5622i) q^{97} +(3.09828 - 11.5630i) q^{98} +(4.92177 + 1.84997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 12 q^{4} - 2 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 12 * q^4 - 2 * q^6 + 4 * q^7 + 4 * q^9	\( 8 q + 2 q^{3} - 12 q^{4} - 2 q^{6} + 4 q^{7} + 4 q^{9} - 8 q^{13} - 4 q^{16} - 4 q^{18} - 16 q^{19} + 4 q^{21} - 4 q^{22} + 18 q^{24} - 4 q^{27} - 20 q^{28} + 8 q^{31} - 16 q^{33} - 36 q^{34} - 36 q^{36} + 28 q^{37} - 14 q^{39} + 16 q^{42} - 36 q^{43} + 14 q^{48} - 48 q^{52} + 46 q^{54} - 16 q^{57} - 28 q^{58} + 28 q^{61} + 8 q^{63} - 40 q^{66} + 40 q^{67} - 12 q^{72} + 28 q^{73} - 8 q^{76} + 80 q^{78} + 16 q^{79} + 4 q^{81} + 24 q^{82} + 4 q^{84} + 34 q^{87} + 12 q^{88} + 8 q^{91} - 4 q^{93} + 64 q^{94} + 16 q^{96} - 20 q^{97} + 40 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 - 12 * q^4 - 2 * q^6 + 4 * q^7 + 4 * q^9 - 8 * q^13 - 4 * q^16 - 4 * q^18 - 16 * q^19 + 4 * q^21 - 4 * q^22 + 18 * q^24 - 4 * q^27 - 20 * q^28 + 8 * q^31 - 16 * q^33 - 36 * q^34 - 36 * q^36 + 28 * q^37 - 14 * q^39 + 16 * q^42 - 36 * q^43 + 14 * q^48 - 48 * q^52 + 46 * q^54 - 16 * q^57 - 28 * q^58 + 28 * q^61 + 8 * q^63 - 40 * q^66 + 40 * q^67 - 12 * q^72 + 28 * q^73 - 8 * q^76 + 80 * q^78 + 16 * q^79 + 4 * q^81 + 24 * q^82 + 4 * q^84 + 34 * q^87 + 12 * q^88 + 8 * q^91 - 4 * q^93 + 64 * q^94 + 16 * q^96 - 20 * q^97 + 40 * q^99

Introduction

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