LMFDB - Embedded newform 575.2.p.c.174.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(49,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 16]))

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

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

chi := DirichletCharacter("575.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.p (of order $22$, degree $10$, 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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{22})$
Twist minimal:	no (minimal twist has level 115)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			174.2
Character	$\chi$	$=$	575.174
Dual form			575.2.p.c.499.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.215109 + 0.186393i) q^{2} +(0.770157 - 1.19839i) q^{3} +(-0.273100 + 1.89945i) q^{4} +(0.0577033 + 0.401335i) q^{6} +(-0.393517 + 1.34020i) q^{7} +(-0.603063 - 0.938384i) q^{8} +(0.403254 + 0.883004i) q^{9} +O(q^{10})$	\(q+(-0.215109 + 0.186393i) q^{2} +(0.770157 - 1.19839i) q^{3} +(-0.273100 + 1.89945i) q^{4} +(0.0577033 + 0.401335i) q^{6} +(-0.393517 + 1.34020i) q^{7} +(-0.603063 - 0.938384i) q^{8} +(0.403254 + 0.883004i) q^{9} +(-3.15749 + 3.64393i) q^{11} +(2.06595 + 1.79016i) q^{12} +(-0.0804117 - 0.273857i) q^{13} +(-0.165154 - 0.361637i) q^{14} +(-3.37787 - 0.991834i) q^{16} +(-0.472917 + 0.0679951i) q^{17} +(-0.251329 - 0.114778i) q^{18} +(-0.140789 + 0.979208i) q^{19} +(1.30300 + 1.50375i) q^{21} -1.37237i q^{22} +(-1.21649 + 4.63898i) q^{23} -1.58900 q^{24} +(0.0683422 + 0.0439209i) q^{26} +(5.59883 + 0.804990i) q^{27} +(-2.43817 - 1.11347i) q^{28} +(-0.0219083 - 0.152376i) q^{29} +(-3.01445 + 1.93727i) q^{31} +(2.94080 - 1.34302i) q^{32} +(1.93508 + 6.59029i) q^{33} +(0.0890547 - 0.102775i) q^{34} +(-1.78735 + 0.524814i) q^{36} +(3.74020 - 1.70809i) q^{37} +(-0.152232 - 0.236878i) q^{38} +(-0.390116 - 0.114549i) q^{39} +(-2.86572 + 6.27505i) q^{41} +(-0.560575 - 0.0805985i) q^{42} +(5.81663 - 9.05086i) q^{43} +(-6.05917 - 6.99266i) q^{44} +(-0.602996 - 1.22463i) q^{46} +9.42683i q^{47} +(-3.79009 + 3.28414i) q^{48} +(4.24751 + 2.72971i) q^{49} +(-0.282735 + 0.619104i) q^{51} +(0.542139 - 0.0779478i) q^{52} +(1.35702 - 4.62159i) q^{53} +(-1.35440 + 0.870421i) q^{54} +(1.49493 - 0.438952i) q^{56} +(1.06504 + 0.922863i) q^{57} +(0.0331144 + 0.0286938i) q^{58} +(-6.57113 + 1.92946i) q^{59} +(9.16678 - 5.89113i) q^{61} +(0.287342 - 0.978595i) q^{62} +(-1.34208 + 0.192963i) q^{63} +(2.54266 - 5.56764i) q^{64} +(-1.64464 - 1.05694i) q^{66} +(-5.33316 + 4.62121i) q^{67} -0.916853i q^{68} +(4.62241 + 5.03057i) q^{69} +(7.91831 + 9.13822i) q^{71} +(0.585409 - 0.910914i) q^{72} +(-6.75135 - 0.970698i) q^{73} +(-0.486174 + 1.06457i) q^{74} +(-1.82151 - 0.534844i) q^{76} +(-3.64106 - 5.66560i) q^{77} +(0.105268 - 0.0480745i) q^{78} +(11.4955 - 3.37537i) q^{79} +(3.36959 - 3.88872i) q^{81} +(-0.553183 - 1.88397i) q^{82} +(5.91956 - 2.70337i) q^{83} +(-3.21215 + 2.06432i) q^{84} +(0.435806 + 3.03110i) q^{86} +(-0.199478 - 0.0910986i) q^{87} +(5.32357 + 0.765414i) q^{88} +(9.20422 + 5.91519i) q^{89} +0.398665 q^{91} +(-8.47931 - 3.57757i) q^{92} +5.10448i q^{93} +(-1.75709 - 2.02779i) q^{94} +(0.655420 - 4.55855i) q^{96} +(-14.2356 - 6.50117i) q^{97} +(-1.42247 + 0.204521i) q^{98} +(-4.49088 - 1.31864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{4} - 18 q^{6} + 34 q^{9}+O(q^{10}) $ 40 * q + 8 * q^4 - 18 * q^6 + 34 * q^9	$ 40 q + 8 q^{4} - 18 q^{6} + 34 q^{9} - 16 q^{11} - 6 q^{14} - 72 q^{16} - 48 q^{19} + 50 q^{21} - 4 q^{26} - 24 q^{29} + 20 q^{31} + 14 q^{34} + 86 q^{36} + 104 q^{39} + 20 q^{41} - 12 q^{44} - 66 q^{46} - 8 q^{49} + 100 q^{51} - 46 q^{54} - 82 q^{59} - 26 q^{61} - 32 q^{64} + 112 q^{66} + 90 q^{69} - 38 q^{71} - 16 q^{74} + 8 q^{76} + 166 q^{79} + 24 q^{81} - 56 q^{84} - 146 q^{86} + 10 q^{89} - 168 q^{91} + 74 q^{94} + 28 q^{96} - 124 q^{99}+O(q^{100}) $ 40 * q + 8 * q^4 - 18 * q^6 + 34 * q^9 - 16 * q^11 - 6 * q^14 - 72 * q^16 - 48 * q^19 + 50 * q^21 - 4 * q^26 - 24 * q^29 + 20 * q^31 + 14 * q^34 + 86 * q^36 + 104 * q^39 + 20 * q^41 - 12 * q^44 - 66 * q^46 - 8 * q^49 + 100 * q^51 - 46 * q^54 - 82 * q^59 - 26 * q^61 - 32 * q^64 + 112 * q^66 + 90 * q^69 - 38 * q^71 - 16 * q^74 + 8 * q^76 + 166 * q^79 + 24 * q^81 - 56 * q^84 - 146 * q^86 + 10 * q^89 - 168 * q^91 + 74 * q^94 + 28 * q^96 - 124 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$-1$

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 $

$2$	−0.215109	+	0.186393i	−0.152105	+	0.131800i	−0.727589	−	0.686013i	$-0.759359\pi$
$2$	−0.215109	+	0.186393i	−0.152105	+	0.131800i	0.575484	+	0.817813i	$0.304814\pi$
$3$	0.770157	−	1.19839i	0.444650	−	0.691889i	−0.544506	−	0.838757i	$-0.683283\pi$
$3$	0.770157	−	1.19839i	0.444650	−	0.691889i	0.989156	+	0.146868i	$0.0469192\pi$
$4$	−0.273100	+	1.89945i	−0.136550	+	0.949727i
$5$		0			0
$5$		0			0
$6$	0.0577033	+	0.401335i	0.0235573	+	0.163844i
$7$	−0.393517	+	1.34020i	−0.148735	+	0.506546i	−0.999829	−	0.0184669i	$-0.994121\pi$
$7$	−0.393517	+	1.34020i	−0.148735	+	0.506546i	0.851094	+	0.525013i	$0.175940\pi$
$8$	−0.603063	−	0.938384i	−0.213215	−	0.331769i
$9$	0.403254	+	0.883004i	0.134418	+	0.294335i
$10$		0			0
$11$	−3.15749	+	3.64393i	−0.952018	+	1.09869i	0.0430085	+	0.999075i	$0.486306\pi$
$11$	−3.15749	+	3.64393i	−0.952018	+	1.09869i	−0.995026	+	0.0996124i	$0.968240\pi$
$12$	2.06595	+	1.79016i	0.596389	+	0.516774i
$13$	−0.0804117	−	0.273857i	−0.0223022	−	0.0759543i	0.947590	−	0.319489i	$-0.103511\pi$
$13$	−0.0804117	−	0.273857i	−0.0223022	−	0.0759543i	−0.969892	+	0.243535i	$0.921693\pi$
$14$	−0.165154	−	0.361637i	−0.0441392	−	0.0966514i
$15$		0			0
$16$	−3.37787	−	0.991834i	−0.844469	−	0.247958i
$17$	−0.472917	+	0.0679951i	−0.114699	+	0.0164912i	−0.199425	−	0.979913i	$-0.563908\pi$
$17$	−0.472917	+	0.0679951i	−0.114699	+	0.0164912i	0.0847262	+	0.996404i	$0.472998\pi$
$18$	−0.251329	−	0.114778i	−0.0592388	−	0.0270535i
$19$	−0.140789	+	0.979208i	−0.0322992	+	0.224646i	−0.999577	−	0.0290727i	$-0.990745\pi$
$19$	−0.140789	+	0.979208i	−0.0322992	+	0.224646i	0.967278	+	0.253718i	$0.0816536\pi$
$20$		0			0
$21$	1.30300	+	1.50375i	0.284339	+	0.328144i
$22$		−	1.37237i		−	0.292591i
$23$	−1.21649	+	4.63898i	−0.253655	+	0.967295i
$23$	−1.21649	+	4.63898i	−0.253655	+	0.967295i
$24$	−1.58900			−0.324354
$25$		0			0
$26$	0.0683422	+	0.0439209i	0.0134030	+	0.00861359i
$27$	5.59883	+	0.804990i	1.07749	+	0.154920i
$28$	−2.43817	−	1.11347i	−0.460771	−	0.210427i
$29$	−0.0219083	−	0.152376i	−0.00406828	−	0.0282955i	0.987686	−	0.156448i	$-0.0500044\pi$
$29$	−0.0219083	−	0.152376i	−0.00406828	−	0.0282955i	−0.991754	+	0.128153i	$0.959095\pi$
$30$		0			0
$31$	−3.01445	+	1.93727i	−0.541411	+	0.347944i	−0.782591	−	0.622537i	$-0.786102\pi$
$31$	−3.01445	+	1.93727i	−0.541411	+	0.347944i	0.241179	+	0.970481i	$0.422466\pi$
$32$	2.94080	−	1.34302i	0.519864	−	0.237414i
$33$	1.93508	+	6.59029i	0.336855	+	1.14722i
$34$	0.0890547	−	0.102775i	0.0152728	−	0.0176257i
$35$		0			0
$36$	−1.78735	+	0.524814i	−0.297892	+	0.0874690i
$37$	3.74020	−	1.70809i	0.614886	−	0.280809i	−0.0835254	−	0.996506i	$-0.526618\pi$
$37$	3.74020	−	1.70809i	0.614886	−	0.280809i	0.698411	+	0.715697i	$0.253891\pi$
$38$	−0.152232	−	0.236878i	−0.0246953	−	0.0384267i
$39$	−0.390116	−	0.114549i	−0.0624686	−	0.0183424i
$40$		0			0
$41$	−2.86572	+	6.27505i	−0.447550	+	0.979998i	0.542600	+	0.839991i	$0.317440\pi$
$41$	−2.86572	+	6.27505i	−0.447550	+	0.979998i	−0.990150	+	0.140007i	$0.955287\pi$
$42$	−0.560575	−	0.0805985i	−0.0864986	−	0.0124366i
$43$	5.81663	−	9.05086i	0.887028	−	1.38024i	−0.0375681	−	0.999294i	$-0.511961\pi$
$43$	5.81663	−	9.05086i	0.887028	−	1.38024i	0.924596	−	0.380949i	$-0.124403\pi$
$44$	−6.05917	−	6.99266i	−0.913454	−	1.05418i
$45$		0			0
$46$	−0.602996	−	1.22463i	−0.0889069	−	0.180562i
$47$			9.42683i			1.37504i	0.726163	+	0.687522i	$0.241302\pi$
$47$			9.42683i			1.37504i	−0.726163	+	0.687522i	$0.758698\pi$
$48$	−3.79009	+	3.28414i	−0.547053	+	0.474024i
$49$	4.24751	+	2.72971i	0.606787	+	0.389958i
$50$		0			0
$51$	−0.282735	+	0.619104i	−0.0395909	+	0.0866919i
$52$	0.542139	−	0.0779478i	0.0751812	−	0.0108094i
$53$	1.35702	−	4.62159i	0.186401	−	0.634824i	−0.812270	−	0.583282i	$-0.801768\pi$
$53$	1.35702	−	4.62159i	0.186401	−	0.634824i	0.998671	−	0.0515417i	$-0.0164135\pi$
$54$	−1.35440	+	0.870421i	−0.184311	+	0.118449i
$55$		0			0
$56$	1.49493	−	0.438952i	0.199769	−	0.0586575i
$57$	1.06504	+	0.922863i	0.141068	+	0.122236i
$58$	0.0331144	+	0.0286938i	0.00434814	+	0.00376768i
$59$	−6.57113	+	1.92946i	−0.855488	+	0.251194i	−0.679932	−	0.733275i	$-0.737991\pi$
$59$	−6.57113	+	1.92946i	−0.855488	+	0.251194i	−0.175556	+	0.984469i	$0.556172\pi$
$60$		0			0
$61$	9.16678	−	5.89113i	1.17369	−	0.754282i	0.199471	−	0.979904i	$-0.436078\pi$
$61$	9.16678	−	5.89113i	1.17369	−	0.754282i	0.974215	+	0.225621i	$0.0724412\pi$
$62$	0.287342	−	0.978595i	0.0364924	−	0.124282i
$63$	−1.34208	+	0.192963i	−0.169087	+	0.0243110i
$64$	2.54266	−	5.56764i	0.317832	−	0.695955i
$65$		0			0
$66$	−1.64464	−	1.05694i	−0.202441	−	0.130101i
$67$	−5.33316	+	4.62121i	−0.651550	+	0.564571i	−0.916670	−	0.399644i	$-0.869134\pi$
$67$	−5.33316	+	4.62121i	−0.651550	+	0.564571i	0.265121	+	0.964215i	$0.414588\pi$
$68$		−	0.916853i		−	0.111185i
$69$	4.62241	+	5.03057i	0.556473	+	0.605609i
$70$		0			0
$71$	7.91831	+	9.13822i	0.939731	+	1.08451i	0.996286	+	0.0861075i	$0.0274428\pi$
$71$	7.91831	+	9.13822i	0.939731	+	1.08451i	−0.0565552	+	0.998399i	$0.518012\pi$
$72$	0.585409	−	0.910914i	0.0689911	−	0.107352i
$73$	−6.75135	−	0.970698i	−0.790186	−	0.113612i	−0.264607	−	0.964356i	$-0.585242\pi$
$73$	−6.75135	−	0.970698i	−0.790186	−	0.113612i	−0.525579	+	0.850745i	$0.676151\pi$
$74$	−0.486174	+	1.06457i	−0.0565166	+	0.123754i
$75$		0			0
$76$	−1.82151	−	0.534844i	−0.208942	−	0.0613508i
$77$	−3.64106	−	5.66560i	−0.414937	−	0.645655i
$78$	0.105268	−	0.0480745i	0.0119193	−	0.00544336i
$79$	11.4955	−	3.37537i	1.29334	−	0.379759i	0.438537	−	0.898713i	$-0.355497\pi$
$79$	11.4955	−	3.37537i	1.29334	−	0.379759i	0.854802	+	0.518954i	$0.173678\pi$
$80$		0			0
$81$	3.36959	−	3.88872i	0.374399	−	0.432080i
$82$	−0.553183	−	1.88397i	−0.0610888	−	0.208049i
$83$	5.91956	−	2.70337i	0.649756	−	0.296733i	−0.0631388	−	0.998005i	$-0.520111\pi$
$83$	5.91956	−	2.70337i	0.649756	−	0.296733i	0.712895	+	0.701271i	$0.247384\pi$
$84$	−3.21215	+	2.06432i	−0.350474	+	0.225236i
$85$		0			0
$86$	0.435806	+	3.03110i	0.0469942	+	0.326852i
$87$	−0.199478	−	0.0910986i	−0.0213863	−	0.00976680i
$88$	5.32357	+	0.765414i	0.567495	+	0.0815934i
$89$	9.20422	+	5.91519i	0.975645	+	0.627009i	0.928285	−	0.371869i	$-0.121283\pi$
$89$	9.20422	+	5.91519i	0.975645	+	0.627009i	0.0473599	+	0.998878i	$0.484919\pi$
$90$		0			0
$91$	0.398665			0.0417915
$92$	−8.47931	−	3.57757i	−0.884029	−	0.372987i
$93$			5.10448i			0.529310i
$94$	−1.75709	−	2.02779i	−0.181230	−	0.209151i
$95$		0			0
$96$	0.655420	−	4.55855i	0.0668935	−	0.465255i
$97$	−14.2356	−	6.50117i	−1.44540	−	0.660094i	−0.470434	−	0.882435i	$-0.655903\pi$
$97$	−14.2356	−	6.50117i	−1.44540	−	0.660094i	−0.974969	+	0.222341i	$0.928630\pi$
$98$	−1.42247	+	0.204521i	−0.143692	+	0.0206597i
$99$	−4.49088	−	1.31864i	−0.451350	−	0.132528i
$100$		0			0
$101$	−7.64997	−	16.7511i	−0.761201	−	1.66680i	−0.745123	−	0.666927i	$-0.767609\pi$
$101$	−7.64997	−	16.7511i	−0.761201	−	1.66680i	−0.0160775	−	0.999871i	$-0.505118\pi$
$102$	−0.0545777	−	0.185875i	−0.00540400	−	0.0184043i
$103$	−10.0181	−	8.68070i	−0.987109	−	0.855335i	0.00237206	−	0.999997i	$-0.499245\pi$
$103$	−10.0181	−	8.68070i	−0.987109	−	0.855335i	−0.989481	+	0.144662i	$0.953790\pi$
$104$	−0.208490	+	0.240610i	−0.0204441	+	0.0235938i
$105$		0			0
$106$	0.569523	+	1.24708i	0.0553170	+	0.121127i
$107$	−2.85330	−	4.43983i	−0.275839	−	0.429214i	0.675500	−	0.737360i	$-0.263928\pi$
$107$	−2.85330	−	4.43983i	−0.275839	−	0.429214i	−0.951339	+	0.308146i	$0.900292\pi$
$108$	−3.05808	+	10.4149i	−0.294264	+	1.00217i
$109$	1.42192	+	9.88966i	0.136195	+	0.947258i	0.937248	+	0.348664i	$0.113365\pi$
$109$	1.42192	+	9.88966i	0.136195	+	0.947258i	−0.801053	+	0.598594i	$0.795726\pi$
$110$		0			0
$111$	0.833586	−	5.79771i	0.0791204	−	0.550295i
$112$	2.65850	−	4.13671i	0.251205	−	0.390882i
$113$	2.79303	−	2.42018i	0.262746	−	0.227671i	−0.513518	−	0.858079i	$-0.671658\pi$
$113$	2.79303	−	2.42018i	0.262746	−	0.227671i	0.776264	+	0.630408i	$0.217112\pi$
$114$	−0.401115			−0.0375678
$115$		0			0
$116$	0.295414			0.0274285
$117$	0.209390	−	0.181438i	0.0193581	−	0.0167739i
$118$	1.05387	−	1.63985i	0.0970166	−	0.150961i
$119$	0.0949739	−	0.660558i	0.00870624	−	0.0605533i
$120$		0			0
$121$	−1.74307	−	12.1233i	−0.158461	−	1.10212i
$122$	−0.873790	+	2.97586i	−0.0791093	+	0.269421i
$123$	5.31289	+	8.26701i	0.479047	+	0.745412i
$124$	−2.85651	−	6.25488i	−0.256522	−	0.561704i
$125$		0			0
$126$	0.252727	−	0.291663i	0.0225147	−	0.0259834i
$127$	10.4454	+	9.05096i	0.926877	+	0.803143i	0.980722	−	0.195406i	$-0.0626025\pi$
$127$	10.4454	+	9.05096i	0.926877	+	0.803143i	−0.0538457	+	0.998549i	$0.517148\pi$
$128$	2.31248	+	7.87557i	0.204396	+	0.696109i
$129$	−6.36671	−	13.9412i	−0.560558	−	1.22745i
$130$		0			0
$131$	−5.21153	−	1.53024i	−0.455334	−	0.133698i	0.0460199	−	0.998941i	$-0.485346\pi$
$131$	−5.21153	−	1.53024i	−0.455334	−	0.133698i	−0.501354	+	0.865242i	$0.667164\pi$
$132$	−13.0464	+	1.87579i	−1.13555	+	0.163267i
$133$	−1.25693	−	0.574019i	−0.108989	−	0.0497738i
$134$	0.285849	−	1.98813i	0.0246936	−	0.171748i
$135$		0			0
$136$	0.349004	+	0.402772i	0.0299269	+	0.0345374i
$137$		−	19.5590i		−	1.67104i	−0.549460	−	0.835520i	$-0.685166\pi$
$137$		−	19.5590i		−	1.67104i	0.549460	−	0.835520i	$-0.314834\pi$
$138$	−1.93198	−	0.220534i	−0.164461	−	0.0187731i
$139$	11.0234			0.934992			0.467496	−	0.883995i	$-0.345156\pi$
$139$	11.0234			0.934992			0.467496	+	0.883995i	$0.345156\pi$
$140$		0			0
$141$	11.2970	+	7.26014i	0.951379	+	0.611414i
$142$	−3.40660	−	0.489795i	−0.285875	−	0.0411026i
$143$	1.25182	+	0.571685i	0.104682	+	0.0478067i
$144$	−0.486350	−	3.38264i	−0.0405291	−	0.281886i
$145$		0			0
$146$	1.63321	−	1.04960i	0.135165	−	0.0868654i
$147$	6.54249	−	2.98786i	0.539616	−	0.246434i
$148$	2.22300	+	7.57083i	0.182729	+	0.622318i
$149$	−6.50751	+	7.51007i	−0.533116	+	0.615249i	−0.956866	−	0.290531i	$-0.906168\pi$
$149$	−6.50751	+	7.51007i	−0.533116	+	0.615249i	0.423750	+	0.905779i	$0.360714\pi$
$150$		0			0
$151$	19.4770	−	5.71897i	1.58502	−	0.465403i	0.633691	−	0.773586i	$-0.281539\pi$
$151$	19.4770	−	5.71897i	1.58502	−	0.465403i	0.951327	+	0.308182i	$0.0997207\pi$
$152$	1.00378	−	0.458410i	0.0814171	−	0.0371820i
$153$	−0.250746	−	0.390168i	−0.0202716	−	0.0315432i
$154$	1.83925	+	0.540053i	0.148211	+	0.0435187i
$155$		0			0
$156$	0.324120	−	0.709725i	0.0259504	−	0.0568235i
$157$	−15.8422	−	2.27777i	−1.26435	−	0.181786i	−0.522666	−	0.852537i	$-0.675063\pi$
$157$	−15.8422	−	2.27777i	−1.26435	−	0.181786i	−0.741682	+	0.670752i	$0.765972\pi$
$158$	−1.84363	+	2.86874i	−0.146671	+	0.228225i
$159$	−4.49333	−	5.18558i	−0.356344	−	0.411243i
$160$		0			0
$161$	−5.73844	−	3.45585i	−0.452252	−	0.272359i
$162$			1.46457i			0.115067i
$163$	11.8242	−	10.2457i	0.926140	−	0.802505i	−0.0544617	−	0.998516i	$-0.517344\pi$
$163$	11.8242	−	10.2457i	0.926140	−	0.802505i	0.980602	+	0.196011i	$0.0627988\pi$
$164$	−11.1365	−	7.15702i	−0.869617	−	0.558869i
$165$		0			0
$166$	−0.769460	+	1.68488i	−0.0597216	+	0.130772i
$167$	10.0683	−	1.44760i	0.779108	−	0.112019i	0.258724	−	0.965951i	$-0.416698\pi$
$167$	10.0683	−	1.44760i	0.779108	−	0.112019i	0.520384	+	0.853932i	$0.325789\pi$
$168$	0.625299	−	2.12957i	0.0482429	−	0.164300i
$169$	10.8678	−	6.98429i	0.835982	−	0.537253i
$170$		0			0
$171$	−0.921418	+	0.270553i	−0.0704626	+	0.0206897i
$172$	15.6032	+	13.5202i	1.18973	+	1.03091i
$173$	−3.41088	−	2.95554i	−0.259324	−	0.224706i	0.515489	−	0.856896i	$-0.327610\pi$
$173$	−3.41088	−	2.95554i	−0.259324	−	0.224706i	−0.774813	+	0.632191i	$0.782156\pi$
$174$	0.0598896	−	0.0175852i	0.00454022	−	0.00133313i
$175$		0			0
$176$	14.2798	−	9.17705i	1.07638	−	0.691746i
$177$	−2.74856	+	9.36074i	−0.206595	+	0.703597i
$178$	−3.08246	+	0.443190i	−0.231040	+	0.0332185i
$179$	−0.247518	+	0.541990i	−0.0185004	+	0.0405102i	−0.918657	−	0.395057i	$-0.870725\pi$
$179$	−0.247518	+	0.541990i	−0.0185004	+	0.0405102i	0.900156	+	0.435567i	$0.143452\pi$
$180$		0			0
$181$	2.38858	+	1.53505i	0.177542	+	0.114099i	0.626393	−	0.779507i	$-0.284530\pi$
$181$	2.38858	+	1.53505i	0.177542	+	0.114099i	−0.448852	+	0.893606i	$0.648167\pi$
$182$	−0.0857564	+	0.0743083i	−0.00635669	+	0.00550810i
$183$		−	15.5225i		−	1.14745i
$184$	5.08677	−	1.65607i	0.375001	−	0.122087i
$185$		0			0
$186$	−0.951438	−	1.09802i	−0.0697628	−	0.0805106i
$187$	1.24546	−	1.93797i	0.0910769	−	0.141718i
$188$	−17.9058	−	2.57447i	−1.30592	−	0.187762i
$189$	−3.28208	+	7.18675i	−0.238736	+	0.522759i
$190$		0			0
$191$	−15.0790	−	4.42758i	−1.09107	−	0.320368i	−0.313774	−	0.949498i	$-0.601593\pi$
$191$	−15.0790	−	4.42758i	−1.09107	−	0.320368i	−0.777301	+	0.629129i	$0.783412\pi$
$192$	−4.71395	−	7.33505i	−0.340200	−	0.529361i
$193$	18.8022	−	8.58667i	1.35341	−	0.618082i	0.399102	−	0.916906i	$-0.369322\pi$
$193$	18.8022	−	8.58667i	1.35341	−	0.618082i	0.954308	+	0.298825i	$0.0965946\pi$
$194$	4.27397	−	1.25495i	0.306853	−	0.0901002i
$195$		0			0
$196$	−6.34494	+	7.32246i	−0.453210	+	0.523033i
$197$	2.24806	+	7.65620i	0.160168	+	0.545482i	0.999997	+	0.00263008i	$0.000837181\pi$
$197$	2.24806	+	7.65620i	0.160168	+	0.545482i	−0.839829	+	0.542852i	$0.817345\pi$
$198$	1.21181	−	0.553416i	0.0861197	−	0.0393296i
$199$	−4.32669	+	2.78059i	−0.306711	+	0.197111i	−0.684937	−	0.728602i	$-0.740170\pi$
$199$	−4.32669	+	2.78059i	−0.306711	+	0.197111i	0.378227	+	0.925713i	$0.376534\pi$
$200$		0			0
$201$	1.43063	+	9.95025i	0.100909	+	0.701837i
$202$	4.76786	+	2.17741i	0.335466	+	0.153202i
$203$	0.212835	+	0.0306010i	0.0149381	+	0.00214777i
$204$	−1.09874	−	0.706120i	−0.0769275	−	0.0494383i
$205$		0			0
$206$	3.77299			0.262877
$207$	−4.58679	+	0.796528i	−0.318804	+	0.0553625i
$208$			1.00481i			0.0696710i
$209$	−3.12363	−	3.60486i	−0.216066	−	0.249353i
$210$		0			0
$211$	−3.81714	+	26.5488i	−0.262783	+	1.82769i	0.248910	+	0.968527i	$0.419928\pi$
$211$	−3.81714	+	26.5488i	−0.262783	+	1.82769i	−0.511693	+	0.859168i	$0.670982\pi$
$212$	8.40788	+	3.83975i	0.577456	+	0.263715i
$213$	17.0495	−	2.45134i	1.16821	−	0.167963i
$214$	1.44132	+	0.423210i	0.0985267	+	0.0289301i
$215$		0			0
$216$	−2.62106	−	5.73931i	−0.178340	−	0.390511i
$217$	−1.41008	−	4.80230i	−0.0957226	−	0.326001i
$218$	−2.14923	−	1.86232i	−0.145564	−	0.126132i
$219$	−6.36287	+	7.34315i	−0.429963	+	0.496204i
$220$		0			0
$221$	0.0566490	+	0.124044i	0.00381062	+	0.00834410i
$222$	0.901341	+	1.40251i	0.0604940	+	0.0941305i
$223$	−1.50282	+	5.11814i	−0.100636	+	0.342736i	−0.994384	−	0.105835i	$-0.966249\pi$
$223$	−1.50282	+	5.11814i	−0.100636	+	0.342736i	0.893747	+	0.448571i	$0.148067\pi$
$224$	0.642652	+	4.46974i	0.0429390	+	0.298647i
$225$		0			0
$226$	−0.149702	+	1.04120i	−0.00995805	+	0.0692597i
$227$	−4.03396	+	6.27697i	−0.267744	+	0.416617i	−0.948927	−	0.315496i	$-0.897829\pi$
$227$	−4.03396	+	6.27697i	−0.267744	+	0.416617i	0.681183	+	0.732113i	$0.261466\pi$
$228$	−2.04380	+	1.77096i	−0.135354	+	0.117285i
$229$	23.1789			1.53171			0.765853	−	0.643016i	$-0.222317\pi$
$229$	23.1789			1.53171			0.765853	+	0.643016i	$0.222317\pi$
$230$		0			0
$231$	−9.59377			−0.631224
$232$	−0.129775	+	0.112451i	−0.00852015	+	0.00738275i
$233$	−13.1783	+	20.5058i	−0.863339	+	1.34338i	0.0748270	+	0.997197i	$0.476160\pi$
$233$	−13.1783	+	20.5058i	−0.863339	+	1.34338i	−0.938166	+	0.346185i	$0.887477\pi$
$234$	−0.0112230	+	0.0780577i	−0.000733671	+	0.00510279i
$235$		0			0
$236$	−1.87034	−	13.0085i	−0.121749	−	0.846781i
$237$	4.80830	−	16.3756i	0.312333	−	1.06371i
$238$	0.102694	+	0.159794i	0.00665663	+	0.0103579i
$239$	0.487763	+	1.06805i	0.0315508	+	0.0690865i	0.924751	−	0.380572i	$-0.124273\pi$
$239$	0.487763	+	1.06805i	0.0315508	+	0.0690865i	−0.893200	+	0.449659i	$0.851546\pi$
$240$		0			0
$241$	−4.31739	+	4.98254i	−0.278108	+	0.320953i	−0.877569	−	0.479450i	$-0.840836\pi$
$241$	−4.31739	+	4.98254i	−0.278108	+	0.320953i	0.599461	+	0.800404i	$0.295382\pi$
$242$	2.63464	+	2.28293i	0.169361	+	0.146752i
$243$	2.71570	+	9.24883i	0.174212	+	0.593313i
$244$	8.68649	+	19.0207i	0.556095	+	1.21768i
$245$		0			0
$246$	−2.68376	−	0.788023i	−0.171110	−	0.0502425i
$247$	0.279484	−	0.0401837i	0.0177831	−	0.00255683i
$248$	3.63581	+	1.66042i	0.230874	+	0.105437i
$249$	1.31930	−	9.17594i	0.0836073	−	0.581502i
$250$		0			0
$251$	2.65036	+	3.05867i	0.167289	+	0.193062i	0.833204	−	0.552966i	$-0.186504\pi$
$251$	2.65036	+	3.05867i	0.167289	+	0.193062i	−0.665915	+	0.746028i	$0.731959\pi$
$252$		−	2.60193i		−	0.163906i
$253$	−13.0631	−	19.0803i	−0.821270	−	1.19957i
$254$	−3.93393			−0.246836
$255$		0			0
$256$	8.33284	+	5.35519i	0.520803	+	0.334700i
$257$	0.628540	+	0.0903704i	0.0392072	+	0.00563715i	0.161891	−	0.986809i	$-0.448241\pi$
$257$	0.628540	+	0.0903704i	0.0392072	+	0.00563715i	−0.122683	+	0.992446i	$0.539150\pi$
$258$	3.96807	+	1.81216i	0.247041	+	0.112820i
$259$	0.817347	+	5.68477i	0.0507874	+	0.353234i
$260$		0			0
$261$	0.125714	−	0.0807914i	0.00778149	−	0.00500086i
$262$	1.40627	−	0.642223i	0.0868798	−	0.0396767i
$263$	6.09727	+	20.7654i	0.375974	+	1.28045i	0.902647	+	0.430381i	$0.141621\pi$
$263$	6.09727	+	20.7654i	0.375974	+	1.28045i	−0.526674	+	0.850067i	$0.676561\pi$
$264$	5.01725	−	5.79021i	0.308790	−	0.356363i
$265$		0			0
$266$	0.377369	−	0.110806i	0.0231380	−	0.00679392i
$267$	14.1774	−	6.47459i	0.867642	−	0.396239i
$268$	−7.32129	−	11.3921i	−0.447219	−	0.695886i
$269$	−0.600207	−	0.176237i	−0.0365953	−	0.0107453i	0.263384	−	0.964691i	$-0.415161\pi$
$269$	−0.600207	−	0.176237i	−0.0365953	−	0.0107453i	−0.299979	+	0.953946i	$0.596980\pi$
$270$		0			0
$271$	−1.53336	+	3.35760i	−0.0931452	+	0.203959i	−0.950470	−	0.310816i	$-0.899398\pi$
$271$	−1.53336	+	3.35760i	−0.0931452	+	0.203959i	0.857325	+	0.514776i	$0.172125\pi$
$272$	1.66489	+	0.239375i	0.100949	+	0.0145143i
$273$	0.307035	−	0.477755i	0.0185826	−	0.0289151i
$274$	3.64566	+	4.20732i	0.220242	+	0.254173i
$275$		0			0
$276$	−10.8177	+	7.40621i	−0.651149	+	0.445801i
$277$			18.1797i			1.09231i	0.837683	+	0.546156i	$0.183909\pi$
$277$			18.1797i			1.09231i	−0.837683	+	0.546156i	$0.816091\pi$
$278$	−2.37123	+	2.05468i	−0.142217	+	0.123232i
$279$	−2.92621	−	1.88056i	−0.175187	−	0.112586i
$280$		0			0
$281$	2.09803	−	4.59405i	0.125158	−	0.274058i	−0.836673	−	0.547703i	$-0.815502\pi$
$281$	2.09803	−	4.59405i	0.125158	−	0.274058i	0.961831	+	0.273645i	$0.0882295\pi$
$282$	−3.78332	+	0.543959i	−0.225293	+	0.0323923i
$283$	0.285131	−	0.971066i	0.0169493	−	0.0577239i	−0.950584	−	0.310467i	$-0.899515\pi$
$283$	0.285131	−	0.971066i	0.0169493	−	0.0577239i	0.967533	+	0.252743i	$0.0813328\pi$
$284$	−19.5201	+	12.5448i	−1.15831	+	0.744398i
$285$		0			0
$286$	−0.375834	+	0.110355i	−0.0222236	+	0.00652542i
$287$	−7.28209	−	6.30996i	−0.429848	−	0.372465i
$288$	2.37178	+	2.05516i	0.139758	+	0.121101i
$289$	−16.0924	+	4.72514i	−0.946609	+	0.277949i
$290$		0			0
$291$	−18.7545	+	12.0528i	−1.09941	+	0.706548i
$292$	3.68759	−	12.5588i	0.215800	−	0.734947i
$293$	−25.4376	+	3.65738i	−1.48608	+	0.213666i	−0.837063	−	0.547106i	$-0.815729\pi$
$293$	−25.4376	+	3.65738i	−1.48608	+	0.213666i	−0.649018	+	0.760773i	$0.724820\pi$
$294$	−0.850432	+	1.86219i	−0.0495982	+	0.108605i
$295$		0			0
$296$	−3.85843	−	2.47966i	−0.224267	−	0.144127i
$297$	−20.6116	+	17.8600i	−1.19600	+	1.03634i
$298$		−	2.82843i		−	0.163847i
$299$	1.36824	−	0.0398850i	0.0791272	−	0.00230661i
$300$		0			0
$301$	9.84097	+	11.3571i	0.567224	+	0.654612i
$302$	−3.12371	+	4.86058i	−0.179749	+	0.279695i
$303$	−25.9660	−	3.73335i	−1.49171	−	0.214475i
$304$	1.44678	−	3.16800i	0.0829784	−	0.181697i
$305$		0			0
$306$	0.126662	+	0.0371913i	0.00724079	+	0.00212609i
$307$	14.6708	+	22.8282i	0.837305	+	1.30287i	0.950948	+	0.309351i	$0.100112\pi$
$307$	14.6708	+	22.8282i	0.837305	+	1.30287i	−0.113643	+	0.993522i	$0.536252\pi$
$308$	11.7559	−	5.36875i	0.669855	−	0.305913i
$309$	−18.1183	+	5.32002i	−1.03072	+	0.302645i
$310$		0			0
$311$	−17.6451	+	20.3635i	−1.00056	+	1.15471i	−0.0126133	+	0.999920i	$0.504015\pi$
$311$	−17.6451	+	20.3635i	−1.00056	+	1.15471i	−0.987948	+	0.154788i	$0.950530\pi$
$312$	0.127774	+	0.435159i	0.00723379	+	0.0246360i
$313$	12.2569	−	5.59753i	0.692800	−	0.316391i	−0.0377142	−	0.999289i	$-0.512008\pi$
$313$	12.2569	−	5.59753i	0.692800	−	0.316391i	0.730514	+	0.682897i	$0.239280\pi$
$314$	3.83236	−	2.46291i	0.216273	−	0.138990i
$315$		0			0
$316$	3.27195	+	22.7569i	0.184061	+	1.28018i
$317$	5.34770	+	2.44221i	0.300357	+	0.137168i	0.559893	−	0.828565i	$-0.310842\pi$
$317$	5.34770	+	2.44221i	0.300357	+	0.137168i	−0.259536	+	0.965733i	$0.583570\pi$
$318$	1.93311	+	0.277939i	0.108403	+	0.0155861i
$319$	0.624423	+	0.401292i	0.0349610	+	0.0224680i
$320$		0			0
$321$	−7.51812			−0.419621
$322$	1.87853	−	0.326220i	0.104687	−	0.0181795i
$323$		−	0.472657i		−	0.0262993i
$324$	6.46620	+	7.46240i	0.359234	+	0.414578i
$325$		0			0
$326$	−0.633757	+	4.40788i	−0.0351006	+	0.244130i
$327$	12.9467	+	5.91258i	0.715957	+	0.326966i
$328$	7.61662	−	1.09510i	0.420557	−	0.0604670i
$329$	−12.6338	−	3.70962i	−0.696524	−	0.204518i
$330$		0			0
$331$	−6.04014	−	13.2261i	−0.331996	−	0.726970i	0.667854	−	0.744293i	$-0.267213\pi$
$331$	−6.04014	−	13.2261i	−0.331996	−	0.726970i	−0.999850	+	0.0173223i	$0.994486\pi$
$332$	3.51830	+	11.9822i	0.193092	+	0.657609i
$333$	3.01651	+	2.61382i	0.165304	+	0.143236i
$334$	−1.89596	+	2.18805i	−0.103742	+	0.119725i
$335$		0			0
$336$	−2.90992	−	6.37183i	−0.158749	−	0.347612i
$337$	−8.96566	−	13.9508i	−0.488391	−	0.759951i	0.506355	−	0.862325i	$-0.330992\pi$
$337$	−8.96566	−	13.9508i	−0.488391	−	0.759951i	−0.994746	+	0.102374i	$0.967356\pi$
$338$	−1.03593	+	3.52805i	−0.0563472	+	0.191901i
$339$	−0.749236	−	5.21105i	−0.0406929	−	0.283025i
$340$		0			0
$341$	2.45880	−	17.1014i	0.133152	−	0.926090i
$342$	0.147776	−	0.229944i	0.00799081	−	0.0124339i
$343$	−12.7191	+	11.0212i	−0.686766	+	0.595086i
$344$	−12.0010			−0.647049
$345$		0			0
$346$	1.28460			0.0690606
$347$	11.7122	−	10.1487i	0.628743	−	0.544809i	−0.281144	−	0.959666i	$-0.590714\pi$
$347$	11.7122	−	10.1487i	0.628743	−	0.544809i	0.909887	+	0.414857i	$0.136168\pi$
$348$	0.227515	−	0.354020i	0.0121961	−	0.0189775i
$349$	0.162561	−	1.13064i	0.00870168	−	0.0605215i	−0.985008	−	0.172509i	$-0.944813\pi$
$349$	0.162561	−	1.13064i	0.00870168	−	0.0605215i	0.993710	+	0.111988i	$0.0357217\pi$
$350$		0			0
$351$	−0.229759	−	1.59801i	−0.0122636	−	0.0852954i
$352$	−4.39166	+	14.9566i	−0.234076	+	0.797191i
$353$	−5.87070	−	9.13499i	−0.312466	−	0.486206i	0.649129	−	0.760678i	$-0.275133\pi$
$353$	−5.87070	−	9.13499i	−0.312466	−	0.486206i	−0.961595	+	0.274472i	$0.911497\pi$
$354$	−1.15354	−	2.52589i	−0.0613097	−	0.134250i
$355$		0			0
$356$	−13.7493	+	15.8675i	−0.728712	+	0.840978i
$357$	−0.718460	−	0.622549i	−0.0380249	−	0.0329488i
$358$	−0.0477796	−	0.162722i	−0.00252523	−	0.00860015i
$359$	−3.39979	−	7.44451i	−0.179434	−	0.392906i	0.798448	−	0.602064i	$-0.205655\pi$
$359$	−3.39979	−	7.44451i	−0.179434	−	0.392906i	−0.977882	+	0.209158i	$0.932928\pi$
$360$		0			0
$361$	17.2913	+	5.07720i	0.910071	+	0.267221i
$362$	−0.799925	+	0.115012i	−0.0420431	+	0.00604489i
$363$	−15.8708	−	7.24797i	−0.833003	−	0.380420i
$364$	−0.108876	+	0.757246i	−0.00570663	+	0.0396905i
$365$		0			0
$366$	2.89327	+	3.33902i	0.151234	+	0.174533i
$367$		−	1.28779i		−	0.0672223i	−0.999435	−	0.0336112i	$-0.989299\pi$
$367$		−	1.28779i		−	0.0672223i	0.999435	−	0.0336112i	$-0.0107008\pi$
$368$	8.71024	−	14.4634i	0.454053	−	0.753954i
$369$	−6.69651			−0.348606
$370$		0			0
$371$	5.65982	+	3.63734i	0.293843	+	0.188841i
$372$	−9.69572	−	1.39403i	−0.502700	−	0.0722773i
$373$	17.3106	+	7.90548i	0.896308	+	0.409330i	0.809653	−	0.586908i	$-0.199655\pi$
$373$	17.3106	+	7.90548i	0.896308	+	0.409330i	0.0866545	+	0.996238i	$0.472382\pi$
$374$	0.0933148	+	0.649019i	0.00482519	+	0.0335600i
$375$		0			0
$376$	8.84599	−	5.68497i	0.456197	−	0.293180i
$377$	−0.0399675	+	0.0182526i	−0.00205843	+	0.000940054i
$378$	−0.633554	−	2.15769i	−0.0325865	−	0.110979i
$379$	2.95818	−	3.41392i	0.151951	−	0.175361i	−0.674670	−	0.738119i	$-0.735714\pi$
$379$	2.95818	−	3.41392i	0.151951	−	0.175361i	0.826622	+	0.562758i	$0.190260\pi$
$380$		0			0
$381$	18.8911	−	5.54694i	0.967822	−	0.284178i
$382$	4.06888	−	1.85820i	0.208182	−	0.0950736i
$383$	20.0487	+	31.1963i	1.02444	+	1.59406i	0.781389	+	0.624044i	$0.214512\pi$
$383$	20.0487	+	31.1963i	1.02444	+	1.59406i	0.243050	+	0.970014i	$0.421852\pi$
$384$	11.2190	+	3.29418i	0.572515	+	0.168106i
$385$		0			0
$386$	−2.44402	+	5.35166i	−0.124397	+	0.272392i
$387$	10.3375	+	1.48631i	0.525486	+	0.0755534i
$388$	16.2364	−	25.2643i	0.824278	−	1.28260i
$389$	0.759670	+	0.876706i	0.0385168	+	0.0444508i	0.774681	−	0.632352i	$-0.217910\pi$
$389$	0.759670	+	0.876706i	0.0385168	+	0.0444508i	−0.736164	+	0.676803i	$0.763365\pi$
$390$		0			0
$391$	0.259868	−	2.27657i	0.0131421	−	0.115131i
$392$		−	5.63198i		−	0.284458i
$393$	−5.84752	+	5.06691i	−0.294969	+	0.255592i
$394$	−1.91064	−	1.22789i	−0.0962566	−	0.0618603i
$395$		0			0
$396$	3.73115	−	8.17009i	0.187498	−	0.410562i
$397$	12.3522	−	1.77598i	0.619940	−	0.0891340i	0.174814	−	0.984602i	$-0.444068\pi$
$397$	12.3522	−	1.77598i	0.619940	−	0.0891340i	0.445127	+	0.895468i	$0.353159\pi$
$398$	0.412426	−	1.40459i	0.0206730	−	0.0704059i
$399$	−1.65593	+	1.06420i	−0.0829001	+	0.0532767i
$400$		0			0
$401$	18.8475	−	5.53414i	0.941201	−	0.276362i	0.225082	−	0.974340i	$-0.427735\pi$
$401$	18.8475	−	5.53414i	0.941201	−	0.276362i	0.716119	+	0.697978i	$0.245917\pi$
$402$	−2.16240	−	1.87373i	−0.107851	−	0.0934530i
$403$	0.772932	+	0.669749i	0.0385025	+	0.0333626i
$404$	33.9072	−	9.95604i	1.68694	−	0.495331i
$405$		0			0
$406$	−0.0514864	+	0.0330883i	−0.00255523	+	0.00164215i
$407$	−5.58546	+	19.0223i	−0.276861	+	0.942902i
$408$	0.751465	−	0.108044i	0.0372031	−	0.00534899i
$409$	4.16456	−	9.11912i	0.205924	−	0.450912i	−0.778287	−	0.627909i	$-0.783911\pi$
$409$	4.16456	−	9.11912i	0.205924	−	0.450912i	0.984211	+	0.176997i	$0.0566384\pi$
$410$		0			0
$411$	−23.4393	−	15.0635i	−1.15617	−	0.743028i
$412$	19.2245	−	16.6581i	0.947124	−	0.820688i
$413$		−	9.56587i		−	0.470706i
$414$	0.838192	−	1.02628i	0.0411949	−	0.0504392i
$415$		0			0
$416$	−0.604269	−	0.697364i	−0.0296267	−	0.0341911i
$417$	8.48974	−	13.2103i	0.415744	−	0.646911i
$418$	1.34384	+	0.193215i	0.0657293	+	0.00945045i
$419$	−2.05722	+	4.50468i	−0.100502	+	0.220068i	−0.953203	−	0.302330i	$-0.902235\pi$
$419$	−2.05722	+	4.50468i	−0.100502	+	0.220068i	0.852701	+	0.522399i	$0.174963\pi$
$420$		0			0
$421$	−0.214743	−	0.0630541i	−0.0104659	−	0.00307307i	0.276495	−	0.961015i	$-0.410827\pi$
$421$	−0.214743	−	0.0630541i	−0.0104659	−	0.00307307i	−0.286961	+	0.957942i	$0.592645\pi$
$422$	−4.12740	−	6.42237i	−0.200919	−	0.312636i
$423$	−8.32393	+	3.80141i	−0.404723	+	0.184831i
$424$	−5.15519	+	1.51370i	−0.250358	+	0.0735118i
$425$		0			0
$426$	−3.21058	+	3.70520i	−0.155553	+	0.179518i
$427$	4.28799	+	14.6035i	0.207510	+	0.706715i
$428$	9.21248	−	4.20720i	0.445302	−	0.203363i
$429$	1.64919	−	1.05987i	0.0796238	−	0.0511711i
$430$		0			0
$431$	0.635308	+	4.41866i	0.0306017	+	0.212840i	0.999385	−	0.0350702i	$-0.0111655\pi$
$431$	0.635308	+	4.41866i	0.0306017	+	0.212840i	−0.968783	+	0.247910i	$0.920256\pi$
$432$	−18.1137	−	8.27226i	−0.871497	−	0.397999i
$433$	−17.2359	−	2.47814i	−0.828303	−	0.119092i	−0.284893	−	0.958559i	$-0.591958\pi$
$433$	−17.2359	−	2.47814i	−0.828303	−	0.119092i	−0.543410	+	0.839467i	$0.682867\pi$
$434$	1.19844	+	0.770188i	0.0575267	+	0.0369702i
$435$		0			0
$436$	−19.1733			−0.918233
$437$	−4.37126	−	1.84431i	−0.209106	−	0.0882253i
$438$		−	2.76557i		−	0.132144i
$439$	14.7508	+	17.0234i	0.704018	+	0.812481i	0.989290	−	0.145966i	$-0.0466291\pi$
$439$	14.7508	+	17.0234i	0.704018	+	0.812481i	−0.285271	+	0.958447i	$0.592084\pi$
$440$		0			0
$441$	−0.697516	+	4.85133i	−0.0332150	+	0.231016i
$442$	−0.0353066	−	0.0161240i	−0.00167936	−	0.000766939i
$443$	24.9079	−	3.58121i	1.18341	−	0.170149i	0.477617	−	0.878568i	$-0.341501\pi$
$443$	24.9079	−	3.58121i	1.18341	−	0.170149i	0.705792	+	0.708419i	$0.250591\pi$
$444$	10.7848	+	3.16671i	0.511826	+	0.150286i
$445$		0			0
$446$	−0.630715	−	1.38107i	−0.0298652	−	0.0653957i
$447$	3.98817	+	13.5824i	0.188634	+	0.642428i
$448$	6.46115	+	5.59862i	0.305261	+	0.264510i
$449$	16.9078	−	19.5127i	0.797930	−	0.920861i	−0.200335	−	0.979727i	$-0.564203\pi$
$449$	16.9078	−	19.5127i	0.797930	−	0.920861i	0.998266	+	0.0588666i	$0.0187487\pi$
$450$		0			0
$451$	−13.8174	−	30.2559i	−0.650636	−	1.42469i
$452$	3.83423	+	5.96618i	0.180347	+	0.280626i
$453$	8.14683	−	27.7455i	0.382771	−	1.30360i
$454$	−0.302241	−	2.10213i	−0.0141849	−	0.0986580i
$455$		0			0
$456$	0.223714	−	1.55596i	0.0104763	−	0.0728646i
$457$	18.9827	−	29.5376i	0.887973	−	1.38171i	−0.0360394	−	0.999350i	$-0.511474\pi$
$457$	18.9827	−	29.5376i	0.887973	−	1.38171i	0.924012	−	0.382363i	$-0.124889\pi$
$458$	−4.98599	+	4.32038i	−0.232980	+	0.201878i
$459$	−2.70251			−0.126143
$460$		0			0
$461$	26.7881			1.24765			0.623824	−	0.781565i	$-0.285578\pi$
$461$	26.7881			1.24765			0.623824	+	0.781565i	$0.285578\pi$
$462$	2.06370	−	1.78821i	0.0960122	−	0.0831950i
$463$	−7.06099	+	10.9871i	−0.328152	+	0.510614i	−0.965653	−	0.259835i	$-0.916332\pi$
$463$	−7.06099	+	10.9871i	−0.328152	+	0.510614i	0.637501	+	0.770449i	$0.279968\pi$
$464$	−0.0771279	+	0.536436i	−0.00358057	+	0.0249034i
$465$		0			0
$466$	−0.987372	−	6.86732i	−0.0457391	−	0.318123i
$467$	1.09396	−	3.72568i	0.0506224	−	0.172404i	−0.930302	−	0.366795i	$-0.880455\pi$
$467$	1.09396	−	3.72568i	0.0506224	−	0.172404i	0.980924	+	0.194391i	$0.0622732\pi$
$468$	0.287448	+	0.447278i	0.0132873	+	0.0206754i
$469$	−4.09464	−	8.96601i	−0.189073	−	0.414012i
$470$		0			0
$471$	−14.9307	+	17.2309i	−0.687968	+	0.793958i
$472$	5.77338	+	5.00266i	0.265741	+	0.230266i
$473$	14.6148	+	49.7734i	0.671988	+	2.28858i
$474$	2.01798	+	4.41876i	0.0926889	+	0.202960i
$475$		0			0
$476$	1.22876	+	0.360797i	0.0563202	+	0.0165371i
$477$	4.62810	−	0.665420i	0.211906	−	0.0304675i
$478$	−0.303999	−	0.138832i	−0.0139046	−	0.00635002i
$479$	−2.80762	+	19.5274i	−0.128283	+	0.892231i	0.819446	+	0.573156i	$0.194281\pi$
$479$	−2.80762	+	19.5274i	−0.128283	+	0.892231i	−0.947730	+	0.319075i	$0.896628\pi$
$480$		0			0
$481$	−0.768530	−	0.886931i	−0.0350419	−	0.0404406i
$482$		−	1.87652i		−	0.0854731i
$483$	−8.56094	+	4.21532i	−0.389536	+	0.191804i
$484$	23.5037			1.06835
$485$		0			0
$486$	−2.30809	−	1.48332i	−0.104697	−	0.0672846i
$487$	−37.3513	−	5.37031i	−1.69255	−	0.243352i	−0.772460	−	0.635063i	$-0.780974\pi$
$487$	−37.3513	−	5.37031i	−1.69255	−	0.243352i	−0.920088	+	0.391711i	$0.871883\pi$
$488$	−11.0563	−	5.04924i	−0.500495	−	0.228568i
$489$	−3.17185	−	22.0607i	−0.143436	−	0.997620i
$490$		0			0
$491$	−5.59270	+	3.59421i	−0.252395	+	0.162204i	−0.660721	−	0.750632i	$-0.729749\pi$
$491$	−5.59270	+	3.59421i	−0.252395	+	0.162204i	0.408326	+	0.912836i	$0.366113\pi$
$492$	−17.1538	+	7.83386i	−0.773351	+	0.353178i
$493$	0.0207216	+	0.0705714i	0.000933256	+	0.00317838i
$494$	−0.0526295	+	0.0607377i	−0.00236791	+	0.00273272i
$495$		0			0
$496$	12.1039	−	3.55402i	0.543480	−	0.159580i
$497$	−15.3630	+	7.01604i	−0.689124	+	0.314712i
$498$	1.42654	+	2.21973i	0.0639246	+	0.0994686i
$499$	−26.8862	−	7.89451i	−1.20359	−	0.353407i	−0.382368	−	0.924010i	$-0.624891\pi$
$499$	−26.8862	−	7.89451i	−1.20359	−	0.353407i	−0.821226	+	0.570603i	$0.806709\pi$
$500$		0			0
$501$	6.01938	−	13.1806i	0.268926	−	0.588866i
$502$	−1.14023	−	0.163940i	−0.0508910	−	0.00731701i
$503$	18.4041	−	28.6373i	0.820597	−	1.27687i	−0.137520	−	0.990499i	$-0.543913\pi$
$503$	18.4041	−	28.6373i	0.820597	−	1.27687i	0.958117	−	0.286375i	$-0.0924505\pi$
$504$	0.990435	+	1.14302i	0.0441175	+	0.0509143i
$505$		0			0
$506$	6.36642	+	1.66948i	0.283022	+	0.0742172i
$507$		−	18.4028i		−	0.817297i
$508$	−20.0445	+	17.3687i	−0.889332	+	0.770610i
$509$	17.4206	+	11.1955i	0.772154	+	0.496234i	0.866421	−	0.499313i	$-0.166414\pi$
$509$	17.4206	+	11.1955i	0.772154	+	0.496234i	−0.0942670	+	0.995547i	$0.530051\pi$
$510$		0			0
$511$	3.95770	−	8.66615i	0.175078	−	0.383368i
$512$	−19.0397	+	2.73749i	−0.841442	+	0.120981i
$513$	−1.57650	+	5.36908i	−0.0696044	+	0.237051i
$514$	−0.152049	+	0.0977158i	−0.00670658	+	0.00431006i
$515$		0			0
$516$	28.2193	−	8.28594i	1.24229	−	0.364768i
$517$	−34.3507	−	29.7651i	−1.51074	−	1.30907i
$518$	−1.23542	−	1.07050i	−0.0542812	−	0.0470349i
$519$	−6.16879	+	1.81132i	−0.270780	+	0.0795082i
$520$		0			0
$521$	15.4670	−	9.94007i	0.677624	−	0.435482i	−0.156043	−	0.987750i	$-0.549874\pi$
$521$	15.4670	−	9.94007i	0.677624	−	0.435482i	0.833667	+	0.552268i	$0.186237\pi$
$522$	−0.0119832	+	0.0408111i	−0.000524491	+	0.00178625i
$523$	−29.9296	+	4.30323i	−1.30873	+	0.188167i	−0.761144	−	0.648583i	$-0.775362\pi$
$523$	−29.9296	+	4.30323i	−1.30873	+	0.188167i	−0.547585	+	0.836750i	$0.684453\pi$
$524$	4.32990	−	9.48115i	0.189152	−	0.414186i
$525$		0			0
$526$	−5.18209	−	3.33033i	−0.225950	−	0.145209i
$527$	1.29386	−	1.12113i	0.0563614	−	0.0488374i
$528$		−	24.1805i		−	1.05232i
$529$	−20.0403	−	11.2865i	−0.871318	−	0.490718i
$530$		0			0
$531$	−4.35355	−	5.02427i	−0.188928	−	0.218035i
$532$	1.43359	−	2.23071i	0.0621540	−	0.0967135i
$533$	1.94890	+	0.280210i	0.0844164	+	0.0121372i
$534$	−1.84286	+	4.03530i	−0.0797484	+	0.174625i
$535$		0			0
$536$	7.55271	+	2.21767i	0.326227	+	0.0957890i
$537$	0.458886	+	0.714040i	0.0198024	+	0.0308131i
$538$	0.161959	−	0.0739642i	0.00698255	−	0.00318882i
$539$	−23.3583	+	6.85862i	−1.00611	+	0.295422i
$540$		0			0
$541$	27.0168	−	31.1791i	1.16154	−	1.34049i	0.231593	−	0.972813i	$-0.425606\pi$
$541$	27.0168	−	31.1791i	1.16154	−	1.34049i	0.929952	−	0.367681i	$-0.119848\pi$
$542$	−0.295992	−	1.00806i	−0.0127139	−	0.0432997i
$543$	3.67916	−	1.68022i	0.157888	−	0.0721049i
$544$	−1.29943	+	0.835095i	−0.0557127	+	0.0358044i
$545$		0			0
$546$	0.0230043	+	0.159998i	0.000984493	+	0.00684730i
$547$	−4.74643	−	2.16762i	−0.202943	−	0.0926809i	0.311351	−	0.950295i	$-0.399219\pi$
$547$	−4.74643	−	2.16762i	−0.202943	−	0.0926809i	−0.514294	+	0.857614i	$0.671946\pi$
$548$	37.1515	+	5.34157i	1.58703	+	0.228181i
$549$	8.89844	+	5.71868i	0.379776	+	0.244067i
$550$		0			0
$551$	0.152292			0.00648786
$552$	1.93300	−	7.37135i	0.0822739	−	0.313745i
$553$			16.7344i			0.711620i
$554$	−3.38856	−	3.91061i	−0.143966	−	0.166146i
$555$		0			0
$556$	−3.01049	+	20.9384i	−0.127673	+	0.887987i
$557$	18.6493	+	8.51684i	0.790195	+	0.360870i	0.769280	−	0.638911i	$-0.220615\pi$
$557$	18.6493	+	8.51684i	0.790195	+	0.360870i	0.0209146	+	0.999781i	$0.493342\pi$
$558$	0.979975	−	0.140899i	0.0414856	−	0.00596473i
$559$	−2.94637	−	0.865131i	−0.124618	−	0.0365911i
$560$		0			0
$561$	−1.36324	−	2.98508i	−0.0575561	−	0.126030i
$562$	0.404992	+	1.37928i	0.0170836	+	0.0581813i
$563$	−32.1806	−	27.8847i	−1.35625	−	1.17520i	−0.967210	−	0.253978i	$-0.918261\pi$
$563$	−32.1806	−	27.8847i	−1.35625	−	1.17520i	−0.389042	−	0.921220i	$-0.627194\pi$
$564$	−16.8755	+	19.4754i	−0.710587	+	0.820061i
$565$		0			0
$566$	0.119666	+	0.262031i	0.00502992	+	0.0110140i
$567$	3.88565	+	6.04619i	0.163182	+	0.253916i
$568$	3.79992	−	12.9413i	0.159441	−	0.543007i
$569$	−4.55153	−	31.6566i	−0.190810	−	1.32711i	−0.829870	−	0.557957i	$-0.811586\pi$
$569$	−4.55153	−	31.6566i	−0.190810	−	1.32711i	0.639060	−	0.769157i	$-0.279324\pi$
$570$		0			0
$571$	2.19537	−	15.2691i	0.0918734	−	0.638994i	−0.890903	−	0.454194i	$-0.849927\pi$
$571$	2.19537	−	15.2691i	0.0918734	−	0.638994i	0.982776	−	0.184800i	$-0.0591636\pi$
$572$	−1.42776	+	2.22164i	−0.0596976	+	0.0928913i
$573$	−16.9191	+	14.6605i	−0.706806	+	0.612451i
$574$	2.74257			0.114473
$575$		0			0
$576$	5.94159			0.247566
$577$	−29.5406	+	25.5971i	−1.22979	+	1.06562i	−0.234166	+	0.972197i	$0.575236\pi$
$577$	−29.5406	+	25.5971i	−1.22979	+	1.06562i	−0.995626	+	0.0934247i	$0.970219\pi$
$578$	2.58087	−	4.01592i	0.107350	−	0.167040i
$579$	4.19047	−	29.1454i	0.174150	−	1.21124i
$580$		0			0
$581$	1.29360	+	8.99719i	0.0536676	+	0.373266i
$582$	1.78771	−	6.08838i	0.0741029	−	0.252371i
$583$	12.5560	+	19.5375i	0.520015	+	0.809160i
$584$	3.16060	+	6.92076i	0.130787	+	0.286383i
$585$		0			0
$586$	4.79015	−	5.52812i	0.197879	−	0.228365i
$587$	−28.1874	−	24.4245i	−1.16342	−	1.00811i	−0.999767	−	0.0215889i	$-0.993128\pi$
$587$	−28.1874	−	24.4245i	−1.16342	−	1.00811i	−0.163651	−	0.986518i	$-0.552327\pi$
$588$	3.88854	+	13.2431i	0.160361	+	0.546138i
$589$	−1.47259	−	3.22452i	−0.0606769	−	0.132864i
$590$		0			0
$591$	10.9065	+	3.20242i	0.448632	+	0.131730i
$592$	−14.3281	+	2.06007i	−0.588881	+	0.0846683i
$593$	−42.7839	−	19.5387i	−1.75692	−	0.802360i	−0.986277	−	0.165097i	$-0.947206\pi$
$593$	−42.7839	−	19.5387i	−1.75692	−	0.802360i	−0.770647	−	0.637263i	$-0.780067\pi$
$594$	1.10475	−	7.68369i	0.0453283	−	0.315266i
$595$		0			0
$596$	−12.4878	−	14.4117i	−0.511521	−	0.590327i
$597$			7.32654i			0.299855i
$598$	−0.286886	+	0.263609i	−0.0117316	+	0.0107798i
$599$	−26.3109			−1.07503			−0.537517	−	0.843253i	$-0.680637\pi$
$599$	−26.3109			−1.07503			−0.537517	+	0.843253i	$0.680637\pi$
$600$		0			0
$601$	−25.2339	−	16.2168i	−1.02931	−	0.661498i	−0.0869905	−	0.996209i	$-0.527725\pi$
$601$	−25.2339	−	16.2168i	−1.02931	−	0.661498i	−0.942321	+	0.334711i	$0.891361\pi$
$602$	−4.23376	−	0.608723i	−0.172555	−	0.0248097i
$603$	−6.23117	−	2.84568i	−0.253753	−	0.115885i
$604$	5.54374	+	38.5576i	0.225572	+	1.56889i
$605$		0			0
$606$	6.28138	−	4.03680i	0.255164	−	0.163984i
$607$	1.98912	−	0.908402i	0.0807360	−	0.0368709i	−0.374638	−	0.927171i	$-0.622233\pi$
$607$	1.98912	−	0.908402i	0.0807360	−	0.0368709i	0.455374	+	0.890300i	$0.349506\pi$
$608$	0.901061	+	3.06873i	0.0365429	+	0.124454i
$609$	0.200588	−	0.231491i	0.00812824	−	0.00938049i
$610$		0			0
$611$	2.58160	−	0.758027i	0.104441	−	0.0306665i
$612$	0.809584	−	0.369725i	0.0327255	−	0.0149452i
$613$	18.4399	+	28.6930i	0.744780	+	1.15890i	0.982263	+	0.187508i	$0.0600412\pi$
$613$	18.4399	+	28.6930i	0.744780	+	1.15890i	−0.237483	+	0.971392i	$0.576322\pi$
$614$	−7.41082	−	2.17601i	−0.299076	−	0.0878167i
$615$		0			0
$616$	−3.12072	+	6.83343i	−0.125737	+	0.275327i
$617$	13.8474	+	1.99096i	0.557476	+	0.0801529i	0.415293	−	0.909688i	$-0.363679\pi$
$617$	13.8474	+	1.99096i	0.557476	+	0.0801529i	0.142182	+	0.989840i	$0.454588\pi$
$618$	2.90580	−	4.52151i	0.116888	−	0.181882i
$619$	20.8146	+	24.0213i	0.836608	+	0.965497i	0.999777	−	0.0211014i	$-0.00671729\pi$
$619$	20.8146	+	24.0213i	0.836608	+	0.965497i	−0.163170	+	0.986598i	$0.552172\pi$
$620$		0			0
$621$	−10.5452	+	24.9936i	−0.423166	+	1.00296i
$622$		−	7.66929i		−	0.307510i
$623$	−11.5495	+	10.0077i	−0.462722	+	0.400951i
$624$	1.20415	+	0.773861i	0.0482046	+	0.0309792i
$625$		0			0
$626$	−1.59322	+	3.48867i	−0.0636780	+	0.139435i
$627$	−6.72570	+	0.967010i	−0.268599	+	0.0386187i
$628$	8.65303	−	29.4695i	0.345294	−	1.17596i
$629$	−1.65266	+	1.06210i	−0.0658960	+	0.0423488i
$630$		0			0
$631$	28.3310	−	8.31873i	1.12784	−	0.331164i	0.335981	−	0.941869i	$-0.390932\pi$
$631$	28.3310	−	8.31873i	1.12784	−	0.331164i	0.791858	+	0.610705i	$0.209114\pi$
$632$	−10.0999	−	8.75159i	−0.401752	−	0.348120i
$633$	28.8759	+	25.0212i	1.14772	+	0.994502i
$634$	−1.60555	+	0.471432i	−0.0637645	+	0.0187229i
$635$		0			0
$636$	11.0769	−	7.11869i	0.439228	−	0.282274i
$637$	0.406000	−	1.38271i	0.0160863	−	0.0547849i
$638$	−0.209117	+	0.0300665i	−0.00827901	+	0.00119034i
$639$	−4.87599	+	10.6769i	−0.192891	+	0.422373i
$640$		0			0
$641$	−33.6984	−	21.6567i	−1.33101	−	0.855387i	−0.334792	−	0.942292i	$-0.608666\pi$
$641$	−33.6984	−	21.6567i	−1.33101	−	0.855387i	−0.996217	+	0.0869046i	$0.972302\pi$
$642$	1.61721	−	1.40132i	0.0638263	−	0.0553058i
$643$		−	29.7612i		−	1.17367i	−0.809707	−	0.586834i	$-0.800374\pi$
$643$		−	29.7612i		−	1.17367i	0.809707	−	0.586834i	$-0.199626\pi$
$644$	8.13139	−	9.95610i	0.320422	−	0.392325i
$645$		0			0
$646$	0.0880998	+	0.101673i	0.00346624	+	0.00400025i
$647$	−14.5540	+	22.6465i	−0.572178	+	0.890326i	−0.999908	−	0.0135807i	$-0.995677\pi$
$647$	−14.5540	+	22.6465i	−0.572178	+	0.890326i	0.427730	+	0.903906i	$0.359313\pi$
$648$	−5.68119	−	0.816832i	−0.223178	−	0.0320882i
$649$	13.7174	−	30.0370i	0.538456	−	1.17906i
$650$		0			0
$651$	−6.84100	−	2.00870i	−0.268120	−	0.0787271i
$652$	16.2320	+	25.2576i	0.635696	+	0.989162i
$653$	31.3566	−	14.3201i	1.22708	−	0.560388i	0.306846	−	0.951759i	$-0.400726\pi$
$653$	31.3566	−	14.3201i	1.22708	−	0.560388i	0.920233	+	0.391371i	$0.127999\pi$
$654$	−3.88702	+	1.14133i	−0.151995	+	0.0446296i
$655$		0			0
$656$	15.9038	−	18.3540i	0.620941	−	0.716604i
$657$	−1.86538	−	6.35291i	−0.0727755	−	0.247851i
$658$	3.40909	−	1.55688i	0.132900	−	0.0606934i
$659$	20.8466	−	13.3973i	0.812069	−	0.521885i	−0.0674645	−	0.997722i	$-0.521491\pi$
$659$	20.8466	−	13.3973i	0.812069	−	0.521885i	0.879534	+	0.475836i	$0.157855\pi$
$660$		0			0
$661$	−2.66397	−	18.5283i	−0.103616	−	0.720668i	−0.973712	−	0.227784i	$-0.926852\pi$
$661$	−2.66397	−	18.5283i	−0.103616	−	0.720668i	0.870095	−	0.492884i	$-0.164057\pi$
$662$	3.76453	+	1.71920i	0.146313	+	0.0668187i
$663$	0.192281	+	0.0276459i	0.00746759	+	0.00107368i
$664$	−6.10667	−	3.92452i	−0.236985	−	0.152301i
$665$		0			0
$666$	−1.13607			−0.0440220
$667$	0.733520	+	0.0837308i	0.0284020	+	0.00324207i
$668$			19.5196i			0.755236i
$669$	4.97611	+	5.74273i	0.192387	+	0.222027i
$670$		0			0
$671$	−7.47709	+	52.0043i	−0.288650	+	2.00760i
$672$	5.85143	+	2.67226i	0.225724	+	0.103085i
$673$	−8.64633	+	1.24315i	−0.333291	+	0.0479201i	−0.306929	−	0.951732i	$-0.599301\pi$
$673$	−8.64633	+	1.24315i	−0.333291	+	0.0479201i	−0.0263623	+	0.999652i	$0.508392\pi$
$674$	4.52893	+	1.32981i	0.174448	+	0.0512225i
$675$		0			0
$676$	10.2983	+	22.5502i	0.396090	+	0.867316i
$677$	1.65735	+	5.64443i	0.0636973	+	0.216933i	0.985191	−	0.171460i	$-0.0548485\pi$
$677$	1.65735	+	5.64443i	0.0636973	+	0.216933i	−0.921494	+	0.388393i	$0.873030\pi$
$678$	1.13247	+	0.981290i	0.0434922	+	0.0376862i
$679$	14.3148	−	16.5201i	0.549351	−	0.633984i
$680$		0			0
$681$	4.41546	+	9.66850i	0.169201	+	0.370498i
$682$	2.65866	+	4.13695i	0.101805	+	0.158412i
$683$	−3.72646	+	12.6911i	−0.142589	+	0.485613i	−0.999557	−	0.0297560i	$-0.990527\pi$
$683$	−3.72646	+	12.6911i	−0.142589	+	0.485613i	0.856968	+	0.515369i	$0.172345\pi$
$684$	−0.262263	−	1.82408i	−0.0100279	−	0.0697454i
$685$		0			0
$686$	0.681724	−	4.74149i	0.0260283	−	0.181031i
$687$	17.8514	−	27.7773i	0.681073	−	1.05977i
$688$	−28.6248	+	24.8035i	−1.09131	+	0.945626i
$689$	−1.37477			−0.0523747
$690$		0			0
$691$	−9.66154			−0.367542			−0.183771	−	0.982969i	$-0.558831\pi$
$691$	−9.66154			−0.367542			−0.183771	+	0.982969i	$0.558831\pi$
$692$	6.54543	−	5.67164i	0.248820	−	0.215604i
$693$	3.53447	−	5.49974i	0.134263	−	0.208918i
$694$	−0.627755	+	4.36613i	−0.0238293	+	0.165736i
$695$		0			0
$696$	0.0348124	+	0.242125i	0.00131956	+	0.00917774i
$697$	0.928573	−	3.16243i	0.0351722	−	0.119786i
$698$	0.175774	+	0.273510i	0.00665315	+	0.0103525i
$699$	14.4246	+	31.5854i	0.545588	+	1.19467i
$700$		0			0
$701$	−8.68025	+	10.0175i	−0.327848	+	0.378357i	−0.895613	−	0.444834i	$-0.853263\pi$
$701$	−8.68025	+	10.0175i	−0.327848	+	0.378357i	0.567765	+	0.823191i	$0.307808\pi$
$702$	0.347281	+	0.300920i	0.0131073	+	0.0113575i
$703$	1.14600	+	3.90292i	0.0432222	+	0.147201i
$704$	12.2597	+	26.8450i	0.462055	+	1.01176i
$705$		0			0
$706$	2.96554	+	0.870760i	0.111609	+	0.0327715i
$707$	25.4602	−	3.66062i	0.957528	−	0.137672i
$708$	−17.0297	−	7.77719i	−0.640014	−	0.292285i
$709$	0.315324	−	2.19313i	0.0118423	−	0.0823647i	−0.983043	−	0.183374i	$-0.941298\pi$
$709$	0.315324	−	2.19313i	0.0118423	−	0.0823647i	0.994885	+	0.101009i	$0.0322072\pi$
$710$		0			0
$711$	7.61605	+	8.78939i	0.285624	+	0.329628i
$712$		−	12.2043i		−	0.457377i
$713$	−5.31992	−	16.3406i	−0.199233	−	0.611962i
$714$	0.270586			0.0101264
$715$		0			0
$716$	−0.961887	−	0.618167i	−0.0359474	−	0.0231020i
$717$	1.65559	+	0.238038i	0.0618293	+	0.00888971i
$718$	2.11893	+	0.967682i	0.0790777	+	0.0361136i
$719$	−2.01326	−	14.0026i	−0.0750820	−	0.522207i	−0.992304	−	0.123829i	$-0.960482\pi$
$719$	−2.01326	−	14.0026i	−0.0750820	−	0.522207i	0.917221	−	0.398378i	$-0.130427\pi$
$720$		0			0
$721$	15.5761	−	10.0102i	0.580085	−	0.372798i
$722$	−4.66587	+	2.13083i	−0.173646	+	0.0793014i
$723$	2.64594	+	9.01124i	0.0984036	+	0.335132i
$724$	−3.56807	+	4.11777i	−0.132606	+	0.153036i
$725$		0			0
$726$	4.76493	−	1.39911i	0.176843	−	0.0519258i
$727$	−8.19925	+	3.74447i	−0.304093	+	0.138875i	−0.561617	−	0.827397i	$-0.689821\pi$
$727$	−8.19925	+	3.74447i	−0.304093	+	0.138875i	0.257524	+	0.966272i	$0.417093\pi$
$728$	−0.240420	−	0.374101i	−0.00891057	−	0.0138651i
$729$	27.9864	+	8.21756i	1.03654	+	0.304354i
$730$		0			0
$731$	−2.13537	+	4.67580i	−0.0789794	+	0.172941i
$732$	29.4842	+	4.23919i	1.08977	+	0.156685i
$733$	22.6695	−	35.2744i	0.837317	−	1.30289i	−0.113625	−	0.993524i	$-0.536246\pi$
$733$	22.6695	−	35.2744i	0.837317	−	1.30289i	0.950943	−	0.309368i	$-0.100117\pi$
$734$	0.240036	+	0.277016i	0.00885987	+	0.0102248i
$735$		0			0
$736$	2.65279	+	15.2761i	0.0977832	+	0.563083i
$737$		−	34.0251i		−	1.25333i
$738$	1.44048	−	1.24818i	0.0530247	−	0.0459462i
$739$	−0.419683	−	0.269714i	−0.0154383	−	0.00992158i	0.532899	−	0.846179i	$-0.321103\pi$
$739$	−0.419683	−	0.269714i	−0.0154383	−	0.00992158i	−0.548337	+	0.836257i	$0.684739\pi$
$740$		0			0
$741$	0.167091	−	0.365878i	0.00613823	−	0.0134409i
$742$	−1.89545	+	0.272525i	−0.0695842	+	0.0100047i
$743$	−0.00268980	+	0.00916062i	−9.86792e−5	+	0.000336070i	−0.959542	−	0.281565i	$-0.909147\pi$
$743$	−0.00268980	+	0.00916062i	−9.86792e−5	+	0.000336070i	0.959444	+	0.281901i	$0.0909648\pi$
$744$	4.78996	−	3.07832i	0.175609	−	0.112857i
$745$		0			0
$746$	−5.19718	+	1.52603i	−0.190282	+	0.0558719i
$747$	4.77417	+	4.13684i	0.174678	+	0.151359i
$748$	3.34095	+	2.89495i	0.122157	+	0.105850i
$749$	7.07306	−	2.07684i	0.258444	−	0.0758860i
$750$		0			0
$751$	−29.6324	+	19.0436i	−1.08130	+	0.694909i	−0.954857	−	0.297065i	$-0.903992\pi$
$751$	−29.6324	+	19.0436i	−1.08130	+	0.694909i	−0.126443	+	0.991974i	$0.540356\pi$
$752$	9.34985	−	31.8427i	0.340954	−	1.16118i
$753$	5.70667	−	0.820495i	0.207963	−	0.0299005i
$754$	0.00519522	−	0.0113759i	0.000189199	−	0.000414287i
$755$		0			0
$756$	−12.7546	−	8.19686i	−0.463879	−	0.298117i
$757$	10.4538	−	9.05830i	0.379951	−	0.329229i	−0.443858	−	0.896097i	$-0.646390\pi$
$757$	10.4538	−	9.05830i	0.379951	−	0.329229i	0.823809	+	0.566868i	$0.191845\pi$
$758$			1.28575i			0.0467004i
$759$	−32.9263	+	0.959822i	−1.19515	+	0.0348393i
$760$		0			0
$761$	11.9772	+	13.8224i	0.434172	+	0.501061i	0.930102	−	0.367301i	$-0.119718\pi$
$761$	11.9772	+	13.8224i	0.434172	+	0.501061i	−0.495930	+	0.868362i	$0.665173\pi$
$762$	−3.02974	+	4.71437i	−0.109756	+	0.170783i
$763$	−13.8136	−	1.98610i	−0.500087	−	0.0719016i
$764$	12.5280	−	27.4326i	0.453249	−	0.992477i
$765$		0			0
$766$	−10.1274	−	2.97368i	−0.365918	−	0.107443i
$767$	1.05679	+	1.64440i	0.0381585	+	0.0593758i
$768$	12.8352	−	5.86164i	0.463150	−	0.211514i
$769$	−14.7987	+	4.34528i	−0.533653	+	0.156695i	−0.537446	−	0.843298i	$-0.680611\pi$
$769$	−14.7987	+	4.34528i	−0.533653	+	0.156695i	0.00379292	+	0.999993i	$0.498793\pi$
$770$		0			0
$771$	0.592373	−	0.683635i	0.0213338	−	0.0246205i
$772$	11.1751	+	38.0589i	0.402200	+	1.36977i
$773$	−2.39642	+	1.09441i	−0.0861932	+	0.0393631i	−0.458045	−	0.888929i	$-0.651450\pi$
$773$	−2.39642	+	1.09441i	−0.0861932	+	0.0393631i	0.371852	+	0.928292i	$0.378723\pi$
$774$	−2.50073	+	1.60712i	−0.0898868	+	0.0577668i
$775$		0			0
$776$	2.48435	+	17.2791i	0.0891831	+	0.620282i
$777$	7.44204	+	3.39867i	0.266982	+	0.121926i
$778$	−0.326823	−	0.0469901i	−0.0117172	−	0.00168468i
$779$	−5.74112	−	3.68959i	−0.205697	−	0.132193i
$780$		0			0
$781$	−58.3010			−2.08617
$782$	0.368436	+	0.538147i	0.0131752	+	0.0192441i
$783$		−	0.870762i		−	0.0311185i
$784$	−11.6401	−	13.4334i	−0.415719	−	0.479765i
$785$		0			0
$786$	0.313418	−	2.17987i	0.0111793	−	0.0777535i
$787$	−16.7544	−	7.65149i	−0.597231	−	0.272746i	0.0937771	−	0.995593i	$-0.470106\pi$
$787$	−16.7544	−	7.65149i	−0.597231	−	0.272746i	−0.691008	+	0.722847i	$0.742833\pi$
$788$	−15.1565	+	2.17918i	−0.539929	+	0.0776301i
$789$	29.5808	+	8.68571i	1.05311	+	0.309220i
$790$		0			0
$791$	2.14440	+	4.69559i	0.0762462	+	0.166956i
$792$	1.47089	+	5.00939i	0.0522658	+	0.178001i
$793$	−2.35044	−	2.03667i	−0.0834667	−	0.0723243i
$794$	−2.32604	+	2.68440i	−0.0825481	+	0.0952656i
$795$		0			0
$796$	−4.09999	−	8.97772i	−0.145320	−	0.318207i
$797$	26.8192	+	41.7315i	0.949986	+	1.47821i	0.876781	+	0.480890i	$0.159686\pi$
$797$	26.8192	+	41.7315i	0.949986	+	1.47821i	0.0732048	+	0.997317i	$0.476677\pi$
$798$	0.157845	−	0.537572i	0.00558767	−	0.0190298i
$799$	−0.640979	−	4.45811i	−0.0226762	−	0.157716i
$800$		0			0
$801$	−1.51150	+	10.5127i	−0.0534061	+	0.371447i
$802$	−3.02275	+	4.70349i	−0.106737	+	0.166086i
$803$	24.8545	−	21.5365i	0.877095	−	0.760007i
$804$	−19.2907			−0.680332
$805$		0			0
$806$	−0.291101			−0.0102536
$807$	−0.673453	+	0.583551i	−0.0237067	+	0.0205420i
$808$	−11.1056	+	17.2806i	−0.390692	+	0.607929i
$809$	1.30421	−	9.07096i	0.0458535	−	0.318918i	−0.953966	−	0.299915i	$-0.903042\pi$
$809$	1.30421	−	9.07096i	0.0458535	−	0.318918i	0.999819	−	0.0190030i	$-0.00604921\pi$
$810$		0			0
$811$	0.665879	+	4.63129i	0.0233822	+	0.162627i	0.998167	−	0.0605205i	$-0.0192761\pi$
$811$	0.665879	+	4.63129i	0.0233822	+	0.162627i	−0.974785	+	0.223147i	$0.928367\pi$
$812$	−0.116250	+	0.395913i	−0.00407959	+	0.0138938i
$813$	2.84277	+	4.42344i	0.0997004	+	0.155137i
$814$	−2.34415	−	5.13296i	−0.0821622	−	0.179910i
$815$		0			0
$816$	1.56909	−	1.81083i	0.0549292	−	0.0633917i
$817$	8.04375	+	6.96995i	0.281415	+	0.243848i
$818$	0.803905	+	2.73785i	0.0281079	+	0.0957266i
$819$	0.160763	+	0.352023i	0.00561753	+	0.0123007i
$820$		0			0
$821$	−10.9770	−	3.22314i	−0.383101	−	0.112489i	0.0845109	−	0.996423i	$-0.473067\pi$
$821$	−10.9770	−	3.22314i	−0.383101	−	0.112489i	−0.467612	+	0.883934i	$0.654885\pi$
$822$	7.84973	−	1.12862i	0.273791	−	0.0393652i
$823$	33.1678	+	15.1472i	1.15616	+	0.527998i	0.898817	−	0.438323i	$-0.144427\pi$
$823$	33.1678	+	15.1472i	1.15616	+	0.527998i	0.257338	+	0.966322i	$0.417155\pi$
$824$	−2.10431	+	14.6358i	−0.0733071	+	0.509862i
$825$		0			0
$826$	1.78301	+	2.05770i	0.0620388	+	0.0715966i
$827$			41.7751i			1.45266i	0.687345	+	0.726331i	$0.258776\pi$
$827$			41.7751i			1.45266i	−0.687345	+	0.726331i	$0.741224\pi$
$828$	−0.260313	−	8.92993i	−0.00904651	−	0.310336i
$829$	−44.3330			−1.53975			−0.769874	−	0.638196i	$-0.779681\pi$
$829$	−44.3330			−1.53975			−0.769874	+	0.638196i	$0.779681\pi$
$830$		0			0
$831$	21.7863	+	14.0012i	0.755759	+	0.485697i
$832$	−1.72920	−	0.248621i	−0.0599491	−	0.00861938i
$833$	−2.19432	−	1.00211i	−0.0760288	−	0.0347212i
$834$	0.636086	+	4.42408i	0.0220259	+	0.153193i
$835$		0			0
$836$	7.70033	−	4.94870i	0.266321	−	0.171154i
$837$	−18.4369	+	8.41984i	−0.637271	+	0.291032i
$838$	−0.397114	−	1.35245i	−0.0137181	−	0.0467195i
$839$	−6.10437	+	7.04482i	−0.210746	+	0.243214i	−0.851275	−	0.524720i	$-0.824170\pi$
$839$	−6.10437	+	7.04482i	−0.210746	+	0.243214i	0.640528	+	0.767934i	$0.278715\pi$
$840$		0			0
$841$	27.8026	−	8.16357i	0.958709	−	0.281502i
$842$	0.0579459	−	0.0264630i	0.00199695	−	0.000911975i
$843$	−3.88964	−	6.05239i	−0.133966	−	0.208455i
$844$	−49.3857	−	14.5010i	−1.69993	−	0.499144i
$845$		0			0
$846$	1.08199	−	2.36924i	0.0371997	−	0.0814560i
$847$	16.9335	+	2.43467i	0.581843	+	0.0836563i
$848$	−9.16769	+	14.2652i	−0.314820	+	0.489869i
$849$	−0.944117	−	1.08957i	−0.0324020	−	0.0373939i
$850$		0			0
$851$	3.37391	+	19.4286i	0.115656	+	0.666004i
$852$			33.0541i			1.13242i
$853$	−2.51747	+	2.18140i	−0.0861965	+	0.0746897i	−0.696893	−	0.717175i	$-0.745435\pi$
$853$	−2.51747	+	2.18140i	−0.0861965	+	0.0746897i	0.610697	+	0.791865i	$0.290889\pi$
$854$	−3.64438	−	2.34210i	−0.124708	−	0.0801450i
$855$		0			0
$856$	−2.44554	+	5.35499i	−0.0835869	+	0.183030i
$857$	49.2593	−	7.08241i	1.68266	−	0.241931i	0.766360	−	0.642412i	$-0.222066\pi$
$857$	49.2593	−	7.08241i	1.68266	−	0.241931i	0.916305	+	0.400481i	$0.131157\pi$
$858$	−0.157203	+	0.535386i	−0.00536684	+	0.0182778i
$859$	18.2530	−	11.7305i	0.622784	−	0.400239i	−0.190847	−	0.981620i	$-0.561124\pi$
$859$	18.2530	−	11.7305i	0.622784	−	0.400239i	0.813632	+	0.581380i	$0.197487\pi$
$860$		0			0
$861$	−13.1701	+	3.86710i	−0.448837	+	0.131790i
$862$	−0.960267	−	0.832076i	−0.0327068	−	0.0283406i
$863$	−15.1896	−	13.1619i	−0.517060	−	0.448035i	0.356822	−	0.934172i	$-0.383860\pi$
$863$	−15.1896	−	13.1619i	−0.517060	−	0.448035i	−0.873883	+	0.486137i	$0.838406\pi$
$864$	17.5461	−	5.15201i	0.596931	−	0.175275i
$865$		0			0
$866$	4.16950	−	2.67957i	0.141685	−	0.0910556i
$867$	−6.73109	+	22.9240i	−0.228600	+	0.778539i
$868$	9.50684	−	1.36688i	0.322683	−	0.0463948i
$869$	−23.9971	+	52.5463i	−0.814046	+	1.78251i
$870$		0			0
$871$	1.69440	+	1.08892i	0.0574125	+	0.0368968i
$872$	8.42280	−	7.29839i	0.285232	−	0.247155i
$873$		−	15.1917i		−	0.514161i
$874$	1.28406	−	0.418044i	0.0434341	−	0.0141406i
$875$		0			0
$876$	−12.2103	−	14.0914i	−0.412547	−	0.476104i
$877$	−3.64010	+	5.66411i	−0.122918	+	0.191263i	−0.897259	−	0.441504i	$-0.854445\pi$
$877$	−3.64010	+	5.66411i	−0.122918	+	0.191263i	0.774341	+	0.632768i	$0.218081\pi$
$878$	−6.34606	−	0.912426i	−0.214169	−	0.0307929i
$879$	−15.2080	+	33.3009i	−0.512953	+	1.12321i
$880$		0			0
$881$	−51.9226	−	15.2459i	−1.74932	−	0.513646i	−0.758834	−	0.651284i	$-0.774231\pi$
$881$	−51.9226	−	15.2459i	−1.74932	−	0.513646i	−0.990483	+	0.137638i	$0.956049\pi$
$882$	−0.754211	−	1.17358i	−0.0253956	−	0.0395163i
$883$	−0.638600	+	0.291639i	−0.0214906	+	0.00981442i	−0.426131	−	0.904661i	$-0.640124\pi$
$883$	−0.638600	+	0.291639i	−0.0214906	+	0.00981442i	0.404641	+	0.914476i	$0.367397\pi$
$884$	−0.251086	+	0.0737256i	−0.00844495	+	0.00247966i
$885$		0			0
$886$	−4.69039	+	5.41300i	−0.157577	+	0.181853i
$887$	7.93514	+	27.0246i	0.266436	+	0.907397i	0.978667	+	0.205452i	$0.0658665\pi$
$887$	7.93514	+	27.0246i	0.266436	+	0.907397i	−0.712231	+	0.701945i	$0.752315\pi$
$888$	−5.94319	+	2.71416i	−0.199440	+	0.0910814i
$889$	−16.2405	+	10.4371i	−0.544689	+	0.350050i
$890$		0			0
$891$	3.53078	+	24.5571i	0.118286	+	0.822695i
$892$	−9.31125	−	4.25231i	−0.311764	−	0.142378i
$893$	−9.23083	−	1.32719i	−0.308898	−	0.0444128i
$894$	−3.38956	−	2.17834i	−0.113364	−	0.0728545i
$895$		0			0
$896$	−11.4648			−0.383012
$897$	1.00596	−	1.67040i	0.0335880	−	0.0557729i
$898$			7.34885i			0.245234i
$899$	0.361235	+	0.416887i	0.0120479	+	0.0139040i
$900$		0			0
$901$	−0.327512	+	2.27790i	−0.0109110	+	0.0758877i
$902$	8.61172	+	3.93284i	0.286739	+	0.130949i
$903$	21.1893	−	3.04656i	0.705135	−	0.101383i
$904$	−3.95543	−	1.16142i	−0.131556	−	0.0386282i
$905$		0			0
$906$	3.41912	+	7.48682i	0.113593	+	0.248733i
$907$	−5.21316	−	17.7544i	−0.173100	−	0.589524i	−0.999645	−	0.0266534i	$-0.991515\pi$
$907$	−5.21316	−	17.7544i	−0.173100	−	0.589524i	0.826545	−	0.562871i	$-0.190303\pi$
$908$	−10.8211	−	9.37657i	−0.359112	−	0.311172i
$909$	11.7064	−	13.5099i	0.388277	−	0.448095i
$910$		0			0
$911$	−13.4591	−	29.4714i	−0.445920	−	0.976429i	−0.990474	−	0.137703i	$-0.956028\pi$
$911$	−13.4591	−	29.4714i	−0.445920	−	0.976429i	0.544553	−	0.838726i	$-0.316699\pi$
$912$	−2.68225	−	4.17366i	−0.0888181	−	0.138204i
$913$	−8.84001	+	30.1063i	−0.292562	+	0.996374i
$914$	1.42226	+	9.89204i	0.0470442	+	0.327200i
$915$		0			0
$916$	−6.33017	+	44.0273i	−0.209155	+	1.45470i
$917$	4.10165	−	6.38230i	0.135449	−	0.210762i
$918$	0.581334	−	0.503729i	0.0191869	−	0.0166255i
$919$	−3.23843			−0.106826			−0.0534130	−	0.998573i	$-0.517010\pi$
$919$	−3.23843			−0.106826			−0.0534130	+	0.998573i	$0.517010\pi$
$920$		0			0
$921$	38.6558			1.27375
$922$	−5.76236	+	4.99311i	−0.189773	+	0.164439i
$923$	1.86584	−	2.90330i	0.0614149	−	0.0955634i
$924$	2.62006	−	18.2229i	0.0861936	−	0.599490i
$925$		0			0
$926$	−0.529038	−	3.67954i	−0.0173853	−	0.120917i
$927$	3.62526	−	12.3465i	0.119069	−	0.405513i
$928$	−0.269071	−	0.418683i	−0.00883270	−	0.0137440i
$929$	6.25892	+	13.7051i	0.205349	+	0.449651i	0.984084	−	0.177701i	$-0.0568661\pi$
$929$	6.25892	+	13.7051i	0.205349	+	0.449651i	−0.778736	+	0.627352i	$0.784139\pi$
$930$		0			0
$931$	−3.27095	+	3.77488i	−0.107201	+	0.123717i
$932$	−35.3509	−	30.6317i	−1.15796	−	1.00338i
$933$	10.8139	+	36.8287i	0.354031	+	1.20572i
$934$	0.459120	+	1.00533i	0.0150229	+	0.0328955i
$935$		0			0
$936$	−0.296534	−	0.0870702i	−0.00969252	−	0.00284598i
$937$	2.41024	−	0.346540i	0.0787390	−	0.0113210i	−0.102833	−	0.994699i	$-0.532791\pi$
$937$	2.41024	−	0.346540i	0.0787390	−	0.0113210i	0.181572	+	0.983378i	$0.441882\pi$
$938$	2.55199	+	1.16546i	0.0833255	+	0.0380535i
$939$	2.73171	−	18.9995i	0.0891460	−	0.620024i
$940$		0			0
$941$	32.9339	+	38.0077i	1.07361	+	1.23902i	0.969666	+	0.244434i	$0.0786023\pi$
$941$	32.9339	+	38.0077i	1.07361	+	1.23902i	0.103949	+	0.994583i	$0.466852\pi$
$942$		−	6.48948i		−	0.211439i
$943$	−25.6237	−	20.9275i	−0.834424	−	0.681494i
$944$	24.1102			0.784719
$945$		0			0
$946$	−12.4212	−	7.98260i	−0.403847	−	0.259537i
$947$	−10.4350	−	1.50033i	−0.339093	−	0.0487542i	−0.0293348	−	0.999570i	$-0.509339\pi$
$947$	−10.4350	−	1.50033i	−0.339093	−	0.0487542i	−0.309758	+	0.950815i	$0.600248\pi$
$948$	29.7915	+	13.6053i	0.967582	+	0.441880i
$949$	0.277055	+	1.92696i	0.00899359	+	0.0625518i
$950$		0			0
$951$	7.04529	−	4.52773i	0.228459	−	0.146822i
$952$	−0.677133	+	0.309236i	−0.0219460	+	0.0100224i
$953$	−6.89767	−	23.4913i	−0.223438	−	0.760958i	−0.992549	−	0.121844i	$-0.961119\pi$
$953$	−6.89767	−	23.4913i	−0.223438	−	0.760958i	0.769112	−	0.639114i	$-0.220699\pi$
$954$	−0.871515	+	1.00578i	−0.0282164	+	0.0325634i
$955$		0			0
$956$	−2.16192	+	0.634798i	−0.0699216	+	0.0205308i
$957$	0.961807	−	0.439243i	0.0310908	−	0.0141987i
$958$	−3.03583	−	4.72384i	−0.0980831	−	0.152620i
$959$	26.2129	+	7.69681i	0.846459	+	0.248543i
$960$		0			0
$961$	−7.54397	+	16.5190i	−0.243354	+	0.532871i
$962$	0.330635	+	0.0475381i	0.0106601	+	0.00153269i
$963$	2.76978	−	4.30986i	0.0892548	−	0.138883i
$964$	−8.28502	−	9.56142i	−0.266842	−	0.307953i
$965$		0			0
$966$	1.05583	−	2.50245i	0.0339707	−	0.0805150i
$967$		−	41.3872i		−	1.33092i	−0.746432	−	0.665462i	$-0.768235\pi$
$967$		−	41.3872i		−	1.33092i	0.746432	−	0.665462i	$-0.231765\pi$
$968$	−10.3251	+	8.94678i	−0.331862	+	0.287560i
$969$	−0.566426	−	0.364020i	−0.0181962	−	0.0116940i
$970$		0			0
$971$	11.7039	−	25.6280i	0.375596	−	0.822441i	−0.623576	−	0.781763i	$-0.714321\pi$
$971$	11.7039	−	25.6280i	0.375596	−	0.822441i	0.999172	−	0.0406780i	$-0.0129518\pi$
$972$	−18.3094	+	2.63249i	−0.587274	+	0.0844372i
$973$	−4.33789	+	14.7735i	−0.139066	+	0.473617i
$974$	9.03558	−	5.80681i	0.289519	−	0.186062i
$975$		0			0
$976$	−36.8073	+	10.8076i	−1.17817	+	0.345943i
$977$	−13.6189	−	11.8008i	−0.435706	−	0.377542i	0.409210	−	0.912440i	$-0.365804\pi$
$977$	−13.6189	−	11.8008i	−0.435706	−	0.377542i	−0.844916	+	0.534899i	$0.820350\pi$
$978$	4.79425	+	4.15424i	0.153303	+	0.132838i
$979$	−50.6168	+	14.8624i	−1.61772	+	0.475005i
$980$		0			0
$981$	−8.15921	+	5.24361i	−0.260504	+	0.167415i
$982$	0.533104	−	1.81558i	0.0170120	−	0.0579376i
$983$	−17.7273	+	2.54880i	−0.565413	+	0.0812941i	−0.419093	−	0.907943i	$-0.637652\pi$
$983$	−17.7273	+	2.54880i	−0.565413	+	0.0812941i	−0.146320	+	0.989237i	$0.546743\pi$
$984$	4.55363	−	9.97106i	0.145164	−	0.317866i
$985$		0			0
$986$	−0.0176114	−	0.0113182i	−0.000560862	−	0.000360444i
$987$	−14.1756	+	12.2832i	−0.451213	+	0.390978i
$988$			0.541841i			0.0172383i
$989$	34.9109	+	37.9935i	1.11010	+	1.20812i
$990$		0			0
$991$	−29.6112	−	34.1732i	−0.940632	−	1.08555i	−0.996200	−	0.0870922i	$-0.972243\pi$
$991$	−29.6112	−	34.1732i	−0.940632	−	1.08555i	0.0555684	−	0.998455i	$-0.482303\pi$
$992$	−6.26310	+	9.74557i	−0.198854	+	0.309422i
$993$	−20.5018	−	2.94771i	−0.650605	−	0.0935429i
$994$	1.99697	−	4.37276i	0.0633402	−	0.138696i
$995$		0			0
$996$	17.0690	+	5.01190i	0.540851	+	0.158808i
$997$	2.60192	+	4.04866i	0.0824036	+	0.128222i	0.880009	−	0.474957i	$-0.157537\pi$
$997$	2.60192	+	4.04866i	0.0824036	+	0.128222i	−0.797605	+	0.603180i	$0.793900\pi$
$998$	7.25495	−	3.31322i	0.229651	−	0.104878i
$999$	22.3158	−	6.55250i	0.706039	−	0.207312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.p.c.174.2		40
5.2	odd	4		575.2.k.c.151.1		20
5.3	odd	4		115.2.g.b.36.2	yes	20
5.4	even	2	inner	575.2.p.c.174.3		40
23.16	even	11	inner	575.2.p.c.499.3		40
115.39	even	22	inner	575.2.p.c.499.2		40
115.62	odd	44		575.2.k.c.476.1		20
115.73	odd	44		2645.2.a.t.1.6		10
115.88	even	44		2645.2.a.u.1.6		10
115.108	odd	44		115.2.g.b.16.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.b.16.2	✓	20	115.108	odd	44
115.2.g.b.36.2	yes	20	5.3	odd	4
575.2.k.c.151.1		20	5.2	odd	4
575.2.k.c.476.1		20	115.62	odd	44
575.2.p.c.174.2		40	1.1	even	1	trivial
575.2.p.c.174.3		40	5.4	even	2	inner
575.2.p.c.499.2		40	115.39	even	22	inner
575.2.p.c.499.3		40	23.16	even	11	inner
2645.2.a.t.1.6		10	115.73	odd	44
2645.2.a.u.1.6		10	115.88	even	44

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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.p (of order \(22\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.215109 + 0.186393i) q^{2} +(0.770157 - 1.19839i) q^{3} +(-0.273100 + 1.89945i) q^{4} +(0.0577033 + 0.401335i) q^{6} +(-0.393517 + 1.34020i) q^{7} +(-0.603063 - 0.938384i) q^{8} +(0.403254 + 0.883004i) q^{9} +O(q^{10})\)	\(q+(-0.215109 + 0.186393i) q^{2} +(0.770157 - 1.19839i) q^{3} +(-0.273100 + 1.89945i) q^{4} +(0.0577033 + 0.401335i) q^{6} +(-0.393517 + 1.34020i) q^{7} +(-0.603063 - 0.938384i) q^{8} +(0.403254 + 0.883004i) q^{9} +(-3.15749 + 3.64393i) q^{11} +(2.06595 + 1.79016i) q^{12} +(-0.0804117 - 0.273857i) q^{13} +(-0.165154 - 0.361637i) q^{14} +(-3.37787 - 0.991834i) q^{16} +(-0.472917 + 0.0679951i) q^{17} +(-0.251329 - 0.114778i) q^{18} +(-0.140789 + 0.979208i) q^{19} +(1.30300 + 1.50375i) q^{21} -1.37237i q^{22} +(-1.21649 + 4.63898i) q^{23} -1.58900 q^{24} +(0.0683422 + 0.0439209i) q^{26} +(5.59883 + 0.804990i) q^{27} +(-2.43817 - 1.11347i) q^{28} +(-0.0219083 - 0.152376i) q^{29} +(-3.01445 + 1.93727i) q^{31} +(2.94080 - 1.34302i) q^{32} +(1.93508 + 6.59029i) q^{33} +(0.0890547 - 0.102775i) q^{34} +(-1.78735 + 0.524814i) q^{36} +(3.74020 - 1.70809i) q^{37} +(-0.152232 - 0.236878i) q^{38} +(-0.390116 - 0.114549i) q^{39} +(-2.86572 + 6.27505i) q^{41} +(-0.560575 - 0.0805985i) q^{42} +(5.81663 - 9.05086i) q^{43} +(-6.05917 - 6.99266i) q^{44} +(-0.602996 - 1.22463i) q^{46} +9.42683i q^{47} +(-3.79009 + 3.28414i) q^{48} +(4.24751 + 2.72971i) q^{49} +(-0.282735 + 0.619104i) q^{51} +(0.542139 - 0.0779478i) q^{52} +(1.35702 - 4.62159i) q^{53} +(-1.35440 + 0.870421i) q^{54} +(1.49493 - 0.438952i) q^{56} +(1.06504 + 0.922863i) q^{57} +(0.0331144 + 0.0286938i) q^{58} +(-6.57113 + 1.92946i) q^{59} +(9.16678 - 5.89113i) q^{61} +(0.287342 - 0.978595i) q^{62} +(-1.34208 + 0.192963i) q^{63} +(2.54266 - 5.56764i) q^{64} +(-1.64464 - 1.05694i) q^{66} +(-5.33316 + 4.62121i) q^{67} -0.916853i q^{68} +(4.62241 + 5.03057i) q^{69} +(7.91831 + 9.13822i) q^{71} +(0.585409 - 0.910914i) q^{72} +(-6.75135 - 0.970698i) q^{73} +(-0.486174 + 1.06457i) q^{74} +(-1.82151 - 0.534844i) q^{76} +(-3.64106 - 5.66560i) q^{77} +(0.105268 - 0.0480745i) q^{78} +(11.4955 - 3.37537i) q^{79} +(3.36959 - 3.88872i) q^{81} +(-0.553183 - 1.88397i) q^{82} +(5.91956 - 2.70337i) q^{83} +(-3.21215 + 2.06432i) q^{84} +(0.435806 + 3.03110i) q^{86} +(-0.199478 - 0.0910986i) q^{87} +(5.32357 + 0.765414i) q^{88} +(9.20422 + 5.91519i) q^{89} +0.398665 q^{91} +(-8.47931 - 3.57757i) q^{92} +5.10448i q^{93} +(-1.75709 - 2.02779i) q^{94} +(0.655420 - 4.55855i) q^{96} +(-14.2356 - 6.50117i) q^{97} +(-1.42247 + 0.204521i) q^{98} +(-4.49088 - 1.31864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{4} - 18 q^{6} + 34 q^{9}+O(q^{10}) \) 40 * q + 8 * q^4 - 18 * q^6 + 34 * q^9	\( 40 q + 8 q^{4} - 18 q^{6} + 34 q^{9} - 16 q^{11} - 6 q^{14} - 72 q^{16} - 48 q^{19} + 50 q^{21} - 4 q^{26} - 24 q^{29} + 20 q^{31} + 14 q^{34} + 86 q^{36} + 104 q^{39} + 20 q^{41} - 12 q^{44} - 66 q^{46} - 8 q^{49} + 100 q^{51} - 46 q^{54} - 82 q^{59} - 26 q^{61} - 32 q^{64} + 112 q^{66} + 90 q^{69} - 38 q^{71} - 16 q^{74} + 8 q^{76} + 166 q^{79} + 24 q^{81} - 56 q^{84} - 146 q^{86} + 10 q^{89} - 168 q^{91} + 74 q^{94} + 28 q^{96} - 124 q^{99}+O(q^{100}) \) 40 * q + 8 * q^4 - 18 * q^6 + 34 * q^9 - 16 * q^11 - 6 * q^14 - 72 * q^16 - 48 * q^19 + 50 * q^21 - 4 * q^26 - 24 * q^29 + 20 * q^31 + 14 * q^34 + 86 * q^36 + 104 * q^39 + 20 * q^41 - 12 * q^44 - 66 * q^46 - 8 * q^49 + 100 * q^51 - 46 * q^54 - 82 * q^59 - 26 * q^61 - 32 * q^64 + 112 * q^66 + 90 * q^69 - 38 * q^71 - 16 * q^74 + 8 * q^76 + 166 * q^79 + 24 * q^81 - 56 * q^84 - 146 * q^86 + 10 * q^89 - 168 * q^91 + 74 * q^94 + 28 * q^96 - 124 * q^99

Introduction

L-functions

Modular forms

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Database

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