LMFDB - Embedded newform 731.2.f.c.259.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(259,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("731.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.f (of order $4$, degree $2$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			259.19
Character	$\chi$	$=$	731.259
Dual form			731.2.f.c.302.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.831038i q^{2} +(-0.711849 + 0.711849i) q^{3} +1.30938 q^{4} +(0.619206 - 0.619206i) q^{5} +(-0.591574 - 0.591574i) q^{6} +(2.80838 + 2.80838i) q^{7} +2.75022i q^{8} +1.98654i q^{9} +O(q^{10})$	\(q+0.831038i q^{2} +(-0.711849 + 0.711849i) q^{3} +1.30938 q^{4} +(0.619206 - 0.619206i) q^{5} +(-0.591574 - 0.591574i) q^{6} +(2.80838 + 2.80838i) q^{7} +2.75022i q^{8} +1.98654i q^{9} +(0.514584 + 0.514584i) q^{10} +(-1.65119 - 1.65119i) q^{11} +(-0.932077 + 0.932077i) q^{12} +0.606864 q^{13} +(-2.33387 + 2.33387i) q^{14} +0.881562i q^{15} +0.333214 q^{16} +(1.58968 - 3.80433i) q^{17} -1.65089 q^{18} -0.918662i q^{19} +(0.810773 - 0.810773i) q^{20} -3.99828 q^{21} +(1.37220 - 1.37220i) q^{22} +(-0.0627679 - 0.0627679i) q^{23} +(-1.95774 - 1.95774i) q^{24} +4.23317i q^{25} +0.504327i q^{26} +(-3.54966 - 3.54966i) q^{27} +(3.67722 + 3.67722i) q^{28} +(-3.46816 + 3.46816i) q^{29} -0.732611 q^{30} +(3.62669 - 3.62669i) q^{31} +5.77735i q^{32} +2.35079 q^{33} +(3.16154 + 1.32108i) q^{34} +3.47793 q^{35} +2.60113i q^{36} +(1.28004 - 1.28004i) q^{37} +0.763443 q^{38} +(-0.431995 + 0.431995i) q^{39} +(1.70295 + 1.70295i) q^{40} +(0.348131 + 0.348131i) q^{41} -3.32272i q^{42} +1.00000i q^{43} +(-2.16202 - 2.16202i) q^{44} +(1.23008 + 1.23008i) q^{45} +(0.0521625 - 0.0521625i) q^{46} -2.60356 q^{47} +(-0.237198 + 0.237198i) q^{48} +8.77397i q^{49} -3.51793 q^{50} +(1.57650 + 3.83972i) q^{51} +0.794613 q^{52} -4.50774i q^{53} +(2.94991 - 2.94991i) q^{54} -2.04485 q^{55} +(-7.72365 + 7.72365i) q^{56} +(0.653948 + 0.653948i) q^{57} +(-2.88217 - 2.88217i) q^{58} +8.50219i q^{59} +1.15429i q^{60} +(-5.64683 - 5.64683i) q^{61} +(3.01392 + 3.01392i) q^{62} +(-5.57896 + 5.57896i) q^{63} -4.13477 q^{64} +(0.375774 - 0.375774i) q^{65} +1.95360i q^{66} +5.37771 q^{67} +(2.08149 - 4.98129i) q^{68} +0.0893625 q^{69} +2.89029i q^{70} +(1.41646 - 1.41646i) q^{71} -5.46343 q^{72} +(-8.64635 + 8.64635i) q^{73} +(1.06376 + 1.06376i) q^{74} +(-3.01338 - 3.01338i) q^{75} -1.20287i q^{76} -9.27431i q^{77} +(-0.359005 - 0.359005i) q^{78} +(7.96590 + 7.96590i) q^{79} +(0.206328 - 0.206328i) q^{80} -0.905982 q^{81} +(-0.289310 + 0.289310i) q^{82} -16.4933i q^{83} -5.23525 q^{84} +(-1.37132 - 3.34000i) q^{85} -0.831038 q^{86} -4.93761i q^{87} +(4.54112 - 4.54112i) q^{88} -13.4891 q^{89} +(-1.02224 + 1.02224i) q^{90} +(1.70430 + 1.70430i) q^{91} +(-0.0821867 - 0.0821867i) q^{92} +5.16331i q^{93} -2.16366i q^{94} +(-0.568841 - 0.568841i) q^{95} +(-4.11260 - 4.11260i) q^{96} +(8.56739 - 8.56739i) q^{97} -7.29150 q^{98} +(3.28015 - 3.28015i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) $ 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7	$ 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) $ 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7 + 4 * q^10 - 6 * q^11 - 14 * q^12 + 16 * q^13 + 6 * q^14 + 44 * q^16 + 8 * q^17 - 16 * q^18 + 12 * q^20 + 28 * q^21 + 14 * q^22 + 6 * q^23 + 62 * q^24 - 4 * q^27 + 34 * q^28 - 12 * q^29 - 96 * q^30 + 14 * q^31 - 44 * q^33 + 6 * q^34 - 32 * q^35 + 8 * q^37 + 72 * q^38 - 32 * q^39 - 84 * q^40 + 24 * q^41 + 4 * q^44 + 48 * q^45 - 4 * q^46 - 8 * q^47 + 38 * q^48 - 64 * q^50 + 28 * q^51 - 48 * q^52 + 34 * q^54 + 56 * q^55 - 26 * q^56 - 102 * q^57 + 76 * q^58 - 40 * q^61 + 34 * q^62 + 4 * q^63 - 204 * q^64 + 18 * q^65 - 20 * q^67 + 30 * q^68 - 16 * q^69 - 26 * q^71 + 144 * q^72 + 8 * q^73 - 80 * q^74 + 142 * q^75 - 32 * q^78 - 22 * q^79 - 32 * q^80 - 32 * q^81 + 100 * q^82 - 20 * q^84 - 2 * q^85 + 12 * q^86 + 34 * q^88 + 68 * q^89 - 10 * q^90 - 28 * q^91 + 68 * q^92 - 62 * q^95 + 62 * q^96 - 2 * q^97 - 32 * q^98 + 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$			0.831038i			0.587633i	0.955862	+	0.293816i	$0.0949254\pi$
$2$			0.831038i			0.587633i	−0.955862	+	0.293816i	$0.905075\pi$
$3$	−0.711849	+	0.711849i	−0.410986	+	0.410986i	−0.882082	−	0.471096i	$-0.843859\pi$
$3$	−0.711849	+	0.711849i	−0.410986	+	0.410986i	0.471096	+	0.882082i	$0.343859\pi$
$4$	1.30938			0.654688
$5$	0.619206	−	0.619206i	0.276917	−	0.276917i	−0.554960	−	0.831877i	$-0.687266\pi$
$5$	0.619206	−	0.619206i	0.276917	−	0.276917i	0.831877	+	0.554960i	$0.187266\pi$
$6$	−0.591574	−	0.591574i	−0.241509	−	0.241509i
$7$	2.80838	+	2.80838i	1.06147	+	1.06147i	0.997983	+	0.0634840i	$0.0202212\pi$
$7$	2.80838	+	2.80838i	1.06147	+	1.06147i	0.0634840	+	0.997983i	$0.479779\pi$
$8$			2.75022i			0.972349i
$9$			1.98654i			0.662181i
$10$	0.514584	+	0.514584i	0.162726	+	0.162726i
$11$	−1.65119	−	1.65119i	−0.497852	−	0.497852i	0.412917	−	0.910769i	$-0.364510\pi$
$11$	−1.65119	−	1.65119i	−0.497852	−	0.497852i	−0.910769	+	0.412917i	$0.864510\pi$
$12$	−0.932077	+	0.932077i	−0.269067	+	0.269067i
$13$	0.606864			0.168314			0.0841569	−	0.996453i	$-0.473180\pi$
$13$	0.606864			0.168314			0.0841569	+	0.996453i	$0.473180\pi$
$14$	−2.33387	+	2.33387i	−0.623753	+	0.623753i
$15$			0.881562i			0.227618i
$16$	0.333214			0.0833036
$17$	1.58968	−	3.80433i	0.385554	−	0.922685i
$17$	1.58968	−	3.80433i	0.385554	−	0.922685i
$18$	−1.65089			−0.389119
$19$		−	0.918662i		−	0.210755i	−0.994432	−	0.105378i	$-0.966395\pi$
$19$		−	0.918662i		−	0.210755i	0.994432	−	0.105378i	$-0.0336052\pi$
$20$	0.810773	−	0.810773i	0.181294	−	0.181294i
$21$	−3.99828			−0.872496
$22$	1.37220	−	1.37220i	0.292554	−	0.292554i
$23$	−0.0627679	−	0.0627679i	−0.0130880	−	0.0130880i	0.700532	−	0.713621i	$-0.252946\pi$
$23$	−0.0627679	−	0.0627679i	−0.0130880	−	0.0130880i	−0.713621	+	0.700532i	$0.752946\pi$
$24$	−1.95774	−	1.95774i	−0.399622	−	0.399622i
$25$			4.23317i			0.846634i
$26$			0.504327i			0.0989067i
$27$	−3.54966	−	3.54966i	−0.683133	−	0.683133i
$28$	3.67722	+	3.67722i	0.694929	+	0.694929i
$29$	−3.46816	+	3.46816i	−0.644021	+	0.644021i	−0.951541	−	0.307521i	$-0.900501\pi$
$29$	−3.46816	+	3.46816i	−0.644021	+	0.644021i	0.307521	+	0.951541i	$0.400501\pi$
$30$	−0.732611			−0.133756
$31$	3.62669	−	3.62669i	0.651373	−	0.651373i	−0.301951	−	0.953323i	$-0.597638\pi$
$31$	3.62669	−	3.62669i	0.651373	−	0.651373i	0.953323	+	0.301951i	$0.0976379\pi$
$32$			5.77735i			1.02130i
$33$	2.35079			0.409220
$34$	3.16154	+	1.32108i	0.542200	+	0.226564i
$35$	3.47793			0.587877
$36$			2.60113i			0.433522i
$37$	1.28004	−	1.28004i	0.210437	−	0.210437i	−0.594016	−	0.804453i	$-0.702458\pi$
$37$	1.28004	−	1.28004i	0.210437	−	0.210437i	0.804453	+	0.594016i	$0.202458\pi$
$38$	0.763443			0.123847
$39$	−0.431995	+	0.431995i	−0.0691746	+	0.0691746i
$40$	1.70295	+	1.70295i	0.269260	+	0.269260i
$41$	0.348131	+	0.348131i	0.0543690	+	0.0543690i	0.733769	−	0.679400i	$-0.237760\pi$
$41$	0.348131	+	0.348131i	0.0543690	+	0.0543690i	−0.679400	+	0.733769i	$0.737760\pi$
$42$		−	3.32272i		−	0.512707i
$43$			1.00000i			0.152499i
$43$			1.00000i			0.152499i
$44$	−2.16202	−	2.16202i	−0.325937	−	0.325937i
$45$	1.23008	+	1.23008i	0.183369	+	0.183369i
$46$	0.0521625	−	0.0521625i	0.00769094	−	0.00769094i
$47$	−2.60356			−0.379768			−0.189884	−	0.981807i	$-0.560811\pi$
$47$	−2.60356			−0.379768			−0.189884	+	0.981807i	$0.560811\pi$
$48$	−0.237198	+	0.237198i	−0.0342366	+	0.0342366i
$49$			8.77397i			1.25342i
$50$	−3.51793			−0.497510
$51$	1.57650	+	3.83972i	0.220754	+	0.537668i
$52$	0.794613			0.110193
$53$		−	4.50774i		−	0.619185i	−0.950869	−	0.309593i	$-0.899807\pi$
$53$		−	4.50774i		−	0.619185i	0.950869	−	0.309593i	$-0.100193\pi$
$54$	2.94991	−	2.94991i	0.401431	−	0.401431i
$55$	−2.04485			−0.275727
$56$	−7.72365	+	7.72365i	−1.03212	+	1.03212i
$57$	0.653948	+	0.653948i	0.0866175	+	0.0866175i
$58$	−2.88217	−	2.88217i	−0.378448	−	0.378448i
$59$			8.50219i			1.10689i	0.832886	+	0.553445i	$0.186687\pi$
$59$			8.50219i			1.10689i	−0.832886	+	0.553445i	$0.813313\pi$
$60$			1.15429i			0.149019i
$61$	−5.64683	−	5.64683i	−0.723002	−	0.723002i	0.246213	−	0.969216i	$-0.420814\pi$
$61$	−5.64683	−	5.64683i	−0.723002	−	0.723002i	−0.969216	+	0.246213i	$0.920814\pi$
$62$	3.01392	+	3.01392i	0.382768	+	0.382768i
$63$	−5.57896	+	5.57896i	−0.702883	+	0.702883i
$64$	−4.13477			−0.516846
$65$	0.375774	−	0.375774i	0.0466090	−	0.0466090i
$66$			1.95360i			0.240471i
$67$	5.37771			0.656992			0.328496	−	0.944505i	$-0.393458\pi$
$67$	5.37771			0.656992			0.328496	+	0.944505i	$0.393458\pi$
$68$	2.08149	−	4.98129i	0.252417	−	0.604071i
$69$	0.0893625			0.0107580
$70$			2.89029i			0.345456i
$71$	1.41646	−	1.41646i	0.168103	−	0.168103i	−0.618042	−	0.786145i	$-0.712074\pi$
$71$	1.41646	−	1.41646i	0.168103	−	0.168103i	0.786145	+	0.618042i	$0.212074\pi$
$72$	−5.46343			−0.643871
$73$	−8.64635	+	8.64635i	−1.01198	+	1.01198i	−0.0120514	+	0.999927i	$0.503836\pi$
$73$	−8.64635	+	8.64635i	−1.01198	+	1.01198i	−0.999927	+	0.0120514i	$0.996164\pi$
$74$	1.06376	+	1.06376i	0.123660	+	0.123660i
$75$	−3.01338	−	3.01338i	−0.347955	−	0.347955i
$76$		−	1.20287i		−	0.137979i
$77$		−	9.27431i		−	1.05691i
$78$	−0.359005	−	0.359005i	−0.0406493	−	0.0406493i
$79$	7.96590	+	7.96590i	0.896234	+	0.896234i	0.995101	−	0.0988671i	$-0.0315219\pi$
$79$	7.96590	+	7.96590i	0.896234	+	0.896234i	−0.0988671	+	0.995101i	$0.531522\pi$
$80$	0.206328	−	0.206328i	0.0230682	−	0.0230682i
$81$	−0.905982			−0.100665
$82$	−0.289310	+	0.289310i	−0.0319490	+	0.0319490i
$83$		−	16.4933i		−	1.81038i	−0.425012	−	0.905188i	$-0.639730\pi$
$83$		−	16.4933i		−	1.81038i	0.425012	−	0.905188i	$-0.360270\pi$
$84$	−5.23525			−0.571212
$85$	−1.37132	−	3.34000i	−0.148741	−	0.362274i
$86$	−0.831038			−0.0896132
$87$		−	4.93761i		−	0.529367i
$88$	4.54112	−	4.54112i	0.484085	−	0.484085i
$89$	−13.4891			−1.42984			−0.714918	−	0.699208i	$-0.753536\pi$
$89$	−13.4891			−1.42984			−0.714918	+	0.699208i	$0.753536\pi$
$90$	−1.02224	+	1.02224i	−0.107754	+	0.107754i
$91$	1.70430	+	1.70430i	0.178660	+	0.178660i
$92$	−0.0821867	−	0.0821867i	−0.00856856	−	0.00856856i
$93$			5.16331i			0.535410i
$94$		−	2.16366i		−	0.223164i
$95$	−0.568841	−	0.568841i	−0.0583618	−	0.0583618i
$96$	−4.11260	−	4.11260i	−0.419740	−	0.419740i
$97$	8.56739	−	8.56739i	0.869887	−	0.869887i	−0.122573	−	0.992460i	$-0.539114\pi$
$97$	8.56739	−	8.56739i	0.869887	−	0.869887i	0.992460	+	0.122573i	$0.0391145\pi$
$98$	−7.29150			−0.736553
$99$	3.28015	−	3.28015i	0.329668	−	0.329668i
$100$			5.54281i			0.554281i
$101$	−12.4802			−1.24182			−0.620912	−	0.783880i	$-0.713237\pi$
$101$	−12.4802			−1.24182			−0.620912	+	0.783880i	$0.713237\pi$
$102$	−3.19095	+	1.31013i	−0.315951	+	0.129722i
$103$	11.2063			1.10419			0.552097	−	0.833780i	$-0.313828\pi$
$103$	11.2063			1.10419			0.552097	+	0.833780i	$0.313828\pi$
$104$			1.66901i			0.163660i
$105$	−2.47576	+	2.47576i	−0.241609	+	0.241609i
$106$	3.74610			0.363854
$107$	9.02545	−	9.02545i	0.872523	−	0.872523i	−0.120224	−	0.992747i	$-0.538361\pi$
$107$	9.02545	−	9.02545i	0.872523	−	0.872523i	0.992747	+	0.120224i	$0.0383613\pi$
$108$	−4.64784	−	4.64784i	−0.447239	−	0.447239i
$109$	1.17001	+	1.17001i	0.112067	+	0.112067i	0.760916	−	0.648850i	$-0.224750\pi$
$109$	1.17001	+	1.17001i	0.112067	+	0.112067i	−0.648850	+	0.760916i	$0.724750\pi$
$110$		−	1.69935i		−	0.162026i
$111$			1.82239i			0.172974i
$112$	0.935791	+	0.935791i	0.0884240	+	0.0884240i
$113$	1.69984	+	1.69984i	0.159908	+	0.159908i	0.782526	−	0.622618i	$-0.213931\pi$
$113$	1.69984	+	1.69984i	0.159908	+	0.159908i	−0.622618	+	0.782526i	$0.713931\pi$
$114$	−0.543456	+	0.543456i	−0.0508993	+	0.0508993i
$115$	−0.0777325			−0.00724859
$116$	−4.54112	+	4.54112i	−0.421632	+	0.421632i
$117$			1.20556i			0.111454i
$118$	−7.06564			−0.650445
$119$	15.1484	−	6.21957i	1.38865	−	0.570148i
$120$	−2.42449			−0.221324
$121$		−	5.54716i		−	0.504287i
$122$	4.69273	−	4.69273i	0.424860	−	0.424860i
$123$	−0.495633			−0.0446898
$124$	4.74870	−	4.74870i	0.426446	−	0.426446i
$125$	5.71723	+	5.71723i	0.511365	+	0.511365i
$126$	−4.63633	−	4.63633i	−0.413037	−	0.413037i
$127$		−	1.02002i		−	0.0905119i	−0.998975	−	0.0452559i	$-0.985590\pi$
$127$		−	1.02002i		−	0.0905119i	0.998975	−	0.0452559i	$-0.0144103\pi$
$128$			8.11855i			0.717585i
$129$	−0.711849	−	0.711849i	−0.0626748	−	0.0626748i
$130$	0.312282	+	0.312282i	0.0273890	+	0.0273890i
$131$	9.77139	−	9.77139i	0.853730	−	0.853730i	−0.136860	−	0.990590i	$-0.543701\pi$
$131$	9.77139	−	9.77139i	0.853730	−	0.853730i	0.990590	+	0.136860i	$0.0437011\pi$
$132$	3.07807			0.267911
$133$	2.57995	−	2.57995i	0.223710	−	0.223710i
$134$			4.46909i			0.386070i
$135$	−4.39594			−0.378343
$136$	10.4627	+	4.37196i	0.897172	+	0.374893i
$137$	6.18977			0.528828			0.264414	−	0.964409i	$-0.414822\pi$
$137$	6.18977			0.528828			0.264414	+	0.964409i	$0.414822\pi$
$138$			0.0742636i			0.00632174i
$139$	8.05838	−	8.05838i	0.683503	−	0.683503i	−0.277285	−	0.960788i	$-0.589435\pi$
$139$	8.05838	−	8.05838i	0.683503	−	0.683503i	0.960788	+	0.277285i	$0.0894347\pi$
$140$	4.55391			0.384876
$141$	1.85334	−	1.85334i	0.156079	−	0.156079i
$142$	1.17713	+	1.17713i	0.0987828	+	0.0987828i
$143$	−1.00205	−	1.00205i	−0.0837953	−	0.0837953i
$144$			0.661944i			0.0551620i
$145$			4.29501i			0.356681i
$146$	−7.18545	−	7.18545i	−0.594672	−	0.594672i
$147$	−6.24574	−	6.24574i	−0.515140	−	0.515140i
$148$	1.67605	−	1.67605i	0.137771	−	0.137771i
$149$	20.9513			1.71640			0.858198	−	0.513318i	$-0.171584\pi$
$149$	20.9513			1.71640			0.858198	+	0.513318i	$0.171584\pi$
$150$	2.50423	−	2.50423i	0.204470	−	0.204470i
$151$			15.9129i			1.29498i	0.762076	+	0.647488i	$0.224180\pi$
$151$			15.9129i			1.29498i	−0.762076	+	0.647488i	$0.775820\pi$
$152$	2.52652			0.204928
$153$	7.55746	+	3.15796i	0.610985	+	0.255306i
$154$	7.70731			0.621073
$155$		−	4.49133i		−	0.360753i
$156$	−0.565644	+	0.565644i	−0.0452878	+	0.0452878i
$157$	−1.63364			−0.130379			−0.0651893	−	0.997873i	$-0.520765\pi$
$157$	−1.63364			−0.130379			−0.0651893	+	0.997873i	$0.520765\pi$
$158$	−6.61997	+	6.61997i	−0.526656	+	0.526656i
$159$	3.20883	+	3.20883i	0.254477	+	0.254477i
$160$	3.57737	+	3.57737i	0.282816	+	0.282816i
$161$		−	0.352552i		−	0.0277850i
$162$		−	0.752906i		−	0.0591539i
$163$	−12.2803	−	12.2803i	−0.961865	−	0.961865i	0.0374340	−	0.999299i	$-0.488082\pi$
$163$	−12.2803	−	12.2803i	−0.961865	−	0.961865i	−0.999299	+	0.0374340i	$0.988082\pi$
$164$	0.455834	+	0.455834i	0.0355947	+	0.0355947i
$165$	1.45562	−	1.45562i	0.113320	−	0.113320i
$166$	13.7066			1.06384
$167$	15.6482	−	15.6482i	1.21089	−	1.21089i	0.240158	−	0.970734i	$-0.422801\pi$
$167$	15.6482	−	15.6482i	1.21089	−	1.21089i	0.970734	−	0.240158i	$-0.0771992\pi$
$168$		−	10.9961i		−	0.848370i
$169$	−12.6317			−0.971670
$170$	2.77567	−	1.13962i	0.212884	−	0.0874051i
$171$	1.82496			0.139558
$172$			1.30938i			0.0998389i
$173$	2.12029	−	2.12029i	0.161203	−	0.161203i	−0.621897	−	0.783099i	$-0.713638\pi$
$173$	2.12029	−	2.12029i	0.161203	−	0.161203i	0.783099	+	0.621897i	$0.213638\pi$
$174$	4.10334			0.311073
$175$	−11.8883	+	11.8883i	−0.898674	+	0.898674i
$176$	−0.550199	−	0.550199i	−0.0414728	−	0.0414728i
$177$	−6.05227	−	6.05227i	−0.454916	−	0.454916i
$178$		−	11.2099i		−	0.840219i
$179$		−	11.3469i		−	0.848105i	−0.905638	−	0.424053i	$-0.860607\pi$
$179$		−	11.3469i		−	0.848105i	0.905638	−	0.424053i	$-0.139393\pi$
$180$	1.61063	+	1.61063i	0.120050	+	0.120050i
$181$	4.66393	+	4.66393i	0.346667	+	0.346667i	0.858867	−	0.512199i	$-0.171169\pi$
$181$	4.66393	+	4.66393i	0.346667	+	0.346667i	−0.512199	+	0.858867i	$0.671169\pi$
$182$	−1.41634	+	1.41634i	−0.104986	+	0.104986i
$183$	8.03938			0.594288
$184$	0.172625	−	0.172625i	0.0127261	−	0.0127261i
$185$		−	1.58522i		−	0.116547i
$186$	−4.29091			−0.314624
$187$	−8.90652	+	3.65680i	−0.651309	+	0.267412i
$188$	−3.40903			−0.248629
$189$		−	19.9376i		−	1.45025i
$190$	0.472728	−	0.472728i	0.0342953	−	0.0342953i
$191$	−14.8257			−1.07275			−0.536374	−	0.843980i	$-0.680207\pi$
$191$	−14.8257			−1.07275			−0.536374	+	0.843980i	$0.680207\pi$
$192$	2.94333	−	2.94333i	0.212417	−	0.212417i
$193$	−15.3604	−	15.3604i	−1.10566	−	1.10566i	−0.993714	−	0.111949i	$-0.964291\pi$
$193$	−15.3604	−	15.3604i	−1.10566	−	1.10566i	−0.111949	−	0.993714i	$-0.535709\pi$
$194$	7.11983	+	7.11983i	0.511174	+	0.511174i
$195$			0.534988i			0.0383113i
$196$			11.4884i			0.820601i
$197$	−5.66132	−	5.66132i	−0.403352	−	0.403352i	0.476060	−	0.879413i	$-0.342064\pi$
$197$	−5.66132	−	5.66132i	−0.403352	−	0.403352i	−0.879413	+	0.476060i	$0.842064\pi$
$198$	2.72593	+	2.72593i	0.193724	+	0.193724i
$199$	7.43732	−	7.43732i	0.527217	−	0.527217i	−0.392524	−	0.919742i	$-0.628398\pi$
$199$	7.43732	−	7.43732i	0.527217	−	0.527217i	0.919742	+	0.392524i	$0.128398\pi$
$200$	−11.6421			−0.823223
$201$	−3.82812	+	3.82812i	−0.270015	+	0.270015i
$202$		−	10.3715i		−	0.729736i
$203$	−19.4798			−1.36721
$204$	2.06423	+	5.02763i	0.144525	+	0.352005i
$205$	0.431130			0.0301114
$206$			9.31290i			0.648861i
$207$	0.124691	−	0.124691i	0.00866663	−	0.00866663i
$208$	0.202216			0.0140211
$209$	−1.51688	+	1.51688i	−0.104925	+	0.104925i
$210$	−2.05745	−	2.05745i	−0.141977	−	0.141977i
$211$	2.77985	+	2.77985i	0.191373	+	0.191373i	0.796289	−	0.604916i	$-0.206793\pi$
$211$	2.77985	+	2.77985i	0.191373	+	0.191373i	−0.604916	+	0.796289i	$0.706793\pi$
$212$		−	5.90232i		−	0.405373i
$213$			2.01661i			0.138176i
$214$	7.50049	+	7.50049i	0.512723	+	0.512723i
$215$	0.619206	+	0.619206i	0.0422295	+	0.0422295i
$216$	9.76235	−	9.76235i	0.664244	−	0.664244i
$217$	20.3702			1.38282
$218$	−0.972323	+	0.972323i	−0.0658540	+	0.0658540i
$219$		−	12.3098i		−	0.831818i
$220$	−2.67747			−0.180515
$221$	0.964719	−	2.30871i	0.0648940	−	0.155301i
$222$	−1.51448			−0.101645
$223$		−	6.33197i		−	0.424020i	−0.977268	−	0.212010i	$-0.931999\pi$
$223$		−	6.33197i		−	0.424020i	0.977268	−	0.212010i	$-0.0680009\pi$
$224$	−16.2250	+	16.2250i	−1.08408	+	1.08408i
$225$	−8.40937			−0.560625
$226$	−1.41263	+	1.41263i	−0.0939671	+	0.0939671i
$227$	−17.0451	−	17.0451i	−1.13132	−	1.13132i	−0.989958	−	0.141364i	$-0.954851\pi$
$227$	−17.0451	−	17.0451i	−1.13132	−	1.13132i	−0.141364	−	0.989958i	$-0.545149\pi$
$228$	0.856264	+	0.856264i	0.0567074	+	0.0567074i
$229$			23.4464i			1.54938i	0.632338	+	0.774692i	$0.282095\pi$
$229$			23.4464i			1.54938i	−0.632338	+	0.774692i	$0.717905\pi$
$230$		−	0.0645987i		−	0.00425951i
$231$	6.60191	+	6.60191i	0.434374	+	0.434374i
$232$	−9.53819	−	9.53819i	−0.626213	−	0.626213i
$233$	5.37831	−	5.37831i	0.352345	−	0.352345i	−0.508637	−	0.860981i	$-0.669850\pi$
$233$	5.37831	−	5.37831i	0.352345	−	0.352345i	0.860981	+	0.508637i	$0.169850\pi$
$234$	−1.00187			−0.0654942
$235$	−1.61214	+	1.61214i	−0.105164	+	0.105164i
$236$			11.1326i			0.724668i
$237$	−11.3410			−0.736679
$238$	5.16871	+	12.5889i	0.335037	+	0.816018i
$239$	−10.4053			−0.673061			−0.336530	−	0.941673i	$-0.609254\pi$
$239$	−10.4053			−0.673061			−0.336530	+	0.941673i	$0.609254\pi$
$240$			0.293749i			0.0189614i
$241$	7.03329	−	7.03329i	0.453054	−	0.453054i	−0.443313	−	0.896367i	$-0.646197\pi$
$241$	7.03329	−	7.03329i	0.453054	−	0.453054i	0.896367	+	0.443313i	$0.146197\pi$
$242$	4.60990			0.296336
$243$	11.2939	−	11.2939i	0.724505	−	0.724505i
$244$	−7.39382	−	7.39382i	−0.473341	−	0.473341i
$245$	5.43289	+	5.43289i	0.347095	+	0.347095i
$246$		−	0.411890i		−	0.0262612i
$247$		−	0.557503i		−	0.0354731i
$248$	9.97418	+	9.97418i	0.633361	+	0.633361i
$249$	11.7407	+	11.7407i	0.744039	+	0.744039i
$250$	−4.75124	+	4.75124i	−0.300495	+	0.300495i
$251$	3.59156			0.226697			0.113349	−	0.993555i	$-0.463842\pi$
$251$	3.59156			0.226697			0.113349	+	0.993555i	$0.463842\pi$
$252$	−7.30496	+	7.30496i	−0.460169	+	0.460169i
$253$			0.207283i			0.0130318i
$254$	0.847673			0.0531878
$255$	3.35375	+	1.40140i	0.210020	+	0.0877590i
$256$	−15.0164			−0.938523
$257$			22.4642i			1.40128i	0.713516	+	0.700638i	$0.247101\pi$
$257$			22.4642i			1.40128i	−0.713516	+	0.700638i	$0.752899\pi$
$258$	0.591574	−	0.591574i	0.0368298	−	0.0368298i
$259$	7.18967			0.446744
$260$	0.492029	−	0.492029i	0.0305143	−	0.0305143i
$261$	−6.88964	−	6.88964i	−0.426458	−	0.426458i
$262$	8.12040	+	8.12040i	0.501680	+	0.501680i
$263$		−	5.18799i		−	0.319905i	−0.987125	−	0.159953i	$-0.948866\pi$
$263$		−	5.18799i		−	0.319905i	0.987125	−	0.159953i	$-0.0511342\pi$
$264$			6.46519i			0.397905i
$265$	−2.79122	−	2.79122i	−0.171463	−	0.171463i
$266$	2.14404	+	2.14404i	0.131459	+	0.131459i
$267$	9.60216	−	9.60216i	0.587643	−	0.587643i
$268$	7.04145			0.430125
$269$	16.3134	−	16.3134i	0.994645	−	0.994645i	−0.00534094	−	0.999986i	$-0.501700\pi$
$269$	16.3134	−	16.3134i	0.994645	−	0.994645i	0.999986	+	0.00534094i	$0.00170008\pi$
$270$		−	3.65320i		−	0.222327i
$271$	17.0308			1.03455			0.517274	−	0.855820i	$-0.326947\pi$
$271$	17.0308			1.03455			0.517274	+	0.855820i	$0.326947\pi$
$272$	0.529704	−	1.26766i	0.0321180	−	0.0768630i
$273$	−2.42641			−0.146853
$274$			5.14394i			0.310757i
$275$	6.98975	−	6.98975i	0.421498	−	0.421498i
$276$	0.117009			0.00704312
$277$	−13.1074	+	13.1074i	−0.787547	+	0.787547i	−0.981091	−	0.193545i	$-0.938002\pi$
$277$	−13.1074	+	13.1074i	−0.787547	+	0.787547i	0.193545	+	0.981091i	$0.438002\pi$
$278$	6.69682	+	6.69682i	0.401649	+	0.401649i
$279$	7.20457	+	7.20457i	0.431326	+	0.431326i
$280$			9.56506i			0.571621i
$281$			6.88066i			0.410466i	0.978713	+	0.205233i	$0.0657952\pi$
$281$			6.88066i			0.410466i	−0.978713	+	0.205233i	$0.934205\pi$
$282$	1.54020	+	1.54020i	0.0917173	+	0.0917173i
$283$	−5.73885	−	5.73885i	−0.341139	−	0.341139i	0.515656	−	0.856795i	$-0.327548\pi$
$283$	−5.73885	−	5.73885i	−0.341139	−	0.341139i	−0.856795	+	0.515656i	$0.827548\pi$
$284$	1.85468	−	1.85468i	0.110055	−	0.110055i
$285$	0.809857			0.0479718
$286$	0.832739	−	0.832739i	0.0492409	−	0.0492409i
$287$			1.95537i			0.115422i
$288$	−11.4770			−0.676286
$289$	−11.9458	−	12.0953i	−0.702697	−	0.711490i
$290$	−3.56931			−0.209597
$291$			12.1974i			0.715023i
$292$	−11.3213	+	11.3213i	−0.662530	+	0.662530i
$293$	−1.58836			−0.0927929			−0.0463964	−	0.998923i	$-0.514774\pi$
$293$	−1.58836			−0.0927929			−0.0463964	+	0.998923i	$0.514774\pi$
$294$	5.19045	−	5.19045i	0.302713	−	0.302713i
$295$	5.26460	+	5.26460i	0.306517	+	0.306517i
$296$	3.52039	+	3.52039i	0.204618	+	0.204618i
$297$			11.7223i			0.680198i
$298$			17.4113i			1.00861i
$299$	−0.0380916	−	0.0380916i	−0.00220289	−	0.00220289i
$300$	−3.94564	−	3.94564i	−0.227802	−	0.227802i
$301$	−2.80838	+	2.80838i	−0.161872	+	0.161872i
$302$	−13.2242			−0.760970
$303$	8.88399	−	8.88399i	0.510372	−	0.510372i
$304$		−	0.306111i		−	0.0175567i
$305$	−6.99310			−0.400424
$306$	−2.62439	+	6.28054i	−0.150026	+	0.359035i
$307$	−8.22656			−0.469514			−0.234757	−	0.972054i	$-0.575430\pi$
$307$	−8.22656			−0.469514			−0.234757	+	0.972054i	$0.575430\pi$
$308$		−	12.1436i		−	0.691943i
$309$	−7.97722	+	7.97722i	−0.453808	+	0.453808i
$310$	3.73247			0.211990
$311$	−17.6906	+	17.6906i	−1.00314	+	1.00314i	−0.00314768	+	0.999995i	$0.501002\pi$
$311$	−17.6906	+	17.6906i	−1.00314	+	1.00314i	−0.999995	+	0.00314768i	$0.998998\pi$
$312$	−1.18808	−	1.18808i	−0.0672619	−	0.0672619i
$313$	8.24133	+	8.24133i	0.465827	+	0.465827i	0.900560	−	0.434732i	$-0.143157\pi$
$313$	8.24133	+	8.24133i	0.465827	+	0.465827i	−0.434732	+	0.900560i	$0.643157\pi$
$314$		−	1.35762i		−	0.0766148i
$315$			6.90905i			0.389281i
$316$	10.4304	+	10.4304i	0.586753	+	0.586753i
$317$	−19.6155	−	19.6155i	−1.10171	−	1.10171i	−0.994204	−	0.107510i	$-0.965712\pi$
$317$	−19.6155	−	19.6155i	−1.10171	−	1.10171i	−0.107510	−	0.994204i	$-0.534288\pi$
$318$	−2.66666	+	2.66666i	−0.149539	+	0.149539i
$319$	11.4532			0.641253
$320$	−2.56027	+	2.56027i	−0.143124	+	0.143124i
$321$			12.8495i			0.717189i
$322$	0.292984			0.0163274
$323$	−3.49489	−	1.46038i	−0.194461	−	0.0812575i
$324$	−1.18627			−0.0659039
$325$			2.56896i			0.142500i
$326$	10.2054	−	10.2054i	0.565224	−	0.565224i
$327$	−1.66574			−0.0921156
$328$	−0.957436	+	0.957436i	−0.0528656	+	0.0528656i
$329$	−7.31177	−	7.31177i	−0.403111	−	0.403111i
$330$	1.20968	+	1.20968i	0.0665906	+	0.0665906i
$331$		−	8.71943i		−	0.479263i	−0.970864	−	0.239632i	$-0.922973\pi$
$331$		−	8.71943i		−	0.479263i	0.970864	−	0.239632i	$-0.0770267\pi$
$332$		−	21.5959i		−	1.18523i
$333$	2.54285	+	2.54285i	0.139348	+	0.139348i
$334$	13.0042	+	13.0042i	0.711560	+	0.711560i
$335$	3.32991	−	3.32991i	0.181933	−	0.181933i
$336$	−1.33228			−0.0726820
$337$	−7.80858	+	7.80858i	−0.425360	+	0.425360i	−0.887044	−	0.461684i	$-0.847245\pi$
$337$	−7.80858	+	7.80858i	−0.425360	+	0.425360i	0.461684	+	0.887044i	$0.347245\pi$
$338$		−	10.4974i		−	0.570985i
$339$	−2.42006			−0.131440
$340$	−1.79558	−	4.37331i	−0.0973789	−	0.237176i
$341$	−11.9767			−0.648574
$342$			1.51661i			0.0820090i
$343$	−4.98196	+	4.98196i	−0.269001	+	0.269001i
$344$	−2.75022			−0.148282
$345$	0.0553338	−	0.0553338i	0.00297907	−	0.00297907i
$346$	1.76204	+	1.76204i	0.0947280	+	0.0947280i
$347$	−4.21144	−	4.21144i	−0.226082	−	0.226082i	0.584972	−	0.811054i	$-0.301106\pi$
$347$	−4.21144	−	4.21144i	−0.226082	−	0.226082i	−0.811054	+	0.584972i	$0.801106\pi$
$348$		−	6.46518i		−	0.346570i
$349$			26.7552i			1.43217i	0.698011	+	0.716087i	$0.254069\pi$
$349$			26.7552i			1.43217i	−0.698011	+	0.716087i	$0.745931\pi$
$350$	−9.87966	−	9.87966i	−0.528090	−	0.528090i
$351$	−2.15416	−	2.15416i	−0.114981	−	0.114981i
$352$	9.53948	−	9.53948i	0.508456	−	0.508456i
$353$	−6.37934			−0.339538			−0.169769	−	0.985484i	$-0.554302\pi$
$353$	−6.37934			−0.339538			−0.169769	+	0.985484i	$0.554302\pi$
$354$	5.02967	−	5.02967i	0.267324	−	0.267324i
$355$		−	1.75416i		−	0.0931012i
$356$	−17.6622			−0.936096
$357$	−6.35598	+	15.2108i	−0.336394	+	0.805039i
$358$	9.42969			0.498375
$359$			3.20220i			0.169005i	0.996423	+	0.0845027i	$0.0269302\pi$
$359$			3.20220i			0.169005i	−0.996423	+	0.0845027i	$0.973070\pi$
$360$	−3.38298	+	3.38298i	−0.178299	+	0.178299i
$361$	18.1561			0.955582
$362$	−3.87590	+	3.87590i	−0.203713	+	0.203713i
$363$	3.94874	+	3.94874i	0.207255	+	0.207255i
$364$	2.23157	+	2.23157i	0.116966	+	0.116966i
$365$			10.7077i			0.560469i
$366$			6.68103i			0.349223i
$367$	−14.6393	−	14.6393i	−0.764166	−	0.764166i	0.212906	−	0.977073i	$-0.431707\pi$
$367$	−14.6393	−	14.6393i	−0.764166	−	0.764166i	−0.977073	+	0.212906i	$0.931707\pi$
$368$	−0.0209152	−	0.0209152i	−0.00109028	−	0.00109028i
$369$	−0.691578	+	0.691578i	−0.0360021	+	0.0360021i
$370$	1.31738			0.0684871
$371$	12.6594	−	12.6594i	0.657245	−	0.657245i
$372$			6.76071i			0.350526i
$373$	−13.2663			−0.686901			−0.343450	−	0.939171i	$-0.611596\pi$
$373$	−13.2663			−0.686901			−0.343450	+	0.939171i	$0.611596\pi$
$374$	−3.03894	−	7.40166i	−0.157140	−	0.382731i
$375$	−8.13961			−0.420327
$376$		−	7.16035i		−	0.369267i
$377$	−2.10470	+	2.10470i	−0.108398	+	0.108398i
$378$	16.5689			0.852212
$379$	−0.165892	+	0.165892i	−0.00852130	+	0.00852130i	−0.711355	−	0.702833i	$-0.751918\pi$
$379$	−0.165892	+	0.165892i	−0.00852130	+	0.00852130i	0.702833	+	0.711355i	$0.251918\pi$
$380$	−0.744826	−	0.744826i	−0.0382088	−	0.0382088i
$381$	0.726098	+	0.726098i	0.0371991	+	0.0371991i
$382$		−	12.3207i		−	0.630383i
$383$		−	3.54357i		−	0.181068i	−0.995893	−	0.0905341i	$-0.971143\pi$
$383$		−	3.54357i		−	0.181068i	0.995893	−	0.0905341i	$-0.0288574\pi$
$384$	−5.77918	−	5.77918i	−0.294917	−	0.294917i
$385$	−5.74271	−	5.74271i	−0.292675	−	0.292675i
$386$	12.7651	−	12.7651i	0.649724	−	0.649724i
$387$	−1.98654			−0.100982
$388$	11.2179	−	11.2179i	0.569504	−	0.569504i
$389$			4.93519i			0.250224i	0.992143	+	0.125112i	$0.0399290\pi$
$389$			4.93519i			0.250224i	−0.992143	+	0.125112i	$0.960071\pi$
$390$	−0.444596			−0.0225130
$391$	−0.338571	+	0.139009i	−0.0171222	+	0.00702999i
$392$	−24.1303			−1.21876
$393$			13.9115i			0.701742i
$394$	4.70477	−	4.70477i	0.237023	−	0.237023i
$395$	9.86506			0.496365
$396$	4.29495	−	4.29495i	0.215830	−	0.215830i
$397$	8.48654	+	8.48654i	0.425927	+	0.425927i	0.887238	−	0.461311i	$-0.152621\pi$
$397$	8.48654	+	8.48654i	0.425927	+	0.425927i	−0.461311	+	0.887238i	$0.652621\pi$
$398$	6.18070	+	6.18070i	0.309810	+	0.309810i
$399$			3.67307i			0.183883i
$400$			1.41055i			0.0705276i
$401$	19.4525	+	19.4525i	0.971410	+	0.971410i	0.999603	−	0.0281922i	$-0.00897506\pi$
$401$	19.4525	+	19.4525i	0.971410	+	0.971410i	−0.0281922	+	0.999603i	$0.508975\pi$
$402$	−3.18131	−	3.18131i	−0.158669	−	0.158669i
$403$	2.20091	−	2.20091i	0.109635	−	0.109635i
$404$	−16.3412			−0.813007
$405$	−0.560989	+	0.560989i	−0.0278758	+	0.0278758i
$406$		−	16.1885i		−	0.803419i
$407$	−4.22717			−0.209533
$408$	−10.5601	+	4.33571i	−0.522801	+	0.214650i
$409$	25.3807			1.25499			0.627497	−	0.778619i	$-0.284079\pi$
$409$	25.3807			1.25499			0.627497	+	0.778619i	$0.284079\pi$
$410$			0.358285i			0.0176944i
$411$	−4.40618	+	4.40618i	−0.217341	+	0.217341i
$412$	14.6733			0.722902
$413$	−23.8773	+	23.8773i	−1.17493	+	1.17493i
$414$	0.103623	+	0.103623i	0.00509280	+	0.00509280i
$415$	−10.2127	−	10.2127i	−0.501324	−	0.501324i
$416$			3.50607i			0.171899i
$417$			11.4727i			0.561820i
$418$	−1.26059	−	1.26059i	−0.0616573	−	0.0616573i
$419$	20.6036	+	20.6036i	1.00655	+	1.00655i	0.999978	+	0.00657472i	$0.00209281\pi$
$419$	20.6036	+	20.6036i	1.00655	+	1.00655i	0.00657472	+	0.999978i	$0.497907\pi$
$420$	−3.24170	+	3.24170i	−0.158179	+	0.158179i
$421$	−33.3828			−1.62698			−0.813490	−	0.581580i	$-0.802435\pi$
$421$	−33.3828			−1.62698			−0.813490	+	0.581580i	$0.802435\pi$
$422$	−2.31016	+	2.31016i	−0.112457	+	0.112457i
$423$		−	5.17208i		−	0.251475i
$424$	12.3973			0.602064
$425$	16.1044	+	6.72938i	0.781177	+	0.326423i
$426$	−1.67588			−0.0811967
$427$		−	31.7169i		−	1.53489i
$428$	11.8177	−	11.8177i	0.571230	−	0.571230i
$429$	1.42661			0.0688774
$430$	−0.514584	+	0.514584i	−0.0248154	+	0.0248154i
$431$	9.66626	+	9.66626i	0.465607	+	0.465607i	0.900488	−	0.434881i	$-0.143209\pi$
$431$	9.66626	+	9.66626i	0.465607	+	0.465607i	−0.434881	+	0.900488i	$0.643209\pi$
$432$	−1.18280	−	1.18280i	−0.0569074	−	0.0569074i
$433$		−	14.9067i		−	0.716371i	−0.933650	−	0.358185i	$-0.883396\pi$
$433$		−	14.9067i		−	0.716371i	0.933650	−	0.358185i	$-0.116604\pi$
$434$			16.9284i			0.812591i
$435$	−3.05739	−	3.05739i	−0.146591	−	0.146591i
$436$	1.53198	+	1.53198i	0.0733686	+	0.0733686i
$437$	−0.0576625	+	0.0576625i	−0.00275837	+	0.00275837i
$438$	10.2299			0.488804
$439$	15.8822	−	15.8822i	0.758014	−	0.758014i	−0.217947	−	0.975961i	$-0.569936\pi$
$439$	15.8822	−	15.8822i	0.758014	−	0.758014i	0.975961	+	0.217947i	$0.0699360\pi$
$440$		−	5.62378i		−	0.268103i
$441$	−17.4299			−0.829993
$442$	1.91863	+	0.801718i	0.0912598	+	0.0381339i
$443$	−30.5211			−1.45010			−0.725050	−	0.688696i	$-0.758183\pi$
$443$	−30.5211			−1.45010			−0.725050	+	0.688696i	$0.758183\pi$
$444$			2.38619i			0.113244i
$445$	−8.35250	+	8.35250i	−0.395946	+	0.395946i
$446$	5.26211			0.249168
$447$	−14.9141	+	14.9141i	−0.705415	+	0.705415i
$448$	−11.6120	−	11.6120i	−0.548615	−	0.548615i
$449$	−4.39986	−	4.39986i	−0.207642	−	0.207642i	0.595622	−	0.803265i	$-0.296906\pi$
$449$	−4.39986	−	4.39986i	−0.207642	−	0.207642i	−0.803265	+	0.595622i	$0.796906\pi$
$450$		−	6.98851i		−	0.329442i
$451$		−	1.14966i		−	0.0541353i
$452$	2.22573	+	2.22573i	0.104690	+	0.104690i
$453$	−11.3276	−	11.3276i	−0.532217	−	0.532217i
$454$	14.1651	−	14.1651i	0.664802	−	0.664802i
$455$	2.11063			0.0989478
$456$	−1.79850	+	1.79850i	−0.0842225	+	0.0842225i
$457$			28.9331i			1.35343i	0.736244	+	0.676716i	$0.236598\pi$
$457$			28.9331i			1.35343i	−0.736244	+	0.676716i	$0.763402\pi$
$458$	−19.4849			−0.910469
$459$	−19.1469	+	7.86127i	−0.893701	+	0.366932i
$460$	−0.101781			−0.00474556
$461$			5.91043i			0.275276i	0.990483	+	0.137638i	$0.0439510\pi$
$461$			5.91043i			0.275276i	−0.990483	+	0.137638i	$0.956049\pi$
$462$	−5.48644	+	5.48644i	−0.255252	+	0.255252i
$463$	20.3780			0.947045			0.473523	−	0.880782i	$-0.342982\pi$
$463$	20.3780			0.947045			0.473523	+	0.880782i	$0.342982\pi$
$464$	−1.15564	+	1.15564i	−0.0536492	+	0.0536492i
$465$	3.19715	+	3.19715i	0.148264	+	0.148264i
$466$	4.46958	+	4.46958i	0.207049	+	0.207049i
$467$			40.8559i			1.89059i	0.326222	+	0.945293i	$0.394224\pi$
$467$			40.8559i			1.89059i	−0.326222	+	0.945293i	$0.605776\pi$
$468$			1.57853i			0.0729677i
$469$	15.1027	+	15.1027i	0.697376	+	0.697376i
$470$	−1.33975	−	1.33975i	−0.0617980	−	0.0617980i
$471$	1.16290	−	1.16290i	0.0535838	−	0.0535838i
$472$	−23.3829			−1.07628
$473$	1.65119	−	1.65119i	0.0759217	−	0.0759217i
$474$		−	9.42483i		−	0.432897i
$475$	3.88885			0.178433
$476$	19.8350	−	8.14376i	0.909134	−	0.373269i
$477$	8.95481			0.410013
$478$		−	8.64718i		−	0.395513i
$479$	−14.5049	+	14.5049i	−0.662744	+	0.662744i	−0.956026	−	0.293282i	$-0.905253\pi$
$479$	−14.5049	+	14.5049i	−0.662744	+	0.662744i	0.293282	+	0.956026i	$0.405253\pi$
$480$	−5.09309			−0.232467
$481$	0.776810	−	0.776810i	0.0354195	−	0.0354195i
$482$	5.84493	+	5.84493i	0.266229	+	0.266229i
$483$	0.250964	+	0.250964i	0.0114192	+	0.0114192i
$484$		−	7.26332i		−	0.330151i
$485$		−	10.6100i		−	0.481773i
$486$	9.38568	+	9.38568i	0.425743	+	0.425743i
$487$	7.36626	+	7.36626i	0.333797	+	0.333797i	0.854027	−	0.520229i	$-0.174154\pi$
$487$	7.36626	+	7.36626i	0.333797	+	0.333797i	−0.520229	+	0.854027i	$0.674154\pi$
$488$	15.5300	−	15.5300i	0.703011	−	0.703011i
$489$	17.4834			0.790626
$490$	−4.51494	+	4.51494i	−0.203964	+	0.203964i
$491$			0.996703i			0.0449806i	0.999747	+	0.0224903i	$0.00715948\pi$
$491$			0.996703i			0.0449806i	−0.999747	+	0.0224903i	$0.992841\pi$
$492$	−0.648970			−0.0292578
$493$	7.68076	+	18.7073i	0.345924	+	0.842533i
$494$	0.463306			0.0208451
$495$		−	4.06218i		−	0.182581i
$496$	1.20846	−	1.20846i	0.0542617	−	0.0542617i
$497$	7.95591			0.356871
$498$	−9.75700	+	9.75700i	−0.437222	+	0.437222i
$499$	11.5566	+	11.5566i	0.517344	+	0.517344i	0.916767	−	0.399423i	$-0.130789\pi$
$499$	11.5566	+	11.5566i	0.517344	+	0.517344i	−0.399423	+	0.916767i	$0.630789\pi$
$500$	7.48600	+	7.48600i	0.334784	+	0.334784i
$501$			22.2783i			0.995319i
$502$			2.98472i			0.133215i
$503$	2.08245	+	2.08245i	0.0928520	+	0.0928520i	0.752007	−	0.659155i	$-0.229086\pi$
$503$	2.08245	+	2.08245i	0.0928520	+	0.0928520i	−0.659155	+	0.752007i	$0.729086\pi$
$504$	−15.3434	−	15.3434i	−0.683448	−	0.683448i
$505$	−7.72779	+	7.72779i	−0.343882	+	0.343882i
$506$	−0.172260			−0.00765790
$507$	8.99187	−	8.99187i	0.399343	−	0.399343i
$508$		−	1.33559i		−	0.0592570i
$509$	−1.71260			−0.0759099			−0.0379549	−	0.999279i	$-0.512084\pi$
$509$	−1.71260			−0.0759099			−0.0379549	+	0.999279i	$0.512084\pi$
$510$	−1.16462	+	2.78710i	−0.0515701	+	0.123415i
$511$	−48.5644			−2.14836
$512$			3.75792i			0.166078i
$513$	−3.26094	+	3.26094i	−0.143974	+	0.143974i
$514$	−18.6686			−0.823436
$515$	6.93903	−	6.93903i	0.305770	−	0.305770i
$516$	−0.932077	−	0.932077i	−0.0410324	−	0.0410324i
$517$	4.29896	+	4.29896i	0.189068	+	0.189068i
$518$			5.97489i			0.262522i
$519$			3.01865i			0.132504i
$520$	1.03346	+	1.03346i	0.0453202	+	0.0453202i
$521$	9.14499	+	9.14499i	0.400649	+	0.400649i	0.878462	−	0.477812i	$-0.158570\pi$
$521$	9.14499	+	9.14499i	0.400649	+	0.400649i	−0.477812	+	0.878462i	$0.658570\pi$
$522$	5.72556	−	5.72556i	0.250601	−	0.250601i
$523$	25.0661			1.09606			0.548032	−	0.836458i	$-0.315377\pi$
$523$	25.0661			1.09606			0.548032	+	0.836458i	$0.315377\pi$
$524$	12.7944	−	12.7944i	0.558927	−	0.558927i
$525$		−	16.9254i		−	0.738685i
$526$	4.31142			0.187987
$527$	−8.03185	−	19.5624i	−0.349873	−	0.852151i
$528$	0.783317			0.0340895
$529$		−	22.9921i		−	0.999657i
$530$	2.31961	−	2.31961i	0.100757	−	0.100757i
$531$	−16.8900			−0.732962
$532$	3.37812	−	3.37812i	0.146460	−	0.146460i
$533$	0.211268	+	0.211268i	0.00915105	+	0.00915105i
$534$	7.97977	+	7.97977i	0.345318	+	0.345318i
$535$		−	11.1772i		−	0.483233i
$536$			14.7899i			0.638826i
$537$	8.07726	+	8.07726i	0.348559	+	0.348559i
$538$	13.5571	+	13.5571i	0.584486	+	0.584486i
$539$	14.4875	−	14.4875i	0.624019	−	0.624019i
$540$	−5.75594			−0.247696
$541$	−9.52392	+	9.52392i	−0.409465	+	0.409465i	−0.881552	−	0.472087i	$-0.843501\pi$
$541$	−9.52392	+	9.52392i	−0.409465	+	0.409465i	0.472087	+	0.881552i	$0.343501\pi$
$542$			14.1533i			0.607935i
$543$	−6.64003			−0.284951
$544$	21.9789	+	9.18413i	0.942339	+	0.393766i
$545$	1.44895			0.0620663
$546$		−	2.01644i		−	0.0862957i
$547$	−16.0409	+	16.0409i	−0.685859	+	0.685859i	−0.961314	−	0.275455i	$-0.911172\pi$
$547$	−16.0409	+	16.0409i	−0.685859	+	0.685859i	0.275455	+	0.961314i	$0.411172\pi$
$548$	8.10473			0.346217
$549$	11.2177	−	11.2177i	0.478758	−	0.478758i
$550$	5.80875	+	5.80875i	0.247686	+	0.247686i
$551$	3.18606	+	3.18606i	0.135731	+	0.135731i
$552$			0.245766i			0.0104605i
$553$			44.7425i			1.90264i
$554$	−10.8927	−	10.8927i	−0.462788	−	0.462788i
$555$	1.12843	+	1.12843i	0.0478993	+	0.0478993i
$556$	10.5514	−	10.5514i	0.447481	−	0.447481i
$557$	−41.3749			−1.75311			−0.876556	−	0.481300i	$-0.840165\pi$
$557$	−41.3749			−1.75311			−0.876556	+	0.481300i	$0.840165\pi$
$558$	−5.98728	+	5.98728i	−0.253462	+	0.253462i
$559$			0.606864i			0.0256676i
$560$	1.15889			0.0489722
$561$	3.73700	−	8.94318i	0.157776	−	0.377581i
$562$	−5.71809			−0.241203
$563$			1.73587i			0.0731582i	0.999331	+	0.0365791i	$0.0116461\pi$
$563$			1.73587i			0.0731582i	−0.999331	+	0.0365791i	$0.988354\pi$
$564$	2.42672	−	2.42672i	0.102183	−	0.102183i
$565$	2.10510			0.0885624
$566$	4.76920	−	4.76920i	0.200465	−	0.200465i
$567$	−2.54434	−	2.54434i	−0.106852	−	0.106852i
$568$	3.89557	+	3.89557i	0.163455	+	0.163455i
$569$			28.7821i			1.20661i	0.797511	+	0.603304i	$0.206150\pi$
$569$			28.7821i			1.20661i	−0.797511	+	0.603304i	$0.793850\pi$
$570$			0.673022i			0.0281898i
$571$	−22.3183	−	22.3183i	−0.933991	−	0.933991i	0.0639616	−	0.997952i	$-0.479626\pi$
$571$	−22.3183	−	22.3183i	−0.933991	−	0.933991i	−0.997952	+	0.0639616i	$0.979626\pi$
$572$	−1.31205	−	1.31205i	−0.0548598	−	0.0548598i
$573$	10.5536	−	10.5536i	0.440885	−	0.440885i
$574$	−1.62499			−0.0678256
$575$	0.265707	−	0.265707i	0.0110808	−	0.0110808i
$576$		−	8.21390i		−	0.342246i
$577$	−19.5709			−0.814749			−0.407374	−	0.913261i	$-0.633556\pi$
$577$	−19.5709			−0.814749			−0.407374	+	0.913261i	$0.633556\pi$
$578$	10.0517	−	9.92745i	0.418095	−	0.412928i
$579$	21.8685			0.908824
$580$			5.62377i			0.233515i
$581$	46.3194	−	46.3194i	1.92165	−	1.92165i
$582$	−10.1365			−0.420171
$583$	−7.44312	+	7.44312i	−0.308262	+	0.308262i
$584$	−23.7793	−	23.7793i	−0.983996	−	0.983996i
$585$	0.746491	+	0.746491i	0.0308636	+	0.0308636i
$586$		−	1.31999i		−	0.0545281i
$587$			14.3894i			0.593916i	0.954891	+	0.296958i	$0.0959721\pi$
$587$			14.3894i			0.593916i	−0.954891	+	0.296958i	$0.904028\pi$
$588$	−8.17801	−	8.17801i	−0.337256	−	0.337256i
$589$	−3.33170	−	3.33170i	−0.137280	−	0.137280i
$590$	−4.37509	+	4.37509i	−0.180119	+	0.180119i
$591$	8.06000			0.331544
$592$	0.426527	−	0.426527i	0.0175302	−	0.0175302i
$593$			25.3744i			1.04200i	0.853556	+	0.521002i	$0.174442\pi$
$593$			25.3744i			1.04200i	−0.853556	+	0.521002i	$0.825558\pi$
$594$	−9.74170			−0.399707
$595$	5.52879	−	13.2312i	0.226658	−	0.542425i
$596$	27.4331			1.12370
$597$			10.5885i			0.433358i
$598$	0.0316556	−	0.0316556i	0.00129449	−	0.00129449i
$599$	−12.6399			−0.516453			−0.258227	−	0.966084i	$-0.583138\pi$
$599$	−12.6399			−0.516453			−0.258227	+	0.966084i	$0.583138\pi$
$600$	8.28744	−	8.28744i	0.338333	−	0.338333i
$601$	−20.8656	−	20.8656i	−0.851125	−	0.851125i	0.139147	−	0.990272i	$-0.455564\pi$
$601$	−20.8656	−	20.8656i	−0.851125	−	0.851125i	−0.990272	+	0.139147i	$0.955564\pi$
$602$	−2.33387	−	2.33387i	−0.0951214	−	0.0951214i
$603$			10.6831i			0.435048i
$604$			20.8360i			0.847804i
$605$	−3.43483	−	3.43483i	−0.139646	−	0.139646i
$606$	7.38294	+	7.38294i	0.299911	+	0.299911i
$607$	8.92696	−	8.92696i	0.362334	−	0.362334i	−0.502337	−	0.864672i	$-0.667526\pi$
$607$	8.92696	−	8.92696i	0.362334	−	0.362334i	0.864672	+	0.502337i	$0.167526\pi$
$608$	5.30743			0.215245
$609$	13.8667	−	13.8667i	0.561905	−	0.561905i
$610$		−	5.81153i		−	0.235302i
$611$	−1.58001			−0.0639202
$612$	9.89556	+	4.13496i	0.400004	+	0.167146i
$613$	34.8426			1.40728			0.703639	−	0.710557i	$-0.251557\pi$
$613$	34.8426			1.40728			0.703639	+	0.710557i	$0.251557\pi$
$614$		−	6.83659i		−	0.275902i
$615$	−0.306899	+	0.306899i	−0.0123754	+	0.0123754i
$616$	25.5064			1.02768
$617$	0.970404	−	0.970404i	0.0390670	−	0.0390670i	−0.687303	−	0.726370i	$-0.741206\pi$
$617$	0.970404	−	0.970404i	0.0390670	−	0.0390670i	0.726370	+	0.687303i	$0.241206\pi$
$618$	−6.62938	−	6.62938i	−0.266673	−	0.266673i
$619$	−8.91115	−	8.91115i	−0.358169	−	0.358169i	0.504968	−	0.863138i	$-0.331504\pi$
$619$	−8.91115	−	8.91115i	−0.358169	−	0.358169i	−0.863138	+	0.504968i	$0.831504\pi$
$620$		−	5.88084i		−	0.236180i
$621$			0.445610i			0.0178817i
$622$	−14.7016	−	14.7016i	−0.589480	−	0.589480i
$623$	−37.8823	−	37.8823i	−1.51772	−	1.51772i
$624$	−0.143947	+	0.143947i	−0.00576249	+	0.00576249i
$625$	−14.0856			−0.563422
$626$	−6.84886	+	6.84886i	−0.273735	+	0.273735i
$627$		−	2.15958i		−	0.0862454i
$628$	−2.13905			−0.0853573
$629$	−2.83484	−	6.90454i	−0.113033	−	0.275302i
$630$	−5.74169			−0.228754
$631$		−	33.1461i		−	1.31952i	−0.751475	−	0.659762i	$-0.770657\pi$
$631$		−	33.1461i		−	1.31952i	0.751475	−	0.659762i	$-0.229343\pi$
$632$	−21.9080	+	21.9080i	−0.871452	+	0.871452i
$633$	−3.95766			−0.157303
$634$	16.3012	−	16.3012i	0.647403	−	0.647403i
$635$	−0.631600	−	0.631600i	−0.0250643	−	0.0250643i
$636$	4.20156	+	4.20156i	0.166603	+	0.166603i
$637$			5.32460i			0.210969i
$638$			9.51801i			0.376822i
$639$	2.81386	+	2.81386i	0.111315	+	0.111315i
$640$	5.02705	+	5.02705i	0.198712	+	0.198712i
$641$	−15.0249	+	15.0249i	−0.593448	+	0.593448i	−0.938561	−	0.345113i	$-0.887841\pi$
$641$	−15.0249	+	15.0249i	−0.593448	+	0.593448i	0.345113	+	0.938561i	$0.387841\pi$
$642$	−10.6784			−0.421444
$643$	19.2502	−	19.2502i	0.759152	−	0.759152i	−0.217016	−	0.976168i	$-0.569632\pi$
$643$	19.2502	−	19.2502i	0.759152	−	0.759152i	0.976168	+	0.217016i	$0.0696324\pi$
$644$		−	0.461623i		−	0.0181905i
$645$	−0.881562			−0.0347115
$646$	1.21363	−	2.90439i	0.0477496	−	0.114272i
$647$	−10.9154			−0.429128			−0.214564	−	0.976710i	$-0.568833\pi$
$647$	−10.9154			−0.429128			−0.214564	+	0.976710i	$0.568833\pi$
$648$		−	2.49165i		−	0.0978812i
$649$	14.0387	−	14.0387i	0.551067	−	0.551067i
$650$	−2.13490			−0.0837378
$651$	−14.5005	+	14.5005i	−0.568320	+	0.568320i
$652$	−16.0795	−	16.0795i	−0.629721	−	0.629721i
$653$	23.6066	+	23.6066i	0.923797	+	0.923797i	0.997295	−	0.0734988i	$-0.0234165\pi$
$653$	23.6066	+	23.6066i	0.923797	+	0.923797i	−0.0734988	+	0.997295i	$0.523417\pi$
$654$		−	1.38429i		−	0.0541301i
$655$		−	12.1010i		−	0.472825i
$656$	0.116002	+	0.116002i	0.00452913	+	0.00452913i
$657$	−17.1763	−	17.1763i	−0.670113	−	0.670113i
$658$	6.07636	−	6.07636i	0.236881	−	0.236881i
$659$	−10.7394			−0.418349			−0.209175	−	0.977878i	$-0.567078\pi$
$659$	−10.7394			−0.418349			−0.209175	+	0.977878i	$0.567078\pi$
$660$	1.90596	−	1.90596i	0.0741893	−	0.0741893i
$661$		−	47.6111i		−	1.85186i	−0.377697	−	0.925929i	$-0.623284\pi$
$661$		−	47.6111i		−	1.85186i	0.377697	−	0.925929i	$-0.376716\pi$
$662$	7.24618			0.281631
$663$	0.956719	+	2.33019i	0.0371559	+	0.0904970i
$664$	45.3602			1.76032
$665$		−	3.19504i		−	0.123898i
$666$	−2.11321	+	2.11321i	−0.0818852	+	0.0818852i
$667$	0.435378			0.0168579
$668$	20.4893	−	20.4893i	0.792756	−	0.792756i
$669$	4.50740	+	4.50740i	0.174266	+	0.174266i
$670$	2.76728	+	2.76728i	0.106910	+	0.106910i
$671$			18.6479i			0.719896i
$672$		−	23.0995i		−	0.891081i
$673$	−2.78531	−	2.78531i	−0.107366	−	0.107366i	0.651383	−	0.758749i	$-0.274189\pi$
$673$	−2.78531	−	2.78531i	−0.107366	−	0.107366i	−0.758749	+	0.651383i	$0.774189\pi$
$674$	−6.48923	−	6.48923i	−0.249956	−	0.249956i
$675$	15.0263	−	15.0263i	0.578364	−	0.578364i
$676$	−16.5397			−0.636141
$677$	7.80284	−	7.80284i	0.299888	−	0.299888i	−0.541082	−	0.840970i	$-0.681985\pi$
$677$	7.80284	−	7.80284i	0.299888	−	0.299888i	0.840970	+	0.541082i	$0.181985\pi$
$678$		−	2.01116i		−	0.0772383i
$679$	48.1209			1.84671
$680$	9.18573	−	3.77144i	0.352257	−	0.144628i
$681$	24.2670			0.929915
$682$		−	9.95308i		−	0.381123i
$683$	7.95577	−	7.95577i	0.304419	−	0.304419i	−0.538321	−	0.842740i	$-0.680941\pi$
$683$	7.95577	−	7.95577i	0.304419	−	0.304419i	0.842740	+	0.538321i	$0.180941\pi$
$684$	2.38956			0.0913671
$685$	3.83274	−	3.83274i	0.146441	−	0.146441i
$686$	−4.14020	−	4.14020i	−0.158074	−	0.158074i
$687$	−16.6903	−	16.6903i	−0.636776	−	0.636776i
$688$			0.333214i			0.0127037i
$689$		−	2.73558i		−	0.104217i
$690$	0.0459845	+	0.0459845i	0.00175060	+	0.00175060i
$691$	11.1917	+	11.1917i	0.425751	+	0.425751i	0.887178	−	0.461427i	$-0.152662\pi$
$691$	11.1917	+	11.1917i	0.425751	+	0.425751i	−0.461427	+	0.887178i	$0.652662\pi$
$692$	2.77625	−	2.77625i	0.105537	−	0.105537i
$693$	18.4238			0.699863
$694$	3.49987	−	3.49987i	0.132853	−	0.132853i
$695$		−	9.97959i		−	0.378547i
$696$	13.5795			0.514729
$697$	1.87782	−	0.770989i	0.0711276	−	0.0292033i
$698$	−22.2346			−0.841593
$699$			7.65708i			0.289617i
$700$	−15.5663	+	15.5663i	−0.588350	+	0.588350i
$701$	17.8393			0.673783			0.336891	−	0.941544i	$-0.390624\pi$
$701$	17.8393			0.673783			0.336891	+	0.941544i	$0.390624\pi$
$702$	1.79019	−	1.79019i	0.0675665	−	0.0675665i
$703$	−1.17592	−	1.17592i	−0.0443508	−	0.0443508i
$704$	6.82728	+	6.82728i	0.257313	+	0.257313i
$705$		−	2.29520i		−	0.0864421i
$706$		−	5.30147i		−	0.199524i
$707$	−35.0490	−	35.0490i	−1.31815	−	1.31815i
$708$	−7.92469	−	7.92469i	−0.297828	−	0.297828i
$709$	−14.2700	+	14.2700i	−0.535922	+	0.535922i	−0.922329	−	0.386407i	$-0.873716\pi$
$709$	−14.2700	+	14.2700i	−0.535922	+	0.535922i	0.386407	+	0.922329i	$0.373716\pi$
$710$	1.45777			0.0547093
$711$	−15.8246	+	15.8246i	−0.593469	+	0.593469i
$712$		−	37.0978i		−	1.39030i
$713$	−0.455279			−0.0170503
$714$	−12.6407	−	5.28206i	−0.473068	−	0.197676i
$715$	−1.24095			−0.0464087
$716$		−	14.8573i		−	0.555244i
$717$	7.40698	−	7.40698i	0.276619	−	0.276619i
$718$	−2.66115			−0.0993132
$719$	−26.0122	+	26.0122i	−0.970091	+	0.970091i	−0.999566	−	0.0294749i	$-0.990616\pi$
$719$	−26.0122	+	26.0122i	−0.970091	+	0.970091i	0.0294749	+	0.999566i	$0.490616\pi$
$720$	0.409880	+	0.409880i	0.0152753	+	0.0152753i
$721$	31.4716	+	31.4716i	1.17207	+	1.17207i
$722$			15.0884i			0.561531i
$723$			10.0133i			0.372398i
$724$	6.10684	+	6.10684i	0.226959	+	0.226959i
$725$	−14.6813	−	14.6813i	−0.545250	−	0.545250i
$726$	−3.28155	+	3.28155i	−0.121790	+	0.121790i
$727$	−35.3537			−1.31120			−0.655599	−	0.755109i	$-0.727584\pi$
$727$	−35.3537			−1.31120			−0.655599	+	0.755109i	$0.727584\pi$
$728$	−4.68721	+	4.68721i	−0.173719	+	0.173719i
$729$			13.3612i			0.494858i
$730$	−8.89854			−0.329350
$731$	3.80433	+	1.58968i	0.140708	+	0.0587964i
$732$	10.5266			0.389073
$733$			14.8453i			0.548325i	0.961683	+	0.274163i	$0.0884007\pi$
$733$			14.8453i			0.548325i	−0.961683	+	0.274163i	$0.911599\pi$
$734$	12.1658	−	12.1658i	0.449049	−	0.449049i
$735$	−7.73479			−0.285302
$736$	0.362632	−	0.362632i	0.0133668	−	0.0133668i
$737$	−8.87961	−	8.87961i	−0.327085	−	0.327085i
$738$	−0.574727	−	0.574727i	−0.0211560	−	0.0211560i
$739$		−	43.4289i		−	1.59756i	−0.601624	−	0.798779i	$-0.705480\pi$
$739$		−	43.4289i		−	1.59756i	0.601624	−	0.798779i	$-0.294520\pi$
$740$		−	2.07564i		−	0.0763021i
$741$	0.396858	+	0.396858i	0.0145789	+	0.0145789i
$742$	10.5205	+	10.5205i	0.386219	+	0.386219i
$743$	−3.75127	+	3.75127i	−0.137621	+	0.137621i	−0.772561	−	0.634940i	$-0.781025\pi$
$743$	−3.75127	+	3.75127i	−0.137621	+	0.137621i	0.634940	+	0.772561i	$0.281025\pi$
$744$	−14.2002			−0.520605
$745$	12.9732	−	12.9732i	0.475300	−	0.475300i
$746$		−	11.0248i		−	0.403645i
$747$	32.7647			1.19880
$748$	−11.6620	+	4.78813i	−0.426404	+	0.175071i
$749$	50.6937			1.85231
$750$		−	6.76432i		−	0.246998i
$751$	−29.8902	+	29.8902i	−1.09071	+	1.09071i	−0.0952553	+	0.995453i	$0.530367\pi$
$751$	−29.8902	+	29.8902i	−1.09071	+	1.09071i	−0.995453	+	0.0952553i	$0.969633\pi$
$752$	−0.867543			−0.0316360
$753$	−2.55665	+	2.55665i	−0.0931694	+	0.0931694i
$754$	−1.74909	−	1.74909i	−0.0636980	−	0.0636980i
$755$	9.85337	+	9.85337i	0.358601	+	0.358601i
$756$		−	26.1058i		−	0.949458i
$757$		−	15.2572i		−	0.554531i	−0.960793	−	0.277266i	$-0.910572\pi$
$757$		−	15.2572i		−	0.554531i	0.960793	−	0.277266i	$-0.0894282\pi$
$758$	−0.137863	−	0.137863i	−0.00500739	−	0.00500739i
$759$	−0.147554	−	0.147554i	−0.00535588	−	0.00535588i
$760$	1.56444	−	1.56444i	0.0567480	−	0.0567480i
$761$	6.09480			0.220936			0.110468	−	0.993880i	$-0.464765\pi$
$761$	6.09480			0.220936			0.110468	+	0.993880i	$0.464765\pi$
$762$	−0.603415	+	0.603415i	−0.0218594	+	0.0218594i
$763$			6.57166i			0.237910i
$764$	−19.4124			−0.702315
$765$	6.63505	−	2.72420i	0.239891	−	0.0984935i
$766$	2.94484			0.106402
$767$			5.15967i			0.186305i
$768$	10.6894	−	10.6894i	0.385720	−	0.385720i
$769$	−19.9462			−0.719277			−0.359638	−	0.933092i	$-0.617100\pi$
$769$	−19.9462			−0.719277			−0.359638	+	0.933092i	$0.617100\pi$
$770$	4.77241	−	4.77241i	0.171986	−	0.171986i
$771$	−15.9911	−	15.9911i	−0.575905	−	0.575905i
$772$	−20.1125	−	20.1125i	−0.723864	−	0.723864i
$773$			10.2755i			0.369584i	0.982778	+	0.184792i	$0.0591611\pi$
$773$			10.2755i			0.369584i	−0.982778	+	0.184792i	$0.940839\pi$
$774$		−	1.65089i		−	0.0593401i
$775$	15.3524	+	15.3524i	0.551474	+	0.551474i
$776$	23.5622	+	23.5622i	0.845833	+	0.845833i
$777$	−5.11796	+	5.11796i	−0.183606	+	0.183606i
$778$	−4.10133			−0.147040
$779$	0.319815	−	0.319815i	0.0114586	−	0.0114586i
$780$			0.700500i			0.0250819i
$781$	−4.67768			−0.167381
$782$	−0.115522	−	0.281365i	−0.00413105	−	0.0100616i
$783$	24.6216			0.879904
$784$			2.92361i			0.104415i
$785$	−1.01156	+	1.01156i	−0.0361041	+	0.0361041i
$786$	−11.5610			−0.412367
$787$	4.37793	−	4.37793i	0.156056	−	0.156056i	−0.624760	−	0.780817i	$-0.714803\pi$
$787$	4.37793	−	4.37793i	0.156056	−	0.156056i	0.780817	+	0.624760i	$0.214803\pi$
$788$	−7.41279	−	7.41279i	−0.264070	−	0.264070i
$789$	3.69307	+	3.69307i	0.131477	+	0.131477i
$790$			8.19824i			0.291680i
$791$			9.54760i			0.339474i
$792$	9.02114	+	9.02114i	0.320552	+	0.320552i
$793$	−3.42686	−	3.42686i	−0.121691	−	0.121691i
$794$	−7.05264	+	7.05264i	−0.250289	+	0.250289i
$795$	3.97385			0.140938
$796$	9.73824	−	9.73824i	0.345163	−	0.345163i
$797$		−	1.47187i		−	0.0521365i	−0.999660	−	0.0260682i	$-0.991701\pi$
$797$		−	1.47187i		−	0.0521365i	0.999660	−	0.0260682i	$-0.00829872\pi$
$798$	−3.05246			−0.108056
$799$	−4.13882	+	9.90479i	−0.146421	+	0.350406i
$800$	−24.4565			−0.864668
$801$		−	26.7966i		−	0.946811i
$802$	−16.1658	+	16.1658i	−0.570833	+	0.570833i
$803$	28.5535			1.00763
$804$	−5.01244	+	5.01244i	−0.176775	+	0.176775i
$805$	−0.218302	−	0.218302i	−0.00769414	−	0.00769414i
$806$	1.82904	+	1.82904i	0.0644251	+	0.0644251i
$807$			23.2253i			0.817570i
$808$		−	34.3232i		−	1.20749i
$809$	8.03554	+	8.03554i	0.282515	+	0.282515i	0.834111	−	0.551596i	$-0.185981\pi$
$809$	8.03554	+	8.03554i	0.282515	+	0.282515i	−0.551596	+	0.834111i	$0.685981\pi$
$810$	−0.466204	−	0.466204i	−0.0163807	−	0.0163807i
$811$	−3.66798	+	3.66798i	−0.128800	+	0.128800i	−0.768568	−	0.639768i	$-0.779030\pi$
$811$	−3.66798	+	3.66798i	−0.128800	+	0.128800i	0.639768	+	0.768568i	$0.279030\pi$
$812$	−25.5064			−0.895097
$813$	−12.1234	+	12.1234i	−0.425185	+	0.425185i
$814$		−	3.51294i		−	0.123128i
$815$	−15.2080			−0.532714
$816$	0.525311	+	1.27945i	0.0183896	+	0.0447897i
$817$	0.918662			0.0321399
$818$			21.0923i			0.737476i
$819$	−3.38567	+	3.38567i	−0.118305	+	0.118305i
$820$	0.564510			0.0197136
$821$	−7.09843	+	7.09843i	−0.247737	+	0.247737i	−0.820041	−	0.572304i	$-0.806050\pi$
$821$	−7.09843	+	7.09843i	−0.247737	+	0.247737i	0.572304	+	0.820041i	$0.306050\pi$
$822$	−3.66170	−	3.66170i	−0.127717	−	0.127717i
$823$	33.4375	+	33.4375i	1.16556	+	1.16556i	0.983240	+	0.182316i	$0.0583595\pi$
$823$	33.4375	+	33.4375i	1.16556	+	1.16556i	0.182316	+	0.983240i	$0.441640\pi$
$824$			30.8199i			1.07366i
$825$			9.95129i			0.346460i
$826$	−19.8430	−	19.8430i	−0.690426	−	0.690426i
$827$	−1.21785	−	1.21785i	−0.0423487	−	0.0423487i	0.685615	−	0.727964i	$-0.259533\pi$
$827$	−1.21785	−	1.21785i	−0.0423487	−	0.0423487i	−0.727964	+	0.685615i	$0.759533\pi$
$828$	0.163267	−	0.163267i	0.00567394	−	0.00567394i
$829$	−10.5823			−0.367537			−0.183768	−	0.982970i	$-0.558830\pi$
$829$	−10.5823			−0.367537			−0.183768	+	0.982970i	$0.558830\pi$
$830$	8.48718	−	8.48718i	0.294594	−	0.294594i
$831$		−	18.6610i		−	0.647341i
$832$	−2.50924			−0.0869924
$833$	33.3791	+	13.9478i	1.15652	+	0.483262i
$834$	−9.53424			−0.330144
$835$		−	19.3789i		−	0.670634i
$836$	−1.98617	+	1.98617i	−0.0686931	+	0.0686931i
$837$	−25.7471			−0.889948
$838$	−17.1224	+	17.1224i	−0.591484	+	0.591484i
$839$	−5.23284	−	5.23284i	−0.180658	−	0.180658i	0.610985	−	0.791642i	$-0.290774\pi$
$839$	−5.23284	−	5.23284i	−0.180658	−	0.180658i	−0.791642	+	0.610985i	$0.790774\pi$
$840$	−6.80887	−	6.80887i	−0.234928	−	0.234928i
$841$			4.94377i			0.170475i
$842$		−	27.7424i		−	0.956066i
$843$	−4.89799	−	4.89799i	−0.168696	−	0.168696i
$844$	3.63987	+	3.63987i	0.125289	+	0.125289i
$845$	−7.82163	+	7.82163i	−0.269072	+	0.269072i
$846$	4.29820			0.147775
$847$	15.5785	−	15.5785i	0.535284	−	0.535284i
$848$		−	1.50204i		−	0.0515803i
$849$	8.17038			0.280407
$850$	−5.59237	+	13.3833i	−0.191817	+	0.459045i
$851$	−0.160691			−0.00550841
$852$			2.64050i			0.0904620i
$853$	1.24518	−	1.24518i	0.0426340	−	0.0426340i	−0.685468	−	0.728102i	$-0.740403\pi$
$853$	1.24518	−	1.24518i	0.0426340	−	0.0426340i	0.728102	+	0.685468i	$0.240403\pi$
$854$	26.3579			0.901950
$855$	1.13003	−	1.13003i	0.0386461	−	0.0386461i
$856$	24.8219	+	24.8219i	0.848397	+	0.848397i
$857$	−34.2703	−	34.2703i	−1.17065	−	1.17065i	−0.982054	−	0.188598i	$-0.939606\pi$
$857$	−34.2703	−	34.2703i	−1.17065	−	1.17065i	−0.188598	−	0.982054i	$-0.560394\pi$
$858$			1.18557i			0.0404746i
$859$			38.6951i			1.32026i	0.751151	+	0.660131i	$0.229499\pi$
$859$			38.6951i			1.32026i	−0.751151	+	0.660131i	$0.770501\pi$
$860$	0.810773	+	0.810773i	0.0276471	+	0.0276471i
$861$	−1.39193	−	1.39193i	−0.0474367	−	0.0474367i
$862$	−8.03303	+	8.03303i	−0.273606	+	0.273606i
$863$	40.7706			1.38785			0.693924	−	0.720049i	$-0.255880\pi$
$863$	40.7706			1.38785			0.693924	+	0.720049i	$0.255880\pi$
$864$	20.5076	−	20.5076i	0.697684	−	0.697684i
$865$		−	2.62579i		−	0.0892796i
$866$	12.3880			0.420963
$867$	17.1137	+	0.106405i	0.581211	+	0.00361371i
$868$	26.6723			0.905316
$869$		−	26.3064i		−	0.892383i
$870$	2.54081	−	2.54081i	0.0861416	−	0.0861416i
$871$	3.26354			0.110581
$872$	−3.21778	+	3.21778i	−0.108968	+	0.108968i
$873$	17.0195	+	17.0195i	0.576023	+	0.576023i
$874$	−0.0479197	−	0.0479197i	−0.00162091	−	0.00162091i
$875$			32.1123i			1.08559i
$876$		−	16.1181i		−	0.544581i
$877$	−36.3420	−	36.3420i	−1.22718	−	1.22718i	−0.965025	−	0.262158i	$-0.915566\pi$
$877$	−36.3420	−	36.3420i	−1.22718	−	1.22718i	−0.262158	−	0.965025i	$-0.584434\pi$
$878$	13.1987	+	13.1987i	0.445434	+	0.445434i
$879$	1.13067	−	1.13067i	0.0381366	−	0.0381366i
$880$	−0.681373			−0.0229691
$881$	−33.7328	+	33.7328i	−1.13649	+	1.13649i	−0.147410	+	0.989076i	$0.547094\pi$
$881$	−33.7328	+	33.7328i	−1.13649	+	1.13649i	−0.989076	+	0.147410i	$0.952906\pi$
$882$		−	14.4849i		−	0.487731i
$883$	−47.1454			−1.58657			−0.793285	−	0.608850i	$-0.791631\pi$
$883$	−47.1454			−1.58657			−0.793285	+	0.608850i	$0.791631\pi$
$884$	1.26318	−	3.02297i	0.0424853	−	0.101673i
$885$	−7.49520			−0.251948
$886$		−	25.3642i		−	0.852126i
$887$	17.1532	−	17.1532i	0.575949	−	0.575949i	−0.357836	−	0.933785i	$-0.616485\pi$
$887$	17.1532	−	17.1532i	0.575949	−	0.575949i	0.933785	+	0.357836i	$0.116485\pi$
$888$	−5.01197			−0.168191
$889$	2.86459	−	2.86459i	0.0960754	−	0.0960754i
$890$	−6.94125	−	6.94125i	−0.232671	−	0.232671i
$891$	1.49595	+	1.49595i	0.0501161	+	0.0501161i
$892$		−	8.29092i		−	0.277600i
$893$			2.39179i			0.0800382i
$894$	−12.3942	−	12.3942i	−0.414525	−	0.414525i
$895$	−7.02605	−	7.02605i	−0.234855	−	0.234855i
$896$	−22.7999	+	22.7999i	−0.761693	+	0.761693i
$897$	0.0542309			0.00181072
$898$	3.65646	−	3.65646i	0.122018	−	0.122018i
$899$			25.1559i			0.838995i
$900$	−11.0110			−0.367034
$901$	−17.1489	−	7.16585i	−0.571313	−	0.238729i
$902$	0.955411			0.0318117
$903$		−	3.99828i		−	0.133054i
$904$	−4.67494	+	4.67494i	−0.155486	+	0.155486i
$905$	5.77586			0.191996
$906$	9.41366	−	9.41366i	0.312748	−	0.312748i
$907$	−1.66585	−	1.66585i	−0.0553137	−	0.0553137i	0.678909	−	0.734223i	$-0.262453\pi$
$907$	−1.66585	−	1.66585i	−0.0553137	−	0.0553137i	−0.734223	+	0.678909i	$0.762453\pi$
$908$	−22.3184	−	22.3184i	−0.740662	−	0.740662i
$909$		−	24.7924i		−	0.822312i
$910$			1.75401i			0.0581450i
$911$	2.76265	+	2.76265i	0.0915306	+	0.0915306i	0.751390	−	0.659859i	$-0.229384\pi$
$911$	2.76265	+	2.76265i	0.0915306	+	0.0915306i	−0.659859	+	0.751390i	$0.729384\pi$
$912$	0.217905	+	0.217905i	0.00721555	+	0.00721555i
$913$	−27.2335	+	27.2335i	−0.901298	+	0.901298i
$914$	−24.0445			−0.795321
$915$	4.97803	−	4.97803i	0.164569	−	0.164569i
$916$			30.7002i			1.01436i
$917$	54.8835			1.81241
$918$	−6.53301	−	15.9118i	−0.215622	−	0.525168i
$919$	23.2636			0.767395			0.383697	−	0.923459i	$-0.374651\pi$
$919$	23.2636			0.767395			0.383697	+	0.923459i	$0.374651\pi$
$920$		−	0.213781i		−	0.00704816i
$921$	5.85606	−	5.85606i	0.192964	−	0.192964i
$922$	−4.91179			−0.161761
$923$	0.859599	−	0.859599i	0.0282940	−	0.0282940i
$924$	8.64437	+	8.64437i	0.284379	+	0.284379i
$925$	5.41862	+	5.41862i	0.178163	+	0.178163i
$926$			16.9349i			0.556515i
$927$			22.2619i			0.731176i
$928$	−20.0368	−	20.0368i	−0.657739	−	0.657739i
$929$	−31.9330	−	31.9330i	−1.04769	−	1.04769i	−0.998804	−	0.0488836i	$-0.984434\pi$
$929$	−31.9330	−	31.9330i	−1.04769	−	1.04769i	−0.0488836	−	0.998804i	$-0.515566\pi$
$930$	−2.65695	+	2.65695i	−0.0871249	+	0.0871249i
$931$	8.06031			0.264166
$932$	7.04222	−	7.04222i	0.230676	−	0.230676i
$933$		−	25.1861i		−	0.824555i
$934$	−33.9528			−1.11097
$935$	−3.25065	+	7.77928i	−0.106308	+	0.254410i
$936$	−3.31556			−0.108372
$937$			9.99598i			0.326555i	0.986580	+	0.163277i	$0.0522065\pi$
$937$			9.99598i			0.326555i	−0.986580	+	0.163277i	$0.947793\pi$
$938$	−12.5509	+	12.5509i	−0.409801	+	0.409801i
$939$	−11.7332			−0.382897
$940$	−2.11089	+	2.11089i	−0.0688498	+	0.0688498i
$941$	−16.7584	−	16.7584i	−0.546307	−	0.546307i	0.379063	−	0.925371i	$-0.376246\pi$
$941$	−16.7584	−	16.7584i	−0.546307	−	0.546307i	−0.925371	+	0.379063i	$0.876246\pi$
$942$	0.966418	+	0.966418i	0.0314876	+	0.0314876i
$943$		−	0.0437029i		−	0.00142316i
$944$			2.83305i			0.0922079i
$945$	−12.3455	−	12.3455i	−0.401598	−	0.401598i
$946$	1.37220	+	1.37220i	0.0446141	+	0.0446141i
$947$	7.61582	−	7.61582i	0.247481	−	0.247481i	−0.572455	−	0.819936i	$-0.694009\pi$
$947$	7.61582	−	7.61582i	0.247481	−	0.247481i	0.819936	+	0.572455i	$0.194009\pi$
$948$	−14.8497			−0.482295
$949$	−5.24716	+	5.24716i	−0.170330	+	0.170330i
$950$			3.23178i			0.104853i
$951$	27.9265			0.905578
$952$	17.1052	+	41.6614i	0.554382	+	1.35025i
$953$	14.3482			0.464782			0.232391	−	0.972622i	$-0.425345\pi$
$953$	14.3482			0.464782			0.232391	+	0.972622i	$0.425345\pi$
$954$			7.44179i			0.240937i
$955$	−9.18015	+	9.18015i	−0.297063	+	0.297063i
$956$	−13.6244			−0.440645
$957$	−8.15291	+	8.15291i	−0.263546	+	0.263546i
$958$	−12.0541	−	12.0541i	−0.389450	−	0.389450i
$959$	17.3832	+	17.3832i	0.561333	+	0.561333i
$960$		−	3.64505i		−	0.117644i
$961$			4.69426i			0.151428i
$962$	0.645559	+	0.645559i	0.0208137	+	0.0208137i
$963$	17.9294	+	17.9294i	0.577768	+	0.577768i
$964$	9.20921	−	9.20921i	0.296609	−	0.296609i
$965$	−19.0225			−0.612354
$966$	−0.208560	+	0.208560i	−0.00671032	+	0.00671032i
$967$		−	37.0103i		−	1.19017i	−0.803663	−	0.595085i	$-0.797118\pi$
$967$		−	37.0103i		−	1.19017i	0.803663	−	0.595085i	$-0.202882\pi$
$968$	15.2559			0.490343
$969$	3.52740	−	1.44827i	0.113316	−	0.0465250i
$970$	8.81728			0.283106
$971$		−	7.51559i		−	0.241187i	−0.992702	−	0.120593i	$-0.961520\pi$
$971$		−	7.51559i		−	0.241187i	0.992702	−	0.120593i	$-0.0384797\pi$
$972$	14.7880	−	14.7880i	0.474324	−	0.474324i
$973$	45.2619			1.45103
$974$	−6.12164	+	6.12164i	−0.196150	+	0.196150i
$975$	−1.82871	−	1.82871i	−0.0585656	−	0.0585656i
$976$	−1.88160	−	1.88160i	−0.0602287	−	0.0602287i
$977$			45.6684i			1.46106i	0.682880	+	0.730531i	$0.260727\pi$
$977$			45.6684i			1.46106i	−0.682880	+	0.730531i	$0.739273\pi$
$978$			14.5294i			0.464598i
$979$	22.2729	+	22.2729i	0.711847	+	0.711847i
$980$	7.11369	+	7.11369i	0.227239	+	0.227239i
$981$	−2.32427	+	2.32427i	−0.0742084	+	0.0742084i
$982$	−0.828298			−0.0264321
$983$	−5.54585	+	5.54585i	−0.176885	+	0.176885i	−0.789997	−	0.613111i	$-0.789918\pi$
$983$	−5.54585	+	5.54585i	−0.176885	+	0.176885i	0.613111	+	0.789997i	$0.289918\pi$
$984$		−	1.36310i		−	0.0434540i
$985$	−7.01104			−0.223390
$986$	−15.5465	+	6.38300i	−0.495100	+	0.203276i
$987$	10.4098			0.331346
$988$		−	0.729980i		−	0.0232238i
$989$	0.0627679	−	0.0627679i	0.00199590	−	0.00199590i
$990$	3.37583			0.107291
$991$	−27.7435	+	27.7435i	−0.881301	+	0.881301i	−0.993667	−	0.112366i	$-0.964157\pi$
$991$	−27.7435	+	27.7435i	−0.881301	+	0.881301i	0.112366	+	0.993667i	$0.464157\pi$
$992$	20.9526	+	20.9526i	0.665247	+	0.665247i
$993$	6.20692	+	6.20692i	0.196971	+	0.196971i
$994$			6.61166i			0.209709i
$995$		−	9.21046i		−	0.291991i
$996$	15.3730	+	15.3730i	0.487113	+	0.487113i
$997$	−26.1561	−	26.1561i	−0.828373	−	0.828373i	0.158919	−	0.987292i	$-0.449199\pi$
$997$	−26.1561	−	26.1561i	−0.828373	−	0.828373i	−0.987292	+	0.158919i	$0.949199\pi$
$998$	−9.60398	+	9.60398i	−0.304009	+	0.304009i
$999$	−9.08742			−0.287513

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.f.c.259.19	✓	56
17.13	even	4	inner	731.2.f.c.302.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.f.c.259.19	✓	56	1.1	even	1	trivial
731.2.f.c.302.10	yes	56	17.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.831038i q^{2} +(-0.711849 + 0.711849i) q^{3} +1.30938 q^{4} +(0.619206 - 0.619206i) q^{5} +(-0.591574 - 0.591574i) q^{6} +(2.80838 + 2.80838i) q^{7} +2.75022i q^{8} +1.98654i q^{9} +O(q^{10})\)	\(q+0.831038i q^{2} +(-0.711849 + 0.711849i) q^{3} +1.30938 q^{4} +(0.619206 - 0.619206i) q^{5} +(-0.591574 - 0.591574i) q^{6} +(2.80838 + 2.80838i) q^{7} +2.75022i q^{8} +1.98654i q^{9} +(0.514584 + 0.514584i) q^{10} +(-1.65119 - 1.65119i) q^{11} +(-0.932077 + 0.932077i) q^{12} +0.606864 q^{13} +(-2.33387 + 2.33387i) q^{14} +0.881562i q^{15} +0.333214 q^{16} +(1.58968 - 3.80433i) q^{17} -1.65089 q^{18} -0.918662i q^{19} +(0.810773 - 0.810773i) q^{20} -3.99828 q^{21} +(1.37220 - 1.37220i) q^{22} +(-0.0627679 - 0.0627679i) q^{23} +(-1.95774 - 1.95774i) q^{24} +4.23317i q^{25} +0.504327i q^{26} +(-3.54966 - 3.54966i) q^{27} +(3.67722 + 3.67722i) q^{28} +(-3.46816 + 3.46816i) q^{29} -0.732611 q^{30} +(3.62669 - 3.62669i) q^{31} +5.77735i q^{32} +2.35079 q^{33} +(3.16154 + 1.32108i) q^{34} +3.47793 q^{35} +2.60113i q^{36} +(1.28004 - 1.28004i) q^{37} +0.763443 q^{38} +(-0.431995 + 0.431995i) q^{39} +(1.70295 + 1.70295i) q^{40} +(0.348131 + 0.348131i) q^{41} -3.32272i q^{42} +1.00000i q^{43} +(-2.16202 - 2.16202i) q^{44} +(1.23008 + 1.23008i) q^{45} +(0.0521625 - 0.0521625i) q^{46} -2.60356 q^{47} +(-0.237198 + 0.237198i) q^{48} +8.77397i q^{49} -3.51793 q^{50} +(1.57650 + 3.83972i) q^{51} +0.794613 q^{52} -4.50774i q^{53} +(2.94991 - 2.94991i) q^{54} -2.04485 q^{55} +(-7.72365 + 7.72365i) q^{56} +(0.653948 + 0.653948i) q^{57} +(-2.88217 - 2.88217i) q^{58} +8.50219i q^{59} +1.15429i q^{60} +(-5.64683 - 5.64683i) q^{61} +(3.01392 + 3.01392i) q^{62} +(-5.57896 + 5.57896i) q^{63} -4.13477 q^{64} +(0.375774 - 0.375774i) q^{65} +1.95360i q^{66} +5.37771 q^{67} +(2.08149 - 4.98129i) q^{68} +0.0893625 q^{69} +2.89029i q^{70} +(1.41646 - 1.41646i) q^{71} -5.46343 q^{72} +(-8.64635 + 8.64635i) q^{73} +(1.06376 + 1.06376i) q^{74} +(-3.01338 - 3.01338i) q^{75} -1.20287i q^{76} -9.27431i q^{77} +(-0.359005 - 0.359005i) q^{78} +(7.96590 + 7.96590i) q^{79} +(0.206328 - 0.206328i) q^{80} -0.905982 q^{81} +(-0.289310 + 0.289310i) q^{82} -16.4933i q^{83} -5.23525 q^{84} +(-1.37132 - 3.34000i) q^{85} -0.831038 q^{86} -4.93761i q^{87} +(4.54112 - 4.54112i) q^{88} -13.4891 q^{89} +(-1.02224 + 1.02224i) q^{90} +(1.70430 + 1.70430i) q^{91} +(-0.0821867 - 0.0821867i) q^{92} +5.16331i q^{93} -2.16366i q^{94} +(-0.568841 - 0.568841i) q^{95} +(-4.11260 - 4.11260i) q^{96} +(8.56739 - 8.56739i) q^{97} -7.29150 q^{98} +(3.28015 - 3.28015i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7	\( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) \) 56 * q - 4 * q^3 - 60 * q^4 - 2 * q^5 + 8 * q^6 + 4 * q^7 + 4 * q^10 - 6 * q^11 - 14 * q^12 + 16 * q^13 + 6 * q^14 + 44 * q^16 + 8 * q^17 - 16 * q^18 + 12 * q^20 + 28 * q^21 + 14 * q^22 + 6 * q^23 + 62 * q^24 - 4 * q^27 + 34 * q^28 - 12 * q^29 - 96 * q^30 + 14 * q^31 - 44 * q^33 + 6 * q^34 - 32 * q^35 + 8 * q^37 + 72 * q^38 - 32 * q^39 - 84 * q^40 + 24 * q^41 + 4 * q^44 + 48 * q^45 - 4 * q^46 - 8 * q^47 + 38 * q^48 - 64 * q^50 + 28 * q^51 - 48 * q^52 + 34 * q^54 + 56 * q^55 - 26 * q^56 - 102 * q^57 + 76 * q^58 - 40 * q^61 + 34 * q^62 + 4 * q^63 - 204 * q^64 + 18 * q^65 - 20 * q^67 + 30 * q^68 - 16 * q^69 - 26 * q^71 + 144 * q^72 + 8 * q^73 - 80 * q^74 + 142 * q^75 - 32 * q^78 - 22 * q^79 - 32 * q^80 - 32 * q^81 + 100 * q^82 - 20 * q^84 - 2 * q^85 + 12 * q^86 + 34 * q^88 + 68 * q^89 - 10 * q^90 - 28 * q^91 + 68 * q^92 - 62 * q^95 + 62 * q^96 - 2 * q^97 - 32 * q^98 + 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more