LMFDB - Embedded newform 403.2.k.e.157.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.3
Character	$\chi$	$=$	403.157
Dual form			403.2.k.e.326.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.84627 - 1.34139i) q^{2} +(1.79347 - 1.30303i) q^{3} +(0.991339 + 3.05103i) q^{4} +4.23714 q^{5} -5.05910 q^{6} +(-0.0173329 - 0.0533453i) q^{7} +(0.851924 - 2.62195i) q^{8} +(0.591588 - 1.82072i) q^{9} +O(q^{10})$	\(q+(-1.84627 - 1.34139i) q^{2} +(1.79347 - 1.30303i) q^{3} +(0.991339 + 3.05103i) q^{4} +4.23714 q^{5} -5.05910 q^{6} +(-0.0173329 - 0.0533453i) q^{7} +(0.851924 - 2.62195i) q^{8} +(0.591588 - 1.82072i) q^{9} +(-7.82289 - 5.68366i) q^{10} +(0.271289 + 0.834943i) q^{11} +(5.75352 + 4.18018i) q^{12} +(-0.809017 + 0.587785i) q^{13} +(-0.0395557 + 0.121740i) q^{14} +(7.59917 - 5.52112i) q^{15} +(0.100772 - 0.0732150i) q^{16} +(0.353144 - 1.08687i) q^{17} +(-3.53453 + 2.56799i) q^{18} +(-0.556943 - 0.404643i) q^{19} +(4.20044 + 12.9276i) q^{20} +(-0.100597 - 0.0730877i) q^{21} +(0.619113 - 1.90543i) q^{22} +(-0.879648 + 2.70728i) q^{23} +(-1.88859 - 5.81247i) q^{24} +12.9533 q^{25} +2.28211 q^{26} +(0.743670 + 2.28878i) q^{27} +(0.145575 - 0.105766i) q^{28} +(2.51927 + 1.83036i) q^{29} -21.4361 q^{30} +(0.0713465 - 5.56731i) q^{31} -5.79803 q^{32} +(1.57451 + 1.14395i) q^{33} +(-2.10991 + 1.53294i) q^{34} +(-0.0734420 - 0.226031i) q^{35} +6.14153 q^{36} -6.60106 q^{37} +(0.485482 + 1.49416i) q^{38} +(-0.685044 + 2.10835i) q^{39} +(3.60972 - 11.1096i) q^{40} +(-8.33202 - 6.05357i) q^{41} +(0.0876890 + 0.269879i) q^{42} +(-4.63127 - 3.36482i) q^{43} +(-2.27849 + 1.65542i) q^{44} +(2.50664 - 7.71464i) q^{45} +(5.25559 - 3.81841i) q^{46} +(-5.60130 + 4.06958i) q^{47} +(0.0853297 - 0.262618i) q^{48} +(5.66057 - 4.11265i) q^{49} +(-23.9153 - 17.3755i) q^{50} +(-0.782867 - 2.40942i) q^{51} +(-2.59536 - 1.88564i) q^{52} +(-0.871224 + 2.68135i) q^{53} +(1.69714 - 5.22326i) q^{54} +(1.14949 + 3.53777i) q^{55} -0.154635 q^{56} -1.52612 q^{57} +(-2.19602 - 6.75867i) q^{58} +(-9.59199 + 6.96899i) q^{59} +(24.3784 + 17.7120i) q^{60} -3.17687 q^{61} +(-7.59967 + 10.1830i) q^{62} -0.107381 q^{63} +(10.5032 + 7.63100i) q^{64} +(-3.42792 + 2.49053i) q^{65} +(-1.37248 - 4.22406i) q^{66} -1.89328 q^{67} +3.66614 q^{68} +(1.95005 + 6.00162i) q^{69} +(-0.167603 + 0.515829i) q^{70} +(1.80708 - 5.56162i) q^{71} +(-4.26985 - 3.10223i) q^{72} +(3.78622 + 11.6528i) q^{73} +(12.1873 + 8.85462i) q^{74} +(23.2314 - 16.8786i) q^{75} +(0.682457 - 2.10039i) q^{76} +(0.0398380 - 0.0289440i) q^{77} +(4.09290 - 2.97366i) q^{78} +(3.67015 - 11.2956i) q^{79} +(0.426984 - 0.310222i) q^{80} +(8.96250 + 6.51164i) q^{81} +(7.26294 + 22.3530i) q^{82} +(-13.9026 - 10.1008i) q^{83} +(0.123267 - 0.379378i) q^{84} +(1.49632 - 4.60520i) q^{85} +(4.03703 + 12.4247i) q^{86} +6.90325 q^{87} +2.42030 q^{88} +(0.611759 + 1.88280i) q^{89} +(-14.9763 + 10.8809i) q^{90} +(0.0453782 + 0.0329692i) q^{91} -9.13200 q^{92} +(-7.12642 - 10.0778i) q^{93} +15.8004 q^{94} +(-2.35985 - 1.71453i) q^{95} +(-10.3986 + 7.55501i) q^{96} +(4.72866 + 14.5533i) q^{97} -15.9676 q^{98} +1.68069 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) $ 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.84627	−	1.34139i	−1.30551	−	0.948508i	−0.305516	−	0.952187i	$-0.598829\pi$
$2$	−1.84627	−	1.34139i	−1.30551	−	0.948508i	−0.999993	+	0.00367946i	$0.998829\pi$
$3$	1.79347	−	1.30303i	1.03546	−	0.752305i	0.0660655	−	0.997815i	$-0.478955\pi$
$3$	1.79347	−	1.30303i	1.03546	−	0.752305i	0.969394	+	0.245510i	$0.0789554\pi$
$4$	0.991339	+	3.05103i	0.495669	+	1.52551i
$5$	4.23714			1.89491			0.947453	−	0.319896i	$-0.103648\pi$
$5$	4.23714			1.89491			0.947453	+	0.319896i	$0.103648\pi$
$6$	−5.05910			−2.06537
$7$	−0.0173329	−	0.0533453i	−0.00655123	−	0.0201626i	0.947727	−	0.319081i	$-0.103374\pi$
$7$	−0.0173329	−	0.0533453i	−0.00655123	−	0.0201626i	−0.954279	+	0.298918i	$0.903374\pi$
$8$	0.851924	−	2.62195i	0.301201	−	0.927000i
$9$	0.591588	−	1.82072i	0.197196	−	0.606907i
$10$	−7.82289	−	5.68366i	−2.47382	−	1.79733i
$11$	0.271289	+	0.834943i	0.0817969	+	0.251745i	0.983589	−	0.180426i	$-0.0577477\pi$
$11$	0.271289	+	0.834943i	0.0817969	+	0.251745i	−0.901792	+	0.432171i	$0.857748\pi$
$12$	5.75352	+	4.18018i	1.66090	+	1.20671i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$14$	−0.0395557	+	0.121740i	−0.0105717	+	0.0325364i
$15$	7.59917	−	5.52112i	1.96210	−	1.42555i
$16$	0.100772	−	0.0732150i	0.0251930	−	0.0183038i
$17$	0.353144	−	1.08687i	0.0856500	−	0.263604i	−0.899054	−	0.437837i	$-0.855745\pi$
$17$	0.353144	−	1.08687i	0.0856500	−	0.263604i	0.984704	+	0.174233i	$0.0557447\pi$
$18$	−3.53453	+	2.56799i	−0.833097	+	0.605281i
$19$	−0.556943	−	0.404643i	−0.127772	−	0.0928315i	0.522064	−	0.852906i	$-0.325162\pi$
$19$	−0.556943	−	0.404643i	−0.127772	−	0.0928315i	−0.649836	+	0.760075i	$0.725162\pi$
$20$	4.20044	+	12.9276i	0.939246	+	2.89070i
$21$	−0.100597	−	0.0730877i	−0.0219520	−	0.0159490i
$22$	0.619113	−	1.90543i	0.131995	−	0.406240i
$23$	−0.879648	+	2.70728i	−0.183419	+	0.564506i	−0.999918	−	0.0128415i	$-0.995912\pi$
$23$	−0.879648	+	2.70728i	−0.183419	+	0.564506i	0.816498	+	0.577348i	$0.195912\pi$
$24$	−1.88859	−	5.81247i	−0.385506	−	1.18647i
$25$	12.9533			2.59067
$26$	2.28211			0.447559
$27$	0.743670	+	2.28878i	0.143119	+	0.440476i
$28$	0.145575	−	0.105766i	0.0275111	−	0.0199880i
$29$	2.51927	+	1.83036i	0.467817	+	0.339889i	0.796590	−	0.604520i	$-0.206635\pi$
$29$	2.51927	+	1.83036i	0.467817	+	0.339889i	−0.328773	+	0.944409i	$0.606635\pi$
$30$	−21.4361			−3.91368
$31$	0.0713465	−	5.56731i	0.0128142	−	0.999918i
$31$	0.0713465	−	5.56731i	0.0128142	−	0.999918i
$32$	−5.79803			−1.02496
$33$	1.57451	+	1.14395i	0.274086	+	0.199135i
$34$	−2.10991	+	1.53294i	−0.361847	+	0.262897i
$35$	−0.0734420	−	0.226031i	−0.0124140	−	0.0382062i
$36$	6.14153			1.02359
$37$	−6.60106			−1.08521			−0.542604	−	0.839989i	$-0.682562\pi$
$37$	−6.60106			−1.08521			−0.542604	+	0.839989i	$0.682562\pi$
$38$	0.485482	+	1.49416i	0.0787555	+	0.242385i
$39$	−0.685044	+	2.10835i	−0.109695	+	0.337606i
$40$	3.60972	−	11.1096i	0.570746	−	1.75658i
$41$	−8.33202	−	6.05357i	−1.30124	−	0.945409i	−0.301276	−	0.953537i	$-0.597413\pi$
$41$	−8.33202	−	6.05357i	−1.30124	−	0.945409i	−0.999967	+	0.00812818i	$0.997413\pi$
$42$	0.0876890	+	0.269879i	0.0135307	+	0.0416432i
$43$	−4.63127	−	3.36482i	−0.706262	−	0.513130i	0.175703	−	0.984443i	$-0.443780\pi$
$43$	−4.63127	−	3.36482i	−0.706262	−	0.513130i	−0.881966	+	0.471314i	$0.843780\pi$
$44$	−2.27849	+	1.65542i	−0.343496	+	0.249564i
$45$	2.50664	−	7.71464i	0.373668	−	1.15003i
$46$	5.25559	−	3.81841i	0.774894	−	0.562993i
$47$	−5.60130	+	4.06958i	−0.817034	+	0.593610i	−0.915861	−	0.401495i	$-0.868491\pi$
$47$	−5.60130	+	4.06958i	−0.817034	+	0.593610i	0.0988277	+	0.995105i	$0.468491\pi$
$48$	0.0853297	−	0.262618i	0.0123163	−	0.0379056i
$49$	5.66057	−	4.11265i	0.808653	−	0.587521i
$50$	−23.9153	−	17.3755i	−3.38214	−	2.45727i
$51$	−0.782867	−	2.40942i	−0.109623	−	0.337386i
$52$	−2.59536	−	1.88564i	−0.359911	−	0.261491i
$53$	−0.871224	+	2.68135i	−0.119672	+	0.368312i	−0.992893	−	0.119013i	$-0.962027\pi$
$53$	−0.871224	+	2.68135i	−0.119672	+	0.368312i	0.873221	+	0.487325i	$0.162027\pi$
$54$	1.69714	−	5.22326i	0.230951	−	0.710796i
$55$	1.14949	+	3.53777i	0.154997	+	0.477033i
$56$	−0.154635			−0.0206640
$57$	−1.52612			−0.202140
$58$	−2.19602	−	6.75867i	−0.288352	−	0.887456i
$59$	−9.59199	+	6.96899i	−1.24877	+	0.907285i	−0.998150	−	0.0608001i	$-0.980635\pi$
$59$	−9.59199	+	6.96899i	−1.24877	+	0.907285i	−0.250621	+	0.968085i	$0.580635\pi$
$60$	24.3784	+	17.7120i	3.14724	+	2.28661i
$61$	−3.17687			−0.406757			−0.203378	−	0.979100i	$-0.565192\pi$
$61$	−3.17687			−0.406757			−0.203378	+	0.979100i	$0.565192\pi$
$62$	−7.59967	+	10.1830i	−0.965159	+	1.29325i
$63$	−0.107381			−0.0135287
$64$	10.5032	+	7.63100i	1.31290	+	0.953875i
$65$	−3.42792	+	2.49053i	−0.425181	+	0.308912i
$66$	−1.37248	−	4.22406i	−0.168941	−	0.519946i
$67$	−1.89328			−0.231301			−0.115651	−	0.993290i	$-0.536895\pi$
$67$	−1.89328			−0.231301			−0.115651	+	0.993290i	$0.536895\pi$
$68$	3.66614			0.444585
$69$	1.95005	+	6.00162i	0.234758	+	0.722511i
$70$	−0.167603	+	0.515829i	−0.0200324	+	0.0616533i
$71$	1.80708	−	5.56162i	0.214461	−	0.660043i	−0.784730	−	0.619837i	$-0.787199\pi$
$71$	1.80708	−	5.56162i	0.214461	−	0.660043i	0.999191	−	0.0402058i	$-0.0128014\pi$
$72$	−4.26985	−	3.10223i	−0.503207	−	0.365601i
$73$	3.78622	+	11.6528i	0.443144	+	1.36386i	0.884507	+	0.466528i	$0.154495\pi$
$73$	3.78622	+	11.6528i	0.443144	+	1.36386i	−0.441363	+	0.897329i	$0.645505\pi$
$74$	12.1873	+	8.85462i	1.41675	+	1.02933i
$75$	23.2314	−	16.8786i	2.68253	−	1.94897i
$76$	0.682457	−	2.10039i	0.0782832	−	0.240931i
$77$	0.0398380	−	0.0289440i	0.00453996	−	0.00329848i
$78$	4.09290	−	2.97366i	0.463429	−	0.336701i
$79$	3.67015	−	11.2956i	0.412924	−	1.27085i	−0.501171	−	0.865348i	$-0.667097\pi$
$79$	3.67015	−	11.2956i	0.412924	−	1.27085i	0.914095	−	0.405501i	$-0.132903\pi$
$80$	0.426984	−	0.310222i	0.0477383	−	0.0346839i
$81$	8.96250	+	6.51164i	0.995833	+	0.723515i
$82$	7.26294	+	22.3530i	0.802057	+	2.46848i
$83$	−13.9026	−	10.1008i	−1.52601	−	1.10871i	−0.958408	−	0.285401i	$-0.907873\pi$
$83$	−13.9026	−	10.1008i	−1.52601	−	1.10871i	−0.567597	−	0.823307i	$-0.692127\pi$
$84$	0.123267	−	0.379378i	0.0134496	−	0.0413935i
$85$	1.49632	−	4.60520i	0.162299	−	0.499504i
$86$	4.03703	+	12.4247i	0.435324	+	1.33979i
$87$	6.90325			0.740106
$88$	2.42030			0.258005
$89$	0.611759	+	1.88280i	0.0648464	+	0.199577i	0.978230	−	0.207523i	$-0.0665402\pi$
$89$	0.611759	+	1.88280i	0.0648464	+	0.199577i	−0.913384	+	0.407100i	$0.866540\pi$
$90$	−14.9763	+	10.8809i	−1.57864	+	1.14695i
$91$	0.0453782	+	0.0329692i	0.00475693	+	0.00345611i
$92$	−9.13200			−0.952077
$93$	−7.12642	−	10.0778i	−0.738975	−	1.04501i
$94$	15.8004			1.62969
$95$	−2.35985	−	1.71453i	−0.242115	−	0.175907i
$96$	−10.3986	+	7.55501i	−1.06130	+	0.771080i
$97$	4.72866	+	14.5533i	0.480123	+	1.47767i	0.838922	+	0.544251i	$0.183186\pi$
$97$	4.72866	+	14.5533i	0.480123	+	1.47767i	−0.358799	+	0.933415i	$0.616814\pi$
$98$	−15.9676			−1.61297
$99$	1.68069			0.168916
$100$	12.8411	+	39.5209i	1.28411	+	3.95209i
$101$	−3.00055	+	9.23473i	−0.298566	+	0.918890i	0.683435	+	0.730012i	$0.260485\pi$
$101$	−3.00055	+	9.23473i	−0.298566	+	0.918890i	−0.982000	+	0.188879i	$0.939515\pi$
$102$	−1.78659	+	5.49856i	−0.176899	+	0.544439i
$103$	−0.911574	−	0.662297i	−0.0898200	−	0.0652581i	0.541969	−	0.840399i	$-0.317679\pi$
$103$	−0.911574	−	0.662297i	−0.0898200	−	0.0652581i	−0.631789	+	0.775140i	$0.717679\pi$
$104$	0.851924	+	2.62195i	0.0835380	+	0.257104i
$105$	−0.426242	−	0.309683i	−0.0415969	−	0.0302219i
$106$	5.20526	−	3.78184i	0.505579	−	0.367325i
$107$	−4.38418	+	13.4931i	−0.423834	+	1.30443i	0.480271	+	0.877120i	$0.340538\pi$
$107$	−4.38418	+	13.4931i	−0.423834	+	1.30443i	−0.904106	+	0.427308i	$0.859462\pi$
$108$	−6.24591	+	4.53792i	−0.601013	+	0.436661i
$109$	8.33774	−	6.05773i	0.798611	−	0.580225i	−0.111895	−	0.993720i	$-0.535692\pi$
$109$	8.33774	−	6.05773i	0.798611	−	0.580225i	0.910506	+	0.413495i	$0.135692\pi$
$110$	2.62327	−	8.07359i	0.250119	−	0.769786i
$111$	−11.8388	+	8.60139i	−1.12369	+	0.816408i
$112$	−0.00565235	−	0.00410667i	−0.000534097	−	0.000388044i
$113$	−2.62001	−	8.06356i	−0.246470	−	0.758556i	−0.995391	−	0.0958972i	$-0.969428\pi$
$113$	−2.62001	−	8.06356i	−0.246470	−	0.758556i	0.748921	−	0.662659i	$-0.230572\pi$
$114$	2.81763	+	2.04713i	0.263895	+	0.191731i
$115$	−3.72719	+	11.4711i	−0.347562	+	1.06969i
$116$	−3.08702	+	9.50088i	−0.286623	+	0.882134i
$117$	0.591588	+	1.82072i	0.0546923	+	0.168326i
$118$	27.0575			2.49085
$119$	−0.0641001			−0.00587605
$120$	−8.00220	−	24.6282i	−0.730497	−	2.24824i
$121$	8.27565	−	6.01262i	0.752332	−	0.546601i
$122$	5.86536	+	4.26143i	0.531025	+	0.385812i
$123$	−22.8312			−2.05862
$124$	17.0567	−	5.30141i	1.53174	−	0.476080i
$125$	33.6993			3.01416
$126$	0.198254	+	0.144040i	0.0176619	+	0.0128321i
$127$	−7.08129	+	5.14486i	−0.628363	+	0.456532i	−0.855833	−	0.517253i	$-0.826955\pi$
$127$	−7.08129	+	5.14486i	−0.628363	+	0.456532i	0.227470	+	0.973785i	$0.426955\pi$
$128$	−5.57213	−	17.1492i	−0.492511	−	1.51579i
$129$	−12.6905			−1.11734
$130$	9.66962			0.848082
$131$	4.73895	+	14.5850i	0.414044	+	1.27430i	0.913104	+	0.407728i	$0.133679\pi$
$131$	4.73895	+	14.5850i	0.414044	+	1.27430i	−0.499060	+	0.866567i	$0.666321\pi$
$132$	−1.92934	+	5.93790i	−0.167927	+	0.516828i
$133$	−0.0119323	+	0.0367239i	−0.00103466	+	0.00318437i
$134$	3.49551	+	2.53963i	0.301966	+	0.219391i
$135$	3.15103	+	9.69788i	0.271198	+	0.834661i
$136$	−2.54886	−	1.85185i	−0.218563	−	0.158795i
$137$	4.64830	−	3.37719i	0.397131	−	0.288533i	−0.371240	−	0.928537i	$-0.621067\pi$
$137$	4.64830	−	3.37719i	0.397131	−	0.288533i	0.768372	+	0.640004i	$0.221067\pi$
$138$	4.45022	−	13.6964i	0.378828	−	1.16591i
$139$	−0.390877	+	0.283989i	−0.0331538	+	0.0240876i	−0.604239	−	0.796803i	$-0.706523\pi$
$139$	−0.390877	+	0.283989i	−0.0331538	+	0.0240876i	0.571085	+	0.820891i	$0.306523\pi$
$140$	0.616821	−	0.448147i	0.0521309	−	0.0378753i
$141$	−4.74296	+	14.5973i	−0.399429	+	1.22932i
$142$	−10.7967	+	7.84424i	−0.906036	+	0.658274i
$143$	−0.710245	−	0.516023i	−0.0593937	−	0.0431520i
$144$	−0.0736887	−	0.226791i	−0.00614073	−	0.0188992i
$145$	10.6745	+	7.75548i	0.886469	+	0.644058i
$146$	8.64059	−	26.5930i	0.715100	−	2.20085i
$147$	4.79315	−	14.7518i	0.395333	−	1.21671i
$148$	−6.54389	−	20.1400i	−0.537904	−	1.65550i
$149$	−4.63354			−0.379594			−0.189797	−	0.981823i	$-0.560783\pi$
$149$	−4.63354			−0.379594			−0.189797	+	0.981823i	$0.560783\pi$
$150$	−65.5322			−5.35068
$151$	−6.27484	−	19.3120i	−0.510640	−	1.57159i	−0.791078	−	0.611715i	$-0.790480\pi$
$151$	−6.27484	−	19.3120i	−0.510640	−	1.57159i	0.280439	−	0.959872i	$-0.409520\pi$
$152$	−1.53543	+	1.11555i	−0.124540	+	0.0904833i
$153$	−1.76996	−	1.28595i	−0.143093	−	0.103963i
$154$	−0.112377			−0.00905559
$155$	0.302305	−	23.5894i	0.0242817	−	1.89475i
$156$	−7.11174			−0.569395
$157$	−15.2196	−	11.0577i	−1.21466	−	0.882500i	−0.219012	−	0.975722i	$-0.570283\pi$
$157$	−15.2196	−	11.0577i	−1.21466	−	0.882500i	−0.995645	+	0.0932224i	$0.970283\pi$
$158$	−21.9278	+	15.9315i	−1.74449	+	1.26744i
$159$	1.93137	+	5.94415i	0.153168	+	0.471402i
$160$	−24.5670			−1.94219
$161$	0.159667			0.0125835
$162$	−7.81252	−	24.0445i	−0.613809	−	1.88911i
$163$	6.70555	−	20.6376i	0.525219	−	1.61646i	−0.238663	−	0.971102i	$-0.576709\pi$
$163$	6.70555	−	20.6376i	0.525219	−	1.61646i	0.763882	−	0.645356i	$-0.223291\pi$
$164$	10.2097	−	31.4224i	0.797247	−	2.45367i
$165$	6.67140	+	4.84705i	0.519368	+	0.377343i
$166$	12.1187	+	37.2976i	0.940595	+	2.89485i
$167$	6.95777	+	5.05512i	0.538408	+	0.391177i	0.823494	−	0.567326i	$-0.192022\pi$
$167$	6.95777	+	5.05512i	0.538408	+	0.391177i	−0.285085	+	0.958502i	$0.592022\pi$
$168$	−0.277333	+	0.201494i	−0.0213967	+	0.0155456i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	−8.93998	+	6.49528i	−0.685665	+	0.498165i
$171$	−1.06622	+	0.774657i	−0.0815361	+	0.0592395i
$172$	5.67499	−	17.4658i	0.432714	−	1.33176i
$173$	13.2570	−	9.63176i	1.00791	−	0.732289i	0.0441403	−	0.999025i	$-0.485945\pi$
$173$	13.2570	−	9.63176i	1.00791	−	0.732289i	0.963770	+	0.266736i	$0.0859451\pi$
$174$	−12.7453	−	9.25997i	−0.966215	−	0.701996i
$175$	−0.224519	−	0.690999i	−0.0169720	−	0.0522346i
$176$	0.0884687	+	0.0642763i	0.00666858	+	0.00484501i
$177$	−8.12212	+	24.9973i	−0.610496	+	1.87891i
$178$	1.39610	−	4.29677i	0.104642	−	0.322056i
$179$	5.51195	+	16.9640i	0.411983	+	1.26795i	0.914922	+	0.403631i	$0.132252\pi$
$179$	5.51195	+	16.9640i	0.411983	+	1.26795i	−0.502939	+	0.864322i	$0.667748\pi$
$180$	26.0225			1.93960
$181$	11.4946			0.854386			0.427193	−	0.904160i	$-0.359502\pi$
$181$	11.4946			0.854386			0.427193	+	0.904160i	$0.359502\pi$
$182$	−0.0395557	−	0.121740i	−0.00293206	−	0.00902396i
$183$	−5.69762	+	4.13956i	−0.421180	+	0.306005i
$184$	6.34896	+	4.61279i	0.468051	+	0.340059i
$185$	−27.9696			−2.05637
$186$	−0.360949	+	28.1656i	−0.0264661	+	2.06520i
$187$	1.00327			0.0733667
$188$	−17.9692	−	13.0554i	−1.31054	−	0.952162i
$189$	0.109206	−	0.0793426i	0.00794355	−	0.00577132i
$190$	2.05705	+	6.33096i	0.149234	+	0.459296i
$191$	9.47329			0.685464			0.342732	−	0.939433i	$-0.388648\pi$
$191$	9.47329			0.685464			0.342732	+	0.939433i	$0.388648\pi$
$192$	28.7805			2.07706
$193$	−1.82014	−	5.60183i	−0.131017	−	0.403228i	0.863932	−	0.503608i	$-0.167994\pi$
$193$	−1.82014	−	5.60183i	−0.131017	−	0.403228i	−0.994949	+	0.100379i	$0.967994\pi$
$194$	10.7913	−	33.2123i	0.774773	−	2.38451i
$195$	−2.90263	+	8.93336i	−0.207861	+	0.639731i
$196$	18.1593	+	13.1935i	1.29710	+	0.942395i
$197$	7.79302	+	23.9845i	0.555230	+	1.70882i	0.695336	+	0.718685i	$0.255256\pi$
$197$	7.79302	+	23.9845i	0.555230	+	1.70882i	−0.140106	+	0.990137i	$0.544744\pi$
$198$	−3.10301	−	2.25447i	−0.220521	−	0.160218i
$199$	−17.9311	+	13.0277i	−1.27110	+	0.923511i	−0.999246	−	0.0388262i	$-0.987638\pi$
$199$	−17.9311	+	13.0277i	−1.27110	+	0.923511i	−0.271858	+	0.962337i	$0.587638\pi$
$200$	11.0352	−	33.9630i	0.780310	−	2.40155i
$201$	−3.39554	+	2.46701i	−0.239503	+	0.174009i
$202$	17.9272	−	13.0249i	1.26135	−	0.916428i
$203$	0.0539746	−	0.166117i	0.00378828	−	0.0116591i
$204$	6.57511	−	4.77710i	0.460350	−	0.334464i
$205$	−35.3039	−	25.6498i	−2.46573	−	1.79146i
$206$	0.794609	+	2.44556i	0.0553630	+	0.170390i
$207$	4.40881	+	3.20319i	0.306433	+	0.222637i
$208$	−0.0384914	+	0.118464i	−0.00266890	+	0.00821403i
$209$	0.186761	−	0.574791i	0.0129185	−	0.0397592i
$210$	0.371550	+	1.14351i	0.0256394	+	0.0789100i
$211$	3.16637			0.217982			0.108991	−	0.994043i	$-0.465238\pi$
$211$	3.16637			0.217982			0.108991	+	0.994043i	$0.465238\pi$
$212$	−9.04455			−0.621182
$213$	−4.00602	−	12.3293i	−0.274488	−	0.844788i
$214$	26.1939	−	19.0310i	1.79058	−	1.30093i
$215$	−19.6233	−	14.2572i	−1.33830	−	0.972332i
$216$	6.63463			0.451429
$217$	−0.298226	+	0.0926917i	−0.0202449	+	0.00629233i
$218$	−23.5195			−1.59294
$219$	21.9744	+	15.9654i	1.48489	+	1.07884i
$220$	−9.65429	+	7.01425i	−0.650892	+	0.472901i
$221$	0.353144	+	1.08687i	0.0237550	+	0.0731105i
$222$	33.3954			2.24136
$223$	−0.707343			−0.0473672			−0.0236836	−	0.999720i	$-0.507539\pi$
$223$	−0.707343			−0.0473672			−0.0236836	+	0.999720i	$0.507539\pi$
$224$	0.100497	+	0.309297i	0.00671473	+	0.0206658i
$225$	7.66303	−	23.5844i	0.510869	−	1.57229i
$226$	−5.97916	+	18.4020i	−0.397728	+	1.22408i
$227$	8.15333	+	5.92374i	0.541155	+	0.393172i	0.824514	−	0.565842i	$-0.191449\pi$
$227$	8.15333	+	5.92374i	0.541155	+	0.393172i	−0.283359	+	0.959014i	$0.591449\pi$
$228$	−1.51290	−	4.65624i	−0.100195	−	0.308367i
$229$	10.8193	+	7.86069i	0.714960	+	0.519449i	0.884770	−	0.466028i	$-0.154315\pi$
$229$	10.8193	+	7.86069i	0.714960	+	0.519449i	−0.169810	+	0.985477i	$0.554315\pi$
$230$	22.2686	−	16.1791i	1.46835	−	1.06682i
$231$	0.0337333	−	0.103820i	0.00221949	−	0.00683088i
$232$	6.94534	−	5.04609i	0.455984	−	0.331292i
$233$	13.6637	−	9.92726i	0.895139	−	0.650357i	−0.0420738	−	0.999115i	$-0.513396\pi$
$233$	13.6637	−	9.92726i	0.895139	−	0.650357i	0.937213	+	0.348758i	$0.113396\pi$
$234$	1.35007	−	4.15509i	0.0882569	−	0.271627i
$235$	−23.7335	+	17.2434i	−1.54820	+	1.12483i
$236$	−30.7715	−	22.3568i	−2.00305	−	1.45530i
$237$	−8.13616	−	25.0405i	−0.528501	−	1.62656i
$238$	0.118346	+	0.0859834i	0.00767123	+	0.00557348i
$239$	−1.77295	+	5.45657i	−0.114682	+	0.352956i	−0.991881	−	0.127172i	$-0.959410\pi$
$239$	−1.77295	+	5.45657i	−0.114682	+	0.352956i	0.877198	+	0.480128i	$0.159410\pi$
$240$	0.361553	−	1.11275i	0.0233382	−	0.0718275i
$241$	2.10662	+	6.48350i	0.135699	+	0.417639i	0.995698	−	0.0926567i	$-0.0295359\pi$
$241$	2.10662	+	6.48350i	0.135699	+	0.417639i	−0.859999	+	0.510296i	$0.829536\pi$
$242$	−23.3444			−1.50063
$243$	17.3391			1.11230
$244$	−3.14936	−	9.69272i	−0.201617	−	0.620513i
$245$	23.9846	−	17.4258i	1.53232	−	1.11330i
$246$	42.1525	+	30.6256i	2.68755	+	1.95262i
$247$	0.688420			0.0438031
$248$	−14.5364	−	4.92999i	−0.923064	−	0.313055i
$249$	−38.0955			−2.41420
$250$	−62.2180	−	45.2040i	−3.93501	−	2.85895i
$251$	16.2932	−	11.8377i	1.02842	−	0.747188i	0.0604247	−	0.998173i	$-0.480754\pi$
$251$	16.2932	−	11.8377i	1.02842	−	0.747188i	0.967991	+	0.250985i	$0.0807545\pi$
$252$	−0.106451	−	0.327622i	−0.00670577	−	0.0206382i
$253$	−2.49906			−0.157115
$254$	19.9752			1.25336
$255$	−3.31711	−	10.2090i	−0.207726	−	0.639314i
$256$	−4.69251	+	14.4421i	−0.293282	+	0.902629i
$257$	−3.41166	+	10.5000i	−0.212814	+	0.654973i	0.786488	+	0.617606i	$0.211897\pi$
$257$	−3.41166	+	10.5000i	−0.212814	+	0.654973i	−0.999302	+	0.0373677i	$0.988103\pi$
$258$	23.4301	+	17.0229i	1.45869	+	1.05980i
$259$	0.114416	+	0.352136i	0.00710945	+	0.0218806i
$260$	−10.9969	−	7.98971i	−0.681998	−	0.495501i
$261$	4.82295	−	3.50408i	0.298533	−	0.216897i
$262$	10.8148	−	33.2846i	0.668141	−	2.05633i
$263$	−10.5488	+	7.66416i	−0.650467	+	0.472592i	−0.863430	−	0.504468i	$-0.831689\pi$
$263$	−10.5488	+	7.66416i	−0.650467	+	0.472592i	0.212963	+	0.977060i	$0.431689\pi$
$264$	4.34073	−	3.15372i	0.267153	−	0.194098i
$265$	−3.69149	+	11.3613i	−0.226767	+	0.697916i
$266$	0.0712915	−	0.0517963i	0.00437116	−	0.00317584i
$267$	3.55052	+	2.57960i	0.217288	+	0.157869i
$268$	−1.87688	−	5.77646i	−0.114649	−	0.352853i
$269$	−21.4237	−	15.5652i	−1.30622	−	0.949028i	−0.306229	−	0.951958i	$-0.599067\pi$
$269$	−21.4237	−	15.5652i	−1.30622	−	0.949028i	−0.999996	+	0.00292988i	$0.999067\pi$
$270$	7.19101	−	22.1317i	0.437631	−	1.34689i
$271$	−4.33742	+	13.3492i	−0.263479	+	0.810906i	0.728561	+	0.684981i	$0.240190\pi$
$271$	−4.33742	+	13.3492i	−0.263479	+	0.810906i	−0.992040	+	0.125925i	$0.959810\pi$
$272$	−0.0439879	−	0.135381i	−0.00266716	−	0.00820867i
$273$	0.124344			0.00752566
$274$	−13.1122			−0.792134
$275$	3.51410	+	10.8153i	0.211908	+	0.652187i
$276$	−16.3780	+	11.8993i	−0.985837	+	0.716253i
$277$	11.9299	+	8.66760i	0.716800	+	0.520786i	0.885360	−	0.464906i	$-0.153912\pi$
$277$	11.9299	+	8.66760i	0.716800	+	0.520786i	−0.168560	+	0.985691i	$0.553912\pi$
$278$	1.10260			0.0661299
$279$	−10.0943	−	3.42346i	−0.604330	−	0.204957i
$280$	−0.655210			−0.0391563
$281$	14.1962	+	10.3142i	0.846875	+	0.615291i	0.924283	−	0.381709i	$-0.124664\pi$
$281$	14.1962	+	10.3142i	0.846875	+	0.615291i	−0.0774076	+	0.997000i	$0.524664\pi$
$282$	28.3375	−	20.5884i	1.68748	−	1.22602i
$283$	−4.84312	−	14.9056i	−0.287894	−	0.886046i	−0.985516	−	0.169581i	$-0.945759\pi$
$283$	−4.84312	−	14.9056i	−0.287894	−	0.886046i	0.697622	−	0.716466i	$-0.254241\pi$
$284$	18.7601			1.11321
$285$	−6.46639			−0.383036
$286$	0.619113	+	1.90543i	0.0366089	+	0.112671i
$287$	−0.178511	+	0.549400i	−0.0105372	+	0.0324301i
$288$	−3.43004	+	10.5566i	−0.202117	+	0.622053i
$289$	12.6967	+	9.22471i	0.746866	+	0.542630i
$290$	−9.30485	−	28.6374i	−0.546400	−	1.68165i
$291$	27.4441	+	19.9393i	1.60880	+	1.16886i
$292$	−31.7996	+	23.1037i	−1.86093	+	1.35204i
$293$	−4.74677	+	14.6091i	−0.277309	+	0.853470i	0.711290	+	0.702899i	$0.248111\pi$
$293$	−4.74677	+	14.6091i	−0.277309	+	0.853470i	−0.988599	+	0.150572i	$0.951889\pi$
$294$	−28.6374	+	20.8063i	−1.67017	+	1.21345i
$295$	−40.6426	+	29.5286i	−2.36630	+	1.71922i
$296$	−5.62360	+	17.3077i	−0.326865	+	1.00599i
$297$	−1.70925	+	1.24184i	−0.0991809	+	0.0720591i
$298$	8.55475	+	6.21539i	0.495563	+	0.360048i
$299$	−0.879648	−	2.70728i	−0.0508713	−	0.156566i
$300$	74.5272	+	54.1472i	4.30283	+	3.12619i
$301$	−0.0992235	+	0.305379i	−0.00571915	+	0.0176017i
$302$	−14.3199	+	44.0721i	−0.824018	+	2.53607i
$303$	6.65176	+	20.4720i	0.382134	+	1.17609i
$304$	−0.0857502			−0.00491811
$305$	−13.4608			−0.770766
$306$	1.54286	+	4.74843i	0.0881993	+	0.271450i
$307$	8.30531	−	6.03416i	0.474009	−	0.344388i	−0.324993	−	0.945717i	$-0.605362\pi$
$307$	8.30531	−	6.03416i	0.474009	−	0.344388i	0.799002	+	0.601329i	$0.205362\pi$
$308$	0.127802	+	0.0928536i	0.00728219	+	0.00529082i
$309$	−2.49787			−0.142099
$310$	−32.2008	+	43.1469i	−1.82888	+	2.45058i
$311$	13.5782			0.769950			0.384975	−	0.922927i	$-0.374210\pi$
$311$	13.5782			0.769950			0.384975	+	0.922927i	$0.374210\pi$
$312$	4.94438	+	3.59230i	0.279921	+	0.203374i
$313$	−6.61630	+	4.80703i	−0.373976	+	0.271709i	−0.758858	−	0.651257i	$-0.774242\pi$
$313$	−6.61630	+	4.80703i	−0.373976	+	0.271709i	0.384882	+	0.922966i	$0.374242\pi$
$314$	13.2668	+	40.8309i	0.748687	+	2.30422i
$315$	−0.454987			−0.0256356
$316$	38.1014			2.14337
$317$	−3.78307	−	11.6431i	−0.212479	−	0.653942i	−0.999323	−	0.0367904i	$-0.988287\pi$
$317$	−3.78307	−	11.6431i	−0.212479	−	0.653942i	0.786844	−	0.617151i	$-0.211713\pi$
$318$	4.40761	−	13.5652i	0.247166	−	0.760700i
$319$	−0.844793	+	2.60001i	−0.0472994	+	0.145572i
$320$	44.5034	+	32.3336i	2.48781	+	1.80750i
$321$	9.71906	+	29.9122i	0.542465	+	1.66954i
$322$	−0.294789	−	0.214176i	−0.0164279	−	0.0119356i
$323$	−0.636474	+	0.462425i	−0.0354143	+	0.0257300i
$324$	−10.9823	+	33.8001i	−0.610128	+	1.87778i
$325$	−10.4795	+	7.61377i	−0.581296	+	0.422336i
$326$	−40.0633	+	29.1077i	−2.21890	+	1.61213i
$327$	7.06008	−	21.7287i	0.390423	−	1.20160i
$328$	−22.9704	+	16.6890i	−1.26833	+	0.921495i
$329$	0.314180	+	0.228265i	0.0173213	+	0.0125847i
$330$	−5.81539	−	17.8979i	−0.320127	−	0.985248i
$331$	−12.5439	−	9.11368i	−0.689475	−	0.500933i	0.187012	−	0.982358i	$-0.440120\pi$
$331$	−12.5439	−	9.11368i	−0.689475	−	0.500933i	−0.876488	+	0.481424i	$0.840120\pi$
$332$	17.0357	−	52.4304i	0.934954	−	2.87749i
$333$	−3.90511	+	12.0187i	−0.213999	+	0.658621i
$334$	−6.06502	−	18.6662i	−0.331863	−	1.02137i
$335$	−8.02210			−0.438294
$336$	−0.0154884			−0.000844963
$337$	−0.916750	−	2.82147i	−0.0499386	−	0.153695i	0.922977	−	0.384854i	$-0.125748\pi$
$337$	−0.916750	−	2.82147i	−0.0499386	−	0.153695i	−0.972916	+	0.231159i	$0.925748\pi$
$338$	−1.84627	+	1.34139i	−0.100424	+	0.0729621i
$339$	−15.2060	−	11.0478i	−0.825875	−	0.600033i
$340$	15.5339			0.842446
$341$	4.66774	−	1.45078i	0.252772	−	0.0785642i
$342$	3.00765			0.162635
$343$	−0.635152	−	0.461465i	−0.0342950	−	0.0249168i
$344$	−12.7679	+	9.27640i	−0.688398	+	0.500150i
$345$	8.26261	+	25.4297i	0.444844	+	1.36909i
$346$	−37.3959			−2.01042
$347$	−14.0215			−0.752714			−0.376357	−	0.926475i	$-0.622823\pi$
$347$	−14.0215			−0.752714			−0.376357	+	0.926475i	$0.622823\pi$
$348$	6.84346	+	21.0620i	0.366848	+	1.12904i
$349$	10.0368	−	30.8901i	0.537258	−	1.65351i	−0.201460	−	0.979497i	$-0.564569\pi$
$349$	10.0368	−	30.8901i	0.537258	−	1.65351i	0.738718	−	0.674015i	$-0.235431\pi$
$350$	−0.512378	+	1.57694i	−0.0273878	+	0.0842908i
$351$	−1.94695	−	1.41455i	−0.103921	−	0.0755028i
$352$	−1.57294	−	4.84102i	−0.0838382	−	0.258027i
$353$	6.22197	+	4.52052i	0.331162	+	0.240603i	0.740923	−	0.671589i	$-0.234388\pi$
$353$	6.22197	+	4.52052i	0.331162	+	0.240603i	−0.409762	+	0.912193i	$0.634388\pi$
$354$	48.5268	−	35.2568i	2.57917	−	1.87388i
$355$	7.65685	−	23.5653i	0.406383	−	1.25072i
$356$	−5.13802	+	3.73299i	−0.272314	+	0.197848i
$357$	−0.114962	+	0.0835245i	−0.00608441	+	0.00442058i
$358$	12.5789	−	38.7139i	0.664816	−	2.04609i
$359$	−22.3730	+	16.2550i	−1.18080	+	0.857904i	−0.992262	−	0.124162i	$-0.960376\pi$
$359$	−22.3730	+	16.2550i	−1.18080	+	0.857904i	−0.188541	+	0.982065i	$0.560376\pi$
$360$	−18.0920	−	13.1446i	−0.953530	−	0.692780i
$361$	−5.72487	−	17.6193i	−0.301309	−	0.927334i
$362$	−21.2221	−	15.4188i	−1.11541	−	0.810392i
$363$	7.00750	−	21.5669i	0.367798	−	1.13197i
$364$	−0.0556047	+	0.171134i	−0.00291448	+	0.00896985i
$365$	16.0427	+	49.3745i	0.839716	+	2.58438i
$366$	16.0721			0.840103
$367$	−13.5972			−0.709770			−0.354885	−	0.934910i	$-0.615480\pi$
$367$	−13.5972			−0.709770			−0.354885	+	0.934910i	$0.615480\pi$
$368$	0.109570	+	0.337221i	0.00571171	+	0.0175788i
$369$	−15.9510	+	11.5891i	−0.830375	+	0.603303i
$370$	51.6394	+	37.5182i	2.68460	+	1.95048i
$371$	0.158138			0.00821013
$372$	23.6828	−	31.7334i	1.22790	−	1.64530i
$373$	−6.42790			−0.332824			−0.166412	−	0.986056i	$-0.553218\pi$
$373$	−6.42790			−0.332824			−0.166412	+	0.986056i	$0.553218\pi$
$374$	−1.85231	−	1.34579i	−0.0957809	−	0.0695889i
$375$	60.4387	−	43.9113i	3.12104	−	2.26757i
$376$	5.89837	+	18.1533i	0.304185	+	0.936185i
$377$	−3.11399			−0.160379
$378$	−0.308053			−0.0158445
$379$	−1.55078	−	4.77280i	−0.0796580	−	0.245162i	0.903295	−	0.429020i	$-0.141141\pi$
$379$	−1.55078	−	4.77280i	−0.0796580	−	0.245162i	−0.982953	+	0.183858i	$0.941141\pi$
$380$	2.89167	−	8.89963i	0.148339	−	0.456541i
$381$	−5.99616	+	18.4543i	−0.307193	+	0.945441i
$382$	−17.4902	−	12.7074i	−0.894879	−	0.650167i
$383$	−10.2897	−	31.6685i	−0.525780	−	1.61818i	−0.762768	−	0.646672i	$-0.776160\pi$
$383$	−10.2897	−	31.6685i	−0.525780	−	1.61818i	0.236989	−	0.971512i	$-0.423840\pi$
$384$	−32.3394	−	23.4960i	−1.65031	−	1.19902i
$385$	0.168799	−	0.122640i	0.00860280	−	0.00625030i
$386$	−4.15377	+	12.7840i	−0.211422	+	0.650689i
$387$	−8.86620	+	6.44167i	−0.450694	+	0.327448i
$388$	−39.7149	+	28.8545i	−2.01622	+	1.46487i
$389$	−7.95929	+	24.4962i	−0.403552	+	1.24201i	0.518546	+	0.855050i	$0.326473\pi$
$389$	−7.95929	+	24.4962i	−0.403552	+	1.24201i	−0.922098	+	0.386956i	$0.873527\pi$
$390$	17.3422	−	12.5998i	0.878155	−	0.638017i
$391$	2.63180	+	1.91212i	0.133096	+	0.0966999i
$392$	−5.96079	−	18.3454i	−0.301065	−	0.926583i
$393$	27.5038	+	19.9827i	1.38738	+	1.00799i
$394$	17.7846	−	54.7352i	0.895973	−	2.75752i
$395$	15.5509	−	47.8608i	0.782452	−	2.40814i
$396$	1.66613	+	5.12783i	0.0837264	+	0.257683i
$397$	12.0705			0.605800			0.302900	−	0.953022i	$-0.402045\pi$
$397$	12.0705			0.605800			0.302900	+	0.953022i	$0.402045\pi$
$398$	50.5810			2.53539
$399$	0.0264522	+	0.0814114i	0.00132427	+	0.00407567i
$400$	1.30533	−	0.948378i	0.0652665	−	0.0474189i
$401$	−18.8766	−	13.7147i	−0.942653	−	0.684878i	0.00640475	−	0.999979i	$-0.497961\pi$
$401$	−18.8766	−	13.7147i	−0.942653	−	0.684878i	−0.949058	+	0.315102i	$0.897961\pi$
$402$	9.57830			0.477722
$403$	3.21466	+	4.54598i	0.160134	+	0.226452i
$404$	−31.1500			−1.54977
$405$	37.9753	+	27.5907i	1.88701	+	1.37099i
$406$	−0.322479	+	0.234295i	−0.0160044	+	0.0116279i
$407$	−1.79080	−	5.51151i	−0.0887666	−	0.273196i
$408$	−6.98431			−0.345775
$409$	20.3159			1.00456			0.502278	−	0.864706i	$-0.332495\pi$
$409$	20.3159			1.00456			0.502278	+	0.864706i	$0.332495\pi$
$410$	30.7741	+	94.7128i	1.51982	+	4.67753i
$411$	3.93600	−	12.1138i	0.194149	−	0.597528i
$412$	1.11701	−	3.43780i	0.0550310	−	0.169368i
$413$	0.538020	+	0.390894i	0.0264742	+	0.0192347i
$414$	−3.84311	−	11.8279i	−0.188879	−	0.581309i
$415$	−58.9071	−	42.7985i	−2.89163	−	2.10090i
$416$	4.69070	−	3.40800i	0.229981	−	0.167091i
$417$	−0.330980	+	1.01865i	−0.0162081	+	0.0498835i
$418$	−1.11583	+	0.810699i	−0.0545771	+	0.0396526i
$419$	17.2756	−	12.5515i	0.843970	−	0.613180i	−0.0795066	−	0.996834i	$-0.525334\pi$
$419$	17.2756	−	12.5515i	0.843970	−	0.613180i	0.923477	+	0.383654i	$0.125334\pi$
$420$	0.522300	−	1.60748i	0.0254856	−	0.0784368i
$421$	0.199517	−	0.144957i	0.00972385	−	0.00706479i	−0.582913	−	0.812535i	$-0.698087\pi$
$421$	0.199517	−	0.144957i	0.00972385	−	0.00706479i	0.592637	+	0.805470i	$0.298087\pi$
$422$	−5.84597	−	4.24734i	−0.284577	−	0.206757i
$423$	4.09591	+	12.6059i	0.199150	+	0.612921i
$424$	6.28816	+	4.56861i	0.305380	+	0.221871i
$425$	4.57439	−	14.0785i	0.221890	−	0.682908i
$426$	−9.14220	+	28.1368i	−0.442941	+	1.36323i
$427$	0.0550645	+	0.169471i	0.00266476	+	0.00820128i
$428$	−45.5141			−2.20000
$429$	−1.94620			−0.0939633
$430$	17.1055	+	52.6452i	0.824898	+	2.53878i
$431$	−12.1460	+	8.82458i	−0.585052	+	0.425065i	−0.840542	−	0.541747i	$-0.817763\pi$
$431$	−12.1460	+	8.82458i	−0.585052	+	0.425065i	0.255490	+	0.966812i	$0.417763\pi$
$432$	0.242514	+	0.176197i	0.0116680	+	0.00847728i
$433$	−2.46998			−0.118700			−0.0593498	−	0.998237i	$-0.518903\pi$
$433$	−2.46998			−0.118700			−0.0593498	+	0.998237i	$0.518903\pi$
$434$	0.674941	+	0.228904i	0.0323982	+	0.0109878i
$435$	29.2500			1.40243
$436$	26.7478	+	19.4334i	1.28099	+	0.930692i
$437$	1.58539	−	1.15186i	0.0758397	−	0.0551008i
$438$	−19.1549	−	58.9527i	−0.915256	−	2.81687i
$439$	−18.2840			−0.872647			−0.436323	−	0.899790i	$-0.643720\pi$
$439$	−18.2840			−0.872647			−0.436323	+	0.899790i	$0.643720\pi$
$440$	10.2551			0.488894
$441$	−4.13926	−	12.7393i	−0.197107	−	0.606634i
$442$	0.805914	−	2.48035i	0.0383334	−	0.117978i
$443$	9.94397	−	30.6044i	0.472452	−	1.45406i	−0.376911	−	0.926250i	$-0.623014\pi$
$443$	9.94397	−	30.6044i	0.472452	−	1.45406i	0.849363	−	0.527809i	$-0.176986\pi$
$444$	−37.9793	−	27.5936i	−1.80242	−	1.30953i
$445$	2.59211	+	7.97769i	0.122878	+	0.378179i
$446$	1.30594	+	0.948825i	0.0618383	+	0.0449281i
$447$	−8.31010	+	6.03764i	−0.393054	+	0.285571i
$448$	0.225027	−	0.692562i	0.0106315	−	0.0327205i
$449$	13.8752	−	10.0809i	0.654810	−	0.475747i	−0.210097	−	0.977681i	$-0.567378\pi$
$449$	13.8752	−	10.0809i	0.654810	−	0.475747i	0.864906	+	0.501934i	$0.167378\pi$
$450$	−45.7839	+	33.2640i	−2.15828	+	1.56808i
$451$	2.79400	−	8.59903i	0.131564	−	0.404913i
$452$	22.0048	−	15.9874i	1.03502	−	0.751986i
$453$	−36.4179	−	26.4591i	−1.71106	−	1.24316i
$454$	−7.10717	−	21.8736i	−0.333556	−	1.02658i
$455$	0.192274	+	0.139695i	0.00901393	+	0.00654900i
$456$	−1.30014	+	4.00142i	−0.0608847	+	0.187384i
$457$	−0.455098	+	1.40065i	−0.0212886	+	0.0655196i	−0.961136	−	0.276074i	$-0.910967\pi$
$457$	−0.455098	+	1.40065i	−0.0212886	+	0.0655196i	0.939848	+	0.341593i	$0.110967\pi$
$458$	−9.43108	−	29.0259i	−0.440685	−	1.35629i
$459$	2.75022			0.128369
$460$	−38.6935			−1.80410
$461$	0.0118777	+	0.0365557i	0.000553198	+	0.00170257i	0.951333	−	0.308166i	$-0.0997151\pi$
$461$	0.0118777	+	0.0365557i	0.000553198	+	0.00170257i	−0.950780	+	0.309868i	$0.899715\pi$
$462$	−0.201545	+	0.146431i	−0.00937670	+	0.00681257i
$463$	27.1561	+	19.7301i	1.26205	+	0.916933i	0.998856	−	0.0478094i	$-0.0152240\pi$
$463$	27.1561	+	19.7301i	1.26205	+	0.916933i	0.263194	+	0.964743i	$0.415224\pi$
$464$	0.387882			0.0180069
$465$	−30.1956	−	42.7008i	−1.40029	−	1.98020i
$466$	−38.5432			−1.78548
$467$	−2.48538	−	1.80573i	−0.115010	−	0.0835594i	0.528794	−	0.848750i	$-0.322645\pi$
$467$	−2.48538	−	1.80573i	−0.115010	−	0.0835594i	−0.643803	+	0.765191i	$0.722645\pi$
$468$	−4.96861	+	3.60990i	−0.229674	+	0.166868i
$469$	0.0328161	+	0.100998i	0.00151531	+	0.00466364i
$470$	66.9485			3.08810
$471$	−41.7044			−1.92164
$472$	10.1007	+	31.0868i	0.464923	+	1.43089i
$473$	1.55301	−	4.77969i	0.0714077	−	0.219770i
$474$	−18.5676	+	57.1453i	−0.852840	+	2.62477i
$475$	−7.21427	−	5.24147i	−0.331013	−	0.240495i
$476$	−0.0635450	−	0.195571i	−0.00291258	−	0.00896399i
$477$	4.36659	+	3.17251i	0.199932	+	0.145259i
$478$	10.5927	−	7.69608i	0.484501	−	0.352010i
$479$	6.93379	−	21.3400i	0.316813	−	0.975050i	−0.658189	−	0.752853i	$-0.728677\pi$
$479$	6.93379	−	21.3400i	0.316813	−	0.975050i	0.975002	−	0.222197i	$-0.0713229\pi$
$480$	−44.0602	+	32.0116i	−2.01106	+	1.46112i
$481$	5.34037	−	3.88001i	0.243500	−	0.176913i
$482$	4.80754	−	14.7961i	0.218977	−	0.673943i
$483$	0.286358	−	0.208051i	0.0130298	−	0.00946667i
$484$	26.5486	+	19.2887i	1.20676	+	0.876759i
$485$	20.0360	+	61.6644i	0.909787	+	2.80004i
$486$	−32.0127	−	23.2586i	−1.45212	−	1.05503i
$487$	5.31005	−	16.3427i	0.240621	−	0.740557i	−0.755704	−	0.654913i	$-0.772705\pi$
$487$	5.31005	−	16.3427i	0.240621	−	0.740557i	0.996326	−	0.0856438i	$-0.0272947\pi$
$488$	−2.70645	+	8.32960i	−0.122515	+	0.377063i
$489$	−14.8652	−	45.7504i	−0.672227	−	2.06890i
$490$	−67.6569			−3.05643
$491$	33.6511			1.51865			0.759326	−	0.650710i	$-0.225529\pi$
$491$	33.6511			1.51865			0.759326	+	0.650710i	$0.225529\pi$
$492$	−22.6335	−	69.6586i	−1.02040	−	3.14045i
$493$	2.87902	−	2.09173i	0.129665	−	0.0942068i
$494$	−1.27101	−	0.923441i	−0.0571853	−	0.0415476i
$495$	7.12131			0.320079
$496$	−0.400421	−	0.566251i	−0.0179794	−	0.0254254i
$497$	−0.328008			−0.0147132
$498$	70.3345	+	51.1010i	3.15176	+	2.28989i
$499$	0.443997	−	0.322583i	0.0198761	−	0.0144408i	−0.577803	−	0.816176i	$-0.696090\pi$
$499$	0.443997	−	0.322583i	0.0198761	−	0.0144408i	0.597679	+	0.801736i	$0.296090\pi$
$500$	33.4075	+	102.818i	1.49403	+	4.59814i
$501$	19.0655			0.851784
$502$	−45.9605			−2.05132
$503$	−2.70559	−	8.32694i	−0.120636	−	0.371280i	0.872445	−	0.488713i	$-0.162533\pi$
$503$	−2.70559	−	8.32694i	−0.120636	−	0.371280i	−0.993081	+	0.117433i	$0.962533\pi$
$504$	−0.0914803	+	0.281547i	−0.00407486	+	0.0125411i
$505$	−12.7137	+	39.1288i	−0.565753	+	1.74121i
$506$	4.61394	+	3.35222i	0.205115	+	0.149024i
$507$	−0.685044	−	2.10835i	−0.0304239	−	0.0936351i
$508$	−22.7171	−	16.5049i	−1.00791	−	0.732287i
$509$	−35.3543	+	25.6864i	−1.56705	+	1.13853i	−0.637135	+	0.770752i	$0.719881\pi$
$509$	−35.3543	+	25.6864i	−1.56705	+	1.13853i	−0.929914	+	0.367776i	$0.880119\pi$
$510$	−7.57003	+	23.2981i	−0.335206	+	1.03166i
$511$	0.555995	−	0.403954i	0.0245958	−	0.0178699i
$512$	−1.13991	+	0.828193i	−0.0503774	+	0.0366013i
$513$	0.511957	−	1.57564i	0.0226035	−	0.0695663i
$514$	20.3835	−	14.8095i	0.899078	−	0.653218i
$515$	−3.86246	−	2.80624i	−0.170200	−	0.123658i
$516$	−12.5806	−	38.7191i	−0.553829	−	1.70451i
$517$	−4.91744	−	3.57273i	−0.216269	−	0.157129i
$518$	0.261110	−	0.803613i	0.0114725	−	0.0353087i
$519$	11.2255	−	34.5485i	0.492745	−	1.51651i
$520$	3.60972	+	11.1096i	0.158297	+	0.487187i
$521$	−2.27586			−0.0997071			−0.0498535	−	0.998757i	$-0.515875\pi$
$521$	−2.27586			−0.0997071			−0.0498535	+	0.998757i	$0.515875\pi$
$522$	−13.6048			−0.595466
$523$	−2.21433	−	6.81500i	−0.0968257	−	0.297999i	0.890899	−	0.454201i	$-0.150075\pi$
$523$	−2.21433	−	6.81500i	−0.0968257	−	0.297999i	−0.987725	+	0.156202i	$0.950075\pi$
$524$	−39.8013	+	28.9173i	−1.73873	+	1.26326i
$525$	−1.30306	−	0.946729i	−0.0568702	−	0.0413186i
$526$	29.7566			1.29745
$527$	−6.02572	−	2.04360i	−0.262484	−	0.0890208i
$528$	0.242420			0.0105500
$529$	12.0518	+	8.75616i	0.523992	+	0.380703i
$530$	22.0554	−	16.0242i	0.958025	−	0.696046i
$531$	7.01408	+	21.5871i	0.304385	+	0.936801i
$532$	−0.123875			−0.00537065
$533$	10.2989			0.446097
$534$	−3.09495	−	9.52528i	−0.133932	−	0.412199i
$535$	−18.5764	+	57.1722i	−0.803126	+	2.47177i
$536$	−1.61293	+	4.96409i	−0.0696681	+	0.214416i
$537$	31.9902	+	23.2422i	1.38048	+	1.00298i
$538$	18.6748	+	57.4751i	0.805128	+	2.47793i
$539$	4.96948	+	3.61054i	0.214051	+	0.155517i
$540$	−26.4648	+	19.2278i	−1.13886	+	0.827432i
$541$	−9.36908	+	28.8351i	−0.402808	+	1.23972i	0.519903	+	0.854225i	$0.325968\pi$
$541$	−9.36908	+	28.8351i	−0.402808	+	1.23972i	−0.922712	+	0.385491i	$0.874032\pi$
$542$	25.9145	−	18.8280i	1.11313	−	0.808733i
$543$	20.6152	−	14.9778i	0.884683	−	0.642760i
$544$	−2.04754	+	6.30167i	−0.0877875	+	0.270182i
$545$	35.3282	−	25.6674i	1.51329	−	1.09947i
$546$	−0.229573	−	0.166794i	−0.00982481	−	0.00713814i
$547$	−7.68086	−	23.6392i	−0.328410	−	1.01074i	−0.969878	−	0.243591i	$-0.921674\pi$
$547$	−7.68086	−	23.6392i	−0.328410	−	1.01074i	0.641468	−	0.767150i	$-0.278326\pi$
$548$	14.9119	+	10.8342i	0.637007	+	0.462813i
$549$	−1.87940	+	5.78420i	−0.0802108	+	0.246864i
$550$	8.01958	−	24.6817i	0.341956	−	1.05243i
$551$	−0.662450	−	2.03881i	−0.0282213	−	0.0868563i
$552$	17.3973			0.740476
$553$	−0.666179			−0.0283288
$554$	−10.3992	−	32.0054i	−0.441820	−	1.35978i
$555$	−50.1626	+	36.4453i	−2.12928	+	1.54702i
$556$	−1.25395	−	0.911048i	−0.0531793	−	0.0386370i
$557$	−30.5936			−1.29629			−0.648147	−	0.761515i	$-0.724456\pi$
$557$	−30.5936			−1.29629			−0.648147	+	0.761515i	$0.724456\pi$
$558$	14.0446	+	19.8610i	0.594555	+	0.840785i
$559$	5.72457			0.242123
$560$	−0.0239498	−	0.0174005i	−0.00101206	−	0.000735306i
$561$	1.79934	−	1.30730i	0.0759683	−	0.0551942i
$562$	−12.3747	−	38.0854i	−0.521995	−	1.60653i
$563$	27.7489			1.16948			0.584739	−	0.811221i	$-0.301197\pi$
$563$	27.7489			1.16948			0.584739	+	0.811221i	$0.301197\pi$
$564$	−49.2387			−2.07333
$565$	−11.1013	−	34.1664i	−0.467037	−	1.43739i
$566$	−11.0526	+	34.0163i	−0.464574	+	1.42981i
$567$	0.192019	−	0.590973i	0.00806402	−	0.0248185i
$568$	−13.0428	−	9.47615i	−0.547264	−	0.397611i
$569$	−9.22136	−	28.3804i	−0.386580	−	1.18977i	−0.935328	−	0.353782i	$-0.884895\pi$
$569$	−9.22136	−	28.3804i	−0.386580	−	1.18977i	0.548748	−	0.835988i	$-0.315105\pi$
$570$	11.9387	+	8.67397i	0.500057	+	0.363313i
$571$	9.31889	−	6.77057i	0.389983	−	0.283339i	−0.375465	−	0.926836i	$-0.622517\pi$
$571$	9.31889	−	6.77057i	0.389983	−	0.283339i	0.765449	+	0.643497i	$0.222517\pi$
$572$	0.870307	−	2.67853i	0.0363894	−	0.111995i
$573$	16.9901	−	12.3440i	0.709770	−	0.515678i
$574$	1.06654	−	0.774887i	0.0445165	−	0.0323432i
$575$	−11.3944	+	35.0682i	−0.475178	+	1.46245i
$576$	20.1075	−	14.6089i	0.837812	−	0.608706i
$577$	12.0639	+	8.76494i	0.502227	+	0.364889i	0.809867	−	0.586614i	$-0.199539\pi$
$577$	12.0639	+	8.76494i	0.502227	+	0.364889i	−0.307640	+	0.951503i	$0.599539\pi$
$578$	−11.0676	−	34.0626i	−0.460352	−	1.41682i
$579$	−10.5637	−	7.67500i	−0.439013	−	0.318962i
$580$	−13.0801	+	40.2565i	−0.543123	+	1.67156i
$581$	−0.297858	+	0.916713i	−0.0123572	+	0.0380317i
$582$	−23.9228	−	73.6267i	−0.991631	−	3.05193i
$583$	−2.47513			−0.102509
$584$	33.7786			1.39777
$585$	2.50664	+	7.71464i	0.103637	+	0.318961i
$586$	28.3603	−	20.6050i	1.17155	−	0.851183i
$587$	−6.81458	−	4.95108i	−0.281268	−	0.204353i	0.438202	−	0.898876i	$-0.355615\pi$
$587$	−6.81458	−	4.95108i	−0.281268	−	0.204353i	−0.719470	+	0.694523i	$0.755615\pi$
$588$	49.7598			2.05206
$589$	−2.29251	+	3.07181i	−0.0944612	+	0.126572i
$590$	114.646			4.71992
$591$	45.2290	+	32.8608i	1.86047	+	1.35171i
$592$	−0.665201	+	0.483297i	−0.0273396	+	0.0198634i
$593$	−0.385190	−	1.18549i	−0.0158179	−	0.0486824i	0.942836	−	0.333257i	$-0.108148\pi$
$593$	−0.385190	−	1.18549i	−0.0158179	−	0.0486824i	−0.958654	+	0.284575i	$0.908148\pi$
$594$	4.82154			0.197830
$595$	−0.271601			−0.0111346
$596$	−4.59340	−	14.1370i	−0.188153	−	0.579076i
$597$	−15.1834	+	46.7296i	−0.621414	+	1.91252i
$598$	−2.00746	+	6.17831i	−0.0820909	+	0.252650i
$599$	−29.2621	−	21.2601i	−1.19562	−	0.868666i	−0.201769	−	0.979433i	$-0.564669\pi$
$599$	−29.2621	−	21.2601i	−1.19562	−	0.868666i	−0.993846	+	0.110767i	$0.964669\pi$
$600$	−24.4635	−	75.2908i	−0.998717	−	3.07374i
$601$	−8.04420	−	5.84445i	−0.328130	−	0.238400i	0.411507	−	0.911407i	$-0.365003\pi$
$601$	−8.04420	−	5.84445i	−0.328130	−	0.238400i	−0.739637	+	0.673006i	$0.765003\pi$
$602$	0.592826	−	0.430713i	0.0241618	−	0.0175546i
$603$	−1.12004	+	3.44714i	−0.0456117	+	0.140378i
$604$	52.7009	−	38.2894i	2.14437	−	1.55798i
$605$	35.0651	−	25.4763i	1.42560	−	1.03576i
$606$	15.1801	−	46.7194i	0.616648	−	1.89785i
$607$	6.53318	−	4.74663i	0.265174	−	0.192660i	−0.447251	−	0.894408i	$-0.647597\pi$
$607$	6.53318	−	4.74663i	0.265174	−	0.192660i	0.712425	+	0.701748i	$0.247597\pi$
$608$	3.22917	+	2.34613i	0.130960	+	0.0951482i
$609$	−0.119654	−	0.368256i	−0.00484861	−	0.0149225i
$610$	24.8523	+	18.0563i	1.00624	+	0.731077i
$611$	2.13951	−	6.58472i	0.0865552	−	0.266389i
$612$	2.16885	−	6.67502i	0.0876704	−	0.269822i
$613$	8.59732	+	26.4598i	0.347243	+	1.06870i	0.960372	+	0.278721i	$0.0899103\pi$
$613$	8.59732	+	26.4598i	0.347243	+	1.06870i	−0.613130	+	0.789982i	$0.710090\pi$
$614$	−23.4280			−0.945477
$615$	−96.7390			−3.90089
$616$	−0.0419509	−	0.129111i	−0.00169025	−	0.00520205i
$617$	−12.2036	+	8.86644i	−0.491299	+	0.356949i	−0.805684	−	0.592346i	$-0.798202\pi$
$617$	−12.2036	+	8.86644i	−0.491299	+	0.356949i	0.314385	+	0.949296i	$0.398202\pi$
$618$	4.61174	+	3.35063i	0.185511	+	0.134782i
$619$	−39.8432			−1.60143			−0.800716	−	0.599044i	$-0.795547\pi$
$619$	−39.8432			−1.60143			−0.800716	+	0.599044i	$0.795547\pi$
$620$	72.2717	−	22.4628i	2.90250	−	0.902127i
$621$	−6.85053			−0.274902
$622$	−25.0690	−	18.2137i	−1.00518	−	0.730304i
$623$	0.0898350	−	0.0652689i	0.00359916	−	0.00261494i
$624$	0.0853297	+	0.262618i	0.00341592	+	0.0105131i
$625$	78.0220			3.12088
$626$	18.6636			0.745947
$627$	−0.414021	−	1.27423i	−0.0165344	−	0.0508877i
$628$	18.6495	−	57.3974i	0.744197	−	2.29040i
$629$	−2.33113	+	7.17447i	−0.0929481	+	0.286065i
$630$	0.840028	+	0.610316i	0.0334675	+	0.0243156i
$631$	−4.83412	−	14.8779i	−0.192443	−	0.592279i	−0.999997	−	0.00248504i	$-0.999209\pi$
$631$	−4.83412	−	14.8779i	−0.192443	−	0.592279i	0.807554	−	0.589794i	$-0.200791\pi$
$632$	−26.4897	−	19.2459i	−1.05370	−	0.765561i
$633$	5.67878	−	4.12588i	0.225711	−	0.163989i
$634$	−8.63340	+	26.5709i	−0.342876	+	1.05526i
$635$	−30.0044	+	21.7995i	−1.19069	+	0.865085i
$636$	−16.2211	+	11.7853i	−0.643209	+	0.467319i
$637$	−2.16215	+	6.65440i	−0.0856674	+	0.263657i
$638$	5.04734	−	3.66711i	0.199826	−	0.145182i
$639$	−9.05711	−	6.58038i	−0.358294	−	0.260316i
$640$	−23.6099	−	72.6637i	−0.933262	−	2.87228i
$641$	−30.1743	−	21.9229i	−1.19181	−	0.865902i	−0.198358	−	0.980130i	$-0.563561\pi$
$641$	−30.1743	−	21.9229i	−1.19181	−	0.865902i	−0.993455	+	0.114227i	$0.963561\pi$
$642$	22.1800	−	68.2630i	0.875375	−	2.69413i
$643$	−0.0333437	+	0.102621i	−0.00131495	+	0.00404699i	−0.951712	−	0.306993i	$-0.900677\pi$
$643$	−0.0333437	+	0.102621i	−0.00131495	+	0.00404699i	0.950397	+	0.311040i	$0.100677\pi$
$644$	0.158284	+	0.487149i	0.00623728	+	0.0191964i
$645$	−53.7714			−2.11725
$646$	1.79539			0.0706389
$647$	4.92705	+	15.1639i	0.193702	+	0.596154i	0.999989	+	0.00462953i	$0.00147363\pi$
$647$	4.92705	+	15.1639i	0.193702	+	0.596154i	−0.806287	+	0.591524i	$0.798526\pi$
$648$	24.7086	−	17.9518i	0.970644	−	0.705214i
$649$	−8.42092	−	6.11815i	−0.330550	−	0.240159i
$650$	29.5610			1.15948
$651$	−0.414079	+	0.554838i	−0.0162290	+	0.0217458i
$652$	69.6132			2.72626
$653$	−21.9982	−	15.9826i	−0.860856	−	0.625448i	0.0672620	−	0.997735i	$-0.478574\pi$
$653$	−21.9982	−	15.9826i	−0.860856	−	0.625448i	−0.928118	+	0.372287i	$0.878574\pi$
$654$	−42.1815	+	30.6466i	−1.64943	+	1.19838i
$655$	20.0796	+	61.7985i	0.784573	+	2.41467i
$656$	−1.28285			−0.0500867
$657$	23.4564			0.915120
$658$	−0.273867	−	0.842877i	−0.0106765	−	0.0328588i
$659$	−5.64207	+	17.3645i	−0.219784	+	0.676426i	0.778995	+	0.627030i	$0.215730\pi$
$659$	−5.64207	+	17.3645i	−0.219784	+	0.676426i	−0.998779	+	0.0493958i	$0.984270\pi$
$660$	−8.17488	+	25.1597i	−0.318207	+	0.979339i
$661$	−3.46835	−	2.51990i	−0.134903	−	0.0980129i	0.518287	−	0.855207i	$-0.326570\pi$
$661$	−3.46835	−	2.51990i	−0.134903	−	0.0980129i	−0.653190	+	0.757194i	$0.726570\pi$
$662$	10.9344	+	33.6526i	0.424977	+	1.30795i
$663$	2.04957	+	1.48910i	0.0795988	+	0.0578319i
$664$	−38.3278	+	27.8467i	−1.48741	+	1.08066i
$665$	−0.0505589	+	0.155604i	−0.00196059	+	0.00603408i
$666$	23.3317	−	16.9515i	0.904084	−	0.656855i
$667$	−7.17136	+	5.21030i	−0.277676	+	0.201744i
$668$	−8.52579	+	26.2397i	−0.329873	+	1.01524i
$669$	−1.26860	+	0.921690i	−0.0490468	+	0.0356346i
$670$	14.8109	+	10.7608i	0.572197	+	0.415725i
$671$	−0.861852	−	2.65251i	−0.0332714	−	0.102399i
$672$	0.583262	+	0.423765i	0.0224998	+	0.0163471i
$673$	−5.17510	+	15.9273i	−0.199486	+	0.613953i	0.800409	+	0.599454i	$0.204615\pi$
$673$	−5.17510	+	15.9273i	−0.199486	+	0.613953i	−0.999895	+	0.0144995i	$0.995385\pi$
$674$	−2.09213	+	6.43891i	−0.0805857	+	0.248017i
$675$	9.63300	+	29.6473i	0.370775	+	1.14113i
$676$	3.20804			0.123386
$677$	27.4409			1.05464			0.527320	−	0.849667i	$-0.323197\pi$
$677$	27.4409			1.05464			0.527320	+	0.849667i	$0.323197\pi$
$678$	13.2549	+	40.7944i	0.509051	+	1.56670i
$679$	0.694390	−	0.504504i	0.0266482	−	0.0193611i
$680$	−10.7999	−	7.84655i	−0.414155	−	0.300902i
$681$	22.3415			0.856130
$682$	−10.5640	−	3.58274i	−0.404515	−	0.137190i
$683$	−19.3310			−0.739682			−0.369841	−	0.929095i	$-0.620588\pi$
$683$	−19.3310			−0.739682			−0.369841	+	0.929095i	$0.620588\pi$
$684$	−3.42049	−	2.48513i	−0.130786	−	0.0950213i
$685$	19.6955	−	14.3096i	0.752526	−	0.546742i
$686$	0.553655	+	1.70398i	0.0211387	+	0.0650581i
$687$	29.6468			1.13110
$688$	−0.713057			−0.0271850
$689$	−0.871224	−	2.68135i	−0.0331910	−	0.102151i
$690$	18.8562	−	58.0334i	0.717844	−	2.20930i
$691$	−1.68080	+	5.17298i	−0.0639407	+	0.196789i	−0.977923	−	0.208964i	$-0.932991\pi$
$691$	−1.68080	+	5.17298i	−0.0639407	+	0.196789i	0.913983	+	0.405753i	$0.132991\pi$
$692$	42.5289	+	30.8991i	1.61671	+	1.17461i
$693$	−0.0291313	−	0.0896569i	−0.00110661	−	0.00340578i
$694$	25.8875	+	18.8083i	0.982674	+	0.713955i
$695$	−1.65620	+	1.20330i	−0.0628233	+	0.0456438i
$696$	5.88104	−	18.1000i	0.222920	−	0.686078i
$697$	−9.52182	+	6.91800i	−0.360665	+	0.262038i
$698$	−59.9665	+	43.5682i	−2.26976	+	1.64908i
$699$	11.5699	−	35.6085i	0.437614	−	1.34684i
$700$	1.88568	−	1.37003i	0.0712721	−	0.0517822i
$701$	29.9520	+	21.7614i	1.13127	+	0.821917i	0.985879	−	0.167457i	$-0.0535555\pi$
$701$	29.9520	+	21.7614i	1.13127	+	0.821917i	0.145393	+	0.989374i	$0.453555\pi$
$702$	1.69714	+	5.22326i	0.0640544	+	0.197139i
$703$	3.67642	+	2.67107i	0.138659	+	0.100741i
$704$	−3.52205	+	10.8398i	−0.132742	+	0.408539i
$705$	−20.0966	+	61.8509i	−0.756881	+	2.32944i
$706$	−5.42362	−	16.6922i	−0.204121	−	0.628219i
$707$	0.544638			0.0204832
$708$	−84.3193			−3.16891
$709$	−7.11030	−	21.8832i	−0.267033	−	0.821842i	−0.991218	−	0.132237i	$-0.957784\pi$
$709$	−7.11030	−	21.8832i	−0.267033	−	0.821842i	0.724185	−	0.689605i	$-0.242216\pi$
$710$	−45.7470	+	33.2371i	−1.71685	+	1.24737i
$711$	−18.3948	−	13.3646i	−0.689860	−	0.501213i
$712$	5.45779			0.204539
$713$	15.0095	+	5.09042i	0.562110	+	0.190638i
$714$	0.324289			0.0121362
$715$	−3.00941	−	2.18646i	−0.112545	−	0.0817690i
$716$	−46.2936	+	33.6342i	−1.73007	+	1.25697i
$717$	3.93036	+	12.0964i	0.146782	+	0.451748i
$718$	63.1109			2.35528
$719$	17.5801			0.655628			0.327814	−	0.944742i	$-0.393688\pi$
$719$	17.5801			0.655628			0.327814	+	0.944742i	$0.393688\pi$
$720$	−0.312229	−	0.960943i	−0.0116361	−	0.0358122i
$721$	−0.0195302	+	0.0601077i	−0.000727342	+	0.00223853i
$722$	−13.0648	+	40.2093i	−0.486222	+	1.49644i
$723$	12.2264	+	8.88297i	0.454703	+	0.330361i
$724$	11.3950	+	35.0703i	0.423493	+	1.30338i
$725$	32.6330	+	23.7092i	1.21196	+	0.880539i
$726$	−41.8674	+	30.4184i	−1.55384	+	1.12893i
$727$	4.58624	−	14.1150i	0.170094	−	0.523496i	−0.829281	−	0.558832i	$-0.811250\pi$
$727$	4.58624	−	14.1150i	0.170094	−	0.523496i	0.999376	+	0.0353351i	$0.0112498\pi$
$728$	0.125102	−	0.0908922i	0.00463660	−	0.00336869i
$729$	4.20967	−	3.05850i	0.155914	−	0.113278i
$730$	36.6114	−	112.678i	1.35505	−	4.17041i
$731$	−5.29261	+	3.84530i	−0.195754	+	0.142224i
$732$	−18.2782	−	13.2799i	−0.675581	−	0.490839i
$733$	4.26034	+	13.1120i	0.157359	+	0.484302i	0.998392	−	0.0566820i	$-0.0180521\pi$
$733$	4.26034	+	13.1120i	0.157359	+	0.484302i	−0.841033	+	0.540984i	$0.818052\pi$
$734$	25.1042	+	18.2392i	0.926611	+	0.673223i
$735$	20.3092	−	62.5054i	0.749118	−	2.30555i
$736$	5.10022	−	15.6969i	0.187997	−	0.578594i
$737$	−0.513628	−	1.58078i	−0.0189197	−	0.0582289i
$738$	44.9953			1.65630
$739$	23.3186			0.857789			0.428895	−	0.903355i	$-0.358903\pi$
$739$	23.3186			0.857789			0.428895	+	0.903355i	$0.358903\pi$
$740$	−27.7274	−	85.3360i	−1.01928	−	3.13701i
$741$	1.23466	−	0.897033i	0.0453563	−	0.0329533i
$742$	−0.291966	−	0.212125i	−0.0107184	−	0.00778737i
$743$	−5.54064			−0.203266			−0.101633	−	0.994822i	$-0.532407\pi$
$743$	−5.54064			−0.203266			−0.101633	+	0.994822i	$0.532407\pi$
$744$	−32.4946	+	10.0996i	−1.19131	+	0.370271i
$745$	−19.6329			−0.719295
$746$	11.8676	+	8.62234i	0.434505	+	0.315686i
$747$	−26.6153	+	19.3372i	−0.973805	+	0.707511i
$748$	0.994585	+	3.06102i	0.0363656	+	0.111922i
$749$	0.795784			0.0290773
$750$	−170.488			−6.22535
$751$	4.99939	+	15.3865i	0.182430	+	0.561463i	0.999895	−	0.0145164i	$-0.00462087\pi$
$751$	4.99939	+	15.3865i	0.182430	+	0.561463i	−0.817464	+	0.575979i	$0.804621\pi$
$752$	−0.266499	+	0.820199i	−0.00971821	+	0.0299096i
$753$	13.7964	−	42.4610i	0.502769	−	1.54737i
$754$	5.74927	+	4.17709i	0.209376	+	0.152121i
$755$	−26.5874	−	81.8275i	−0.967613	−	2.97801i
$756$	0.350336	+	0.254534i	0.0127416	+	0.00925732i
$757$	−19.4681	+	14.1444i	−0.707579	+	0.514086i	−0.882392	−	0.470516i	$-0.844068\pi$
$757$	−19.4681	+	14.1444i	−0.707579	+	0.514086i	0.174813	+	0.984602i	$0.444068\pi$
$758$	−3.53904	+	10.8921i	−0.128544	+	0.395617i
$759$	−4.48199	+	3.25635i	−0.162686	+	0.118198i
$760$	−6.50582	+	4.72675i	−0.235991	+	0.171457i
$761$	3.21289	−	9.88824i	0.116467	−	0.358449i	−0.875783	−	0.482705i	$-0.839654\pi$
$761$	3.21289	−	9.88824i	0.116467	−	0.358449i	0.992250	+	0.124256i	$0.0396544\pi$
$762$	35.8249	−	26.0283i	1.29780	−	0.942908i
$763$	−0.467669	−	0.339781i	−0.0169307	−	0.0123009i
$764$	9.39124	+	28.9033i	0.339763	+	1.04568i
$765$	−7.49957	−	5.44876i	−0.271148	−	0.197000i
$766$	−23.4823	+	72.2711i	−0.848450	+	2.61126i
$767$	3.66381	−	11.2761i	0.132293	−	0.407155i
$768$	10.4026	+	32.0159i	0.375371	+	1.15527i
$769$	43.8645			1.58179			0.790897	−	0.611950i	$-0.209615\pi$
$769$	43.8645			1.58179			0.790897	+	0.611950i	$0.209615\pi$
$770$	−0.476157			−0.0171595
$771$	7.56315	+	23.2770i	0.272380	+	0.838300i
$772$	15.2869	−	11.1066i	0.550189	−	0.399736i
$773$	−44.1816	−	32.0998i	−1.58910	−	1.15455i	−0.905207	−	0.424971i	$-0.860284\pi$
$773$	−44.1816	−	32.0998i	−1.58910	−	1.15455i	−0.683896	−	0.729579i	$-0.739716\pi$
$774$	25.0102			0.898973
$775$	0.924174	−	72.1151i	0.0331973	−	2.59045i
$776$	42.1866			1.51441
$777$	0.664045	+	0.482457i	0.0238225	+	0.0173080i
$778$	47.5540	−	34.5500i	1.70489	−	1.23868i
$779$	2.19093	+	6.74299i	0.0784982	+	0.241593i
$780$	−30.1334			−1.07895
$781$	5.13388			0.183705
$782$	−2.29412	−	7.06056i	−0.0820374	−	0.252485i
$783$	−2.31578	+	7.12725i	−0.0827594	+	0.254707i
$784$	0.269319	−	0.828878i	0.00961853	−	0.0296028i
$785$	−64.4876	−	46.8530i	−2.30166	−	1.67225i
$786$	−23.9748	−	73.7869i	−0.855153	−	2.63189i
$787$	5.20723	+	3.78327i	0.185618	+	0.134859i	0.676714	−	0.736246i	$-0.263404\pi$
$787$	5.20723	+	3.78327i	0.185618	+	0.134859i	−0.491096	+	0.871105i	$0.663404\pi$
$788$	−65.4517	+	47.5534i	−2.33162	+	1.69402i
$789$	−8.93232	+	27.4908i	−0.317999	+	0.978700i
$790$	−92.9113	+	67.5040i	−3.30564	+	2.40168i
$791$	−0.384740	+	0.279530i	−0.0136798	+	0.00993895i
$792$	1.43182	−	4.40669i	0.0508775	−	0.156585i
$793$	2.57014	−	1.86732i	0.0912685	−	0.0663104i
$794$	−22.2853	−	16.1912i	−0.790877	−	0.574606i
$795$	8.18349	+	25.1862i	0.290238	+	0.893262i
$796$	−57.5238	−	41.7935i	−2.03888	−	1.48133i
$797$	−15.4512	+	47.5538i	−0.547308	+	1.68444i	0.168130	+	0.985765i	$0.446227\pi$
$797$	−15.4512	+	47.5538i	−0.547308	+	1.68444i	−0.715438	+	0.698676i	$0.753773\pi$
$798$	0.0603669	−	0.185790i	0.00213696	−	0.00657690i
$799$	2.44502	+	7.52501i	0.0864987	+	0.266216i
$800$	−75.1037			−2.65532
$801$	3.78997			0.133912
$802$	16.4545	+	50.6419i	0.581030	+	1.78823i
$803$	−8.70226	+	6.32256i	−0.307096	+	0.223118i
$804$	−10.8930	−	7.91425i	−0.384168	−	0.279114i
$805$	0.676532			0.0238446
$806$	0.162821	−	12.7052i	0.00573512	−	0.447522i
$807$	−58.7047			−2.06650
$808$	21.6568	+	15.7346i	0.761883	+	0.553541i
$809$	−0.185157	+	0.134525i	−0.00650978	+	0.00472963i	−0.591035	−	0.806646i	$-0.701281\pi$
$809$	−0.185157	+	0.134525i	−0.00650978	+	0.00472963i	0.584526	+	0.811375i	$0.301281\pi$
$810$	−33.1027	−	101.880i	−1.16311	−	3.57969i
$811$	31.1339			1.09326			0.546630	−	0.837375i	$-0.315911\pi$
$811$	31.1339			1.09326			0.546630	+	0.837375i	$0.315911\pi$
$812$	0.560334			0.0196639
$813$	9.61540	+	29.5932i	0.337227	+	1.03788i
$814$	−4.08681	+	12.5779i	−0.143242	+	0.440855i
$815$	28.4123	−	87.4442i	0.995240	−	3.06304i
$816$	−0.255296	−	0.185484i	−0.00893716	−	0.00649323i
$817$	1.21781	+	3.74802i	0.0426057	+	0.131127i
$818$	−37.5086	−	27.2516i	−1.31146	−	0.952830i
$819$	0.0868729	−	0.0631169i	0.00303559	−	0.00220548i
$820$	43.2601	−	133.141i	1.51071	−	4.64948i
$821$	25.9965	−	18.8876i	0.907285	−	0.659181i	−0.0330415	−	0.999454i	$-0.510519\pi$
$821$	25.9965	−	18.8876i	0.907285	−	0.659181i	0.940327	+	0.340273i	$0.110519\pi$
$822$	−23.5162	+	17.0855i	−0.820223	+	0.595927i
$823$	−12.1884	+	37.5121i	−0.424862	+	1.30759i	0.478264	+	0.878216i	$0.341266\pi$
$823$	−12.1884	+	37.5121i	−0.424862	+	1.30759i	−0.903126	+	0.429375i	$0.858734\pi$
$824$	−2.51310	+	1.82588i	−0.0875480	+	0.0636074i
$825$	20.3951	+	14.8179i	0.710066	+	0.515893i
$826$	−0.468986	−	1.44339i	−0.0163181	−	0.0502220i
$827$	6.28566	+	4.56680i	0.218574	+	0.158803i	0.691685	−	0.722200i	$-0.256869\pi$
$827$	6.28566	+	4.56680i	0.218574	+	0.158803i	−0.473111	+	0.881003i	$0.656869\pi$
$828$	−5.40239	+	16.6268i	−0.187746	+	0.577822i
$829$	−5.41073	+	16.6525i	−0.187922	+	0.578366i	−0.999986	−	0.00520247i	$-0.998344\pi$
$829$	−5.41073	+	16.6525i	−0.187922	+	0.578366i	0.812064	+	0.583568i	$0.198344\pi$
$830$	51.3487	+	158.035i	1.78234	+	5.48548i
$831$	32.6901			1.13401
$832$	−12.9826			−0.450092
$833$	−2.47090	−	7.60464i	−0.0856115	−	0.263485i
$834$	1.97749	−	1.43673i	0.0684748	−	0.0497498i
$835$	29.4810	+	21.4192i	1.02023	+	0.741243i
$836$	1.93885			0.0670565
$837$	12.7954	−	3.97694i	0.442274	−	0.137463i
$838$	−48.7319			−1.68342
$839$	39.0020	+	28.3366i	1.34650	+	0.978290i	0.999178	+	0.0405440i	$0.0129091\pi$
$839$	39.0020	+	28.3366i	1.34650	+	0.978290i	0.347323	+	0.937746i	$0.387091\pi$
$840$	−1.17510	+	0.853759i	−0.0405447	+	0.0294575i
$841$	−5.96497	−	18.3583i	−0.205689	−	0.633045i
$842$	−0.562806			−0.0193956
$843$	38.9001			1.33979
$844$	3.13895	+	9.66068i	0.108047	+	0.332534i
$845$	1.30935	−	4.02976i	0.0450429	−	0.138628i
$846$	9.34733	−	28.7681i	0.321368	−	0.989069i
$847$	−0.464186	−	0.337251i	−0.0159496	−	0.0115881i
$848$	0.108520	+	0.333991i	0.00372660	+	0.0114693i
$849$	−28.1085	−	20.4220i	−0.964680	−	0.700881i
$850$	−27.3304	+	19.8567i	−0.937424	+	0.681078i
$851$	5.80661	−	17.8709i	0.199048	−	0.612607i
$852$	33.6456	−	24.4450i	1.15268	−	0.837471i
$853$	−0.498550	+	0.362218i	−0.0170700	+	0.0124021i	−0.596288	−	0.802771i	$-0.703358\pi$
$853$	−0.498550	+	0.362218i	−0.0170700	+	0.0124021i	0.579218	+	0.815173i	$0.303358\pi$
$854$	0.125663	−	0.386752i	0.00430011	−	0.0132344i
$855$	−4.51773	+	3.28233i	−0.154503	+	0.112253i
$856$	31.6433	+	22.9902i	1.08155	+	0.785789i
$857$	−10.7069	−	32.9526i	−0.365742	−	1.12564i	−0.949515	−	0.313721i	$-0.898424\pi$
$857$	−10.7069	−	32.9526i	−0.365742	−	1.12564i	0.583773	−	0.811917i	$-0.301576\pi$
$858$	3.59320	+	2.61061i	0.122670	+	0.0891249i
$859$	−3.74740	+	11.5333i	−0.127860	+	0.393512i	−0.994411	−	0.105576i	$-0.966331\pi$
$859$	−3.74740	+	11.5333i	−0.127860	+	0.393512i	0.866552	+	0.499088i	$0.166331\pi$
$860$	24.0457	−	74.0050i	0.819951	−	2.52355i
$861$	0.395732	+	1.21794i	0.0134865	+	0.0415072i
$862$	34.2620			1.16697
$863$	41.3296			1.40688			0.703438	−	0.710757i	$-0.251647\pi$
$863$	41.3296			1.40688			0.703438	+	0.710757i	$0.251647\pi$
$864$	−4.31182	−	13.2704i	−0.146691	−	0.451469i
$865$	56.1717	−	40.8111i	1.90989	−	1.38762i
$866$	4.56024	+	3.31321i	0.154963	+	0.112587i
$867$	34.7913			1.18157
$868$	−0.578448	−	0.818007i	−0.0196338	−	0.0277650i
$869$	10.4268			0.353706
$870$	−54.0034	−	39.2358i	−1.83089	−	1.33022i
$871$	1.53170	−	1.11284i	0.0518996	−	0.0377073i
$872$	−8.77994	−	27.0219i	−0.297326	−	0.915076i
$873$	29.2950			0.991484
$874$	−4.47216			−0.151273
$875$	−0.584108	−	1.79770i	−0.0197465	−	0.0607734i
$876$	−26.9266	+	82.8716i	−0.909767	+	2.79997i
$877$	1.03942	−	3.19902i	0.0350989	−	0.108023i	−0.931972	−	0.362530i	$-0.881913\pi$
$877$	1.03942	−	3.19902i	0.0350989	−	0.108023i	0.967071	+	0.254507i	$0.0819131\pi$
$878$	33.7571	+	24.5260i	1.13925	+	0.827712i
$879$	10.5229	+	32.3861i	0.354928	+	1.09236i
$880$	0.374854	+	0.272347i	0.0126363	+	0.00918083i
$881$	40.9248	−	29.7336i	1.37879	−	1.00175i	0.381800	−	0.924245i	$-0.375304\pi$
$881$	40.9248	−	29.7336i	1.37879	−	1.00175i	0.996992	−	0.0775055i	$-0.0246955\pi$
$882$	−9.44625	+	29.0726i	−0.318072	+	0.978924i
$883$	−29.6000	+	21.5057i	−0.996120	+	0.723723i	−0.961253	−	0.275668i	$-0.911101\pi$
$883$	−29.6000	+	21.5057i	−0.996120	+	0.723723i	−0.0348671	+	0.999392i	$0.511101\pi$
$884$	−2.96597	+	2.15490i	−0.0997564	+	0.0724772i
$885$	−34.4145	+	105.917i	−1.15683	+	3.56036i
$886$	−59.4117	+	43.1652i	−1.99598	+	1.45016i
$887$	−30.6577	−	22.2741i	−1.02938	−	0.747891i	−0.0611982	−	0.998126i	$-0.519492\pi$
$887$	−30.6577	−	22.2741i	−1.02938	−	0.747891i	−0.968185	+	0.250235i	$0.919492\pi$
$888$	12.4667	+	38.3685i	0.418354	+	1.28756i
$889$	0.397193	+	0.288578i	0.0133214	+	0.00967859i
$890$	5.91548	−	18.2060i	0.198287	−	0.610266i
$891$	−3.00541	+	9.24971i	−0.100685	+	0.309877i
$892$	−0.701217	−	2.15812i	−0.0234785	−	0.0722593i
$893$	4.76634			0.159499
$894$	23.4415			0.784002
$895$	23.3549	+	71.8790i	0.780668	+	2.40265i
$896$	−0.818250	+	0.594493i	−0.0273358	+	0.0198606i
$897$	−5.10529	−	3.70921i	−0.170461	−	0.123847i
$898$	−39.1397			−1.30611
$899$	10.3699	−	13.8950i	0.345856	−	0.463423i
$900$	79.5533			2.65178
$901$	2.60660	+	1.89381i	0.0868384	+	0.0630918i
$902$	−16.6931	+	12.1283i	−0.555821	+	0.403828i
$903$	0.219964	+	0.676978i	0.00731993	+	0.0225284i
$904$	−23.3743			−0.777418
$905$	48.7042			1.61898
$906$	31.7451	+	97.7013i	1.05466	+	3.24591i
$907$	−3.96344	+	12.1982i	−0.131604	+	0.405035i	−0.995046	−	0.0994124i	$-0.968304\pi$
$907$	−3.96344	+	12.1982i	−0.131604	+	0.405035i	0.863443	+	0.504447i	$0.168304\pi$
$908$	−9.99078	+	30.7484i	−0.331556	+	1.02042i
$909$	15.0388	+	10.9263i	0.498805	+	0.362403i
$910$	−0.167603	−	0.515829i	−0.00555598	−	0.0170996i
$911$	15.6570	+	11.3755i	0.518739	+	0.376886i	0.816129	−	0.577870i	$-0.196116\pi$
$911$	15.6570	+	11.3755i	0.518739	+	0.376886i	−0.297389	+	0.954756i	$0.596116\pi$
$912$	−0.153790	+	0.111735i	−0.00509250	+	0.00369992i
$913$	4.66198	−	14.3481i	0.154289	−	0.474853i
$914$	2.71905	−	1.97551i	0.0899383	−	0.0653440i
$915$	−24.1416	+	17.5399i	−0.798097	+	0.579851i
$916$	−13.2576	+	40.8026i	−0.438042	+	1.34816i
$917$	0.695900	−	0.505601i	0.0229806	−	0.0166964i
$918$	−5.07764	−	3.68912i	−0.167587	−	0.121759i
$919$	−2.50349	−	7.70495i	−0.0825825	−	0.254163i	0.901237	−	0.433327i	$-0.142661\pi$
$919$	−2.50349	−	7.70495i	−0.0825825	−	0.254163i	−0.983819	+	0.179164i	$0.942661\pi$
$920$	26.9014	+	19.5450i	0.886913	+	0.644380i
$921$	7.03261	−	21.6441i	0.231732	−	0.713199i
$922$	0.0271062	−	0.0834242i	0.000892694	−	0.00274743i
$923$	1.80708	+	5.56162i	0.0594808	+	0.183063i
$924$	0.350200			0.0115207
$925$	−85.5057			−2.81141
$926$	−23.6717	−	72.8540i	−0.777900	−	2.39413i
$927$	−1.74513	+	1.26791i	−0.0573177	+	0.0416438i
$928$	−14.6068	−	10.6125i	−0.479492	−	0.348371i
$929$	40.0028			1.31245			0.656224	−	0.754566i	$-0.272153\pi$
$929$	40.0028			1.31245			0.656224	+	0.754566i	$0.272153\pi$
$930$	−1.52939	+	119.341i	−0.0501507	+	3.91336i
$931$	−4.81677			−0.157863
$932$	43.8337	+	31.8471i	1.43582	+	1.04318i
$933$	24.3521	−	17.6928i	0.797252	−	0.579238i
$934$	2.16648	+	6.66774i	0.0708894	+	0.218175i
$935$	4.25101			0.139023
$936$	5.27783			0.172511
$937$	1.21410	+	3.73660i	0.0396628	+	0.122069i	0.968927	−	0.247345i	$-0.0795582\pi$
$937$	1.21410	+	3.73660i	0.0396628	+	0.122069i	−0.929265	+	0.369415i	$0.879558\pi$
$938$	0.0748901	−	0.230488i	0.00244525	−	0.00752570i
$939$	−5.60243	+	17.2425i	−0.182828	+	0.562688i
$940$	−76.1379	−	55.3174i	−2.48335	−	1.80426i
$941$	−16.9431	−	52.1456i	−0.552330	−	1.69990i	−0.702893	−	0.711296i	$-0.748109\pi$
$941$	−16.9431	−	52.1456i	−0.552330	−	1.69990i	0.150563	−	0.988600i	$-0.451891\pi$
$942$	76.9975	+	55.9420i	2.50871	+	1.82269i
$943$	23.7179	−	17.2321i	0.772362	−	0.561154i
$944$	−0.456368	+	1.40456i	−0.0148535	+	0.0457144i
$945$	0.462720	−	0.336185i	0.0150523	−	0.0109361i
$946$	−9.27872	+	6.74138i	−0.301677	+	0.219181i
$947$	−0.246950	+	0.760035i	−0.00802481	+	0.0246978i	−0.954989	−	0.296642i	$-0.904133\pi$
$947$	−0.246950	+	0.760035i	−0.00802481	+	0.0246978i	0.946964	+	0.321340i	$0.104133\pi$
$948$	68.3337	−	49.6473i	2.21937	−	1.61247i
$949$	−9.91246	−	7.20182i	−0.321772	−	0.233781i
$950$	6.28860	+	19.3543i	0.204029	+	0.627937i
$951$	−21.9561	−	15.9521i	−0.711977	−	0.517281i
$952$	−0.0546084	+	0.168067i	−0.00176987	+	0.00544710i
$953$	−5.75676	+	17.7175i	−0.186480	+	0.573926i	−0.999971	−	0.00765173i	$-0.997564\pi$
$953$	−5.75676	+	17.7175i	−0.186480	+	0.573926i	0.813491	+	0.581578i	$0.197564\pi$
$954$	−3.80631	−	11.7146i	−0.123234	−	0.379275i
$955$	40.1396			1.29889
$956$	−18.4057			−0.595284
$957$	1.87278	+	5.76382i	0.0605384	+	0.186318i
$958$	−41.4270	+	30.0985i	−1.33845	+	0.972437i
$959$	−0.260726	−	0.189428i	−0.00841928	−	0.00611696i
$960$	121.947			3.93582
$961$	−30.9898	−	0.794415i	−0.999672	−	0.0256263i
$962$	−15.0644			−0.485695
$963$	21.9736	+	15.9647i	0.708088	+	0.514456i
$964$	−17.6930	+	12.8547i	−0.569852	+	0.414022i
$965$	−7.71220	−	23.7357i	−0.248264	−	0.764079i
$966$	−0.807773			−0.0259897
$967$	19.6077			0.630540			0.315270	−	0.949002i	$-0.397905\pi$
$967$	19.6077			0.630540			0.315270	+	0.949002i	$0.397905\pi$
$968$	−8.71456	−	26.8207i	−0.280097	−	0.862049i
$969$	−0.538941	+	1.65869i	−0.0173133	+	0.0532848i
$970$	45.7244	−	140.725i	1.46812	−	4.51841i
$971$	−10.6907	−	7.76724i	−0.343080	−	0.249262i	0.402880	−	0.915253i	$-0.368009\pi$
$971$	−10.6907	−	7.76724i	−0.343080	−	0.249262i	−0.745960	+	0.665990i	$0.768009\pi$
$972$	17.1889	+	52.9021i	0.551336	+	1.69684i
$973$	0.0219245	+	0.0159291i	0.000702868	+	0.000510663i
$974$	−31.7257	+	23.0501i	−1.01656	+	0.738572i
$975$	−8.87360	+	27.3101i	−0.284183	+	0.874624i
$976$	−0.320139	+	0.232595i	−0.0102474	+	0.00744518i
$977$	23.0276	−	16.7305i	0.736719	−	0.535257i	−0.154963	−	0.987920i	$-0.549526\pi$
$977$	23.0276	−	16.7305i	0.736719	−	0.535257i	0.891682	+	0.452663i	$0.149526\pi$
$978$	−33.9240	+	104.407i	−1.08477	+	3.33858i
$979$	−1.40607	+	1.02157i	−0.0449381	+	0.0326495i
$980$	76.9436	+	55.9028i	2.45787	+	1.78575i
$981$	−6.09692	−	18.7644i	−0.194660	−	0.599101i
$982$	−62.1289	−	45.1393i	−1.98261	−	1.44045i
$983$	−13.7502	+	42.3186i	−0.438562	+	1.34975i	0.450831	+	0.892610i	$0.351128\pi$
$983$	−13.7502	+	42.3186i	−0.438562	+	1.34975i	−0.889392	+	0.457145i	$0.848872\pi$
$984$	−19.4504	+	59.8623i	−0.620058	+	1.90834i
$985$	33.0201	+	101.625i	1.05211	+	3.23806i
$986$	−8.12127			−0.258634
$987$	0.860908			0.0274030
$988$	0.682457	+	2.10039i	0.0217119	+	0.0668222i
$989$	13.1834	−	9.57828i	0.419207	−	0.304572i
$990$	−13.1479	−	9.55248i	−0.417866	−	0.303598i
$991$	29.7191			0.944060			0.472030	−	0.881583i	$-0.343521\pi$
$991$	29.7191			0.944060			0.472030	+	0.881583i	$0.343521\pi$
$992$	−0.413669	+	32.2794i	−0.0131340	+	1.02487i
$993$	−34.3725			−1.09078
$994$	0.605591	+	0.439988i	0.0192082	+	0.0139556i
$995$	−75.9766	+	55.2003i	−2.40862	+	1.74997i
$996$	−37.7655	−	116.230i	−1.19665	−	3.68290i
$997$	39.7949			1.26032			0.630159	−	0.776466i	$-0.282990\pi$
$997$	39.7949			1.26032			0.630159	+	0.776466i	$0.282990\pi$
$998$	−1.25245			−0.0396456
$999$	−4.90902	−	15.1084i	−0.155314	−	0.478008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.e.157.3	✓	68
31.16	even	5	inner	403.2.k.e.326.3	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.e.157.3	✓	68	1.1	even	1	trivial
403.2.k.e.326.3	yes	68	31.16	even	5	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.84627 - 1.34139i) q^{2} +(1.79347 - 1.30303i) q^{3} +(0.991339 + 3.05103i) q^{4} +4.23714 q^{5} -5.05910 q^{6} +(-0.0173329 - 0.0533453i) q^{7} +(0.851924 - 2.62195i) q^{8} +(0.591588 - 1.82072i) q^{9} +O(q^{10})\)	\(q+(-1.84627 - 1.34139i) q^{2} +(1.79347 - 1.30303i) q^{3} +(0.991339 + 3.05103i) q^{4} +4.23714 q^{5} -5.05910 q^{6} +(-0.0173329 - 0.0533453i) q^{7} +(0.851924 - 2.62195i) q^{8} +(0.591588 - 1.82072i) q^{9} +(-7.82289 - 5.68366i) q^{10} +(0.271289 + 0.834943i) q^{11} +(5.75352 + 4.18018i) q^{12} +(-0.809017 + 0.587785i) q^{13} +(-0.0395557 + 0.121740i) q^{14} +(7.59917 - 5.52112i) q^{15} +(0.100772 - 0.0732150i) q^{16} +(0.353144 - 1.08687i) q^{17} +(-3.53453 + 2.56799i) q^{18} +(-0.556943 - 0.404643i) q^{19} +(4.20044 + 12.9276i) q^{20} +(-0.100597 - 0.0730877i) q^{21} +(0.619113 - 1.90543i) q^{22} +(-0.879648 + 2.70728i) q^{23} +(-1.88859 - 5.81247i) q^{24} +12.9533 q^{25} +2.28211 q^{26} +(0.743670 + 2.28878i) q^{27} +(0.145575 - 0.105766i) q^{28} +(2.51927 + 1.83036i) q^{29} -21.4361 q^{30} +(0.0713465 - 5.56731i) q^{31} -5.79803 q^{32} +(1.57451 + 1.14395i) q^{33} +(-2.10991 + 1.53294i) q^{34} +(-0.0734420 - 0.226031i) q^{35} +6.14153 q^{36} -6.60106 q^{37} +(0.485482 + 1.49416i) q^{38} +(-0.685044 + 2.10835i) q^{39} +(3.60972 - 11.1096i) q^{40} +(-8.33202 - 6.05357i) q^{41} +(0.0876890 + 0.269879i) q^{42} +(-4.63127 - 3.36482i) q^{43} +(-2.27849 + 1.65542i) q^{44} +(2.50664 - 7.71464i) q^{45} +(5.25559 - 3.81841i) q^{46} +(-5.60130 + 4.06958i) q^{47} +(0.0853297 - 0.262618i) q^{48} +(5.66057 - 4.11265i) q^{49} +(-23.9153 - 17.3755i) q^{50} +(-0.782867 - 2.40942i) q^{51} +(-2.59536 - 1.88564i) q^{52} +(-0.871224 + 2.68135i) q^{53} +(1.69714 - 5.22326i) q^{54} +(1.14949 + 3.53777i) q^{55} -0.154635 q^{56} -1.52612 q^{57} +(-2.19602 - 6.75867i) q^{58} +(-9.59199 + 6.96899i) q^{59} +(24.3784 + 17.7120i) q^{60} -3.17687 q^{61} +(-7.59967 + 10.1830i) q^{62} -0.107381 q^{63} +(10.5032 + 7.63100i) q^{64} +(-3.42792 + 2.49053i) q^{65} +(-1.37248 - 4.22406i) q^{66} -1.89328 q^{67} +3.66614 q^{68} +(1.95005 + 6.00162i) q^{69} +(-0.167603 + 0.515829i) q^{70} +(1.80708 - 5.56162i) q^{71} +(-4.26985 - 3.10223i) q^{72} +(3.78622 + 11.6528i) q^{73} +(12.1873 + 8.85462i) q^{74} +(23.2314 - 16.8786i) q^{75} +(0.682457 - 2.10039i) q^{76} +(0.0398380 - 0.0289440i) q^{77} +(4.09290 - 2.97366i) q^{78} +(3.67015 - 11.2956i) q^{79} +(0.426984 - 0.310222i) q^{80} +(8.96250 + 6.51164i) q^{81} +(7.26294 + 22.3530i) q^{82} +(-13.9026 - 10.1008i) q^{83} +(0.123267 - 0.379378i) q^{84} +(1.49632 - 4.60520i) q^{85} +(4.03703 + 12.4247i) q^{86} +6.90325 q^{87} +2.42030 q^{88} +(0.611759 + 1.88280i) q^{89} +(-14.9763 + 10.8809i) q^{90} +(0.0453782 + 0.0329692i) q^{91} -9.13200 q^{92} +(-7.12642 - 10.0778i) q^{93} +15.8004 q^{94} +(-2.35985 - 1.71453i) q^{95} +(-10.3986 + 7.55501i) q^{96} +(4.72866 + 14.5533i) q^{97} -15.9676 q^{98} +1.68069 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

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