LMFDB - Embedded newform 731.2.u.b.52.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(52,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("731.52");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.u (of order $21$, degree $12$, 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:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			52.15
Character	$\chi$	$=$	731.52
Dual form			731.2.u.b.239.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.123719 - 0.155139i) q^{2} +(-1.15042 - 0.173398i) q^{3} +(0.436280 - 1.91147i) q^{4} +(1.32212 + 0.901405i) q^{5} +(0.115429 + 0.199928i) q^{6} +(-1.26206 + 2.18595i) q^{7} +(-0.708080 + 0.340993i) q^{8} +(-1.57331 - 0.485303i) q^{9} +O(q^{10})$	\(q+(-0.123719 - 0.155139i) q^{2} +(-1.15042 - 0.173398i) q^{3} +(0.436280 - 1.91147i) q^{4} +(1.32212 + 0.901405i) q^{5} +(0.115429 + 0.199928i) q^{6} +(-1.26206 + 2.18595i) q^{7} +(-0.708080 + 0.340993i) q^{8} +(-1.57331 - 0.485303i) q^{9} +(-0.0237284 - 0.316634i) q^{10} +(0.0539477 + 0.236360i) q^{11} +(-0.833352 + 2.12335i) q^{12} +(-0.208745 + 2.78551i) q^{13} +(0.495268 - 0.0746497i) q^{14} +(-1.36469 - 1.26625i) q^{15} +(-3.39242 - 1.63370i) q^{16} +(-0.826239 + 0.563320i) q^{17} +(0.119360 + 0.304124i) q^{18} +(-3.76162 + 1.16031i) q^{19} +(2.29982 - 2.13392i) q^{20} +(1.83094 - 2.29593i) q^{21} +(0.0299944 - 0.0376118i) q^{22} +(-5.50847 + 5.11111i) q^{23} +(0.873718 - 0.269506i) q^{24} +(-0.891240 - 2.27084i) q^{25} +(0.457969 - 0.312238i) q^{26} +(4.87043 + 2.34548i) q^{27} +(3.62776 + 3.36607i) q^{28} +(-3.03378 + 0.457269i) q^{29} +(-0.0276060 + 0.368377i) q^{30} +(2.18729 - 5.57312i) q^{31} +(0.516019 + 2.26083i) q^{32} +(-0.0210782 - 0.281269i) q^{33} +(0.189615 + 0.0584885i) q^{34} +(-3.63902 + 1.75246i) q^{35} +(-1.61405 + 2.79561i) q^{36} +(2.17228 + 3.76249i) q^{37} +(0.645395 + 0.440023i) q^{38} +(0.723149 - 3.16832i) q^{39} +(-1.24354 - 0.187433i) q^{40} +(3.37663 + 4.23416i) q^{41} -0.582711 q^{42} +(-2.84174 + 5.90969i) q^{43} +0.475332 q^{44} +(-1.64265 - 2.05982i) q^{45} +(1.47444 + 0.222236i) q^{46} +(-1.33974 + 5.86979i) q^{47} +(3.61943 + 2.46769i) q^{48} +(0.314414 + 0.544582i) q^{49} +(-0.242033 + 0.419214i) q^{50} +(1.04820 - 0.504787i) q^{51} +(5.23335 + 1.61428i) q^{52} +(-0.303992 - 4.05649i) q^{53} +(-0.238692 - 1.04578i) q^{54} +(-0.141731 + 0.361125i) q^{55} +(0.148244 - 1.97818i) q^{56} +(4.52864 - 0.682583i) q^{57} +(0.446279 + 0.414086i) q^{58} +(-2.44363 - 1.17679i) q^{59} +(-3.01578 + 2.05613i) q^{60} +(-1.62059 - 4.12920i) q^{61} +(-1.13522 + 0.350169i) q^{62} +(3.04646 - 2.82671i) q^{63} +(-4.40835 + 5.52790i) q^{64} +(-2.78686 + 3.49461i) q^{65} +(-0.0410280 + 0.0380685i) q^{66} +(-14.2060 + 4.38197i) q^{67} +(0.716297 + 1.82509i) q^{68} +(7.22332 - 4.92477i) q^{69} +(0.722092 + 0.347741i) q^{70} +(3.02310 + 2.80502i) q^{71} +(1.27952 - 0.192856i) q^{72} +(-0.268430 + 3.58195i) q^{73} +(0.314958 - 0.802499i) q^{74} +(0.631542 + 2.76697i) q^{75} +(0.576768 + 7.69643i) q^{76} +(-0.584757 - 0.180374i) q^{77} +(-0.580999 + 0.279794i) q^{78} +(-2.60530 + 4.51251i) q^{79} +(-3.01255 - 5.21789i) q^{80} +(-1.11524 - 0.760356i) q^{81} +(0.239130 - 1.04770i) q^{82} +(8.38686 + 1.26412i) q^{83} +(-3.58979 - 4.50145i) q^{84} -1.60016 q^{85} +(1.26840 - 0.290278i) q^{86} +3.56942 q^{87} +(-0.118797 - 0.148966i) q^{88} +(2.61256 + 0.393780i) q^{89} +(-0.116331 + 0.509680i) q^{90} +(-5.82555 - 3.97179i) q^{91} +(7.36649 + 12.7591i) q^{92} +(-3.48268 + 6.03217i) q^{93} +(1.07639 - 0.518361i) q^{94} +(-6.01921 - 1.85668i) q^{95} +(-0.201616 - 2.69038i) q^{96} +(-3.37767 - 14.7986i) q^{97} +(0.0455868 - 0.116153i) q^{98} +(0.0298297 - 0.398050i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9}+O(q^{10}) $ 348 * q + 6 * q^2 - 3 * q^3 - 54 * q^4 + q^5 - 12 * q^6 + 49 * q^7 - 2 * q^8 + 8 * q^9	\( 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9} - 4 q^{10} - 16 q^{11} - 12 q^{12} - 9 q^{13} - 3 q^{14} - 14 q^{15} - 30 q^{16} - 29 q^{17} - 204 q^{18} - 8 q^{19} + 61 q^{20} + 26 q^{21} + 85 q^{22} - 79 q^{23} - 12 q^{24} + 22 q^{25} - 14 q^{26} + 12 q^{27} - 15 q^{28} + 54 q^{29} - 46 q^{30} - 52 q^{31} + 33 q^{32} + 39 q^{33} + 3 q^{34} + 32 q^{35} - 161 q^{36} + 68 q^{37} - 29 q^{38} + 61 q^{39} + 107 q^{40} + 63 q^{41} - 56 q^{42} - 45 q^{43} - 74 q^{44} + 144 q^{45} - 22 q^{46} - 70 q^{47} + 168 q^{48} - 119 q^{49} + 97 q^{50} - 6 q^{51} + 27 q^{52} + 10 q^{53} - 34 q^{54} - 78 q^{55} - 44 q^{56} - 40 q^{57} - 38 q^{58} - 47 q^{59} - 72 q^{60} - 76 q^{61} - 41 q^{62} + 63 q^{63} - 112 q^{64} - 31 q^{65} - 598 q^{66} - 39 q^{67} - 20 q^{68} - 17 q^{69} - 72 q^{70} - 37 q^{71} + 245 q^{72} + 14 q^{73} + 77 q^{74} - 121 q^{75} + 152 q^{76} + 59 q^{77} + 220 q^{78} + 4 q^{79} - 42 q^{80} - 109 q^{81} + 148 q^{82} + 59 q^{83} + 390 q^{84} + 2 q^{85} + 12 q^{86} - 78 q^{87} + 344 q^{88} - 103 q^{89} - 75 q^{90} + 148 q^{91} + 28 q^{92} + 140 q^{93} + 24 q^{94} - 302 q^{95} + 22 q^{96} + 57 q^{97} - 72 q^{98} - 128 q^{99}+O(q^{100}) \) 348 * q + 6 * q^2 - 3 * q^3 - 54 * q^4 + q^5 - 12 * q^6 + 49 * q^7 - 2 * q^8 + 8 * q^9 - 4 * q^10 - 16 * q^11 - 12 * q^12 - 9 * q^13 - 3 * q^14 - 14 * q^15 - 30 * q^16 - 29 * q^17 - 204 * q^18 - 8 * q^19 + 61 * q^20 + 26 * q^21 + 85 * q^22 - 79 * q^23 - 12 * q^24 + 22 * q^25 - 14 * q^26 + 12 * q^27 - 15 * q^28 + 54 * q^29 - 46 * q^30 - 52 * q^31 + 33 * q^32 + 39 * q^33 + 3 * q^34 + 32 * q^35 - 161 * q^36 + 68 * q^37 - 29 * q^38 + 61 * q^39 + 107 * q^40 + 63 * q^41 - 56 * q^42 - 45 * q^43 - 74 * q^44 + 144 * q^45 - 22 * q^46 - 70 * q^47 + 168 * q^48 - 119 * q^49 + 97 * q^50 - 6 * q^51 + 27 * q^52 + 10 * q^53 - 34 * q^54 - 78 * q^55 - 44 * q^56 - 40 * q^57 - 38 * q^58 - 47 * q^59 - 72 * q^60 - 76 * q^61 - 41 * q^62 + 63 * q^63 - 112 * q^64 - 31 * q^65 - 598 * q^66 - 39 * q^67 - 20 * q^68 - 17 * q^69 - 72 * q^70 - 37 * q^71 + 245 * q^72 + 14 * q^73 + 77 * q^74 - 121 * q^75 + 152 * q^76 + 59 * q^77 + 220 * q^78 + 4 * q^79 - 42 * q^80 - 109 * q^81 + 148 * q^82 + 59 * q^83 + 390 * q^84 + 2 * q^85 + 12 * q^86 - 78 * q^87 + 344 * q^88 - 103 * q^89 - 75 * q^90 + 148 * q^91 + 28 * q^92 + 140 * q^93 + 24 * q^94 - 302 * q^95 + 22 * q^96 + 57 * q^97 - 72 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{1}{21}\right)$

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 $

$2$	−0.123719	−	0.155139i	−0.0874829	−	0.109700i	0.736164	−	0.676804i	$-0.236635\pi$
$2$	−0.123719	−	0.155139i	−0.0874829	−	0.109700i	−0.823647	+	0.567104i	$0.808064\pi$
$3$	−1.15042	−	0.173398i	−0.664196	−	0.100112i	−0.191713	−	0.981451i	$-0.561404\pi$
$3$	−1.15042	−	0.173398i	−0.664196	−	0.100112i	−0.472483	+	0.881340i	$0.656642\pi$
$4$	0.436280	−	1.91147i	0.218140	−	0.955734i
$5$	1.32212	+	0.901405i	0.591269	+	0.403120i	0.821660	−	0.569978i	$-0.193048\pi$
$5$	1.32212	+	0.901405i	0.591269	+	0.403120i	−0.230391	+	0.973098i	$0.574001\pi$
$6$	0.115429	+	0.199928i	0.0471236	+	0.0816204i
$7$	−1.26206	+	2.18595i	−0.477013	+	0.826212i	−0.999653	−	0.0263422i	$-0.991614\pi$
$7$	−1.26206	+	2.18595i	−0.477013	+	0.826212i	0.522640	+	0.852554i	$0.324947\pi$
$8$	−0.708080	+	0.340993i	−0.250344	+	0.120559i
$9$	−1.57331	−	0.485303i	−0.524438	−	0.161768i
$10$	−0.0237284	−	0.316634i	−0.00750358	−	0.100128i
$11$	0.0539477	+	0.236360i	0.0162658	+	0.0712653i	0.982409	−	0.186740i	$-0.0597921\pi$
$11$	0.0539477	+	0.236360i	0.0162658	+	0.0712653i	−0.966144	+	0.258005i	$0.916935\pi$
$12$	−0.833352	+	2.12335i	−0.240568	+	0.612957i
$13$	−0.208745	+	2.78551i	−0.0578956	+	0.772563i	0.890401	+	0.455177i	$0.150424\pi$
$13$	−0.208745	+	2.78551i	−0.0578956	+	0.772563i	−0.948297	+	0.317386i	$0.897195\pi$
$14$	0.495268	−	0.0746497i	0.132366	−	0.0199510i
$15$	−1.36469	−	1.26625i	−0.352362	−	0.326944i
$16$	−3.39242	−	1.63370i	−0.848105	−	0.408426i
$17$	−0.826239	+	0.563320i	−0.200392	+	0.136625i
$17$	−0.826239	+	0.563320i	−0.200392	+	0.136625i
$18$	0.119360	+	0.304124i	0.0281334	+	0.0716828i
$19$	−3.76162	+	1.16031i	−0.862975	+	0.266192i	−0.694482	−	0.719510i	$-0.744366\pi$
$19$	−3.76162	+	1.16031i	−0.862975	+	0.266192i	−0.168493	+	0.985703i	$0.553890\pi$
$20$	2.29982	−	2.13392i	0.514255	−	0.477159i
$21$	1.83094	−	2.29593i	0.399544	−	0.501012i
$22$	0.0299944	−	0.0376118i	0.00639483	−	0.00801886i
$23$	−5.50847	+	5.11111i	−1.14859	+	1.06574i	−0.151586	+	0.988444i	$0.548438\pi$
$23$	−5.50847	+	5.11111i	−1.14859	+	1.06574i	−0.997008	+	0.0772958i	$0.975371\pi$
$24$	0.873718	−	0.269506i	0.178347	−	0.0550128i
$25$	−0.891240	−	2.27084i	−0.178248	−	0.454169i
$26$	0.457969	−	0.312238i	0.0898150	−	0.0612349i
$27$	4.87043	+	2.34548i	0.937315	+	0.451387i
$28$	3.62776	+	3.36607i	0.685583	+	0.636128i
$29$	−3.03378	+	0.457269i	−0.563360	+	0.0849128i	−0.424547	−	0.905406i	$-0.639567\pi$
$29$	−3.03378	+	0.457269i	−0.563360	+	0.0849128i	−0.138813	+	0.990319i	$0.544329\pi$
$30$	−0.0276060	+	0.368377i	−0.00504015	+	0.0672561i
$31$	2.18729	−	5.57312i	0.392849	−	1.00096i	−0.588460	−	0.808526i	$-0.700266\pi$
$31$	2.18729	−	5.57312i	0.392849	−	1.00096i	0.981309	−	0.192437i	$-0.0616390\pi$
$32$	0.516019	+	2.26083i	0.0912202	+	0.399662i
$33$	−0.0210782	−	0.281269i	−0.00366924	−	0.0489626i
$34$	0.189615	+	0.0584885i	0.0325187	+	0.0100307i
$35$	−3.63902	+	1.75246i	−0.615106	+	0.296219i
$36$	−1.61405	+	2.79561i	−0.269008	+	0.465935i
$37$	2.17228	+	3.76249i	0.357120	+	0.618550i	0.987478	−	0.157754i	$-0.0504254\pi$
$37$	2.17228	+	3.76249i	0.357120	+	0.618550i	−0.630358	+	0.776304i	$0.717092\pi$
$38$	0.645395	+	0.440023i	0.104697	+	0.0713811i
$39$	0.723149	−	3.16832i	0.115796	−	0.507337i
$40$	−1.24354	−	0.187433i	−0.196621	−	0.0296358i
$41$	3.37663	+	4.23416i	0.527341	+	0.661265i	0.972150	−	0.234361i	$-0.0752996\pi$
$41$	3.37663	+	4.23416i	0.527341	+	0.661265i	−0.444808	+	0.895626i	$0.646728\pi$
$42$	−0.582711			−0.0899143
$43$	−2.84174	+	5.90969i	−0.433362	+	0.901220i
$43$	−2.84174	+	5.90969i	−0.433362	+	0.901220i
$44$	0.475332			0.0716590
$45$	−1.64265	−	2.05982i	−0.244872	−	0.307060i
$46$	1.47444	+	0.222236i	0.217394	+	0.0327669i
$47$	−1.33974	+	5.86979i	−0.195421	+	0.856197i	0.778198	+	0.628019i	$0.216134\pi$
$47$	−1.33974	+	5.86979i	−0.195421	+	0.856197i	−0.973619	+	0.228178i	$0.926723\pi$
$48$	3.61943	+	2.46769i	0.522420	+	0.356180i
$49$	0.314414	+	0.544582i	0.0449163	+	0.0777974i
$50$	−0.242033	+	0.419214i	−0.0342287	+	0.0592858i
$51$	1.04820	−	0.504787i	0.146778	−	0.0706844i
$52$	5.23335	+	1.61428i	0.725735	+	0.223860i
$53$	−0.303992	−	4.05649i	−0.0417565	−	0.557201i	−0.978373	−	0.206846i	$-0.933680\pi$
$53$	−0.303992	−	4.05649i	−0.0417565	−	0.557201i	0.936617	−	0.350355i	$-0.113939\pi$
$54$	−0.238692	−	1.04578i	−0.0324818	−	0.142312i
$55$	−0.141731	+	0.361125i	−0.0191110	+	0.0486941i
$56$	0.148244	−	1.97818i	0.0198100	−	0.264346i
$57$	4.52864	−	0.682583i	0.599834	−	0.0904104i
$58$	0.446279	+	0.414086i	0.0585993	+	0.0543722i
$59$	−2.44363	−	1.17679i	−0.318133	−	0.153205i	0.268001	−	0.963419i	$-0.413637\pi$
$59$	−2.44363	−	1.17679i	−0.318133	−	0.153205i	−0.586135	+	0.810214i	$0.699351\pi$
$60$	−3.01578	+	2.05613i	−0.389336	+	0.265445i
$61$	−1.62059	−	4.12920i	−0.207496	−	0.528690i	0.788803	−	0.614646i	$-0.210701\pi$
$61$	−1.62059	−	4.12920i	−0.207496	−	0.528690i	−0.996299	+	0.0859555i	$0.972606\pi$
$62$	−1.13522	+	0.350169i	−0.144173	+	0.0444715i
$63$	3.04646	−	2.82671i	0.383818	−	0.356131i
$64$	−4.40835	+	5.52790i	−0.551044	+	0.690988i
$65$	−2.78686	+	3.49461i	−0.345668	+	0.433453i
$66$	−0.0410280	+	0.0380685i	−0.00505020	+	0.00468590i
$67$	−14.2060	+	4.38197i	−1.73554	+	0.535342i	−0.991190	−	0.132450i	$-0.957716\pi$
$67$	−14.2060	+	4.38197i	−1.73554	+	0.535342i	−0.744348	+	0.667792i	$0.767239\pi$
$68$	0.716297	+	1.82509i	0.0868638	+	0.221325i
$69$	7.22332	−	4.92477i	0.869585	−	0.592873i
$70$	0.722092	+	0.347741i	0.0863065	+	0.0415630i
$71$	3.02310	+	2.80502i	0.358775	+	0.332895i	0.838880	−	0.544316i	$-0.183211\pi$
$71$	3.02310	+	2.80502i	0.358775	+	0.332895i	−0.480105	+	0.877211i	$0.659401\pi$
$72$	1.27952	−	0.192856i	0.150793	−	0.0227283i
$73$	−0.268430	+	3.58195i	−0.0314174	+	0.419236i	0.959215	+	0.282678i	$0.0912229\pi$
$73$	−0.268430	+	3.58195i	−0.0314174	+	0.419236i	−0.990632	+	0.136557i	$0.956396\pi$
$74$	0.314958	−	0.802499i	0.0366131	−	0.0932886i
$75$	0.631542	+	2.76697i	0.0729242	+	0.319502i
$76$	0.576768	+	7.69643i	0.0661598	+	0.882842i
$77$	−0.584757	−	0.180374i	−0.0666393	−	0.0205555i
$78$	−0.580999	+	0.279794i	−0.0657851	+	0.0316805i
$79$	−2.60530	+	4.51251i	−0.293119	+	0.507697i	−0.974546	−	0.224190i	$-0.928026\pi$
$79$	−2.60530	+	4.51251i	−0.293119	+	0.507697i	0.681427	+	0.731886i	$0.261360\pi$
$80$	−3.01255	−	5.21789i	−0.336813	−	0.583378i
$81$	−1.11524	−	0.760356i	−0.123915	−	0.0844840i
$82$	0.239130	−	1.04770i	0.0264075	−	0.115699i
$83$	8.38686	+	1.26412i	0.920578	+	0.138755i	0.592199	−	0.805792i	$-0.298260\pi$
$83$	8.38686	+	1.26412i	0.920578	+	0.138755i	0.328378	+	0.944546i	$0.393498\pi$
$84$	−3.58979	−	4.50145i	−0.391678	−	0.491149i
$85$	−1.60016			−0.173562
$86$	1.26840	−	0.290278i	0.136776	−	0.0313015i
$87$	3.56942			0.382682
$88$	−0.118797	−	0.148966i	−0.0126638	−	0.0158799i
$89$	2.61256	+	0.393780i	0.276931	+	0.0417406i	0.286039	−	0.958218i	$-0.407661\pi$
$89$	2.61256	+	0.393780i	0.276931	+	0.0417406i	−0.00910854	+	0.999959i	$0.502899\pi$
$90$	−0.116331	+	0.509680i	−0.0122624	+	0.0537250i
$91$	−5.82555	−	3.97179i	−0.610683	−	0.416357i
$92$	7.36649	+	12.7591i	0.768010	+	1.33023i
$93$	−3.48268	+	6.03217i	−0.361137	+	0.625507i
$94$	1.07639	−	0.518361i	0.111021	−	0.0534649i
$95$	−6.01921	−	1.85668i	−0.617558	−	0.190491i
$96$	−0.201616	−	2.69038i	−0.0205774	−	0.274586i
$97$	−3.37767	−	14.7986i	−0.342951	−	1.50257i	−0.792812	−	0.609467i	$-0.791384\pi$
$97$	−3.37767	−	14.7986i	−0.342951	−	1.50257i	0.449861	−	0.893099i	$-0.351474\pi$
$98$	0.0455868	−	0.116153i	0.00460497	−	0.0117333i
$99$	0.0298297	−	0.398050i	0.00299800	−	0.0400056i
$100$	−4.72948	+	0.712854i	−0.472948	+	0.0712854i
$101$	−3.90905	−	3.62707i	−0.388965	−	0.360907i	0.461316	−	0.887236i	$-0.347377\pi$
$101$	−3.90905	−	3.62707i	−0.388965	−	0.360907i	−0.850281	+	0.526329i	$0.823568\pi$
$102$	−0.207995	−	0.100165i	−0.0205946	−	0.00991784i
$103$	−9.73997	+	6.64060i	−0.959707	+	0.654317i	−0.938435	−	0.345456i	$-0.887724\pi$
$103$	−9.73997	+	6.64060i	−0.959707	+	0.654317i	−0.0212725	+	0.999774i	$0.506772\pi$
$104$	−0.802033	−	2.04355i	−0.0786458	−	0.200386i
$105$	4.49028	−	1.38507i	0.438206	−	0.135169i
$106$	−0.591711	+	0.549027i	−0.0574720	+	0.0533262i
$107$	11.3097	−	14.1819i	1.09335	−	1.37102i	0.170725	−	0.985319i	$-0.445389\pi$
$107$	11.3097	−	14.1819i	1.09335	−	1.37102i	0.922625	−	0.385698i	$-0.126039\pi$
$108$	6.60818	−	8.28639i	0.635872	−	0.797358i
$109$	−7.04400	+	6.53587i	−0.674692	+	0.626023i	−0.941216	−	0.337805i	$-0.890315\pi$
$109$	−7.04400	+	6.53587i	−0.674692	+	0.626023i	0.266524	+	0.963828i	$0.414125\pi$
$110$	0.0735596	−	0.0226901i	0.00701363	−	0.00216342i
$111$	−1.84662	−	4.70512i	−0.175274	−	0.446591i
$112$	7.85263	−	5.35383i	0.742004	−	0.505890i
$113$	0.280892	+	0.135271i	0.0264241	+	0.0127252i	0.447049	−	0.894509i	$-0.352475\pi$
$113$	0.280892	+	0.135271i	0.0264241	+	0.0127252i	−0.420625	+	0.907235i	$0.638189\pi$
$114$	−0.666177	−	0.618122i	−0.0623932	−	0.0578924i
$115$	−11.8900	+	1.79213i	−1.10875	+	0.167117i
$116$	−0.449524	+	5.99848i	−0.0417373	+	0.556945i
$117$	1.68024	−	4.28119i	0.155338	−	0.395796i
$118$	0.119758	+	0.524695i	0.0110246	+	0.0483021i
$119$	−0.188628	−	2.51706i	−0.0172915	−	0.230739i
$120$	1.39809	+	0.431254i	0.127628	+	0.0393680i
$121$	9.85770	−	4.74722i	0.896155	−	0.431565i
$122$	−0.440103	+	0.762280i	−0.0398450	+	0.0690136i
$123$	−3.15036	−	5.45658i	−0.284058	−	0.492003i
$124$	−9.69858	−	6.61238i	−0.870958	−	0.593809i
$125$	2.64897	−	11.6059i	0.236931	−	1.03806i
$126$	−0.815440	−	0.122908i	−0.0726452	−	0.0109495i
$127$	−4.57008	−	5.73070i	−0.405529	−	0.508518i	0.536568	−	0.843857i	$-0.319720\pi$
$127$	−4.57008	−	5.73070i	−0.405529	−	0.508518i	−0.942097	+	0.335339i	$0.891149\pi$
$128$	6.04093			0.533948
$129$	4.29394	−	6.30589i	0.378060	−	0.555203i
$130$	0.886941			0.0777899
$131$	−10.2753	−	12.8849i	−0.897761	−	1.12576i	−0.991493	−	0.130160i	$-0.958451\pi$
$131$	−10.2753	−	12.8849i	−0.897761	−	1.12576i	0.0937316	−	0.995598i	$-0.470120\pi$
$132$	−0.546832	−	0.0824217i	−0.0475956	−	0.00717389i
$133$	2.21101	−	9.68709i	0.191719	−	0.839977i
$134$	2.43737	+	1.66177i	0.210557	+	0.143555i
$135$	4.32506	+	7.49122i	0.372242	+	0.644742i
$136$	0.392955	−	0.680617i	0.0336956	−	0.0583625i
$137$	12.1818	−	5.86645i	1.04076	−	0.501205i	0.166187	−	0.986094i	$-0.446855\pi$
$137$	12.1818	−	5.86645i	1.04076	−	0.501205i	0.874575	+	0.484890i	$0.161140\pi$
$138$	−1.65769	−	0.511330i	−0.141112	−	0.0435273i
$139$	0.866709	+	11.5654i	0.0735133	+	0.980967i	0.904997	+	0.425418i	$0.139873\pi$
$139$	0.866709	+	11.5654i	0.0735133	+	0.980967i	−0.831484	+	0.555549i	$0.812508\pi$
$140$	1.76214	+	7.72043i	0.148928	+	0.652495i
$141$	2.55908	−	6.52043i	0.215513	−	0.549119i
$142$	0.0611535	−	0.816037i	0.00513189	−	0.0684803i
$143$	−0.669647	+	0.100933i	−0.0559987	+	0.00844044i
$144$	4.54450	+	4.21668i	0.378708	+	0.351390i
$145$	−4.42320	−	2.13010i	−0.367327	−	0.176895i
$146$	0.588911	−	0.401513i	0.0487387	−	0.0332295i
$147$	−0.267280	−	0.681017i	−0.0220449	−	0.0561694i
$148$	8.13961	−	2.51074i	0.669071	−	0.206381i
$149$	6.99167	−	6.48732i	0.572780	−	0.531462i	−0.339727	−	0.940524i	$-0.610335\pi$
$149$	6.99167	−	6.48732i	0.572780	−	0.531462i	0.912507	+	0.409062i	$0.134144\pi$
$150$	0.351131	−	0.440305i	0.0286698	−	0.0359507i
$151$	8.05781	−	10.1042i	0.655736	−	0.822266i	−0.337136	−	0.941456i	$-0.609458\pi$
$151$	8.05781	−	10.1042i	0.655736	−	0.822266i	0.992872	+	0.119190i	$0.0380296\pi$
$152$	2.26787	−	2.10428i	0.183949	−	0.170679i
$153$	1.57331	−	0.485303i	0.127195	−	0.0392344i
$154$	0.0443628	+	0.113035i	0.00357486	+	0.00910859i
$155$	7.91549	−	5.39669i	0.635788	−	0.433473i
$156$	−5.74065	−	2.76455i	−0.459620	−	0.221341i
$157$	1.32453	+	1.22899i	0.105709	+	0.0980839i	0.731257	−	0.682102i	$-0.238934\pi$
$157$	1.32453	+	1.22899i	0.105709	+	0.0980839i	−0.625548	+	0.780186i	$0.715124\pi$
$158$	1.02239	−	0.154101i	0.0813372	−	0.0122596i
$159$	−0.353669	+	4.71938i	−0.0280478	+	0.374271i
$160$	−1.35568	+	3.45422i	−0.107176	+	0.273080i
$161$	−4.22062	−	18.4918i	−0.332632	−	1.45735i
$162$	0.0200155	+	0.267088i	0.00157256	+	0.0209844i
$163$	6.93244	+	2.13838i	0.542991	+	0.167491i	0.554104	−	0.832448i	$-0.313061\pi$
$163$	6.93244	+	2.13838i	0.542991	+	0.167491i	−0.0111126	+	0.999938i	$0.503537\pi$
$164$	9.56663	−	4.60704i	0.747028	−	0.359750i
$165$	0.225669	−	0.390870i	0.0175683	−	0.0304292i
$166$	−0.841504	−	1.45753i	−0.0653134	−	0.113126i
$167$	2.59417	+	1.76867i	0.200743	+	0.136864i	0.659519	−	0.751688i	$-0.270760\pi$
$167$	2.59417	+	1.76867i	0.200743	+	0.136864i	−0.458777	+	0.888552i	$0.651712\pi$
$168$	−0.513556	+	2.25004i	−0.0396217	+	0.173594i
$169$	5.13928	+	0.774623i	0.395330	+	0.0595864i
$170$	0.197971	+	0.248248i	0.0151837	+	0.0190398i
$171$	6.48131			0.495638
$172$	10.0564	+	8.01019i	0.766793	+	0.610771i
$173$	9.11002			0.692622			0.346311	−	0.938120i	$-0.387434\pi$
$173$	9.11002			0.692622			0.346311	+	0.938120i	$0.387434\pi$
$174$	−0.441607	−	0.553758i	−0.0334781	−	0.0419803i
$175$	6.08875	+	0.917731i	0.460266	+	0.0693740i
$176$	0.203129	−	0.889968i	0.0153115	−	0.0670839i
$177$	2.60715	+	1.77753i	0.195966	+	0.133607i
$178$	−0.262134	−	0.454029i	−0.0196477	−	0.0340309i
$179$	−7.38395	+	12.7894i	−0.551903	+	0.955923i	0.446235	+	0.894916i	$0.352765\pi$
$179$	−7.38395	+	12.7894i	−0.551903	+	0.955923i	−0.998137	+	0.0610074i	$0.980569\pi$
$180$	−4.65394	+	2.24122i	−0.346884	+	0.167051i
$181$	−18.1469	−	5.59759i	−1.34885	−	0.416066i	−0.465612	−	0.884989i	$-0.654166\pi$
$181$	−18.1469	−	5.59759i	−1.34885	−	0.416066i	−0.883239	+	0.468923i	$0.844642\pi$
$182$	0.104553	+	1.39516i	0.00774996	+	0.103416i
$183$	1.14837	+	5.03133i	0.0848899	+	0.371927i
$184$	2.15758	−	5.49742i	0.159059	−	0.405275i
$185$	−0.519523	+	6.93256i	−0.0381961	+	0.509692i
$186$	1.36670	−	0.205997i	0.100211	−	0.0151044i
$187$	−0.177720	−	0.164900i	−0.0129962	−	0.0120587i
$188$	10.6354	+	5.12175i	0.775668	+	0.373542i
$189$	−11.2739	+	7.68639i	−0.820053	+	0.559103i
$190$	0.456649	+	1.16352i	0.0331288	+	0.0844108i
$191$	−16.2834	+	5.02277i	−1.17823	+	0.363435i	−0.821190	−	0.570655i	$-0.806689\pi$
$191$	−16.2834	+	5.02277i	−1.17823	+	0.363435i	−0.357037	+	0.934090i	$0.616213\pi$
$192$	6.02999	−	5.59502i	0.435177	−	0.403786i
$193$	−9.77474	+	12.2571i	−0.703601	+	0.882288i	−0.997287	−	0.0736143i	$-0.976547\pi$
$193$	−9.77474	+	12.2571i	−0.703601	+	0.882288i	0.293686	+	0.955902i	$0.405118\pi$
$194$	−1.87795	+	2.35488i	−0.134829	+	0.169070i
$195$	3.81203	−	3.53704i	0.272985	−	0.253293i
$196$	1.17812	−	0.363403i	0.0841516	−	0.0259573i
$197$	−1.03140	−	2.62796i	−0.0734841	−	0.187234i	0.889412	−	0.457106i	$-0.151114\pi$
$197$	−1.03140	−	2.62796i	−0.0734841	−	0.187234i	−0.962896	+	0.269872i	$0.913019\pi$
$198$	−0.0654438	+	0.0446188i	−0.00465089	+	0.00317092i
$199$	−0.0903002	−	0.0434863i	−0.00640121	−	0.00308266i	0.430680	−	0.902505i	$-0.358274\pi$
$199$	−0.0903002	−	0.0434863i	−0.00640121	−	0.00308266i	−0.437082	+	0.899422i	$0.643988\pi$
$200$	1.40541	+	1.30403i	0.0993776	+	0.0922089i
$201$	17.1027	−	2.57782i	1.20633	−	0.181825i
$202$	−0.0790753	+	1.05519i	−0.00556372	+	0.0742426i
$203$	2.82925	−	7.20880i	0.198574	−	0.505959i
$204$	−0.507576	−	2.22383i	−0.0355374	−	0.155699i
$205$	0.647611	+	8.64177i	0.0452311	+	0.603568i
$206$	2.23524	+	0.689480i	0.155737	+	0.0480384i
$207$	11.1470	−	5.36811i	0.774769	−	0.373109i
$208$	5.25886	−	9.10861i	0.364636	−	0.631568i
$209$	−0.477181	−	0.826502i	−0.0330073	−	0.0571703i
$210$	−0.770413	−	0.525259i	−0.0531636	−	0.0362463i
$211$	−0.975113	+	4.27225i	−0.0671296	+	0.294114i	−0.997338	−	0.0729180i	$-0.976769\pi$
$211$	−0.975113	+	4.27225i	−0.0671296	+	0.294114i	0.930208	+	0.367032i	$0.119626\pi$
$212$	−7.88647	−	1.18869i	−0.541645	−	0.0816398i
$213$	−2.99145	−	3.75116i	−0.204971	−	0.257025i
$214$	−3.59940			−0.246050
$215$	−9.08414	+	5.25175i	−0.619534	+	0.358166i
$216$	−4.24845			−0.289070
$217$	9.42208	+	11.8149i	0.639613	+	0.802049i
$218$	1.88545	+	0.284186i	0.127699	+	0.0192475i
$219$	0.929912	−	4.07421i	0.0628376	−	0.275310i
$220$	0.628444	+	0.428466i	0.0423697	+	0.0288872i
$221$	−1.39666	−	2.41909i	−0.0939497	−	0.162726i
$222$	−0.501486	+	0.868599i	−0.0336575	+	0.0582966i
$223$	−22.2000	+	10.6909i	−1.48662	+	0.715919i	−0.988504	−	0.151192i	$-0.951689\pi$
$223$	−22.2000	+	10.6909i	−1.48662	+	0.715919i	−0.498116	+	0.867111i	$0.665975\pi$
$224$	−5.59331	−	1.72531i	−0.373718	−	0.115277i
$225$	0.300154	+	4.00527i	0.0200102	+	0.267018i
$226$	−0.0137661	−	0.0603130i	−0.000915705	−	0.00401196i
$227$	9.73845	−	24.8132i	0.646364	−	1.64691i	−0.110926	−	0.993829i	$-0.535382\pi$
$227$	9.73845	−	24.8132i	0.646364	−	1.64691i	0.757290	−	0.653079i	$-0.226523\pi$
$228$	0.671021	−	8.95416i	0.0444395	−	0.593004i
$229$	−11.2617	+	1.69742i	−0.744191	+	0.112169i	−0.510183	−	0.860066i	$-0.670422\pi$
$229$	−11.2617	+	1.69742i	−0.744191	+	0.112169i	−0.234008	+	0.972235i	$0.575184\pi$
$230$	1.74906	+	1.62289i	0.115329	+	0.107010i
$231$	0.641441	+	0.308902i	0.0422037	+	0.0203242i
$232$	1.99224	−	1.35828i	0.130797	−	0.0891757i
$233$	−2.40938	−	6.13901i	−0.157844	−	0.402180i	0.829972	−	0.557805i	$-0.188356\pi$
$233$	−2.40938	−	6.13901i	−0.157844	−	0.402180i	−0.987816	+	0.155625i	$0.950261\pi$
$234$	−0.872059	+	0.268994i	−0.0570083	+	0.0175847i
$235$	−7.06236	+	6.55291i	−0.460697	+	0.427465i
$236$	−3.31550	+	4.15751i	−0.215821	+	0.270631i
$237$	3.77965	−	4.73953i	0.245515	−	0.307866i
$238$	−0.367158	+	0.340673i	−0.0237993	+	0.0220825i
$239$	−25.7558	+	7.94462i	−1.66601	+	0.513895i	−0.977428	−	0.211268i	$-0.932241\pi$
$239$	−25.7558	+	7.94462i	−1.66601	+	0.513895i	−0.688577	+	0.725163i	$0.741764\pi$
$240$	2.56093	+	6.52515i	0.165307	+	0.421196i
$241$	24.8320	−	16.9302i	1.59957	−	1.09057i	0.658388	−	0.752679i	$-0.271239\pi$
$241$	24.8320	−	16.9302i	1.59957	−	1.09057i	0.941185	−	0.337891i	$-0.109714\pi$
$242$	−1.95607	−	0.941994i	−0.125741	−	0.0605536i
$243$	−10.7370	−	9.96246i	−0.688778	−	0.639092i
$244$	−8.59987	+	1.29622i	−0.550550	+	0.0829821i
$245$	−0.0751956	+	1.00342i	−0.00480407	+	0.0641058i
$246$	−0.456769	+	1.16383i	−0.0291225	+	0.0742030i
$247$	−2.44683	−	10.7203i	−0.155688	−	0.682113i
$248$	0.351622	+	4.69207i	0.0223280	+	0.297947i
$249$	−9.42924	−	2.90853i	−0.597554	−	0.184321i
$250$	−2.12826	+	1.02492i	−0.134603	+	0.0648215i
$251$	−5.17105	+	8.95651i	−0.326394	+	0.565330i	−0.981793	−	0.189952i	$-0.939167\pi$
$251$	−5.17105	+	8.95651i	−0.326394	+	0.565330i	0.655400	+	0.755282i	$0.272500\pi$
$252$	−4.07405	−	7.05646i	−0.256641	−	0.444515i
$253$	−1.50523	−	1.02625i	−0.0946332	−	0.0645198i
$254$	−0.323649	+	1.41800i	−0.0203075	+	0.0889732i
$255$	1.84086	+	0.277466i	0.115279	+	0.0173756i
$256$	8.06933	+	10.1186i	0.504333	+	0.632413i
$257$	−5.49741			−0.342919			−0.171459	−	0.985191i	$-0.554848\pi$
$257$	−5.49741			−0.342919			−0.171459	+	0.985191i	$0.554848\pi$
$258$	−1.50953	+	0.114003i	−0.0939795	+	0.00709753i
$259$	−10.9662			−0.681404
$260$	5.46399	+	6.85163i	0.338862	+	0.424920i
$261$	4.99501	+	0.752877i	0.309183	+	0.0466019i
$262$	−0.727691	+	3.18822i	−0.0449569	+	0.196969i
$263$	−0.795951	−	0.542670i	−0.0490804	−	0.0334625i	0.538531	−	0.842605i	$-0.318979\pi$
$263$	−0.795951	−	0.542670i	−0.0490804	−	0.0334625i	−0.587612	+	0.809143i	$0.699932\pi$
$264$	0.110836	+	0.191973i	0.00682147	+	0.0118151i
$265$	3.25462	−	5.63717i	0.199930	−	0.346289i
$266$	−1.77639	+	0.855466i	−0.108918	+	0.0524520i
$267$	−2.93726	−	0.906026i	−0.179758	−	0.0554479i
$268$	2.17820	+	29.0661i	0.133055	+	1.77549i
$269$	1.56504	+	6.85689i	0.0954222	+	0.418072i	0.999965	−	0.00830980i	$-0.00264512\pi$
$269$	1.56504	+	6.85689i	0.0954222	+	0.418072i	−0.904543	+	0.426382i	$0.859788\pi$
$270$	0.627089	−	1.59780i	0.0381634	−	0.0972388i
$271$	−1.29041	+	17.2193i	−0.0783869	+	1.04600i	0.809857	+	0.586628i	$0.199545\pi$
$271$	−1.29041	+	17.2193i	−0.0783869	+	1.04600i	−0.888244	+	0.459373i	$0.848074\pi$
$272$	3.72325	−	0.561189i	0.225755	−	0.0340271i
$273$	6.01314	+	5.57937i	0.363932	+	0.337679i
$274$	−2.41724	−	1.16408i	−0.146031	−	0.0703248i
$275$	0.488657	−	0.333161i	0.0294671	−	0.0200903i
$276$	−6.26216	−	15.9557i	−0.376938	−	0.960422i
$277$	−19.2928	+	5.95103i	−1.15919	+	0.357563i	−0.813941	−	0.580948i	$-0.802682\pi$
$277$	−19.2928	+	5.95103i	−1.15919	+	0.357563i	−0.345250	+	0.938511i	$0.612206\pi$
$278$	1.68702	−	1.56533i	0.101181	−	0.0938822i
$279$	−6.14595	+	7.70678i	−0.367948	+	0.461393i
$280$	1.97914	−	2.48176i	0.118276	−	0.148314i
$281$	17.9876	−	16.6900i	1.07305	−	0.995644i	0.0730510	−	0.997328i	$-0.476726\pi$
$281$	17.9876	−	16.6900i	1.07305	−	0.995644i	0.999999	+	0.00168372i	$0.000535946\pi$
$282$	−1.32818	+	0.409690i	−0.0790922	+	0.0243967i
$283$	9.03616	+	23.0238i	0.537144	+	1.36862i	0.899639	+	0.436634i	$0.143830\pi$
$283$	9.03616	+	23.0238i	0.537144	+	1.36862i	−0.362495	+	0.931986i	$0.618075\pi$
$284$	6.68063	−	4.55478i	0.396422	−	0.270276i
$285$	6.60268	+	3.17969i	0.391109	+	0.188348i
$286$	0.0985070	+	0.0914011i	0.00582484	+	0.00540466i
$287$	−13.5172	+	2.03739i	−0.797894	+	0.120263i
$288$	0.285327	−	3.80742i	0.0168130	−	0.224354i
$289$	0.365341	−	0.930874i	0.0214906	−	0.0547573i
$290$	0.216774	+	0.949748i	0.0127294	+	0.0557711i
$291$	1.31971	+	17.6103i	0.0773626	+	1.03233i
$292$	6.72967	+	2.07583i	0.393824	+	0.121479i
$293$	7.23253	−	3.48300i	0.422529	−	0.203479i	−0.210522	−	0.977589i	$-0.567517\pi$
$293$	7.23253	−	3.48300i	0.422529	−	0.203479i	0.633051	+	0.774110i	$0.281802\pi$
$294$	−0.0725849	+	0.125721i	−0.00423324	+	0.00733218i
$295$	−2.17000	−	3.75855i	−0.126342	−	0.218831i
$296$	−2.82113	−	1.92341i	−0.163975	−	0.111796i
$297$	−0.291629	+	1.27771i	−0.0169220	+	0.0741403i
$298$	−1.87144	−	0.282075i	−0.108410	−	0.0163402i
$299$	−13.0872	−	16.4108i	−0.756852	−	0.949063i
$300$	5.56450			0.321267
$301$	−9.33185	−	13.6703i	−0.537879	−	0.787943i
$302$	−2.56446			−0.147568
$303$	3.86813	+	4.85048i	0.222218	+	0.278653i
$304$	14.6566	+	2.20912i	0.840613	+	0.126702i
$305$	1.57947	−	6.92010i	0.0904400	−	0.396244i
$306$	−0.269939	−	0.184041i	−0.0154314	−	0.0105210i
$307$	−0.120883	−	0.209375i	−0.00689913	−	0.0119496i	0.862555	−	0.505963i	$-0.168863\pi$
$307$	−0.120883	−	0.209375i	−0.00689913	−	0.0119496i	−0.869454	+	0.494013i	$0.835529\pi$
$308$	−0.599897	+	1.03905i	−0.0341823	+	0.0592055i
$309$	12.3565	−	5.95060i	0.702939	−	0.338518i
$310$	−1.81654	−	0.560328i	−0.103173	−	0.0318245i
$311$	−0.907477	−	12.1094i	−0.0514583	−	0.686663i	−0.961966	−	0.273170i	$-0.911928\pi$
$311$	−0.907477	−	12.1094i	−0.0514583	−	0.686663i	0.910507	−	0.413493i	$-0.135691\pi$
$312$	0.568329	+	2.49001i	0.0321753	+	0.140969i
$313$	−2.43499	+	6.20425i	−0.137634	+	0.350685i	−0.983027	−	0.183459i	$-0.941271\pi$
$313$	−2.43499	+	6.20425i	−0.137634	+	0.350685i	0.845394	+	0.534144i	$0.179366\pi$
$314$	0.0267937	−	0.357537i	0.00151206	−	0.0201770i
$315$	6.57579	−	0.991141i	0.370504	−	0.0558445i
$316$	7.48887	+	6.94866i	0.421282	+	0.390893i
$317$	30.2571	+	14.5710i	1.69941	+	0.818391i	0.993974	+	0.109612i	$0.0349609\pi$
$317$	30.2571	+	14.5710i	1.69941	+	0.818391i	0.705431	+	0.708778i	$0.250753\pi$
$318$	0.775917	−	0.529012i	0.0435113	−	0.0296655i
$319$	−0.271746	−	0.692398i	−0.0152149	−	0.0387668i
$320$	−10.8112	+	3.33482i	−0.604366	+	0.186422i
$321$	−15.4700	+	14.3541i	−0.863454	+	0.801168i
$322$	−2.34662	+	2.94257i	−0.130772	+	0.163983i
$323$	2.45437	−	3.07769i	0.136565	−	0.171247i
$324$	−1.93995	+	1.80001i	−0.107775	+	0.100001i
$325$	6.51151	−	2.00853i	0.361194	−	0.111413i
$326$	−0.525932	−	1.34005i	−0.0291287	−	0.0742187i
$327$	9.23688	−	6.29760i	0.510800	−	0.348258i
$328$	−3.83475	−	1.84672i	−0.211738	−	0.101968i
$329$	−11.1402	−	10.3366i	−0.614181	−	0.569877i
$330$	−0.0885590	+	0.0133481i	−0.00487501	+	0.000734790i
$331$	−0.499054	+	6.65942i	−0.0274305	+	0.366035i	0.966550	+	0.256478i	$0.0825621\pi$
$331$	−0.499054	+	6.65942i	−0.0274305	+	0.366035i	−0.993981	+	0.109557i	$0.965057\pi$
$332$	6.07534	−	15.4797i	0.333428	−	0.849560i
$333$	−1.59172	−	6.97380i	−0.0872259	−	0.382162i
$334$	−0.0465583	−	0.621277i	−0.00254755	−	0.0339948i
$335$	−22.7319	−	7.01187i	−1.24198	−	0.383099i
$336$	−9.96218	+	4.79753i	−0.543482	+	0.261727i
$337$	−9.32499	+	16.1514i	−0.507965	+	0.879821i	0.491993	+	0.870599i	$0.336269\pi$
$337$	−9.32499	+	16.1514i	−0.507965	+	0.879821i	−0.999957	+	0.00922155i	$0.997065\pi$
$338$	−0.515655	−	0.893141i	−0.0280479	−	0.0485805i
$339$	−0.299689	−	0.204325i	−0.0162769	−	0.0110974i
$340$	−0.698120	+	3.05866i	−0.0378609	+	0.165879i
$341$	1.43527	+	0.216331i	0.0777240	+	0.0117150i
$342$	−0.801864	−	1.00551i	−0.0433599	−	0.0543715i
$343$	−19.2561			−1.03973
$344$	−0.00298480	−	5.15355i	−0.000160930	−	0.277861i
$345$	13.9893			0.753158
$346$	−1.12709	−	1.41332i	−0.0605925	−	0.0759806i
$347$	23.5239	+	3.54566i	1.26283	+	0.190341i	0.746116	−	0.665816i	$-0.231916\pi$
$347$	23.5239	+	3.54566i	1.26283	+	0.190341i	0.516715	+	0.856157i	$0.327155\pi$
$348$	1.55727	−	6.82284i	0.0834783	−	0.365743i
$349$	−12.4361	−	8.47882i	−0.665692	−	0.453861i	0.182743	−	0.983161i	$-0.441502\pi$
$349$	−12.4361	−	8.47882i	−0.665692	−	0.453861i	−0.848435	+	0.529300i	$0.822455\pi$
$350$	−0.610921	−	1.05815i	−0.0326551	−	0.0565602i
$351$	−7.55004	+	13.0770i	−0.402991	+	0.698001i
$352$	−0.506532	+	0.243933i	−0.0269983	+	0.0130017i
$353$	3.81783	+	1.17764i	0.203202	+	0.0626796i	0.394686	−	0.918816i	$-0.370854\pi$
$353$	3.81783	+	1.17764i	0.203202	+	0.0626796i	−0.191483	+	0.981496i	$0.561330\pi$
$354$	−0.0467913	−	0.624386i	−0.00248693	−	0.0331858i
$355$	1.46843	+	6.43360i	0.0779361	+	0.341460i
$356$	1.89250	−	4.82202i	0.100303	−	0.255567i
$357$	−0.219452	+	2.92839i	−0.0116147	+	0.154987i
$358$	2.89767	−	0.436754i	0.153147	−	0.0230832i
$359$	9.70483	+	9.00476i	0.512201	+	0.475253i	0.893414	−	0.449234i	$-0.148303\pi$
$359$	9.70483	+	9.00476i	0.512201	+	0.475253i	−0.381213	+	0.924487i	$0.624494\pi$
$360$	1.86551	+	0.898384i	0.0983212	+	0.0473490i
$361$	−2.89507	+	1.97382i	−0.152372	+	0.103886i
$362$	1.37672	+	3.50783i	0.0723590	+	0.184368i
$363$	−12.1637	+	3.75200i	−0.638427	+	0.196929i
$364$	−10.1335	+	9.40253i	−0.531141	+	0.492827i
$365$	−3.58368	+	4.49380i	−0.187579	+	0.235216i
$366$	0.638482	−	0.800631i	0.0333740	−	0.0418496i
$367$	−9.41413	+	8.73504i	−0.491414	+	0.455965i	−0.886534	−	0.462664i	$-0.846894\pi$
$367$	−9.41413	+	8.73504i	−0.491414	+	0.455965i	0.395120	+	0.918630i	$0.370703\pi$
$368$	27.0371	−	8.33983i	1.40940	−	0.434744i
$369$	−3.25765	−	8.30036i	−0.169587	−	0.432100i
$370$	1.13979	−	0.777094i	0.0592547	−	0.0403992i
$371$	9.25093	+	4.45501i	0.480284	+	0.231293i
$372$	10.0109	+	9.28874i	0.519040	+	0.481599i
$373$	−7.13014	+	1.07470i	−0.369185	+	0.0556457i	−0.331015	−	0.943626i	$-0.607391\pi$
$373$	−7.13014	+	1.07470i	−0.369185	+	0.0556457i	−0.0381701	+	0.999271i	$0.512153\pi$
$374$	−0.00359506	+	0.0479728i	−0.000185896	+	0.00248061i
$375$	−5.05988	+	12.8924i	−0.261291	+	0.665759i
$376$	−1.05292	−	4.61313i	−0.0543000	−	0.237904i
$377$	−0.640442	−	8.54610i	−0.0329844	−	0.440147i
$378$	2.58726	+	0.798063i	0.133074	+	0.0410480i
$379$	−9.20357	+	4.43221i	−0.472756	+	0.227667i	−0.655063	−	0.755575i	$-0.727358\pi$
$379$	−9.20357	+	4.43221i	−0.472756	+	0.227667i	0.182307	+	0.983242i	$0.441644\pi$
$380$	−6.17505	+	10.6955i	−0.316773	+	0.548667i
$381$	4.26383	+	7.38517i	0.218443	+	0.378354i
$382$	2.79381	+	1.90478i	0.142944	+	0.0974572i
$383$	1.56554	−	6.85910i	0.0799956	−	0.350483i	−0.919051	−	0.394138i	$-0.871043\pi$
$383$	1.56554	−	6.85910i	0.0799956	−	0.350483i	0.999047	+	0.0436549i	$0.0139002\pi$
$384$	−6.94962	−	1.04749i	−0.354646	−	0.0534544i
$385$	−0.610528	−	0.765578i	−0.0311154	−	0.0390175i
$386$	3.11089			0.158340
$387$	7.33895	−	7.91870i	0.373060	−	0.402530i
$388$	−29.7606			−1.51086
$389$	−6.54907	−	8.21227i	−0.332051	−	0.416379i	0.587578	−	0.809168i	$-0.300082\pi$
$389$	−6.54907	−	8.21227i	−0.332051	−	0.416379i	−0.919629	+	0.392789i	$0.871510\pi$
$390$	−1.02036	−	0.153794i	−0.0516678	−	0.00778766i
$391$	1.67212	−	7.32603i	0.0845626	−	0.370493i
$392$	−0.408329	−	0.278394i	−0.0206237	−	0.0140610i
$393$	9.58677	+	16.6048i	0.483589	+	0.837600i
$394$	−0.280096	+	0.485140i	−0.0141110	+	0.0244410i
$395$	−7.51210	+	3.61764i	−0.377975	+	0.182023i
$396$	−0.747846	−	0.230680i	−0.0375807	−	0.0115921i
$397$	0.252228	+	3.36575i	0.0126590	+	0.168922i	0.999950	+	0.00999943i	$0.00318297\pi$
$397$	0.252228	+	3.36575i	0.0126590	+	0.168922i	−0.987291	+	0.158923i	$0.949198\pi$
$398$	0.00442546	+	0.0193892i	0.000221828	+	0.000971894i
$399$	−4.22332	+	10.7609i	−0.211431	+	0.538716i
$400$	−0.686423	+	9.15968i	−0.0343211	+	0.457984i
$401$	−16.0858	+	2.42455i	−0.803289	+	0.121076i	−0.537838	−	0.843048i	$-0.680759\pi$
$401$	−16.0858	+	2.42455i	−0.803289	+	0.121076i	−0.265451	+	0.964124i	$0.585521\pi$
$402$	−2.51586	−	2.33438i	−0.125480	−	0.116428i
$403$	15.0674	+	7.25609i	0.750562	+	0.361452i
$404$	−8.63846	+	5.88961i	−0.429780	+	0.293019i
$405$	−0.789086	−	2.01056i	−0.0392100	−	0.0999055i
$406$	−1.46840	+	0.452942i	−0.0728756	+	0.0224791i
$407$	−0.772115	+	0.716418i	−0.0382723	+	0.0355115i
$408$	−0.570082	+	0.714860i	−0.0282232	+	0.0353908i
$409$	−5.09072	+	6.38356i	−0.251720	+	0.315647i	−0.891596	−	0.452831i	$-0.850414\pi$
$409$	−5.09072	+	6.38356i	−0.251720	+	0.315647i	0.639876	+	0.768478i	$0.278986\pi$
$410$	1.26056	−	1.16963i	0.0622545	−	0.0577637i
$411$	−15.0315	+	4.63659i	−0.741447	+	0.228706i
$412$	8.44393	+	21.5148i	0.416003	+	1.05996i
$413$	5.65641	−	3.85647i	0.278334	−	0.189765i
$414$	−2.21190	−	1.06520i	−0.108709	−	0.0523516i
$415$	9.94894	+	9.23127i	0.488374	+	0.453145i
$416$	−6.40529	+	0.965442i	−0.314045	+	0.0473347i
$417$	1.00834	−	13.4554i	0.0493788	−	0.658914i
$418$	−0.0691863	+	0.176284i	−0.00338401	+	0.00862233i
$419$	2.84221	+	12.4525i	0.138851	+	0.608345i	0.995689	+	0.0927590i	$0.0295686\pi$
$419$	2.84221	+	12.4525i	0.138851	+	0.608345i	−0.856838	+	0.515586i	$0.827574\pi$
$420$	−0.688493	−	9.18730i	−0.0335950	−	0.448294i
$421$	27.5972	+	8.51262i	1.34501	+	0.414880i	0.881906	−	0.471425i	$-0.156260\pi$
$421$	27.5972	+	8.51262i	1.34501	+	0.414880i	0.463101	+	0.886305i	$0.346737\pi$
$422$	0.783435	−	0.377282i	0.0381370	−	0.0183658i
$423$	4.95647	−	8.58485i	0.240992	−	0.417410i
$424$	1.59848	+	2.76866i	0.0776293	+	0.134458i
$425$	2.01559	+	1.37421i	0.0977704	+	0.0666587i
$426$	−0.211852	+	0.928183i	−0.0102642	+	0.0449706i
$427$	11.0715	+	1.66876i	0.535788	+	0.0807571i
$428$	−22.1741	−	27.8054i	−1.07182	−	1.34403i
$429$	0.787878			0.0380391
$430$	1.93864	+	0.759564i	0.0934895	+	0.0366294i
$431$	28.6387			1.37948			0.689738	−	0.724059i	$-0.257726\pi$
$431$	28.6387			1.37948			0.689738	+	0.724059i	$0.257726\pi$
$432$	−12.6907	−	15.9137i	−0.610583	−	0.765647i
$433$	28.9848	+	4.36876i	1.39292	+	0.209949i	0.802263	−	0.596971i	$-0.203629\pi$
$433$	28.9848	+	4.36876i	1.39292	+	0.209949i	0.590660	+	0.806921i	$0.298867\pi$
$434$	0.667263	−	2.92347i	0.0320297	−	0.140331i
$435$	4.71920	+	3.21749i	0.226268	+	0.154267i
$436$	9.41996	+	16.3158i	0.451134	+	0.781387i
$437$	14.7903	−	25.6175i	0.707516	−	1.22545i
$438$	−0.747118	+	0.359793i	−0.0356987	+	0.0171916i
$439$	15.0662	+	4.64732i	0.719072	+	0.221804i	0.632632	−	0.774453i	$-0.281975\pi$
$439$	15.0662	+	4.64732i	0.719072	+	0.221804i	0.0864402	+	0.996257i	$0.472451\pi$
$440$	−0.0227842	−	0.304035i	−0.00108620	−	0.0144943i
$441$	−0.230385	−	1.00938i	−0.0109707	−	0.0480659i
$442$	−0.202502	+	0.515966i	−0.00963202	+	0.0245420i
$443$	−1.94838	+	25.9993i	−0.0925702	+	1.23526i	0.736624	+	0.676303i	$0.236419\pi$
$443$	−1.94838	+	25.9993i	−0.0925702	+	1.23526i	−0.829194	+	0.558961i	$0.811200\pi$
$444$	−9.79934	+	1.47701i	−0.465056	+	0.0700959i
$445$	3.09915	+	2.87559i	0.146914	+	0.136316i
$446$	4.40515	+	2.12141i	0.208590	+	0.100452i
$447$	−9.16826	+	6.25081i	−0.433644	+	0.295653i
$448$	−6.52011	−	16.6130i	−0.308046	−	0.784889i
$449$	−13.1931	+	4.06954i	−0.622621	+	0.192053i	−0.589985	−	0.807414i	$-0.700866\pi$
$449$	−13.1931	+	4.06954i	−0.622621	+	0.192053i	−0.0326361	+	0.999467i	$0.510390\pi$
$450$	0.584240	−	0.542096i	0.0275414	−	0.0255546i
$451$	−0.818627	+	1.02653i	−0.0385476	+	0.0483372i
$452$	0.381113	−	0.477901i	0.0179261	−	0.0224786i
$453$	−11.0219	+	10.2269i	−0.517856	+	0.480500i
$454$	−5.05433	+	1.55906i	−0.237212	+	0.0731701i
$455$	−4.12187	−	10.5023i	−0.193236	−	0.492358i
$456$	−2.97389	+	2.02756i	−0.139265	+	0.0949492i
$457$	21.1914	+	10.2052i	0.991291	+	0.477381i	0.857974	−	0.513693i	$-0.171723\pi$
$457$	21.1914	+	10.2052i	0.991291	+	0.477381i	0.133317	+	0.991073i	$0.457437\pi$
$458$	1.65662	+	1.53712i	0.0774089	+	0.0718250i
$459$	−5.34539	+	0.805688i	−0.249502	+	0.0376063i
$460$	−1.76178	+	23.5093i	−0.0821432	+	1.09612i
$461$	−7.95043	+	20.2574i	−0.370289	+	0.943480i	0.617344	+	0.786693i	$0.288209\pi$
$461$	−7.95043	+	20.2574i	−0.370289	+	0.943480i	−0.987633	+	0.156787i	$0.949887\pi$
$462$	−0.0314360	−	0.137730i	−0.00146253	−	0.00640777i
$463$	−2.54333	−	33.9384i	−0.118199	−	1.57725i	−0.669416	−	0.742888i	$-0.733455\pi$
$463$	−2.54333	−	33.9384i	−0.118199	−	1.57725i	0.551217	−	0.834362i	$-0.314164\pi$
$464$	11.0389	+	3.40505i	0.512469	+	0.158076i
$465$	−10.0419	+	4.83594i	−0.465684	+	0.224261i
$466$	−0.654314	+	1.13330i	−0.0303105	+	0.0524993i
$467$	19.2324	+	33.3114i	0.889968	+	1.54147i	0.839911	+	0.542724i	$0.182607\pi$
$467$	19.2324	+	33.3114i	0.889968	+	1.54147i	0.0500568	+	0.998746i	$0.484060\pi$
$468$	−7.45029	−	5.07952i	−0.344390	−	0.234801i
$469$	8.35003	−	36.5839i	0.385569	−	1.68929i
$470$	1.89036	+	0.284927i	0.0871960	+	0.0131427i
$471$	−1.31067	−	1.64353i	−0.0603924	−	0.0757297i
$472$	2.13156			0.0981131
$473$	−1.55012	−	0.352861i	−0.0712747	−	0.0162246i
$474$	−1.20290			−0.0552512
$475$	5.98738	+	7.50794i	0.274720	+	0.344488i
$476$	−4.89357	−	0.737588i	−0.224297	−	0.0338073i
$477$	−1.49035	+	6.52966i	−0.0682385	+	0.298972i
$478$	4.41902	+	3.01284i	0.202121	+	0.137804i
$479$	3.36033	+	5.82027i	0.153538	+	0.265935i	0.932526	−	0.361104i	$-0.117600\pi$
$479$	3.36033	+	5.82027i	0.153538	+	0.265935i	−0.778988	+	0.627039i	$0.784267\pi$
$480$	2.15856	−	3.73874i	0.0985245	−	0.170649i
$481$	−10.9339	+	5.26550i	−0.498544	+	0.240086i
$482$	−5.69875	−	1.75783i	−0.259571	−	0.0800670i
$483$	1.64906	+	22.0052i	0.0750348	+	1.00127i
$484$	−4.77344	−	20.9138i	−0.216974	−	0.950627i
$485$	8.87380	−	22.6101i	0.402939	−	1.02667i
$486$	−0.217196	+	2.89828i	−0.00985221	+	0.131469i
$487$	−5.06977	+	0.764145i	−0.229733	+	0.0346267i	−0.262900	−	0.964823i	$-0.584679\pi$
$487$	−5.06977	+	0.764145i	−0.229733	+	0.0346267i	0.0331666	+	0.999450i	$0.489441\pi$
$488$	2.55554	+	2.37119i	0.115684	+	0.107339i
$489$	−7.60445	−	3.66211i	−0.343885	−	0.165606i
$490$	0.164972	−	0.112476i	0.00745269	−	0.00508116i
$491$	8.34376	+	21.2596i	0.376549	+	0.959431i	0.986021	+	0.166623i	$0.0532863\pi$
$491$	8.34376	+	21.2596i	0.376549	+	0.959431i	−0.609472	+	0.792808i	$0.708619\pi$
$492$	−11.8045	+	3.64121i	−0.532188	+	0.164158i
$493$	2.24904	−	2.08681i	0.101292	−	0.0939850i
$494$	−1.36041	+	1.70590i	−0.0612078	+	0.0767522i
$495$	0.398243	−	0.499381i	0.0178997	−	0.0224455i
$496$	−16.5250	+	15.3330i	−0.741996	+	0.688472i
$497$	−9.94697	+	3.06823i	−0.446182	+	0.137629i
$498$	0.715352	+	1.82269i	0.0320557	+	0.0816766i
$499$	17.7380	−	12.0936i	0.794062	−	0.541382i	−0.0969889	−	0.995285i	$-0.530921\pi$
$499$	17.7380	−	12.0936i	0.794062	−	0.541382i	0.891051	+	0.453903i	$0.149969\pi$
$500$	−21.0286	−	10.1269i	−0.940429	−	0.452887i
$501$	−2.67770	−	2.48455i	−0.119631	−	0.111001i
$502$	2.02927	−	0.305863i	0.0905706	−	0.0136513i
$503$	−0.497710	+	6.64148i	−0.0221918	+	0.296129i	0.975054	+	0.221966i	$0.0712475\pi$
$503$	−0.497710	+	6.64148i	−0.0221918	+	0.296129i	−0.997246	+	0.0741628i	$0.976372\pi$
$504$	−1.19325	+	3.04036i	−0.0531517	+	0.135428i
$505$	−1.89877	−	8.31904i	−0.0844940	−	0.370193i
$506$	0.0270148	+	0.360488i	0.00120096	+	0.0160256i
$507$	−5.77803	−	1.78229i	−0.256611	−	0.0791541i
$508$	−12.9479	+	6.23538i	−0.574470	+	0.276650i
$509$	−7.01453	+	12.1495i	−0.310913	+	0.538518i	−0.978560	−	0.205960i	$-0.933968\pi$
$509$	−7.01453	+	12.1495i	−0.310913	+	0.538518i	0.667647	+	0.744478i	$0.267302\pi$
$510$	−0.184705	−	0.319918i	−0.00817887	−	0.0141662i
$511$	−7.49119	−	5.10741i	−0.331391	−	0.225938i
$512$	3.25993	−	14.2827i	0.144070	−	0.631212i
$513$	−21.0422	−	3.17160i	−0.929035	−	0.140029i
$514$	0.680136	+	0.852864i	0.0299995	+	0.0376182i
$515$	−18.8632			−0.831214
$516$	−10.1801	−	10.9589i	−0.448156	−	0.482437i
$517$	−1.45966			−0.0641959
$518$	1.35673	+	1.70128i	0.0596112	+	0.0747501i
$519$	−10.4804	−	1.57966i	−0.460037	−	0.0693394i
$520$	0.781681	−	3.42477i	0.0342790	−	0.150186i
$521$	7.42972	+	5.06549i	0.325502	+	0.221923i	0.715034	−	0.699089i	$-0.246411\pi$
$521$	7.42972	+	5.06549i	0.325502	+	0.221923i	−0.389533	+	0.921013i	$0.627363\pi$
$522$	−0.501179	−	0.868068i	−0.0219360	−	0.0379943i
$523$	−1.20159	+	2.08121i	−0.0525418	+	0.0910051i	−0.891100	−	0.453807i	$-0.850066\pi$
$523$	−1.20159	+	2.08121i	−0.0525418	+	0.0910051i	0.838558	+	0.544812i	$0.183399\pi$
$524$	−29.1120	+	14.0196i	−1.27176	+	0.612448i
$525$	−6.84550	−	2.11156i	−0.298762	−	0.0921559i
$526$	0.0142852	+	0.190622i	0.000622862	+	0.00831152i
$527$	1.33223	+	5.83688i	0.0580328	+	0.254258i
$528$	−0.388004	+	0.988617i	−0.0168857	+	0.0430240i
$529$	2.50096	−	33.3730i	0.108738	−	1.45100i
$530$	−1.27721	+	0.192508i	−0.0554783	+	0.00836201i
$531$	3.27350	+	3.03736i	0.142058	+	0.131810i
$532$	−17.5519	−	8.45257i	−0.760973	−	0.366465i
$533$	−12.4992	+	8.52180i	−0.541400	+	0.369120i
$534$	0.222836	+	0.567778i	0.00964308	+	0.0245702i
$535$	27.7364	−	8.55554i	1.19915	−	0.369888i
$536$	8.56475	−	7.94693i	0.369941	−	0.343255i
$537$	10.7123	−	13.4328i	0.462271	−	0.579669i
$538$	0.870147	−	1.09113i	0.0375147	−	0.0470420i
$539$	−0.111756	+	0.103694i	−0.00481365	+	0.00446642i
$540$	16.2062	−	4.99894i	0.697403	−	0.215120i
$541$	7.41483	+	18.8927i	0.318789	+	0.812260i	0.997001	+	0.0773937i	$0.0246598\pi$
$541$	7.41483	+	18.8927i	0.318789	+	0.812260i	−0.678212	+	0.734866i	$0.737245\pi$
$542$	2.83105	−	1.93017i	0.121604	−	0.0829081i
$543$	19.9060	+	9.58624i	0.854249	+	0.411385i
$544$	−1.69993	−	1.57730i	−0.0728837	−	0.0676262i
$545$	−15.2045	+	2.29170i	−0.651287	+	0.0981658i
$546$	0.121638	−	1.62315i	0.00520564	−	0.0694645i
$547$	−1.06346	+	2.70965i	−0.0454703	+	0.115856i	−0.951805	−	0.306705i	$-0.900774\pi$
$547$	−1.06346	+	2.70965i	−0.0454703	+	0.115856i	0.906334	+	0.422561i	$0.138869\pi$
$548$	−5.89885	−	25.8446i	−0.251986	−	1.10402i
$549$	0.545786	+	7.28301i	0.0232936	+	0.310831i
$550$	−0.112143	−	0.0345914i	−0.00478178	−	0.00147498i
$551$	10.8814	−	5.24019i	0.463562	−	0.223240i
$552$	−3.43537	+	5.95024i	−0.146219	+	0.253259i
$553$	−6.57608	−	11.3901i	−0.279643	−	0.484356i
$554$	3.31013	+	2.25681i	0.140634	+	0.0958826i
$555$	1.79976	−	7.88528i	0.0763957	−	0.334712i
$556$	22.4851	+	3.38908i	0.953580	+	0.143729i
$557$	2.35286	+	2.95040i	0.0996940	+	0.125012i	0.829176	−	0.558988i	$-0.188810\pi$
$557$	2.35286	+	2.95040i	0.0996940	+	0.125012i	−0.729482	+	0.684000i	$0.760239\pi$
$558$	1.95600			0.0828040
$559$	−15.8683	−	9.14934i	−0.671159	−	0.386976i
$560$	15.2081			0.642658
$561$	0.175860	+	0.220521i	0.00742481	+	0.00931042i
$562$	−4.81470	−	0.725699i	−0.203096	−	0.0306118i
$563$	8.32361	−	36.4681i	0.350798	−	1.53695i	−0.424545	−	0.905407i	$-0.639566\pi$
$563$	8.32361	−	36.4681i	0.350798	−	1.53695i	0.775343	−	0.631540i	$-0.217577\pi$
$564$	−11.3471	−	7.73634i	−0.477800	−	0.325759i
$565$	0.249439	+	0.432041i	0.0104940	+	0.0181761i
$566$	2.45394	−	4.25035i	0.103147	−	0.178656i
$567$	3.06959	−	1.47824i	0.128911	−	0.0620802i
$568$	−3.09709	−	0.955325i	−0.129951	−	0.0400845i
$569$	0.615960	+	8.21941i	0.0258224	+	0.344576i	0.995119	+	0.0986815i	$0.0314625\pi$
$569$	0.615960	+	8.21941i	0.0258224	+	0.344576i	−0.969297	+	0.245894i	$0.920918\pi$
$570$	−0.323586	−	1.41772i	−0.0135535	−	0.0593820i
$571$	−2.40795	+	6.13536i	−0.100770	+	0.256757i	−0.972364	−	0.233472i	$-0.924991\pi$
$571$	−2.40795	+	6.13536i	−0.100770	+	0.256757i	0.871594	+	0.490228i	$0.163087\pi$
$572$	−0.0992233	+	1.32404i	−0.00414874	+	0.0553610i
$573$	19.6037	−	2.95479i	0.818958	−	0.123438i
$574$	1.98842	+	1.84498i	0.0829949	+	0.0770080i
$575$	16.5159	+	7.95363i	0.688760	+	0.331689i
$576$	9.61843	−	6.55774i	0.400768	−	0.273239i
$577$	−0.433495	−	1.10453i	−0.0180466	−	0.0459821i	0.921566	−	0.388221i	$-0.126910\pi$
$577$	−0.433495	−	1.10453i	−0.0180466	−	0.0459821i	−0.939613	+	0.342239i	$0.888815\pi$
$578$	−0.189615	+	0.0584885i	−0.00788694	+	0.00243280i
$579$	13.3704	−	12.4060i	0.555656	−	0.515574i
$580$	−6.00138	+	7.52549i	−0.249194	+	0.312479i
$581$	−13.3480	+	16.7379i	−0.553769	+	0.694404i
$582$	2.56877	−	2.38347i	0.106479	−	0.0987980i
$583$	0.942393	−	0.290690i	0.0390299	−	0.0120391i
$584$	−1.03135	−	2.62784i	−0.0426776	−	0.108741i
$585$	6.08056	−	4.14565i	0.251400	−	0.171402i
$586$	−1.43516	−	0.691134i	−0.0592857	−	0.0285505i
$587$	35.4666	+	32.9082i	1.46386	+	1.35827i	0.769533	+	0.638607i	$0.220489\pi$
$587$	35.4666	+	32.9082i	1.46386	+	1.35827i	0.694329	+	0.719658i	$0.255701\pi$
$588$	−1.41835	+	0.213782i	−0.0584919	+	0.00881623i
$589$	−1.76122	+	23.5019i	−0.0725700	+	0.968379i
$590$	−0.314628	+	0.801659i	−0.0129530	+	0.0330038i
$591$	0.730860	+	3.20210i	0.0300635	+	0.131717i
$592$	−1.22248	−	16.3128i	−0.0502435	−	0.670452i
$593$	−9.35330	−	2.88511i	−0.384094	−	0.118477i	0.0966941	−	0.995314i	$-0.469173\pi$
$593$	−9.35330	−	2.88511i	−0.384094	−	0.118477i	−0.480788	+	0.876837i	$0.659649\pi$
$594$	0.234303	−	0.112834i	0.00961358	−	0.00462966i
$595$	2.01950	−	3.49788i	0.0827915	−	0.143399i
$596$	−9.34998	−	16.1946i	−0.382990	−	0.663359i
$597$	0.0963429	+	0.0656855i	0.00394305	+	0.00268833i
$598$	−0.926823	+	4.06068i	−0.0379006	+	0.166053i
$599$	−6.50432	−	0.980369i	−0.265759	−	0.0400568i	0.0148107	−	0.999890i	$-0.495285\pi$
$599$	−6.50432	−	0.980369i	−0.265759	−	0.0400568i	−0.280570	+	0.959834i	$0.590524\pi$
$600$	−1.39070	−	1.74388i	−0.0567751	−	0.0711937i
$601$	27.9807			1.14136			0.570678	−	0.821174i	$-0.306680\pi$
$601$	27.9807			1.14136			0.570678	+	0.821174i	$0.306680\pi$
$602$	−0.966268	+	3.13902i	−0.0393822	+	0.127937i
$603$	24.4771			0.996783
$604$	−15.7984	−	19.8105i	−0.642826	−	0.806078i
$605$	17.3122	+	2.60940i	0.703841	+	0.106087i
$606$	0.273937	−	1.20020i	0.0111279	−	0.0487547i
$607$	−29.0840	−	19.8291i	−1.18048	−	0.804840i	−0.196049	−	0.980594i	$-0.562811\pi$
$607$	−29.0840	−	19.8291i	−1.18048	−	0.804840i	−0.984434	+	0.175754i	$0.943764\pi$
$608$	−4.56432	−	7.90564i	−0.185108	−	0.320616i
$609$	−4.50482	+	7.80258i	−0.182545	+	0.316177i
$610$	−1.26899	+	0.611114i	−0.0513799	+	0.0247433i
$611$	−16.0707	−	4.95716i	−0.650152	−	0.200545i
$612$	−0.241236	−	3.21907i	−0.00975138	−	0.130123i
$613$	8.73407	+	38.2665i	0.352766	+	1.54557i	0.770764	+	0.637120i	$0.219875\pi$
$613$	8.73407	+	38.2665i	0.352766	+	1.54557i	−0.417999	+	0.908448i	$0.637268\pi$
$614$	−0.0175267	+	0.0446574i	−0.000707321	+	0.00180222i
$615$	0.753442	−	10.0540i	0.0303817	−	0.405416i
$616$	0.475561	−	0.0716793i	0.0191609	−	0.00288804i
$617$	−21.1490	−	19.6234i	−0.851427	−	0.790009i	0.128007	−	0.991773i	$-0.459142\pi$
$617$	−21.1490	−	19.6234i	−0.851427	−	0.790009i	−0.979434	+	0.201764i	$0.935333\pi$
$618$	−2.45192	−	1.18078i	−0.0986305	−	0.0474980i
$619$	9.55050	−	6.51142i	0.383867	−	0.261716i	−0.355977	−	0.934495i	$-0.615852\pi$
$619$	9.55050	−	6.51142i	0.383867	−	0.261716i	0.739844	+	0.672779i	$0.234899\pi$
$620$	−6.86223	−	17.4847i	−0.275594	−	0.702202i
$621$	−38.8166	+	11.9733i	−1.55766	+	0.480473i
$622$	−1.76638	+	1.63896i	−0.0708253	+	0.0657162i
$623$	−4.15798	+	5.21395i	−0.166586	+	0.208892i
$624$	−7.62932	+	9.56687i	−0.305417	+	0.382981i
$625$	5.02257	−	4.66026i	0.200903	−	0.186411i
$626$	1.26378	−	0.389824i	0.0505107	−	0.0155805i
$627$	0.405646	+	1.03357i	0.0161999	+	0.0412767i
$628$	2.92704	−	1.99562i	0.116802	−	0.0796340i
$629$	−3.91431	−	1.88503i	−0.156074	−	0.0751611i
$630$	−0.967318	−	0.897540i	−0.0385389	−	0.0357589i
$631$	−27.6788	+	4.17191i	−1.10188	+	0.166081i	−0.674704	−	0.738089i	$-0.735729\pi$
$631$	−27.6788	+	4.17191i	−1.10188	+	0.166081i	−0.427173	+	0.904170i	$0.640490\pi$
$632$	0.306024	−	4.08360i	0.0121730	−	0.162437i
$633$	1.86259	−	4.74581i	0.0740314	−	0.188629i
$634$	−1.48285	−	6.49678i	−0.0588914	−	0.258020i
$635$	−0.876506	−	11.6962i	−0.0347831	−	0.464148i
$636$	8.86665	+	2.73500i	0.351586	+	0.108450i
$637$	−1.58257	+	0.762127i	−0.0627038	+	0.0301966i
$638$	−0.0737978	+	0.127822i	−0.00292168	+	0.00506051i
$639$	−3.39499	−	5.88030i	−0.134304	−	0.232621i
$640$	7.98682	+	5.44532i	0.315707	+	0.215245i
$641$	5.26912	−	23.0855i	0.208118	−	0.911823i	−0.757701	−	0.652602i	$-0.773677\pi$
$641$	5.26912	−	23.0855i	0.208118	−	0.911823i	0.965818	−	0.259220i	$-0.0834656\pi$
$642$	4.14083	+	0.624130i	0.163426	+	0.0246324i
$643$	−23.3653	−	29.2992i	−0.921438	−	1.15545i	−0.987498	−	0.157631i	$-0.949614\pi$
$643$	−23.3653	−	29.2992i	−0.921438	−	1.15545i	0.0660600	−	0.997816i	$-0.478957\pi$
$644$	−37.1878			−1.46540
$645$	11.3612	−	4.46656i	0.447349	−	0.175870i
$646$	−0.781124			−0.0307329
$647$	22.7661	+	28.5477i	0.895026	+	1.12233i	0.991899	+	0.127031i	$0.0405447\pi$
$647$	22.7661	+	28.5477i	0.895026	+	1.12233i	−0.0968724	+	0.995297i	$0.530884\pi$
$648$	1.04895	+	0.158104i	0.0412068	+	0.00621092i
$649$	0.146318	−	0.641062i	0.00574350	−	0.0251639i
$650$	−1.11720	−	0.761696i	−0.0438203	−	0.0298762i
$651$	−8.79069	−	15.2259i	−0.344534	−	0.596751i
$652$	7.11193	−	12.3182i	0.278525	−	0.482419i
$653$	−11.4559	+	5.51686i	−0.448303	+	0.215892i	−0.644393	−	0.764694i	$-0.722890\pi$
$653$	−11.4559	+	5.51686i	−0.448303	+	0.215892i	0.196090	+	0.980586i	$0.437176\pi$
$654$	−2.11979	−	0.653867i	−0.0828902	−	0.0255682i
$655$	−1.97073	−	26.2976i	−0.0770028	−	1.02753i
$656$	−4.53759	−	19.8805i	−0.177163	−	0.776202i
$657$	2.16066	−	5.50527i	0.0842953	−	0.214781i
$658$	−0.225353	+	3.00713i	−0.00878519	+	0.117230i
$659$	37.0601	−	5.58591i	1.44366	−	0.217596i	0.619963	−	0.784631i	$-0.287147\pi$
$659$	37.0601	−	5.58591i	1.44366	−	0.217596i	0.823694	+	0.567034i	$0.191909\pi$
$660$	−0.648681	−	0.601888i	−0.0252499	−	0.0234285i
$661$	16.2477	+	7.82448i	0.631962	+	0.304337i	0.722306	−	0.691574i	$-0.243082\pi$
$661$	16.2477	+	7.82448i	0.631962	+	0.304337i	−0.0903438	+	0.995911i	$0.528797\pi$
$662$	1.09488	−	0.746476i	0.0425537	−	0.0290126i
$663$	1.18729	+	3.02515i	0.0461103	+	0.117487i
$664$	−6.36962	+	1.96477i	−0.247189	+	0.0762478i
$665$	11.6552	−	10.8144i	0.451969	−	0.419366i
$666$	−0.884983	+	1.10973i	−0.0342924	+	0.0430013i
$667$	14.3743	−	18.0249i	0.556577	−	0.697925i
$668$	4.51255	−	4.18703i	0.174596	−	0.162001i
$669$	27.3931	−	8.44966i	1.05908	−	0.326683i
$670$	1.72456	+	4.39412i	0.0666257	+	0.169760i
$671$	0.888552	−	0.605805i	0.0343022	−	0.0233868i
$672$	6.13550	+	2.95470i	0.236682	+	0.113980i
$673$	17.2388	+	15.9953i	0.664508	+	0.616573i	0.938549	−	0.345145i	$-0.112170\pi$
$673$	17.2388	+	15.9953i	0.664508	+	0.616573i	−0.274042	+	0.961718i	$0.588361\pi$
$674$	3.65940	−	0.551565i	0.140955	−	0.0212455i
$675$	0.985484	−	13.1504i	0.0379313	−	0.506158i
$676$	3.72283	−	9.48563i	0.143186	−	0.364832i
$677$	4.99988	+	21.9059i	0.192161	+	0.841912i	0.975444	+	0.220247i	$0.0706862\pi$
$677$	4.99988	+	21.9059i	0.192161	+	0.841912i	−0.783283	+	0.621665i	$0.786457\pi$
$678$	0.00537860	+	0.0717725i	0.000206564	+	0.00275641i
$679$	36.6117	+	11.2932i	1.40503	+	0.433394i
$680$	1.13304	−	0.545645i	0.0434503	−	0.0209245i
$681$	−15.5059	+	26.8570i	−0.594187	+	1.02916i
$682$	−0.144009	−	0.249430i	−0.00551438	−	0.00955119i
$683$	−17.9014	−	12.2050i	−0.684977	−	0.467010i	0.170156	−	0.985417i	$-0.445573\pi$
$683$	−17.9014	−	12.2050i	−0.684977	−	0.467010i	−0.855134	+	0.518407i	$0.826525\pi$
$684$	2.82767	−	12.3888i	0.108119	−	0.473698i
$685$	21.3938	+	3.22460i	0.817416	+	0.123206i
$686$	2.38235	+	2.98737i	0.0909585	+	0.114058i
$687$	13.2500			0.505519
$688$	19.2951	−	15.4056i	0.735618	−	0.587333i
$689$	11.3629			0.432890
$690$	−1.73075	−	2.17029i	−0.0658884	−	0.0826215i
$691$	−36.3330	−	5.47632i	−1.38217	−	0.208329i	−0.584487	−	0.811403i	$-0.698704\pi$
$691$	−36.3330	−	5.47632i	−1.38217	−	0.208329i	−0.797685	+	0.603074i	$0.793942\pi$
$692$	3.97452	−	17.4135i	0.151089	−	0.661962i
$693$	0.832471	+	0.567569i	0.0316230	+	0.0215602i
$694$	−2.36030	−	4.08816i	−0.0895957	−	0.155184i
$695$	−9.27924	+	16.0721i	−0.351982	+	0.609650i
$696$	−2.52744	+	1.21715i	−0.0958022	+	0.0461359i
$697$	−5.17509	−	1.59630i	−0.196021	−	0.0604644i
$698$	0.223195	+	2.97833i	0.00844805	+	0.112731i
$699$	1.70731	+	7.48023i	0.0645766	+	0.282928i
$700$	4.41061	−	11.2381i	0.166706	−	0.424759i
$701$	1.16738	−	15.5775i	0.0440912	−	0.588356i	−0.930779	−	0.365582i	$-0.880870\pi$
$701$	1.16738	−	15.5775i	0.0440912	−	0.588356i	0.974870	−	0.222773i	$-0.0715110\pi$
$702$	2.96285	−	0.446578i	0.111826	−	0.0168550i
$703$	−12.5369	−	11.6326i	−0.472839	−	0.438730i
$704$	−1.54440	−	0.743742i	−0.0582067	−	0.0280308i
$705$	9.26095	−	6.31401i	0.348788	−	0.237799i
$706$	−0.289641	−	0.737992i	−0.0109008	−	0.0277747i
$707$	12.8620	−	3.96741i	0.483727	−	0.149210i
$708$	4.53513	−	4.20799i	0.170441	−	0.158146i
$709$	−4.77718	+	5.99039i	−0.179411	+	0.224974i	−0.863402	−	0.504516i	$-0.831671\pi$
$709$	−4.77718	+	5.99039i	−0.179411	+	0.224974i	0.683992	+	0.729490i	$0.260242\pi$
$710$	0.816432	−	1.02377i	0.0306401	−	0.0384215i
$711$	6.28888	−	5.83523i	0.235852	−	0.218838i
$712$	−1.98418	+	0.612037i	−0.0743601	+	0.0229371i
$713$	16.4362	+	41.8788i	0.615542	+	1.56837i
$714$	0.481459	−	0.328253i	0.0180181	−	0.0122846i
$715$	−0.976333	−	0.470177i	−0.0365128	−	0.0175836i
$716$	21.2250	+	19.6939i	0.793217	+	0.735997i
$717$	31.0076	−	4.67365i	1.15800	−	0.174541i
$718$	0.196317	−	2.61966i	0.00732647	−	0.0977650i
$719$	8.51179	−	21.6877i	0.317436	−	0.808815i	−0.679721	−	0.733471i	$-0.737899\pi$
$719$	8.51179	−	21.6877i	0.317436	−	0.808815i	0.997158	−	0.0753441i	$-0.0240055\pi$
$720$	2.20743	+	9.67138i	0.0822661	+	0.360431i
$721$	−2.22360	−	29.6719i	−0.0828113	−	1.10504i
$722$	0.664394	+	0.204938i	0.0247262	+	0.00762702i
$723$	−31.5030	+	15.1710i	−1.17161	+	0.564217i
$724$	−18.6168	+	32.2452i	−0.691887	+	1.19838i
$725$	3.74222	+	6.48171i	0.138983	+	0.240725i
$726$	2.08697	+	1.42287i	0.0774546	+	0.0528076i
$727$	3.67797	−	16.1142i	0.136408	−	0.597643i	−0.859799	−	0.510632i	$-0.829411\pi$
$727$	3.67797	−	16.1142i	0.136408	−	0.597643i	0.996207	−	0.0870109i	$-0.0277315\pi$
$728$	5.47931	+	0.825873i	0.203077	+	0.0306089i
$729$	13.1493	+	16.4887i	0.487011	+	0.610693i
$730$	1.14054			0.0422131
$731$	−0.981091	−	6.48363i	−0.0362870	−	0.239806i
$732$	10.1182			0.373981
$733$	−1.21298	−	1.52103i	−0.0448025	−	0.0561806i	0.758925	−	0.651178i	$-0.225725\pi$
$733$	−1.21298	−	1.52103i	−0.0448025	−	0.0561806i	−0.803728	+	0.594997i	$0.797153\pi$
$734$	2.51986	+	0.379808i	0.0930097	+	0.0140190i
$735$	0.260497	−	1.14131i	0.00960858	−	0.0420979i
$736$	−14.3978	−	9.81626i	−0.530711	−	0.361832i
$737$	−1.80210	−	3.12134i	−0.0663813	−	0.114976i
$738$	−0.884677	+	1.53231i	−0.0325654	+	0.0564050i
$739$	−13.7642	+	6.62848i	−0.506324	+	0.243833i	−0.669565	−	0.742754i	$-0.733519\pi$
$739$	−13.7642	+	6.62848i	−0.506324	+	0.243833i	0.163241	+	0.986586i	$0.447805\pi$
$740$	13.0247	+	4.01759i	0.478798	+	0.147690i
$741$	0.956012	+	12.7571i	0.0351200	+	0.468643i
$742$	−0.453373	−	1.98636i	−0.0166438	−	0.0729214i
$743$	1.06748	−	2.71989i	0.0391620	−	0.0997831i	−0.909955	−	0.414707i	$-0.863884\pi$
$743$	1.06748	−	2.71989i	0.0391620	−	0.0997831i	0.949117	+	0.314924i	$0.101979\pi$
$744$	0.409083	−	5.45883i	0.0149977	−	0.200130i
$745$	15.0915	−	2.27468i	0.552910	−	0.0833378i
$746$	1.04887	+	0.973205i	0.0384017	+	0.0356316i
$747$	−12.5817	−	6.05902i	−0.460340	−	0.221688i
$748$	−0.392737	+	0.267764i	−0.0143599	+	0.00979042i
$749$	16.7274	+	42.6208i	0.611208	+	1.55733i
$750$	2.62612	−	0.810051i	0.0958923	−	0.0295789i
$751$	−0.771269	+	0.715633i	−0.0281440	+	0.0261138i	−0.694119	−	0.719860i	$-0.744206\pi$
$751$	−0.771269	+	0.715633i	−0.0281440	+	0.0261138i	0.665975	+	0.745974i	$0.268016\pi$
$752$	14.1345	−	17.7241i	0.515431	−	0.646330i
$753$	7.50193	−	9.40712i	0.273385	−	0.342815i
$754$	−1.24660	+	1.15668i	−0.0453986	+	0.0421237i
$755$	19.7613	−	6.09556i	0.719188	−	0.221840i
$756$	9.77373	+	24.9031i	0.355467	+	0.905715i
$757$	26.8121	−	18.2802i	0.974503	−	0.664405i	0.0323106	−	0.999478i	$-0.489713\pi$
$757$	26.8121	−	18.2802i	0.974503	−	0.664405i	0.942192	+	0.335073i	$0.108761\pi$
$758$	1.82627	+	0.879485i	0.0663331	+	0.0319443i
$759$	1.55370	+	1.44163i	0.0563958	+	0.0523277i
$760$	4.89519	−	0.737832i	0.177567	−	0.0267640i
$761$	−1.35574	+	18.0911i	−0.0491456	+	0.655803i	0.917179	+	0.398476i	$0.130461\pi$
$761$	−1.35574	+	18.0911i	−0.0491456	+	0.655803i	−0.966324	+	0.257327i	$0.917158\pi$
$762$	0.618212	−	1.57518i	0.0223954	−	0.0570627i
$763$	−5.39716	−	23.6465i	−0.195390	−	0.856060i
$764$	2.49673	+	33.3166i	0.0903286	+	1.20535i
$765$	2.51756	+	0.776565i	0.0910226	+	0.0280768i
$766$	−1.25780	+	0.605726i	−0.0454463	+	0.0218858i
$767$	3.78806	−	6.56112i	0.136779	−	0.236908i
$768$	−7.52858	−	13.0399i	−0.271664	−	0.470536i
$769$	−32.9135	−	22.4401i	−1.18689	−	0.809209i	−0.201496	−	0.979489i	$-0.564580\pi$
$769$	−32.9135	−	22.4401i	−1.18689	−	0.809209i	−0.985396	+	0.170280i	$0.945533\pi$
$770$	−0.0432370	+	0.189434i	−0.00155815	+	0.00682672i
$771$	6.32434	+	0.953241i	0.227766	+	0.0343301i
$772$	19.1646	+	24.0316i	0.689749	+	0.864918i
$773$	−38.1707			−1.37290			−0.686452	−	0.727175i	$-0.740833\pi$
$773$	−38.1707			−1.37290			−0.686452	+	0.727175i	$0.740833\pi$
$774$	−2.13647	−	0.158862i	−0.0767939	−	0.00571018i
$775$	−14.6051			−0.524630
$776$	7.43787	+	9.32679i	0.267004	+	0.334812i
$777$	12.6157	+	1.90151i	0.452586	+	0.0682164i
$778$	−0.463799	+	2.03203i	−0.0166280	+	0.0728520i
$779$	−17.6145	−	12.0094i	−0.631106	−	0.430281i
$780$	−5.09784	−	8.82971i	−0.182532	−	0.316154i
$781$	−0.499907	+	0.865865i	−0.0178881	+	0.0309831i
$782$	−1.34343	+	0.646961i	−0.0480409	+	0.0231353i
$783$	−15.8484	−	4.88857i	−0.566374	−	0.174703i
$784$	−0.176941	−	2.36111i	−0.00631931	−	0.0843253i
$785$	0.643374	+	2.81881i	0.0229630	+	0.100608i
$786$	1.38998	−	3.54162i	0.0495791	−	0.126325i
$787$	−1.08772	+	14.5146i	−0.0387729	+	0.517389i	0.943678	+	0.330866i	$0.107341\pi$
$787$	−1.08772	+	14.5146i	−0.0387729	+	0.517389i	−0.982451	+	0.186523i	$0.940278\pi$
$788$	−5.47324	+	0.824958i	−0.194976	+	0.0293879i
$789$	0.821582	+	0.762316i	0.0292491	+	0.0271392i
$790$	1.49063	+	0.717850i	0.0530343	+	0.0255400i
$791$	−0.650197	+	0.443297i	−0.0231184	+	0.0157618i
$792$	0.114611	+	0.292023i	0.00407251	+	0.0103766i
$793$	11.8402	−	3.65223i	0.420459	−	0.129695i
$794$	0.490954	−	0.455539i	0.0174233	−	0.0161665i
$795$	−4.72166	+	5.92078i	−0.167460	+	0.209988i
$796$	−0.122519	+	0.153634i	−0.00434257	+	0.00544541i
$797$	−39.9528	+	37.0708i	−1.41520	+	1.31311i	−0.529927	+	0.848043i	$0.677781\pi$
$797$	−39.9528	+	37.0708i	−1.41520	+	1.31311i	−0.885274	+	0.465071i	$0.846029\pi$
$798$	2.19194	−	0.676123i	0.0775938	−	0.0239345i
$799$	−2.19963	−	5.60455i	−0.0778172	−	0.198275i
$800$	4.67409	−	3.18674i	0.165254	−	0.112668i
$801$	−3.91927	−	1.88742i	−0.138481	−	0.0666888i
$802$	2.36627	+	2.19558i	0.0835561	+	0.0775287i
$803$	−0.861112	+	0.129792i	−0.0303880	+	0.00458025i
$804$	2.53415	−	33.8159i	0.0893727	−	1.19260i
$805$	11.0884	−	28.2528i	0.390814	−	0.995779i
$806$	−0.738429	−	3.23527i	−0.0260101	−	0.113958i
$807$	−0.611485	−	8.15969i	−0.0215253	−	0.287235i
$808$	4.00472	+	1.23529i	0.140886	+	0.0434575i
$809$	37.5879	−	18.1014i	1.32152	−	0.636410i	0.365801	−	0.930693i	$-0.380795\pi$
$809$	37.5879	−	18.1014i	1.32152	−	0.636410i	0.955718	+	0.294282i	$0.0950806\pi$
$810$	−0.214291	+	0.371164i	−0.00752943	+	0.0130414i
$811$	−1.67328	−	2.89821i	−0.0587570	−	0.101770i	0.835151	−	0.550021i	$-0.185380\pi$
$811$	−1.67328	−	2.89821i	−0.0587570	−	0.101770i	−0.893908	+	0.448251i	$0.852047\pi$
$812$	−12.5451	−	8.55307i	−0.440245	−	0.300154i
$813$	4.47032	−	19.5858i	0.156781	−	0.686902i
$814$	0.206670	+	0.0311505i	0.00724379	+	0.00109183i
$815$	7.23797	+	9.07612i	0.253535	+	0.317923i
$816$	−4.38061			−0.153352
$817$	3.83250	−	25.5273i	0.134082	−	0.893088i
$818$	1.62016			0.0566477
$819$	7.23789	+	9.07603i	0.252913	+	0.317142i
$820$	16.8010	+	2.53235i	0.586717	+	0.0884333i
$821$	0.731362	−	3.20431i	0.0255247	−	0.111831i	−0.960561	−	0.278070i	$-0.910305\pi$
$821$	0.731362	−	3.20431i	0.0255247	−	0.111831i	0.986085	+	0.166239i	$0.0531624\pi$
$822$	2.57900	+	1.75833i	0.0899530	+	0.0613289i
$823$	0.333224	+	0.577160i	0.0116154	+	0.0201185i	0.871775	−	0.489907i	$-0.162969\pi$
$823$	0.333224	+	0.577160i	0.0116154	+	0.0201185i	−0.860159	+	0.510026i	$0.829636\pi$
$824$	4.63227	−	8.02333i	0.161373	−	0.279506i
$825$	−0.619931	+	0.298543i	−0.0215832	+	0.0103939i
$826$	−1.29810	−	0.400410i	−0.0451666	−	0.0139321i
$827$	−0.345106	−	4.60512i	−0.0120005	−	0.160136i	−0.999984	−	0.00557906i	$-0.998224\pi$
$827$	−0.345106	−	4.60512i	−0.0120005	−	0.160136i	0.987984	−	0.154557i	$-0.0493949\pi$
$828$	−5.39775	−	23.6491i	−0.187585	−	0.821863i
$829$	−6.40952	+	16.3312i	−0.222612	+	0.567206i	−0.997926	−	0.0643700i	$-0.979496\pi$
$829$	−6.40952	+	16.3312i	−0.222612	+	0.567206i	0.775314	+	0.631576i	$0.217591\pi$
$830$	0.201255	−	2.68556i	0.00698566	−	0.0932171i
$831$	23.2267	−	3.50087i	0.805726	−	0.121444i
$832$	−14.4778	−	13.4335i	−0.501928	−	0.465721i
$833$	−0.566555	−	0.272838i	−0.0196300	−	0.00945329i
$834$	−2.21222	+	1.50826i	−0.0766027	+	0.0522269i
$835$	1.83550	+	4.67679i	0.0635203	+	0.161847i
$836$	−1.78802	+	0.551530i	−0.0618399	+	0.0190751i
$837$	23.7247	−	22.0133i	0.820045	−	0.760890i
$838$	1.58024	−	1.98156i	0.0545884	−	0.0684517i
$839$	17.6162	−	22.0900i	0.608178	−	0.762631i	−0.378450	−	0.925622i	$-0.623543\pi$
$839$	17.6162	−	22.0900i	0.608178	−	0.762631i	0.986628	+	0.162991i	$0.0521141\pi$
$840$	−2.70718	+	2.51189i	−0.0934065	+	0.0866685i
$841$	−18.7169	+	5.77339i	−0.645409	+	0.199082i
$842$	−2.09367	−	5.33459i	−0.0721528	−	0.183842i
$843$	−23.5873	+	16.0816i	−0.812391	+	0.553879i
$844$	7.74085	+	3.72780i	0.266451	+	0.128316i
$845$	6.09649	+	5.65672i	0.209726	+	0.194597i
$846$	−1.94506	+	0.293170i	−0.0668725	+	0.0100794i
$847$	−2.06382	+	27.5397i	−0.0709136	+	0.946276i
$848$	−5.59583	+	14.2579i	−0.192162	+	0.489620i
$849$	−6.40312	−	28.0539i	−0.219754	−	0.962807i
$850$	−0.0361743	−	0.482713i	−0.00124077	−	0.0165569i
$851$	−31.1964	−	9.62282i	−1.06940	−	0.329866i
$852$	−8.47533	+	4.08151i	−0.290360	+	0.139830i
$853$	8.35462	−	14.4706i	0.286057	−	0.495465i	−0.686808	−	0.726839i	$-0.740989\pi$
$853$	8.35462	−	14.4706i	0.286057	−	0.495465i	0.972865	+	0.231374i	$0.0743220\pi$
$854$	−1.11087	−	1.92409i	−0.0380132	−	0.0658408i
$855$	8.56905	+	5.84228i	0.293055	+	0.199802i
$856$	−3.17223	+	13.8985i	−0.108425	+	0.475039i
$857$	45.7753	+	6.89951i	1.56365	+	0.235683i	0.873079	−	0.487579i	$-0.162120\pi$
$857$	45.7753	+	6.89951i	1.56365	+	0.235683i	0.690574	+	0.723262i	$0.257358\pi$
$858$	−0.0974758	−	0.122231i	−0.00332777	−	0.00417289i
$859$	−57.3504			−1.95677			−0.978385	−	0.206792i	$-0.933698\pi$
$859$	−57.3504			−1.95677			−0.978385	+	0.206792i	$0.933698\pi$
$860$	6.07532	+	19.6553i	0.207167	+	0.670240i
$861$	15.9037			0.541998
$862$	−3.54316	−	4.44298i	−0.120681	−	0.151329i
$863$	−43.7020	−	6.58702i	−1.48763	−	0.224225i	−0.645611	−	0.763666i	$-0.723397\pi$
$863$	−43.7020	−	6.58702i	−1.48763	−	0.224225i	−0.842023	+	0.539441i	$0.818635\pi$
$864$	−2.78948	+	12.2215i	−0.0949001	+	0.415785i
$865$	12.0445	+	8.21181i	0.409526	+	0.279210i
$866$	−2.90822	−	5.03719i	−0.0988254	−	0.171171i
$867$	−0.581708	+	1.00755i	−0.0197558	+	0.0342181i
$868$	26.6945	−	12.8554i	0.906071	−	0.436341i
$869$	−1.20713	−	0.372349i	−0.0409490	−	0.0126311i
$870$	−0.0846967	−	1.13020i	−0.00287149	−	0.0383174i
$871$	−9.24060	−	40.4857i	−0.313106	−	1.37181i
$872$	2.75902	−	7.02988i	0.0934323	−	0.238062i
$873$	−1.86764	+	24.9220i	−0.0632102	+	0.843481i
$874$	−5.80414	+	0.874833i	−0.196328	+	0.0295917i
$875$	22.0268	+	20.4379i	0.744641	+	0.690926i
$876$	−7.38202	−	3.55499i	−0.249415	−	0.120112i
$877$	−45.4740	+	31.0037i	−1.53555	+	1.04692i	−0.559641	+	0.828735i	$0.689061\pi$
$877$	−45.4740	+	31.0037i	−1.53555	+	1.04692i	−0.975908	+	0.218184i	$0.929987\pi$
$878$	−1.14300	−	2.91233i	−0.0385745	−	0.0982863i
$879$	−8.92441	+	2.75281i	−0.301013	+	0.0928501i
$880$	1.07078	−	0.993541i	0.0360961	−	0.0334923i
$881$	21.2260	−	26.6166i	0.715122	−	0.896735i	−0.282928	−	0.959141i	$-0.591306\pi$
$881$	21.2260	−	26.6166i	0.715122	−	0.896735i	0.998051	+	0.0624059i	$0.0198773\pi$
$882$	−0.128092	+	0.160622i	−0.00431308	+	0.00540843i
$883$	24.1504	−	22.4083i	0.812726	−	0.754099i	−0.159737	−	0.987160i	$-0.551065\pi$
$883$	24.1504	−	22.4083i	0.812726	−	0.754099i	0.972462	+	0.233061i	$0.0748740\pi$
$884$	−5.23335	+	1.61428i	−0.176017	+	0.0542939i
$885$	1.84469	+	4.70020i	0.0620086	+	0.157995i
$886$	4.27456	−	2.91435i	0.143607	−	0.0979094i
$887$	−29.0565	−	13.9929i	−0.975621	−	0.469834i	−0.123024	−	0.992404i	$-0.539259\pi$
$887$	−29.0565	−	13.9929i	−0.975621	−	0.469834i	−0.852597	+	0.522570i	$0.824973\pi$
$888$	2.91197	+	2.70192i	0.0977194	+	0.0906704i
$889$	18.2947	−	2.75749i	0.613586	−	0.0924832i
$890$	0.0626921	−	0.836567i	0.00210144	−	0.0280418i
$891$	0.119553	−	0.304617i	0.00400519	−	0.0102051i
$892$	10.7500	+	47.0988i	0.359936	+	1.57698i
$893$	−1.77116	−	23.6344i	−0.0592695	−	0.790896i
$894$	2.10404	+	0.649010i	0.0703696	+	0.0217061i
$895$	−21.2909	+	10.2531i	−0.711675	+	0.342725i
$896$	−7.62401	+	13.2052i	−0.254700	+	0.441154i
$897$	12.2102	+	21.1487i	0.407687	+	0.706134i
$898$	2.26359	+	1.54329i	0.0755370	+	0.0515002i
$899$	−4.08735	+	17.9078i	−0.136321	+	0.597260i
$900$	7.78690	+	1.17369i	0.259563	+	0.0391229i
$901$	2.53627	+	3.18038i	0.0844954	+	0.105954i
$902$	0.260535			0.00867485
$903$	8.36516	+	17.3447i	0.278375	+	0.577197i
$904$	−0.245021			−0.00814926
$905$	−18.9467	−	23.7584i	−0.629809	−	0.789756i
$906$	2.95022	+	0.444673i	0.0980143	+	0.0147733i
$907$	−11.3245	+	49.6157i	−0.376022	+	1.64746i	0.333479	+	0.942758i	$0.391777\pi$
$907$	−11.3245	+	49.6157i	−0.376022	+	1.64746i	−0.709501	+	0.704704i	$0.751080\pi$
$908$	−43.1809	−	29.4402i	−1.43301	−	0.977008i
$909$	4.38994	+	7.60359i	0.145605	+	0.252195i
$910$	−1.11937	+	1.93881i	−0.0371068	+	0.0642709i
$911$	−33.7447	+	16.2506i	−1.11801	+	0.538405i	−0.899277	−	0.437379i	$-0.855907\pi$
$911$	−33.7447	+	16.2506i	−1.11801	+	0.538405i	−0.218733	+	0.975785i	$0.570192\pi$
$912$	−16.4782	−	5.08285i	−0.545648	−	0.168310i
$913$	0.153665	+	2.05052i	0.00508557	+	0.0678622i
$914$	−1.03855	−	4.55020i	−0.0343523	−	0.150507i
$915$	−3.01699	+	7.68716i	−0.0997385	+	0.254130i
$916$	−1.66867	+	22.2669i	−0.0551344	+	0.735718i
$917$	41.1338	−	6.19992i	1.35836	−	0.204740i
$918$	0.786323	+	0.729601i	0.0259525	+	0.0240804i
$919$	−25.6336	−	12.3445i	−0.845576	−	0.407208i	−0.0396421	−	0.999214i	$-0.512622\pi$
$919$	−25.6336	−	12.3445i	−0.845576	−	0.407208i	−0.805933	+	0.592006i	$0.798336\pi$
$920$	7.80798	−	5.32339i	0.257421	−	0.175507i
$921$	0.102761	+	0.261830i	0.00338608	+	0.00862759i
$922$	4.12634	−	1.27281i	0.135894	−	0.0419177i
$923$	−8.44449	+	7.83534i	−0.277954	+	0.257903i
$924$	0.870304	−	1.09133i	0.0286309	−	0.0359020i
$925$	6.60801	−	8.28618i	0.217270	−	0.272448i
$926$	−4.95052	+	4.59341i	−0.162684	+	0.150949i
$927$	18.5467	−	5.72091i	0.609155	−	0.187899i
$928$	−2.59930	−	6.62291i	−0.0853262	−	0.217408i
$929$	−33.1057	+	22.5711i	−1.08616	+	0.740534i	−0.967619	−	0.252415i	$-0.918775\pi$
$929$	−33.1057	+	22.5711i	−1.08616	+	0.740534i	−0.118544	+	0.992949i	$0.537823\pi$
$930$	1.99263	+	0.959599i	0.0653408	+	0.0314665i
$931$	−1.81459	−	1.68369i	−0.0594707	−	0.0551808i
$932$	−12.7857	+	1.92713i	−0.418809	+	0.0631253i
$933$	−1.05577	+	14.0883i	−0.0345645	+	0.461231i
$934$	2.78850	−	7.10497i	0.0912424	−	0.232482i
$935$	−0.0863252	−	0.378215i	−0.00282314	−	0.0123690i
$936$	0.270110	+	3.60437i	0.00882883	+	0.117813i
$937$	−32.2020	−	9.93301i	−1.05199	−	0.324497i	−0.279916	−	0.960024i	$-0.590307\pi$
$937$	−32.2020	−	9.93301i	−1.05199	−	0.324497i	−0.772079	+	0.635527i	$0.780783\pi$
$938$	−6.70866	+	3.23072i	−0.219045	+	0.105487i
$939$	3.87707	−	6.71528i	0.126523	−	0.219145i
$940$	9.44451	+	16.3584i	0.308046	+	0.533551i
$941$	8.88313	+	6.05642i	0.289582	+	0.197434i	0.699394	−	0.714736i	$-0.253453\pi$
$941$	8.88313	+	6.05642i	0.289582	+	0.197434i	−0.409812	+	0.912170i	$0.634406\pi$
$942$	−0.0928203	+	0.406672i	−0.00302425	+	0.0132501i
$943$	−40.2413	−	6.06540i	−1.31044	−	0.197517i
$944$	6.36729	+	7.98433i	0.207238	+	0.259868i
$945$	−21.8339			−0.710258
$946$	0.137038	+	0.284141i	0.00445548	+	0.00923822i
$947$	11.2527			0.365662			0.182831	−	0.983144i	$-0.441474\pi$
$947$	11.2527			0.365662			0.182831	+	0.983144i	$0.441474\pi$
$948$	−7.41048	−	9.29245i	−0.240681	−	0.301805i
$949$	−9.92154	−	1.49543i	−0.322067	−	0.0485438i
$950$	0.424021	−	1.85776i	0.0137570	−	0.0602736i
$951$	−32.2818	−	22.0094i	−1.04681	−	0.713702i
$952$	0.991864	+	1.71796i	0.0321465	+	0.0556794i
$953$	18.6724	−	32.3415i	0.604858	−	1.04764i	−0.387216	−	0.921989i	$-0.626563\pi$
$953$	18.6724	−	32.3415i	0.604858	−	1.04764i	0.992074	−	0.125656i	$-0.0401034\pi$
$954$	1.19739	−	0.576634i	0.0387670	−	0.0186692i
$955$	−26.0561	−	8.03726i	−0.843157	−	0.260080i
$956$	3.94913	+	52.6975i	0.127724	+	1.70436i
$957$	0.192562	+	0.843670i	0.00622465	+	0.0272720i
$958$	0.487214	−	1.24140i	0.0157412	−	0.0401078i
$959$	−2.55039	+	34.0326i	−0.0823565	+	1.09897i
$960$	13.0157	−	1.96181i	0.420081	−	0.0633170i
$961$	−3.55087	−	3.29472i	−0.114544	−	0.106281i
$962$	2.16963	+	1.04484i	0.0699516	+	0.0336869i
$963$	−24.6762	+	16.8240i	−0.795181	+	0.542145i
$964$	−21.5278	−	54.8520i	−0.693364	−	1.76666i
$965$	−23.9720	+	7.39438i	−0.771686	+	0.238033i
$966$	3.20985	−	2.97830i	0.103275	−	0.0958253i
$967$	21.3264	−	26.7425i	0.685811	−	0.859980i	−0.310064	−	0.950716i	$-0.600350\pi$
$967$	21.3264	−	26.7425i	0.685811	−	0.859980i	0.995875	+	0.0907358i	$0.0289219\pi$
$968$	−5.36127	+	6.72282i	−0.172318	+	0.216080i
$969$	−3.35723	+	3.11505i	−0.107850	+	0.100070i
$970$	−4.60557	+	1.42063i	−0.147876	+	0.0456137i
$971$	6.00056	+	15.2892i	0.192567	+	0.490653i	0.994248	−	0.107099i	$-0.0341561\pi$
$971$	6.00056	+	15.2892i	0.192567	+	0.490653i	−0.801681	+	0.597752i	$0.796061\pi$
$972$	−23.7273	+	16.1770i	−0.761052	+	0.518877i
$973$	−26.3753	−	12.7017i	−0.845553	−	0.407197i
$974$	0.745778	+	0.691981i	0.0238963	+	0.0221725i
$975$	−7.83926	+	1.18158i	−0.251057	+	0.0378408i
$976$	−1.24816	+	16.6556i	−0.0399527	+	0.533131i
$977$	−13.8280	+	35.2332i	−0.442398	+	1.12721i	0.519662	+	0.854372i	$0.326058\pi$
$977$	−13.8280	+	35.2332i	−0.442398	+	1.12721i	−0.962060	+	0.272839i	$0.912037\pi$
$978$	0.372681	+	1.63282i	0.0119170	+	0.0522119i
$979$	0.0478676	+	0.638749i	0.00152985	+	0.0204145i
$980$	1.88519	+	0.581504i	0.0602202	+	0.0185755i
$981$	14.2543	−	6.86451i	0.455105	−	0.219167i
$982$	2.26591	−	3.92467i	0.0723080	−	0.125241i
$983$	21.1852	+	36.6939i	0.675703	+	1.17035i	0.976263	+	0.216590i	$0.0694934\pi$
$983$	21.1852	+	36.6939i	0.675703	+	1.17035i	−0.300559	+	0.953763i	$0.597173\pi$
$984$	4.09136	+	2.78944i	0.130428	+	0.0889242i
$985$	1.00522	−	4.40418i	0.0320291	−	0.140329i
$986$	−0.601996	−	0.0907363i	−0.0191715	−	0.00288963i
$987$	11.0236	+	13.8232i	0.350886	+	0.439997i
$988$	−21.5589			−0.685881
$989$	−14.5514	−	47.0778i	−0.462709	−	1.49699i
$990$	−0.126744			−0.00402819
$991$	30.1736	+	37.8366i	0.958497	+	1.20192i	0.979358	+	0.202135i	$0.0647881\pi$
$991$	30.1736	+	37.8366i	0.958497	+	1.20192i	−0.0208601	+	0.999782i	$0.506640\pi$
$992$	13.7286	+	2.06925i	0.435882	+	0.0656987i
$993$	1.72885	−	7.57460i	0.0548635	−	0.240373i
$994$	1.70664	+	1.16357i	0.0541312	+	0.0369061i
$995$	−0.0801888	−	0.138891i	−0.00254215	−	0.00440314i
$996$	−9.67336	+	16.7547i	−0.306512	+	0.530895i
$997$	−37.2377	+	17.9327i	−1.17933	+	0.567935i	−0.917716	−	0.397238i	$-0.869969\pi$
$997$	−37.2377	+	17.9327i	−1.17933	+	0.567935i	−0.261613	+	0.965173i	$0.584254\pi$
$998$	−4.07072	−	1.25565i	−0.128857	−	0.0397470i
$999$	1.75508	+	23.4200i	0.0555284	+	0.740975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.u.b.52.15	✓	348
43.24	even	21	inner	731.2.u.b.239.15	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.u.b.52.15	✓	348	1.1	even	1	trivial
731.2.u.b.239.15	yes	348	43.24	even	21	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.u (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.123719 - 0.155139i) q^{2} +(-1.15042 - 0.173398i) q^{3} +(0.436280 - 1.91147i) q^{4} +(1.32212 + 0.901405i) q^{5} +(0.115429 + 0.199928i) q^{6} +(-1.26206 + 2.18595i) q^{7} +(-0.708080 + 0.340993i) q^{8} +(-1.57331 - 0.485303i) q^{9} +O(q^{10})\)	\(q+(-0.123719 - 0.155139i) q^{2} +(-1.15042 - 0.173398i) q^{3} +(0.436280 - 1.91147i) q^{4} +(1.32212 + 0.901405i) q^{5} +(0.115429 + 0.199928i) q^{6} +(-1.26206 + 2.18595i) q^{7} +(-0.708080 + 0.340993i) q^{8} +(-1.57331 - 0.485303i) q^{9} +(-0.0237284 - 0.316634i) q^{10} +(0.0539477 + 0.236360i) q^{11} +(-0.833352 + 2.12335i) q^{12} +(-0.208745 + 2.78551i) q^{13} +(0.495268 - 0.0746497i) q^{14} +(-1.36469 - 1.26625i) q^{15} +(-3.39242 - 1.63370i) q^{16} +(-0.826239 + 0.563320i) q^{17} +(0.119360 + 0.304124i) q^{18} +(-3.76162 + 1.16031i) q^{19} +(2.29982 - 2.13392i) q^{20} +(1.83094 - 2.29593i) q^{21} +(0.0299944 - 0.0376118i) q^{22} +(-5.50847 + 5.11111i) q^{23} +(0.873718 - 0.269506i) q^{24} +(-0.891240 - 2.27084i) q^{25} +(0.457969 - 0.312238i) q^{26} +(4.87043 + 2.34548i) q^{27} +(3.62776 + 3.36607i) q^{28} +(-3.03378 + 0.457269i) q^{29} +(-0.0276060 + 0.368377i) q^{30} +(2.18729 - 5.57312i) q^{31} +(0.516019 + 2.26083i) q^{32} +(-0.0210782 - 0.281269i) q^{33} +(0.189615 + 0.0584885i) q^{34} +(-3.63902 + 1.75246i) q^{35} +(-1.61405 + 2.79561i) q^{36} +(2.17228 + 3.76249i) q^{37} +(0.645395 + 0.440023i) q^{38} +(0.723149 - 3.16832i) q^{39} +(-1.24354 - 0.187433i) q^{40} +(3.37663 + 4.23416i) q^{41} -0.582711 q^{42} +(-2.84174 + 5.90969i) q^{43} +0.475332 q^{44} +(-1.64265 - 2.05982i) q^{45} +(1.47444 + 0.222236i) q^{46} +(-1.33974 + 5.86979i) q^{47} +(3.61943 + 2.46769i) q^{48} +(0.314414 + 0.544582i) q^{49} +(-0.242033 + 0.419214i) q^{50} +(1.04820 - 0.504787i) q^{51} +(5.23335 + 1.61428i) q^{52} +(-0.303992 - 4.05649i) q^{53} +(-0.238692 - 1.04578i) q^{54} +(-0.141731 + 0.361125i) q^{55} +(0.148244 - 1.97818i) q^{56} +(4.52864 - 0.682583i) q^{57} +(0.446279 + 0.414086i) q^{58} +(-2.44363 - 1.17679i) q^{59} +(-3.01578 + 2.05613i) q^{60} +(-1.62059 - 4.12920i) q^{61} +(-1.13522 + 0.350169i) q^{62} +(3.04646 - 2.82671i) q^{63} +(-4.40835 + 5.52790i) q^{64} +(-2.78686 + 3.49461i) q^{65} +(-0.0410280 + 0.0380685i) q^{66} +(-14.2060 + 4.38197i) q^{67} +(0.716297 + 1.82509i) q^{68} +(7.22332 - 4.92477i) q^{69} +(0.722092 + 0.347741i) q^{70} +(3.02310 + 2.80502i) q^{71} +(1.27952 - 0.192856i) q^{72} +(-0.268430 + 3.58195i) q^{73} +(0.314958 - 0.802499i) q^{74} +(0.631542 + 2.76697i) q^{75} +(0.576768 + 7.69643i) q^{76} +(-0.584757 - 0.180374i) q^{77} +(-0.580999 + 0.279794i) q^{78} +(-2.60530 + 4.51251i) q^{79} +(-3.01255 - 5.21789i) q^{80} +(-1.11524 - 0.760356i) q^{81} +(0.239130 - 1.04770i) q^{82} +(8.38686 + 1.26412i) q^{83} +(-3.58979 - 4.50145i) q^{84} -1.60016 q^{85} +(1.26840 - 0.290278i) q^{86} +3.56942 q^{87} +(-0.118797 - 0.148966i) q^{88} +(2.61256 + 0.393780i) q^{89} +(-0.116331 + 0.509680i) q^{90} +(-5.82555 - 3.97179i) q^{91} +(7.36649 + 12.7591i) q^{92} +(-3.48268 + 6.03217i) q^{93} +(1.07639 - 0.518361i) q^{94} +(-6.01921 - 1.85668i) q^{95} +(-0.201616 - 2.69038i) q^{96} +(-3.37767 - 14.7986i) q^{97} +(0.0455868 - 0.116153i) q^{98} +(0.0298297 - 0.398050i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9}+O(q^{10}) \) 348 * q + 6 * q^2 - 3 * q^3 - 54 * q^4 + q^5 - 12 * q^6 + 49 * q^7 - 2 * q^8 + 8 * q^9	\( 348 q + 6 q^{2} - 3 q^{3} - 54 q^{4} + q^{5} - 12 q^{6} + 49 q^{7} - 2 q^{8} + 8 q^{9} - 4 q^{10} - 16 q^{11} - 12 q^{12} - 9 q^{13} - 3 q^{14} - 14 q^{15} - 30 q^{16} - 29 q^{17} - 204 q^{18} - 8 q^{19} + 61 q^{20} + 26 q^{21} + 85 q^{22} - 79 q^{23} - 12 q^{24} + 22 q^{25} - 14 q^{26} + 12 q^{27} - 15 q^{28} + 54 q^{29} - 46 q^{30} - 52 q^{31} + 33 q^{32} + 39 q^{33} + 3 q^{34} + 32 q^{35} - 161 q^{36} + 68 q^{37} - 29 q^{38} + 61 q^{39} + 107 q^{40} + 63 q^{41} - 56 q^{42} - 45 q^{43} - 74 q^{44} + 144 q^{45} - 22 q^{46} - 70 q^{47} + 168 q^{48} - 119 q^{49} + 97 q^{50} - 6 q^{51} + 27 q^{52} + 10 q^{53} - 34 q^{54} - 78 q^{55} - 44 q^{56} - 40 q^{57} - 38 q^{58} - 47 q^{59} - 72 q^{60} - 76 q^{61} - 41 q^{62} + 63 q^{63} - 112 q^{64} - 31 q^{65} - 598 q^{66} - 39 q^{67} - 20 q^{68} - 17 q^{69} - 72 q^{70} - 37 q^{71} + 245 q^{72} + 14 q^{73} + 77 q^{74} - 121 q^{75} + 152 q^{76} + 59 q^{77} + 220 q^{78} + 4 q^{79} - 42 q^{80} - 109 q^{81} + 148 q^{82} + 59 q^{83} + 390 q^{84} + 2 q^{85} + 12 q^{86} - 78 q^{87} + 344 q^{88} - 103 q^{89} - 75 q^{90} + 148 q^{91} + 28 q^{92} + 140 q^{93} + 24 q^{94} - 302 q^{95} + 22 q^{96} + 57 q^{97} - 72 q^{98} - 128 q^{99}+O(q^{100}) \) 348 * q + 6 * q^2 - 3 * q^3 - 54 * q^4 + q^5 - 12 * q^6 + 49 * q^7 - 2 * q^8 + 8 * q^9 - 4 * q^10 - 16 * q^11 - 12 * q^12 - 9 * q^13 - 3 * q^14 - 14 * q^15 - 30 * q^16 - 29 * q^17 - 204 * q^18 - 8 * q^19 + 61 * q^20 + 26 * q^21 + 85 * q^22 - 79 * q^23 - 12 * q^24 + 22 * q^25 - 14 * q^26 + 12 * q^27 - 15 * q^28 + 54 * q^29 - 46 * q^30 - 52 * q^31 + 33 * q^32 + 39 * q^33 + 3 * q^34 + 32 * q^35 - 161 * q^36 + 68 * q^37 - 29 * q^38 + 61 * q^39 + 107 * q^40 + 63 * q^41 - 56 * q^42 - 45 * q^43 - 74 * q^44 + 144 * q^45 - 22 * q^46 - 70 * q^47 + 168 * q^48 - 119 * q^49 + 97 * q^50 - 6 * q^51 + 27 * q^52 + 10 * q^53 - 34 * q^54 - 78 * q^55 - 44 * q^56 - 40 * q^57 - 38 * q^58 - 47 * q^59 - 72 * q^60 - 76 * q^61 - 41 * q^62 + 63 * q^63 - 112 * q^64 - 31 * q^65 - 598 * q^66 - 39 * q^67 - 20 * q^68 - 17 * q^69 - 72 * q^70 - 37 * q^71 + 245 * q^72 + 14 * q^73 + 77 * q^74 - 121 * q^75 + 152 * q^76 + 59 * q^77 + 220 * q^78 + 4 * q^79 - 42 * q^80 - 109 * q^81 + 148 * q^82 + 59 * q^83 + 390 * q^84 + 2 * q^85 + 12 * q^86 - 78 * q^87 + 344 * q^88 - 103 * q^89 - 75 * q^90 + 148 * q^91 + 28 * q^92 + 140 * q^93 + 24 * q^94 - 302 * q^95 + 22 * q^96 + 57 * q^97 - 72 * q^98 - 128 * q^99

Introduction

L-functions

Modular forms

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Database

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