LMFDB - Embedded newform 354.2.e.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			49.1
Character	$\chi$	$=$	354.49
Dual form			354.2.e.a.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.370138 + 0.928977i) q^{2} +(-0.994138 - 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(-0.571390 + 0.672692i) q^{5} +(0.468408 - 0.883512i) q^{6} +(2.39323 + 1.43996i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +O(q^{10})$	\(q+(-0.370138 + 0.928977i) q^{2} +(-0.994138 - 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(-0.571390 + 0.672692i) q^{5} +(0.468408 - 0.883512i) q^{6} +(2.39323 + 1.43996i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +(-0.413422 - 0.779797i) q^{10} +(0.00747993 - 0.137959i) q^{11} +(0.647386 + 0.762162i) q^{12} +(1.63030 - 0.358857i) q^{13} +(-2.22351 + 1.69027i) q^{14} +(0.640771 - 0.606971i) q^{15} +(0.0541389 + 0.998533i) q^{16} +(-6.54182 + 3.93608i) q^{17} +(-0.561187 + 0.827689i) q^{18} +(-1.82881 + 6.58680i) q^{19} +(0.877436 - 0.0954270i) q^{20} +(-2.22351 - 1.69027i) q^{21} +(0.125392 + 0.0580127i) q^{22} +(0.710818 + 1.04838i) q^{23} +(-0.947653 + 0.319302i) q^{24} +(0.682882 + 4.16539i) q^{25} +(-0.270068 + 1.64734i) q^{26} +(-0.947653 - 0.319302i) q^{27} +(-0.747215 - 2.69123i) q^{28} +(1.80045 + 4.51878i) q^{29} +(0.326688 + 0.819925i) q^{30} +(-0.497109 - 1.79042i) q^{31} +(-0.947653 - 0.319302i) q^{32} +(-0.0223521 + 0.136342i) q^{33} +(-1.23515 - 7.53409i) q^{34} +(-2.33611 + 0.787129i) q^{35} +(-0.561187 - 0.827689i) q^{36} +(10.5533 + 4.88245i) q^{37} +(-5.44207 - 4.13695i) q^{38} +(-1.65955 + 0.180486i) q^{39} +(-0.236123 + 0.850439i) q^{40} +(-3.81151 + 5.62156i) q^{41} +(2.39323 - 1.43996i) q^{42} +(-0.690339 - 12.7326i) q^{43} +(-0.100305 + 0.0950138i) q^{44} +(-0.702640 + 0.534133i) q^{45} +(-1.23702 + 0.272289i) q^{46} +(-2.53668 - 2.98641i) q^{47} +(0.0541389 - 0.998533i) q^{48} +(0.375206 + 0.707713i) q^{49} +(-4.12231 - 0.907390i) q^{50} +(6.92904 - 3.20571i) q^{51} +(-1.43038 - 0.860630i) q^{52} +(1.57744 - 2.97536i) q^{53} +(0.647386 - 0.762162i) q^{54} +(0.0885301 + 0.0838602i) q^{55} +(2.77666 + 0.301980i) q^{56} +(2.53025 - 6.35045i) q^{57} -4.86425 q^{58} +(5.93499 - 4.87606i) q^{59} -0.882610 q^{60} +(0.922489 - 2.31527i) q^{61} +(1.84726 + 0.200902i) q^{62} +(2.02773 + 1.92077i) q^{63} +(0.647386 - 0.762162i) q^{64} +(-0.690138 + 1.30174i) q^{65} +(-0.118385 - 0.0712299i) q^{66} +(4.36883 - 2.02124i) q^{67} +(7.45617 + 1.64123i) q^{68} +(-0.593301 - 1.11909i) q^{69} +(0.133461 - 2.46154i) q^{70} +(4.05398 + 4.77271i) q^{71} +(0.976621 - 0.214970i) q^{72} +(-5.74523 + 4.36741i) q^{73} +(-8.44185 + 7.99654i) q^{74} +(-0.228520 - 4.21481i) q^{75} +(5.85745 - 3.52431i) q^{76} +(0.216557 - 0.319397i) q^{77} +(0.446593 - 1.60848i) q^{78} +(-3.72224 + 0.404818i) q^{79} +(-0.702640 - 0.534133i) q^{80} +(0.907575 + 0.419889i) q^{81} +(-3.81151 - 5.62156i) q^{82} +(-2.15335 + 0.725548i) q^{83} +(0.451862 + 2.75624i) q^{84} +(1.09016 - 6.64967i) q^{85} +(12.0838 + 4.07149i) q^{86} +(-1.30133 - 4.68695i) q^{87} +(-0.0511390 - 0.128349i) q^{88} +(3.86142 + 9.69143i) q^{89} +(-0.236123 - 0.850439i) q^{90} +(4.41843 + 1.48874i) q^{91} +(0.204918 - 1.24995i) q^{92} +(0.300616 + 1.83367i) q^{93} +(3.71322 - 1.25113i) q^{94} +(-3.38592 - 4.99386i) q^{95} +(0.907575 + 0.419889i) q^{96} +(5.79436 + 4.40476i) q^{97} +(-0.796327 + 0.0866058i) q^{98} +(0.0369622 - 0.133126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{18}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.370138	+	0.928977i	−0.261727	+	0.656886i
$2$	−0.370138	+	0.928977i	−0.261727	+	0.656886i
$3$	−0.994138	−	0.108119i	−0.573966	−	0.0624225i
$3$	−0.994138	−	0.108119i	−0.573966	−	0.0624225i
$4$	−0.725995	−	0.687699i	−0.362998	−	0.343850i
$5$	−0.571390	+	0.672692i	−0.255533	+	0.300837i	−0.874938	−	0.484235i	$-0.839098\pi$
$5$	−0.571390	+	0.672692i	−0.255533	+	0.300837i	0.619405	+	0.785072i	$0.287374\pi$
$6$	0.468408	−	0.883512i	0.191227	−	0.360692i
$7$	2.39323	+	1.43996i	0.904555	+	0.544253i	0.890162	−	0.455643i	$-0.150591\pi$
$7$	2.39323	+	1.43996i	0.904555	+	0.544253i	0.0143931	+	0.999896i	$0.495418\pi$
$8$	0.907575	−	0.419889i	0.320876	−	0.148453i
$9$	0.976621	+	0.214970i	0.325540	+	0.0716568i
$10$	−0.413422	−	0.779797i	−0.130736	−	0.246593i
$11$	0.00747993	−	0.137959i	0.00225528	−	0.0415963i	−0.997189	−	0.0749253i	$-0.976128\pi$
$11$	0.00747993	−	0.137959i	0.00225528	−	0.0415963i	0.999444	+	0.0333290i	$0.0106109\pi$
$12$	0.647386	+	0.762162i	0.186884	+	0.220017i
$13$	1.63030	−	0.358857i	0.452165	−	0.0995290i	0.0169513	−	0.999856i	$-0.494604\pi$
$13$	1.63030	−	0.358857i	0.452165	−	0.0995290i	0.435213	+	0.900327i	$0.356673\pi$
$14$	−2.22351	+	1.69027i	−0.594259	+	0.451744i
$15$	0.640771	−	0.606971i	0.165446	−	0.156719i
$16$	0.0541389	+	0.998533i	0.0135347	+	0.249633i
$17$	−6.54182	+	3.93608i	−1.58662	+	0.954640i	−0.598475	+	0.801141i	$0.704226\pi$
$17$	−6.54182	+	3.93608i	−1.58662	+	0.954640i	−0.988149	+	0.153499i	$0.950946\pi$
$18$	−0.561187	+	0.827689i	−0.132273	+	0.195088i
$19$	−1.82881	+	6.58680i	−0.419559	+	1.51111i	0.388185	+	0.921581i	$0.373102\pi$
$19$	−1.82881	+	6.58680i	−0.419559	+	1.51111i	−0.807744	+	0.589533i	$0.799312\pi$
$20$	0.877436	−	0.0954270i	0.196201	−	0.0213381i
$21$	−2.22351	−	1.69027i	−0.485210	−	0.368847i
$22$	0.125392	+	0.0580127i	0.0267337	+	0.0123683i
$23$	0.710818	+	1.04838i	0.148216	+	0.218602i	0.894548	−	0.446971i	$-0.147497\pi$
$23$	0.710818	+	1.04838i	0.148216	+	0.218602i	−0.746332	+	0.665573i	$0.768187\pi$
$24$	−0.947653	+	0.319302i	−0.193439	+	0.0651772i
$25$	0.682882	+	4.16539i	0.136576	+	0.833079i
$26$	−0.270068	+	1.64734i	−0.0529646	+	0.323070i
$27$	−0.947653	−	0.319302i	−0.182376	−	0.0614496i
$28$	−0.747215	−	2.69123i	−0.141210	−	0.508594i
$29$	1.80045	+	4.51878i	0.334334	+	0.839116i	0.996003	+	0.0893197i	$0.0284693\pi$
$29$	1.80045	+	4.51878i	0.334334	+	0.839116i	−0.661669	+	0.749796i	$0.730151\pi$
$30$	0.326688	+	0.819925i	0.0596448	+	0.149697i
$31$	−0.497109	−	1.79042i	−0.0892833	−	0.321570i	0.905399	−	0.424562i	$-0.139572\pi$
$31$	−0.497109	−	1.79042i	−0.0892833	−	0.321570i	−0.994682	+	0.102993i	$0.967158\pi$
$32$	−0.947653	−	0.319302i	−0.167523	−	0.0564451i
$33$	−0.0223521	+	0.136342i	−0.00389100	+	0.0237341i
$34$	−1.23515	−	7.53409i	−0.211827	−	1.29209i
$35$	−2.33611	+	0.787129i	−0.394876	+	0.133049i
$36$	−0.561187	−	0.827689i	−0.0935312	−	0.137948i
$37$	10.5533	+	4.88245i	1.73494	+	0.802671i	0.990910	+	0.134529i	$0.0429522\pi$
$37$	10.5533	+	4.88245i	1.73494	+	0.802671i	0.744034	+	0.668141i	$0.232910\pi$
$38$	−5.44207	−	4.13695i	−0.882820	−	0.671102i
$39$	−1.65955	+	0.180486i	−0.265740	+	0.0289010i
$40$	−0.236123	+	0.850439i	−0.0373344	+	0.134466i
$41$	−3.81151	+	5.62156i	−0.595258	+	0.877940i	−0.999323	−	0.0367903i	$-0.988287\pi$
$41$	−3.81151	+	5.62156i	−0.595258	+	0.877940i	0.404065	+	0.914730i	$0.367597\pi$
$42$	2.39323	−	1.43996i	0.369283	−	0.222190i
$43$	−0.690339	−	12.7326i	−0.105276	−	1.94170i	−0.286140	−	0.958188i	$-0.592372\pi$
$43$	−0.690339	−	12.7326i	−0.105276	−	1.94170i	0.180864	−	0.983508i	$-0.442111\pi$
$44$	−0.100305	+	0.0950138i	−0.0151215	+	0.0143239i
$45$	−0.702640	+	0.534133i	−0.104743	+	0.0796239i
$46$	−1.23702	+	0.272289i	−0.182389	+	0.0401468i
$47$	−2.53668	−	2.98641i	−0.370012	−	0.435612i	0.545371	−	0.838195i	$-0.316389\pi$
$47$	−2.53668	−	2.98641i	−0.370012	−	0.435612i	−0.915384	+	0.402582i	$0.868113\pi$
$48$	0.0541389	−	0.998533i	0.00781428	−	0.144126i
$49$	0.375206	+	0.707713i	0.0536008	+	0.101102i
$50$	−4.12231	−	0.907390i	−0.582983	−	0.128324i
$51$	6.92904	−	3.20571i	0.970259	−	0.448890i
$52$	−1.43038	−	0.860630i	−0.198358	−	0.119348i
$53$	1.57744	−	2.97536i	0.216677	−	0.408697i	−0.751216	−	0.660056i	$-0.770533\pi$
$53$	1.57744	−	2.97536i	0.216677	−	0.408697i	0.967894	+	0.251359i	$0.0808774\pi$
$54$	0.647386	−	0.762162i	0.0880981	−	0.103717i
$55$	0.0885301	+	0.0838602i	0.0119374	+	0.0113077i
$56$	2.77666	+	0.301980i	0.371047	+	0.0403537i
$57$	2.53025	−	6.35045i	0.335140	−	0.841138i
$58$	−4.86425			−0.638708
$59$	5.93499	−	4.87606i	0.772669	−	0.634809i
$59$	5.93499	−	4.87606i	0.772669	−	0.634809i
$60$	−0.882610			−0.113945
$61$	0.922489	−	2.31527i	0.118113	−	0.296440i	−0.858020	−	0.513617i	$-0.828305\pi$
$61$	0.922489	−	2.31527i	0.118113	−	0.296440i	0.976132	+	0.217176i	$0.0696846\pi$
$62$	1.84726	+	0.200902i	0.234602	+	0.0255145i
$63$	2.02773	+	1.92077i	0.255470	+	0.241994i
$64$	0.647386	−	0.762162i	0.0809233	−	0.0952703i
$65$	−0.690138	+	1.30174i	−0.0856011	+	0.161461i
$66$	−0.118385	−	0.0712299i	−0.0145722	−	0.00876779i
$67$	4.36883	−	2.02124i	0.533737	−	0.246933i	−0.134458	−	0.990919i	$-0.542929\pi$
$67$	4.36883	−	2.02124i	0.533737	−	0.246933i	0.668195	+	0.743986i	$0.267067\pi$
$68$	7.45617	+	1.64123i	0.904194	+	0.199028i
$69$	−0.593301	−	1.11909i	−0.0714251	−	0.134722i
$70$	0.133461	−	2.46154i	0.0159516	−	0.294211i
$71$	4.05398	+	4.77271i	0.481119	+	0.566417i	0.948150	−	0.317824i	$-0.102952\pi$
$71$	4.05398	+	4.77271i	0.481119	+	0.566417i	−0.467031	+	0.884241i	$0.654676\pi$
$72$	0.976621	−	0.214970i	0.115096	−	0.0253345i
$73$	−5.74523	+	4.36741i	−0.672428	+	0.511167i	−0.884770	−	0.466029i	$-0.845684\pi$
$73$	−5.74523	+	4.36741i	−0.672428	+	0.511167i	0.212341	+	0.977196i	$0.431891\pi$
$74$	−8.44185	+	7.99654i	−0.981345	+	0.929579i
$75$	−0.228520	−	4.21481i	−0.0263872	−	0.486684i
$76$	5.85745	−	3.52431i	0.671895	−	0.404266i
$77$	0.216557	−	0.319397i	0.0246789	−	0.0363987i
$78$	0.446593	−	1.60848i	0.0505667	−	0.182125i
$79$	−3.72224	+	0.404818i	−0.418785	+	0.0455456i	−0.315086	−	0.949063i	$-0.602033\pi$
$79$	−3.72224	+	0.404818i	−0.418785	+	0.0455456i	−0.103699	+	0.994609i	$0.533068\pi$
$80$	−0.702640	−	0.534133i	−0.0785575	−	0.0597179i
$81$	0.907575	+	0.419889i	0.100842	+	0.0466543i
$82$	−3.81151	−	5.62156i	−0.420911	−	0.620797i
$83$	−2.15335	+	0.725548i	−0.236361	+	0.0796392i	−0.434989	−	0.900436i	$-0.643248\pi$
$83$	−2.15335	+	0.725548i	−0.236361	+	0.0796392i	0.198628	+	0.980075i	$0.436351\pi$
$84$	0.451862	+	2.75624i	0.0493022	+	0.300730i
$85$	1.09016	−	6.64967i	0.118244	−	0.721258i
$86$	12.0838	+	4.07149i	1.30303	+	0.439041i
$87$	−1.30133	−	4.68695i	−0.139517	−	0.502494i
$88$	−0.0511390	−	0.128349i	−0.00545143	−	0.0136821i
$89$	3.86142	+	9.69143i	0.409310	+	1.02729i	0.978713	+	0.205232i	$0.0657948\pi$
$89$	3.86142	+	9.69143i	0.409310	+	1.02729i	−0.569404	+	0.822058i	$0.692826\pi$
$90$	−0.236123	−	0.850439i	−0.0248896	−	0.0896442i
$91$	4.41843	+	1.48874i	0.463177	+	0.156062i
$92$	0.204918	−	1.24995i	0.0213642	−	0.130316i
$93$	0.300616	+	1.83367i	0.0311724	+	0.190143i
$94$	3.71322	−	1.25113i	0.382990	−	0.129044i
$95$	−3.38592	−	4.99386i	−0.347388	−	0.512359i
$96$	0.907575	+	0.419889i	0.0926290	+	0.0428548i
$97$	5.79436	+	4.40476i	0.588328	+	0.447235i	0.856508	−	0.516134i	$-0.172629\pi$
$97$	5.79436	+	4.40476i	0.588328	+	0.447235i	−0.268180	+	0.963369i	$0.586422\pi$
$98$	−0.796327	+	0.0866058i	−0.0804412	+	0.00874850i
$99$	0.0369622	−	0.133126i	0.00371484	−	0.0133797i
$100$	2.36877	−	3.49367i	0.236877	−	0.349367i
$101$	6.01698	−	3.62030i	0.598712	−	0.360233i	−0.183711	−	0.982980i	$-0.558811\pi$
$101$	6.01698	−	3.62030i	0.598712	−	0.360233i	0.782423	+	0.622747i	$0.213983\pi$
$102$	0.413332	+	7.62347i	0.0409260	+	0.754836i
$103$	10.2520	−	9.71126i	1.01016	−	0.956879i	0.0110919	−	0.999938i	$-0.496469\pi$
$103$	10.2520	−	9.71126i	1.01016	−	0.956879i	0.999072	+	0.0430600i	$0.0137107\pi$
$104$	1.32894	−	1.01024i	0.130314	−	0.0990618i
$105$	2.40752	−	0.529936i	0.234950	−	0.0517165i
$106$	2.18017	+	2.56670i	0.211757	+	0.249299i
$107$	0.628591	−	11.5937i	0.0607681	−	1.12080i	−0.796066	−	0.605210i	$-0.793089\pi$
$107$	0.628591	−	11.5937i	0.0607681	−	1.12080i	0.856834	−	0.515592i	$-0.172428\pi$
$108$	0.468408	+	0.883512i	0.0450726	+	0.0850160i
$109$	−13.8791	−	3.05502i	−1.32938	−	0.292618i	−0.507188	−	0.861835i	$-0.669315\pi$
$109$	−13.8791	−	3.05502i	−1.32938	−	0.292618i	−0.822187	+	0.569218i	$0.807246\pi$
$110$	−0.110673	+	0.0512026i	−0.0105522	+	0.00488197i
$111$	−9.96350	−	5.99484i	−0.945694	−	0.569005i
$112$	−1.30828	+	2.46768i	−0.123621	+	0.233174i
$113$	−1.81031	+	2.13126i	−0.170300	+	0.200492i	−0.840690	−	0.541516i	$-0.817851\pi$
$113$	−1.81031	+	2.13126i	−0.170300	+	0.200492i	0.670391	+	0.742008i	$0.266126\pi$
$114$	4.96288	+	4.70109i	0.464816	+	0.440297i
$115$	−1.11139	−	0.120871i	−0.103638	−	0.0112713i
$116$	1.80045	−	4.51878i	0.167167	−	0.419558i
$117$	1.66933			0.154330
$118$	2.33298	+	7.31828i	0.214768	+	0.673702i
$119$	−21.3239			−1.95475
$120$	0.326688	−	0.819925i	0.0298224	−	0.0748485i
$121$	10.9165	+	1.18725i	0.992413	+	0.107931i
$122$	1.80939	+	1.71394i	0.163814	+	0.155173i
$123$	4.39697	−	5.17651i	0.396461	−	0.466750i
$124$	−0.870375	+	1.64170i	−0.0781619	+	0.147429i
$125$	−6.97357	−	4.19586i	−0.623735	−	0.375289i
$126$	−2.53489	+	1.17276i	−0.225826	+	0.104478i
$127$	−5.69638	−	1.25387i	−0.505472	−	0.111263i	−0.0450888	−	0.998983i	$-0.514357\pi$
$127$	−5.69638	−	1.25387i	−0.505472	−	0.111263i	−0.460384	+	0.887720i	$0.652288\pi$
$128$	0.468408	+	0.883512i	0.0414018	+	0.0780922i
$129$	−0.690339	+	12.7326i	−0.0607810	+	1.12104i
$130$	−0.953839	−	1.12295i	−0.0836572	−	0.0984889i
$131$	16.2837	−	3.58432i	1.42271	−	0.313163i	0.564066	−	0.825729i	$-0.309236\pi$
$131$	16.2837	−	3.58432i	1.42271	−	0.313163i	0.858648	+	0.512566i	$0.171305\pi$
$132$	0.109990	−	0.0836120i	0.00957338	−	0.00727749i
$133$	−13.8615	+	13.1303i	−1.20194	+	1.13854i
$134$	0.260610	+	4.80668i	0.0225133	+	0.415234i
$135$	0.756271	−	0.455033i	0.0650894	−	0.0391630i
$136$	−4.28448	+	6.31913i	−0.367391	+	0.541861i
$137$	0.588317	−	2.11892i	0.0502633	−	0.181032i	−0.934157	−	0.356861i	$-0.883847\pi$
$137$	0.588317	−	2.11892i	0.0502633	−	0.181032i	0.984421	+	0.175829i	$0.0562607\pi$
$138$	1.25921	−	0.136947i	0.107191	−	0.0116577i
$139$	−1.17056	−	0.889840i	−0.0992860	−	0.0754752i	0.554353	−	0.832281i	$-0.312966\pi$
$139$	−1.17056	−	0.889840i	−0.0992860	−	0.0754752i	−0.653639	+	0.756806i	$0.726759\pi$
$140$	2.23732	+	1.03509i	0.189088	+	0.0874813i
$141$	2.19892	+	3.24316i	0.185182	+	0.273124i
$142$	−5.93427	+	1.99949i	−0.497993	+	0.167793i
$143$	−0.0373131	−	0.227600i	−0.00312027	−	0.0190328i
$144$	−0.161782	+	0.986827i	−0.0134818	+	0.0822355i
$145$	−4.06850	−	1.37084i	−0.337871	−	0.113842i
$146$	−1.93069	−	6.95373i	−0.159785	−	0.575495i
$147$	−0.296489	−	0.744131i	−0.0244540	−	0.0613749i
$148$	−4.30395	−	10.8021i	−0.353783	−	0.887928i
$149$	0.683766	+	2.46270i	0.0560163	+	0.201752i	0.986263	−	0.165182i	$-0.0528211\pi$
$149$	0.683766	+	2.46270i	0.0560163	+	0.201752i	−0.930247	+	0.366934i	$0.880407\pi$
$150$	4.00004	+	1.34777i	0.326602	+	0.110045i
$151$	−1.84732	+	11.2682i	−0.150333	+	0.916992i	0.798680	+	0.601756i	$0.205532\pi$
$151$	−1.84732	+	11.2682i	−0.150333	+	0.916992i	−0.949013	+	0.315236i	$0.897916\pi$
$152$	1.10594	+	6.74591i	0.0897033	+	0.547166i
$153$	−7.23502	+	2.43776i	−0.584916	+	0.197081i
$154$	0.216557	+	0.319397i	0.0174506	+	0.0257378i
$155$	1.48845	+	0.688629i	0.119555	+	0.0553120i
$156$	1.32894	+	1.01024i	0.106401	+	0.0808836i
$157$	3.19387	−	0.347354i	0.254898	−	0.0277219i	0.0202224	−	0.999796i	$-0.493563\pi$
$157$	3.19387	−	0.347354i	0.254898	−	0.0277219i	0.234676	+	0.972074i	$0.424597\pi$
$158$	1.00168	−	3.60771i	0.0796891	−	0.287014i
$159$	−1.88988	+	2.78737i	−0.149877	+	0.221053i
$160$	0.756271	−	0.455033i	0.0597885	−	0.0359735i
$161$	0.191530	+	3.53256i	0.0150946	+	0.278404i
$162$	−0.725995	+	0.687699i	−0.0570396	+	0.0540308i
$163$	−7.89365	+	6.00059i	−0.618278	+	0.470003i	−0.866822	−	0.498618i	$-0.833841\pi$
$163$	−7.89365	+	6.00059i	−0.618278	+	0.470003i	0.248544	+	0.968621i	$0.420048\pi$
$164$	6.63308	−	1.46005i	0.517957	−	0.114011i
$165$	−0.0789443	−	0.0929404i	−0.00614580	−	0.00723540i
$166$	0.123020	−	2.26896i	0.00954818	−	0.176106i
$167$	−10.3301	−	19.4847i	−0.799370	−	1.50777i	−0.860390	−	0.509635i	$-0.829780\pi$
$167$	−10.3301	−	19.4847i	−0.799370	−	1.50777i	0.0610204	−	0.998137i	$-0.480565\pi$
$168$	−2.72773	−	0.600419i	−0.210449	−	0.0463233i
$169$	−9.26937	+	4.28847i	−0.713029	+	0.329882i
$170$	5.77388	+	3.47403i	0.442836	+	0.266446i
$171$	−3.20202	+	6.03966i	−0.244865	+	0.461864i
$172$	−8.25499	+	9.71852i	−0.629437	+	0.741030i
$173$	−12.0124	−	11.3787i	−0.913285	−	0.865109i	0.0779855	−	0.996954i	$-0.475151\pi$
$173$	−12.0124	−	11.3787i	−0.913285	−	0.865109i	−0.991270	+	0.131845i	$0.957910\pi$
$174$	4.83574	+	0.525918i	0.366596	+	0.0398698i
$175$	−4.36370	+	10.9521i	−0.329865	+	0.827898i
$176$	0.138162			0.0104143
$177$	−6.42739	+	4.20579i	−0.483112	+	0.316127i
$178$	−10.4324			−0.781939
$179$	7.31558	−	18.3607i	0.546792	−	1.37234i	−0.352835	−	0.935686i	$-0.614782\pi$
$179$	7.31558	−	18.3607i	0.546792	−	1.37234i	0.899627	−	0.436659i	$-0.143838\pi$
$180$	0.877436	+	0.0954270i	0.0654003	+	0.00711271i
$181$	6.46793	+	6.12675i	0.480758	+	0.455398i	0.889288	−	0.457347i	$-0.151200\pi$
$181$	6.46793	+	6.12675i	0.480758	+	0.455398i	−0.408531	+	0.912745i	$0.633959\pi$
$182$	−3.01843	+	3.55358i	−0.223741	+	0.263409i
$183$	−1.16741	+	2.20196i	−0.0862972	+	0.162774i
$184$	1.08532	+	0.653017i	0.0800111	+	0.0481411i
$185$	−9.31441	+	4.30930i	−0.684809	+	0.316826i
$186$	−1.81471	−	0.399448i	−0.133061	−	0.0292889i
$187$	0.494086	+	0.931946i	0.0361312	+	0.0681506i
$188$	−0.212134	+	3.91259i	−0.0154715	+	0.285355i
$189$	−1.80817	−	2.12874i	−0.131525	−	0.154843i
$190$	5.89244	−	1.29702i	0.427482	−	0.0940959i
$191$	−1.89231	+	1.43850i	−0.136923	+	0.104086i	−0.671394	−	0.741101i	$-0.734304\pi$
$191$	−1.89231	+	1.43850i	−0.136923	+	0.104086i	0.534471	+	0.845187i	$0.320511\pi$
$192$	−0.725995	+	0.687699i	−0.0523942	+	0.0496304i
$193$	−1.07471	−	19.8219i	−0.0773595	−	1.42681i	−0.737336	−	0.675526i	$-0.763916\pi$
$193$	−1.07471	−	19.8219i	−0.0773595	−	1.42681i	0.659976	−	0.751286i	$-0.270566\pi$
$194$	−6.23663	+	3.75245i	−0.447764	+	0.269411i
$195$	0.826836	−	1.21949i	0.0592109	−	0.0873296i
$196$	0.214296	−	0.771825i	0.0153069	−	0.0551304i
$197$	23.1553	−	2.51829i	1.64974	−	0.179420i	0.764525	−	0.644595i	$-0.222974\pi$
$197$	23.1553	−	2.51829i	1.64974	−	0.179420i	0.885219	+	0.465174i	$0.154008\pi$
$198$	0.109990	+	0.0836120i	0.00781663	+	0.00594205i
$199$	12.8415	+	5.94111i	0.910309	+	0.421154i	0.818423	−	0.574616i	$-0.194848\pi$
$199$	12.8415	+	5.94111i	0.910309	+	0.421154i	0.0918860	+	0.995770i	$0.470710\pi$
$200$	2.36877	+	3.49367i	0.167497	+	0.247040i
$201$	−4.56175	+	1.53703i	−0.321761	+	0.108414i
$202$	1.13606	+	6.92965i	0.0799328	+	0.487568i
$203$	−2.19797	+	13.4070i	−0.154267	+	0.940989i
$204$	−7.23502	−	2.43776i	−0.506552	−	0.170677i
$205$	−1.60372	−	5.77608i	−0.112009	−	0.403419i
$206$	5.22686	+	13.1184i	0.364172	+	0.914004i
$207$	0.468829	+	1.17667i	0.0325859	+	0.0817844i
$208$	0.446593	+	1.60848i	0.0309657	+	0.111528i
$209$	0.895030	+	0.301571i	0.0619105	+	0.0208601i
$210$	−0.398818	+	2.43268i	−0.0275211	+	0.167871i
$211$	0.830769	+	5.06746i	0.0571925	+	0.348859i	0.999885	+	0.0151947i	$0.00483680\pi$
$211$	0.830769	+	5.06746i	0.0571925	+	0.348859i	−0.942692	+	0.333664i	$0.891715\pi$
$212$	−3.19136	+	1.07530i	−0.219184	+	0.0738516i
$213$	−3.51419	−	5.18305i	−0.240788	−	0.355136i
$214$	10.5376	+	4.87521i	0.720334	+	0.333262i
$215$	8.95954	+	6.81087i	0.611036	+	0.464497i
$216$	−0.994138	+	0.108119i	−0.0676425	+	0.00735657i
$217$	1.38844	−	5.00071i	0.0942534	−	0.339470i
$218$	7.97522	−	11.7626i	0.540150	−	0.796662i
$219$	6.18375	−	3.72064i	0.417859	−	0.251418i
$220$	−0.00660187	−	0.121764i	−0.000445098	−	0.00820934i
$221$	−9.25266	+	8.76458i	−0.622401	+	0.589570i
$222$	9.25694	−	7.03694i	0.621285	−	0.472289i
$223$	−28.2486	+	6.21798i	−1.89166	+	0.416387i	−0.999384	−	0.0350973i	$-0.988826\pi$
$223$	−28.2486	+	6.21798i	−1.89166	+	0.416387i	−0.892279	+	0.451484i	$0.850895\pi$
$224$	−1.80817	−	2.12874i	−0.120813	−	0.142233i
$225$	−0.228520	+	4.21481i	−0.0152347	+	0.280987i
$226$	−1.30983	−	2.47060i	−0.0871284	−	0.164342i
$227$	−3.68670	−	0.811505i	−0.244695	−	0.0538614i	0.0909294	−	0.995857i	$-0.471016\pi$
$227$	−3.68670	−	0.811505i	−0.244695	−	0.0538614i	−0.335624	+	0.941996i	$0.608947\pi$
$228$	−6.20415	+	2.87035i	−0.410880	+	0.190093i
$229$	2.85526	+	1.71795i	0.188681	+	0.113526i	0.606760	−	0.794885i	$-0.292469\pi$
$229$	2.85526	+	1.71795i	0.188681	+	0.113526i	−0.418079	+	0.908411i	$0.637297\pi$
$230$	0.523654	−	0.987716i	0.0345287	−	0.0651281i
$231$	−0.249820	+	0.294111i	−0.0164370	+	0.0193511i
$232$	3.53143	+	3.34514i	0.231849	+	0.219620i
$233$	−11.4086	−	1.24076i	−0.747405	−	0.0812851i	−0.273513	−	0.961868i	$-0.588186\pi$
$233$	−11.4086	−	1.24076i	−0.747405	−	0.0812851i	−0.473892	+	0.880583i	$0.657151\pi$
$234$	−0.617883	+	1.55077i	−0.0403923	+	0.101377i
$235$	3.45836			0.225599
$236$	−7.66204	−	0.541490i	−0.498756	−	0.0352480i
$237$	3.74419			0.243211
$238$	7.89277	−	19.8094i	0.511613	−	1.28405i
$239$	16.5165	+	1.79628i	1.06836	+	0.116191i	0.625366	−	0.780332i	$-0.284950\pi$
$239$	16.5165	+	1.79628i	1.06836	+	0.116191i	0.442997	+	0.896523i	$0.353915\pi$
$240$	0.640771	+	0.606971i	0.0413616	+	0.0391798i
$241$	−4.05291	+	4.77145i	−0.261071	+	0.307356i	−0.877043	−	0.480411i	$-0.840487\pi$
$241$	−4.05291	+	4.77145i	−0.261071	+	0.307356i	0.615973	+	0.787768i	$0.288763\pi$
$242$	−5.14355	+	9.70177i	−0.330640	+	0.623653i
$243$	−0.856857	−	0.515554i	−0.0549674	−	0.0330728i
$244$	−2.26194	+	1.04648i	−0.144806	+	0.0669942i
$245$	−0.690462	−	0.151982i	−0.0441120	−	0.00970978i
$246$	3.18137	+	6.00070i	0.202837	+	0.382591i
$247$	−0.617806	+	11.3948i	−0.0393100	+	0.725031i
$248$	−1.20294	−	1.41621i	−0.0763869	−	0.0899297i
$249$	2.21917	−	0.488477i	0.140634	−	0.0309560i
$250$	6.47904	−	4.92524i	0.409771	−	0.311500i
$251$	19.2214	−	18.2075i	1.21325	−	1.14925i	0.228817	−	0.973469i	$-0.426514\pi$
$251$	19.2214	−	18.2075i	1.21325	−	1.14925i	0.984430	−	0.175779i	$-0.0562445\pi$
$252$	−0.151212	−	2.78893i	−0.00952544	−	0.175686i
$253$	0.149950	−	0.0902221i	0.00942729	−	0.00567221i
$254$	3.27326	−	4.82770i	0.205383	−	0.302917i
$255$	−1.80272	+	6.49282i	−0.112891	+	0.406596i
$256$	−0.994138	+	0.108119i	−0.0621336	+	0.00675744i
$257$	5.29028	+	4.02156i	0.329998	+	0.250858i	0.757032	−	0.653377i	$-0.226648\pi$
$257$	5.29028	+	4.02156i	0.329998	+	0.250858i	−0.427034	+	0.904236i	$0.640442\pi$
$258$	−11.5727	−	5.35411i	−0.720486	−	0.333332i
$259$	18.2258	+	26.8811i	1.13250	+	1.67031i
$260$	1.39624	−	0.470449i	0.0865913	−	0.0291760i
$261$	0.786949	+	4.80017i	0.0487109	+	0.297123i
$262$	−2.69748	+	16.4539i	−0.166651	+	1.01652i
$263$	5.91344	+	1.99247i	0.364638	+	0.122861i	0.495656	−	0.868519i	$-0.334928\pi$
$263$	5.91344	+	1.99247i	0.364638	+	0.122861i	−0.131017	+	0.991380i	$0.541824\pi$
$264$	0.0369622	+	0.133126i	0.00227487	+	0.00819333i
$265$	1.10017	+	2.76122i	0.0675829	+	0.169620i
$266$	−7.06707	−	17.7370i	−0.433310	−	1.08753i
$267$	−2.79096	−	10.0521i	−0.170804	−	0.615179i
$268$	−4.56175	−	1.53703i	−0.278653	−	0.0938892i
$269$	−1.76324	+	10.7553i	−0.107507	+	0.655762i	0.877010	+	0.480472i	$0.159535\pi$
$269$	−1.76324	+	10.7553i	−0.107507	+	0.655762i	−0.984517	+	0.175290i	$0.943914\pi$
$270$	0.142790	+	0.870983i	0.00868995	+	0.0530064i
$271$	−3.34386	+	1.12668i	−0.203125	+	0.0684409i	−0.419025	−	0.907975i	$-0.637628\pi$
$271$	−3.34386	+	1.12668i	−0.203125	+	0.0684409i	0.215900	+	0.976416i	$0.430732\pi$
$272$	−4.28448	−	6.31913i	−0.259784	−	0.383153i
$273$	−4.23156	−	1.95773i	−0.256106	−	0.118487i
$274$	1.75067	+	1.33083i	0.105762	+	0.0803982i
$275$	0.579762	−	0.0630530i	0.0349610	−	0.00380224i
$276$	−0.338860	+	1.22046i	−0.0203970	+	0.0734633i
$277$	7.95846	−	11.7378i	0.478177	−	0.705259i	−0.509725	−	0.860337i	$-0.670253\pi$
$277$	7.95846	−	11.7378i	0.478177	−	0.705259i	0.987902	+	0.155079i	$0.0495631\pi$
$278$	1.25991	−	0.758063i	0.0755645	−	0.0454656i
$279$	−0.100598	−	1.85543i	−0.00602267	−	0.111082i
$280$	−1.78969	+	1.69529i	−0.106955	+	0.101313i
$281$	22.1481	−	16.8365i	1.32124	−	1.00438i	0.322924	−	0.946425i	$-0.395334\pi$
$281$	22.1481	−	16.8365i	1.32124	−	1.00438i	0.998319	−	0.0579583i	$-0.0184591\pi$
$282$	−3.82673	+	0.842327i	−0.227878	+	0.0501598i
$283$	−7.51496	−	8.84729i	−0.446718	−	0.525917i	0.492004	−	0.870593i	$-0.336265\pi$
$283$	−7.51496	−	8.84729i	−0.446718	−	0.525917i	−0.938722	+	0.344676i	$0.887989\pi$
$284$	0.339022	−	6.25288i	0.0201172	−	0.371040i
$285$	2.82614	+	5.33067i	0.167406	+	0.315761i
$286$	0.225246	+	0.0495803i	0.0133191	+	0.00293175i
$287$	−17.2166	+	7.96526i	−1.01627	+	0.470174i
$288$	−0.856857	−	0.515554i	−0.0504908	−	0.0303793i
$289$	19.3397	−	36.4786i	1.13763	−	2.14580i
$290$	2.77939	−	3.27215i	0.163211	−	0.192147i
$291$	−5.28415	−	5.00541i	−0.309762	−	0.293423i
$292$	7.17448	+	0.780271i	0.419855	+	0.0456619i
$293$	−2.90966	+	7.30270i	−0.169984	+	0.426628i	−0.989146	−	0.146934i	$-0.953060\pi$
$293$	−2.90966	+	7.30270i	−0.169984	+	0.426628i	0.819162	+	0.573562i	$0.194439\pi$
$294$	0.801022			0.0467166
$295$	−0.111105	+	6.77855i	−0.00646876	+	0.394662i
$296$	11.6280			0.675862
$297$	−0.0511390	+	0.128349i	−0.00296738	+	0.00744757i
$298$	−2.54088	−	0.276337i	−0.147189	−	0.0160078i
$299$	1.53507	+	1.45409i	0.0887752	+	0.0840923i
$300$	−2.73262	+	3.21709i	−0.157768	+	0.185739i
$301$	16.6822	−	31.4660i	0.961546	−	1.81367i
$302$	−9.78411	−	5.88691i	−0.563012	−	0.338753i
$303$	−6.37313	+	2.94853i	−0.366127	+	0.169388i
$304$	−6.67615	−	1.46953i	−0.382903	−	0.0842834i
$305$	1.03037	+	1.94348i	0.0589986	+	0.111283i
$306$	0.413332	−	7.62347i	0.0236286	−	0.435805i
$307$	−2.68754	−	3.16401i	−0.153386	−	0.180580i	0.680102	−	0.733117i	$-0.261935\pi$
$307$	−2.68754	−	3.16401i	−0.153386	−	0.180580i	−0.833488	+	0.552538i	$0.813660\pi$
$308$	−0.376868	+	0.0829550i	−0.0214741	+	0.00472680i
$309$	−11.2419	+	8.54589i	−0.639531	+	0.486159i
$310$	−1.19065	+	1.12784i	−0.0676244	+	0.0640573i
$311$	0.0959767	+	1.77019i	0.00544234	+	0.100378i	0.999992	−	0.00388148i	$-0.00123551\pi$
$311$	0.0959767	+	1.77019i	0.00544234	+	0.100378i	−0.994550	+	0.104259i	$0.966753\pi$
$312$	−1.43038	+	0.860630i	−0.0809792	+	0.0487236i
$313$	−8.62530	+	12.7214i	−0.487531	+	0.719054i	−0.989292	−	0.145952i	$-0.953375\pi$
$313$	−8.62530	+	12.7214i	−0.487531	+	0.719054i	0.501761	+	0.865006i	$0.332686\pi$
$314$	−0.859489	+	3.09560i	−0.0485037	+	0.174695i
$315$	−2.45071	+	0.266530i	−0.138082	+	0.0150173i
$316$	2.98072	+	2.26589i	0.167679	+	0.127466i
$317$	23.3037	+	10.7814i	1.30887	+	0.605546i	0.945354	−	0.326044i	$-0.105716\pi$
$317$	23.3037	+	10.7814i	1.30887	+	0.605546i	0.363511	+	0.931590i	$0.381578\pi$
$318$	−1.88988	−	2.78737i	−0.105979	−	0.156308i
$319$	0.636874	−	0.214588i	0.0356581	−	0.0120146i
$320$	0.142790	+	0.870983i	0.00798223	+	0.0486894i
$321$	−1.87840	+	11.4577i	−0.104842	+	0.639509i
$322$	−3.35255	−	1.12961i	−0.186831	−	0.0629505i
$323$	−13.9624	−	50.2880i	−0.776888	−	2.79810i
$324$	−0.370138	−	0.928977i	−0.0205632	−	0.0516098i
$325$	2.60808	+	6.54580i	0.144670	+	0.363095i
$326$	−2.65267	−	9.55406i	−0.146918	−	0.529151i
$327$	13.4674	+	4.53770i	0.744750	+	0.250935i
$328$	−1.09880	+	6.70240i	−0.0606712	+	0.370078i
$329$	−1.77055	−	10.7999i	−0.0976135	−	0.595416i
$330$	0.115560	−	0.0389366i	0.00636136	−	0.00214339i
$331$	13.8277	+	20.3943i	0.760037	+	1.12097i	0.989055	+	0.147548i	$0.0471382\pi$
$331$	13.8277	+	20.3943i	0.760037	+	1.12097i	−0.229018	+	0.973422i	$0.573551\pi$
$332$	2.06228	+	0.954113i	0.113182	+	0.0523637i
$333$	9.25694	+	7.03694i	0.507277	+	0.385622i
$334$	21.9244	−	2.38442i	1.19965	−	0.130470i
$335$	−1.13664	+	4.09379i	−0.0621010	+	0.223668i
$336$	1.56741	−	2.31176i	0.0855094	−	0.126117i
$337$	19.6653	−	11.8322i	1.07124	−	0.644543i	0.133206	−	0.991088i	$-0.457473\pi$
$337$	19.6653	−	11.8322i	1.07124	−	0.644543i	0.938033	+	0.346545i	$0.112645\pi$
$338$	−0.552939	−	10.1984i	−0.0300759	−	0.554717i
$339$	2.03013	−	1.92304i	0.110261	−	0.104445i
$340$	−5.36442	+	4.07793i	−0.290927	+	0.221157i
$341$	−0.250724	+	0.0551885i	−0.0135775	+	0.00298862i
$342$	−4.42551	−	5.21011i	−0.239304	−	0.281731i
$343$	0.937358	−	17.2885i	0.0506126	−	0.933494i
$344$	−5.97279	−	11.2659i	−0.322031	−	0.607416i
$345$	1.09181	+	0.240325i	0.0587809	+	0.0129386i
$346$	15.0168	−	6.94752i	0.807309	−	0.373501i
$347$	−7.34735	−	4.42075i	−0.394426	−	0.237319i	0.304500	−	0.952512i	$-0.401511\pi$
$347$	−7.34735	−	4.42075i	−0.394426	−	0.237319i	−0.698926	+	0.715194i	$0.746338\pi$
$348$	−2.27846	+	4.29763i	−0.122138	+	0.230377i
$349$	−17.4816	+	20.5809i	−0.935768	+	1.10167i	0.0588711	+	0.998266i	$0.481250\pi$
$349$	−17.4816	+	20.5809i	−0.935768	+	1.10167i	−0.994639	+	0.103406i	$0.967026\pi$
$350$	−8.55904	−	8.10755i	−0.457500	−	0.433367i
$351$	−1.65955	−	0.180486i	−0.0885800	−	0.00963365i
$352$	−0.0511390	+	0.128349i	−0.00272572	+	0.00684103i
$353$	3.95970			0.210754			0.105377	−	0.994432i	$-0.466395\pi$
$353$	3.95970			0.210754			0.105377	+	0.994432i	$0.466395\pi$
$354$	−1.52806	−	7.52762i	−0.0812154	−	0.400088i
$355$	−5.52697			−0.293341
$356$	3.86142	−	9.69143i	0.204655	−	0.513645i
$357$	21.1989	+	2.30551i	1.12196	+	0.122021i
$358$	14.3489	+	13.5920i	0.758363	+	0.718360i
$359$	10.5563	−	12.4279i	0.557143	−	0.655919i	−0.409421	−	0.912346i	$-0.634269\pi$
$359$	10.5563	−	12.4279i	0.557143	−	0.655919i	0.966564	+	0.256427i	$0.0825452\pi$
$360$	−0.413422	+	0.779797i	−0.0217893	+	0.0410989i
$361$	−23.7610	−	14.2965i	−1.25058	−	0.752449i
$362$	−8.08564	+	3.74081i	−0.424972	+	0.196613i
$363$	−10.7242	−	2.36057i	−0.562874	−	0.123898i
$364$	−2.18395	−	4.11937i	−0.114470	−	0.215914i
$365$	0.344844	−	6.36027i	0.0180499	−	0.332911i
$366$	−1.61347	−	1.89952i	−0.0843375	−	0.0992897i
$367$	8.00580	−	1.76221i	0.417899	−	0.0919866i	−0.00104303	−	0.999999i	$-0.500332\pi$
$367$	8.00580	−	1.76221i	0.417899	−	0.0919866i	0.418942	+	0.908013i	$0.362401\pi$
$368$	−1.00836	+	0.766533i	−0.0525643	+	0.0399583i
$369$	−4.93087	+	4.67077i	−0.256691	+	0.243150i
$370$	−0.555625	−	10.2479i	−0.0288856	−	0.532763i
$371$	8.05956	−	4.84927i	0.418431	−	0.251762i
$372$	1.04277	−	1.53797i	0.0540652	−	0.0797402i
$373$	2.59264	−	9.33786i	0.134242	−	0.483496i	−0.865610	−	0.500719i	$-0.833069\pi$
$373$	2.59264	−	9.33786i	0.134242	−	0.483496i	0.999852	+	0.0172235i	$0.00548267\pi$
$374$	−1.04864	+	0.114046i	−0.0542237	+	0.00589718i
$375$	6.47904	+	4.92524i	0.334576	+	0.254338i
$376$	−3.55619	−	1.64527i	−0.183396	−	0.0848482i
$377$	4.55687	+	6.72088i	0.234691	+	0.346143i
$378$	2.64682	−	0.891819i	0.136138	−	0.0458702i
$379$	1.82369	+	11.1240i	0.0936766	+	0.571402i	0.991402	+	0.130848i	$0.0417699\pi$
$379$	1.82369	+	11.1240i	0.0936766	+	0.571402i	−0.897726	+	0.440555i	$0.854782\pi$
$380$	−0.976111	+	5.95401i	−0.0500734	+	0.305434i
$381$	5.52742	+	1.86241i	0.283179	+	0.0954140i
$382$	−0.635915	−	2.29036i	−0.0325362	−	0.117185i
$383$	7.38527	+	18.5356i	0.377369	+	0.947126i	0.987894	+	0.155129i	$0.0495793\pi$
$383$	7.38527	+	18.5356i	0.377369	+	0.947126i	−0.610525	+	0.791997i	$0.709041\pi$
$384$	−0.370138	−	0.928977i	−0.0188885	−	0.0474066i
$385$	0.0911177	+	0.328176i	0.00464379	+	0.0167254i
$386$	18.8119	+	6.33846i	0.957500	+	0.322619i
$387$	2.06292	−	12.5833i	0.104864	−	0.639644i
$388$	−1.17753	−	7.18261i	−0.0597800	−	0.364642i
$389$	−34.9825	+	11.7870i	−1.77368	+	0.597623i	−0.999380	−	0.0351950i	$-0.988795\pi$
$389$	−34.9825	+	11.7870i	−1.77368	+	0.597623i	−0.774301	+	0.632818i	$0.781898\pi$
$390$	0.826836	+	1.21949i	0.0418684	+	0.0617513i
$391$	−8.77654	−	4.06046i	−0.443849	−	0.205346i
$392$	0.637688	+	0.484758i	0.0322081	+	0.0244840i
$393$	−16.5758	+	1.80273i	−0.836138	+	0.0909355i
$394$	−6.23122	+	22.4428i	−0.313924	+	1.13065i
$395$	1.85453	−	2.73523i	0.0933117	−	0.137624i
$396$	−0.118385	+	0.0712299i	−0.00594907	+	0.00357944i
$397$	−0.557349	−	10.2797i	−0.0279725	−	0.515923i	−0.978623	−	0.205660i	$-0.934066\pi$
$397$	−0.557349	−	10.2797i	−0.0279725	−	0.515923i	0.950651	−	0.310263i	$-0.100417\pi$
$398$	−10.2723	+	9.73042i	−0.514903	+	0.487742i
$399$	15.1999	−	11.5546i	0.760945	−	0.578455i
$400$	−4.12231	+	0.907390i	−0.206116	+	0.0453695i
$401$	15.8434	+	18.6523i	0.791183	+	0.931453i	0.998907	−	0.0467348i	$-0.0148816\pi$
$401$	15.8434	+	18.6523i	0.791183	+	0.931453i	−0.207724	+	0.978187i	$0.566606\pi$
$402$	0.260610	−	4.80668i	0.0129981	−	0.239735i
$403$	−1.45294	−	2.74054i	−0.0723763	−	0.136516i
$404$	−6.85798	−	1.50956i	−0.341197	−	0.0751032i
$405$	−0.801035	+	0.370598i	−0.0398038	+	0.0184152i
$406$	−11.6413	−	7.00432i	−0.577747	−	0.347619i
$407$	0.752517	−	1.41940i	0.0373009	−	0.0703570i
$408$	4.94258	−	5.81885i	0.244694	−	0.288076i
$409$	2.61972	+	2.48153i	0.129537	+	0.122704i	0.749726	−	0.661749i	$-0.230185\pi$
$409$	2.61972	+	2.48153i	0.129537	+	0.122704i	−0.620189	+	0.784453i	$0.712944\pi$
$410$	5.95944	+	0.648128i	0.294316	+	0.0320088i
$411$	−0.813964	+	2.04290i	−0.0401499	+	0.100769i
$412$	−14.1214			−0.695710
$413$	21.2251	−	3.12339i	1.04442	−	0.153692i
$414$	−1.26663			−0.0622516
$415$	0.742332	−	1.86311i	0.0364396	−	0.0914566i
$416$	−1.65955	−	0.180486i	−0.0813659	−	0.00884907i
$417$	1.06749	+	1.01118i	0.0522754	+	0.0495179i
$418$	−0.611437	+	0.719839i	−0.0299064	+	0.0352085i
$419$	−4.73387	+	8.92903i	−0.231265	+	0.436212i	−0.971800	−	0.235806i	$-0.924227\pi$
$419$	−4.73387	+	8.92903i	−0.231265	+	0.436212i	0.740535	+	0.672017i	$0.234572\pi$
$420$	−2.11229	−	1.27092i	−0.103069	−	0.0620146i
$421$	−32.7959	+	15.1730i	−1.59838	+	0.739487i	−0.998176	−	0.0603630i	$-0.980774\pi$
$421$	−32.7959	+	15.1730i	−1.59838	+	0.739487i	−0.600199	+	0.799850i	$0.704912\pi$
$422$	−5.01506	−	1.10390i	−0.244129	−	0.0537369i
$423$	−1.83538	−	3.46190i	−0.0892393	−	0.168323i
$424$	0.182321	−	3.36271i	0.00885429	−	0.163308i
$425$	−20.8626	−	24.5614i	−1.01199	−	1.19140i
$426$	6.11566	−	1.34616i	0.296305	−	0.0652216i
$427$	5.54163	−	4.21263i	0.268178	−	0.203864i
$428$	−8.42931	+	7.98467i	−0.407446	+	0.385954i
$429$	0.0124865	+	0.230300i	0.000602853	+	0.0111190i
$430$	−9.64340	+	5.80224i	−0.465046	+	0.279809i
$431$	−17.8559	+	26.3354i	−0.860087	+	1.26853i	0.101722	+	0.994813i	$0.467565\pi$
$431$	−17.8559	+	26.3354i	−0.860087	+	1.26853i	−0.961809	+	0.273721i	$0.911746\pi$
$432$	0.267528	−	0.963550i	0.0128715	−	0.0463588i
$433$	−5.84459	+	0.635638i	−0.280873	+	0.0305468i	−0.247471	−	0.968895i	$-0.579600\pi$
$433$	−5.84459	+	0.635638i	−0.280873	+	0.0305468i	−0.0334018	+	0.999442i	$0.510634\pi$
$434$	4.13163	+	3.14078i	0.198324	+	0.150762i
$435$	3.89644	+	1.80269i	0.186820	+	0.0864321i
$436$	7.97522	+	11.7626i	0.381944	+	0.563325i
$437$	−8.20540	+	2.76472i	−0.392518	+	0.132255i
$438$	1.16755	+	7.12171i	0.0557875	+	0.340289i
$439$	3.53034	−	21.5341i	0.168494	−	1.02777i	−0.758220	−	0.651999i	$-0.773931\pi$
$439$	3.53034	−	21.5341i	0.168494	−	1.02777i	0.926714	−	0.375768i	$-0.122621\pi$
$440$	0.115560	+	0.0389366i	0.00550910	+	0.00185623i
$441$	0.214296	+	0.771825i	0.0102046	+	0.0367536i
$442$	−4.71733	−	11.8396i	−0.224381	−	0.563153i
$443$	6.09561	+	15.2988i	0.289611	+	0.726870i	0.999740	+	0.0227978i	$0.00725740\pi$
$443$	6.09561	+	15.2988i	0.289611	+	0.726870i	−0.710129	+	0.704072i	$0.751363\pi$
$444$	3.11081	+	11.2041i	0.147632	+	0.531724i
$445$	−8.72573	−	2.94004i	−0.413639	−	0.139371i
$446$	4.67951	−	28.5438i	0.221581	−	1.35159i
$447$	−0.413493	−	2.52219i	−0.0195575	−	0.119296i
$448$	2.64682	−	0.891819i	0.125051	−	0.0421345i
$449$	5.00953	+	7.38851i	0.236415	+	0.348685i	0.927326	−	0.374254i	$-0.122101\pi$
$449$	5.00953	+	7.38851i	0.236415	+	0.348685i	−0.690912	+	0.722939i	$0.742791\pi$
$450$	−3.83087	−	1.77235i	−0.180589	−	0.0835494i
$451$	0.747036	+	0.567882i	0.0351766	+	0.0267405i
$452$	2.77994	−	0.302337i	0.130758	−	0.0142207i
$453$	3.05480	−	11.0024i	0.143527	−	0.516938i
$454$	2.11846	−	3.12449i	0.0994242	−	0.146640i
$455$	−3.52611	+	2.12159i	−0.165307	+	0.0994616i
$456$	−0.370092	−	6.82594i	−0.0173311	−	0.319654i
$457$	17.7644	−	16.8273i	0.830982	−	0.787148i	−0.148451	−	0.988920i	$-0.547429\pi$
$457$	17.7644	−	16.8273i	0.830982	−	0.787148i	0.979433	+	0.201772i	$0.0646700\pi$
$458$	−2.65278	+	2.01659i	−0.123956	+	0.0942291i
$459$	7.45617	−	1.64123i	0.348024	−	0.0766059i
$460$	0.723741	+	0.852054i	0.0337446	+	0.0397272i
$461$	−0.0605734	+	1.11721i	−0.00282118	+	0.0520337i	−0.999605	−	0.0281037i	$-0.991053\pi$
$461$	−0.0605734	+	1.11721i	−0.00282118	+	0.0520337i	0.996784	+	0.0801374i	$0.0255359\pi$
$462$	−0.180754	−	0.340939i	−0.00840945	−	0.0158619i
$463$	11.8285	+	2.60364i	0.549715	+	0.121001i	0.481139	−	0.876644i	$-0.340223\pi$
$463$	11.8285	+	2.60364i	0.549715	+	0.121001i	0.0685763	+	0.997646i	$0.478154\pi$
$464$	−4.41468	+	2.04245i	−0.204946	+	0.0948182i
$465$	−1.40527	−	0.845521i	−0.0651677	−	0.0392101i
$466$	5.37541	−	10.1391i	0.249011	−	0.469685i
$467$	−22.5886	+	26.5933i	−1.04527	+	1.23059i	−0.0728571	+	0.997342i	$0.523212\pi$
$467$	−22.5886	+	26.5933i	−1.04527	+	1.23059i	−0.972417	+	0.233249i	$0.925064\pi$
$468$	−1.21193	−	1.14800i	−0.0560213	−	0.0530662i
$469$	13.3661	+	1.45365i	0.617189	+	0.0671234i
$470$	−1.28007	+	3.21274i	−0.0590454	+	0.148193i
$471$	−3.21270			−0.148033
$472$	3.33904	−	6.91743i	0.153692	−	0.318400i
$473$	−1.76174			−0.0810048
$474$	−1.38587	+	3.47827i	−0.0636550	+	0.159762i
$475$	−28.6855	−	3.11973i	−1.31618	−	0.143143i
$476$	15.4810	+	14.6644i	0.709572	+	0.672142i
$477$	2.18017	−	2.56670i	0.0998232	−	0.117521i
$478$	−7.78208	+	14.6786i	−0.355944	+	0.671382i
$479$	4.65139	+	2.79865i	0.212528	+	0.127874i	0.617838	−	0.786306i	$-0.288009\pi$
$479$	4.65139	+	2.79865i	0.212528	+	0.127874i	−0.405310	+	0.914179i	$0.632836\pi$
$480$	−0.801035	+	0.370598i	−0.0365621	+	0.0169154i
$481$	18.9571	+	4.17277i	0.864369	+	0.190262i
$482$	−2.93243	−	5.53115i	−0.133569	−	0.251937i
$483$	0.191530	−	3.53256i	0.00871490	−	0.160737i
$484$	−7.10889	−	8.36923i	−0.323131	−	0.380420i
$485$	−6.27388	+	1.38099i	−0.284882	+	0.0627073i
$486$	0.796093	−	0.605174i	0.0361115	−	0.0274513i
$487$	−24.4427	+	23.1534i	−1.10761	+	1.04918i	−0.109128	+	0.994028i	$0.534806\pi$
$487$	−24.4427	+	23.1534i	−1.10761	+	1.04918i	−0.998478	+	0.0551525i	$0.982436\pi$
$488$	−0.134930	−	2.48863i	−0.00610797	−	0.112655i
$489$	8.49615	−	5.11197i	0.384209	−	0.231171i
$490$	0.396754	−	0.585168i	0.0179235	−	0.0264352i
$491$	−3.40630	+	12.2684i	−0.153724	+	0.553665i	0.846064	+	0.533082i	$0.178966\pi$
$491$	−3.40630	+	12.2684i	−0.153724	+	0.553665i	−0.999788	+	0.0205834i	$0.993448\pi$
$492$	−6.75206	+	0.734331i	−0.304406	+	0.0331062i
$493$	−29.5645	−	22.4743i	−1.33152	−	1.01219i
$494$	−10.3568	−	4.79156i	−0.465974	−	0.215582i
$495$	0.0684329	+	0.100931i	0.00307583	+	0.00453651i
$496$	1.76088	−	0.593311i	0.0790661	−	0.0266405i
$497$	2.82959	+	17.2597i	0.126925	+	0.774205i
$498$	−0.367617	+	2.24236i	−0.0164733	+	0.100483i
$499$	27.8029	+	9.36788i	1.24463	+	0.419364i	0.863119	−	0.505001i	$-0.168508\pi$
$499$	27.8029	+	9.36788i	1.24463	+	0.419364i	0.381509	+	0.924365i	$0.375404\pi$
$500$	2.17729	+	7.84190i	0.0973715	+	0.350700i
$501$	8.16291	+	20.4874i	0.364692	+	0.915308i
$502$	9.79977	+	24.5956i	0.437385	+	1.09775i
$503$	6.34955	+	22.8690i	0.283112	+	1.01968i	0.959170	+	0.282830i	$0.0912732\pi$
$503$	6.34955	+	22.8690i	0.283112	+	1.01968i	−0.676058	+	0.736849i	$0.736313\pi$
$504$	2.64682	+	0.891819i	0.117899	+	0.0397248i
$505$	−1.00270	+	6.11618i	−0.0446194	+	0.272166i
$506$	0.0283119	+	0.172695i	0.00125862	+	0.00767723i
$507$	9.67870	−	3.26113i	0.429846	−	0.144832i
$508$	3.27326	+	4.82770i	0.145228	+	0.214195i
$509$	27.7261	+	12.8274i	1.22894	+	0.568567i	0.923483	−	0.383640i	$-0.125330\pi$
$509$	27.7261	+	12.8274i	1.22894	+	0.568567i	0.305454	+	0.952207i	$0.401192\pi$
$510$	−5.36442	−	4.07793i	−0.237541	−	0.180574i
$511$	−20.0385	+	2.17932i	−0.886453	+	0.0964075i
$512$	0.267528	−	0.963550i	0.0118232	−	0.0425833i
$513$	3.83626	−	5.65805i	0.169375	−	0.249809i
$514$	−5.69407	+	3.42601i	−0.251155	+	0.151115i
$515$	0.674769	+	12.4454i	0.0297339	+	0.548409i
$516$	9.25735	−	8.76903i	0.407532	−	0.386035i
$517$	−0.430977	+	0.327620i	−0.0189543	+	0.0144087i
$518$	−31.7180	+	6.98165i	−1.39361	+	0.306756i
$519$	10.7117	+	12.6108i	0.470192	+	0.553553i
$520$	−0.0797666	+	1.47121i	−0.00349800	+	0.0645167i
$521$	16.5413	+	31.2001i	0.724686	+	1.36690i	0.922243	+	0.386611i	$0.126354\pi$
$521$	16.5413	+	31.2001i	0.724686	+	1.36690i	−0.197557	+	0.980291i	$0.563301\pi$
$522$	−4.75053	−	1.04567i	−0.207925	−	0.0457678i
$523$	6.70397	−	3.10159i	0.293144	−	0.135623i	−0.267805	−	0.963473i	$-0.586298\pi$
$523$	6.70397	−	3.10159i	0.293144	−	0.135623i	0.560949	+	0.827850i	$0.310436\pi$
$524$	−14.2868	−	8.59610i	−0.624123	−	0.375522i
$525$	5.52225	−	10.4161i	0.241011	−	0.454594i
$526$	−4.03975	+	4.75596i	−0.176141	+	0.207370i
$527$	10.2992	+	9.75596i	0.448642	+	0.424976i
$528$	−0.137352	−	0.0149379i	−0.00597748	−	0.000650090i
$529$	7.91934	−	19.8761i	0.344319	−	0.864176i
$530$	−2.97232			−0.129109
$531$	6.84444	−	3.48621i	0.297023	−	0.151289i
$532$	19.0931			0.827789
$533$	−4.19658	+	10.5326i	−0.181774	+	0.456219i
$534$	10.3712	+	1.12794i	0.448807	+	0.0488107i
$535$	7.43980	+	7.04735i	0.321651	+	0.304684i
$536$	3.11635	−	3.66885i	0.134606	−	0.158470i
$537$	−9.25784	+	17.4621i	−0.399505	+	0.753547i
$538$	−9.33878	−	5.61895i	−0.402623	−	0.242250i
$539$	0.100442	−	0.0464694i	0.00432635	−	0.00200158i
$540$	−0.861975	−	0.189735i	−0.0370935	−	0.00816490i
$541$	15.9463	+	30.0778i	0.685583	+	1.29315i	0.944901	+	0.327355i	$0.106157\pi$
$541$	15.9463	+	30.0778i	0.685583	+	1.29315i	−0.259318	+	0.965792i	$0.583498\pi$
$542$	0.191033	−	3.52340i	0.00820558	−	0.151343i
$543$	−5.76760	−	6.79014i	−0.247511	−	0.291393i
$544$	7.45617	−	1.64123i	0.319681	−	0.0703670i
$545$	9.98545	−	7.59074i	0.427730	−	0.325152i
$546$	3.38495	−	3.20639i	0.144862	−	0.137221i
$547$	1.05339	+	19.4286i	0.0450397	+	0.830708i	0.930567	+	0.366121i	$0.119314\pi$
$547$	1.05339	+	19.4286i	0.0450397	+	0.830708i	−0.885527	+	0.464587i	$0.846203\pi$
$548$	−1.88430	+	1.13374i	−0.0804932	+	0.0484312i
$549$	1.39864	−	2.06284i	0.0596924	−	0.0880397i
$550$	−0.156017	+	0.561924i	−0.00665261	+	0.0239605i
$551$	−33.0569	+	3.59516i	−1.40827	+	0.153159i
$552$	−1.00836	−	0.766533i	−0.0429185	−	0.0326258i
$553$	−9.49110	−	4.39105i	−0.403602	−	0.186726i
$554$	7.95846	+	11.7378i	0.338122	+	0.498693i
$555$	9.72573	−	3.27698i	0.412834	−	0.139100i
$556$	0.237882	+	1.45102i	0.0100884	+	0.0615368i
$557$	6.86214	−	41.8572i	0.290758	−	1.77355i	−0.287586	−	0.957755i	$-0.592853\pi$
$557$	6.86214	−	41.8572i	0.290758	−	1.77355i	0.578344	−	0.815793i	$-0.303699\pi$
$558$	1.76088	+	0.593311i	0.0745442	+	0.0251169i
$559$	−5.69462	−	20.5102i	−0.240857	−	0.867488i
$560$	−0.912449	−	2.29007i	−0.0385580	−	0.0967733i
$561$	−0.390429	−	0.979903i	−0.0164839	−	0.0413715i
$562$	7.44290	+	26.8069i	0.313960	+	1.13078i
$563$	11.9163	+	4.01507i	0.502212	+	0.169215i	0.558994	−	0.829172i	$-0.311187\pi$
$563$	11.9163	+	4.01507i	0.502212	+	0.169215i	−0.0567819	+	0.998387i	$0.518084\pi$
$564$	0.633916	−	3.86672i	0.0266927	−	0.162818i
$565$	−0.399290	−	2.43556i	−0.0167983	−	0.102465i
$566$	11.0005	−	3.70650i	0.462386	−	0.155796i
$567$	1.56741	+	2.31176i	0.0658252	+	0.0970848i
$568$	5.68330	+	2.62937i	0.238466	+	0.110326i
$569$	−26.8313	−	20.3966i	−1.12483	−	0.855070i	−0.134103	−	0.990967i	$-0.542815\pi$
$569$	−26.8313	−	20.3966i	−1.12483	−	0.855070i	−0.990723	+	0.135897i	$0.956608\pi$
$570$	−5.99813	+	0.652336i	−0.251234	+	0.0273233i
$571$	4.02923	−	14.5120i	0.168618	−	0.607307i	−0.830144	−	0.557550i	$-0.811742\pi$
$571$	4.02923	−	14.5120i	0.168618	−	0.607307i	0.998761	−	0.0497568i	$-0.0158446\pi$
$572$	−0.129431	+	0.190896i	−0.00541178	+	0.00798178i
$573$	2.03675	−	1.22547i	0.0850865	−	0.0511948i
$574$	−1.02701	−	18.9421i	−0.0428666	−	0.790628i
$575$	−3.88150	+	3.67675i	−0.161870	+	0.153331i
$576$	0.796093	−	0.605174i	0.0331705	−	0.0252156i
$577$	−24.4686	+	5.38594i	−1.01864	+	0.224220i	−0.692742	−	0.721185i	$-0.743598\pi$
$577$	−24.4686	+	5.38594i	−1.01864	+	0.224220i	−0.325898	+	0.945405i	$0.605667\pi$
$578$	26.7294	+	31.4682i	1.11179	+	1.30891i
$579$	−1.07471	+	19.8219i	−0.0446635	+	0.823771i
$580$	2.01099	+	3.79313i	0.0835018	+	0.157501i
$581$	−6.19822	−	1.36433i	−0.257145	−	0.0566020i
$582$	6.60578	−	3.05616i	0.273818	−	0.126682i
$583$	−0.398679	−	0.239877i	−0.0165116	−	0.00993470i
$584$	−3.38040	+	6.37611i	−0.139882	+	0.263845i
$585$	−0.953839	+	1.12295i	−0.0394364	+	0.0464281i
$586$	−5.70706	−	5.40602i	−0.235757	−	0.223320i
$587$	18.4985	+	2.01183i	0.763515	+	0.0830373i	0.481587	−	0.876398i	$-0.340061\pi$
$587$	18.4985	+	2.01183i	0.763515	+	0.0830373i	0.281928	+	0.959436i	$0.409026\pi$
$588$	−0.296489	+	0.744131i	−0.0122270	+	0.0306875i
$589$	12.7023			0.523388
$590$	−6.25599	−	2.61221i	−0.257555	−	0.107543i
$591$	−23.2918			−0.958096
$592$	−4.30395	+	10.8021i	−0.176891	+	0.443964i
$593$	6.39701	+	0.695716i	0.262694	+	0.0285696i	0.238518	−	0.971138i	$-0.423338\pi$
$593$	6.39701	+	0.695716i	0.262694	+	0.0285696i	0.0241756	+	0.999708i	$0.492304\pi$
$594$	−0.100305	−	0.0950138i	−0.00411556	−	0.00389847i
$595$	12.1842	−	14.3444i	0.499505	−	0.588063i
$596$	1.19719	−	2.25814i	0.0490387	−	0.0924969i
$597$	−12.1239	−	7.29469i	−0.496197	−	0.298552i
$598$	−1.91900	+	0.887826i	−0.0784739	+	0.0363059i
$599$	−20.3085	−	4.47025i	−0.829785	−	0.182649i	−0.220285	−	0.975436i	$-0.570699\pi$
$599$	−20.3085	−	4.47025i	−0.829785	−	0.182649i	−0.609500	+	0.792786i	$0.708630\pi$
$600$	−1.97715	−	3.72930i	−0.0807169	−	0.152248i
$601$	1.97877	−	36.4963i	0.0807158	−	1.48872i	−0.625225	−	0.780445i	$-0.714993\pi$
$601$	1.97877	−	36.4963i	0.0807158	−	1.48872i	0.705941	−	0.708271i	$-0.250525\pi$
$602$	23.0564	+	27.1441i	0.939710	+	1.10631i
$603$	4.70119	−	1.03481i	0.191447	−	0.0421408i
$604$	9.09027	−	6.91024i	0.369878	−	0.281174i
$605$	−7.03625	+	6.66509i	−0.286064	+	0.270974i
$606$	−0.380172	−	7.01185i	−0.0154434	−	0.284837i
$607$	−22.1479	+	13.3259i	−0.898954	+	0.540883i	−0.888405	−	0.459061i	$-0.848186\pi$
$607$	−22.1479	+	13.3259i	−0.898954	+	0.540883i	−0.0105498	+	0.999944i	$0.503358\pi$
$608$	3.83626	−	5.65805i	0.155581	−	0.229464i
$609$	3.63464	−	13.0908i	0.147283	−	0.530466i
$610$	−2.18682	+	0.237831i	−0.0885418	+	0.00962950i
$611$	−5.20725	−	3.95845i	−0.210663	−	0.160142i
$612$	6.92904	+	3.20571i	0.280090	+	0.129583i
$613$	−15.9252	−	23.4879i	−0.643212	−	0.948667i	−0.999896	−	0.0144418i	$-0.995403\pi$
$613$	−15.9252	−	23.4879i	−0.643212	−	0.948667i	0.356683	−	0.934225i	$-0.383907\pi$
$614$	3.93406	−	1.32554i	0.158766	−	0.0534943i
$615$	0.969815	+	5.91561i	0.0391067	+	0.238540i
$616$	0.0624301	−	0.380807i	0.00251538	−	0.0153431i
$617$	19.0057	+	6.40376i	0.765140	+	0.257806i	0.674696	−	0.738096i	$-0.264275\pi$
$617$	19.0057	+	6.40376i	0.765140	+	0.257806i	0.0904442	+	0.995902i	$0.471171\pi$
$618$	−3.77787	−	13.6066i	−0.151968	−	0.547339i
$619$	−3.80312	−	9.54511i	−0.152860	−	0.383650i	0.832526	−	0.553986i	$-0.186894\pi$
$619$	−3.80312	−	9.54511i	−0.152860	−	0.383650i	−0.985386	+	0.170336i	$0.945515\pi$
$620$	−0.607036	−	1.52355i	−0.0243791	−	0.0611870i
$621$	−0.338860	−	1.22046i	−0.0135980	−	0.0489755i
$622$	−1.67999	−	0.566053i	−0.0673613	−	0.0226967i
$623$	−4.71399	+	28.7541i	−0.188862	+	1.15201i
$624$	−0.270068	−	1.64734i	−0.0108114	−	0.0659464i
$625$	−13.1931	+	4.44526i	−0.527723	+	0.177810i
$626$	−8.62530	−	12.7214i	−0.344736	−	0.508448i
$627$	−0.857178	−	0.396573i	−0.0342324	−	0.0158376i
$628$	−2.55761	−	1.94424i	−0.102060	−	0.0775838i
$629$	−88.2552	+	9.59833i	−3.51896	+	0.382711i
$630$	0.659500	−	2.37530i	0.0262751	−	0.0946343i
$631$	−7.61685	+	11.2340i	−0.303222	+	0.447219i	−0.948523	−	0.316710i	$-0.897422\pi$
$631$	−7.61685	+	11.2340i	−0.303222	+	0.447219i	0.645300	+	0.763929i	$0.276732\pi$
$632$	−3.20824	+	1.93033i	−0.127617	+	0.0767845i
$633$	−0.278009	−	5.12758i	−0.0110499	−	0.203803i
$634$	−18.6413	+	17.6580i	−0.740340	+	0.701287i
$635$	4.09832	−	3.11546i	0.162637	−	0.123633i
$636$	3.28892	−	0.723945i	0.130414	−	0.0287063i
$637$	0.865666	+	1.01914i	0.0342990	+	0.0403799i
$638$	−0.0363843	+	0.671069i	−0.00144047	+	0.0265679i
$639$	2.93321	+	5.53261i	0.116036	+	0.218867i
$640$	−0.861975	−	0.189735i	−0.0340726	−	0.00749994i
$641$	−18.9665	+	8.77481i	−0.749130	+	0.346584i	−0.757026	−	0.653384i	$-0.773349\pi$
$641$	−18.9665	+	8.77481i	−0.749130	+	0.346584i	0.00789646	+	0.999969i	$0.497486\pi$
$642$	−9.94871	−	5.98594i	−0.392644	−	0.236246i
$643$	21.6913	−	40.9141i	0.855420	−	1.61349i	0.0674967	−	0.997719i	$-0.478499\pi$
$643$	21.6913	−	40.9141i	0.855420	−	1.61349i	0.787923	−	0.615774i	$-0.211156\pi$
$644$	2.29029	−	2.69633i	0.0902500	−	0.106250i
$645$	−8.17064	−	7.73964i	−0.321718	−	0.304748i
$646$	51.8844	+	5.64277i	2.04136	+	0.222012i
$647$	12.1283	−	30.4397i	0.476812	−	1.19671i	−0.472207	−	0.881488i	$-0.656543\pi$
$647$	12.1283	−	30.4397i	0.476812	−	1.19671i	0.949019	−	0.315219i	$-0.102078\pi$
$648$	1.00000			0.0392837
$649$	−0.628304	−	0.855259i	−0.0246631	−	0.0335718i
$650$	−7.04624			−0.276376
$651$	−1.92097	+	4.82128i	−0.0752888	+	0.188961i
$652$	9.85736	+	1.07205i	0.386044	+	0.0419848i
$653$	25.3173	+	23.9819i	0.990744	+	0.938483i	0.998108	−	0.0614901i	$-0.0195853\pi$
$653$	25.3173	+	23.9819i	0.990744	+	0.938483i	−0.00736350	+	0.999973i	$0.502344\pi$
$654$	−9.20022	+	10.8313i	−0.359757	+	0.423539i
$655$	−6.89320	+	13.0020i	−0.269340	+	0.508029i
$656$	−5.81967	−	3.50158i	−0.227220	−	0.136714i
$657$	−6.54977	+	3.03025i	−0.255531	+	0.118221i
$658$	10.6882	+	2.35264i	0.416668	+	0.0917156i
$659$	−9.36005	−	17.6549i	−0.364616	−	0.687738i	0.631539	−	0.775344i	$-0.282423\pi$
$659$	−9.36005	−	17.6549i	−0.364616	−	0.687738i	−0.996155	+	0.0876054i	$0.972079\pi$
$660$	−0.00660187	+	0.121764i	−0.000256977	+	0.00473967i
$661$	−18.7986	−	22.1314i	−0.731181	−	0.860812i	0.263410	−	0.964684i	$-0.415153\pi$
$661$	−18.7986	−	22.1314i	−0.731181	−	0.860812i	−0.994591	+	0.103872i	$0.966877\pi$
$662$	−24.0639	+	5.29688i	−0.935272	+	0.205869i
$663$	10.1460	−	7.71281i	0.394039	−	0.299541i
$664$	−1.64968	+	1.56266i	−0.0640199	+	0.0606429i
$665$	−0.912335	−	16.8270i	−0.0353788	−	0.652524i
$666$	−9.96350	+	5.99484i	−0.386078	+	0.232295i
$667$	−3.45760	+	5.09958i	−0.133879	+	0.197456i
$668$	−5.89999	+	21.2498i	−0.228277	+	0.822181i
$669$	28.7552	−	3.12732i	1.11174	−	0.120909i
$670$	−3.38232	−	2.57118i	−0.130671	−	0.0993332i
$671$	−0.312513	−	0.144584i	−0.0120644	−	0.00558160i
$672$	1.56741	+	2.31176i	0.0604643	+	0.0891781i
$673$	22.0405	−	7.42630i	0.849597	−	0.286263i	0.139375	−	0.990240i	$-0.455491\pi$
$673$	22.0405	−	7.42630i	0.849597	−	0.286263i	0.710223	+	0.703977i	$0.248594\pi$
$674$	3.71299	+	22.6482i	0.143019	+	0.872376i
$675$	0.682882	−	4.16539i	0.0262841	−	0.160326i
$676$	9.67870	+	3.26113i	0.372258	+	0.125428i
$677$	−11.3807	−	40.9897i	−0.437397	−	1.57536i	−0.773665	−	0.633595i	$-0.781579\pi$
$677$	−11.3807	−	40.9897i	−0.437397	−	1.57536i	0.336268	−	0.941766i	$-0.390835\pi$
$678$	1.03503	+	2.59773i	0.0397501	+	0.0997653i
$679$	7.52456	+	18.8852i	0.288766	+	0.724748i
$680$	−1.80272	−	6.49282i	−0.0691312	−	0.248988i
$681$	3.57735	+	1.20535i	0.137084	+	0.0461891i
$682$	0.0415336	−	0.253344i	0.00159040	−	0.00970104i
$683$	−7.84074	−	47.8264i	−0.300018	−	1.83003i	−0.519573	−	0.854426i	$-0.673909\pi$
$683$	−7.84074	−	47.8264i	−0.300018	−	1.83003i	0.219555	−	0.975600i	$-0.429539\pi$
$684$	6.47813	−	2.18273i	0.247697	−	0.0834589i
$685$	1.08923	+	1.60649i	0.0416172	+	0.0613807i
$686$	15.7137	+	7.26993i	0.599952	+	0.277567i
$687$	−2.65278	−	2.01659i	−0.101210	−	0.0769377i
$688$	12.6765	−	1.37865i	0.483287	−	0.0525607i
$689$	1.50397	−	5.41681i	0.0572967	−	0.206364i
$690$	−0.627375	+	0.925309i	−0.0238838	+	0.0352259i
$691$	2.43277	−	1.46375i	0.0925470	−	0.0556837i	−0.468528	−	0.883449i	$-0.655215\pi$
$691$	2.43277	−	1.46375i	0.0925470	−	0.0556837i	0.561075	+	0.827765i	$0.310388\pi$
$692$	0.895787	+	16.5218i	0.0340527	+	0.628066i
$693$	0.280155	−	0.265377i	0.0106422	−	0.0100808i
$694$	6.82631	−	5.18923i	0.259123	−	0.196980i
$695$	1.26744	−	0.278984i	0.0480766	−	0.0105825i
$696$	−3.14905	−	3.70735i	−0.119364	−	0.140527i
$697$	2.80730	−	51.7776i	0.106334	−	1.96122i
$698$	−12.6486	−	23.8578i	−0.478756	−	0.903030i
$699$	11.2076	+	2.46698i	0.423911	+	0.0933098i
$700$	10.6998	−	4.95023i	0.404413	−	0.187101i
$701$	−11.0009	−	6.61900i	−0.415497	−	0.249996i	0.292423	−	0.956289i	$-0.405539\pi$
$701$	−11.0009	−	6.61900i	−0.415497	−	0.249996i	−0.707920	+	0.706293i	$0.750366\pi$
$702$	0.781929	−	1.47487i	0.0295120	−	0.0556655i
$703$	−51.4597	+	60.5830i	−1.94084	+	2.28493i
$704$	−0.100305	−	0.0950138i	−0.00378038	−	0.00358097i
$705$	−3.43809	−	0.373915i	−0.129486	−	0.0140825i
$706$	−1.46564	+	3.67847i	−0.0551599	+	0.138441i
$707$	19.6131			0.737626
$708$	7.55857	+	1.36673i	0.284069	+	0.0513648i
$709$	2.85674			0.107287			0.0536435	−	0.998560i	$-0.482917\pi$
$709$	2.85674			0.107287			0.0536435	+	0.998560i	$0.482917\pi$
$710$	2.04574	−	5.13442i	0.0767753	−	0.192691i
$711$	−3.72224	−	0.404818i	−0.139595	−	0.0151819i
$712$	7.57386	+	7.17434i	0.283842	+	0.268870i
$713$	1.52369	−	1.79382i	0.0570625	−	0.0671792i
$714$	−9.98828	+	18.8399i	−0.373802	+	0.705065i
$715$	0.174425	+	0.104948i	0.00652312	+	0.00392483i
$716$	−17.9377	+	8.29888i	−0.670365	+	0.310144i
$717$	−16.2255	−	3.57149i	−0.605951	−	0.133380i
$718$	7.63792	+	14.4066i	0.285044	+	0.537651i
$719$	−0.238039	+	4.39036i	−0.00887734	+	0.163733i	0.990733	+	0.135823i	$0.0433679\pi$
$719$	−0.238039	+	4.39036i	−0.00887734	+	0.163733i	−0.999610	+	0.0279098i	$0.991115\pi$
$720$	−0.571390	−	0.672692i	−0.0212944	−	0.0250698i
$721$	38.5193	−	8.47874i	1.43453	−	0.315765i
$722$	22.0760	−	16.7817i	0.821584	−	0.624552i
$723$	4.54503	−	4.30528i	0.169032	−	0.160115i
$724$	−0.482326	−	8.89599i	−0.0179255	−	0.330617i
$725$	−17.5930	+	10.5854i	−0.653388	+	0.393130i
$726$	6.16235	−	9.08878i	0.228706	−	0.337316i
$727$	−14.0161	+	50.4816i	−0.519830	+	1.87226i	−0.0316790	+	0.999498i	$0.510085\pi$
$727$	−14.0161	+	50.4816i	−0.519830	+	1.87226i	−0.488151	+	0.872759i	$0.662328\pi$
$728$	4.63516	−	0.504104i	0.171791	−	0.0186833i
$729$	0.796093	+	0.605174i	0.0294849	+	0.0224139i
$730$	5.78090	+	2.67453i	0.213961	+	0.0989887i
$731$	54.6324	+	80.5768i	2.02065	+	2.98024i
$732$	2.36182	−	0.795790i	0.0872954	−	0.0294132i
$733$	3.54192	+	21.6048i	0.130824	+	0.797990i	0.967980	+	0.251026i	$0.0807681\pi$
$733$	3.54192	+	21.6048i	0.130824	+	0.797990i	−0.837156	+	0.546963i	$0.815784\pi$
$734$	−1.32620	+	8.08946i	−0.0489509	+	0.298587i
$735$	0.669982	+	0.225743i	0.0247127	+	0.00832666i
$736$	−0.338860	−	1.22046i	−0.0124905	−	0.0449869i
$737$	−0.246170	−	0.617839i	−0.00906777	−	0.0227584i
$738$	−2.51393	−	6.30949i	−0.0925391	−	0.232256i
$739$	−12.4881	−	44.9780i	−0.459381	−	1.65454i	−0.723707	−	0.690108i	$-0.757563\pi$
$739$	−12.4881	−	44.9780i	−0.459381	−	1.65454i	0.264326	−	0.964434i	$-0.414851\pi$
$740$	9.72573	+	3.27698i	0.357525	+	0.120464i
$741$	1.84617	−	11.2612i	0.0678209	−	0.413689i
$742$	1.52171	+	9.28204i	0.0558639	+	0.340755i
$743$	18.8274	−	6.34368i	0.690709	−	0.232727i	0.0480114	−	0.998847i	$-0.484712\pi$
$743$	18.8274	−	6.34368i	0.690709	−	0.232727i	0.642698	+	0.766120i	$0.277815\pi$
$744$	1.04277	+	1.53797i	0.0382299	+	0.0563848i
$745$	−2.04734	−	0.947199i	−0.0750086	−	0.0347027i
$746$	7.71502	+	5.86480i	0.282467	+	0.214726i
$747$	−2.25898	+	0.245679i	−0.0826516	+	0.00898891i
$748$	0.282194	−	1.01637i	0.0103180	−	0.0371622i
$749$	18.1988	−	26.8412i	0.664968	−	0.980755i
$750$	−6.97357	+	4.19586i	−0.254639	+	0.153211i
$751$	−2.52203	−	46.5162i	−0.0920304	−	1.69740i	−0.572111	−	0.820176i	$-0.693876\pi$
$751$	−2.52203	−	46.5162i	−0.0920304	−	1.69740i	0.480081	−	0.877224i	$-0.340607\pi$
$752$	2.84469	−	2.69464i	0.103735	−	0.0982633i
$753$	−21.0774	+	16.0226i	−0.768101	+	0.583895i
$754$	−7.93021	+	1.74557i	−0.288801	+	0.0635699i
$755$	−6.52447	−	7.68121i	−0.237450	−	0.279548i
$756$	−0.151212	+	2.78893i	−0.00549951	+	0.101433i
$757$	−1.66562	−	3.14170i	−0.0605381	−	0.114187i	0.851396	−	0.524523i	$-0.175756\pi$
$757$	−1.66562	−	3.14170i	−0.0605381	−	0.114187i	−0.911934	+	0.410336i	$0.865411\pi$
$758$	−11.0090	−	2.42326i	−0.399864	−	0.0880167i
$759$	−0.158826	+	0.0734807i	−0.00576502	+	0.00266718i
$760$	−5.16984	−	3.11059i	−0.187530	−	0.112833i
$761$	−23.6677	+	44.6420i	−0.857953	+	1.61827i	−0.0741612	+	0.997246i	$0.523628\pi$
$761$	−23.6677	+	44.6420i	−0.857953	+	1.61827i	−0.783791	+	0.621024i	$0.786717\pi$
$762$	−3.77604	+	4.44550i	−0.136792	+	0.161044i
$763$	−28.8167	−	27.2967i	−1.04324	−	0.988205i
$764$	2.36307	+	0.256999i	0.0854928	+	0.00929790i
$765$	2.49415	−	6.25985i	0.0901763	−	0.226325i
$766$	−19.9527			−0.720921
$767$	7.92602	−	10.0793i	0.286192	−	0.363941i
$768$	1.00000			0.0360844
$769$	1.31776	−	3.30732i	0.0475195	−	0.119265i	−0.903301	−	0.429007i	$-0.858863\pi$
$769$	1.31776	−	3.30732i	0.0475195	−	0.119265i	0.950821	+	0.309742i	$0.100243\pi$
$770$	−0.338594	−	0.0368244i	−0.0122021	−	0.00132706i
$771$	−4.82446	−	4.56997i	−0.173749	−	0.164583i
$772$	−12.8513	+	15.1297i	−0.462528	+	0.544530i
$773$	20.9006	−	39.4228i	0.751744	−	1.41794i	−0.151343	−	0.988481i	$-0.548360\pi$
$773$	20.9006	−	39.4228i	0.751744	−	1.41794i	0.903087	−	0.429458i	$-0.141295\pi$
$774$	10.9260	+	6.57396i	0.392727	+	0.236296i
$775$	7.11835	−	3.29330i	0.255699	−	0.118299i
$776$	7.10832	+	1.56466i	0.255174	+	0.0561680i
$777$	−15.2126	−	28.6940i	−0.545750	−	1.02939i
$778$	1.99853	−	36.8607i	0.0716507	−	1.32152i
$779$	−30.0575	−	35.3864i	−1.07692	−	1.26785i
$780$	−1.43892	+	0.316731i	−0.0515217	+	0.0113408i
$781$	0.688763	−	0.523584i	0.0246459	−	0.0187353i
$782$	7.02061	−	6.65027i	0.251056	−	0.237813i
$783$	−0.263345	−	4.85712i	−0.00941120	−	0.173579i
$784$	−0.686362	+	0.412970i	−0.0245129	+	0.0147489i
$785$	−1.59128	+	2.34696i	−0.0567953	+	0.0837668i
$786$	4.46064	−	16.0658i	0.159106	−	0.573047i
$787$	25.2567	−	2.74683i	0.900304	−	0.0979139i	0.353752	−	0.935339i	$-0.384906\pi$
$787$	25.2567	−	2.74683i	0.900304	−	0.0979139i	0.546552	+	0.837425i	$0.315940\pi$
$788$	−18.5424	−	14.0956i	−0.660547	−	0.502135i
$789$	−5.66335	−	2.62014i	−0.201621	−	0.0932796i
$790$	1.85453	+	2.73523i	0.0659813	+	0.0973152i
$791$	−7.40141	+	2.49383i	−0.263164	+	0.0886702i
$792$	−0.0223521	−	0.136342i	−0.000794247	−	0.00484469i
$793$	0.673085	−	4.10564i	0.0239020	−	0.145796i
$794$	9.75589	+	3.28714i	0.346224	+	0.116656i
$795$	−0.795181	−	2.86398i	−0.0282022	−	0.101575i
$796$	−5.23717	−	13.1443i	−0.185627	−	0.465888i
$797$	0.488519	+	1.22609i	0.0173042	+	0.0434303i	0.937375	−	0.348322i	$-0.113248\pi$
$797$	0.488519	+	1.22609i	0.0173042	+	0.0434303i	−0.920071	+	0.391752i	$0.871869\pi$
$798$	5.10794	+	18.3971i	0.180819	+	0.651251i
$799$	28.3492	+	9.55197i	1.00292	+	0.337924i
$800$	0.682882	−	4.16539i	0.0241435	−	0.147269i
$801$	1.68777	+	10.2949i	0.0596344	+	0.363754i
$802$	−23.1918	+	7.81424i	−0.818932	+	0.275930i
$803$	0.559551	+	0.825276i	0.0197461	+	0.0291233i
$804$	4.36883	+	2.02124i	0.154077	+	0.0712835i
$805$	−2.48576	−	1.88963i	−0.0876116	−	0.0666006i
$806$	3.08369	−	0.335371i	0.108618	−	0.0118130i
$807$	2.91576	−	10.5016i	0.102639	−	0.369674i
$808$	3.94074	−	5.81216i	0.138635	−	0.204471i
$809$	−15.1157	+	9.09479i	−0.531438	+	0.319756i	−0.755857	−	0.654737i	$-0.772779\pi$
$809$	−15.1157	+	9.09479i	−0.531438	+	0.319756i	0.224418	+	0.974493i	$0.427952\pi$
$810$	−0.0477836	−	0.881316i	−0.00167894	−	0.0309663i
$811$	−28.6758	+	27.1632i	−1.00694	+	0.953828i	−0.998935	−	0.0461399i	$-0.985308\pi$
$811$	−28.6758	+	27.1632i	−1.00694	+	0.953828i	−0.00800905	+	0.999968i	$0.502549\pi$
$812$	10.8157	−	8.22190i	0.379558	−	0.288532i
$813$	3.44608	−	0.758539i	0.120859	−	0.0266031i
$814$	1.04005	+	1.22444i	0.0364538	+	0.0429168i
$815$	0.473797	−	8.73867i	0.0165964	−	0.306102i
$816$	3.57614	+	6.74532i	0.125190	+	0.236133i
$817$	85.1292	+	18.7384i	2.97829	+	0.655572i
$818$	−3.27494	+	1.51515i	−0.114506	+	0.0529760i
$819$	3.99509	+	2.40377i	0.139600	+	0.0839944i
$820$	−2.80791	+	5.29628i	−0.0980565	+	0.184954i
$821$	34.8535	−	41.0327i	1.21640	−	1.43205i	0.347051	−	0.937846i	$-0.387183\pi$
$821$	34.8535	−	41.0327i	1.21640	−	1.43205i	0.869345	−	0.494205i	$-0.164541\pi$
$822$	−1.59652	−	1.51231i	−0.0556851	−	0.0527478i
$823$	29.5172	+	3.21019i	1.02891	+	0.111900i	0.606969	−	0.794725i	$-0.292385\pi$
$823$	29.5172	+	3.21019i	1.02891	+	0.111900i	0.421936	+	0.906626i	$0.361351\pi$
$824$	5.22686	−	13.1184i	0.182086	−	0.457002i
$825$	−0.583181			−0.0203038
$826$	−4.95466	+	20.8737i	−0.172395	+	0.726289i
$827$	28.2456			0.982197			0.491098	−	0.871104i	$-0.336596\pi$
$827$	28.2456			0.982197			0.491098	+	0.871104i	$0.336596\pi$
$828$	0.468829	−	1.17667i	0.0162929	−	0.0408922i
$829$	45.3428	+	4.93133i	1.57482	+	0.171272i	0.853412	−	0.521238i	$-0.174529\pi$
$829$	45.3428	+	4.93133i	1.57482	+	0.171272i	0.721409	+	0.692510i	$0.243495\pi$
$830$	1.45602	+	1.37922i	0.0505393	+	0.0478733i
$831$	−9.18089	+	10.8086i	−0.318481	+	0.374945i
$832$	0.781929	−	1.47487i	0.0271085	−	0.0511321i
$833$	−5.24014	−	3.15289i	−0.181560	−	0.109241i
$834$	−1.33449	+	0.617399i	−0.0462095	+	0.0213788i
$835$	19.0097	+	4.18436i	0.657859	+	0.144806i
$836$	−0.442398	−	0.834451i	−0.0153006	−	0.0288601i
$837$	−0.100598	+	1.85543i	−0.00347719	+	0.0641330i
$838$	−6.54268	−	7.70263i	−0.226013	−	0.266083i
$839$	−32.0952	+	7.06470i	−1.10805	+	0.243900i	−0.731058	−	0.682316i	$-0.760973\pi$
$839$	−32.0952	+	7.06470i	−1.10805	+	0.243900i	−0.376993	+	0.926216i	$0.623042\pi$
$840$	1.96250	−	1.49185i	0.0677125	−	0.0514737i
$841$	3.87612	−	3.67165i	0.133659	−	0.126609i
$842$	−1.95635	−	36.0828i	−0.0674203	−	1.24349i
$843$	−23.8386	+	14.3432i	−0.821045	+	0.494006i
$844$	2.88176	−	4.25027i	0.0991942	−	0.146300i
$845$	2.41161	−	8.68582i	0.0829618	−	0.298801i
$846$	3.89537	−	0.423647i	0.133925	−	0.0145653i
$847$	24.4162	+	18.5607i	0.838950	+	0.637754i
$848$	3.05640	+	1.41404i	0.104957	+	0.0485583i
$849$	6.51435	+	9.60794i	0.223572	+	0.329744i
$850$	30.5390	−	10.2898i	1.04748	−	0.352937i
$851$	2.38278	+	14.5343i	0.0816807	+	0.498230i
$852$	−1.01309	+	6.17958i	−0.0347079	+	0.211709i
$853$	−21.4178	−	7.21650i	−0.733331	−	0.247088i	−0.0722334	−	0.997388i	$-0.523013\pi$
$853$	−21.4178	−	7.21650i	−0.733331	−	0.247088i	−0.661098	+	0.750300i	$0.729909\pi$
$854$	1.86227	+	6.70730i	0.0637256	+	0.229519i
$855$	−2.23323	−	5.60498i	−0.0763747	−	0.191686i
$856$	−4.29756	−	10.7861i	−0.146888	−	0.368660i
$857$	−2.24607	−	8.08960i	−0.0767242	−	0.276336i	0.915230	−	0.402931i	$-0.132009\pi$
$857$	−2.24607	−	8.08960i	−0.0767242	−	0.276336i	−0.991954	+	0.126596i	$0.959595\pi$
$858$	−0.218565	−	0.0736430i	−0.00746168	−	0.00251413i
$859$	0.238584	−	1.45530i	0.00814038	−	0.0496541i	−0.982444	−	0.186558i	$-0.940267\pi$
$859$	0.238584	−	1.45530i	0.00814038	−	0.0496541i	0.990584	+	0.136904i	$0.0437151\pi$
$860$	−1.82076	−	11.1061i	−0.0620873	−	0.378716i
$861$	17.9769	−	6.05712i	0.612651	−	0.206426i
$862$	−17.8559	−	26.3354i	−0.608173	−	0.896989i
$863$	−44.1052	−	20.4052i	−1.50136	−	0.694602i	−0.514694	−	0.857374i	$-0.672095\pi$
$863$	−44.1052	−	20.4052i	−1.50136	−	0.694602i	−0.986664	+	0.162772i	$0.947957\pi$
$864$	0.796093	+	0.605174i	0.0270836	+	0.0205884i
$865$	14.5181	−	1.57894i	0.493632	−	0.0536857i
$866$	1.57281	−	5.66476i	0.0534464	−	0.192497i
$867$	−23.1704	+	34.1737i	−0.786907	+	1.16060i
$868$	−4.44699	+	2.67566i	−0.150941	+	0.0908179i
$869$	0.0280063	+	0.516546i	0.000950048	+	0.0175226i
$870$	−3.11687	+	2.95246i	−0.105672	+	0.100098i
$871$	6.39718	−	4.86301i	0.216760	−	0.164777i
$872$	−13.8791	+	3.05502i	−0.470005	+	0.103456i
$873$	4.71200	+	5.54739i	0.159477	+	0.187751i
$874$	0.468770	−	8.64596i	0.0158564	−	0.292454i
$875$	−10.6475	−	20.0833i	−0.359951	−	0.678940i
$876$	−7.04806	−	1.55139i	−0.238132	−	0.0524168i
$877$	−35.8425	+	16.5825i	−1.21032	+	0.559952i	−0.918080	−	0.396395i	$-0.870261\pi$
$877$	−35.8425	+	16.5825i	−1.21032	+	0.559952i	−0.292236	+	0.956346i	$0.594399\pi$
$878$	18.6980	+	11.2502i	0.631026	+	0.379676i
$879$	3.68217	−	6.94530i	0.124196	−	0.234259i
$880$	−0.0789443	+	0.0929404i	−0.00266121	+	0.00313302i
$881$	−18.3790	−	17.4095i	−0.619205	−	0.586542i	0.312429	−	0.949941i	$-0.398857\pi$
$881$	−18.3790	−	17.4095i	−0.619205	−	0.586542i	−0.931634	+	0.363399i	$0.881616\pi$
$882$	−0.796327	−	0.0866058i	−0.0268137	−	0.00291617i
$883$	−4.16770	+	10.4601i	−0.140254	+	0.352012i	−0.982278	−	0.187428i	$-0.939985\pi$
$883$	−4.16770	+	10.4601i	−0.140254	+	0.352012i	0.842024	+	0.539440i	$0.181364\pi$
$884$	12.7448			0.428653
$885$	0.843343	−	6.72680i	0.0283487	−	0.226119i
$886$	−16.4685			−0.553269
$887$	−0.920343	+	2.30989i	−0.0309021	+	0.0775584i	−0.943618	−	0.331036i	$-0.892602\pi$
$887$	−0.920343	+	2.30989i	−0.0309021	+	0.0775584i	0.912716	+	0.408595i	$0.133981\pi$
$888$	−11.5598	−	1.25720i	−0.387921	−	0.0421890i
$889$	−11.8272	−	11.2033i	−0.396673	−	0.375748i
$890$	5.96095	−	7.01778i	0.199812	−	0.235236i
$891$	0.0647162	−	0.122068i	0.00216807	−	0.00408942i
$892$	24.7844	+	14.9123i	0.829844	+	0.499300i
$893$	24.3100	−	11.2470i	0.813502	−	0.376366i
$894$	2.49611	+	0.549435i	0.0834824	+	0.0183759i
$895$	8.17106	+	15.4123i	0.273129	+	0.515175i
$896$	−0.151212	+	2.78893i	−0.00505163	+	0.0931718i
$897$	−1.36885	−	1.61154i	−0.0457046	−	0.0538077i
$898$	−8.71797	+	1.91897i	−0.290923	+	0.0640369i
$899$	7.19551	−	5.46988i	0.239984	−	0.182431i
$900$	3.06443	−	2.90278i	0.102148	−	0.0967593i
$901$	1.39196	+	25.6732i	0.0463729	+	0.855298i
$902$	−0.804056	+	0.483784i	−0.0267721	+	0.0161083i
$903$	−19.9865	+	29.4779i	−0.665108	+	0.980961i
$904$	−0.748099	+	2.69441i	−0.0248814	+	0.0896147i
$905$	−7.81713	+	0.850164i	−0.259850	+	0.0282604i
$906$	9.09027	+	6.91024i	0.302004	+	0.229578i
$907$	−6.54716	−	3.02904i	−0.217395	−	0.100578i	0.308169	−	0.951332i	$-0.400284\pi$
$907$	−6.54716	−	3.02904i	−0.217395	−	0.100578i	−0.525564	+	0.850754i	$0.676146\pi$
$908$	2.11846	+	3.12449i	0.0703035	+	0.103690i
$909$	6.65457	−	2.24218i	0.220718	−	0.0743686i
$910$	−0.665760	−	4.06095i	−0.0220697	−	0.134619i
$911$	−0.438789	+	2.67650i	−0.0145377	+	0.0886763i	−0.993099	−	0.117280i	$-0.962582\pi$
$911$	−0.438789	+	2.67650i	−0.0145377	+	0.0886763i	0.978561	+	0.205957i	$0.0660306\pi$
$912$	6.47813	+	2.18273i	0.214512	+	0.0722776i
$913$	0.0839891	+	0.302501i	0.00277963	+	0.0100113i
$914$	9.05690	+	22.7311i	0.299576	+	0.751878i
$915$	−0.814199	−	2.04348i	−0.0269166	−	0.0675555i
$916$	−0.891471	−	3.21079i	−0.0294550	−	0.106087i
$917$	44.1319	+	14.8698i	1.45736	+	0.491043i
$918$	−1.23515	+	7.53409i	−0.0407661	+	0.248662i
$919$	1.60162	+	9.76944i	0.0528325	+	0.322264i	0.999999	+	0.00152134i	$0.000484257\pi$
$919$	1.60162	+	9.76944i	0.0528325	+	0.322264i	−0.947166	+	0.320743i	$0.896067\pi$
$920$	−1.05942	+	0.356961i	−0.0349281	+	0.0117687i
$921$	2.32969	+	3.43604i	0.0767660	+	0.113221i
$922$	−1.01544	−	0.469793i	−0.0334418	−	0.0154718i
$923$	8.32193	+	6.32617i	0.273920	+	0.208228i
$924$	0.383628	−	0.0417221i	0.0126204	−	0.00137256i
$925$	−13.1307	+	47.2926i	−0.431735	+	1.55497i
$926$	−6.79688	+	10.0247i	−0.223359	+	0.329431i
$927$	12.1000	−	7.28033i	0.397416	−	0.239117i
$928$	−0.263345	−	4.85712i	−0.00864474	−	0.159443i
$929$	28.5934	−	27.0851i	0.938119	−	0.888634i	−0.0558335	−	0.998440i	$-0.517782\pi$
$929$	28.5934	−	27.0851i	0.938119	−	0.888634i	0.993953	+	0.109806i	$0.0350230\pi$
$930$	1.30561	−	0.992501i	0.0428127	−	0.0325454i
$931$	−5.34774	+	1.17713i	−0.175265	+	0.0385788i
$932$	7.42935	+	8.74650i	0.243356	+	0.286501i
$933$	0.0959767	−	1.77019i	0.00314213	−	0.0579533i
$934$	−16.3437	−	30.8274i	−0.534782	−	1.00870i
$935$	−0.909229	−	0.200136i	−0.0297350	−	0.00654516i
$936$	1.51504	−	0.700934i	0.0495208	−	0.0229107i
$937$	−24.7667	−	14.9016i	−0.809092	−	0.486814i	0.0499305	−	0.998753i	$-0.484100\pi$
$937$	−24.7667	−	14.9016i	−0.809092	−	0.486814i	−0.859022	+	0.511938i	$0.828928\pi$
$938$	−6.29771	+	11.8787i	−0.205628	+	0.387855i
$939$	9.95016	−	11.7142i	0.324711	−	0.382280i
$940$	−2.51076	−	2.37832i	−0.0818919	−	0.0775721i
$941$	3.24912	+	0.353363i	0.105918	+	0.0115193i	0.160925	−	0.986967i	$-0.448552\pi$
$941$	3.24912	+	0.353363i	0.105918	+	0.0115193i	−0.0550064	+	0.998486i	$0.517518\pi$
$942$	1.18914	−	2.98452i	0.0387444	−	0.0972411i
$943$	−8.60281			−0.280146
$944$	5.19022	+	5.66230i	0.168927	+	0.184292i
$945$	2.46516			0.0801916
$946$	0.652086	−	1.63661i	0.0212011	−	0.0532109i
$947$	39.5365	+	4.29986i	1.28476	+	0.139727i	0.724898	−	0.688856i	$-0.241887\pi$
$947$	39.5365	+	4.29986i	1.28476	+	0.139727i	0.559866	+	0.828583i	$0.310852\pi$
$948$	−2.71827	−	2.57488i	−0.0882851	−	0.0836281i
$949$	−7.79919	+	9.18192i	−0.253172	+	0.298058i
$950$	13.5157	−	25.4934i	0.438509	−	0.827115i
$951$	−22.0014	−	13.2378i	−0.713444	−	0.429265i
$952$	−19.3530	+	8.95366i	−0.627235	+	0.290190i
$953$	−13.2823	−	2.92365i	−0.430256	−	0.0947064i	−0.00543761	−	0.999985i	$-0.501731\pi$
$953$	−13.2823	−	2.92365i	−0.430256	−	0.0947064i	−0.424818	+	0.905279i	$0.639662\pi$
$954$	1.57744	+	2.97536i	0.0510714	+	0.0963308i
$955$	0.113582	−	2.09489i	0.00367541	−	0.0677890i
$956$	−10.7556	−	12.6625i	−0.347861	−	0.409533i
$957$	−0.656342	+	0.144472i	−0.0212165	+	0.00467011i
$958$	−4.32154	+	3.28515i	−0.139623	+	0.106138i
$959$	4.45914	−	4.22392i	0.143993	−	0.136397i
$960$	−0.0477836	−	0.881316i	−0.00154221	−	0.0284444i
$961$	23.6041	−	14.2021i	0.761422	−	0.458132i
$962$	−10.8932	+	16.0662i	−0.351209	+	0.517995i
$963$	3.10619	−	11.1875i	0.100096	−	0.360512i
$964$	6.22372	−	0.676870i	0.200452	−	0.0218005i
$965$	13.9481	+	10.6031i	0.449006	+	0.341326i
$966$	3.21077	+	1.48546i	0.103305	+	0.0477939i
$967$	14.2880	+	21.0732i	0.459471	+	0.677669i	0.984891	−	0.173174i	$-0.0554023\pi$
$967$	14.2880	+	21.0732i	0.459471	+	0.677669i	−0.525421	+	0.850843i	$0.676092\pi$
$968$	10.4061	−	3.50622i	0.334465	−	0.112694i
$969$	8.44345	+	51.5028i	0.271243	+	1.65451i
$970$	1.03930	−	6.33945i	0.0333699	−	0.203547i
$971$	−21.5248	−	7.25256i	−0.690765	−	0.232746i	−0.0480427	−	0.998845i	$-0.515298\pi$
$971$	−21.5248	−	7.25256i	−0.690765	−	0.232746i	−0.642722	+	0.766100i	$0.722195\pi$
$972$	0.267528	+	0.963550i	0.00858098	+	0.0309059i
$973$	−1.52010	−	3.81515i	−0.0487321	−	0.122308i
$974$	−12.4618	−	31.2767i	−0.399301	−	1.00217i
$975$	−1.88507	−	6.78941i	−0.0603706	−	0.217435i
$976$	2.36182	+	0.795790i	0.0756000	+	0.0254726i
$977$	3.65171	−	22.2745i	0.116829	−	0.712623i	−0.861840	−	0.507180i	$-0.830688\pi$
$977$	3.65171	−	22.2745i	0.116829	−	0.712623i	0.978669	−	0.205443i	$-0.0658636\pi$
$978$	1.60415	+	9.78486i	0.0512949	+	0.312885i
$979$	1.36591	−	0.460227i	0.0436545	−	0.0147089i
$980$	0.396754	+	0.585168i	0.0126738	+	0.0186925i
$981$	−12.8979	−	5.96719i	−0.411797	−	0.190518i
$982$	−10.1363	−	7.70538i	−0.323461	−	0.245889i
$983$	37.4412	−	4.07198i	1.19419	−	0.129876i	0.510649	−	0.859789i	$-0.329405\pi$
$983$	37.4412	−	4.07198i	1.19419	−	0.129876i	0.683540	+	0.729913i	$0.260440\pi$
$984$	1.81702	−	6.54431i	0.0579244	−	0.208625i
$985$	−11.5366	+	17.0153i	−0.367588	+	0.542152i
$986$	31.8211	−	19.1461i	1.01339	−	0.609736i
$987$	0.592498	+	10.9280i	0.0188594	+	0.347842i
$988$	8.28469	−	7.84768i	0.263571	−	0.249668i
$989$	12.8578	−	9.77426i	0.408855	−	0.310803i
$990$	−0.119092	+	0.0262142i	−0.00378500	+	0.000833141i
$991$	27.0097	+	31.7982i	0.857990	+	1.01010i	0.999796	+	0.0202096i	$0.00643334\pi$
$991$	27.0097	+	31.7982i	0.857990	+	1.01010i	−0.141806	+	0.989895i	$0.545291\pi$
$992$	−0.100598	+	1.85543i	−0.00319400	+	0.0589099i
$993$	−11.5416	−	21.7698i	−0.366261	−	0.690842i
$994$	−17.0812	−	3.75987i	−0.541784	−	0.119256i
$995$	−11.3340	+	5.24368i	−0.359313	+	0.166236i
$996$	−1.94703	−	1.17149i	−0.0616941	−	0.0371201i
$997$	0.104108	−	0.196369i	0.00329715	−	0.00621908i	−0.881858	−	0.471515i	$-0.843707\pi$
$997$	0.104108	−	0.196369i	0.00329715	−	0.00621908i	0.885155	+	0.465296i	$0.154052\pi$
$998$	−18.9934	+	22.3608i	−0.601227	+	0.707819i
$999$	−8.44185	−	7.99654i	−0.267088	−	0.252999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.a.49.1	✓	56
59.53	even	29	inner	354.2.e.a.289.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.a.49.1	✓	56	1.1	even	1	trivial
354.2.e.a.289.1	yes	56	59.53	even	29	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.370138 + 0.928977i) q^{2} +(-0.994138 - 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(-0.571390 + 0.672692i) q^{5} +(0.468408 - 0.883512i) q^{6} +(2.39323 + 1.43996i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +O(q^{10})\)	\(q+(-0.370138 + 0.928977i) q^{2} +(-0.994138 - 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(-0.571390 + 0.672692i) q^{5} +(0.468408 - 0.883512i) q^{6} +(2.39323 + 1.43996i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +(-0.413422 - 0.779797i) q^{10} +(0.00747993 - 0.137959i) q^{11} +(0.647386 + 0.762162i) q^{12} +(1.63030 - 0.358857i) q^{13} +(-2.22351 + 1.69027i) q^{14} +(0.640771 - 0.606971i) q^{15} +(0.0541389 + 0.998533i) q^{16} +(-6.54182 + 3.93608i) q^{17} +(-0.561187 + 0.827689i) q^{18} +(-1.82881 + 6.58680i) q^{19} +(0.877436 - 0.0954270i) q^{20} +(-2.22351 - 1.69027i) q^{21} +(0.125392 + 0.0580127i) q^{22} +(0.710818 + 1.04838i) q^{23} +(-0.947653 + 0.319302i) q^{24} +(0.682882 + 4.16539i) q^{25} +(-0.270068 + 1.64734i) q^{26} +(-0.947653 - 0.319302i) q^{27} +(-0.747215 - 2.69123i) q^{28} +(1.80045 + 4.51878i) q^{29} +(0.326688 + 0.819925i) q^{30} +(-0.497109 - 1.79042i) q^{31} +(-0.947653 - 0.319302i) q^{32} +(-0.0223521 + 0.136342i) q^{33} +(-1.23515 - 7.53409i) q^{34} +(-2.33611 + 0.787129i) q^{35} +(-0.561187 - 0.827689i) q^{36} +(10.5533 + 4.88245i) q^{37} +(-5.44207 - 4.13695i) q^{38} +(-1.65955 + 0.180486i) q^{39} +(-0.236123 + 0.850439i) q^{40} +(-3.81151 + 5.62156i) q^{41} +(2.39323 - 1.43996i) q^{42} +(-0.690339 - 12.7326i) q^{43} +(-0.100305 + 0.0950138i) q^{44} +(-0.702640 + 0.534133i) q^{45} +(-1.23702 + 0.272289i) q^{46} +(-2.53668 - 2.98641i) q^{47} +(0.0541389 - 0.998533i) q^{48} +(0.375206 + 0.707713i) q^{49} +(-4.12231 - 0.907390i) q^{50} +(6.92904 - 3.20571i) q^{51} +(-1.43038 - 0.860630i) q^{52} +(1.57744 - 2.97536i) q^{53} +(0.647386 - 0.762162i) q^{54} +(0.0885301 + 0.0838602i) q^{55} +(2.77666 + 0.301980i) q^{56} +(2.53025 - 6.35045i) q^{57} -4.86425 q^{58} +(5.93499 - 4.87606i) q^{59} -0.882610 q^{60} +(0.922489 - 2.31527i) q^{61} +(1.84726 + 0.200902i) q^{62} +(2.02773 + 1.92077i) q^{63} +(0.647386 - 0.762162i) q^{64} +(-0.690138 + 1.30174i) q^{65} +(-0.118385 - 0.0712299i) q^{66} +(4.36883 - 2.02124i) q^{67} +(7.45617 + 1.64123i) q^{68} +(-0.593301 - 1.11909i) q^{69} +(0.133461 - 2.46154i) q^{70} +(4.05398 + 4.77271i) q^{71} +(0.976621 - 0.214970i) q^{72} +(-5.74523 + 4.36741i) q^{73} +(-8.44185 + 7.99654i) q^{74} +(-0.228520 - 4.21481i) q^{75} +(5.85745 - 3.52431i) q^{76} +(0.216557 - 0.319397i) q^{77} +(0.446593 - 1.60848i) q^{78} +(-3.72224 + 0.404818i) q^{79} +(-0.702640 - 0.534133i) q^{80} +(0.907575 + 0.419889i) q^{81} +(-3.81151 - 5.62156i) q^{82} +(-2.15335 + 0.725548i) q^{83} +(0.451862 + 2.75624i) q^{84} +(1.09016 - 6.64967i) q^{85} +(12.0838 + 4.07149i) q^{86} +(-1.30133 - 4.68695i) q^{87} +(-0.0511390 - 0.128349i) q^{88} +(3.86142 + 9.69143i) q^{89} +(-0.236123 - 0.850439i) q^{90} +(4.41843 + 1.48874i) q^{91} +(0.204918 - 1.24995i) q^{92} +(0.300616 + 1.83367i) q^{93} +(3.71322 - 1.25113i) q^{94} +(-3.38592 - 4.99386i) q^{95} +(0.907575 + 0.419889i) q^{96} +(5.79436 + 4.40476i) q^{97} +(-0.796327 + 0.0866058i) q^{98} +(0.0369622 - 0.133126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 56 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} - 18 q^{11} - 2 q^{12} + 13 q^{13} - 20 q^{14} + 4 q^{15} - 2 q^{16} + 21 q^{17} - 2 q^{18} + 20 q^{19} + 4 q^{20} - 20 q^{21} + 11 q^{22} + 34 q^{23} - 2 q^{24} - 28 q^{25} - 16 q^{26} - 2 q^{27} + 9 q^{28} + 38 q^{29} + 4 q^{30} + 34 q^{31} - 2 q^{32} + 11 q^{33} - 8 q^{34} - 19 q^{35} - 2 q^{36} - 29 q^{37} + 20 q^{38} + 13 q^{39} + 4 q^{40} + 43 q^{41} + 9 q^{42} - 65 q^{43} + 11 q^{44} + 4 q^{45} + 5 q^{46} - 60 q^{47} - 2 q^{48} - 13 q^{49} - 86 q^{50} + 21 q^{51} - 16 q^{52} - 15 q^{53} - 2 q^{54} - 15 q^{55} + 9 q^{56} + 20 q^{57} - 78 q^{58} - 2 q^{59} - 54 q^{60} + 4 q^{61} + 5 q^{62} + 9 q^{63} - 2 q^{64} - 57 q^{65} + 11 q^{66} - 56 q^{67} - 8 q^{68} - 53 q^{69} + 10 q^{70} + 23 q^{71} - 2 q^{72} - 21 q^{73} + 30 q^{75} - 9 q^{76} - 57 q^{77} + 13 q^{78} + 99 q^{79} + 4 q^{80} - 2 q^{81} + 43 q^{82} + 33 q^{83} + 9 q^{84} - 45 q^{85} - 7 q^{86} + 9 q^{87} - 18 q^{88} + 32 q^{89} + 4 q^{90} - 75 q^{91} + 34 q^{92} + 5 q^{93} + 27 q^{94} + 82 q^{95} - 2 q^{96} + 70 q^{97} + 45 q^{98} + 11 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 + 4 * q^10 - 18 * q^11 - 2 * q^12 + 13 * q^13 - 20 * q^14 + 4 * q^15 - 2 * q^16 + 21 * q^17 - 2 * q^18 + 20 * q^19 + 4 * q^20 - 20 * q^21 + 11 * q^22 + 34 * q^23 - 2 * q^24 - 28 * q^25 - 16 * q^26 - 2 * q^27 + 9 * q^28 + 38 * q^29 + 4 * q^30 + 34 * q^31 - 2 * q^32 + 11 * q^33 - 8 * q^34 - 19 * q^35 - 2 * q^36 - 29 * q^37 + 20 * q^38 + 13 * q^39 + 4 * q^40 + 43 * q^41 + 9 * q^42 - 65 * q^43 + 11 * q^44 + 4 * q^45 + 5 * q^46 - 60 * q^47 - 2 * q^48 - 13 * q^49 - 86 * q^50 + 21 * q^51 - 16 * q^52 - 15 * q^53 - 2 * q^54 - 15 * q^55 + 9 * q^56 + 20 * q^57 - 78 * q^58 - 2 * q^59 - 54 * q^60 + 4 * q^61 + 5 * q^62 + 9 * q^63 - 2 * q^64 - 57 * q^65 + 11 * q^66 - 56 * q^67 - 8 * q^68 - 53 * q^69 + 10 * q^70 + 23 * q^71 - 2 * q^72 - 21 * q^73 + 30 * q^75 - 9 * q^76 - 57 * q^77 + 13 * q^78 + 99 * q^79 + 4 * q^80 - 2 * q^81 + 43 * q^82 + 33 * q^83 + 9 * q^84 - 45 * q^85 - 7 * q^86 + 9 * q^87 - 18 * q^88 + 32 * q^89 + 4 * q^90 - 75 * q^91 + 34 * q^92 + 5 * q^93 + 27 * q^94 + 82 * q^95 - 2 * q^96 + 70 * q^97 + 45 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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