LMFDB - Embedded newform 71.2.g.a.18.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(2,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(70))

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

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

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

chi := DirichletCharacter("71.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.g (of order $35$, degree $24$, 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:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$5$ over $\Q(\zeta_{35})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			18.1
Character	$\chi$	$=$	71.18
Dual form			71.2.g.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.38426 + 0.214587i) q^{2} +(-0.366835 + 2.70808i) q^{3} +(3.67077 - 0.666146i) q^{4} +(-2.45585 - 1.78428i) q^{5} +(0.293509 - 6.53548i) q^{6} +(-2.65232 + 1.58469i) q^{7} +(-3.99386 + 1.10223i) q^{8} +(-4.30726 - 1.18873i) q^{9} +O(q^{10})$	\(q+(-2.38426 + 0.214587i) q^{2} +(-0.366835 + 2.70808i) q^{3} +(3.67077 - 0.666146i) q^{4} +(-2.45585 - 1.78428i) q^{5} +(0.293509 - 6.53548i) q^{6} +(-2.65232 + 1.58469i) q^{7} +(-3.99386 + 1.10223i) q^{8} +(-4.30726 - 1.18873i) q^{9} +(6.23825 + 3.72718i) q^{10} +(-0.701962 + 1.06343i) q^{11} +(0.457414 + 10.1851i) q^{12} +(-0.743306 - 1.12606i) q^{13} +(5.98377 - 4.34746i) q^{14} +(5.73286 - 5.99610i) q^{15} +(2.30019 - 0.863275i) q^{16} +(-0.953974 + 2.93603i) q^{17} +(10.5247 + 1.90995i) q^{18} +(4.59878 + 4.80995i) q^{19} +(-10.2034 - 4.91371i) q^{20} +(-3.31851 - 7.76404i) q^{21} +(1.44546 - 2.68611i) q^{22} +(1.06965 + 4.68645i) q^{23} +(-1.51986 - 11.2200i) q^{24} +(1.30245 + 4.00853i) q^{25} +(2.01387 + 2.52531i) q^{26} +(1.57704 - 3.68966i) q^{27} +(-8.68043 + 7.58387i) q^{28} +(2.10895 + 3.91908i) q^{29} +(-12.3819 + 15.5264i) q^{30} +(-9.59648 - 3.60162i) q^{31} +(2.16674 - 1.04345i) q^{32} +(-2.62234 - 2.29107i) q^{33} +(1.64448 - 7.20496i) q^{34} +(9.34122 + 0.840725i) q^{35} +(-16.6028 - 1.49428i) q^{36} +(0.313106 - 1.37181i) q^{37} +(-11.9968 - 10.4813i) q^{38} +(3.32214 - 1.59986i) q^{39} +(11.7750 + 4.41923i) q^{40} +(0.117921 - 0.147868i) q^{41} +(9.57823 + 17.7993i) q^{42} +(4.46310 - 3.89929i) q^{43} +(-1.86834 + 4.37120i) q^{44} +(8.45695 + 10.6047i) q^{45} +(-3.55598 - 10.9442i) q^{46} +(-0.720432 - 5.31844i) q^{47} +(1.49403 + 6.54578i) q^{48} +(1.20650 - 2.24206i) q^{49} +(-3.96555 - 9.27787i) q^{50} +(-7.60106 - 3.66048i) q^{51} +(-3.47862 - 3.63836i) q^{52} +(-0.775243 - 0.140686i) q^{53} +(-2.96831 + 9.13551i) q^{54} +(3.62136 - 1.35912i) q^{55} +(8.84631 - 9.25251i) q^{56} +(-14.7127 + 10.6894i) q^{57} +(-5.86926 - 8.89155i) q^{58} +(0.358410 + 7.98061i) q^{59} +(17.0497 - 25.8292i) q^{60} +(6.72480 + 4.01788i) q^{61} +(23.6533 + 6.52790i) q^{62} +(13.3080 - 3.67278i) q^{63} +(-9.16031 + 5.47303i) q^{64} +(-0.183758 + 4.09169i) q^{65} +(6.74397 + 4.89978i) q^{66} +(-0.494350 + 0.0897113i) q^{67} +(-1.54599 + 11.4130i) q^{68} +(-13.0837 + 1.17755i) q^{69} -22.4523 q^{70} +(7.90020 - 2.93033i) q^{71} +18.5129 q^{72} +(0.804439 - 0.0724008i) q^{73} +(-0.452152 + 3.33792i) q^{74} +(-11.3332 + 2.05668i) q^{75} +(20.0852 + 14.5927i) q^{76} +(0.176629 - 3.93294i) q^{77} +(-7.57751 + 4.52735i) q^{78} +(0.628450 - 0.173441i) q^{79} +(-7.18923 - 1.98410i) q^{80} +(-2.09399 - 1.25110i) q^{81} +(-0.249423 + 0.377859i) q^{82} +(-0.0569929 - 1.26905i) q^{83} +(-17.3535 - 26.2894i) q^{84} +(7.58150 - 5.50828i) q^{85} +(-9.80443 + 10.2546i) q^{86} +(-11.3868 + 4.27355i) q^{87} +(1.63139 - 5.02090i) q^{88} +(-9.68310 - 1.75722i) q^{89} +(-22.4392 - 23.4695i) q^{90} +(3.75594 + 1.80877i) q^{91} +(7.04831 + 16.4903i) q^{92} +(13.2738 - 24.6669i) q^{93} +(2.85896 + 12.5259i) q^{94} +(-2.71162 - 20.0180i) q^{95} +(2.03090 + 6.25048i) q^{96} +(-0.808940 - 1.01438i) q^{97} +(-2.39549 + 5.60453i) q^{98} +(4.28766 - 3.74602i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) $ 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{29}{35}\right)$

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 $

$2$	−2.38426	+	0.214587i	−1.68592	+	0.151736i	−0.890703	−	0.454585i	$-0.849788\pi$
$2$	−2.38426	+	0.214587i	−1.68592	+	0.151736i	−0.795220	+	0.606321i	$0.792645\pi$
$3$	−0.366835	+	2.70808i	−0.211792	+	1.56351i	0.503069	+	0.864246i	$0.332204\pi$
$3$	−0.366835	+	2.70808i	−0.211792	+	1.56351i	−0.714861	+	0.699267i	$0.753510\pi$
$4$	3.67077	−	0.666146i	1.83538	−	0.333073i
$5$	−2.45585	−	1.78428i	−1.09829	−	0.797953i	−0.117508	−	0.993072i	$-0.537491\pi$
$5$	−2.45585	−	1.78428i	−1.09829	−	0.797953i	−0.980779	+	0.195119i	$0.937491\pi$
$6$	0.293509	−	6.53548i	0.119825	−	2.66810i
$7$	−2.65232	+	1.58469i	−1.00248	+	0.598957i	−0.917630	−	0.397437i	$-0.869900\pi$
$7$	−2.65232	+	1.58469i	−1.00248	+	0.598957i	−0.0848549	+	0.996393i	$0.527043\pi$
$8$	−3.99386	+	1.10223i	−1.41204	+	0.389699i
$9$	−4.30726	−	1.18873i	−1.43575	−	0.396243i
$10$	6.23825	+	3.72718i	1.97271	+	1.17864i
$11$	−0.701962	+	1.06343i	−0.211649	+	0.320635i	−0.924855	−	0.380320i	$-0.875814\pi$
$11$	−0.701962	+	1.06343i	−0.211649	+	0.320635i	0.713206	+	0.700955i	$0.247243\pi$
$12$	0.457414	+	10.1851i	0.132044	+	2.94019i
$13$	−0.743306	−	1.12606i	−0.206156	−	0.312313i	0.716756	−	0.697324i	$-0.245626\pi$
$13$	−0.743306	−	1.12606i	−0.206156	−	0.312313i	−0.922912	+	0.385011i	$0.874198\pi$
$14$	5.98377	−	4.34746i	1.59923	−	1.16191i
$15$	5.73286	−	5.99610i	1.48022	−	1.54819i
$16$	2.30019	−	0.863275i	0.575047	−	0.215819i
$17$	−0.953974	+	2.93603i	−0.231373	+	0.712092i	0.766209	+	0.642591i	$0.222141\pi$
$17$	−0.953974	+	2.93603i	−0.231373	+	0.712092i	−0.997582	+	0.0695006i	$0.977859\pi$
$18$	10.5247	+	1.90995i	2.48070	+	0.450180i
$19$	4.59878	+	4.80995i	1.05503	+	1.10348i	0.994439	+	0.105315i	$0.0335851\pi$
$19$	4.59878	+	4.80995i	1.05503	+	1.10348i	0.0605938	+	0.998163i	$0.480701\pi$
$20$	−10.2034	−	4.91371i	−2.28156	−	1.09874i
$21$	−3.31851	−	7.76404i	−0.724158	−	1.69425i
$22$	1.44546	−	2.68611i	0.308173	−	0.572681i
$23$	1.06965	+	4.68645i	0.223038	+	0.977193i	0.955176	+	0.296037i	$0.0956653\pi$
$23$	1.06965	+	4.68645i	0.223038	+	0.977193i	−0.732138	+	0.681156i	$0.761478\pi$
$24$	−1.51986	−	11.2200i	−0.310240	−	2.29028i
$25$	1.30245	+	4.00853i	0.260490	+	0.801706i
$26$	2.01387	+	2.52531i	0.394952	+	0.495254i
$27$	1.57704	−	3.68966i	0.303501	−	0.710075i
$28$	−8.68043	+	7.58387i	−1.64045	+	1.43322i
$29$	2.10895	+	3.91908i	0.391622	+	0.727756i	0.997710	−	0.0676422i	$-0.0215476\pi$
$29$	2.10895	+	3.91908i	0.391622	+	0.727756i	−0.606088	+	0.795398i	$0.707262\pi$
$30$	−12.3819	+	15.5264i	−2.26062	+	2.83473i
$31$	−9.59648	−	3.60162i	−1.72358	−	0.646870i	−0.724479	−	0.689297i	$-0.757920\pi$
$31$	−9.59648	−	3.60162i	−1.72358	−	0.646870i	−0.999100	+	0.0424271i	$0.986491\pi$
$32$	2.16674	−	1.04345i	0.383029	−	0.184457i
$33$	−2.62234	−	2.29107i	−0.456492	−	0.398825i
$34$	1.64448	−	7.20496i	0.282027	−	1.23564i
$35$	9.34122	+	0.840725i	1.57895	+	0.142109i
$36$	−16.6028	−	1.49428i	−2.76714	−	0.249047i
$37$	0.313106	−	1.37181i	0.0514742	−	0.225523i	−0.942648	−	0.333789i	$-0.891673\pi$
$37$	0.313106	−	1.37181i	0.0514742	−	0.225523i	0.994122	+	0.108266i	$0.0345298\pi$
$38$	−11.9968	−	10.4813i	−1.94614	−	1.70029i
$39$	3.32214	−	1.59986i	0.531967	−	0.256182i
$40$	11.7750	+	4.41923i	1.86179	+	0.698741i
$41$	0.117921	−	0.147868i	0.0184161	−	0.0230931i	−0.772538	−	0.634968i	$-0.781013\pi$
$41$	0.117921	−	0.147868i	0.0184161	−	0.0230931i	0.790954	+	0.611875i	$0.209585\pi$
$42$	9.57823	+	17.7993i	1.47795	+	2.74650i
$43$	4.46310	−	3.89929i	0.680616	−	0.594637i	−0.246620	−	0.969112i	$-0.579320\pi$
$43$	4.46310	−	3.89929i	0.680616	−	0.594637i	0.927237	+	0.374476i	$0.122177\pi$
$44$	−1.86834	+	4.37120i	−0.281663	+	0.658984i
$45$	8.45695	+	10.6047i	1.26069	+	1.58085i
$46$	−3.55598	−	10.9442i	−0.524300	−	1.61363i
$47$	−0.720432	−	5.31844i	−0.105086	−	0.775774i	−0.964423	−	0.264365i	$-0.914838\pi$
$47$	−0.720432	−	5.31844i	−0.105086	−	0.775774i	0.859337	−	0.511410i	$-0.170877\pi$
$48$	1.49403	+	6.54578i	0.215645	+	0.944802i
$49$	1.20650	−	2.24206i	0.172357	−	0.320294i
$50$	−3.96555	−	9.27787i	−0.560814	−	1.31209i
$51$	−7.60106	−	3.66048i	−1.06436	−	0.512570i
$52$	−3.47862	−	3.63836i	−0.482398	−	0.504549i
$53$	−0.775243	−	0.140686i	−0.106488	−	0.0193247i	0.125051	−	0.992150i	$-0.460090\pi$
$53$	−0.775243	−	0.140686i	−0.106488	−	0.0193247i	−0.231539	+	0.972826i	$0.574376\pi$
$54$	−2.96831	+	9.13551i	−0.403935	+	1.24318i
$55$	3.62136	−	1.35912i	0.488304	−	0.183263i
$56$	8.84631	−	9.25251i	1.18214	−	1.23642i
$57$	−14.7127	+	10.6894i	−1.94875	+	1.41585i
$58$	−5.86926	−	8.89155i	−0.770671	−	1.16752i
$59$	0.358410	+	7.98061i	0.0466610	+	1.03899i	0.876626	+	0.481172i	$0.159789\pi$
$59$	0.358410	+	7.98061i	0.0466610	+	1.03899i	−0.829965	+	0.557815i	$0.811640\pi$
$60$	17.0497	−	25.8292i	2.20111	−	3.33454i
$61$	6.72480	+	4.01788i	0.861022	+	0.514437i	0.874250	−	0.485476i	$-0.161354\pi$
$61$	6.72480	+	4.01788i	0.861022	+	0.514437i	−0.0132278	+	0.999913i	$0.504211\pi$
$62$	23.6533	+	6.52790i	3.00397	+	0.829044i
$63$	13.3080	−	3.67278i	1.67665	−	0.462727i
$64$	−9.16031	+	5.47303i	−1.14504	+	0.684129i
$65$	−0.183758	+	4.09169i	−0.0227924	+	0.507512i
$66$	6.74397	+	4.89978i	0.830126	+	0.603122i
$67$	−0.494350	+	0.0897113i	−0.0603945	+	0.0109600i	−0.208670	−	0.977986i	$-0.566913\pi$
$67$	−0.494350	+	0.0897113i	−0.0603945	+	0.0109600i	0.148276	+	0.988946i	$0.452628\pi$
$68$	−1.54599	+	11.4130i	−0.187479	+	1.38403i
$69$	−13.0837	+	1.17755i	−1.57509	+	0.141761i
$70$	−22.4523			−2.68356
$71$	7.90020	−	2.93033i	0.937581	−	0.347766i
$71$	7.90020	−	2.93033i	0.937581	−	0.347766i
$72$	18.5129			2.18176
$73$	0.804439	−	0.0724008i	0.0941525	−	0.00847388i	−0.0424629	−	0.999098i	$-0.513520\pi$
$73$	0.804439	−	0.0724008i	0.0941525	−	0.00847388i	0.136615	+	0.990624i	$0.456378\pi$
$74$	−0.452152	+	3.33792i	−0.0525616	+	0.388026i
$75$	−11.3332	+	2.05668i	−1.30865	+	0.237485i
$76$	20.0852	+	14.5927i	2.30393	+	1.67390i
$77$	0.176629	−	3.93294i	0.0201287	−	0.448201i
$78$	−7.57751	+	4.52735i	−0.857984	+	0.512622i
$79$	0.628450	−	0.173441i	0.0707062	−	0.0195137i	−0.230505	−	0.973071i	$-0.574038\pi$
$79$	0.628450	−	0.173441i	0.0707062	−	0.0195137i	0.301211	+	0.953558i	$0.402609\pi$
$80$	−7.18923	−	1.98410i	−0.803780	−	0.221829i
$81$	−2.09399	−	1.25110i	−0.232665	−	0.139011i
$82$	−0.249423	+	0.377859i	−0.0275441	+	0.0417276i
$83$	−0.0569929	−	1.26905i	−0.00625579	−	0.139296i	−0.999690	−	0.0248923i	$-0.992076\pi$
$83$	−0.0569929	−	1.26905i	−0.00625579	−	0.139296i	0.993434	−	0.114404i	$-0.0364957\pi$
$84$	−17.3535	−	26.2894i	−1.89342	−	2.86841i
$85$	7.58150	−	5.50828i	0.822329	−	0.597457i
$86$	−9.80443	+	10.2546i	−1.05724	+	1.10579i
$87$	−11.3868	+	4.27355i	−1.22080	+	0.458173i
$88$	1.63139	−	5.02090i	0.173907	−	0.535230i
$89$	−9.68310	−	1.75722i	−1.02641	−	0.186265i	−0.360858	−	0.932621i	$-0.617516\pi$
$89$	−9.68310	−	1.75722i	−1.02641	−	0.186265i	−0.665548	+	0.746355i	$0.731802\pi$
$90$	−22.4392	−	23.4695i	−2.36530	−	2.47390i
$91$	3.75594	+	1.80877i	0.393730	+	0.189610i
$92$	7.04831	+	16.4903i	0.734837	+	1.71924i
$93$	13.2738	−	24.6669i	1.37643	−	2.55784i
$94$	2.85896	+	12.5259i	0.294879	+	1.29195i
$95$	−2.71162	−	20.0180i	−0.278206	−	2.05380i
$96$	2.03090	+	6.25048i	0.207278	+	0.637937i
$97$	−0.808940	−	1.01438i	−0.0821354	−	0.102995i	0.739066	−	0.673633i	$-0.235267\pi$
$97$	−0.808940	−	1.01438i	−0.0821354	−	0.102995i	−0.821201	+	0.570639i	$0.806696\pi$
$98$	−2.39549	+	5.60453i	−0.241981	+	0.566144i
$99$	4.28766	−	3.74602i	0.430926	−	0.376489i
$100$	7.45126	+	13.8468i	0.745126	+	1.38468i
$101$	0.784165	−	0.983312i	0.0780274	−	0.0978432i	−0.741286	−	0.671190i	$-0.765784\pi$
$101$	0.784165	−	0.983312i	0.0780274	−	0.0978432i	0.819313	+	0.573346i	$0.194355\pi$
$102$	18.9084	+	7.09643i	1.87221	+	0.702651i
$103$	−16.5041	+	7.94794i	−1.62619	+	0.783134i	−0.626201	+	0.779662i	$0.715391\pi$
$103$	−16.5041	+	7.94794i	−1.62619	+	0.783134i	−0.999994	+	0.00347215i	$0.998895\pi$
$104$	4.20984	+	3.67803i	0.412809	+	0.360660i
$105$	−5.70344	+	24.9884i	−0.556599	+	2.43862i
$106$	1.87857	+	0.169074i	0.182463	+	0.0164219i
$107$	10.5903	+	0.953143i	1.02380	+	0.0921438i	0.588794	−	0.808283i	$-0.299603\pi$
$107$	10.5903	+	0.953143i	1.02380	+	0.0921438i	0.435007	+	0.900427i	$0.356746\pi$
$108$	3.33108	−	14.5944i	0.320534	−	1.40435i
$109$	5.48892	+	4.79553i	0.525743	+	0.459328i	0.879425	−	0.476038i	$-0.157927\pi$
$109$	5.48892	+	4.79553i	0.525743	+	0.459328i	−0.353682	+	0.935366i	$0.615070\pi$
$110$	−8.34259	+	4.01758i	−0.795435	+	0.383061i
$111$	3.60011	+	1.35114i	0.341707	+	0.128245i
$112$	−4.73282	+	5.93477i	−0.447210	+	0.560783i
$113$	1.25756	+	2.33694i	0.118301	+	0.219840i	0.932859	−	0.360242i	$-0.117306\pi$
$113$	1.25756	+	2.33694i	0.118301	+	0.219840i	−0.814558	+	0.580083i	$0.803020\pi$
$114$	32.7851	−	28.6435i	3.07061	−	2.68271i
$115$	5.73503	−	13.4178i	0.534794	−	1.25121i
$116$	10.3521	+	12.9812i	0.961173	+	1.20527i
$117$	1.86303	+	5.73382i	0.172237	+	0.530092i
$118$	−2.56708	−	18.9509i	−0.236318	−	1.74457i
$119$	−2.12245	−	9.29906i	−0.194565	−	0.852443i
$120$	−16.2871	+	30.2665i	−1.48680	+	2.76294i
$121$	3.68515	+	8.62184i	0.335014	+	0.783803i
$122$	−16.8958	−	8.13660i	−1.52968	−	0.736653i
$123$	0.357181	+	0.373582i	0.0322059	+	0.0336848i
$124$	−37.6257	−	6.82805i	−3.37888	−	0.613177i
$125$	−0.736540	+	2.26684i	−0.0658781	+	0.202752i
$126$	−30.9416	+	11.6126i	−2.75650	+	1.03453i
$127$	−7.12909	+	7.45644i	−0.632604	+	0.661652i	−0.958942	−	0.283601i	$-0.908471\pi$
$127$	−7.12909	+	7.45644i	−0.632604	+	0.661652i	0.326338	+	0.945253i	$0.394185\pi$
$128$	16.7749	−	12.1877i	1.48270	−	1.07725i
$129$	8.92239	+	13.5168i	0.785573	+	1.19009i
$130$	−0.439897	−	9.79507i	−0.0385815	−	0.859085i
$131$	−1.39246	+	2.10949i	−0.121660	+	0.184307i	−0.890300	−	0.455375i	$-0.849505\pi$
$131$	−1.39246	+	2.10949i	−0.121660	+	0.184307i	0.768640	+	0.639682i	$0.220934\pi$
$132$	−11.1522	−	6.66314i	−0.970675	−	0.579952i
$133$	−19.8197	−	5.46990i	−1.71859	−	0.474300i
$134$	1.15941	−	0.319976i	0.100157	−	0.0276417i
$135$	−10.4563	+	6.24737i	−0.899938	+	0.537688i
$136$	0.573842	−	12.7776i	0.0492066	−	1.09567i
$137$	−5.62075	−	4.08371i	−0.480213	−	0.348895i	0.321195	−	0.947013i	$-0.395915\pi$
$137$	−5.62075	−	4.08371i	−0.480213	−	0.348895i	−0.801408	+	0.598118i	$0.795915\pi$
$138$	30.9422	−	5.61518i	2.63397	−	0.477996i
$139$	−2.21258	+	16.3339i	−0.187668	+	1.38542i	0.614778	+	0.788700i	$0.289245\pi$
$139$	−2.21258	+	16.3339i	−0.187668	+	1.38542i	−0.802447	+	0.596724i	$0.796469\pi$
$140$	34.8495	−	3.13651i	2.94532	−	0.265084i
$141$	14.6671			1.23519
$142$	−18.2073	+	8.68193i	−1.52792	+	0.728572i
$143$	1.71925			0.143771
$144$	−10.9337	+	0.984052i	−0.911143	+	0.0820043i
$145$	1.81348	−	13.3876i	0.150601	−	1.11178i
$146$	−1.90245	+	0.345244i	−0.157448	+	0.0285726i
$147$	5.62909	+	4.08977i	0.464279	+	0.337319i
$148$	0.235515	−	5.24415i	0.0193592	−	0.431067i
$149$	3.98355	−	2.38006i	0.326345	−	0.194982i	−0.340376	−	0.940289i	$-0.610554\pi$
$149$	3.98355	−	2.38006i	0.326345	−	0.194982i	0.666721	+	0.745307i	$0.267697\pi$
$150$	26.5800	−	7.33560i	2.17024	−	0.598949i
$151$	−10.3716	−	2.86239i	−0.844032	−	0.232938i	−0.182828	−	0.983145i	$-0.558525\pi$
$151$	−10.3716	−	2.86239i	−0.844032	−	0.232938i	−0.661203	+	0.750207i	$0.729954\pi$
$152$	−23.6686	−	14.1413i	−1.91977	−	1.14701i
$153$	7.59916	−	11.5122i	0.614356	−	0.930709i
$154$	0.422830	+	9.41505i	0.0340726	+	0.758686i
$155$	17.1412	+	25.9678i	1.37681	+	2.08578i
$156$	11.1291	−	8.08573i	0.891037	−	0.647376i
$157$	13.3588	−	13.9722i	1.06615	−	1.11510i	0.0731093	−	0.997324i	$-0.476708\pi$
$157$	13.3588	−	13.9722i	1.06615	−	1.11510i	0.993040	−	0.117780i	$-0.0375779\pi$
$158$	−1.46117	+	0.548385i	−0.116244	+	0.0436272i
$159$	0.665376	−	2.04782i	0.0527677	−	0.162402i
$160$	−7.18297	−	1.30352i	−0.567864	−	0.103052i
$161$	−10.2636	−	10.7349i	−0.808888	−	0.846031i
$162$	5.26107	+	2.53360i	0.413349	+	0.199058i
$163$	9.64580	+	22.5675i	0.755518	+	1.76762i	0.631550	+	0.775335i	$0.282419\pi$
$163$	9.64580	+	22.5675i	0.755518	+	1.76762i	0.123968	+	0.992286i	$0.460438\pi$
$164$	0.334358	−	0.621341i	0.0261090	−	0.0485186i
$165$	2.35217	+	10.3055i	0.183116	+	0.802283i
$166$	0.408206	+	3.01350i	0.0316830	+	0.233893i
$167$	6.26410	+	19.2789i	0.484731	+	1.49185i	0.832370	+	0.554220i	$0.186983\pi$
$167$	6.26410	+	19.2789i	0.484731	+	1.49185i	−0.347640	+	0.937628i	$0.613017\pi$
$168$	21.8114	+	27.3507i	1.68279	+	2.11015i
$169$	4.39382	−	10.2798i	0.337986	−	0.790758i
$170$	−16.8942	+	14.7600i	−1.29573	+	1.13204i
$171$	−14.0904	−	26.1844i	−1.07752	−	2.00237i
$172$	13.7855	−	17.2865i	1.05114	−	1.31808i
$173$	−18.9340	−	7.10605i	−1.43953	−	0.540263i	−0.495056	−	0.868861i	$-0.664852\pi$
$173$	−18.9340	−	7.10605i	−1.43953	−	0.540263i	−0.944470	+	0.328598i	$0.893424\pi$
$174$	26.2321	−	12.6327i	1.98865	−	0.957684i
$175$	−9.80680	−	8.56794i	−0.741324	−	0.647676i
$176$	−0.696614	+	3.05207i	−0.0525093	+	0.230058i
$177$	−21.7436	−	1.95696i	−1.63435	−	0.147094i
$178$	23.4641	+	2.11180i	1.75871	+	0.158286i
$179$	2.75932	−	12.0894i	0.206242	−	0.903604i	−0.760800	−	0.648986i	$-0.775193\pi$
$179$	2.75932	−	12.0894i	0.206242	−	0.903604i	0.967042	−	0.254617i	$-0.0819495\pi$
$180$	38.1078	+	33.2938i	2.84039	+	2.48157i
$181$	19.5553	−	9.41733i	1.45353	−	0.699985i	0.470329	−	0.882491i	$-0.344135\pi$
$181$	19.5553	−	9.41733i	1.45353	−	0.699985i	0.983205	+	0.182506i	$0.0584210\pi$
$182$	−9.34327	−	3.50659i	−0.692569	−	0.259926i
$183$	−13.3477	+	16.7374i	−0.986687	+	1.23727i
$184$	−9.43761	−	17.5380i	−0.695750	−	1.29292i
$185$	−3.21662	+	2.81027i	−0.236490	+	0.206616i
$186$	−26.3550	+	61.6605i	−1.93244	+	4.52117i
$187$	−2.45260	−	3.07546i	−0.179352	−	0.224900i
$188$	−6.18740	−	19.0429i	−0.451262	−	1.38884i
$189$	1.66416	+	12.2853i	0.121050	+	0.893623i
$190$	10.7608	+	47.1461i	0.780670	+	3.42034i
$191$	5.18106	−	9.62802i	0.374888	−	0.696659i	−0.621330	−	0.783549i	$-0.713407\pi$
$191$	5.18106	−	9.62802i	0.374888	−	0.696659i	0.996218	+	0.0868900i	$0.0276929\pi$
$192$	−11.4611	−	26.8146i	−0.827134	−	1.93518i
$193$	−7.89503	−	3.80204i	−0.568297	−	0.273677i	0.127592	−	0.991827i	$-0.459275\pi$
$193$	−7.89503	−	3.80204i	−0.568297	−	0.273677i	−0.695889	+	0.718150i	$0.744989\pi$
$194$	2.14639	+	2.24495i	0.154102	+	0.161178i
$195$	−11.0132	−	1.99861i	−0.788674	−	0.143123i
$196$	2.93525	−	9.03378i	0.209661	−	0.645270i
$197$	−2.53008	+	0.949553i	−0.180260	+	0.0676529i	−0.439873	−	0.898060i	$-0.644977\pi$
$197$	−2.53008	+	0.949553i	−0.180260	+	0.0676529i	0.259613	+	0.965713i	$0.416405\pi$
$198$	−9.41903	+	9.85154i	−0.669381	+	0.700118i
$199$	−1.69934	+	1.23464i	−0.120463	+	0.0875216i	−0.646386	−	0.763011i	$-0.723720\pi$
$199$	−1.69934	+	1.23464i	−0.120463	+	0.0875216i	0.525922	+	0.850533i	$0.323720\pi$
$200$	−9.62014	−	14.5739i	−0.680247	−	1.03053i
$201$	−0.0616009	−	1.37165i	−0.00434499	−	0.0967488i
$202$	−1.65864	+	2.51274i	−0.116702	+	0.176796i
$203$	−11.8042	−	7.05265i	−0.828489	−	0.494999i
$204$	−30.3402	−	8.37335i	−2.12424	−	0.586252i
$205$	−0.553432	+	0.152738i	−0.0386534	+	0.0106677i
$206$	37.6444	−	22.4915i	2.62281	−	1.56706i
$207$	0.963649	−	21.4573i	0.0669783	−	1.49139i
$208$	−2.68184	−	1.94847i	−0.185952	−	0.135102i
$209$	−8.34319	+	1.51407i	−0.577111	+	0.104730i
$210$	8.23628	−	60.8026i	0.568357	−	4.19578i
$211$	11.9009	−	1.07110i	0.819291	−	0.0737375i	0.327939	−	0.944699i	$-0.393646\pi$
$211$	11.9009	−	1.07110i	0.819291	−	0.0737375i	0.491351	+	0.870961i	$0.336503\pi$
$212$	−2.93946			−0.201883
$213$	5.03751	+	22.4694i	0.345164	+	1.53957i
$214$	−25.4545			−1.74003
$215$	−17.9181	+	1.61266i	−1.22200	+	0.109982i
$216$	−2.23159	+	16.4742i	−0.151840	+	1.12093i
$217$	31.1604	−	5.65478i	2.11531	−	0.383872i
$218$	−14.1160	−	10.2559i	−0.956059	−	0.694618i
$219$	−0.0990288	+	2.20505i	−0.00669175	+	0.149003i
$220$	12.3878	−	7.40136i	0.835185	−	0.499000i
$221$	4.01524	−	1.10814i	0.270094	−	0.0745413i
$222$	−8.87351	−	2.44893i	−0.595551	−	0.164362i
$223$	12.5472	+	7.49658i	0.840220	+	0.502008i	0.867394	−	0.497623i	$-0.165794\pi$
$223$	12.5472	+	7.49658i	0.840220	+	0.502008i	−0.0271736	+	0.999631i	$0.508651\pi$
$224$	−4.09335	+	6.20117i	−0.273499	+	0.414333i
$225$	−0.844940	−	18.8141i	−0.0563293	−	1.25427i
$226$	−3.49982	−	5.30200i	−0.232804	−	0.352684i
$227$	−22.4787	+	16.3317i	−1.49196	+	1.08397i	−0.518515	+	0.855068i	$0.673515\pi$
$227$	−22.4787	+	16.3317i	−1.49196	+	1.08397i	−0.973448	+	0.228906i	$0.926485\pi$
$228$	−46.8863	+	49.0393i	−3.10512	+	3.24770i
$229$	−13.1221	+	4.92481i	−0.867134	+	0.325441i	−0.744993	−	0.667072i	$-0.767547\pi$
$229$	−13.1221	+	4.92481i	−0.867134	+	0.325441i	−0.122141	+	0.992513i	$0.538976\pi$
$230$	−10.7945	+	33.2220i	−0.711768	+	2.19060i
$231$	10.5860	+	1.92107i	0.696504	+	0.126397i
$232$	−12.7426	−	13.3277i	−0.836592	−	0.875007i
$233$	5.83138	+	2.80824i	0.382026	+	0.183974i	0.615034	−	0.788501i	$-0.289142\pi$
$233$	5.83138	+	2.80824i	0.382026	+	0.183974i	−0.233007	+	0.972475i	$0.574857\pi$
$234$	−5.67235	−	13.2711i	−0.370813	−	0.867560i
$235$	−7.72030	+	14.3467i	−0.503617	+	0.935877i
$236$	6.63189	+	29.0562i	0.431700	+	1.89140i
$237$	0.239156	+	1.76552i	0.0155349	+	0.114683i
$238$	7.05592	+	21.7159i	0.457367	+	1.40763i
$239$	10.9346	+	13.7115i	0.707300	+	0.886926i	0.997545	−	0.0700266i	$-0.0223084\pi$
$239$	10.9346	+	13.7115i	0.707300	+	0.886926i	−0.290246	+	0.956952i	$0.593737\pi$
$240$	8.01037	−	18.7412i	0.517067	−	1.20974i
$241$	−10.4428	+	9.12356i	−0.672677	+	0.587700i	−0.925011	−	0.379940i	$-0.875945\pi$
$241$	−10.4428	+	9.12356i	−0.672677	+	0.587700i	0.252334	+	0.967640i	$0.418802\pi$
$242$	−10.6365	−	19.7659i	−0.683738	−	1.27060i
$243$	11.6616	−	14.6232i	0.748092	−	0.938078i
$244$	27.3617	+	10.2690i	1.75165	+	0.657406i
$245$	−6.96343	+	3.35341i	−0.444877	+	0.214242i
$246$	−0.931777	−	0.814069i	−0.0594079	−	0.0519032i
$247$	1.99799	−	8.75376i	0.127129	−	0.556989i
$248$	42.2968	+	3.80678i	2.68585	+	0.241731i
$249$	3.45759	+	0.311189i	0.219116	+	0.0197208i
$250$	1.26967	−	5.56277i	0.0803007	−	0.351820i
$251$	−22.0111	−	19.2305i	−1.38933	−	1.21382i	−0.948719	−	0.316120i	$-0.897620\pi$
$251$	−22.0111	−	19.2305i	−1.38933	−	1.21382i	−0.440608	−	0.897699i	$-0.645237\pi$
$252$	46.4041	−	22.3470i	2.92318	−	1.40773i
$253$	−5.73456	−	2.15221i	−0.360528	−	0.135309i
$254$	15.3975	−	19.3079i	0.966126	−	1.21148i
$255$	12.1357	+	22.5520i	0.759969	+	1.41226i
$256$	−21.3086	+	18.6167i	−1.33179	+	1.16355i
$257$	5.26779	−	12.3246i	0.328596	−	0.768788i	−0.671030	−	0.741430i	$-0.734148\pi$
$257$	5.26779	−	12.3246i	0.328596	−	0.768788i	0.999626	−	0.0273577i	$-0.00870931\pi$
$258$	−24.1738	−	30.3130i	−1.50500	−	1.88720i
$259$	1.34343	+	4.13465i	0.0834766	+	0.256915i
$260$	2.05113	+	15.1421i	0.127206	+	0.939071i
$261$	−4.42507	−	19.3875i	−0.273905	−	1.20006i
$262$	2.86731	−	5.32836i	0.177143	−	0.329187i
$263$	3.84662	+	8.99961i	0.237193	+	0.554940i	0.995261	−	0.0972348i	$-0.0309998\pi$
$263$	3.84662	+	8.99961i	0.237193	+	0.554940i	−0.758069	+	0.652175i	$0.773857\pi$
$264$	12.9986	+	6.25978i	0.800007	+	0.385263i
$265$	1.65286	+	1.72875i	0.101534	+	0.106196i
$266$	48.4291	+	8.78858i	2.96938	+	0.538863i
$267$	8.31080	−	25.5780i	0.508613	−	1.56535i
$268$	−1.75488	+	0.658619i	−0.107197	+	0.0402316i
$269$	−21.2588	+	22.2349i	−1.29617	+	1.35569i	−0.397164	+	0.917748i	$0.630006\pi$
$269$	−21.2588	+	22.2349i	−1.29617	+	1.35569i	−0.899005	+	0.437939i	$0.855709\pi$
$270$	23.5900	−	17.1391i	1.43564	−	1.04305i
$271$	10.1019	+	15.3037i	0.613645	+	0.929633i	0.999974	+	0.00727154i	$0.00231462\pi$
$271$	10.1019	+	15.3037i	0.613645	+	0.929633i	−0.386328	+	0.922361i	$0.626257\pi$
$272$	0.340282	+	7.57696i	0.0206326	+	0.459421i
$273$	−6.27610	+	9.50789i	−0.379847	+	0.575444i
$274$	14.2776	+	8.53048i	0.862543	+	0.515345i
$275$	−5.17705	−	1.42877i	−0.312188	−	0.0861583i
$276$	−47.2428	+	13.0382i	−2.84368	+	0.784807i
$277$	24.9371	−	14.8992i	1.49832	−	0.895207i	0.498728	−	0.866758i	$-0.333801\pi$
$277$	24.9371	−	14.8992i	1.49832	−	0.895207i	0.999595	−	0.0284483i	$-0.00905661\pi$
$278$	1.77031	−	39.4190i	0.106176	−	2.36419i
$279$	37.0532	+	26.9207i	2.21832	+	1.61170i
$280$	−38.2342	+	6.93848i	−2.28493	+	0.414654i
$281$	3.09251	−	22.8298i	0.184484	−	1.36191i	−0.627674	−	0.778476i	$-0.715993\pi$
$281$	3.09251	−	22.8298i	0.184484	−	1.36191i	0.812158	−	0.583438i	$-0.198293\pi$
$282$	−34.9700	+	3.14736i	−2.08244	+	0.187423i
$283$	1.53653			0.0913370			0.0456685	−	0.998957i	$-0.485458\pi$
$283$	1.53653			0.0913370			0.0456685	+	0.998957i	$0.485458\pi$
$284$	27.0478	−	16.0193i	1.60499	−	0.950568i
$285$	55.2051			3.27007
$286$	−4.09914	+	0.368929i	−0.242387	+	0.0218153i
$287$	−0.0784392	+	0.579061i	−0.00463012	+	0.0341809i
$288$	−10.5731	+	1.91873i	−0.623025	+	0.113062i
$289$	6.04309	+	4.39056i	0.355476	+	0.258268i
$290$	−1.45098	+	32.3086i	−0.0852046	+	1.89723i
$291$	3.04377	−	1.81857i	0.178429	−	0.106606i
$292$	2.90468	−	0.801641i	0.169984	−	0.0469125i
$293$	12.3801	+	3.41670i	0.723254	+	0.199606i	0.608234	−	0.793758i	$-0.291878\pi$
$293$	12.3801	+	3.41670i	0.723254	+	0.199606i	0.115020	+	0.993363i	$0.463307\pi$
$294$	−14.2988	−	8.54314i	−0.833923	−	0.498246i
$295$	13.3594	−	20.2387i	0.777815	−	1.17834i
$296$	0.261552	+	5.82391i	0.0152024	+	0.338508i
$297$	2.81666	+	4.26706i	0.163439	+	0.247600i
$298$	−8.98707	+	6.52949i	−0.520607	+	0.378243i
$299$	4.48215	−	4.68796i	0.259209	−	0.271112i
$300$	−40.2316	+	15.0992i	−2.32277	+	0.871751i
$301$	−5.65842	+	17.4148i	−0.326146	+	1.00377i
$302$	25.3429	+	4.59905i	1.45832	+	0.264646i
$303$	2.37523	+	2.48430i	0.136454	+	0.142719i
$304$	14.7304	+	7.09377i	0.844845	+	0.406856i
$305$	−9.34606	−	21.8662i	−0.535154	−	1.25205i
$306$	−15.6480	+	29.0788i	−0.894535	+	1.66232i
$307$	−5.22054	−	22.8727i	−0.297952	−	1.30541i	−0.873171	−	0.487414i	$-0.837940\pi$
$307$	−5.22054	−	22.8727i	−0.297952	−	1.30541i	0.575219	−	0.817999i	$-0.304917\pi$
$308$	−1.97155	−	14.5546i	−0.112340	−	0.829325i
$309$	−15.4694	−	47.6100i	−0.880025	−	2.70844i
$310$	−46.4413	−	58.2356i	−2.63769	−	3.30756i
$311$	−1.47602	+	3.45331i	−0.0836972	+	0.195819i	−0.956149	−	0.292881i	$-0.905386\pi$
$311$	−1.47602	+	3.45331i	−0.0836972	+	0.195819i	0.872452	+	0.488700i	$0.162529\pi$
$312$	−11.5047	+	10.0514i	−0.651326	+	0.569047i
$313$	6.43731	+	11.9625i	0.363858	+	0.676162i	0.995040	−	0.0994729i	$-0.0317157\pi$
$313$	6.43731	+	11.9625i	0.363858	+	0.676162i	−0.631182	+	0.775635i	$0.717430\pi$
$314$	−28.8526	+	36.1800i	−1.62824	+	2.04175i
$315$	−39.2357	−	14.7254i	−2.21068	−	0.829683i
$316$	2.19136	−	1.05530i	0.123274	−	0.0593654i
$317$	18.4867	+	16.1513i	1.03831	+	0.907147i	0.995764	−	0.0919470i	$-0.0293090\pi$
$317$	18.4867	+	16.1513i	1.03831	+	0.907147i	0.0425498	+	0.999094i	$0.486452\pi$
$318$	−1.14699	+	5.02530i	−0.0643201	+	0.281805i
$319$	−5.64806	−	0.508335i	−0.316231	−	0.0284613i
$320$	32.2617	+	2.90360i	1.80348	+	0.162316i
$321$	−6.46608	+	28.3297i	−0.360901	+	1.58121i
$322$	26.7747	+	23.3924i	1.49210	+	1.30361i
$323$	−18.5093	+	8.91359i	−1.02988	+	0.495965i
$324$	−8.51997	−	3.19760i	−0.473331	−	0.177644i
$325$	3.54573	−	4.44620i	0.196681	−	0.246631i
$326$	−27.8407	−	51.7368i	−1.54196	−	2.86544i
$327$	−15.0002	+	13.1053i	−0.829514	+	0.724724i
$328$	−0.307973	+	0.720540i	−0.0170050	+	0.0397851i
$329$	10.3389	+	12.9646i	0.570002	+	0.714760i
$330$	−7.81959	−	24.0662i	−0.430454	−	1.32480i
$331$	1.64834	+	12.1685i	0.0906009	+	0.668842i	0.978115	+	0.208063i	$0.0667159\pi$
$331$	1.64834	+	12.1685i	0.0906009	+	0.668842i	−0.887515	+	0.460780i	$0.847570\pi$
$332$	−1.05458	−	4.62041i	−0.0578775	−	0.253578i
$333$	−2.97933	+	5.53653i	−0.163266	+	0.303400i
$334$	−19.0722	−	44.6217i	−1.04359	−	2.44159i
$335$	1.37412	+	0.661740i	0.0750761	+	0.0361547i
$336$	−14.3357	−	14.9940i	−0.782076	−	0.817988i
$337$	−23.2364	−	4.21678i	−1.26577	−	0.229703i	−0.496166	−	0.868228i	$-0.665259\pi$
$337$	−23.2364	−	4.21678i	−1.26577	−	0.229703i	−0.769601	+	0.638525i	$0.779545\pi$
$338$	−8.27006	+	25.4526i	−0.449832	+	1.38444i
$339$	−6.78994	+	2.54831i	−0.368779	+	0.138405i
$340$	24.1606	−	25.2700i	1.31029	−	1.37046i
$341$	10.5664	−	7.67695i	0.572204	−	0.415730i
$342$	39.2140	+	59.4067i	2.12045	+	3.21235i
$343$	−0.617393	−	13.7473i	−0.0333361	−	0.742286i
$344$	−13.5271	+	20.4926i	−0.729330	+	1.10489i
$345$	34.2326	+	20.4530i	1.84302	+	1.10115i
$346$	46.6684	+	12.8797i	2.50891	+	0.692414i
$347$	7.18819	−	1.98381i	0.385882	−	0.106497i	−0.0677123	−	0.997705i	$-0.521570\pi$
$347$	7.18819	−	1.98381i	0.385882	−	0.106497i	0.453595	+	0.891208i	$0.350141\pi$
$348$	−38.9517	+	23.2725i	−2.08803	+	1.24754i
$349$	−0.0514026	+	1.14457i	−0.00275152	+	0.0612673i	−0.999899	−	0.0142101i	$-0.995477\pi$
$349$	−0.0514026	+	1.14457i	−0.00275152	+	0.0612673i	0.997148	+	0.0754774i	$0.0240481\pi$
$350$	25.2205	+	18.3238i	1.34809	+	0.979446i
$351$	−5.32700	+	0.966708i	−0.284334	+	0.0515990i
$352$	−0.411339	+	3.03663i	−0.0219244	+	0.161853i
$353$	27.9697	−	2.51732i	1.48868	−	0.133984i	0.684780	−	0.728749i	$-0.259898\pi$
$353$	27.9697	−	2.51732i	1.48868	−	0.133984i	0.803899	+	0.594766i	$0.202755\pi$
$354$	52.2624			2.77771
$355$	−24.6302	−	6.89970i	−1.30723	−	0.366198i
$356$	−36.7150			−1.94589
$357$	25.9612	−	2.33655i	1.37401	−	0.123663i
$358$	−3.98471	+	29.4163i	−0.210599	+	1.55470i
$359$	4.76110	−	0.864013i	0.251281	−	0.0456009i	−0.0514545	−	0.998675i	$-0.516386\pi$
$359$	4.76110	−	0.864013i	0.251281	−	0.0456009i	0.302736	+	0.953074i	$0.402100\pi$
$360$	−45.4647	−	33.0320i	−2.39620	−	1.74094i
$361$	−1.13438	+	25.2589i	−0.0597042	+	1.32942i
$362$	−44.6040	+	26.6496i	−2.34433	+	1.40067i
$363$	−24.7005	+	6.81690i	−1.29644	+	0.357795i
$364$	14.9921	+	4.13756i	0.785800	+	0.216867i
$365$	−2.10476	−	1.25754i	−0.110168	−	0.0658225i
$366$	28.2326	−	42.7705i	1.47574	−	2.23565i
$367$	−0.413465	−	9.20651i	−0.0215827	−	0.480576i	−0.980456	−	0.196740i	$-0.936964\pi$
$367$	−0.413465	−	9.20651i	−0.0215827	−	0.480576i	0.958873	−	0.283836i	$-0.0916070\pi$
$368$	6.50610	+	9.85632i	0.339154	+	0.513796i
$369$	−0.683690	+	0.496730i	−0.0355915	+	0.0258587i
$370$	7.06619	−	7.39066i	0.367354	−	0.384222i
$371$	2.27914	−	0.855376i	0.118327	−	0.0444089i
$372$	32.2933	−	99.3887i	1.67433	−	5.15306i
$373$	−6.34544	−	1.15153i	−0.328554	−	0.0596238i	0.0117734	−	0.999931i	$-0.496252\pi$
$373$	−6.34544	−	1.15153i	−0.328554	−	0.0596238i	−0.340328	+	0.940307i	$0.610538\pi$
$374$	6.50758	+	6.80639i	0.336499	+	0.351950i
$375$	−5.86860	−	2.82617i	−0.303053	−	0.145943i
$376$	8.73947	+	20.4470i	0.450704	+	1.05447i
$377$	2.84553	−	5.28788i	0.146552	−	0.272340i
$378$	−6.60404	−	28.9342i	−0.339675	−	1.48821i
$379$	−0.472096	−	3.48515i	−0.0242499	−	0.179020i	0.974774	−	0.223195i	$-0.0716485\pi$
$379$	−0.472096	−	3.48515i	−0.0242499	−	0.179020i	−0.999024	+	0.0441744i	$0.985934\pi$
$380$	−23.2886	−	71.6751i	−1.19468	−	3.67685i
$381$	−17.5775	−	22.0414i	−0.900521	−	1.12922i
$382$	−10.2869	+	24.0675i	−0.526325	+	1.23140i
$383$	−13.5658	+	11.8521i	−0.693179	+	0.605612i	−0.930706	−	0.365769i	$-0.880806\pi$
$383$	−13.5658	+	11.8521i	−0.693179	+	0.605612i	0.237527	+	0.971381i	$0.423663\pi$
$384$	26.8516	+	49.8986i	1.37026	+	2.54638i
$385$	−7.45123	+	9.34355i	−0.379750	+	0.476191i
$386$	19.6396	+	7.37088i	0.999631	+	0.375168i
$387$	−23.8589	+	11.4899i	−1.21282	+	0.584063i
$388$	−3.64516	−	3.18468i	−0.185055	−	0.161677i
$389$	0.545922	−	2.39184i	0.0276793	−	0.121271i	−0.959201	−	0.282726i	$-0.908761\pi$
$389$	0.545922	−	2.39184i	0.0276793	−	0.121271i	0.986880	+	0.161455i	$0.0516185\pi$
$390$	26.6872	+	2.40190i	1.35136	+	0.121625i
$391$	−14.7800	−	1.33022i	−0.747456	−	0.0672723i
$392$	−2.34732	+	10.2843i	−0.118558	+	0.519436i
$393$	−5.20186	−	4.54473i	−0.262399	−	0.229251i
$394$	5.82858	−	2.80690i	0.293640	−	0.141410i
$395$	−1.85284	−	0.695384i	−0.0932267	−	0.0349886i
$396$	13.2436	−	16.6070i	0.665517	−	0.834531i
$397$	−0.214338	−	0.398307i	−0.0107573	−	0.0199905i	0.875160	−	0.483833i	$-0.160756\pi$
$397$	−0.214338	−	0.398307i	−0.0107573	−	0.0199905i	−0.885917	+	0.463843i	$0.846470\pi$
$398$	3.78673	−	3.30837i	0.189812	−	0.165833i
$399$	22.0835	−	51.6670i	1.10556	−	2.58658i
$400$	6.45634	+	8.09600i	0.322817	+	0.404800i
$401$	−2.77619	−	8.54423i	−0.138636	−	0.426679i	0.857502	−	0.514481i	$-0.172016\pi$
$401$	−2.77619	−	8.54423i	−0.138636	−	0.426679i	−0.996138	+	0.0878026i	$0.972016\pi$
$402$	0.441211	+	3.25715i	0.0220056	+	0.162452i
$403$	3.07748	+	13.4833i	0.153300	+	0.671652i
$404$	2.22346	−	4.13188i	0.110621	−	0.205569i
$405$	2.91020	+	6.80876i	0.144609	+	0.338330i
$406$	29.6575	+	14.2823i	1.47188	+	0.708819i
$407$	1.23903	+	1.29592i	0.0614162	+	0.0642364i
$408$	34.3923	+	6.24128i	1.70267	+	0.308989i
$409$	−2.28012	+	7.01749i	−0.112745	+	0.346993i	−0.991470	−	0.130335i	$-0.958395\pi$
$409$	−2.28012	+	7.01749i	−0.112745	+	0.346993i	0.878725	+	0.477328i	$0.158395\pi$
$410$	1.28675	−	0.482925i	0.0635480	−	0.0238499i
$411$	13.1209	−	13.7234i	0.647208	−	0.676926i
$412$	−55.2881	+	40.1692i	−2.72385	+	1.97899i
$413$	−13.5974	−	20.5992i	−0.669085	−	1.01362i
$414$	2.30687	+	51.3665i	0.113377	+	2.52453i
$415$	−2.12436	+	3.21827i	−0.104281	+	0.157979i
$416$	−2.78553	−	1.66428i	−0.136572	−	0.0815979i
$417$	−43.4219	−	11.9837i	−2.12638	−	0.586844i
$418$	19.5674	−	5.40026i	0.957073	−	0.264135i
$419$	−9.00848	+	5.38232i	−0.440093	+	0.262943i	−0.715809	−	0.698296i	$-0.753942\pi$
$419$	−9.00848	+	5.38232i	−0.440093	+	0.262943i	0.275716	+	0.961239i	$0.411085\pi$
$420$	−4.29008	+	95.5260i	−0.209334	+	4.66119i
$421$	−13.3390	−	9.69134i	−0.650102	−	0.472327i	0.213204	−	0.977008i	$-0.431610\pi$
$421$	−13.3390	−	9.69134i	−0.650102	−	0.472327i	−0.863306	+	0.504681i	$0.831610\pi$
$422$	−28.1449	+	5.10755i	−1.37007	+	0.248632i
$423$	−3.21910	+	23.7643i	−0.156518	+	1.15546i
$424$	3.25128	−	0.292621i	0.157896	−	0.0142109i
$425$	−13.0117			−0.631158
$426$	−16.8323	−	52.4917i	−0.815529	−	2.54323i
$427$	−24.2034			−1.17129
$428$	39.5094	−	3.55591i	1.90976	−	0.171881i
$429$	−0.630682	+	4.65588i	−0.0304496	+	0.224788i
$430$	42.3753	−	7.68998i	2.04352	−	0.370844i
$431$	−9.26792	−	6.73354i	−0.446420	−	0.324343i	0.341761	−	0.939787i	$-0.388977\pi$
$431$	−9.26792	−	6.73354i	−0.446420	−	0.324343i	−0.788181	+	0.615444i	$0.788977\pi$
$432$	0.442289	−	9.84833i	0.0212796	−	0.473828i
$433$	35.0955	−	20.9686i	1.68658	−	1.00769i	0.747330	−	0.664453i	$-0.231335\pi$
$433$	35.0955	−	20.9686i	1.68658	−	1.00769i	0.939251	−	0.343232i	$-0.111522\pi$
$434$	−73.0810	+	20.1691i	−3.50800	+	0.968146i
$435$	35.5895	+	9.82209i	1.70639	+	0.470933i
$436$	23.3431	+	13.9468i	1.11793	+	0.667933i
$437$	−17.6225	+	26.6970i	−0.842999	+	1.27709i
$438$	−0.237064	−	5.27865i	−0.0113274	−	0.252224i
$439$	−4.77037	−	7.22680i	−0.227677	−	0.344916i	0.702722	−	0.711465i	$-0.251968\pi$
$439$	−4.77037	−	7.22680i	−0.227677	−	0.344916i	−0.930399	+	0.366549i	$0.880539\pi$
$440$	−12.9651	+	9.41971i	−0.618088	+	0.449067i
$441$	−7.86192	+	8.22292i	−0.374377	+	0.391568i
$442$	−9.33556	+	3.50370i	−0.444048	+	0.166654i
$443$	8.02484	−	24.6979i	0.381272	−	1.17343i	−0.557877	−	0.829924i	$-0.688384\pi$
$443$	8.02484	−	24.6979i	0.381272	−	1.17343i	0.939149	−	0.343511i	$-0.111616\pi$
$444$	14.1152	+	2.56153i	0.669878	+	0.121565i
$445$	20.6448	+	21.5928i	0.978658	+	1.02360i
$446$	−31.5243	−	15.1813i	−1.49272	−	0.718856i
$447$	4.98410	+	11.6609i	0.235740	+	0.551540i
$448$	15.6231	−	29.0325i	0.738120	−	1.37166i
$449$	4.29530	+	18.8189i	0.202708	+	0.888121i	0.969279	+	0.245962i	$0.0791039\pi$
$449$	4.29530	+	18.8189i	0.202708	+	0.888121i	−0.766572	+	0.642159i	$0.778039\pi$
$450$	6.05180	+	44.6762i	0.285285	+	2.10606i
$451$	0.0744708	+	0.229198i	0.00350669	+	0.0107925i
$452$	6.17295	+	7.74063i	0.290351	+	0.364089i
$453$	11.5563	−	27.0372i	0.542961	−	1.27032i
$454$	50.0904	−	43.7627i	2.35086	−	2.05388i
$455$	−5.99668	−	11.1437i	−0.281129	−	0.522424i
$456$	46.9783	−	58.9090i	2.19996	−	2.75866i
$457$	1.97514	+	0.741283i	0.0923932	+	0.0346758i	0.397143	−	0.917757i	$-0.370002\pi$
$457$	1.97514	+	0.741283i	0.0923932	+	0.0346758i	−0.304750	+	0.952432i	$0.598573\pi$
$458$	30.2297	−	14.5578i	1.41254	−	0.680243i
$459$	9.32850	+	8.15006i	0.435417	+	0.380412i
$460$	12.1138	−	53.0739i	0.564807	−	2.47458i
$461$	15.7470	+	1.41726i	0.733412	+	0.0660083i	0.450048	−	0.893004i	$-0.351407\pi$
$461$	15.7470	+	1.41726i	0.733412	+	0.0660083i	0.283364	+	0.959012i	$0.408550\pi$
$462$	−25.6518	−	2.30871i	−1.19343	−	0.107411i
$463$	0.373083	−	1.63458i	0.0173386	−	0.0759655i	−0.965518	−	0.260335i	$-0.916167\pi$
$463$	0.373083	−	1.63458i	0.0173386	−	0.0759655i	0.982857	+	0.184369i	$0.0590242\pi$
$464$	8.23423	+	7.19403i	0.382264	+	0.333974i
$465$	−76.6109	+	36.8939i	−3.55275	+	1.71091i
$466$	−14.5061	−	5.44424i	−0.671983	−	0.252199i
$467$	5.77350	−	7.23974i	0.267166	−	0.335015i	−0.630094	−	0.776519i	$-0.716984\pi$
$467$	5.77350	−	7.23974i	0.267166	−	0.335015i	0.897259	+	0.441504i	$0.145555\pi$
$468$	10.6583	+	19.8065i	0.492681	+	0.915555i
$469$	1.16901	−	1.02134i	0.0539800	−	0.0471609i
$470$	15.3285	−	35.8629i	0.707053	−	1.65423i
$471$	32.9375	+	41.3023i	1.51768	+	1.90311i
$472$	−10.2279	−	31.4784i	−0.470779	−	1.44891i
$473$	1.01369	+	7.48333i	0.0466093	+	0.344084i
$474$	−0.949067	−	4.15813i	−0.0435921	−	0.190989i
$475$	−13.2911	+	24.6991i	−0.609839	+	1.13327i
$476$	−13.9856	−	32.7208i	−0.641027	−	1.49976i
$477$	3.17194	+	1.52753i	0.145233	+	0.0699406i
$478$	−29.0132	−	30.3454i	−1.32703	−	1.38797i
$479$	24.5047	+	4.44696i	1.11965	+	0.203187i	0.706663	−	0.707550i	$-0.250200\pi$
$479$	24.5047	+	4.44696i	1.11965	+	0.203187i	0.412987	+	0.910737i	$0.364485\pi$
$480$	6.16500	−	18.9739i	0.281392	−	0.866037i
$481$	−1.77747	+	0.667095i	−0.0810456	+	0.0304169i
$482$	22.9404	−	23.9938i	1.04491	−	1.09289i
$483$	32.8362	−	23.8569i	1.49410	−	1.08552i
$484$	19.2707	+	29.1939i	0.875943	+	1.32700i
$485$	0.176700	+	3.93453i	0.00802353	+	0.178658i
$486$	−24.6663	+	37.3678i	−1.11889	+	1.69504i
$487$	−11.2777	−	6.73812i	−0.511042	−	0.305333i	0.234131	−	0.972205i	$-0.424776\pi$
$487$	−11.2777	−	6.73812i	−0.511042	−	0.305333i	−0.745172	+	0.666872i	$0.767633\pi$
$488$	−31.2865	−	8.63454i	−1.41628	−	0.390867i
$489$	−64.6530	+	17.8431i	−2.92371	+	0.806893i
$490$	15.8830	−	9.48965i	0.717521	−	0.428699i
$491$	0.881446	−	19.6269i	0.0397791	−	0.885751i	−0.875570	−	0.483091i	$-0.839514\pi$
$491$	0.881446	−	19.6269i	0.0397791	−	0.885751i	0.915350	−	0.402660i	$-0.131914\pi$
$492$	1.55999	+	1.13340i	0.0703298	+	0.0510976i
$493$	−13.5184	+	2.45323i	−0.608839	+	0.110488i
$494$	−2.88527	+	21.3000i	−0.129815	+	0.958330i
$495$	−17.2138	+	1.54927i	−0.773701	+	0.0696343i
$496$	−25.1829			−1.13075
$497$	−16.3102	+	20.2916i	−0.731614	+	0.910201i
$498$	−8.31056			−0.372405
$499$	20.8359	−	1.87526i	0.932741	−	0.0839482i	0.387166	−	0.922010i	$-0.373454\pi$
$499$	20.8359	−	1.87526i	0.932741	−	0.0839482i	0.545575	+	0.838062i	$0.316311\pi$
$500$	−1.19362	+	8.81168i	−0.0533804	+	0.394070i
$501$	−54.5068	+	9.89153i	−2.43519	+	0.441921i
$502$	56.6067	+	41.1272i	2.52648	+	1.83560i
$503$	−0.787493	+	17.5349i	−0.0351126	+	0.781842i	0.901774	+	0.432208i	$0.142265\pi$
$503$	−0.787493	+	17.5349i	−0.0351126	+	0.781842i	−0.936886	+	0.349634i	$0.886306\pi$
$504$	−49.1021	+	29.3371i	−2.18718	+	1.30678i
$505$	−3.68029	+	1.01570i	−0.163771	+	0.0451979i
$506$	14.1345	+	3.90087i	0.628354	+	0.173415i
$507$	26.2269	+	15.6698i	1.16478	+	0.695922i
$508$	−21.2022	+	32.1199i	−0.940693	+	1.42509i
$509$	0.236487	+	5.26578i	0.0104821	+	0.233402i	0.997394	+	0.0721432i	$0.0229839\pi$
$509$	0.236487	+	5.26578i	0.0104821	+	0.233402i	−0.986912	+	0.161259i	$0.948445\pi$
$510$	−33.7740	−	51.1655i	−1.49554	−	2.26565i
$511$	−2.01890	+	1.46682i	−0.0893109	+	0.0648882i
$512$	18.1520	−	18.9855i	0.802211	−	0.839047i
$513$	24.9995	−	9.38248i	1.10376	−	0.414246i
$514$	−9.91506	+	30.5154i	−0.437335	+	1.34598i
$515$	54.7128	+	9.92890i	2.41093	+	0.437520i
$516$	41.7562	+	43.6736i	1.83822	+	1.92262i
$517$	6.16149	+	2.96722i	0.270982	+	0.130498i
$518$	−4.09032	−	9.56978i	−0.179718	−	0.420472i
$519$	26.1894	−	48.6681i	1.14959	−	2.13629i
$520$	−3.77610	−	16.5442i	−0.165593	−	0.725510i
$521$	−2.64210	−	19.5048i	−0.115753	−	0.854520i	−0.951985	−	0.306145i	$-0.900961\pi$
$521$	−2.64210	−	19.5048i	−0.115753	−	0.854520i	0.836232	−	0.548375i	$-0.184754\pi$
$522$	14.7108	+	45.2752i	0.643874	+	1.98164i
$523$	7.92634	+	9.93932i	0.346595	+	0.434616i	0.924322	−	0.381614i	$-0.124632\pi$
$523$	7.92634	+	9.93932i	0.346595	+	0.434616i	−0.577727	+	0.816230i	$0.696060\pi$
$524$	−3.70617	+	8.67102i	−0.161905	+	0.378795i
$525$	26.8002	−	23.4146i	1.16966	−	1.02190i
$526$	−11.1025	−	20.6319i	−0.484093	−	0.899595i
$527$	19.7292	−	24.7397i	0.859420	−	1.07768i
$528$	−8.00971	−	3.00610i	−0.348578	−	0.130824i
$529$	−0.0964165	+	0.0464317i	−0.00419202	+	0.00201877i
$530$	−4.31180	−	3.76710i	−0.187293	−	0.163633i
$531$	7.94302	−	34.8006i	0.344698	−	1.51022i
$532$	−76.3974	−	6.87589i	−3.31225	−	0.298108i
$533$	−0.254159	−	0.0228747i	−0.0110089	−	0.000990815i
$534$	−14.3264	+	62.7679i	−0.619963	+	2.71623i
$535$	−24.3074	−	21.2368i	−1.05090	−	0.918145i
$536$	1.87548	−	0.903184i	0.0810085	−	0.0390116i
$537$	31.7269	+	11.9073i	1.36912	+	0.513838i
$538$	45.9150	−	57.5756i	1.97954	−	2.48226i
$539$	1.53734	+	2.85686i	0.0662181	+	0.123054i
$540$	−34.2211	+	29.8981i	−1.47264	+	1.28661i
$541$	−10.7021	+	25.0387i	−0.460117	+	1.07650i	0.515474	+	0.856905i	$0.327616\pi$
$541$	−10.7021	+	25.0387i	−0.460117	+	1.07650i	−0.975592	+	0.219593i	$0.929527\pi$
$542$	−27.3694	−	34.3202i	−1.17562	−	1.47418i
$543$	18.3294	+	56.4120i	0.786588	+	2.42087i
$544$	0.996577	+	7.35703i	0.0427279	+	0.315430i
$545$	−4.92340	−	21.5708i	−0.210895	−	0.923992i
$546$	12.9236	−	24.0160i	0.553078	−	1.02779i
$547$	−0.0853957	−	0.199793i	−0.00365126	−	0.00854254i	0.917692	−	0.397292i	$-0.130050\pi$
$547$	−0.0853957	−	0.199793i	−0.00365126	−	0.00854254i	−0.921343	+	0.388750i	$0.872907\pi$
$548$	−23.3528	−	11.2461i	−0.997584	−	0.480411i
$549$	−24.1893	−	25.3000i	−1.03237	−	1.07978i
$550$	12.6500	+	2.29564i	0.539398	+	0.0978863i
$551$	−9.15200	+	28.1669i	−0.389888	+	1.19995i
$552$	50.9565	−	19.1243i	2.16885	−	0.813984i
$553$	−1.39200	+	1.45592i	−0.0591940	+	0.0619121i
$554$	−56.2592	+	40.8747i	−2.39022	+	1.73660i
$555$	−6.43049	−	9.74178i	−0.272959	−	0.413516i
$556$	2.75891	+	61.4319i	0.117004	+	2.60529i
$557$	8.67973	−	13.1492i	0.367772	−	0.557150i	−0.602821	−	0.797876i	$-0.705957\pi$
$557$	8.67973	−	13.1492i	0.367772	−	0.557150i	0.970593	+	0.240726i	$0.0773854\pi$
$558$	−94.1212	−	56.2348i	−3.98447	−	2.38061i
$559$	−7.70828	−	2.12735i	−0.326026	−	0.0899774i
$560$	22.2123	−	6.13022i	0.938643	−	0.259049i
$561$	9.22831	−	5.51366i	0.389619	−	0.232787i
$562$	−2.47436	+	55.0958i	−0.104374	+	2.32408i
$563$	−24.3346	−	17.6801i	−1.02558	−	0.745129i	−0.0581622	−	0.998307i	$-0.518524\pi$
$563$	−24.3346	−	17.6801i	−1.02558	−	0.745129i	−0.967420	+	0.253178i	$0.918524\pi$
$564$	53.8394	−	9.77041i	2.26705	−	0.411409i
$565$	1.08137	−	7.98299i	0.0454935	−	0.335847i
$566$	−3.66347	+	0.329719i	−0.153987	+	0.0138591i
$567$	7.53654			0.316505
$568$	−28.3224	+	20.4112i	−1.18838	+	0.856435i
$569$	12.7383			0.534017			0.267008	−	0.963694i	$-0.413965\pi$
$569$	12.7383			0.534017			0.267008	+	0.963694i	$0.413965\pi$
$570$	−131.623	+	11.8463i	−5.51308	+	0.496187i
$571$	1.70118	−	12.5586i	0.0711923	−	0.525562i	−0.919876	−	0.392209i	$-0.871711\pi$
$571$	1.70118	−	12.5586i	0.0711923	−	0.525562i	0.991069	−	0.133354i	$-0.0425746\pi$
$572$	6.31098	−	1.14527i	0.263876	−	0.0478863i
$573$	24.1729	+	17.5626i	1.00984	+	0.733690i
$574$	0.0627601	−	1.39746i	0.00261956	−	0.0583289i
$575$	−17.3926	+	10.3916i	−0.725323	+	0.433360i
$576$	45.9618	−	12.6847i	1.91507	−	0.528527i
$577$	11.7202	+	3.23458i	0.487920	+	0.134657i	0.501336	−	0.865253i	$-0.332842\pi$
$577$	11.7202	+	3.23458i	0.487920	+	0.134657i	−0.0134162	+	0.999910i	$0.504271\pi$
$578$	−15.3504	−	9.17145i	−0.638493	−	0.381482i
$579$	13.1924	−	19.9857i	0.548259	−	0.830576i
$580$	−2.26126	−	50.3509i	−0.0938937	−	2.09071i
$581$	2.16221	+	3.27561i	0.0897035	+	0.135895i
$582$	−6.86688	+	4.98908i	−0.284642	+	0.206804i
$583$	0.693800	−	0.725658i	0.0287343	−	0.0300537i
$584$	−3.13301	+	1.17584i	−0.129645	+	0.0486566i
$585$	5.65541	−	17.4056i	0.233822	−	0.719631i
$586$	−30.2506	−	5.48967i	−1.24964	−	0.226776i
$587$	18.2184	+	19.0549i	0.751952	+	0.786481i	0.982437	−	0.186595i	$-0.0597453\pi$
$587$	18.2184	+	19.0549i	0.751952	+	0.786481i	−0.230484	+	0.973076i	$0.574031\pi$
$588$	23.3875	+	11.2628i	0.964483	+	0.464471i
$589$	−26.8085	−	62.7216i	−1.10463	−	2.58440i
$590$	−27.5093	+	51.1209i	−1.13254	+	2.10461i
$591$	−1.64335	−	7.19999i	−0.0675984	−	0.296168i
$592$	−0.464043	−	3.42571i	−0.0190721	−	0.140796i
$593$	11.3182	+	34.8338i	0.464782	+	1.43045i	0.859257	+	0.511544i	$0.170926\pi$
$593$	11.3182	+	34.8338i	0.464782	+	1.43045i	−0.394475	+	0.918907i	$0.629074\pi$
$594$	−7.63130	−	9.56935i	−0.313116	−	0.392635i
$595$	−11.3797	+	26.6241i	−0.466521	+	1.09148i
$596$	13.0372	−	11.3903i	0.534025	−	0.466564i
$597$	−2.72014	−	5.05487i	−0.111328	−	0.206882i
$598$	−9.68062	+	12.1391i	−0.395870	+	0.496405i
$599$	−3.69353	−	1.38621i	−0.150914	−	0.0566388i	0.274775	−	0.961509i	$-0.411397\pi$
$599$	−3.69353	−	1.38621i	−0.150914	−	0.0566388i	−0.425689	+	0.904870i	$0.639968\pi$
$600$	42.9963	−	20.7059i	1.75532	−	0.845317i
$601$	−17.3396	−	15.1491i	−0.707296	−	0.617946i	0.227230	−	0.973841i	$-0.427033\pi$
$601$	−17.3396	−	15.1491i	−0.707296	−	0.617946i	−0.934526	+	0.355895i	$0.884176\pi$
$602$	9.75412	−	42.7356i	0.397548	−	1.74177i
$603$	2.23594	+	0.201238i	0.0910545	+	0.00819505i
$604$	−39.9786	−	3.59814i	−1.62671	−	0.146406i
$605$	6.33358	−	27.7492i	0.257497	−	1.12817i
$606$	−6.19626	−	5.41351i	−0.251706	−	0.219909i
$607$	17.9123	−	8.62609i	0.727036	−	0.350122i	−0.0334816	−	0.999439i	$-0.510660\pi$
$607$	17.9123	−	8.62609i	0.727036	−	0.350122i	0.760518	+	0.649317i	$0.224945\pi$
$608$	14.9833	+	5.62332i	0.607652	+	0.228056i
$609$	23.4294	−	29.3795i	0.949405	−	1.19052i
$610$	26.9756	+	50.1291i	1.09221	+	2.02967i
$611$	−5.45338	+	4.76448i	−0.220620	+	0.192750i
$612$	20.2259	−	47.3209i	0.817585	−	1.91283i
$613$	−4.78812	−	6.00411i	−0.193390	−	0.242504i	0.675677	−	0.737198i	$-0.263851\pi$
$613$	−4.78812	−	6.00411i	−0.193390	−	0.242504i	−0.869067	+	0.494694i	$0.835280\pi$
$614$	17.3553	+	53.4141i	0.700402	+	2.15562i
$615$	−0.210608	−	1.55477i	−0.00849253	−	0.0626944i
$616$	3.62960	+	15.9023i	0.146241	+	0.640722i
$617$	2.72579	−	5.06536i	0.109736	−	0.203924i	−0.819805	−	0.572643i	$-0.805918\pi$
$617$	2.72579	−	5.06536i	0.109736	−	0.203924i	0.929541	+	0.368719i	$0.120204\pi$
$618$	47.0996	+	110.195i	1.89462	+	4.43269i
$619$	9.95375	+	4.79347i	0.400075	+	0.192666i	0.623092	−	0.782149i	$-0.285876\pi$
$619$	9.95375	+	4.79347i	0.400075	+	0.192666i	−0.223017	+	0.974815i	$0.571591\pi$
$620$	80.2197	+	83.9032i	3.22170	+	3.36963i
$621$	18.9783	+	3.44406i	0.761573	+	0.138205i
$622$	2.77816	−	8.55031i	0.111394	−	0.342836i
$623$	28.4674	−	10.6840i	1.14052	−	0.428045i
$624$	6.26042	−	6.54789i	0.250617	−	0.262125i
$625$	22.9028	−	16.6398i	0.916111	−	0.665594i
$626$	−17.9152	−	27.1404i	−0.716035	−	1.08475i
$627$	−1.03964	−	23.1495i	−0.0415194	−	0.924501i
$628$	39.7296	−	60.1877i	1.58538	−	2.40175i
$629$	3.72897	+	2.22795i	0.148684	+	0.0888343i
$630$	96.7079	+	26.6897i	3.85293	+	1.06334i
$631$	−42.9939	+	11.8656i	−1.71156	+	0.472360i	−0.978232	−	0.207516i	$-0.933462\pi$
$631$	−42.9939	+	11.8656i	−1.71156	+	0.472360i	−0.733327	+	0.679876i	$0.762033\pi$
$632$	−2.31877	+	1.38540i	−0.0922356	+	0.0551082i
$633$	−1.46503	+	32.6215i	−0.0582299	+	1.29659i
$634$	−47.5428	−	34.5418i	−1.88816	−	1.37183i
$635$	30.8123	−	5.59160i	1.22275	−	0.221896i
$636$	1.07830	−	7.96030i	0.0427572	−	0.315646i
$637$	−3.42149	+	0.307940i	−0.135564	+	0.0122010i
$638$	13.5755			0.537459
$639$	−37.5116	+	3.23050i	−1.48394	+	0.127797i
$640$	−62.9426			−2.48803
$641$	−5.52973	+	0.497685i	−0.218411	+	0.0196574i	−0.198305	−	0.980140i	$-0.563544\pi$
$641$	−5.52973	+	0.497685i	−0.218411	+	0.0196574i	−0.0201069	+	0.999798i	$0.506401\pi$
$642$	9.33759	−	68.9329i	0.368525	−	2.72056i
$643$	−1.81807	+	0.329931i	−0.0716976	+	0.0130112i	−0.214287	−	0.976771i	$-0.568743\pi$
$643$	−1.81807	+	0.329931i	−0.0716976	+	0.0130112i	0.142590	+	0.989782i	$0.454457\pi$
$644$	−44.8265	−	32.5684i	−1.76641	−	1.28337i
$645$	2.20577	−	49.1153i	0.0868521	−	1.93391i
$646$	42.2181	−	25.2241i	1.66105	−	0.992430i
$647$	15.6670	−	4.32381i	0.615933	−	0.169987i	0.0558717	−	0.998438i	$-0.482206\pi$
$647$	15.6670	−	4.32381i	0.615933	−	0.169987i	0.560061	+	0.828451i	$0.310778\pi$
$648$	9.74210	+	2.68865i	0.382706	+	0.105620i
$649$	−8.73838	−	5.22094i	−0.343012	−	0.204940i
$650$	−7.49982	+	11.3617i	−0.294167	+	0.445644i
$651$	3.88290	+	86.4594i	0.152183	+	3.38861i
$652$	50.4408	+	76.4145i	1.97541	+	2.99262i
$653$	−16.7298	+	12.1549i	−0.654686	+	0.475658i	−0.864864	−	0.502006i	$-0.832596\pi$
$653$	−16.7298	+	12.1549i	−0.654686	+	0.475658i	0.210178	+	0.977663i	$0.432596\pi$
$654$	32.9521	−	34.4652i	1.28853	−	1.34770i
$655$	7.18357	−	2.69604i	0.280685	−	0.105343i
$656$	0.143589	−	0.441922i	0.00560621	−	0.0172542i
$657$	−3.55100	−	0.644411i	−0.138538	−	0.0251409i
$658$	−27.4326	−	28.6923i	−1.06943	−	1.11854i
$659$	19.4081	+	9.34645i	0.756032	+	0.364086i	0.771863	−	0.635789i	$-0.219325\pi$
$659$	19.4081	+	9.34645i	0.756032	+	0.364086i	−0.0158309	+	0.999875i	$0.505039\pi$
$660$	15.4992	+	36.2623i	0.603307	+	1.41151i
$661$	−17.7305	+	32.9488i	−0.689636	+	1.28156i	0.259211	+	0.965821i	$0.416538\pi$
$661$	−17.7305	+	32.9488i	−0.689636	+	1.28156i	−0.948847	+	0.315737i	$0.897748\pi$
$662$	−6.54127	−	28.6592i	−0.254233	−	1.11387i
$663$	1.52799	+	11.2801i	0.0593424	+	0.438083i
$664$	1.62641	+	5.00557i	0.0631169	+	0.194254i
$665$	38.9144	+	48.7971i	1.50904	+	1.89227i
$666$	5.91543	−	13.8398i	0.229218	−	0.536282i
$667$	−16.1108	+	14.0756i	−0.623811	+	0.545008i
$668$	35.8367	+	66.5957i	1.38656	+	2.57666i
$669$	−24.9041	+	31.2288i	−0.962848	+	1.20737i
$670$	−3.41825	−	1.28289i	−0.132058	−	0.0495624i
$671$	−8.99327	+	4.33093i	−0.347181	+	0.167194i
$672$	−15.2917	−	13.3600i	−0.589890	−	0.515371i
$673$	−10.0554	+	44.0556i	−0.387607	+	1.69822i	0.285257	+	0.958451i	$0.407921\pi$
$673$	−10.0554	+	44.0556i	−0.387607	+	1.69822i	−0.672864	+	0.739766i	$0.734936\pi$
$674$	56.3064	+	5.06767i	2.16884	+	0.195199i
$675$	16.8441	+	1.51600i	0.648331	+	0.0583508i
$676$	9.28081	−	40.6619i	0.356954	−	1.56392i
$677$	35.5730	+	31.0792i	1.36718	+	1.19447i	0.959622	+	0.281294i	$0.0907637\pi$
$677$	35.5730	+	31.0792i	1.36718	+	1.19447i	0.407562	+	0.913178i	$0.366379\pi$
$678$	15.6421	−	7.53284i	0.600732	−	0.289297i
$679$	3.75305	+	1.40854i	0.144029	+	0.0540549i
$680$	−24.2080	+	30.3559i	−0.928335	+	1.16410i
$681$	−35.9817	−	66.8652i	−1.37882	−	2.56228i
$682$	−23.5457	+	20.5712i	−0.901610	+	0.787713i
$683$	−17.9689	+	42.0403i	−0.687561	+	1.60863i	0.101876	+	0.994797i	$0.467515\pi$
$683$	−17.9689	+	42.0403i	−0.687561	+	1.60863i	−0.789437	+	0.613832i	$0.789627\pi$
$684$	−69.1654	−	86.7306i	−2.64460	−	3.31623i
$685$	6.51722	+	20.0579i	0.249010	+	0.766375i
$686$	4.42202	+	32.6447i	0.168834	+	1.24638i
$687$	−8.52315	−	37.3424i	−0.325179	−	1.42470i
$688$	6.89981	−	12.8220i	0.263053	−	0.488834i
$689$	0.417822	+	0.977543i	0.0159177	+	0.0372414i
$690$	−86.0083	−	41.4194i	−3.27428	−	1.57681i
$691$	−15.7345	−	16.4570i	−0.598569	−	0.626054i	0.352211	−	0.935920i	$-0.385430\pi$
$691$	−15.7345	−	16.4570i	−0.598569	−	0.626054i	−0.950780	+	0.309867i	$0.899716\pi$
$692$	−74.2360	−	13.4719i	−2.82203	−	0.512123i
$693$	−5.43599	+	16.7303i	−0.206496	+	0.635530i
$694$	−16.7128	+	6.27241i	−0.634409	+	0.238098i
$695$	34.5779	−	36.1657i	1.31162	−	1.37184i
$696$	40.7670	−	29.6190i	1.54527	−	1.12270i
$697$	0.321651	+	0.487281i	0.0121834	+	0.0184571i
$698$	−0.123052	−	2.73997i	−0.00465760	−	0.103709i
$699$	−9.74412	+	14.7617i	−0.368556	+	0.558339i
$700$	−41.7060	−	24.9182i	−1.57634	−	0.941818i
$701$	−25.4327	−	7.01897i	−0.960578	−	0.265103i	−0.249625	−	0.968343i	$-0.580307\pi$
$701$	−25.4327	−	7.01897i	−0.960578	−	0.265103i	−0.710953	+	0.703240i	$0.751736\pi$
$702$	12.4935	−	3.44798i	0.471536	−	0.130136i
$703$	8.03822	−	4.80261i	0.303167	−	0.181134i
$704$	0.610021	−	13.5832i	0.0229910	−	0.511935i
$705$	−36.0200	−	26.1701i	−1.35659	−	0.985623i
$706$	−66.1469	+	12.0039i	−2.48947	+	0.451772i
$707$	−0.521616	+	3.85072i	−0.0196174	+	0.144821i
$708$	−81.1195	+	7.30089i	−3.04866	+	0.274384i
$709$	−9.94608			−0.373533			−0.186766	−	0.982404i	$-0.559801\pi$
$709$	−9.94608			−0.373533			−0.186766	+	0.982404i	$0.559801\pi$
$710$	60.2053	+	11.1653i	2.25946	+	0.419028i
$711$	−2.91308			−0.109249
$712$	40.6098	−	3.65495i	1.52192	−	0.136975i
$713$	6.61392	−	48.8259i	0.247693	−	1.82855i
$714$	−61.3968	+	11.1419i	−2.29772	+	0.416974i
$715$	−4.22222	−	3.06762i	−0.157902	−	0.114723i
$716$	2.07554	−	46.2155i	0.0775666	−	1.72715i
$717$	−41.1432	+	24.5819i	−1.53652	+	0.918028i
$718$	−11.1663	+	3.08170i	−0.416722	+	0.115008i
$719$	−31.4867	−	8.68977i	−1.17425	−	0.324074i	−0.376130	−	0.926567i	$-0.622746\pi$
$719$	−31.4867	−	8.68977i	−1.17425	−	0.324074i	−0.798124	+	0.602493i	$0.794174\pi$
$720$	28.6073	+	17.0921i	1.06613	+	0.636984i
$721$	31.1791	−	47.2344i	1.16117	−	1.75910i
$722$	−2.71558	−	60.4671i	−0.101064	−	2.25035i
$723$	−20.8766	−	31.6267i	−0.776409	−	1.17621i
$724$	65.5096	−	47.5955i	2.43465	−	1.76887i
$725$	−12.9630	+	13.5582i	−0.481432	+	0.503539i
$726$	57.4295	−	21.5536i	2.13141	−	0.799931i
$727$	−0.107686	+	0.331422i	−0.00399384	+	0.0122918i	−0.953034	−	0.302865i	$-0.902057\pi$
$727$	−0.107686	+	0.331422i	−0.00399384	+	0.0122918i	0.949040	+	0.315156i	$0.102057\pi$
$728$	−16.9944	−	3.08403i	−0.629854	−	0.114302i
$729$	30.2659	+	31.6556i	1.12096	+	1.17243i
$730$	5.28814	+	2.54663i	0.195723	+	0.0942552i
$731$	7.19076	+	16.8236i	0.265960	+	0.622244i
$732$	−37.8466	+	70.3307i	−1.39885	+	2.59950i
$733$	3.55740	+	15.5860i	0.131395	+	0.575681i	0.997166	+	0.0752390i	$0.0239720\pi$
$733$	3.55740	+	15.5860i	0.131395	+	0.575681i	−0.865770	+	0.500442i	$0.833171\pi$
$734$	2.96140	+	21.8619i	0.109307	+	0.806939i
$735$	−6.52689	−	20.0877i	−0.240748	−	0.740946i
$736$	7.20772	+	9.03819i	0.265680	+	0.333152i
$737$	0.251614	−	0.588679i	0.00926830	−	0.0216843i
$738$	1.52350	−	1.33104i	0.0560808	−	0.0489963i
$739$	−0.254479	−	0.472901i	−0.00936115	−	0.0173959i	0.875872	−	0.482544i	$-0.160287\pi$
$739$	−0.254479	−	0.472901i	−0.00936115	−	0.0173959i	−0.885233	+	0.465148i	$0.846001\pi$
$740$	−9.93541	+	12.4586i	−0.365233	+	0.457988i
$741$	22.9730	+	8.62191i	0.843934	+	0.316734i
$742$	−5.25050	+	2.52851i	−0.192752	+	0.0928245i
$743$	−2.44950	−	2.14006i	−0.0898634	−	0.0785113i	0.611835	−	0.790985i	$-0.290432\pi$
$743$	−2.44950	−	2.14006i	−0.0898634	−	0.0785113i	−0.701698	+	0.712474i	$0.747575\pi$
$744$	−25.8250	+	113.147i	−0.946792	+	4.14816i
$745$	−14.0297	−	1.26269i	−0.514007	−	0.0462615i
$746$	15.3762	+	1.38389i	0.562964	+	0.0506677i
$747$	−1.26307	+	5.53386i	−0.0462133	+	0.202474i
$748$	−11.0516	−	9.65552i	−0.404088	−	0.353041i
$749$	−29.5993	+	14.2543i	−1.08154	+	0.520840i
$750$	14.5987	+	5.47898i	0.533069	+	0.200064i
$751$	−27.9207	+	35.0115i	−1.01884	+	1.27759i	−0.0586389	+	0.998279i	$0.518676\pi$
$751$	−27.9207	+	35.0115i	−1.01884	+	1.27759i	−0.960202	+	0.279307i	$0.909895\pi$
$752$	−6.24841	−	11.6115i	−0.227856	−	0.423427i
$753$	60.1523	−	52.5535i	2.19207	−	1.91515i
$754$	−5.64976	+	13.2183i	−0.205752	+	0.481381i
$755$	20.3638	+	25.5354i	0.741116	+	0.929330i
$756$	14.2925	+	43.9879i	0.519814	+	1.59982i
$757$	4.14712	+	30.6152i	0.150730	+	1.11273i	0.895389	+	0.445285i	$0.146898\pi$
$757$	4.14712	+	30.6152i	0.150730	+	1.11273i	−0.744659	+	0.667445i	$0.767388\pi$
$758$	1.87346	+	8.20819i	0.0680473	+	0.298135i
$759$	7.93201	−	14.7402i	0.287914	−	0.535034i
$760$	32.8943	+	76.9601i	1.19320	+	2.79164i
$761$	17.7972	+	8.57067i	0.645147	+	0.310686i	0.727695	−	0.685901i	$-0.240592\pi$
$761$	17.7972	+	8.57067i	0.645147	+	0.310686i	−0.0825481	+	0.996587i	$0.526306\pi$
$762$	46.6390	+	48.7806i	1.68955	+	1.76713i
$763$	−22.1578	−	4.02105i	−0.802167	−	0.145572i
$764$	12.6048	−	38.7936i	0.456026	−	1.40350i
$765$	−39.2034	+	14.7133i	−1.41740	+	0.531959i
$766$	29.8010	−	31.1694i	1.07675	−	1.12620i
$767$	8.72024	−	6.33562i	0.314870	−	0.228766i
$768$	−42.5990	−	64.5347i	−1.53716	−	2.32869i
$769$	−1.12497	−	25.0494i	−0.0405674	−	0.903304i	−0.911349	−	0.411634i	$-0.864958\pi$
$769$	−1.12497	−	25.0494i	−0.0405674	−	0.903304i	0.870782	−	0.491670i	$-0.163613\pi$
$770$	15.7606	−	23.8763i	0.567974	−	0.860444i
$771$	31.4437	+	18.7867i	1.13242	+	0.676587i
$772$	−31.5135	−	8.69718i	−1.13420	−	0.313019i
$773$	32.5855	−	8.99301i	1.17202	−	0.323456i	0.374775	−	0.927116i	$-0.377720\pi$
$773$	32.5855	−	8.99301i	1.17202	−	0.323456i	0.797242	+	0.603659i	$0.206291\pi$
$774$	54.4203	−	32.5146i	1.95610	−	1.16871i
$775$	1.93826	−	43.1587i	0.0696243	−	1.55031i
$776$	4.34887	+	3.15964i	0.156115	+	0.113425i
$777$	−11.6898	+	2.12138i	−0.419369	+	0.0761042i
$778$	−0.788360	+	5.81991i	−0.0282641	+	0.208654i
$779$	1.25353	−	0.112820i	0.0449123	−	0.00404218i
$780$	−41.7584			−1.49519
$781$	−2.42945	+	10.4583i	−0.0869325	+	0.374226i
$782$	35.5247			1.27036
$783$	17.7860	−	1.60077i	0.635619	−	0.0572068i
$784$	0.839670	−	6.19869i	0.0299882	−	0.221382i
$785$	−57.7375	+	10.4778i	−2.06074	+	0.373969i
$786$	13.3778	+	9.71955i	0.477171	+	0.346685i
$787$	2.03236	−	45.2540i	0.0724458	−	1.61313i	−0.553217	−	0.833038i	$-0.686600\pi$
$787$	2.03236	−	45.2540i	0.0724458	−	1.61313i	0.625662	−	0.780094i	$-0.284829\pi$
$788$	−8.65478	+	5.17099i	−0.308314	+	0.184209i
$789$	−25.7828	+	7.11559i	−0.917891	+	0.253322i
$790$	4.56687	+	1.26038i	0.162482	+	0.0448422i
$791$	−7.03877	−	4.20547i	−0.250270	−	0.149529i
$792$	−12.9953	+	19.6871i	−0.461768	+	0.699549i
$793$	−0.474207	−	10.5590i	−0.0168396	−	0.374963i
$794$	0.596509	+	0.903672i	0.0211693	+	0.0320701i
$795$	−5.28793	+	3.84190i	−0.187543	+	0.136258i
$796$	−5.41544	+	5.66411i	−0.191945	+	0.200759i
$797$	14.9650	−	5.61648i	0.530089	−	0.198946i	−0.0719560	−	0.997408i	$-0.522924\pi$
$797$	14.9650	−	5.61648i	0.530089	−	0.198946i	0.602045	+	0.798462i	$0.294353\pi$
$798$	−41.5657	+	127.926i	−1.47141	+	4.52853i
$799$	16.3024	+	2.95844i	0.576736	+	0.104662i
$800$	7.00475	+	7.32640i	0.247655	+	0.259027i
$801$	39.6188	+	19.0794i	1.39986	+	0.674137i
$802$	8.45263	+	19.7759i	0.298473	+	0.698311i
$803$	−0.487693	+	0.906285i	−0.0172103	+	0.0319821i
$804$	−1.13984	−	4.99398i	−0.0401992	−	0.176124i
$805$	6.05184	+	44.6765i	0.213299	+	1.57464i
$806$	−10.2308	−	31.4873i	−0.360366	−	1.10909i
$807$	−52.4156	−	65.7270i	−1.84512	−	2.31370i
$808$	−2.04800	+	4.79154i	−0.0720485	+	0.168566i
$809$	23.8942	−	20.8757i	0.840076	−	0.733952i	−0.126050	−	0.992024i	$-0.540230\pi$
$809$	23.8942	−	20.8757i	0.840076	−	0.733952i	0.966126	+	0.258072i	$0.0830872\pi$
$810$	−8.39974	−	15.6093i	−0.295137	−	0.548456i
$811$	−10.3838	+	13.0208i	−0.364624	+	0.457224i	−0.929973	−	0.367628i	$-0.880170\pi$
$811$	−10.3838	+	13.0208i	−0.364624	+	0.457224i	0.565349	+	0.824852i	$0.308741\pi$
$812$	−48.0284	−	18.0254i	−1.68547	−	0.632566i
$813$	−45.1494	+	21.7428i	−1.58346	+	0.762553i
$814$	−3.23224	−	2.82393i	−0.113290	−	0.0989785i
$815$	16.5780	−	72.6330i	0.580702	−	2.54422i
$816$	−20.6439	−	1.85798i	−0.722680	−	0.0650424i
$817$	39.2802	+	3.53528i	1.37424	+	0.123684i
$818$	3.93053	−	17.2208i	0.137428	−	0.602111i
$819$	−14.0277	−	12.2556i	−0.490168	−	0.428247i
$820$	−1.92978	+	0.929331i	−0.0673907	+	0.0324536i
$821$	−26.0509	−	9.77707i	−0.909183	−	0.341222i	−0.147417	−	0.989074i	$-0.547096\pi$
$821$	−26.0509	−	9.77707i	−0.909183	−	0.341222i	−0.761766	+	0.647852i	$0.775667\pi$
$822$	−28.3388	+	35.5357i	−0.988429	+	1.23945i
$823$	−0.855043	−	1.58894i	−0.0298049	−	0.0553868i	0.865258	−	0.501328i	$-0.167155\pi$
$823$	−0.855043	−	1.58894i	−0.0298049	−	0.0553868i	−0.895062	+	0.445941i	$0.852869\pi$
$824$	57.1544	−	49.9343i	1.99107	−	1.73954i
$825$	5.76836	−	13.4958i	0.200829	−	0.469862i
$826$	36.8400	+	46.1959i	1.28183	+	1.60736i
$827$	4.42410	+	13.6160i	0.153841	+	0.473474i	0.998042	−	0.0625532i	$-0.0199243\pi$
$827$	4.42410	+	13.6160i	0.153841	+	0.473474i	−0.844200	+	0.536028i	$0.819924\pi$
$828$	−10.7564	−	79.4068i	−0.373810	−	2.75958i
$829$	3.30474	+	14.4790i	0.114778	+	0.502877i	0.999336	+	0.0364451i	$0.0116034\pi$
$829$	3.30474	+	14.4790i	0.114778	+	0.502877i	−0.884557	+	0.466431i	$0.845539\pi$
$830$	4.37443	−	8.12904i	0.151839	−	0.282163i
$831$	31.2005	+	72.9972i	1.08233	+	2.53225i
$832$	12.9719	+	6.24692i	0.449718	+	0.216573i
$833$	5.43177	+	5.68119i	0.188200	+	0.196841i
$834$	106.101	+	19.2544i	3.67396	+	0.666726i
$835$	19.0153	−	58.5229i	0.658050	−	2.02527i
$836$	−29.6173	+	11.1156i	−1.02434	+	0.384440i
$837$	−28.4227	+	29.7279i	−0.982434	+	1.02755i
$838$	20.3235	−	14.7659i	0.702065	−	0.510080i
$839$	−26.1382	−	39.5977i	−0.902390	−	1.36706i	−0.930045	−	0.367445i	$-0.880232\pi$
$839$	−26.1382	−	39.5977i	−0.902390	−	1.36706i	0.0276548	−	0.999618i	$-0.491196\pi$
$840$	−4.76436	−	106.087i	−0.164386	−	3.66034i
$841$	5.06446	−	7.67232i	0.174636	−	0.264563i
$842$	33.8832	+	20.2443i	1.16769	+	0.697663i
$843$	60.6907	+	16.7496i	2.09030	+	0.576886i
$844$	42.9719	−	11.8595i	1.47915	−	0.408220i
$845$	−29.1326	+	17.4059i	−1.00219	+	0.598782i
$846$	2.57564	−	57.3510i	0.0885522	−	1.97177i
$847$	−23.4372	−	17.0281i	−0.805310	−	0.585092i
$848$	−1.90466	+	0.345644i	−0.0654062	+	0.0118695i
$849$	−0.563652	+	4.16104i	−0.0193445	+	0.142807i
$850$	31.0231	−	2.79213i	1.06408	−	0.0957694i
$851$	6.76382			0.231861
$852$	33.4594	+	79.1241i	1.14630	+	2.71075i
$853$	5.14693			0.176227			0.0881137	−	0.996110i	$-0.471916\pi$
$853$	5.14693			0.176227			0.0881137	+	0.996110i	$0.471916\pi$
$854$	57.7072	−	5.19374i	1.97470	−	0.177726i
$855$	−12.1163	+	89.4461i	−0.414369	+	3.05899i
$856$	−43.3467	+	7.86626i	−1.48156	+	0.268863i
$857$	−13.3531	−	9.70157i	−0.456132	−	0.331399i	0.335880	−	0.941905i	$-0.390966\pi$
$857$	−13.3531	−	9.70157i	−0.456132	−	0.331399i	−0.792012	+	0.610505i	$0.790966\pi$
$858$	0.504616	−	11.2362i	0.0172273	−	0.383596i
$859$	8.41314	−	5.02662i	0.287053	−	0.171506i	−0.362153	−	0.932118i	$-0.617958\pi$
$859$	8.41314	−	5.02662i	0.287053	−	0.171506i	0.649206	+	0.760612i	$0.275101\pi$
$860$	−64.6989	+	17.8558i	−2.20622	+	0.608877i
$861$	−1.53937	−	0.424840i	−0.0524617	−	0.0144785i
$862$	23.5420	+	14.0657i	0.801845	+	0.479080i
$863$	2.62685	−	3.97951i	0.0894190	−	0.135464i	−0.787111	−	0.616812i	$-0.788424\pi$
$863$	2.62685	−	3.97951i	0.0894190	−	0.135464i	0.876530	+	0.481348i	$0.159853\pi$
$864$	−0.432937	−	9.64008i	−0.0147288	−	0.327962i
$865$	33.8198	+	51.2348i	1.14991	+	1.74204i
$866$	−79.1770	+	57.5255i	−2.69054	+	1.95479i
$867$	−14.1068	+	14.7546i	−0.479093	+	0.501092i
$868$	110.616	−	41.5148i	3.75455	−	1.40910i
$869$	−0.256706	+	0.790060i	−0.00870815	+	0.0268009i
$870$	−86.9622	−	15.7813i	−2.94830	−	0.535037i
$871$	0.468474	+	0.489985i	0.0158736	+	0.0166025i
$872$	−27.2078	−	13.1026i	−0.921371	−	0.443709i
$873$	2.27850	+	5.33081i	0.0771154	+	0.180420i
$874$	36.2877	−	67.4339i	1.22745	−	2.28099i
$875$	−1.63869	−	7.17957i	−0.0553979	−	0.242714i
$876$	1.10537	+	8.16019i	0.0373471	+	0.275707i
$877$	−12.8486	−	39.5440i	−0.433867	−	1.33530i	−0.894243	−	0.447581i	$-0.852286\pi$
$877$	−12.8486	−	39.5440i	−0.433867	−	1.33530i	0.460376	−	0.887724i	$-0.347714\pi$
$878$	12.9246	+	16.2069i	0.436183	+	0.546956i
$879$	−13.7942	+	32.2730i	−0.465266	+	1.08854i
$880$	7.15651	−	6.25245i	0.241246	−	0.210770i
$881$	−11.9209	−	22.1528i	−0.401626	−	0.746346i	0.596802	−	0.802388i	$-0.296438\pi$
$881$	−11.9209	−	22.1528i	−0.401626	−	0.746346i	−0.998428	+	0.0560421i	$0.982152\pi$
$882$	16.9803	−	21.2926i	0.571756	−	0.716960i
$883$	6.27471	+	2.35494i	0.211161	+	0.0792500i	0.454714	−	0.890638i	$-0.349742\pi$
$883$	6.27471	+	2.35494i	0.211161	+	0.0792500i	−0.243553	+	0.969888i	$0.578313\pi$
$884$	14.0008	−	6.74245i	0.470899	−	0.226773i
$885$	49.9073	+	43.6027i	1.67761	+	1.46569i
$886$	−13.8334	+	60.6082i	−0.464743	+	2.03617i
$887$	−38.3577	−	3.45225i	−1.28792	−	0.115915i	−0.575580	−	0.817745i	$-0.695224\pi$
$887$	−38.3577	−	3.45225i	−1.28792	−	0.115915i	−0.712344	+	0.701830i	$0.752367\pi$
$888$	−15.8676	−	1.42811i	−0.532481	−	0.0479242i
$889$	7.09250	−	31.0743i	0.237875	−	1.04220i
$890$	−53.8560	−	47.0526i	−1.80526	−	1.57721i
$891$	2.80035	−	1.34858i	0.0938154	−	0.0451791i
$892$	51.0515	+	19.1600i	1.70933	+	0.641523i
$893$	22.2683	−	27.9236i	0.745181	−	0.934427i
$894$	−14.3856	−	26.7330i	−0.481127	−	0.894085i
$895$	−28.3473	+	24.7663i	−0.947545	+	0.827845i
$896$	−25.1787	+	58.9086i	−0.841163	+	1.96800i
$897$	11.0512	+	13.8577i	0.368988	+	0.462697i
$898$	−14.2794	−	43.9475i	−0.476510	−	1.46655i
$899$	−6.12344	−	45.2050i	−0.204228	−	1.50767i
$900$	−15.6345	−	68.4992i	−0.521150	−	2.28331i
$901$	1.15262	−	2.14193i	0.0383993	−	0.0713579i
$902$	−0.226740	−	0.530485i	−0.00754962	−	0.0176632i
$903$	−45.0851	−	21.7118i	−1.50034	−	0.722525i
$904$	−7.59837	−	7.94727i	−0.252718	−	0.264322i
$905$	−64.8279	−	11.7645i	−2.15495	−	0.391066i
$906$	−21.7513	+	66.9435i	−0.722637	+	2.22405i
$907$	−45.9201	+	17.2341i	−1.52475	+	0.572249i	−0.966330	−	0.257307i	$-0.917165\pi$
$907$	−45.9201	+	17.2341i	−1.52475	+	0.572249i	−0.558423	+	0.829557i	$0.688593\pi$
$908$	−71.6348	+	74.9241i	−2.37728	+	2.48644i
$909$	−4.54650	+	3.30322i	−0.150798	+	0.109561i
$910$	16.6889	+	25.2826i	0.553232	+	0.838110i
$911$	−0.415329	−	9.24802i	−0.0137605	−	0.306401i	−0.994056	−	0.108866i	$-0.965278\pi$
$911$	−0.415329	−	9.24802i	−0.0137605	−	0.306401i	0.980296	−	0.197534i	$-0.0632934\pi$
$912$	−24.6141	+	37.2888i	−0.815056	+	1.23476i
$913$	1.38954	+	0.830214i	0.0459872	+	0.0274761i
$914$	−4.86831	−	1.34357i	−0.161029	−	0.0444413i
$915$	62.6440	−	17.2886i	2.07095	−	0.571545i
$916$	−44.8876	+	26.8191i	−1.48313	+	0.886128i
$917$	0.350373	−	7.80166i	0.0115703	−	0.257634i
$918$	−23.9904	−	17.4301i	−0.791802	−	0.575278i
$919$	4.55772	−	0.827105i	0.150345	−	0.0272837i	−0.102862	−	0.994696i	$-0.532800\pi$
$919$	4.55772	−	0.827105i	0.150345	−	0.0272837i	0.253208	+	0.967412i	$0.418514\pi$
$920$	−8.11536	+	59.9100i	−0.267555	+	1.97517i
$921$	63.8562	−	5.74717i	2.10413	−	0.189376i
$922$	−37.8491			−1.24649
$923$	−9.17199	−	6.71797i	−0.301900	−	0.221125i
$924$	40.1383			1.32045
$925$	5.90673	−	0.531615i	0.194212	−	0.0174794i
$926$	−0.538765	+	3.97732i	−0.0177049	+	0.130703i
$927$	80.5353	−	14.6150i	2.64513	−	0.480020i
$928$	8.65889	+	6.29105i	0.284242	+	0.206514i
$929$	−1.09844	+	24.4586i	−0.0360386	+	0.802461i	0.896858	+	0.442318i	$0.145844\pi$
$929$	−1.09844	+	24.4586i	−0.0360386	+	0.802461i	−0.932897	+	0.360143i	$0.882728\pi$
$930$	174.743	−	104.404i	5.73005	−	3.42355i
$931$	16.3326	−	4.50751i	0.535280	−	0.147728i
$932$	23.2763	+	6.42386i	0.762442	+	0.210421i
$933$	−8.81040	−	5.26397i	−0.288440	−	0.172335i
$934$	−12.2119	+	18.5003i	−0.399587	+	0.605348i
$935$	0.535731	+	11.9290i	0.0175203	+	0.390119i
$936$	−13.7607	−	20.8466i	−0.449783	−	0.681392i
$937$	25.8906	−	18.8106i	0.845810	−	0.614517i	−0.0781774	−	0.996939i	$-0.524910\pi$
$937$	25.8906	−	18.8106i	0.845810	−	0.614517i	0.923988	+	0.382422i	$0.124910\pi$
$938$	−2.56806	+	2.68598i	−0.0838501	+	0.0877003i
$939$	−34.7569	+	13.0445i	−1.13425	+	0.425691i
$940$	−18.7824	+	57.8063i	−0.612615	+	1.88543i
$941$	35.1306	+	6.37526i	1.14522	+	0.207827i	0.717817	−	0.696232i	$-0.245142\pi$
$941$	35.1306	+	6.37526i	1.14522	+	0.207827i	0.427407	+	0.904059i	$0.359427\pi$
$942$	−87.3943	−	91.4072i	−2.84746	−	2.97821i
$943$	0.819110	+	0.394463i	0.0266739	+	0.0128455i
$944$	7.71387	+	18.0475i	0.251065	+	0.587396i
$945$	17.8334	−	33.1401i	0.580122	−	1.07805i
$946$	−4.02271	−	17.6247i	−0.130790	−	0.573027i
$947$	5.70588	+	42.1225i	0.185416	+	1.36880i	0.809353	+	0.587323i	$0.199818\pi$
$947$	5.70588	+	42.1225i	0.185416	+	1.36880i	−0.623936	+	0.781475i	$0.714468\pi$
$948$	2.05398	+	6.32150i	0.0667102	+	0.205313i
$949$	−0.679472	−	0.852031i	−0.0220566	−	0.0276581i
$950$	26.3894	−	61.7410i	0.856184	−	2.00314i
$951$	−50.5206	+	44.1385i	−1.63824	+	1.43129i
$952$	18.7265	+	34.7997i	0.606929	+	1.12786i
$953$	−20.3131	+	25.4718i	−0.658005	+	0.825113i	−0.993124	−	0.117063i	$-0.962652\pi$
$953$	−20.3131	+	25.4718i	−0.658005	+	0.825113i	0.335119	+	0.942176i	$0.391223\pi$
$954$	−7.89050	−	2.96136i	−0.255464	−	0.0958774i
$955$	−29.9029	+	14.4005i	−0.967636	+	0.465989i
$956$	49.2722	+	43.0478i	1.59358	+	1.39227i
$957$	3.44852	−	15.1089i	0.111475	−	0.488403i
$958$	−59.3798	−	5.34428i	−1.91848	−	0.172666i
$959$	21.3795	+	1.92419i	0.690379	+	0.0621353i
$960$	−19.6979	+	86.3022i	−0.635748	+	2.78539i
$961$	55.7755	+	48.7296i	1.79921	+	1.57192i
$962$	4.09479	−	1.97195i	0.132021	−	0.0635781i
$963$	−44.4821	−	16.6944i	−1.43342	−	0.537970i
$964$	−32.2553	+	40.4469i	−1.03887	+	1.30271i
$965$	12.6051	+	23.4241i	0.405772	+	0.754050i
$966$	−73.1704	+	63.9271i	−2.35422	+	2.05682i
$967$	6.20058	−	14.5070i	0.199397	−	0.466513i	−0.789752	−	0.613426i	$-0.789791\pi$
$967$	6.20058	−	14.5070i	0.199397	−	0.466513i	0.989149	+	0.146913i	$0.0469338\pi$
$968$	−24.2213	−	30.3725i	−0.778501	−	0.976209i
$969$	−17.3489	−	53.3945i	−0.557327	−	1.71528i
$970$	−1.26560	−	9.34301i	−0.0406358	−	0.299986i
$971$	−4.11000	−	18.0071i	−0.131896	−	0.577875i	−0.997076	−	0.0764137i	$-0.975653\pi$
$971$	−4.11000	−	18.0071i	−0.131896	−	0.577875i	0.865180	−	0.501462i	$-0.167204\pi$
$972$	33.0659	−	61.4467i	1.06059	−	1.97090i
$973$	−20.0157	−	46.8291i	−0.641674	−	1.50127i
$974$	28.3348	+	13.6453i	0.907907	+	0.437225i
$975$	10.7400	+	11.2331i	0.343955	+	0.359749i
$976$	18.9368	+	3.43653i	0.606154	+	0.110001i
$977$	−7.76219	+	23.8896i	−0.248335	+	0.764295i	0.746736	+	0.665121i	$0.231620\pi$
$977$	−7.76219	+	23.8896i	−0.248335	+	0.764295i	−0.995070	+	0.0991741i	$0.968380\pi$
$978$	150.321	−	56.4162i	4.80672	−	1.80399i
$979$	8.66584	−	9.06376i	0.276961	−	0.289679i
$980$	−23.3273	+	16.9483i	−0.745163	+	0.541392i
$981$	−17.9416	−	27.1804i	−0.572833	−	0.867804i
$982$	2.11009	+	46.9848i	0.0673356	+	1.49934i
$983$	4.99384	−	7.56535i	0.159279	−	0.241297i	−0.746167	−	0.665759i	$-0.768108\pi$
$983$	4.99384	−	7.56535i	0.159279	−	0.241297i	0.905446	+	0.424461i	$0.139537\pi$
$984$	−1.83831	−	1.09834i	−0.0586031	−	0.0350137i
$985$	7.90774	+	2.18240i	0.251961	+	0.0695370i
$986$	31.7050	−	8.75001i	1.00969	−	0.278657i
$987$	−38.9018	+	23.2428i	−1.23826	+	0.739825i
$988$	1.50287	−	33.4640i	0.0478127	−	1.06463i
$989$	23.0478	+	16.7452i	0.732878	+	0.532467i
$990$	40.7095	−	7.38769i	1.29383	−	0.234796i
$991$	6.84760	−	50.5510i	0.217521	−	1.60581i	−0.472039	−	0.881578i	$-0.656482\pi$
$991$	6.84760	−	50.5510i	0.217521	−	1.60581i	0.689560	−	0.724228i	$-0.257804\pi$
$992$	−24.5512	+	2.20964i	−0.779500	+	0.0701563i
$993$	−33.5580			−1.06493
$994$	34.5335	−	51.8802i	1.09533	−	1.64554i
$995$	6.37627			0.202141
$996$	12.8993	−	1.16096i	0.408730	−	0.0367864i
$997$	−6.66740	+	49.2207i	−0.211159	+	1.55884i	0.506376	+	0.862313i	$0.330985\pi$
$997$	−6.66740	+	49.2207i	−0.211159	+	1.55884i	−0.717535	+	0.696523i	$0.754730\pi$
$998$	−49.2756	+	8.94220i	−1.55979	+	0.283061i
$999$	−4.56772	−	3.31864i	−0.144516	−	0.104997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.g.a.18.1	yes	120
3.2	odd	2		639.2.v.a.586.5		120
71.2	even	35		5041.2.a.s.1.56		60
71.4	even	35	inner	71.2.g.a.4.1	✓	120
71.69	odd	70		5041.2.a.t.1.56		60
213.146	odd	70		639.2.v.a.217.5		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.g.a.4.1	✓	120	71.4	even	35	inner
71.2.g.a.18.1	yes	120	1.1	even	1	trivial
639.2.v.a.217.5		120	213.146	odd	70
639.2.v.a.586.5		120	3.2	odd	2
5041.2.a.s.1.56		60	71.2	even	35
5041.2.a.t.1.56		60	71.69	odd	70

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.38426 + 0.214587i) q^{2} +(-0.366835 + 2.70808i) q^{3} +(3.67077 - 0.666146i) q^{4} +(-2.45585 - 1.78428i) q^{5} +(0.293509 - 6.53548i) q^{6} +(-2.65232 + 1.58469i) q^{7} +(-3.99386 + 1.10223i) q^{8} +(-4.30726 - 1.18873i) q^{9} +O(q^{10})\)	\(q+(-2.38426 + 0.214587i) q^{2} +(-0.366835 + 2.70808i) q^{3} +(3.67077 - 0.666146i) q^{4} +(-2.45585 - 1.78428i) q^{5} +(0.293509 - 6.53548i) q^{6} +(-2.65232 + 1.58469i) q^{7} +(-3.99386 + 1.10223i) q^{8} +(-4.30726 - 1.18873i) q^{9} +(6.23825 + 3.72718i) q^{10} +(-0.701962 + 1.06343i) q^{11} +(0.457414 + 10.1851i) q^{12} +(-0.743306 - 1.12606i) q^{13} +(5.98377 - 4.34746i) q^{14} +(5.73286 - 5.99610i) q^{15} +(2.30019 - 0.863275i) q^{16} +(-0.953974 + 2.93603i) q^{17} +(10.5247 + 1.90995i) q^{18} +(4.59878 + 4.80995i) q^{19} +(-10.2034 - 4.91371i) q^{20} +(-3.31851 - 7.76404i) q^{21} +(1.44546 - 2.68611i) q^{22} +(1.06965 + 4.68645i) q^{23} +(-1.51986 - 11.2200i) q^{24} +(1.30245 + 4.00853i) q^{25} +(2.01387 + 2.52531i) q^{26} +(1.57704 - 3.68966i) q^{27} +(-8.68043 + 7.58387i) q^{28} +(2.10895 + 3.91908i) q^{29} +(-12.3819 + 15.5264i) q^{30} +(-9.59648 - 3.60162i) q^{31} +(2.16674 - 1.04345i) q^{32} +(-2.62234 - 2.29107i) q^{33} +(1.64448 - 7.20496i) q^{34} +(9.34122 + 0.840725i) q^{35} +(-16.6028 - 1.49428i) q^{36} +(0.313106 - 1.37181i) q^{37} +(-11.9968 - 10.4813i) q^{38} +(3.32214 - 1.59986i) q^{39} +(11.7750 + 4.41923i) q^{40} +(0.117921 - 0.147868i) q^{41} +(9.57823 + 17.7993i) q^{42} +(4.46310 - 3.89929i) q^{43} +(-1.86834 + 4.37120i) q^{44} +(8.45695 + 10.6047i) q^{45} +(-3.55598 - 10.9442i) q^{46} +(-0.720432 - 5.31844i) q^{47} +(1.49403 + 6.54578i) q^{48} +(1.20650 - 2.24206i) q^{49} +(-3.96555 - 9.27787i) q^{50} +(-7.60106 - 3.66048i) q^{51} +(-3.47862 - 3.63836i) q^{52} +(-0.775243 - 0.140686i) q^{53} +(-2.96831 + 9.13551i) q^{54} +(3.62136 - 1.35912i) q^{55} +(8.84631 - 9.25251i) q^{56} +(-14.7127 + 10.6894i) q^{57} +(-5.86926 - 8.89155i) q^{58} +(0.358410 + 7.98061i) q^{59} +(17.0497 - 25.8292i) q^{60} +(6.72480 + 4.01788i) q^{61} +(23.6533 + 6.52790i) q^{62} +(13.3080 - 3.67278i) q^{63} +(-9.16031 + 5.47303i) q^{64} +(-0.183758 + 4.09169i) q^{65} +(6.74397 + 4.89978i) q^{66} +(-0.494350 + 0.0897113i) q^{67} +(-1.54599 + 11.4130i) q^{68} +(-13.0837 + 1.17755i) q^{69} -22.4523 q^{70} +(7.90020 - 2.93033i) q^{71} +18.5129 q^{72} +(0.804439 - 0.0724008i) q^{73} +(-0.452152 + 3.33792i) q^{74} +(-11.3332 + 2.05668i) q^{75} +(20.0852 + 14.5927i) q^{76} +(0.176629 - 3.93294i) q^{77} +(-7.57751 + 4.52735i) q^{78} +(0.628450 - 0.173441i) q^{79} +(-7.18923 - 1.98410i) q^{80} +(-2.09399 - 1.25110i) q^{81} +(-0.249423 + 0.377859i) q^{82} +(-0.0569929 - 1.26905i) q^{83} +(-17.3535 - 26.2894i) q^{84} +(7.58150 - 5.50828i) q^{85} +(-9.80443 + 10.2546i) q^{86} +(-11.3868 + 4.27355i) q^{87} +(1.63139 - 5.02090i) q^{88} +(-9.68310 - 1.75722i) q^{89} +(-22.4392 - 23.4695i) q^{90} +(3.75594 + 1.80877i) q^{91} +(7.04831 + 16.4903i) q^{92} +(13.2738 - 24.6669i) q^{93} +(2.85896 + 12.5259i) q^{94} +(-2.71162 - 20.0180i) q^{95} +(2.03090 + 6.25048i) q^{96} +(-0.808940 - 1.01438i) q^{97} +(-2.39549 + 5.60453i) q^{98} +(4.28766 - 3.74602i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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