LMFDB - Embedded newform 121.2.e.a.12.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,2,Mod(12,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("121.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	121.e (of order $11$, degree $10$, 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:	$0.966189864457$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			12.6
Character	$\chi$	$=$	121.12
Dual form			121.2.e.a.111.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0579015 + 0.0372110i) q^{2} +2.65925 q^{3} +(-0.828862 + 1.81495i) q^{4} +(0.499158 - 3.47172i) q^{5} +(-0.153975 + 0.0989535i) q^{6} +(-1.42926 + 1.64945i) q^{7} +(-0.0391344 - 0.272185i) q^{8} +4.07163 q^{9} +O(q^{10})$	\(q+(-0.0579015 + 0.0372110i) q^{2} +2.65925 q^{3} +(-0.828862 + 1.81495i) q^{4} +(0.499158 - 3.47172i) q^{5} +(-0.153975 + 0.0989535i) q^{6} +(-1.42926 + 1.64945i) q^{7} +(-0.0391344 - 0.272185i) q^{8} +4.07163 q^{9} +(0.100284 + 0.219592i) q^{10} +(-2.91165 - 1.58818i) q^{11} +(-2.20416 + 4.82643i) q^{12} +(-2.25614 + 4.94026i) q^{13} +(0.0213784 - 0.148690i) q^{14} +(1.32739 - 9.23218i) q^{15} +(-2.60084 - 3.00153i) q^{16} +(1.31580 + 0.386353i) q^{17} +(-0.235754 + 0.151510i) q^{18} +(5.33702 - 1.56709i) q^{19} +(5.88728 + 3.78352i) q^{20} +(-3.80076 + 4.38631i) q^{21} +(0.227686 - 0.0163873i) q^{22} +(-1.40004 - 1.61573i) q^{23} +(-0.104068 - 0.723810i) q^{24} +(-7.00620 - 2.05721i) q^{25} +(-0.0531982 - 0.370002i) q^{26} +2.84975 q^{27} +(-1.80902 - 3.96121i) q^{28} +(-6.10887 + 1.79373i) q^{29} +(0.266681 + 0.583950i) q^{30} +(-0.830748 - 1.81908i) q^{31} +(0.789974 + 0.231957i) q^{32} +(-7.74281 - 4.22338i) q^{33} +(-0.0905631 + 0.0265917i) q^{34} +(5.01300 + 5.78531i) q^{35} +(-3.37482 + 7.38983i) q^{36} +(2.25272 + 4.93277i) q^{37} +(-0.250708 + 0.289332i) q^{38} +(-5.99966 + 13.1374i) q^{39} -0.964485 q^{40} +(2.77487 - 1.78330i) q^{41} +(0.0568505 - 0.395404i) q^{42} +(-1.69226 - 11.7700i) q^{43} +(5.29583 - 3.96812i) q^{44} +(2.03239 - 14.1356i) q^{45} +(0.141187 + 0.0414562i) q^{46} +(7.05328 + 4.53286i) q^{47} +(-6.91631 - 7.98184i) q^{48} +(0.318292 + 2.21377i) q^{49} +(0.482220 - 0.141593i) q^{50} +(3.49904 + 1.02741i) q^{51} +(-7.09632 - 8.18959i) q^{52} +(0.336262 - 0.388067i) q^{53} +(-0.165004 + 0.106042i) q^{54} +(-6.96708 + 9.31566i) q^{55} +(0.504890 + 0.324473i) q^{56} +(14.1925 - 4.16729i) q^{57} +(0.286966 - 0.331176i) q^{58} +(1.23948 + 0.796564i) q^{59} +(15.6558 + 10.0614i) q^{60} +(5.61217 + 3.60672i) q^{61} +(0.115792 + 0.0744147i) q^{62} +(-5.81941 + 6.71596i) q^{63} +(7.56707 - 2.22189i) q^{64} +(16.0250 + 10.2987i) q^{65} +(0.605476 - 0.0435781i) q^{66} +(7.99207 - 5.13619i) q^{67} +(-1.79183 + 2.06788i) q^{68} +(-3.72305 - 4.29663i) q^{69} +(-0.505538 - 0.148439i) q^{70} +(4.71573 - 1.38466i) q^{71} +(-0.159341 - 1.10824i) q^{72} +(0.423055 + 0.488231i) q^{73} +(-0.313989 - 0.201789i) q^{74} +(-18.6313 - 5.47063i) q^{75} +(-1.57945 + 10.9853i) q^{76} +(6.78112 - 2.53270i) q^{77} +(-0.141468 - 0.983929i) q^{78} +(-0.167697 + 1.16636i) q^{79} +(-11.7187 + 7.53116i) q^{80} -4.63670 q^{81} +(-0.0943105 + 0.206511i) q^{82} +(-1.14509 + 1.32150i) q^{83} +(-4.81065 - 10.5339i) q^{84} +(1.99810 - 4.37522i) q^{85} +(0.535956 + 0.618527i) q^{86} +(-16.2450 + 4.76997i) q^{87} +(-0.318334 + 0.854660i) q^{88} +(6.13514 + 1.80144i) q^{89} +(0.408320 + 0.894097i) q^{90} +(-4.92411 - 10.7823i) q^{91} +(4.09291 - 1.20179i) q^{92} +(-2.20917 - 4.83741i) q^{93} -0.577067 q^{94} +(-2.77648 - 19.3108i) q^{95} +(2.10074 + 0.616833i) q^{96} +(1.06320 + 7.39472i) q^{97} +(-0.100806 - 0.116337i) q^{98} +(-11.8552 - 6.46649i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 6 q^{2} - 18 q^{3} - 16 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} + 4 q^{8} + 70 q^{9}+O(q^{10}) $ 100 * q - 6 * q^2 - 18 * q^3 - 16 * q^4 - 7 * q^5 - 23 * q^6 - q^7 + 4 * q^8 + 70 * q^9	\( 100 q - 6 q^{2} - 18 q^{3} - 16 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} + 4 q^{8} + 70 q^{9} - 13 q^{10} - 12 q^{11} - 51 q^{12} - 34 q^{13} - 17 q^{14} - 46 q^{15} + 10 q^{16} + 9 q^{17} - 31 q^{18} + 9 q^{19} + 21 q^{20} - 14 q^{21} - 20 q^{22} - 11 q^{23} - 72 q^{24} + 11 q^{25} + 33 q^{26} - 60 q^{27} + 49 q^{28} + 19 q^{29} + 26 q^{30} - 13 q^{31} + 44 q^{32} + q^{33} + 31 q^{34} + 39 q^{35} - 17 q^{36} - 16 q^{37} - 29 q^{38} + 16 q^{39} + 2 q^{40} + 39 q^{41} + 42 q^{42} + 39 q^{43} + 53 q^{44} - 33 q^{45} + 59 q^{46} + 21 q^{47} + 56 q^{48} - 11 q^{49} - 58 q^{50} - 139 q^{51} - 75 q^{52} - 73 q^{53} - 156 q^{54} - 34 q^{55} + 10 q^{56} - 41 q^{57} - 38 q^{58} + 33 q^{59} + 100 q^{60} + 39 q^{61} + 44 q^{62} - 76 q^{63} - 16 q^{64} + 36 q^{65} + 75 q^{66} - 4 q^{67} + 119 q^{68} + 32 q^{69} + 61 q^{70} + 5 q^{71} + 63 q^{72} + 37 q^{73} + 109 q^{74} + 58 q^{75} - 91 q^{76} - 53 q^{77} - 24 q^{78} - 9 q^{79} - 36 q^{80} + 28 q^{81} + 33 q^{82} + 79 q^{83} + 176 q^{84} - 11 q^{85} + 85 q^{86} + 76 q^{87} + 33 q^{88} - 48 q^{89} - 89 q^{90} - 14 q^{91} - 113 q^{92} + 31 q^{93} - 38 q^{94} + 21 q^{95} + 84 q^{96} + 40 q^{97} - 22 q^{98} - 53 q^{99}+O(q^{100}) \) 100 * q - 6 * q^2 - 18 * q^3 - 16 * q^4 - 7 * q^5 - 23 * q^6 - q^7 + 4 * q^8 + 70 * q^9 - 13 * q^10 - 12 * q^11 - 51 * q^12 - 34 * q^13 - 17 * q^14 - 46 * q^15 + 10 * q^16 + 9 * q^17 - 31 * q^18 + 9 * q^19 + 21 * q^20 - 14 * q^21 - 20 * q^22 - 11 * q^23 - 72 * q^24 + 11 * q^25 + 33 * q^26 - 60 * q^27 + 49 * q^28 + 19 * q^29 + 26 * q^30 - 13 * q^31 + 44 * q^32 + q^33 + 31 * q^34 + 39 * q^35 - 17 * q^36 - 16 * q^37 - 29 * q^38 + 16 * q^39 + 2 * q^40 + 39 * q^41 + 42 * q^42 + 39 * q^43 + 53 * q^44 - 33 * q^45 + 59 * q^46 + 21 * q^47 + 56 * q^48 - 11 * q^49 - 58 * q^50 - 139 * q^51 - 75 * q^52 - 73 * q^53 - 156 * q^54 - 34 * q^55 + 10 * q^56 - 41 * q^57 - 38 * q^58 + 33 * q^59 + 100 * q^60 + 39 * q^61 + 44 * q^62 - 76 * q^63 - 16 * q^64 + 36 * q^65 + 75 * q^66 - 4 * q^67 + 119 * q^68 + 32 * q^69 + 61 * q^70 + 5 * q^71 + 63 * q^72 + 37 * q^73 + 109 * q^74 + 58 * q^75 - 91 * q^76 - 53 * q^77 - 24 * q^78 - 9 * q^79 - 36 * q^80 + 28 * q^81 + 33 * q^82 + 79 * q^83 + 176 * q^84 - 11 * q^85 + 85 * q^86 + 76 * q^87 + 33 * q^88 - 48 * q^89 - 89 * q^90 - 14 * q^91 - 113 * q^92 + 31 * q^93 - 38 * q^94 + 21 * q^95 + 84 * q^96 + 40 * q^97 - 22 * q^98 - 53 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	−0.0579015	+	0.0372110i	−0.0409425	+	0.0263122i	−0.560952	−	0.827848i	$-0.689565\pi$
$2$	−0.0579015	+	0.0372110i	−0.0409425	+	0.0263122i	0.520009	+	0.854160i	$0.325928\pi$
$3$	2.65925			1.53532			0.767661	−	0.640857i	$-0.221421\pi$
$3$	2.65925			1.53532			0.767661	+	0.640857i	$0.221421\pi$
$4$	−0.828862	+	1.81495i	−0.414431	+	0.907477i
$5$	0.499158	−	3.47172i	0.223230	−	1.55260i	−0.502474	−	0.864592i	$-0.667577\pi$
$5$	0.499158	−	3.47172i	0.223230	−	1.55260i	0.725704	−	0.688007i	$-0.241514\pi$
$6$	−0.153975	+	0.0989535i	−0.0628599	+	0.0403976i
$7$	−1.42926	+	1.64945i	−0.540209	+	0.623434i	−0.958574	−	0.284845i	$-0.908058\pi$
$7$	−1.42926	+	1.64945i	−0.540209	+	0.623434i	0.418365	+	0.908279i	$0.362603\pi$
$8$	−0.0391344	−	0.272185i	−0.0138361	−	0.0962321i
$9$	4.07163			1.35721
$10$	0.100284	+	0.219592i	0.0317126	+	0.0694410i
$11$	−2.91165	−	1.58818i	−0.877894	−	0.478854i
$11$	−2.91165	−	1.58818i	−0.877894	−	0.478854i
$12$	−2.20416	+	4.82643i	−0.636285	+	1.39327i
$13$	−2.25614	+	4.94026i	−0.625741	+	1.37018i	0.285527	+	0.958371i	$0.407831\pi$
$13$	−2.25614	+	4.94026i	−0.625741	+	1.37018i	−0.911269	+	0.411812i	$0.864896\pi$
$14$	0.0213784	−	0.148690i	0.00571361	−	0.0397390i
$15$	1.32739	−	9.23218i	0.342730	−	2.38374i
$16$	−2.60084	−	3.00153i	−0.650211	−	0.750384i
$17$	1.31580	+	0.386353i	0.319128	+	0.0937043i	0.437373	−	0.899280i	$-0.355909\pi$
$17$	1.31580	+	0.386353i	0.319128	+	0.0937043i	−0.118246	+	0.992984i	$0.537727\pi$
$18$	−0.235754	+	0.151510i	−0.0555676	+	0.0357112i
$19$	5.33702	−	1.56709i	1.22440	−	0.359515i	0.395263	−	0.918568i	$-0.370653\pi$
$19$	5.33702	−	1.56709i	1.22440	−	0.359515i	0.829132	+	0.559053i	$0.188835\pi$
$20$	5.88728	+	3.78352i	1.31644	+	0.846022i
$21$	−3.80076	+	4.38631i	−0.829394	+	0.957171i
$22$	0.227686	−	0.0163873i	0.0485429	−	0.00349379i
$23$	−1.40004	−	1.61573i	−0.291928	−	0.336902i	0.590773	−	0.806838i	$-0.298823\pi$
$23$	−1.40004	−	1.61573i	−0.291928	−	0.336902i	−0.882701	+	0.469935i	$0.844277\pi$
$24$	−0.104068	−	0.723810i	−0.0212428	−	0.147747i
$25$	−7.00620	−	2.05721i	−1.40124	−	0.411441i
$26$	−0.0531982	−	0.370002i	−0.0104330	−	0.0725633i
$27$	2.84975			0.548434
$28$	−1.80902	−	3.96121i	−0.341873	−	0.748597i
$29$	−6.10887	+	1.79373i	−1.13439	+	0.333086i	−0.794431	−	0.607354i	$-0.792231\pi$
$29$	−6.10887	+	1.79373i	−1.13439	+	0.333086i	−0.339957	+	0.940441i	$0.610413\pi$
$30$	0.266681	+	0.583950i	0.0486891	+	0.106614i
$31$	−0.830748	−	1.81908i	−0.149207	−	0.326717i	0.820240	−	0.572020i	$-0.193840\pi$
$31$	−0.830748	−	1.81908i	−0.149207	−	0.326717i	−0.969447	+	0.245303i	$0.921113\pi$
$32$	0.789974	+	0.231957i	0.139649	+	0.0410046i
$33$	−7.74281	−	4.22338i	−1.34785	−	0.735195i
$34$	−0.0905631	+	0.0265917i	−0.0155314	+	0.00456045i
$35$	5.01300	+	5.78531i	0.847352	+	0.977897i
$36$	−3.37482	+	7.38983i	−0.562470	+	1.23164i
$37$	2.25272	+	4.93277i	0.370345	+	0.810943i	0.999435	+	0.0336104i	$0.0107005\pi$
$37$	2.25272	+	4.93277i	0.370345	+	0.810943i	−0.629090	+	0.777333i	$0.716572\pi$
$38$	−0.250708	+	0.289332i	−0.0406702	+	0.0469359i
$39$	−5.99966	+	13.1374i	−0.960714	+	2.10367i
$40$	−0.964485			−0.152498
$41$	2.77487	−	1.78330i	0.433361	−	0.278504i	−0.305719	−	0.952122i	$-0.598897\pi$
$41$	2.77487	−	1.78330i	0.433361	−	0.278504i	0.739080	+	0.673617i	$0.235260\pi$
$42$	0.0568505	−	0.395404i	0.00877222	−	0.0610121i
$43$	−1.69226	−	11.7700i	−0.258068	−	1.79490i	−0.546561	−	0.837419i	$-0.684063\pi$
$43$	−1.69226	−	11.7700i	−0.258068	−	1.79490i	0.288493	−	0.957482i	$-0.406846\pi$
$44$	5.29583	−	3.96812i	0.798376	−	0.598217i
$45$	2.03239	−	14.1356i	0.302970	−	2.10720i
$46$	0.141187	+	0.0414562i	0.0208169	+	0.00611239i
$47$	7.05328	+	4.53286i	1.02883	+	0.661186i	0.942199	−	0.335055i	$-0.108755\pi$
$47$	7.05328	+	4.53286i	1.02883	+	0.661186i	0.0866272	+	0.996241i	$0.472391\pi$
$48$	−6.91631	−	7.98184i	−0.998283	−	1.15208i
$49$	0.318292	+	2.21377i	0.0454703	+	0.316253i
$50$	0.482220	−	0.141593i	0.0681962	−	0.0200242i
$51$	3.49904	+	1.02741i	0.489963	+	0.143866i
$52$	−7.09632	−	8.18959i	−0.984083	−	1.13569i
$53$	0.336262	−	0.388067i	0.0461892	−	0.0533052i	−0.732185	−	0.681106i	$-0.761499\pi$
$53$	0.336262	−	0.388067i	0.0461892	−	0.0533052i	0.778374	+	0.627801i	$0.216045\pi$
$54$	−0.165004	+	0.106042i	−0.0224543	+	0.0144305i
$55$	−6.96708	+	9.31566i	−0.939441	+	1.25612i
$56$	0.504890	+	0.324473i	0.0674687	+	0.0433595i
$57$	14.1925	−	4.16729i	1.87984	−	0.551971i
$58$	0.286966	−	0.331176i	0.0376805	−	0.0434856i
$59$	1.23948	+	0.796564i	0.161366	+	0.103704i	0.618832	−	0.785524i	$-0.287606\pi$
$59$	1.23948	+	0.796564i	0.161366	+	0.103704i	−0.457465	+	0.889227i	$0.651243\pi$
$60$	15.6558	+	10.0614i	2.02115	+	1.29891i
$61$	5.61217	+	3.60672i	0.718564	+	0.461793i	0.848137	−	0.529777i	$-0.177724\pi$
$61$	5.61217	+	3.60672i	0.718564	+	0.461793i	−0.129573	+	0.991570i	$0.541361\pi$
$62$	0.115792	+	0.0744147i	0.0147055	+	0.00945067i
$63$	−5.81941	+	6.71596i	−0.733177	+	0.846131i
$64$	7.56707	−	2.22189i	0.945884	−	0.277737i
$65$	16.0250	+	10.2987i	1.98766	+	1.27739i
$66$	0.605476	−	0.0435781i	0.0745289	−	0.00536409i
$67$	7.99207	−	5.13619i	0.976387	−	0.627486i	0.0479007	−	0.998852i	$-0.484747\pi$
$67$	7.99207	−	5.13619i	0.976387	−	0.627486i	0.928487	+	0.371366i	$0.121111\pi$
$68$	−1.79183	+	2.06788i	−0.217291	+	0.250767i
$69$	−3.72305	−	4.29663i	−0.448203	−	0.517253i
$70$	−0.505538	−	0.148439i	−0.0604233	−	0.0177419i
$71$	4.71573	−	1.38466i	0.559654	−	0.164329i	0.0103419	−	0.999947i	$-0.496708\pi$
$71$	4.71573	−	1.38466i	0.559654	−	0.164329i	0.549312	+	0.835617i	$0.314890\pi$
$72$	−0.159341	−	1.10824i	−0.0187785	−	0.130607i
$73$	0.423055	+	0.488231i	0.0495148	+	0.0571432i	0.779967	−	0.625821i	$-0.215236\pi$
$73$	0.423055	+	0.488231i	0.0495148	+	0.0571432i	−0.730452	+	0.682964i	$0.760691\pi$
$74$	−0.313989	−	0.201789i	−0.0365005	−	0.0234575i
$75$	−18.6313	−	5.47063i	−2.15135	−	0.631694i
$76$	−1.57945	+	10.9853i	−0.181176	+	1.26011i
$77$	6.78112	−	2.53270i	0.772780	−	0.288628i
$78$	−0.141468	−	0.983929i	−0.0160181	−	0.111408i
$79$	−0.167697	+	1.16636i	−0.0188674	+	0.131226i	−0.997078	−	0.0763890i	$-0.975661\pi$
$79$	−0.167697	+	1.16636i	−0.0188674	+	0.131226i	0.978211	+	0.207615i	$0.0665700\pi$
$80$	−11.7187	+	7.53116i	−1.31019	+	0.842009i
$81$	−4.63670			−0.515189
$82$	−0.0943105	+	0.206511i	−0.0104149	+	0.0228053i
$83$	−1.14509	+	1.32150i	−0.125690	+	0.145054i	−0.815106	−	0.579311i	$-0.803322\pi$
$83$	−1.14509	+	1.32150i	−0.125690	+	0.145054i	0.689416	+	0.724365i	$0.257867\pi$
$84$	−4.81065	−	10.5339i	−0.524885	−	1.14934i
$85$	1.99810	−	4.37522i	0.216724	−	0.474560i
$86$	0.535956	+	0.618527i	0.0577937	+	0.0666974i
$87$	−16.2450	+	4.76997i	−1.74165	+	0.511395i
$88$	−0.318334	+	0.854660i	−0.0339345	+	0.0911071i
$89$	6.13514	+	1.80144i	0.650323	+	0.190952i	0.590223	−	0.807240i	$-0.299040\pi$
$89$	6.13514	+	1.80144i	0.650323	+	0.190952i	0.0601003	+	0.998192i	$0.480858\pi$
$90$	0.408320	+	0.894097i	0.0430407	+	0.0942461i
$91$	−4.92411	−	10.7823i	−0.516187	−	1.13029i
$92$	4.09291	−	1.20179i	0.426715	−	0.125295i
$93$	−2.20917	−	4.83741i	−0.229080	−	0.501616i
$94$	−0.577067			−0.0595200
$95$	−2.77648	−	19.3108i	−0.284861	−	1.98125i
$96$	2.10074	+	0.616833i	0.214406	+	0.0629553i
$97$	1.06320	+	7.39472i	0.107952	+	0.750820i	0.969844	+	0.243728i	$0.0783705\pi$
$97$	1.06320	+	7.39472i	0.107952	+	0.750820i	−0.861892	+	0.507092i	$0.830720\pi$
$98$	−0.100806	−	0.116337i	−0.0101830	−	0.0117518i
$99$	−11.8552	−	6.46649i	−1.19149	−	0.649906i
$100$	9.54091	−	11.0108i	0.954091	−	1.10108i
$101$	−15.1644	−	9.74560i	−1.50892	−	0.969723i	−0.993628	−	0.112708i	$-0.964048\pi$
$101$	−15.1644	−	9.74560i	−1.50892	−	0.969723i	−0.515291	−	0.857015i	$-0.672316\pi$
$102$	−0.240830	+	0.0707142i	−0.0238458	+	0.00700175i
$103$	−2.72223	+	1.74947i	−0.268229	+	0.172380i	−0.667841	−	0.744304i	$-0.732781\pi$
$103$	−2.72223	+	1.74947i	−0.268229	+	0.172380i	0.399612	+	0.916685i	$0.369145\pi$
$104$	1.43296	+	0.420755i	0.140513	+	0.0412584i
$105$	13.3309	+	15.3846i	1.30096	+	1.50139i
$106$	−0.00502970	+	0.0349823i	−0.000488528	+	0.00339778i
$107$	0.189625	−	1.31887i	0.0183317	−	0.127500i	−0.978601	−	0.205769i	$-0.934030\pi$
$107$	0.189625	−	1.31887i	0.0183317	−	0.127500i	0.996932	+	0.0782695i	$0.0249395\pi$
$108$	−2.36205	+	5.17216i	−0.227288	+	0.497691i
$109$	−5.21183	+	11.4123i	−0.499202	+	1.09310i	0.477525	+	0.878618i	$0.341534\pi$
$109$	−5.21183	+	11.4123i	−0.499202	+	1.09310i	−0.976728	+	0.214483i	$0.931193\pi$
$110$	0.0567592	−	0.798643i	0.00541177	−	0.0761476i
$111$	5.99056	+	13.1175i	0.568599	+	1.24506i
$112$	8.66816			0.819064
$113$	1.44831	+	10.0732i	0.136245	+	0.947607i	0.937178	+	0.348852i	$0.113429\pi$
$113$	1.44831	+	10.0732i	0.136245	+	0.947607i	−0.800932	+	0.598755i	$0.795662\pi$
$114$	−0.666696	+	0.769409i	−0.0624418	+	0.0720617i
$115$	−6.30818	+	4.05402i	−0.588241	+	0.378040i
$116$	1.80788	−	12.5741i	0.167857	−	1.16747i
$117$	−9.18619	+	20.1149i	−0.849263	+	1.85963i
$118$	−0.101409			−0.00933541
$119$	−2.51788	+	1.61814i	−0.230814	+	0.148335i
$120$	−2.56481			−0.234134
$121$	5.95537	+	9.24844i	0.541397	+	0.840767i
$122$	−0.459162			−0.0415706
$123$	7.37907	−	4.74224i	0.665349	−	0.427594i
$124$	3.99013			0.358324
$125$	−3.35406	+	7.34437i	−0.299996	+	0.656901i
$126$	0.0870448	−	0.605410i	0.00775457	−	0.0539342i
$127$	−1.17059	+	0.752291i	−0.103873	+	0.0667550i	−0.591546	−	0.806271i	$-0.701482\pi$
$127$	−1.17059	+	0.752291i	−0.103873	+	0.0667550i	0.487673	+	0.873026i	$0.337846\pi$
$128$	−1.43379	+	1.65468i	−0.126730	+	0.146255i
$129$	−4.50016	−	31.2993i	−0.396217	−	2.75575i
$130$	−1.31110			−0.114991
$131$	−7.64354	−	16.7370i	−0.667819	−	1.46232i	−0.875052	−	0.484028i	$-0.839173\pi$
$131$	−7.64354	−	16.7370i	−0.667819	−	1.46232i	0.207233	−	0.978292i	$-0.433554\pi$
$132$	14.0830	−	10.5523i	1.22576	−	0.918456i
$133$	−5.04313	+	11.0429i	−0.437295	+	0.957543i
$134$	−0.271630	+	0.594786i	−0.0234652	+	0.0513817i
$135$	1.42247	−	9.89351i	0.122427	−	0.851498i
$136$	0.0536667	−	0.373260i	0.00460188	−	0.0320068i
$137$	2.87330	+	3.31596i	0.245482	+	0.283302i	0.865097	−	0.501604i	$-0.167257\pi$
$137$	2.87330	+	3.31596i	0.245482	+	0.283302i	−0.619615	+	0.784906i	$0.712711\pi$
$138$	0.375452	+	0.110243i	0.0319606	+	0.00938448i
$139$	−4.96872	+	3.19320i	−0.421441	+	0.270844i	−0.734126	−	0.679013i	$-0.762408\pi$
$139$	−4.96872	+	3.19320i	−0.421441	+	0.270844i	0.312685	+	0.949857i	$0.398772\pi$
$140$	−14.6552	+	4.30315i	−1.23859	+	0.363682i
$141$	18.7565	+	12.0540i	1.57958	+	1.01513i
$142$	−0.221523	+	0.255651i	−0.0185898	+	0.0214538i
$143$	14.4151	−	10.8011i	1.20545	−	0.903237i
$144$	−10.5897	−	12.2211i	−0.882474	−	1.01843i
$145$	3.17802	+	22.1036i	0.263920	+	1.83561i
$146$	−0.0426631	−	0.0125270i	−0.00353082	−	0.00103674i
$147$	0.846419	+	5.88698i	0.0698115	+	0.485550i
$148$	−10.8200			−0.889395
$149$	−3.61720	−	7.92056i	−0.296332	−	0.648877i	0.701640	−	0.712532i	$-0.252452\pi$
$149$	−3.61720	−	7.92056i	−0.296332	−	0.648877i	−0.997972	+	0.0636547i	$0.979724\pi$
$150$	1.28235	−	0.376530i	0.104703	−	0.0307436i
$151$	−2.14465	−	4.69612i	−0.174529	−	0.382165i	0.802071	−	0.597228i	$-0.203731\pi$
$151$	−2.14465	−	4.69612i	−0.174529	−	0.382165i	−0.976600	+	0.215063i	$0.931004\pi$
$152$	−0.635399	−	1.39133i	−0.0515377	−	0.112852i
$153$	5.35744	+	1.57309i	0.433124	+	0.127177i
$154$	−0.298392	+	0.398979i	−0.0240451	+	0.0321507i
$155$	−6.73002	+	1.97611i	−0.540568	+	0.158725i
$156$	−18.8709	−	21.7782i	−1.51088	−	1.74365i
$157$	3.83086	−	8.38841i	0.305736	−	0.669468i	−0.692936	−	0.720999i	$-0.743683\pi$
$157$	3.83086	−	8.38841i	0.305736	−	0.669468i	0.998671	+	0.0515317i	$0.0164103\pi$
$158$	−0.0336915	−	0.0737741i	−0.00268035	−	0.00586915i
$159$	0.894207	−	1.03197i	0.0709152	−	0.0818405i
$160$	1.19961	−	2.62678i	0.0948376	−	0.207665i
$161$	4.66607			0.367738
$162$	0.268472	−	0.172536i	0.0210931	−	0.0135557i
$163$	0.984334	−	6.84619i	0.0770990	−	0.536235i	−0.914267	−	0.405112i	$-0.867233\pi$
$163$	0.984334	−	6.84619i	0.0770990	−	0.536235i	0.991366	−	0.131123i	$-0.0418584\pi$
$164$	0.936624	+	6.51437i	0.0731381	+	0.508686i
$165$	−18.5272	+	24.7727i	−1.44234	+	1.92855i
$166$	0.0171279	−	0.119127i	0.00132938	−	0.00924605i
$167$	−12.3680	−	3.63157i	−0.957064	−	0.281019i	−0.234339	−	0.972155i	$-0.575292\pi$
$167$	−12.3680	−	3.63157i	−0.957064	−	0.281019i	−0.722725	+	0.691136i	$0.757111\pi$
$168$	1.34263	+	0.862856i	0.103586	+	0.0665708i
$169$	−10.8028	−	12.4671i	−0.830987	−	0.959011i
$170$	0.0471137	+	0.327683i	0.00361346	+	0.0251321i
$171$	21.7304	−	6.38061i	1.66176	−	0.487938i
$172$	22.7646	+	6.68429i	1.73578	+	0.509672i
$173$	14.8765	+	17.1684i	1.13104	+	1.30529i	0.946588	+	0.322445i	$0.104505\pi$
$173$	14.8765	+	17.1684i	1.13104	+	1.30529i	0.184450	+	0.982842i	$0.440950\pi$
$174$	0.763116	−	0.880682i	0.0578516	−	0.0667644i
$175$	13.4069	−	8.61610i	1.01347	−	0.651316i
$176$	2.80576	+	12.8700i	0.211492	+	0.970114i
$177$	3.29609	+	2.11827i	0.247749	+	0.159219i
$178$	−0.422267	+	0.123989i	−0.0316502	+	0.00929335i
$179$	−10.9399	+	12.6253i	−0.817686	+	0.943660i	−0.999211	−	0.0397262i	$-0.987351\pi$
$179$	−10.9399	+	12.6253i	−0.817686	+	0.943660i	0.181524	+	0.983386i	$0.441897\pi$
$180$	23.9708	+	15.4051i	1.78668	+	1.14823i
$181$	−19.9805	−	12.8407i	−1.48514	−	0.954442i	−0.996642	−	0.0818769i	$-0.973909\pi$
$181$	−19.9805	−	12.8407i	−1.48514	−	0.954442i	−0.488498	−	0.872565i	$-0.662455\pi$
$182$	0.686334	+	0.441080i	0.0508745	+	0.0326950i
$183$	14.9242	+	9.59119i	1.10323	+	0.709001i
$184$	−0.384988	+	0.444300i	−0.0283817	+	0.0327542i
$185$	18.2497	−	5.35858i	1.34174	−	0.393971i
$186$	0.307919	+	0.197888i	0.0225777	+	0.0145098i
$187$	−3.21754	−	3.21465i	−0.235290	−	0.235078i
$188$	−14.0731	+	9.04426i	−1.02639	+	0.659620i
$189$	−4.07302	+	4.70052i	−0.296269	+	0.341912i
$190$	0.879338	+	1.01481i	0.0637939	+	0.0736220i
$191$	−20.8013	−	6.10781i	−1.50513	−	0.441945i	−0.577795	−	0.816182i	$-0.696087\pi$
$191$	−20.8013	−	6.10781i	−1.50513	−	0.441945i	−0.927333	+	0.374237i	$0.877905\pi$
$192$	20.1228	−	5.90858i	1.45224	−	0.426415i
$193$	−1.63735	−	11.3880i	−0.117859	−	0.819728i	−0.959906	−	0.280323i	$-0.909558\pi$
$193$	−1.63735	−	11.3880i	−0.117859	−	0.819728i	0.842047	−	0.539405i	$-0.181351\pi$
$194$	−0.336726	−	0.388602i	−0.0241755	−	0.0279000i
$195$	42.6146	+	27.3868i	3.05170	+	1.96121i
$196$	−4.28171	−	1.25722i	−0.305837	−	0.0898017i
$197$	0.496564	−	3.45368i	0.0353787	−	0.246064i	−0.964456	−	0.264243i	$-0.914878\pi$
$197$	0.496564	−	3.45368i	0.0353787	−	0.246064i	0.999835	+	0.0181790i	$0.00578687\pi$
$198$	0.927055	−	0.0667232i	0.0658830	−	0.00474181i
$199$	1.83928	+	12.7924i	0.130383	+	0.906832i	0.945055	+	0.326911i	$0.106008\pi$
$199$	1.83928	+	12.7924i	0.130383	+	0.906832i	−0.814672	+	0.579921i	$0.803083\pi$
$200$	−0.285758	+	1.98749i	−0.0202062	+	0.140537i
$201$	21.2530	−	13.6584i	1.49907	−	0.963393i
$202$	1.24069			0.0872945
$203$	5.77248	−	12.6400i	0.405149	−	0.887152i
$204$	−4.76492	+	5.49902i	−0.333611	+	0.385008i
$205$	−4.80601	−	10.5237i	−0.335666	−	0.735007i
$206$	0.0925215	−	0.202594i	0.00644628	−	0.0141154i
$207$	−5.70043	−	6.57865i	−0.396207	−	0.457248i
$208$	20.6962	−	6.07697i	1.43503	−	0.421362i
$209$	−18.0283	−	3.91333i	−1.24705	−	0.270691i
$210$	−1.34435	−	0.394738i	−0.0927692	−	0.0272395i
$211$	5.54646	+	12.1451i	0.381834	+	0.836101i	0.998794	+	0.0491055i	$0.0156371\pi$
$211$	5.54646	+	12.1451i	0.381834	+	0.836101i	−0.616959	+	0.786995i	$0.711636\pi$
$212$	0.425610	+	0.931955i	0.0292310	+	0.0640070i
$213$	12.5403	−	3.68217i	0.859249	−	0.252298i
$214$	0.0380969	+	0.0834205i	0.00260425	+	0.00570251i
$215$	−41.7067			−2.84437
$216$	−0.111523	−	0.775659i	−0.00758818	−	0.0527769i
$217$	4.18784	+	1.22966i	0.284289	+	0.0834749i
$218$	−0.122891	−	0.854726i	−0.00832324	−	0.0578894i
$219$	1.12501	+	1.29833i	0.0760212	+	0.0877331i
$220$	−11.1328	−	20.3663i	−0.750570	−	1.37310i
$221$	−4.87731	+	5.62872i	−0.328083	+	0.378628i
$222$	−0.834978	−	0.536608i	−0.0560400	−	0.0360147i
$223$	−1.50540	+	0.442025i	−0.100809	+	0.0296002i	−0.331748	−	0.943368i	$-0.607638\pi$
$223$	−1.50540	+	0.442025i	−0.100809	+	0.0296002i	0.230939	+	0.972968i	$0.425820\pi$
$224$	−1.51168	+	0.971497i	−0.101003	+	0.0649108i
$225$	−28.5267	−	8.37619i	−1.90178	−	0.558412i
$226$	−0.458693	−	0.529360i	−0.0305118	−	0.0352125i
$227$	2.91143	−	20.2495i	0.193239	−	1.34400i	−0.630127	−	0.776492i	$-0.716997\pi$
$227$	2.91143	−	20.2495i	0.193239	−	1.34400i	0.823365	−	0.567512i	$-0.192094\pi$
$228$	−4.20017	+	29.2128i	−0.278163	+	1.93467i
$229$	7.91960	−	17.3415i	0.523342	−	1.14596i	−0.444817	−	0.895621i	$-0.646731\pi$
$229$	7.91960	−	17.3415i	0.523342	−	1.14596i	0.968159	−	0.250337i	$-0.0805414\pi$
$230$	0.214399	−	0.469468i	0.0141370	−	0.0309558i
$231$	18.0327	−	6.73509i	1.18647	−	0.443137i
$232$	0.727292	+	1.59255i	0.0477491	+	0.104556i
$233$	13.7668			0.901893			0.450947	−	0.892551i	$-0.351086\pi$
$233$	13.7668			0.901893			0.450947	+	0.892551i	$0.351086\pi$
$234$	−0.216604	−	1.50651i	−0.0141598	−	0.0984838i
$235$	19.2575	−	22.2244i	1.25622	−	1.44976i
$236$	−2.47308	+	1.58935i	−0.160984	+	0.103458i
$237$	−0.445949	+	3.10165i	−0.0289675	+	0.201474i
$238$	0.0855763	−	0.187386i	0.00554709	−	0.0121464i
$239$	−10.7284			−0.693963			−0.346982	−	0.937872i	$-0.612793\pi$
$239$	−10.7284			−0.693963			−0.346982	+	0.937872i	$0.612793\pi$
$240$	−31.1630	+	20.0273i	−2.01156	+	1.29275i
$241$	−8.89384			−0.572902			−0.286451	−	0.958095i	$-0.592476\pi$
$241$	−8.89384			−0.572902			−0.286451	+	0.958095i	$0.592476\pi$
$242$	−0.688968	−	0.313893i	−0.0442886	−	0.0201778i
$243$	−20.8794			−1.33941
$244$	−11.1977	+	7.19636i	−0.716862	+	0.460700i
$245$	7.84446			0.501164
$246$	−0.250796	+	0.549166i	−0.0159901	+	0.0350135i
$247$	−4.29924	+	29.9018i	−0.273554	+	1.90261i
$248$	−0.462617	+	0.297306i	−0.0293762	+	0.0188790i
$249$	−3.04509	+	3.51422i	−0.192975	+	0.222704i
$250$	−0.0790864	−	0.550058i	−0.00500186	−	0.0347887i
$251$	−9.83938			−0.621056			−0.310528	−	0.950564i	$-0.600506\pi$
$251$	−9.83938			−0.621056			−0.310528	+	0.950564i	$0.600506\pi$
$252$	−7.36567	−	16.1286i	−0.463994	−	1.01600i
$253$	1.51034	+	6.92793i	0.0949544	+	0.435555i
$254$	0.0397852	−	0.0871175i	0.00249635	−	0.00546624i
$255$	5.31345	−	11.6348i	0.332741	−	0.728601i
$256$	−2.22329	+	15.4634i	−0.138956	+	0.966460i
$257$	−0.295904	+	2.05806i	−0.0184580	+	0.128378i	−0.996967	−	0.0778262i	$-0.975202\pi$
$257$	−0.295904	+	2.05806i	−0.0184580	+	0.128378i	0.978509	+	0.206204i	$0.0661112\pi$
$258$	1.42524	+	1.64482i	0.0887318	+	0.102402i
$259$	−11.3561	−	3.33445i	−0.705633	−	0.207193i
$260$	−31.9741	+	20.5485i	−1.98295	+	1.27437i
$261$	−24.8731	+	7.30339i	−1.53960	+	0.452069i
$262$	1.06537	+	0.684674i	0.0658190	+	0.0422993i
$263$	8.75467	−	10.1034i	0.539836	−	0.623004i	−0.418648	−	0.908148i	$-0.637496\pi$
$263$	8.75467	−	10.1034i	0.539836	−	0.623004i	0.958485	+	0.285144i	$0.0920415\pi$
$264$	−0.846531	+	2.27276i	−0.0521004	+	0.139879i
$265$	−1.17941	−	1.36111i	−0.0724507	−	0.0836126i
$266$	−0.118913	−	0.827061i	−0.00729105	−	0.0507104i
$267$	16.3149	+	4.79049i	0.998455	+	0.293173i
$268$	2.69763	+	18.7625i	0.164784	+	1.14610i
$269$	10.3985			0.634008			0.317004	−	0.948424i	$-0.397323\pi$
$269$	10.3985			0.634008			0.317004	+	0.948424i	$0.397323\pi$
$270$	0.285784	+	0.625780i	0.0173923	+	0.0380838i
$271$	22.3182	−	6.55322i	1.35574	−	0.398080i	0.478478	−	0.878100i	$-0.341189\pi$
$271$	22.3182	−	6.55322i	1.35574	−	0.398080i	0.877258	+	0.480020i	$0.159370\pi$
$272$	−2.26253	−	4.95425i	−0.137186	−	0.300396i
$273$	−13.0945	−	28.6729i	−0.792514	−	1.73536i
$274$	−0.289758	−	0.0850807i	−0.0175049	−	0.00513991i
$275$	17.1324	+	17.1170i	1.03312	+	1.03219i
$276$	10.8841	−	3.19585i	0.655145	−	0.192368i
$277$	1.89953	+	2.19218i	0.114132	+	0.131715i	0.809940	−	0.586512i	$-0.199499\pi$
$277$	1.89953	+	2.19218i	0.114132	+	0.131715i	−0.695809	+	0.718227i	$0.744954\pi$
$278$	0.168874	−	0.369782i	0.0101284	−	0.0221781i
$279$	−3.38250	−	7.40665i	−0.202505	−	0.443424i
$280$	1.37850	−	1.59087i	0.0823810	−	0.0950727i
$281$	−3.62114	+	7.92920i	−0.216019	+	0.473016i	−0.986357	−	0.164620i	$-0.947360\pi$
$281$	−3.62114	+	7.92920i	−0.216019	+	0.473016i	0.770338	+	0.637636i	$0.220088\pi$
$282$	−1.53457			−0.0913822
$283$	−10.8134	+	6.94936i	−0.642791	+	0.413097i	−0.821026	−	0.570891i	$-0.806598\pi$
$283$	−10.8134	+	6.94936i	−0.642791	+	0.413097i	0.178235	+	0.983988i	$0.442961\pi$
$284$	−1.39559	+	9.70653i	−0.0828129	+	0.575977i
$285$	−7.38336	−	51.3524i	−0.437353	−	3.04185i
$286$	−0.432735	+	1.16180i	−0.0255882	+	0.0686988i
$287$	−1.02454	+	7.12580i	−0.0604764	+	0.420623i
$288$	3.21648	+	0.944445i	0.189533	+	0.0556520i
$289$	−12.7193	−	8.17417i	−0.748192	−	0.480834i
$290$	−1.00651	−	1.16157i	−0.0591043	−	0.0682100i
$291$	2.82732	+	19.6644i	0.165740	+	1.15275i
$292$	−1.23677	+	0.363149i	−0.0723766	+	0.0212517i
$293$	20.5275	+	6.02742i	1.19923	+	0.352126i	0.819558	−	0.572996i	$-0.194219\pi$
$293$	20.5275	+	6.02742i	1.19923	+	0.352126i	0.379672	+	0.925121i	$0.376037\pi$
$294$	−0.268069	−	0.309368i	−0.0156341	−	0.0180427i
$295$	3.38414	−	3.90551i	0.197032	−	0.227387i
$296$	1.25447	−	0.806199i	0.0729146	−	0.0468594i
$297$	−8.29745	−	4.52591i	−0.481467	−	0.262620i
$298$	0.504173	+	0.324012i	0.0292060	+	0.0187695i
$299$	11.1408	−	3.27123i	0.644289	−	0.189180i
$300$	25.3717	−	29.2805i	1.46484	−	1.69051i
$301$	21.8326	+	14.0310i	1.25841	+	0.808733i
$302$	0.298926	+	0.192108i	0.0172012	+	0.0110546i
$303$	−40.3261	−	25.9160i	−2.31668	−	1.48884i
$304$	−18.5844	−	11.9435i	−1.06589	−	0.685006i
$305$	15.3229	−	17.6835i	0.877385	−	1.01256i
$306$	−0.368740	+	0.108272i	−0.0210795	+	0.00618949i
$307$	21.8673	+	14.0533i	1.24803	+	0.802062i	0.986600	−	0.163160i	$-0.0521687\pi$
$307$	21.8673	+	14.0533i	1.24803	+	0.802062i	0.261433	+	0.965222i	$0.415805\pi$
$308$	−1.02388	+	14.4067i	−0.0583408	+	0.820897i
$309$	−7.23910	+	4.65229i	−0.411818	+	0.264659i
$310$	0.316145	−	0.364851i	0.0179558	−	0.0207221i
$311$	9.13420	+	10.5414i	0.517953	+	0.597750i	0.953117	−	0.302602i	$-0.0978551\pi$
$311$	9.13420	+	10.5414i	0.517953	+	0.597750i	−0.435164	+	0.900351i	$0.643310\pi$
$312$	3.81061	+	1.11889i	0.215733	+	0.0633449i
$313$	−19.1838	+	5.63287i	−1.08433	+	0.318389i	−0.774611	−	0.632438i	$-0.782054\pi$
$313$	−19.1838	+	5.63287i	−1.08433	+	0.318389i	−0.309722	+	0.950827i	$0.600236\pi$
$314$	0.0903289	+	0.628251i	0.00509755	+	0.0354543i
$315$	20.4111	+	23.5557i	1.15004	+	1.32721i
$316$	−1.97789	−	1.27111i	−0.111265	−	0.0715057i
$317$	−15.9809	−	4.69242i	−0.897577	−	0.263553i	−0.199774	−	0.979842i	$-0.564021\pi$
$317$	−15.9809	−	4.69242i	−0.897577	−	0.263553i	−0.697803	+	0.716289i	$0.745839\pi$
$318$	−0.0133753	+	0.0930269i	−0.000750047	+	0.00521669i
$319$	20.6356	+	4.47929i	1.15537	+	0.250792i
$320$	−3.93662	−	27.3798i	−0.220064	−	1.53058i
$321$	0.504260	−	3.50720i	0.0281450	−	0.195753i
$322$	−0.270172	+	0.173629i	−0.0150561	+	0.00967598i
$323$	7.62788			0.424426
$324$	3.84319	−	8.41540i	0.213510	−	0.467522i
$325$	25.9701	−	29.9711i	1.44056	−	1.66250i
$326$	0.197759	+	0.433033i	0.0109529	+	0.0239835i
$327$	−13.8596	+	30.3482i	−0.766436	+	1.67826i
$328$	−0.593980	−	0.685490i	−0.0327971	−	0.0378498i
$329$	−17.5577	+	5.15540i	−0.967987	+	0.284226i
$330$	0.150937	−	2.12379i	0.00830881	−	0.116911i
$331$	−8.72819	−	2.56283i	−0.479745	−	0.140866i	0.0329140	−	0.999458i	$-0.489521\pi$
$331$	−8.72819	−	2.56283i	−0.479745	−	0.140866i	−0.512659	+	0.858592i	$0.671339\pi$
$332$	−1.44935	−	3.17363i	−0.0795434	−	0.174176i
$333$	9.17226	+	20.0844i	0.502637	+	1.10062i
$334$	0.851259	−	0.249952i	0.0465788	−	0.0136768i
$335$	−13.8421	−	30.3100i	−0.756275	−	1.65601i
$336$	23.0508			1.25753
$337$	5.08852	+	35.3914i	0.277189	+	1.92789i	0.363432	+	0.931621i	$0.381605\pi$
$337$	5.08852	+	35.3914i	0.277189	+	1.92789i	−0.0862430	+	0.996274i	$0.527486\pi$
$338$	1.08941	+	0.319881i	0.0592563	+	0.0173992i
$339$	3.85142	+	26.7872i	0.209180	+	1.45488i
$340$	6.28469	+	7.25291i	0.340835	+	0.393345i
$341$	−0.470190	+	6.61591i	−0.0254622	+	0.358272i
$342$	−1.02079	+	1.17806i	−0.0551981	+	0.0637020i
$343$	−16.9589	−	10.8988i	−0.915694	−	0.588481i
$344$	−3.13738	+	0.921219i	−0.169156	+	0.0496688i
$345$	−16.7751	+	10.7807i	−0.903139	+	0.580412i
$346$	−1.50022	−	0.440505i	−0.0806525	−	0.0236817i
$347$	10.6407	+	12.2801i	0.571225	+	0.659229i	0.965695	−	0.259680i	$-0.0836171\pi$
$347$	10.6407	+	12.2801i	0.571225	+	0.659229i	−0.394470	+	0.918909i	$0.629072\pi$
$348$	4.80761	−	33.4376i	0.257715	−	1.79245i
$349$	0.293082	−	2.03843i	0.0156883	−	0.109115i	−0.980473	−	0.196656i	$-0.936992\pi$
$349$	0.293082	−	2.03843i	0.0156883	−	0.109115i	0.996161	+	0.0875412i	$0.0279009\pi$
$350$	−0.455666	+	0.997770i	−0.0243564	+	0.0533331i
$351$	−6.42943	+	14.0785i	−0.343178	+	0.751455i
$352$	−1.93173	−	1.93000i	−0.102962	−	0.102869i
$353$	3.50533	+	7.67561i	0.186570	+	0.408532i	0.979686	−	0.200540i	$-0.0642696\pi$
$353$	3.50533	+	7.67561i	0.186570	+	0.408532i	−0.793115	+	0.609071i	$0.791542\pi$
$354$	−0.269671			−0.0143329
$355$	−2.45327	−	17.0628i	−0.130206	−	0.905602i
$356$	−8.35472	+	9.64186i	−0.442799	+	0.511017i
$357$	−6.69569	+	4.30306i	−0.354374	+	0.227742i
$358$	0.163635	−	1.13811i	0.00864840	−	0.0601509i
$359$	7.15715	−	15.6720i	0.377740	−	0.827135i	−0.621311	−	0.783564i	$-0.713399\pi$
$359$	7.15715	−	15.6720i	0.377740	−	0.827135i	0.999050	−	0.0435704i	$-0.0138733\pi$
$360$	−3.92703			−0.206973
$361$	10.0441	−	6.45498i	0.528639	−	0.339736i
$362$	1.63472			0.0859188
$363$	15.8368	+	24.5939i	0.831218	+	1.29085i
$364$	23.6508			1.23964
$365$	1.90617	−	1.22502i	0.0997736	−	0.0641206i
$366$	−1.22103			−0.0638242
$367$	−12.6443	+	27.6871i	−0.660027	+	1.44526i	0.222470	+	0.974939i	$0.428588\pi$
$367$	−12.6443	+	27.6871i	−0.660027	+	1.44526i	−0.882497	+	0.470318i	$0.844139\pi$
$368$	−1.20839	+	8.40451i	−0.0629915	+	0.438115i
$369$	11.2982	−	7.26094i	0.588163	−	0.377989i
$370$	−0.857284	+	0.989358i	−0.0445681	+	0.0514343i
$371$	0.159493	+	1.10930i	0.00828045	+	0.0575918i
$372$	10.6108			0.550143
$373$	−1.54641	−	3.38616i	−0.0800701	−	0.175329i	0.865363	−	0.501146i	$-0.167088\pi$
$373$	−1.54641	−	3.38616i	−0.0800701	−	0.175329i	−0.945433	+	0.325817i	$0.894361\pi$
$374$	0.305920	+	0.0664049i	0.0158188	+	0.00343371i
$375$	−8.91930	+	19.5306i	−0.460591	+	1.00855i
$376$	0.957754	−	2.09719i	0.0493924	−	0.108154i
$377$	4.92100	−	34.2263i	0.253444	−	1.76274i
$378$	0.0609229	−	0.423728i	0.00313353	−	0.0217942i
$379$	14.5465	+	16.7876i	0.747206	+	0.862321i	0.994294	−	0.106671i	$-0.0340193\pi$
$379$	14.5465	+	16.7876i	0.747206	+	0.862321i	−0.247088	+	0.968993i	$0.579474\pi$
$380$	37.3496	+	10.9668i	1.91599	+	0.562587i
$381$	−3.11289	+	2.00053i	−0.159478	+	0.102490i
$382$	1.43170	−	0.420386i	0.0732522	−	0.0215088i
$383$	−17.2488	−	11.0851i	−0.881371	−	0.566423i	0.0198399	−	0.999803i	$-0.493684\pi$
$383$	−17.2488	−	11.0851i	−0.881371	−	0.566423i	−0.901211	+	0.433380i	$0.857321\pi$
$384$	−3.81282	+	4.40022i	−0.194572	+	0.224548i
$385$	−5.40797	−	24.8063i	−0.275616	−	1.26425i
$386$	0.518565	+	0.598456i	0.0263942	+	0.0304606i
$387$	−6.89028	−	47.9229i	−0.350253	−	2.43606i
$388$	−14.3023	−	4.19954i	−0.726091	−	0.213200i
$389$	−2.72368	−	18.9436i	−0.138096	−	0.960480i	−0.934563	−	0.355798i	$-0.884209\pi$
$389$	−2.72368	−	18.9436i	−0.138096	−	0.960480i	0.796467	−	0.604682i	$-0.206700\pi$
$390$	−3.48654			−0.176548
$391$	−1.21792	−	2.66688i	−0.0615929	−	0.134870i
$392$	0.590100	−	0.173269i	0.0298045	−	0.00875140i
$393$	−20.3261	−	44.5080i	−1.02532	−	2.24513i
$394$	0.0997631	+	0.218451i	0.00502599	+	0.0110054i
$395$	3.96556	+	1.16439i	0.199529	+	0.0585870i
$396$	21.5627	−	16.1567i	1.08357	−	0.811907i
$397$	0.276609	−	0.0812197i	0.0138826	−	0.00407630i	−0.274784	−	0.961506i	$-0.588606\pi$
$397$	0.276609	−	0.0812197i	0.0138826	−	0.00407630i	0.288666	+	0.957430i	$0.406788\pi$
$398$	−0.582516	−	0.672260i	−0.0291989	−	0.0336973i
$399$	−13.4110	+	29.3659i	−0.671388	+	1.47014i
$400$	12.0473	+	26.3798i	0.602363	+	1.31899i
$401$	−22.7216	+	26.2221i	−1.13466	+	1.30947i	−0.189866	+	0.981810i	$0.560805\pi$
$401$	−22.7216	+	26.2221i	−1.13466	+	1.30947i	−0.944796	+	0.327659i	$0.893740\pi$
$402$	−0.722333	+	1.58169i	−0.0360267	+	0.0788874i
$403$	10.8610			0.541027
$404$	30.2571	−	19.4450i	1.50535	−	0.967426i
$405$	−2.31444	+	16.0973i	−0.115006	+	0.799882i
$406$	0.136111	+	0.946673i	0.00675508	+	0.0469826i
$407$	1.27500	−	17.9402i	0.0631996	−	0.889264i
$408$	0.142714	−	0.992594i	0.00706537	−	0.0491407i
$409$	−1.37279	−	0.403087i	−0.0678799	−	0.0199314i	0.247616	−	0.968858i	$-0.420353\pi$
$409$	−1.37279	−	0.403087i	−0.0678799	−	0.0199314i	−0.315496	+	0.948927i	$0.602171\pi$
$410$	0.669873	+	0.430501i	0.0330826	+	0.0212609i
$411$	7.64083	+	8.81798i	0.376894	+	0.434959i
$412$	−0.918857	−	6.39079i	−0.0452688	−	0.314852i
$413$	−3.08543	+	0.905963i	−0.151824	+	0.0445795i
$414$	0.574861	+	0.168795i	0.0282529	+	0.00829580i
$415$	4.01631	+	4.63507i	0.197153	+	0.227527i
$416$	−2.92822	+	3.37935i	−0.143568	+	0.165686i
$417$	−13.2131	+	8.49154i	−0.647048	+	0.415832i
$418$	1.18949	−	0.444264i	0.0581796	−	0.0217297i
$419$	31.3342	+	20.1373i	1.53078	+	0.983771i	0.989757	+	0.142762i	$0.0455983\pi$
$419$	31.3342	+	20.1373i	1.53078	+	0.983771i	0.541021	+	0.841009i	$0.318038\pi$
$420$	−38.9718	+	11.4432i	−1.90163	+	0.558369i
$421$	1.40431	−	1.62066i	0.0684418	−	0.0789861i	−0.720496	−	0.693459i	$-0.756086\pi$
$421$	1.40431	−	1.62066i	0.0684418	−	0.0789861i	0.788938	+	0.614473i	$0.210631\pi$
$422$	−0.773078	−	0.496827i	−0.0376329	−	0.0241852i
$423$	28.7184	+	18.4562i	1.39633	+	0.897369i
$424$	−0.118786	−	0.0763389i	−0.00576874	−	0.00370735i
$425$	−8.42393	−	5.41373i	−0.408620	−	0.262604i
$426$	−0.589086	+	0.679841i	−0.0285413	+	0.0329384i
$427$	−13.9703	+	4.10206i	−0.676072	+	0.198513i
$428$	2.23651	+	1.43732i	0.108106	+	0.0694755i
$429$	38.3335	−	28.7230i	1.85076	−	1.38676i
$430$	2.41488	−	1.55195i	0.116456	−	0.0748415i
$431$	2.36591	−	2.73040i	0.113962	−	0.131519i	−0.695902	−	0.718136i	$-0.744995\pi$
$431$	2.36591	−	2.73040i	0.113962	−	0.131519i	0.809864	+	0.586618i	$0.199541\pi$
$432$	−7.41174	−	8.55361i	−0.356598	−	0.411536i
$433$	20.2324	+	5.94076i	0.972305	+	0.285495i	0.729044	−	0.684466i	$-0.239965\pi$
$433$	20.2324	+	5.94076i	0.972305	+	0.285495i	0.243261	+	0.969961i	$0.421783\pi$
$434$	−0.288239	+	0.0846347i	−0.0138359	+	0.00406259i
$435$	8.45116	+	58.7791i	0.405202	+	2.81824i
$436$	−16.3929	−	18.9185i	−0.785079	−	0.906030i
$437$	−10.0040	−	6.42918i	−0.478556	−	0.307549i
$438$	−0.113452	−	0.0333125i	−0.00542095	−	0.00159173i
$439$	−2.85535	+	19.8594i	−0.136278	+	0.947837i	0.800853	+	0.598861i	$0.204380\pi$
$439$	−2.85535	+	19.8594i	−0.136278	+	0.947837i	−0.937132	+	0.348976i	$0.886529\pi$
$440$	2.80824	+	1.53178i	0.133878	+	0.0730246i
$441$	1.29597	+	9.01366i	0.0617128	+	0.429222i
$442$	0.0729532	−	0.507401i	0.00347003	−	0.0241346i
$443$	11.2329	−	7.21897i	0.533693	−	0.342984i	−0.245875	−	0.969302i	$-0.579075\pi$
$443$	11.2329	−	7.21897i	0.533693	−	0.342984i	0.779568	+	0.626318i	$0.215439\pi$
$444$	−28.7730			−1.36551
$445$	9.31649	−	20.4003i	0.441644	−	0.967065i
$446$	0.0707166	−	0.0816113i	0.00334853	−	0.00386441i
$447$	−9.61905	−	21.0628i	−0.454965	−	0.996235i
$448$	−7.15039	+	15.6572i	−0.337824	+	0.739732i
$449$	9.06539	+	10.4620i	0.427822	+	0.493733i	0.928204	−	0.372072i	$-0.121353\pi$
$449$	9.06539	+	10.4620i	0.427822	+	0.493733i	−0.500382	+	0.865805i	$0.666807\pi$
$450$	1.96342	−	0.576513i	0.0925566	−	0.0271771i
$451$	−10.9116	+	0.785346i	−0.513808	+	0.0369805i
$452$	−19.4829	−	5.72068i	−0.916397	−	0.269078i
$453$	−5.70316	−	12.4882i	−0.267958	−	0.586746i
$454$	0.584927	+	1.28081i	0.0274520	+	0.0601114i
$455$	−39.8910	+	11.7131i	−1.87012	+	0.549117i
$456$	−1.68969	−	3.69990i	−0.0791269	−	0.173264i
$457$	11.7316			0.548782			0.274391	−	0.961618i	$-0.411524\pi$
$457$	11.7316			0.548782			0.274391	+	0.961618i	$0.411524\pi$
$458$	0.186738	+	1.29879i	0.00872571	+	0.0606887i
$459$	3.74969	+	1.10101i	0.175020	+	0.0513906i
$460$	−2.12926	−	14.8093i	−0.0992771	−	0.690487i
$461$	−18.5703	−	21.4313i	−0.864906	−	0.998154i	−0.999973	−	0.00731806i	$-0.997671\pi$
$461$	−18.5703	−	21.4313i	−0.864906	−	0.998154i	0.135067	−	0.990836i	$-0.456875\pi$
$462$	−0.793501	+	1.06099i	−0.0369170	+	0.0493616i
$463$	20.0672	−	23.1588i	0.932602	−	1.07628i	−0.0643237	−	0.997929i	$-0.520489\pi$
$463$	20.0672	−	23.1588i	0.932602	−	1.07628i	0.996926	−	0.0783512i	$-0.0249655\pi$
$464$	21.2721	+	13.6708i	0.987534	+	0.634650i
$465$	−17.8968	+	5.25499i	−0.829946	+	0.243694i
$466$	−0.797118	+	0.512277i	−0.0369258	+	0.0237308i
$467$	2.50848	+	0.736556i	0.116079	+	0.0340838i	0.339256	−	0.940694i	$-0.389825\pi$
$467$	2.50848	+	0.736556i	0.116079	+	0.0340838i	−0.223177	+	0.974778i	$0.571643\pi$
$468$	−28.8936	−	33.3450i	−1.33561	−	1.54137i
$469$	−2.95083	+	20.5235i	−0.136257	+	0.947686i
$470$	−0.288048	+	2.00341i	−0.0132866	+	0.0924106i
$471$	10.1872	−	22.3069i	0.469402	−	1.02785i
$472$	0.168307	−	0.368541i	0.00774696	−	0.0169635i
$473$	−13.7655	+	36.9576i	−0.632940	+	1.69931i
$474$	−0.0895943	−	0.196184i	−0.00411520	−	0.00901103i
$475$	−40.6160			−1.86359
$476$	−0.849882	−	5.91106i	−0.0389543	−	0.270933i
$477$	1.36914	−	1.58007i	0.0626885	−	0.0723464i
$478$	0.621191	−	0.399215i	0.0284126	−	0.0182597i
$479$	−0.372045	+	2.58763i	−0.0169992	+	0.118232i	−0.996554	−	0.0829448i	$-0.973567\pi$
$479$	−0.372045	+	2.58763i	−0.0169992	+	0.118232i	0.979555	+	0.201177i	$0.0644766\pi$
$480$	3.19007	−	6.98528i	0.145606	−	0.318833i
$481$	−29.4517			−1.34288
$482$	0.514966	−	0.330949i	0.0234561	−	0.0150743i
$483$	12.4083			0.564596
$484$	−21.7217	+	3.14304i	−0.987349	+	0.142866i
$485$	26.2031			1.18982
$486$	1.20895	−	0.776944i	0.0548390	−	0.0352429i
$487$	−12.4169			−0.562663			−0.281331	−	0.959611i	$-0.590776\pi$
$487$	−12.4169			−0.562663			−0.281331	+	0.959611i	$0.590776\pi$
$488$	0.762068	−	1.66870i	0.0344972	−	0.0755384i
$489$	2.61759	−	18.2058i	0.118372	−	0.823293i
$490$	−0.454206	+	0.291900i	−0.0205189	+	0.0131867i
$491$	−0.445886	+	0.514580i	−0.0201226	+	0.0232227i	−0.765722	−	0.643172i	$-0.777618\pi$
$491$	−0.445886	+	0.514580i	−0.0201226	+	0.0232227i	0.745599	+	0.666395i	$0.232163\pi$
$492$	2.49072	+	17.3234i	0.112290	+	0.780997i
$493$	−8.73104			−0.393226
$494$	−0.863746	−	1.89134i	−0.0388618	−	0.0850954i
$495$	−28.3674	+	37.9300i	−1.27502	+	1.70482i
$496$	−3.29940	+	7.22468i	−0.148147	+	0.324397i
$497$	−4.45606	+	9.75740i	−0.199881	+	0.437679i
$498$	0.0455474	−	0.316789i	0.00204103	−	0.0141957i
$499$	4.51095	−	31.3744i	0.201938	−	1.40451i	−0.596587	−	0.802548i	$-0.703477\pi$
$499$	4.51095	−	31.3744i	0.201938	−	1.40451i	0.798525	−	0.601961i	$-0.205614\pi$
$500$	−10.5496	−	12.1749i	−0.471795	−	0.544480i
$501$	−32.8896	−	9.65726i	−1.46940	−	0.431455i
$502$	0.569715	−	0.366133i	0.0254276	−	0.0163413i
$503$	24.4907	−	7.19113i	1.09199	−	0.320637i	0.314323	−	0.949316i	$-0.398222\pi$
$503$	24.4907	−	7.19113i	1.09199	−	0.320637i	0.777665	+	0.628679i	$0.216404\pi$
$504$	2.05573	+	1.32113i	0.0915693	+	0.0588480i
$505$	−41.4034	+	47.7821i	−1.84243	+	2.12628i
$506$	−0.345246	−	0.344936i	−0.0153481	−	0.0153343i
$507$	−28.7275	−	33.1533i	−1.27583	−	1.47239i
$508$	−0.395118	−	2.74811i	−0.0175305	−	0.121928i
$509$	−15.3972	−	4.52104i	−0.682471	−	0.200391i	−0.0779218	−	0.996959i	$-0.524828\pi$
$509$	−15.3972	−	4.52104i	−0.682471	−	0.200391i	−0.604549	+	0.796568i	$0.706647\pi$
$510$	0.125287	+	0.871393i	0.00554782	+	0.0385859i
$511$	−1.40997			−0.0623733
$512$	−2.26574	−	4.96129i	−0.100133	−	0.219260i
$513$	15.2091	−	4.46581i	0.671500	−	0.197170i
$514$	−0.0594492	−	0.130176i	−0.00262219	−	0.00574180i
$515$	4.71484	+	10.3241i	0.207761	+	0.454933i
$516$	60.5368	+	17.7752i	2.66499	+	0.782510i
$517$	−13.3376	−	24.4000i	−0.586589	−	1.07311i
$518$	0.781612	−	0.229502i	0.0343421	−	0.0100837i
$519$	39.5603	+	45.6551i	1.73651	+	2.00404i
$520$	2.17602	−	4.76481i	0.0954246	−	0.208951i
$521$	1.43124	+	3.13398i	0.0627038	+	0.137302i	0.938390	−	0.345579i	$-0.112318\pi$
$521$	1.43124	+	3.13398i	0.0627038	+	0.137302i	−0.875686	+	0.482881i	$0.839590\pi$
$522$	1.16842	−	1.34843i	0.0511404	−	0.0590191i
$523$	15.1250	−	33.1192i	0.661372	−	1.44820i	−0.219867	−	0.975530i	$-0.570562\pi$
$523$	15.1250	−	33.1192i	0.661372	−	1.44820i	0.881238	−	0.472672i	$-0.156710\pi$
$524$	36.7124			1.60379
$525$	35.6524	−	22.9124i	1.55600	−	0.999980i
$526$	−0.130949	+	0.910774i	−0.00570967	+	0.0397116i
$527$	−0.390287	−	2.71451i	−0.0170012	−	0.118246i
$528$	7.46123	+	34.2246i	0.324708	+	1.48944i
$529$	2.62277	−	18.2417i	0.114033	−	0.793119i
$530$	0.118938	+	0.0349234i	0.00516634	+	0.00151698i
$531$	5.04670	+	3.24332i	0.219008	+	0.140748i
$532$	−15.8623	−	18.3061i	−0.687720	−	0.793671i
$533$	2.54947	+	17.7319i	0.110430	+	0.768056i
$534$	−1.12292	+	0.329718i	−0.0485933	+	0.0142683i
$535$	−4.48408	−	1.31665i	−0.193864	−	0.0569236i
$536$	−1.71076	−	1.97432i	−0.0738936	−	0.0852778i
$537$	−29.0920	+	33.5739i	−1.25541	+	1.44882i
$538$	−0.602089	+	0.386939i	−0.0259579	+	0.0166821i
$539$	2.58911	−	6.95122i	0.111521	−	0.299410i
$540$	16.7772	+	10.7821i	0.721978	+	0.463987i
$541$	−1.20465	+	0.353716i	−0.0517918	+	0.0152075i	−0.307526	−	0.951540i	$-0.599501\pi$
$541$	−1.20465	+	0.353716i	−0.0517918	+	0.0152075i	0.255734	+	0.966747i	$0.417683\pi$
$542$	−1.04841	+	1.20992i	−0.0450329	+	0.0519707i
$543$	−53.1333	−	34.1467i	−2.28017	−	1.46537i
$544$	0.949828	+	0.610417i	0.0407235	+	0.0261714i
$545$	37.0188	+	23.7905i	1.58571	+	1.01907i
$546$	1.82514	+	1.17294i	0.0781086	+	0.0501974i
$547$	0.0554188	−	0.0639567i	0.00236954	−	0.00273459i	−0.754564	−	0.656227i	$-0.772151\pi$
$547$	0.0554188	−	0.0639567i	0.00236954	−	0.00273459i	0.756933	+	0.653492i	$0.226697\pi$
$548$	−8.39989	+	2.46643i	−0.358825	+	0.105361i
$549$	22.8507	+	14.6852i	0.975244	+	0.626751i
$550$	−1.62893	−	0.353585i	−0.0694577	−	0.0150769i
$551$	−29.7922	+	19.1463i	−1.26919	+	0.815659i
$552$	−1.02378	+	1.18151i	−0.0435750	+	0.0502882i
$553$	−1.68417	−	1.94364i	−0.0716182	−	0.0826518i
$554$	−0.191559	−	0.0562467i	−0.00813855	−	0.00238969i
$555$	48.5305	−	14.2498i	2.06000	−	0.604872i
$556$	−1.67713	−	11.6647i	−0.0711263	−	0.494695i
$557$	7.17140	+	8.27623i	0.303862	+	0.350675i	0.887060	−	0.461655i	$-0.152744\pi$
$557$	7.17140	+	8.27623i	0.303862	+	0.350675i	−0.583198	+	0.812330i	$0.698199\pi$
$558$	0.471461	+	0.302989i	0.0199585	+	0.0128266i
$559$	61.9647	+	18.1945i	2.62083	+	0.769544i
$560$	4.32678	−	30.0934i	0.182840	−	1.27168i
$561$	−8.55625	−	8.54856i	−0.361245	−	0.360920i
$562$	−0.0853840	−	0.593859i	−0.00360171	−	0.0250504i
$563$	5.05161	−	35.1348i	0.212900	−	1.48075i	−0.550504	−	0.834832i	$-0.685564\pi$
$563$	5.05161	−	35.1348i	0.212900	−	1.48075i	0.763404	−	0.645921i	$-0.223526\pi$
$564$	−37.4241	+	24.0510i	−1.57584	+	1.01273i
$565$	35.6943			1.50167
$566$	0.367520	−	0.804756i	0.0154480	−	0.0338264i
$567$	6.62704	−	7.64801i	0.278310	−	0.321186i
$568$	−0.561432	−	1.22936i	−0.0235572	−	0.0515830i
$569$	−7.24071	+	15.8549i	−0.303546	+	0.664674i	−0.998521	−	0.0543600i	$-0.982688\pi$
$569$	−7.24071	+	15.8549i	−0.303546	+	0.664674i	0.694975	+	0.719034i	$0.255415\pi$
$570$	2.33838	+	2.69864i	0.0979441	+	0.113033i
$571$	−5.68075	+	1.66802i	−0.237732	+	0.0698045i	−0.398428	−	0.917199i	$-0.630444\pi$
$571$	−5.68075	+	1.66802i	−0.237732	+	0.0698045i	0.160696	+	0.987004i	$0.448626\pi$
$572$	7.65543	+	35.1154i	0.320090	+	1.46825i
$573$	−55.3159	−	16.2422i	−2.31085	−	0.678528i
$574$	−0.205836	−	0.450718i	−0.00859143	−	0.0188126i
$575$	6.48504	+	14.2003i	0.270445	+	0.592192i
$576$	30.8103	−	9.04673i	1.28376	−	0.376947i
$577$	−6.38609	−	13.9836i	−0.265856	−	0.582144i	0.728877	−	0.684645i	$-0.240043\pi$
$577$	−6.38609	−	13.9836i	−0.265856	−	0.582144i	−0.994733	+	0.102501i	$0.967316\pi$
$578$	1.04063			0.0432846
$579$	−4.35413	−	30.2836i	−0.180951	−	1.25855i
$580$	−42.7512	−	12.5529i	−1.77515	−	0.521230i
$581$	−0.543128	−	3.77754i	−0.0225328	−	0.156719i
$582$	−0.895440	−	1.03339i	−0.0371172	−	0.0428355i
$583$	−1.59540	+	0.595870i	−0.0660746	+	0.0246784i
$584$	0.116333	−	0.134256i	0.00481391	−	0.00555555i
$585$	65.2480	+	41.9324i	2.69767	+	1.73369i
$586$	−1.41286	+	0.414853i	−0.0583647	+	0.0171374i
$587$	33.1347	−	21.2944i	1.36761	−	0.878912i	0.368893	−	0.929472i	$-0.379737\pi$
$587$	33.1347	−	21.2944i	1.36761	−	0.878912i	0.998721	+	0.0505598i	$0.0161006\pi$
$588$	−11.3862	−	3.34328i	−0.469557	−	0.137874i
$589$	−7.28438	−	8.40663i	−0.300148	−	0.346389i
$590$	−0.0506188	+	0.352062i	−0.00208394	+	0.0144942i
$591$	1.32049	−	9.18421i	0.0543177	−	0.377788i
$592$	8.94691	−	19.5910i	0.367716	−	0.805185i
$593$	−0.886270	+	1.94066i	−0.0363948	+	0.0796934i	−0.926956	−	0.375170i	$-0.877584\pi$
$593$	−0.886270	+	1.94066i	−0.0363948	+	0.0796934i	0.890561	+	0.454863i	$0.150312\pi$
$594$	0.648848	−	0.0466998i	0.0266226	−	0.00191611i
$595$	4.36092	+	9.54909i	0.178780	+	0.391474i
$596$	17.3736			0.711651
$597$	4.89110	+	34.0184i	0.200179	+	1.39228i
$598$	−0.523342	+	0.603969i	−0.0214011	+	0.0246981i
$599$	−0.464083	+	0.298248i	−0.0189619	+	0.0121861i	−0.550087	−	0.835107i	$-0.685406\pi$
$599$	−0.464083	+	0.298248i	−0.0189619	+	0.0121861i	0.531126	+	0.847293i	$0.321769\pi$
$600$	−0.759904	+	5.28525i	−0.0310229	+	0.215769i
$601$	−16.8220	+	36.8350i	−0.686184	+	1.50253i	0.169772	+	0.985483i	$0.445697\pi$
$601$	−16.8220	+	36.8350i	−0.686184	+	1.50253i	−0.855956	+	0.517049i	$0.827030\pi$
$602$	−1.78625			−0.0728021
$603$	32.5408	−	20.9127i	1.32516	−	0.851631i
$604$	10.3009			0.419136
$605$	35.0806	−	16.0589i	1.42623	−	0.652888i
$606$	3.29930			0.134025
$607$	4.86465	−	3.12632i	0.197450	−	0.126893i	−0.438180	−	0.898887i	$-0.644377\pi$
$607$	4.86465	−	3.12632i	0.197450	−	0.126893i	0.635630	+	0.771994i	$0.280740\pi$
$608$	4.57960			0.185727
$609$	15.3505	−	33.6129i	0.622034	−	1.36206i
$610$	−0.229194	+	1.59408i	−0.00927981	+	0.0645425i
$611$	−38.3067	+	24.6182i	−1.54972	+	0.995948i
$612$	−7.29566	+	8.41964i	−0.294910	+	0.340344i
$613$	6.30586	+	43.8582i	0.254691	+	1.77142i	0.569237	+	0.822173i	$0.307239\pi$
$613$	6.30586	+	43.8582i	0.254691	+	1.77142i	−0.314546	+	0.949242i	$0.601852\pi$
$614$	−1.78908			−0.0722016
$615$	−12.7804	−	27.9852i	−0.515356	−	1.12847i
$616$	−0.954738	−	1.74661i	−0.0384675	−	0.0703727i
$617$	5.14741	−	11.2712i	0.207227	−	0.453763i	−0.777270	−	0.629167i	$-0.783396\pi$
$617$	5.14741	−	11.2712i	0.207227	−	0.453763i	0.984497	+	0.175404i	$0.0561232\pi$
$618$	0.246038	−	0.538748i	0.00989710	−	0.0216716i
$619$	−3.42507	+	23.8219i	−0.137665	+	0.957484i	0.797512	+	0.603303i	$0.206149\pi$
$619$	−3.42507	+	23.8219i	−0.137665	+	0.957484i	−0.935177	+	0.354180i	$0.884760\pi$
$620$	1.99170	−	13.8526i	0.0799888	−	0.556334i
$621$	−3.98974	−	4.60441i	−0.160103	−	0.184769i
$622$	−0.921141	−	0.270471i	−0.0369344	−	0.0108449i
$623$	−11.7401	+	7.54489i	−0.470356	+	0.302280i
$624$	55.0366	−	16.1602i	2.20323	−	0.646926i
$625$	−6.89070	−	4.42839i	−0.275628	−	0.177135i
$626$	0.901165	−	1.04000i	0.0360178	−	0.0415668i
$627$	−47.9419	−	10.4065i	−1.91461	−	0.415598i
$628$	12.0493	+	13.9057i	0.480820	+	0.554896i
$629$	1.05833	+	7.36087i	0.0421985	+	0.293497i
$630$	−2.05836	−	0.604390i	−0.0820072	−	0.0240795i
$631$	−2.47842	−	17.2378i	−0.0986642	−	0.686225i	−0.977783	−	0.209621i	$-0.932777\pi$
$631$	−2.47842	−	17.2378i	−0.0986642	−	0.686225i	0.879118	−	0.476603i	$-0.158132\pi$
$632$	0.324029			0.0128892
$633$	14.7495	+	32.2968i	0.586238	+	1.28368i
$634$	1.09993	−	0.322968i	0.0436837	−	0.0128267i
$635$	2.02743	+	4.43946i	0.0804562	+	0.176175i
$636$	1.13180	+	2.47831i	0.0448790	+	0.0982712i
$637$	−11.6547	−	3.42213i	−0.461777	−	0.135590i
$638$	−1.36151	+	0.508515i	−0.0539028	+	0.0201323i
$639$	19.2007	−	5.63784i	0.759569	−	0.223029i
$640$	5.02890	+	5.80366i	0.198785	+	0.229410i
$641$	18.2208	−	39.8981i	0.719680	−	1.57588i	−0.0946721	−	0.995509i	$-0.530180\pi$
$641$	18.2208	−	39.8981i	0.719680	−	1.57588i	0.814352	−	0.580371i	$-0.197092\pi$
$642$	0.101309	+	0.221836i	0.00399836	+	0.00875518i
$643$	−22.5046	+	25.9717i	−0.887494	+	1.02422i	0.112041	+	0.993704i	$0.464261\pi$
$643$	−22.5046	+	25.9717i	−0.887494	+	1.02422i	−0.999534	+	0.0305185i	$0.990284\pi$
$644$	−3.86753	+	8.46871i	−0.152402	+	0.333714i
$645$	−110.909			−4.36702
$646$	−0.441665	+	0.283841i	−0.0173771	+	0.0111676i
$647$	2.11722	−	14.7256i	0.0832363	−	0.578921i	−0.904933	−	0.425554i	$-0.860079\pi$
$647$	2.11722	−	14.7256i	0.0832363	−	0.578921i	0.988169	−	0.153367i	$-0.0490117\pi$
$648$	0.181454	+	1.26204i	0.00712820	+	0.0495777i
$649$	−2.34383	−	4.28783i	−0.0920035	−	0.168312i
$650$	−0.388452	+	2.70175i	−0.0152364	+	0.105971i
$651$	11.1365	+	3.26998i	0.436476	+	0.128161i
$652$	11.6097	+	7.46107i	0.454669	+	0.292198i
$653$	20.2357	+	23.3532i	0.791883	+	0.913882i	0.997907	−	0.0646653i	$-0.0205980\pi$
$653$	20.2357	+	23.3532i	0.791883	+	0.913882i	−0.206024	+	0.978547i	$0.566053\pi$
$654$	−0.326799	−	2.27293i	−0.0127788	−	0.0888788i
$655$	−61.9215	+	18.1818i	−2.41947	+	0.710422i
$656$	−12.5696	−	3.69078i	−0.490761	−	0.144101i
$657$	1.72252	+	1.98790i	0.0672021	+	0.0775553i
$658$	0.824778	−	0.951844i	0.0321532	−	0.0371068i
$659$	−29.3399	+	18.8556i	−1.14292	+	0.734510i	−0.968217	−	0.250111i	$-0.919533\pi$
$659$	−29.3399	+	18.8556i	−1.14292	+	0.734510i	−0.174703	+	0.984621i	$0.555897\pi$
$660$	−29.6048	−	54.1593i	−1.15237	−	2.10815i
$661$	13.7913	+	8.86315i	0.536421	+	0.344737i	0.780638	−	0.624984i	$-0.214894\pi$
$661$	13.7913	+	8.86315i	0.536421	+	0.344737i	−0.244217	+	0.969721i	$0.578531\pi$
$662$	0.600740	−	0.176393i	0.0233484	−	0.00685572i
$663$	−12.9700	+	14.9682i	−0.503713	+	0.581316i
$664$	0.404507	+	0.259961i	0.0156979	+	0.0100884i
$665$	35.8206	+	23.0205i	1.38906	+	0.892696i
$666$	−1.27845	−	0.821610i	−0.0495389	−	0.0318367i
$667$	11.4508	+	7.35898i	0.443377	+	0.284941i
$668$	16.8425	−	19.4373i	0.651655	−	0.752050i
$669$	−4.00324	+	1.17546i	−0.154774	+	0.0454458i
$670$	1.92934	+	1.23991i	0.0745371	+	0.0479021i
$671$	−10.6125	−	19.4146i	−0.409692	−	0.749493i
$672$	−4.01994	+	2.58346i	−0.155072	+	0.0996590i
$673$	−3.14865	+	3.63374i	−0.121372	+	0.140070i	−0.813183	−	0.582008i	$-0.802267\pi$
$673$	−3.14865	+	3.63374i	−0.121372	+	0.140070i	0.691812	+	0.722078i	$0.256813\pi$
$674$	−1.61158	−	1.85987i	−0.0620759	−	0.0716394i
$675$	−19.9659	−	5.86251i	−0.768487	−	0.225648i
$676$	31.5814	−	9.27312i	1.21467	−	0.356659i
$677$	0.863203	+	6.00371i	0.0331756	+	0.230741i	0.999663	−	0.0259742i	$-0.00826877\pi$
$677$	0.863203	+	6.00371i	0.0331756	+	0.230741i	−0.966487	+	0.256715i	$0.917360\pi$
$678$	−1.21978	−	1.40770i	−0.0468455	−	0.0540625i
$679$	−13.7168	−	8.81526i	−0.526403	−	0.338299i
$680$	−1.26907	−	0.372631i	−0.0486665	−	0.0142898i
$681$	7.74224	−	53.8485i	0.296683	−	2.06348i
$682$	−0.218960	−	0.400567i	−0.00838441	−	0.0153385i
$683$	0.780998	+	5.43196i	0.0298840	+	0.207848i	0.999293	−	0.0376042i	$-0.0119726\pi$
$683$	0.780998	+	5.43196i	0.0298840	+	0.207848i	−0.969409	+	0.245452i	$0.921064\pi$
$684$	−6.43096	+	44.7283i	−0.245894	+	1.71023i
$685$	12.9463	−	8.32009i	0.494653	−	0.317894i
$686$	1.38750			0.0529750
$687$	21.0602	−	46.1154i	0.803497	−	1.75941i
$688$	−30.9266	+	35.6912i	−1.17907	+	1.36071i
$689$	1.15850	+	2.53676i	0.0441353	+	0.0966429i
$690$	0.570141	−	1.24843i	0.0217049	−	0.0475271i
$691$	−12.2130	−	14.0946i	−0.464605	−	0.536183i	0.474298	−	0.880364i	$-0.342702\pi$
$691$	−12.2130	−	14.0946i	−0.464605	−	0.536183i	−0.938903	+	0.344182i	$0.888156\pi$
$692$	−43.4904	+	12.7699i	−1.65326	+	0.485440i
$693$	27.6102	−	10.3122i	1.04883	−	0.391729i
$694$	−1.07307	−	0.315081i	−0.0407331	−	0.0119603i
$695$	8.60572	+	18.8439i	0.326434	+	0.714790i
$696$	1.93406	+	4.23499i	0.0733102	+	0.160527i
$697$	4.34014	−	1.27438i	0.164395	−	0.0482706i
$698$	0.0588822	+	0.128934i	0.00222872	+	0.00488022i
$699$	36.6094			1.38470
$700$	4.52535	+	31.4745i	0.171042	+	1.18962i
$701$	25.1121	+	7.37357i	0.948469	+	0.278496i	0.719150	−	0.694855i	$-0.244532\pi$
$701$	25.1121	+	7.37357i	0.948469	+	0.278496i	0.229320	+	0.973351i	$0.426350\pi$
$702$	−0.151601	−	1.05441i	−0.00572183	−	0.0397962i
$703$	19.7529	+	22.7961i	0.744995	+	0.859770i
$704$	−25.5614	−	5.54851i	−0.963381	−	0.209117i
$705$	51.2106	−	59.1002i	1.92870	−	2.22584i
$706$	−0.488581	−	0.313992i	−0.0183880	−	0.0118172i
$707$	37.7488	−	11.0840i	1.41969	−	0.416858i
$708$	−6.57656	+	4.22650i	−0.247162	+	0.158842i
$709$	7.55594	+	2.21862i	0.283769	+	0.0833222i	0.420520	−	0.907283i	$-0.361848\pi$
$709$	7.55594	+	2.21862i	0.283769	+	0.0833222i	−0.136751	+	0.990606i	$0.543666\pi$
$710$	0.776973	+	0.896675i	0.0291593	+	0.0336516i
$711$	−0.682801	+	4.74899i	−0.0256071	+	0.178101i
$712$	0.250231	−	1.74039i	0.00937780	−	0.0652240i
$713$	−1.77607	+	3.88904i	−0.0665142	+	0.145646i
$714$	0.227569	−	0.498307i	0.00851656	−	0.0186487i
$715$	−30.3031	−	55.4367i	−1.13327	−	2.07321i
$716$	−13.8467	−	30.3201i	−0.517476	−	1.13311i
$717$	−28.5296			−1.06546
$718$	0.168760	+	1.17375i	0.00629808	+	0.0438041i
$719$	−11.0427	+	12.7440i	−0.411824	+	0.475270i	−0.923329	−	0.384010i	$-0.874543\pi$
$719$	−11.0427	+	12.7440i	−0.411824	+	0.475270i	0.511505	+	0.859280i	$0.329088\pi$
$720$	−47.7143	+	30.6641i	−1.77821	+	1.14278i
$721$	1.00510	−	6.99063i	0.0374319	−	0.260345i
$722$	−0.341374	+	0.747506i	−0.0127046	+	0.0278193i
$723$	−23.6510			−0.879589
$724$	39.8664	−	25.6206i	1.48162	−	0.952181i
$725$	46.4900			1.72660
$726$	−1.83214	−	0.834721i	−0.0679971	−	0.0309794i
$727$	11.8489			0.439451			0.219726	−	0.975562i	$-0.429484\pi$
$727$	11.8489			0.439451			0.219726	+	0.975562i	$0.429484\pi$
$728$	−2.74208	+	1.76223i	−0.101628	+	0.0653126i
$729$	−41.6135			−1.54124
$730$	−0.0647858	+	0.141861i	−0.00239783	+	0.00525052i
$731$	2.32068	−	16.1407i	0.0858334	−	0.596985i
$732$	−29.7777	+	19.1369i	−1.10061	+	0.707322i
$733$	31.9082	−	36.8240i	1.17855	−	1.36012i	0.259622	−	0.965710i	$-0.416402\pi$
$733$	31.9082	−	36.8240i	1.17855	−	1.36012i	0.918933	−	0.394414i	$-0.129052\pi$
$734$	−0.298143	−	2.07363i	−0.0110047	−	0.0765392i
$735$	20.8604			0.769448
$736$	−0.731212	−	1.60113i	−0.0269528	−	0.0590184i
$737$	−31.4273	+	2.26193i	−1.15764	+	0.0833191i
$738$	−0.383998	+	0.840838i	−0.0141352	+	0.0309517i
$739$	−7.42382	+	16.2559i	−0.273090	+	0.597983i	−0.995634	−	0.0933415i	$-0.970245\pi$
$739$	−7.42382	+	16.2559i	−0.273090	+	0.597983i	0.722545	+	0.691324i	$0.242972\pi$
$740$	−5.40086	+	37.5638i	−0.198540	+	1.38087i
$741$	−11.4328	+	79.5166i	−0.419993	+	2.92112i
$742$	−0.0505129	−	0.0582950i	−0.00185439	−	0.00214008i
$743$	41.0608	+	12.0565i	1.50637	+	0.442311i	0.927724	−	0.373266i	$-0.121762\pi$
$743$	41.0608	+	12.0565i	1.50637	+	0.442311i	0.578649	+	0.815577i	$0.303580\pi$
$744$	−1.23022	+	0.790613i	−0.0451020	+	0.0289853i
$745$	−29.3035	+	8.60428i	−1.07360	+	0.315236i
$746$	0.215542	+	0.138520i	0.00789155	+	0.00507159i
$747$	−4.66239	+	5.38068i	−0.170588	+	0.196869i
$748$	8.50133	−	3.17519i	0.310839	−	0.116096i
$749$	1.90439	+	2.19778i	0.0695847	+	0.0803051i
$750$	−0.210311	−	1.46274i	−0.00767947	−	0.0534119i
$751$	44.4855	+	13.0621i	1.62330	+	0.476643i	0.961902	−	0.273394i	$-0.0881464\pi$
$751$	44.4855	+	13.0621i	1.62330	+	0.476643i	0.661395	+	0.750038i	$0.269965\pi$
$752$	−4.73892	−	32.9599i	−0.172811	−	1.20192i
$753$	−26.1654			−0.953521
$754$	0.988663	+	2.16487i	0.0360050	+	0.0788399i
$755$	−17.3741	+	5.10150i	−0.632309	+	0.185663i
$756$	−5.15525	−	11.2884i	−0.187495	−	0.410556i
$757$	16.5469	+	36.2327i	0.601408	+	1.31690i	0.928298	+	0.371837i	$0.121272\pi$
$757$	16.5469	+	36.2327i	0.601408	+	1.31690i	−0.326890	+	0.945062i	$0.606001\pi$
$758$	−1.46695	−	0.430735i	−0.0532820	−	0.0156450i
$759$	4.01638	+	18.4231i	0.145785	+	0.668717i
$760$	−5.14747	+	1.51143i	−0.186718	+	0.0548255i
$761$	−26.0332	−	30.0439i	−0.943703	−	1.08909i	−0.995901	−	0.0904544i	$-0.971168\pi$
$761$	−26.0332	−	30.0439i	−0.943703	−	1.08909i	0.0521977	−	0.998637i	$-0.483377\pi$
$762$	0.105799	−	0.231667i	0.00383269	−	0.00839243i
$763$	−11.3750	−	24.9078i	−0.411803	−	0.901722i
$764$	28.3268	−	32.6909i	1.02483	−	1.18271i
$765$	8.13552	−	17.8143i	0.294140	−	0.644078i
$766$	1.41122			0.0509894
$767$	−6.73168	+	4.32619i	−0.243067	+	0.156210i
$768$	−5.91231	+	41.1210i	−0.213342	+	1.48383i
$769$	−4.22640	−	29.3952i	−0.152408	−	1.06002i	−0.912168	−	0.409816i	$-0.865593\pi$
$769$	−4.22640	−	29.3952i	−0.152408	−	1.06002i	0.759760	−	0.650203i	$-0.225316\pi$
$770$	1.23620	+	1.23509i	0.0445495	+	0.0445095i
$771$	−0.786885	+	5.47290i	−0.0283390	+	0.197102i
$772$	22.0259	+	6.46738i	0.792729	+	0.232766i
$773$	−19.2018	−	12.3403i	−0.690642	−	0.443849i	0.147672	−	0.989036i	$-0.452822\pi$
$773$	−19.2018	−	12.3403i	−0.690642	−	0.443849i	−0.838314	+	0.545188i	$0.816458\pi$
$774$	2.18222	+	2.51841i	0.0784382	+	0.0905225i
$775$	2.07816	+	14.4539i	0.0746495	+	0.519199i
$776$	1.97113	−	0.578775i	0.0707593	−	0.0207768i
$777$	−30.1987	−	8.86715i	−1.08337	−	0.318107i
$778$	0.862617	+	0.995513i	0.0309263	+	0.0356909i
$779$	12.0149	−	13.8660i	0.430479	−	0.496799i
$780$	−85.0274	+	54.6438i	−3.04447	+	1.95656i
$781$	−15.9296	−	3.45778i	−0.570007	−	0.123729i
$782$	0.169757	+	0.109096i	0.00607048	+	0.00390126i
$783$	−17.4087	+	5.11166i	−0.622137	+	0.182676i
$784$	5.81688	−	6.71303i	0.207746	−	0.239751i
$785$	−27.2100	−	17.4868i	−0.971166	−	0.624130i
$786$	2.83310	+	1.82072i	0.101053	+	0.0649430i
$787$	−0.943392	−	0.606281i	−0.0336283	−	0.0216116i	0.523719	−	0.851891i	$-0.324544\pi$
$787$	−0.943392	−	0.606281i	−0.0336283	−	0.0216116i	−0.557347	+	0.830280i	$0.688181\pi$
$788$	5.85669	+	3.76386i	0.208636	+	0.134082i
$789$	23.2809	−	26.8676i	0.828822	−	0.956512i
$790$	−0.272940	+	0.0801425i	−0.00971078	+	0.00285134i
$791$	−18.6853	−	12.0083i	−0.664372	−	0.426966i
$792$	−1.29614	+	3.47986i	−0.0460563	+	0.123652i
$793$	−30.4800	+	19.5883i	−1.08238	+	0.695601i
$794$	−0.0129938	+	0.0149956i	−0.000461132	+	0.000532175i
$795$	−3.13636	−	3.61955i	−0.111235	−	0.128372i
$796$	−24.7422	−	7.26497i	−0.876964	−	0.257500i
$797$	10.1674	−	2.98541i	0.360147	−	0.105749i	−0.0966531	−	0.995318i	$-0.530814\pi$
$797$	10.1674	−	2.98541i	0.360147	−	0.105749i	0.456800	+	0.889570i	$0.348996\pi$
$798$	−0.316221	−	2.19937i	−0.0111941	−	0.0778567i
$799$	7.52939	+	8.68938i	0.266371	+	0.307408i
$800$	−5.05753	−	3.25028i	−0.178811	−	0.114915i
$801$	24.9800	+	7.33480i	0.882626	+	0.259162i
$802$	0.339862	−	2.36379i	0.0120009	−	0.0834684i
$803$	−0.456387	−	2.09344i	−0.0161055	−	0.0738761i
$804$	7.17369	+	49.8941i	0.252997	+	1.75963i
$805$	2.32911	−	16.1993i	0.0820902	−	0.570950i
$806$	−0.628870	+	0.404150i	−0.0221510	+	0.0142356i
$807$	27.6523			0.973407
$808$	−2.05916	+	4.50893i	−0.0724410	+	0.158624i
$809$	−10.3216	+	11.9118i	−0.362888	+	0.418795i	−0.907605	−	0.419825i	$-0.862091\pi$
$809$	−10.3216	+	11.9118i	−0.362888	+	0.418795i	0.544717	+	0.838620i	$0.316637\pi$
$810$	−0.464988	−	1.01818i	−0.0163380	−	0.0357752i
$811$	6.10301	−	13.3637i	0.214306	−	0.469264i	−0.771698	−	0.635990i	$-0.780592\pi$
$811$	6.10301	−	13.3637i	0.214306	−	0.469264i	0.986003	+	0.166725i	$0.0533193\pi$
$812$	18.1564	+	20.9536i	0.637164	+	0.735327i
$813$	59.3498	−	17.4267i	2.08149	−	0.611181i
$814$	0.593749	+	1.08621i	0.0208109	+	0.0380716i
$815$	−23.2767	−	6.83466i	−0.815348	−	0.239408i
$816$	−6.01665	−	13.1746i	−0.210625	−	0.461204i
$817$	−27.4762	−	60.1645i	−0.961271	−	2.10489i
$818$	0.0944856	−	0.0277435i	0.00330361	−	0.000970028i
$819$	−20.0492	−	43.9016i	−0.700575	−	1.53405i
$820$	23.0836			0.806113
$821$	5.46447	+	38.0062i	0.190711	+	1.32643i	0.830131	+	0.557568i	$0.188265\pi$
$821$	5.46447	+	38.0062i	0.190711	+	1.32643i	−0.639420	+	0.768858i	$0.720825\pi$
$822$	−0.770541	−	0.226251i	−0.0268757	−	0.00789142i
$823$	−4.72638	−	32.8727i	−0.164751	−	1.14587i	−0.889526	−	0.456884i	$-0.848966\pi$
$823$	−4.72638	−	32.8727i	−0.164751	−	1.14587i	0.724775	−	0.688985i	$-0.241944\pi$
$824$	0.582713	+	0.672486i	0.0202998	+	0.0234272i
$825$	45.5593	+	45.5183i	1.58617	+	1.58475i
$826$	0.144939	−	0.167268i	0.00504307	−	0.00582001i
$827$	−8.35450	−	5.36911i	−0.290514	−	0.186702i	0.387263	−	0.921969i	$-0.373420\pi$
$827$	−8.35450	−	5.36911i	−0.290514	−	0.186702i	−0.677778	+	0.735267i	$0.737057\pi$
$828$	16.6648	−	4.89323i	0.579142	−	0.170052i
$829$	−15.0990	+	9.70352i	−0.524409	+	0.337017i	−0.775914	−	0.630839i	$-0.782711\pi$
$829$	−15.0990	+	9.70352i	−0.524409	+	0.337017i	0.251505	+	0.967856i	$0.419075\pi$
$830$	−0.405026	−	0.118926i	−0.0140587	−	0.00412799i
$831$	5.05133	+	5.82955i	0.175229	+	0.202225i
$832$	−6.09566	+	42.3962i	−0.211329	+	1.46982i
$833$	−0.436488	+	3.03584i	−0.0151234	+	0.105186i
$834$	0.449078	−	0.983345i	0.0155503	−	0.0340504i
$835$	−18.7814	+	41.1254i	−0.649956	+	1.42320i
$836$	22.0455	−	29.4770i	0.762460	−	1.01948i
$837$	−2.36742	−	5.18393i	−0.0818300	−	0.179183i
$838$	−2.56363			−0.0885590
$839$	1.89923	+	13.2094i	0.0655687	+	0.456041i	0.995984	+	0.0895331i	$0.0285375\pi$
$839$	1.89923	+	13.2094i	0.0655687	+	0.456041i	−0.930415	+	0.366507i	$0.880553\pi$
$840$	3.66578	−	4.23053i	0.126481	−	0.145967i
$841$	9.70446	−	6.23668i	0.334637	−	0.215058i
$842$	−0.0210052	+	0.146094i	−0.000723887	+	0.00503474i
$843$	−9.62954	+	21.0858i	−0.331659	+	0.726232i
$844$	−26.6400			−0.916986
$845$	−48.6747	+	31.2813i	−1.67446	+	1.07611i
$846$	−2.34961			−0.0807811
$847$	−23.7666	−	3.39531i	−0.816630	−	0.116664i
$848$	−2.03936			−0.0700320
$849$	−28.7556	+	18.4801i	−0.986891	+	0.634236i
$850$	0.689208			0.0236396
$851$	4.81612	−	10.5458i	0.165095	−	0.361507i
$852$	−3.71122	+	25.8121i	−0.127144	+	0.884309i
$853$	39.7766	−	25.5628i	1.36192	−	0.875255i	0.363512	−	0.931590i	$-0.381578\pi$
$853$	39.7766	−	25.5628i	1.36192	−	0.875255i	0.998412	+	0.0563346i	$0.0179414\pi$
$854$	0.656261	−	0.757366i	0.0224568	−	0.0259165i
$855$	−11.3048	−	78.6266i	−0.386616	−	2.68897i
$856$	−0.366397			−0.0125232
$857$	1.78571	+	3.91016i	0.0609987	+	0.133568i	0.937676	−	0.347510i	$-0.112973\pi$
$857$	1.78571	+	3.91016i	0.0609987	+	0.133568i	−0.876678	+	0.481078i	$0.840245\pi$
$858$	−1.15075	+	3.08953i	−0.0392861	+	0.105475i
$859$	9.31495	−	20.3969i	0.317822	−	0.695933i	−0.681535	−	0.731786i	$-0.738687\pi$
$859$	9.31495	−	20.3969i	0.317822	−	0.695933i	0.999357	+	0.0358521i	$0.0114145\pi$
$860$	34.5691	−	75.6957i	1.17880	−	2.58120i
$861$	−2.72450	+	18.9493i	−0.0928507	+	0.645791i
$862$	−0.0353884	+	0.246132i	−0.00120533	+	0.00838329i
$863$	−5.62359	−	6.48997i	−0.191429	−	0.220921i	0.651919	−	0.758289i	$-0.273964\pi$
$863$	−5.62359	−	6.48997i	−0.191429	−	0.220921i	−0.843348	+	0.537368i	$0.819419\pi$
$864$	2.25122	+	0.661019i	0.0765882	+	0.0224883i
$865$	67.0294	−	43.0772i	2.27907	−	1.46467i
$866$	−1.39254	+	0.408888i	−0.0473206	+	0.0138946i
$867$	−33.8237	−	21.7372i	−1.14871	−	0.738234i
$868$	−5.70293	+	6.58153i	−0.193570	+	0.223392i
$869$	2.34066	−	3.12969i	0.0794016	−	0.106168i
$870$	−2.67657	−	3.08892i	−0.0907441	−	0.104724i
$871$	7.34289	+	51.0709i	0.248804	+	1.73047i
$872$	3.31022	+	0.971970i	0.112098	+	0.0329150i
$873$	4.32896	+	30.1086i	0.146513	+	1.01902i
$874$	0.818482			0.0276856
$875$	−7.32036	−	16.0294i	−0.247473	−	0.541891i
$876$	−3.28889	+	0.965706i	−0.111121	+	0.0326282i
$877$	−2.80187	−	6.13524i	−0.0946124	−	0.207172i	0.856409	−	0.516299i	$-0.172691\pi$
$877$	−2.80187	−	6.13524i	−0.0946124	−	0.207172i	−0.951021	+	0.309127i	$0.899963\pi$
$878$	−0.573659	−	1.25614i	−0.0193600	−	0.0423926i
$879$	54.5879	+	16.0284i	1.84120	+	0.540626i
$880$	46.0816	−	3.31664i	1.55341	−	0.111804i
$881$	28.7578	−	8.44406i	0.968875	−	0.284488i	0.241251	−	0.970463i	$-0.422442\pi$
$881$	28.7578	−	8.44406i	0.968875	−	0.284488i	0.727625	+	0.685975i	$0.240624\pi$
$882$	−0.410446	−	0.473680i	−0.0138204	−	0.0159496i
$883$	10.8875	−	23.8404i	0.366395	−	0.802293i	−0.633204	−	0.773985i	$-0.718261\pi$
$883$	10.8875	−	23.8404i	0.366395	−	0.802293i	0.999599	−	0.0283086i	$-0.00901210\pi$
$884$	−6.17325	−	13.5175i	−0.207629	−	0.454644i
$885$	8.99929	−	10.3857i	0.302508	−	0.349113i
$886$	−0.381778	+	0.835978i	−0.0128261	+	0.0280852i
$887$	−48.6904			−1.63486			−0.817431	−	0.576026i	$-0.804603\pi$
$887$	−48.6904			−1.63486			−0.817431	+	0.576026i	$0.804603\pi$
$888$	3.33596	−	2.14389i	0.111947	−	0.0719442i
$889$	0.432204	−	3.00604i	0.0144957	−	0.100819i
$890$	0.219676	+	1.52788i	0.00736356	+	0.0512147i
$891$	13.5004	+	7.36392i	0.452282	+	0.246701i
$892$	0.445513	−	3.09861i	0.0149169	−	0.103749i
$893$	44.7468	+	13.1389i	1.49740	+	0.439675i
$894$	1.34072	+	0.861631i	0.0448405	+	0.0288172i
$895$	38.3708	+	44.2822i	1.28259	+	1.48019i
$896$	−0.680062	−	4.72994i	−0.0227193	−	0.158016i
$897$	29.6262	−	8.69904i	0.989190	−	0.290452i
$898$	−0.914201	−	0.268434i	−0.0305073	−	0.00895775i
$899$	8.33787	+	9.62241i	0.278083	+	0.320925i
$900$	38.8471	−	44.8319i	1.29490	−	1.49440i
$901$	0.592384	−	0.380702i	0.0197352	−	0.0126830i
$902$	0.602576	−	0.451505i	0.0200636	−	0.0150335i
$903$	58.0585	+	37.3120i	1.93207	+	1.24166i
$904$	2.68510	−	0.788417i	0.0893051	−	0.0262224i
$905$	−54.5527	+	62.9572i	−1.81339	+	2.09277i
$906$	0.794919	+	0.510864i	0.0264094	+	0.0169723i
$907$	27.5915	+	17.7320i	0.916161	+	0.588781i	0.911541	−	0.411208i	$-0.134893\pi$
$907$	27.5915	+	17.7320i	0.916161	+	0.588781i	0.00461979	+	0.999989i	$0.498529\pi$
$908$	34.3387	+	22.0681i	1.13957	+	0.732357i
$909$	−61.7441	−	39.6805i	−2.04792	−	1.31612i
$910$	1.87389	−	2.16259i	0.0621190	−	0.0716891i
$911$	−5.54106	+	1.62700i	−0.183583	+	0.0539049i	−0.372232	−	0.928140i	$-0.621407\pi$
$911$	−5.54106	+	1.62700i	−0.183583	+	0.0539049i	0.188649	+	0.982045i	$0.439589\pi$
$912$	−49.4207	−	31.7608i	−1.63648	−	1.05170i
$913$	5.43289	−	2.02914i	0.179802	−	0.0671549i
$914$	−0.679278	+	0.436545i	−0.0224685	+	0.0144396i
$915$	40.7474	−	47.0250i	1.34707	−	1.55460i
$916$	24.9098	+	28.7474i	0.823042	+	0.949841i
$917$	38.5315	+	11.3139i	1.27242	+	0.373617i
$918$	−0.258082	+	0.0757797i	−0.00851797	+	0.00250110i
$919$	−0.0227731	−	0.158391i	−0.000751217	−	0.00522483i	0.989442	−	0.144927i	$-0.0462947\pi$
$919$	−0.0227731	−	0.158391i	−0.000751217	−	0.00522483i	−0.990194	+	0.139702i	$0.955386\pi$
$920$	1.35031	+	1.55834i	0.0445185	+	0.0513771i
$921$	58.1507	+	37.3712i	1.91613	+	1.23142i
$922$	1.87273	+	0.549883i	0.0616750	+	0.0181094i
$923$	−3.79876	+	26.4209i	−0.125038	+	0.869656i
$924$	−2.72275	+	38.3110i	−0.0895718	+	1.26034i
$925$	−5.63529	−	39.1943i	−0.185287	−	1.28870i
$926$	−0.300159	+	2.08765i	−0.00986382	+	0.0686044i
$927$	−11.0839	+	7.12320i	−0.364044	+	0.233957i
$928$	−5.24191			−0.172074
$929$	−18.9108	+	41.4088i	−0.620443	+	1.35858i	0.294754	+	0.955573i	$0.404762\pi$
$929$	−18.9108	+	41.4088i	−0.620443	+	1.35858i	−0.915197	+	0.403007i	$0.867965\pi$
$930$	0.840710	−	0.970231i	0.0275680	−	0.0318151i
$931$	5.16790	+	11.3161i	0.169371	+	0.370871i
$932$	−11.4108	+	24.9861i	−0.373773	+	0.818448i
$933$	24.2902	+	28.0323i	0.795224	+	0.917738i
$934$	−0.172653	+	0.0506954i	−0.00564937	+	0.00165880i
$935$	−12.7664	+	9.56576i	−0.417506	+	0.312834i
$936$	5.83449	+	1.71316i	0.190706	+	0.0559964i
$937$	−10.2257	−	22.3913i	−0.334061	−	0.731491i	0.665833	−	0.746101i	$-0.268076\pi$
$937$	−10.2257	−	22.3913i	−0.334061	−	0.731491i	−0.999893	+	0.0146104i	$0.995349\pi$
$938$	−0.592842	−	1.29814i	−0.0193570	−	0.0423859i
$939$	−51.0146	+	14.9792i	−1.66480	+	0.488829i
$940$	24.3744	+	53.3725i	0.795005	+	1.74082i
$941$	−21.5454			−0.702361			−0.351181	−	0.936308i	$-0.614220\pi$
$941$	−21.5454			−0.702361			−0.351181	+	0.936308i	$0.614220\pi$
$942$	0.240207	+	1.67068i	0.00782638	+	0.0544337i
$943$	−6.76623	−	1.98675i	−0.220339	−	0.0646973i
$944$	−0.832775	−	5.79208i	−0.0271045	−	0.188516i
$945$	14.2858	+	16.4867i	0.464717	+	0.536312i
$946$	−0.578184	−	2.65213i	−0.0187984	−	0.0862281i
$947$	−1.38312	+	1.59620i	−0.0449453	+	0.0518697i	−0.777777	−	0.628540i	$-0.783653\pi$
$947$	−1.38312	+	1.59620i	−0.0449453	+	0.0518697i	0.732832	+	0.680410i	$0.238198\pi$
$948$	−5.25972	−	3.38022i	−0.170828	−	0.109784i
$949$	−3.36646	+	0.988483i	−0.109280	+	0.0320875i
$950$	2.35173	−	1.51136i	0.0763001	−	0.0490351i
$951$	−42.4973	−	12.4783i	−1.37807	−	0.404638i
$952$	0.538971	+	0.622006i	0.0174682	+	0.0201593i
$953$	7.43521	−	51.7130i	0.240850	−	1.67515i	−0.407036	−	0.913412i	$-0.633438\pi$
$953$	7.43521	−	51.7130i	0.240850	−	1.67515i	0.647886	−	0.761737i	$-0.275653\pi$
$954$	−0.0204791	+	0.142435i	−0.000663035	+	0.00461151i
$955$	−31.5877	+	69.1674i	−1.02215	+	2.23820i
$956$	8.89238	−	19.4716i	0.287600	−	0.629756i
$957$	54.8754	+	11.9116i	1.77387	+	0.385046i
$958$	−0.0747464	−	0.163672i	−0.00241495	−	0.00528800i
$959$	−9.57620			−0.309232
$960$	−10.4685	−	72.8099i	−0.337869	−	2.34993i
$961$	17.6818	−	20.4058i	0.570379	−	0.658253i
$962$	1.70529	−	1.09593i	0.0549809	−	0.0353341i
$963$	0.772082	−	5.36995i	0.0248800	−	0.173044i
$964$	7.37176	−	16.1419i	0.237429	−	0.519896i
$965$	−40.3533			−1.29902
$966$	−0.718457	+	0.461724i	−0.0231160	+	0.0148557i
$967$	−4.65471			−0.149685			−0.0748427	−	0.997195i	$-0.523845\pi$
$967$	−4.65471			−0.149685			−0.0748427	+	0.997195i	$0.523845\pi$
$968$	2.28423	−	1.98290i	0.0734179	−	0.0637327i
$969$	20.2845			0.651631
$970$	−1.51720	+	0.975043i	−0.0487143	+	0.0313068i
$971$	−44.0562			−1.41383			−0.706916	−	0.707298i	$-0.749914\pi$
$971$	−44.0562			−1.41383			−0.706916	+	0.707298i	$0.749914\pi$
$972$	17.3061	−	37.8952i	0.555095	−	1.21549i
$973$	1.83455	−	12.7596i	0.0588129	−	0.409053i
$974$	0.718956	−	0.462045i	0.0230368	−	0.0148049i
$975$	69.0612	−	79.7008i	2.21173	−	2.55247i
$976$	−3.77068	−	26.2256i	−0.120696	−	0.839462i
$977$	−50.8845			−1.62794			−0.813969	−	0.580908i	$-0.802698\pi$
$977$	−50.8845			−1.62794			−0.813969	+	0.580908i	$0.802698\pi$
$978$	0.525892	+	1.15154i	0.0168162	+	0.0368223i
$979$	−15.0023	−	14.9889i	−0.479477	−	0.479046i
$980$	−6.50197	+	14.2373i	−0.207698	+	0.454795i
$981$	−21.2206	+	46.4667i	−0.677523	+	1.48357i
$982$	0.00666942	−	0.0463868i	0.000212830	−	0.00148026i
$983$	−5.47272	+	38.0636i	−0.174553	+	1.21404i	0.694563	+	0.719432i	$0.255598\pi$
$983$	−5.47272	+	38.0636i	−0.174553	+	1.21404i	−0.869116	+	0.494609i	$0.835311\pi$
$984$	−1.57954	−	1.82289i	−0.0503540	−	0.0581117i
$985$	−11.7423	−	3.44786i	−0.374142	−	0.109858i
$986$	0.505540	−	0.324891i	0.0160997	−	0.0103466i
$987$	−46.6903	+	13.7095i	−1.48617	+	0.436379i
$988$	−50.7070	−	32.5874i	−1.61321	−	1.03674i
$989$	−16.6478	+	19.2126i	−0.529369	+	0.610925i
$990$	0.231102	−	3.25178i	0.00734492	−	0.103348i
$991$	−19.9538	−	23.0280i	−0.633855	−	0.731507i	0.344421	−	0.938815i	$-0.388075\pi$
$991$	−19.9538	−	23.0280i	−0.633855	−	0.731507i	−0.978276	+	0.207308i	$0.933530\pi$
$992$	−0.234319	−	1.62973i	−0.00743965	−	0.0517439i
$993$	−23.2105	−	6.81521i	−0.736562	−	0.216274i
$994$	−0.105071	−	0.730782i	−0.00333264	−	0.0231790i
$995$	45.3298			1.43705
$996$	−3.85419	−	8.43950i	−0.122125	−	0.267416i
$997$	42.2692	−	12.4114i	1.33868	−	0.393072i	0.467482	−	0.884003i	$-0.345161\pi$
$997$	42.2692	−	12.4114i	1.33868	−	0.393072i	0.871199	+	0.490931i	$0.163343\pi$
$998$	0.906281	+	1.98448i	0.0286878	+	0.0628176i
$999$	6.41969	+	14.0572i	0.203110	+	0.444749i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.2.e.a.12.6	✓	100
121.111	even	11	inner	121.2.e.a.111.6	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.2.e.a.12.6	✓	100	1.1	even	1	trivial
121.2.e.a.111.6	yes	100	121.111	even	11	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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	121.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0579015 + 0.0372110i) q^{2} +2.65925 q^{3} +(-0.828862 + 1.81495i) q^{4} +(0.499158 - 3.47172i) q^{5} +(-0.153975 + 0.0989535i) q^{6} +(-1.42926 + 1.64945i) q^{7} +(-0.0391344 - 0.272185i) q^{8} +4.07163 q^{9} +O(q^{10})\)	\(q+(-0.0579015 + 0.0372110i) q^{2} +2.65925 q^{3} +(-0.828862 + 1.81495i) q^{4} +(0.499158 - 3.47172i) q^{5} +(-0.153975 + 0.0989535i) q^{6} +(-1.42926 + 1.64945i) q^{7} +(-0.0391344 - 0.272185i) q^{8} +4.07163 q^{9} +(0.100284 + 0.219592i) q^{10} +(-2.91165 - 1.58818i) q^{11} +(-2.20416 + 4.82643i) q^{12} +(-2.25614 + 4.94026i) q^{13} +(0.0213784 - 0.148690i) q^{14} +(1.32739 - 9.23218i) q^{15} +(-2.60084 - 3.00153i) q^{16} +(1.31580 + 0.386353i) q^{17} +(-0.235754 + 0.151510i) q^{18} +(5.33702 - 1.56709i) q^{19} +(5.88728 + 3.78352i) q^{20} +(-3.80076 + 4.38631i) q^{21} +(0.227686 - 0.0163873i) q^{22} +(-1.40004 - 1.61573i) q^{23} +(-0.104068 - 0.723810i) q^{24} +(-7.00620 - 2.05721i) q^{25} +(-0.0531982 - 0.370002i) q^{26} +2.84975 q^{27} +(-1.80902 - 3.96121i) q^{28} +(-6.10887 + 1.79373i) q^{29} +(0.266681 + 0.583950i) q^{30} +(-0.830748 - 1.81908i) q^{31} +(0.789974 + 0.231957i) q^{32} +(-7.74281 - 4.22338i) q^{33} +(-0.0905631 + 0.0265917i) q^{34} +(5.01300 + 5.78531i) q^{35} +(-3.37482 + 7.38983i) q^{36} +(2.25272 + 4.93277i) q^{37} +(-0.250708 + 0.289332i) q^{38} +(-5.99966 + 13.1374i) q^{39} -0.964485 q^{40} +(2.77487 - 1.78330i) q^{41} +(0.0568505 - 0.395404i) q^{42} +(-1.69226 - 11.7700i) q^{43} +(5.29583 - 3.96812i) q^{44} +(2.03239 - 14.1356i) q^{45} +(0.141187 + 0.0414562i) q^{46} +(7.05328 + 4.53286i) q^{47} +(-6.91631 - 7.98184i) q^{48} +(0.318292 + 2.21377i) q^{49} +(0.482220 - 0.141593i) q^{50} +(3.49904 + 1.02741i) q^{51} +(-7.09632 - 8.18959i) q^{52} +(0.336262 - 0.388067i) q^{53} +(-0.165004 + 0.106042i) q^{54} +(-6.96708 + 9.31566i) q^{55} +(0.504890 + 0.324473i) q^{56} +(14.1925 - 4.16729i) q^{57} +(0.286966 - 0.331176i) q^{58} +(1.23948 + 0.796564i) q^{59} +(15.6558 + 10.0614i) q^{60} +(5.61217 + 3.60672i) q^{61} +(0.115792 + 0.0744147i) q^{62} +(-5.81941 + 6.71596i) q^{63} +(7.56707 - 2.22189i) q^{64} +(16.0250 + 10.2987i) q^{65} +(0.605476 - 0.0435781i) q^{66} +(7.99207 - 5.13619i) q^{67} +(-1.79183 + 2.06788i) q^{68} +(-3.72305 - 4.29663i) q^{69} +(-0.505538 - 0.148439i) q^{70} +(4.71573 - 1.38466i) q^{71} +(-0.159341 - 1.10824i) q^{72} +(0.423055 + 0.488231i) q^{73} +(-0.313989 - 0.201789i) q^{74} +(-18.6313 - 5.47063i) q^{75} +(-1.57945 + 10.9853i) q^{76} +(6.78112 - 2.53270i) q^{77} +(-0.141468 - 0.983929i) q^{78} +(-0.167697 + 1.16636i) q^{79} +(-11.7187 + 7.53116i) q^{80} -4.63670 q^{81} +(-0.0943105 + 0.206511i) q^{82} +(-1.14509 + 1.32150i) q^{83} +(-4.81065 - 10.5339i) q^{84} +(1.99810 - 4.37522i) q^{85} +(0.535956 + 0.618527i) q^{86} +(-16.2450 + 4.76997i) q^{87} +(-0.318334 + 0.854660i) q^{88} +(6.13514 + 1.80144i) q^{89} +(0.408320 + 0.894097i) q^{90} +(-4.92411 - 10.7823i) q^{91} +(4.09291 - 1.20179i) q^{92} +(-2.20917 - 4.83741i) q^{93} -0.577067 q^{94} +(-2.77648 - 19.3108i) q^{95} +(2.10074 + 0.616833i) q^{96} +(1.06320 + 7.39472i) q^{97} +(-0.100806 - 0.116337i) q^{98} +(-11.8552 - 6.46649i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 6 q^{2} - 18 q^{3} - 16 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} + 4 q^{8} + 70 q^{9}+O(q^{10}) \) 100 * q - 6 * q^2 - 18 * q^3 - 16 * q^4 - 7 * q^5 - 23 * q^6 - q^7 + 4 * q^8 + 70 * q^9	\( 100 q - 6 q^{2} - 18 q^{3} - 16 q^{4} - 7 q^{5} - 23 q^{6} - q^{7} + 4 q^{8} + 70 q^{9} - 13 q^{10} - 12 q^{11} - 51 q^{12} - 34 q^{13} - 17 q^{14} - 46 q^{15} + 10 q^{16} + 9 q^{17} - 31 q^{18} + 9 q^{19} + 21 q^{20} - 14 q^{21} - 20 q^{22} - 11 q^{23} - 72 q^{24} + 11 q^{25} + 33 q^{26} - 60 q^{27} + 49 q^{28} + 19 q^{29} + 26 q^{30} - 13 q^{31} + 44 q^{32} + q^{33} + 31 q^{34} + 39 q^{35} - 17 q^{36} - 16 q^{37} - 29 q^{38} + 16 q^{39} + 2 q^{40} + 39 q^{41} + 42 q^{42} + 39 q^{43} + 53 q^{44} - 33 q^{45} + 59 q^{46} + 21 q^{47} + 56 q^{48} - 11 q^{49} - 58 q^{50} - 139 q^{51} - 75 q^{52} - 73 q^{53} - 156 q^{54} - 34 q^{55} + 10 q^{56} - 41 q^{57} - 38 q^{58} + 33 q^{59} + 100 q^{60} + 39 q^{61} + 44 q^{62} - 76 q^{63} - 16 q^{64} + 36 q^{65} + 75 q^{66} - 4 q^{67} + 119 q^{68} + 32 q^{69} + 61 q^{70} + 5 q^{71} + 63 q^{72} + 37 q^{73} + 109 q^{74} + 58 q^{75} - 91 q^{76} - 53 q^{77} - 24 q^{78} - 9 q^{79} - 36 q^{80} + 28 q^{81} + 33 q^{82} + 79 q^{83} + 176 q^{84} - 11 q^{85} + 85 q^{86} + 76 q^{87} + 33 q^{88} - 48 q^{89} - 89 q^{90} - 14 q^{91} - 113 q^{92} + 31 q^{93} - 38 q^{94} + 21 q^{95} + 84 q^{96} + 40 q^{97} - 22 q^{98} - 53 q^{99}+O(q^{100}) \) 100 * q - 6 * q^2 - 18 * q^3 - 16 * q^4 - 7 * q^5 - 23 * q^6 - q^7 + 4 * q^8 + 70 * q^9 - 13 * q^10 - 12 * q^11 - 51 * q^12 - 34 * q^13 - 17 * q^14 - 46 * q^15 + 10 * q^16 + 9 * q^17 - 31 * q^18 + 9 * q^19 + 21 * q^20 - 14 * q^21 - 20 * q^22 - 11 * q^23 - 72 * q^24 + 11 * q^25 + 33 * q^26 - 60 * q^27 + 49 * q^28 + 19 * q^29 + 26 * q^30 - 13 * q^31 + 44 * q^32 + q^33 + 31 * q^34 + 39 * q^35 - 17 * q^36 - 16 * q^37 - 29 * q^38 + 16 * q^39 + 2 * q^40 + 39 * q^41 + 42 * q^42 + 39 * q^43 + 53 * q^44 - 33 * q^45 + 59 * q^46 + 21 * q^47 + 56 * q^48 - 11 * q^49 - 58 * q^50 - 139 * q^51 - 75 * q^52 - 73 * q^53 - 156 * q^54 - 34 * q^55 + 10 * q^56 - 41 * q^57 - 38 * q^58 + 33 * q^59 + 100 * q^60 + 39 * q^61 + 44 * q^62 - 76 * q^63 - 16 * q^64 + 36 * q^65 + 75 * q^66 - 4 * q^67 + 119 * q^68 + 32 * q^69 + 61 * q^70 + 5 * q^71 + 63 * q^72 + 37 * q^73 + 109 * q^74 + 58 * q^75 - 91 * q^76 - 53 * q^77 - 24 * q^78 - 9 * q^79 - 36 * q^80 + 28 * q^81 + 33 * q^82 + 79 * q^83 + 176 * q^84 - 11 * q^85 + 85 * q^86 + 76 * q^87 + 33 * q^88 - 48 * q^89 - 89 * q^90 - 14 * q^91 - 113 * q^92 + 31 * q^93 - 38 * q^94 + 21 * q^95 + 84 * q^96 + 40 * q^97 - 22 * q^98 - 53 * q^99

Introduction

L-functions

Modular forms

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