LMFDB - Embedded newform 690.2.m.d.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 8 x^{18} - 32 x^{17} + 277 x^{16} - 1138 x^{15} + 2950 x^{14} - 6404 x^{13} + \cdots + 7921 $ x^20 - 5x^19 + 8x^18 - 32x^17 + 277x^16 - 1138x^15 + 2950x^14 - 6404x^13 + 24088x^12 - 93423x^11 + 318055x^10 - 798006x^9 + 1869818x^8 - 3381161x^7 + 6172602x^6 - 7296658x^5 + 10759748x^4 - 4308967x^3 + 7994447x^2 + 486652*x + 7921
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			31.2
Root			$-2.42025 + 2.79312i$ of defining polynomial
Character	$\chi$	$=$	690.31
Dual form			690.2.m.d.601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-1.25705 - 0.807858i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-1.25705 - 0.807858i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.841254 + 0.540641i) q^{10} +(-0.517582 - 3.59986i) q^{11} +(0.142315 + 0.989821i) q^{12} +(-2.43129 + 1.56250i) q^{13} +(0.978532 - 1.12929i) q^{14} +(0.415415 - 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-2.69323 + 0.790802i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(-1.45199 - 0.426343i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(-0.212655 + 1.47905i) q^{21} +3.63688 q^{22} +(-3.70148 - 3.04943i) q^{23} -1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(-1.20058 - 2.62891i) q^{26} +(0.959493 + 0.281733i) q^{27} +(0.978532 + 1.12929i) q^{28} +(-5.62431 + 1.65145i) q^{29} +(0.841254 + 0.540641i) q^{30} +(2.97939 - 6.52395i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-3.05954 + 1.96625i) q^{33} +(-0.399467 - 2.77836i) q^{34} +(-0.212655 - 1.47905i) q^{35} +(0.841254 - 0.540641i) q^{36} +(0.584941 - 0.675058i) q^{37} +(0.628644 - 1.37654i) q^{38} +(2.43129 + 1.56250i) q^{39} +(0.959493 - 0.281733i) q^{40} +(-2.84765 - 3.28636i) q^{41} +(-1.43373 - 0.420982i) q^{42} +(0.580310 + 1.27070i) q^{43} +(-0.517582 + 3.59986i) q^{44} -1.00000 q^{45} +(3.54517 - 3.22982i) q^{46} -5.18761 q^{47} +(0.142315 - 0.989821i) q^{48} +(-1.98036 - 4.33639i) q^{49} +(-0.959493 - 0.281733i) q^{50} +(1.83815 + 2.12133i) q^{51} +(2.77302 - 0.814231i) q^{52} +(-6.33832 - 4.07339i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(2.38165 - 2.74857i) q^{55} +(-1.25705 + 0.807858i) q^{56} +(0.215364 + 1.49789i) q^{57} +(-0.834215 - 5.80209i) q^{58} +(-2.60361 + 1.67324i) q^{59} +(-0.654861 + 0.755750i) q^{60} +(3.11472 - 6.82029i) q^{61} +(6.03353 + 3.87752i) q^{62} +(1.43373 - 0.420982i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-2.77302 - 0.814231i) q^{65} +(-1.51082 - 3.30823i) q^{66} +(-0.328062 + 2.28172i) q^{67} +2.80693 q^{68} +(-1.23621 + 4.63376i) q^{69} +1.49426 q^{70} +(-0.0472038 + 0.328309i) q^{71} +(0.415415 + 0.909632i) q^{72} +(-6.08741 - 1.78742i) q^{73} +(0.584941 + 0.675058i) q^{74} +(0.959493 - 0.281733i) q^{75} +(1.27306 + 0.818147i) q^{76} +(-2.25755 + 4.94335i) q^{77} +(-1.89260 + 2.18418i) q^{78} +(1.62691 - 1.04555i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(3.65817 - 2.35096i) q^{82} +(7.84223 - 9.05042i) q^{83} +(0.620738 - 1.35923i) q^{84} +(-2.36134 - 1.51754i) q^{85} +(-1.34035 + 0.393564i) q^{86} +(3.83863 + 4.43002i) q^{87} +(-3.48956 - 1.02463i) q^{88} +(2.81447 + 6.16282i) q^{89} +(0.142315 - 0.989821i) q^{90} +4.31854 q^{91} +(2.69242 + 3.96874i) q^{92} -7.17207 q^{93} +(0.738274 - 5.13481i) q^{94} +(-0.628644 - 1.37654i) q^{95} +(0.959493 + 0.281733i) q^{96} +(9.31155 + 10.7461i) q^{97} +(4.57408 - 1.34307i) q^{98} +(3.05954 + 1.96625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$2$	−0.142315	+	0.989821i	−0.100632	+	0.699909i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$5$	0.654861	+	0.755750i	0.292863	+	0.337981i
$6$	0.959493	−	0.281733i	0.391711	−	0.115017i
$7$	−1.25705	−	0.807858i	−0.475121	−	0.305341i	0.281076	−	0.959685i	$-0.409309\pi$
$7$	−1.25705	−	0.807858i	−0.475121	−	0.305341i	−0.756197	+	0.654344i	$0.772945\pi$
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	−0.841254	+	0.540641i	−0.266028	+	0.170966i
$11$	−0.517582	−	3.59986i	−0.156057	−	1.08540i	−0.905811	−	0.423683i	$-0.860737\pi$
$11$	−0.517582	−	3.59986i	−0.156057	−	1.08540i	0.749754	−	0.661717i	$-0.230172\pi$
$12$	0.142315	+	0.989821i	0.0410828	+	0.285737i
$13$	−2.43129	+	1.56250i	−0.674320	+	0.433359i	−0.832480	−	0.554054i	$-0.813080\pi$
$13$	−2.43129	+	1.56250i	−0.674320	+	0.433359i	0.158161	+	0.987413i	$0.449444\pi$
$14$	0.978532	−	1.12929i	0.261524	−	0.301814i
$15$	0.415415	−	0.909632i	0.107260	−	0.234866i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−2.69323	+	0.790802i	−0.653203	+	0.191798i	−0.591510	−	0.806297i	$-0.701468\pi$
$17$	−2.69323	+	0.790802i	−0.653203	+	0.191798i	−0.0616928	+	0.998095i	$0.519650\pi$
$18$	−0.654861	−	0.755750i	−0.154352	−	0.178132i
$19$	−1.45199	−	0.426343i	−0.333110	−	0.0978099i	0.110901	−	0.993832i	$-0.464627\pi$
$19$	−1.45199	−	0.426343i	−0.333110	−	0.0978099i	−0.444010	+	0.896022i	$0.646445\pi$
$20$	−0.415415	−	0.909632i	−0.0928896	−	0.203400i
$21$	−0.212655	+	1.47905i	−0.0464052	+	0.322755i
$22$	3.63688			0.775386
$23$	−3.70148	−	3.04943i	−0.771812	−	0.635851i
$23$	−3.70148	−	3.04943i	−0.771812	−	0.635851i
$24$	−1.00000			−0.204124
$25$	−0.142315	+	0.989821i	−0.0284630	+	0.197964i
$26$	−1.20058	−	2.62891i	−0.235454	−	0.515572i
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$	0.978532	+	1.12929i	0.184925	+	0.213415i
$29$	−5.62431	+	1.65145i	−1.04441	+	0.306666i	−0.758556	−	0.651608i	$-0.774095\pi$
$29$	−5.62431	+	1.65145i	−1.04441	+	0.306666i	−0.285853	+	0.958274i	$0.592277\pi$
$30$	0.841254	+	0.540641i	0.153591	+	0.0987071i
$31$	2.97939	−	6.52395i	0.535114	−	1.17174i	−0.428280	−	0.903646i	$-0.640880\pi$
$31$	2.97939	−	6.52395i	0.535114	−	1.17174i	0.963394	−	0.268090i	$-0.0863923\pi$
$32$	−0.654861	+	0.755750i	−0.115764	+	0.133599i
$33$	−3.05954	+	1.96625i	−0.532598	+	0.342280i
$34$	−0.399467	−	2.77836i	−0.0685081	−	0.476484i
$35$	−0.212655	−	1.47905i	−0.0359453	−	0.250005i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	0.584941	−	0.675058i	0.0961637	−	0.110979i	−0.705628	−	0.708583i	$-0.749335\pi$
$37$	0.584941	−	0.675058i	0.0961637	−	0.110979i	0.801792	+	0.597604i	$0.203880\pi$
$38$	0.628644	−	1.37654i	0.101980	−	0.223304i
$39$	2.43129	+	1.56250i	0.389319	+	0.250200i
$40$	0.959493	−	0.281733i	0.151709	−	0.0445458i
$41$	−2.84765	−	3.28636i	−0.444728	−	0.513243i	0.488483	−	0.872574i	$-0.337551\pi$
$41$	−2.84765	−	3.28636i	−0.444728	−	0.513243i	−0.933210	+	0.359330i	$0.883005\pi$
$42$	−1.43373	−	0.420982i	−0.221230	−	0.0649589i
$43$	0.580310	+	1.27070i	0.0884964	+	0.193780i	0.948705	−	0.316162i	$-0.102394\pi$
$43$	0.580310	+	1.27070i	0.0884964	+	0.193780i	−0.860209	+	0.509942i	$0.829667\pi$
$44$	−0.517582	+	3.59986i	−0.0780285	+	0.542700i
$45$	−1.00000			−0.149071
$46$	3.54517	−	3.22982i	0.522707	−	0.476212i
$47$	−5.18761			−0.756691			−0.378346	−	0.925664i	$-0.623507\pi$
$47$	−5.18761			−0.756691			−0.378346	+	0.925664i	$0.623507\pi$
$48$	0.142315	−	0.989821i	0.0205414	−	0.142868i
$49$	−1.98036	−	4.33639i	−0.282909	−	0.619484i
$50$	−0.959493	−	0.281733i	−0.135693	−	0.0398430i
$51$	1.83815	+	2.12133i	0.257392	+	0.297046i
$52$	2.77302	−	0.814231i	0.384548	−	0.112914i
$53$	−6.33832	−	4.07339i	−0.870636	−	0.559524i	0.0273115	−	0.999627i	$-0.491305\pi$
$53$	−6.33832	−	4.07339i	−0.870636	−	0.559524i	−0.897947	+	0.440103i	$0.854942\pi$
$54$	−0.415415	+	0.909632i	−0.0565308	+	0.123785i
$55$	2.38165	−	2.74857i	0.321142	−	0.370617i
$56$	−1.25705	+	0.807858i	−0.167981	+	0.107955i
$57$	0.215364	+	1.49789i	0.0285256	+	0.198400i
$58$	−0.834215	−	5.80209i	−0.109538	−	0.761852i
$59$	−2.60361	+	1.67324i	−0.338961	+	0.217837i	−0.699036	−	0.715086i	$-0.746387\pi$
$59$	−2.60361	+	1.67324i	−0.338961	+	0.217837i	0.360075	+	0.932923i	$0.382751\pi$
$60$	−0.654861	+	0.755750i	−0.0845422	+	0.0975669i
$61$	3.11472	−	6.82029i	0.398799	−	0.873248i	−0.598591	−	0.801054i	$-0.704273\pi$
$61$	3.11472	−	6.82029i	0.398799	−	0.873248i	0.997391	−	0.0721939i	$-0.0230000\pi$
$62$	6.03353	+	3.87752i	0.766259	+	0.492445i
$63$	1.43373	−	0.420982i	0.180633	−	0.0530387i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−2.77302	−	0.814231i	−0.343950	−	0.100993i
$66$	−1.51082	−	3.30823i	−0.185969	−	0.407214i
$67$	−0.328062	+	2.28172i	−0.0400792	+	0.278757i	−0.999999	−	0.00151856i	$-0.999517\pi$
$67$	−0.328062	+	2.28172i	−0.0400792	+	0.278757i	0.959920	+	0.280275i	$0.0904257\pi$
$68$	2.80693			0.340390
$69$	−1.23621	+	4.63376i	−0.148823	+	0.557840i
$70$	1.49426			0.178598
$71$	−0.0472038	+	0.328309i	−0.00560206	+	0.0389632i	−0.992431	−	0.122806i	$-0.960811\pi$
$71$	−0.0472038	+	0.328309i	−0.00560206	+	0.0389632i	0.986829	+	0.161769i	$0.0517199\pi$
$72$	0.415415	+	0.909632i	0.0489571	+	0.107201i
$73$	−6.08741	−	1.78742i	−0.712477	−	0.209202i	−0.0946438	−	0.995511i	$-0.530171\pi$
$73$	−6.08741	−	1.78742i	−0.712477	−	0.209202i	−0.617833	+	0.786309i	$0.711989\pi$
$74$	0.584941	+	0.675058i	0.0679980	+	0.0784739i
$75$	0.959493	−	0.281733i	0.110793	−	0.0325317i
$76$	1.27306	+	0.818147i	0.146030	+	0.0938479i
$77$	−2.25755	+	4.94335i	−0.257272	+	0.563347i
$78$	−1.89260	+	2.18418i	−0.214295	+	0.247310i
$79$	1.62691	−	1.04555i	0.183041	−	0.117633i	−0.445911	−	0.895077i	$-0.647120\pi$
$79$	1.62691	−	1.04555i	0.183041	−	0.117633i	0.628953	+	0.777444i	$0.283484\pi$
$80$	0.142315	+	0.989821i	0.0159113	+	0.110665i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	3.65817	−	2.35096i	0.403977	−	0.259621i
$83$	7.84223	−	9.05042i	0.860797	−	0.993412i	−0.139198	−	0.990265i	$-0.544453\pi$
$83$	7.84223	−	9.05042i	0.860797	−	0.993412i	0.999995	−	0.00314774i	$-0.00100196\pi$
$84$	0.620738	−	1.35923i	0.0677280	−	0.148304i
$85$	−2.36134	−	1.51754i	−0.256123	−	0.164600i
$86$	−1.34035	+	0.393564i	−0.144534	+	0.0424391i
$87$	3.83863	+	4.43002i	0.411545	+	0.474948i
$88$	−3.48956	−	1.02463i	−0.371989	−	0.109226i
$89$	2.81447	+	6.16282i	0.298333	+	0.653258i	0.998133	−	0.0610810i	$-0.0194548\pi$
$89$	2.81447	+	6.16282i	0.298333	+	0.653258i	−0.699800	+	0.714339i	$0.746728\pi$
$90$	0.142315	−	0.989821i	0.0150013	−	0.104336i
$91$	4.31854			0.452706
$92$	2.69242	+	3.96874i	0.280704	+	0.413770i
$93$	−7.17207			−0.743709
$94$	0.738274	−	5.13481i	0.0761472	−	0.529615i
$95$	−0.628644	−	1.37654i	−0.0644975	−	0.141230i
$96$	0.959493	+	0.281733i	0.0979278	+	0.0287542i
$97$	9.31155	+	10.7461i	0.945444	+	1.09110i	0.995725	+	0.0923656i	$0.0294429\pi$
$97$	9.31155	+	10.7461i	0.945444	+	1.09110i	−0.0502810	+	0.998735i	$0.516012\pi$
$98$	4.57408	−	1.34307i	0.462052	−	0.135671i
$99$	3.05954	+	1.96625i	0.307495	+	0.197615i
$100$	0.415415	−	0.909632i	0.0415415	−	0.0909632i
$101$	1.34957	−	1.55749i	0.134287	−	0.154976i	−0.684623	−	0.728897i	$-0.740033\pi$
$101$	1.34957	−	1.55749i	0.134287	−	0.154976i	0.818910	+	0.573922i	$0.194579\pi$
$102$	−2.36134	+	1.51754i	−0.233807	+	0.150259i
$103$	0.859270	+	5.97635i	0.0846664	+	0.588868i	0.987349	+	0.158561i	$0.0506854\pi$
$103$	0.859270	+	5.97635i	0.0846664	+	0.588868i	−0.902683	+	0.430307i	$0.858405\pi$
$104$	0.411302	+	2.86067i	0.0403315	+	0.280512i
$105$	−1.25705	+	0.807858i	−0.122676	+	0.0788388i
$106$	4.93397	−	5.69410i	0.479229	−	0.553060i
$107$	−3.32474	+	7.28018i	−0.321415	+	0.703801i	−0.999514	−	0.0311695i	$-0.990077\pi$
$107$	−3.32474	+	7.28018i	−0.321415	+	0.703801i	0.678099	+	0.734971i	$0.262804\pi$
$108$	−0.841254	−	0.540641i	−0.0809497	−	0.0520232i
$109$	13.2463	−	3.88948i	1.26877	−	0.372544i	0.423018	−	0.906121i	$-0.360971\pi$
$109$	13.2463	−	3.88948i	1.26877	−	0.372544i	0.845751	+	0.533577i	$0.179153\pi$
$110$	2.38165	+	2.74857i	0.227082	+	0.262066i
$111$	−0.857048	−	0.251652i	−0.0813474	−	0.0238857i
$112$	−0.620738	−	1.35923i	−0.0586542	−	0.128435i
$113$	−2.74056	+	19.0610i	−0.257810	+	1.79311i	0.290542	+	0.956862i	$0.406164\pi$
$113$	−2.74056	+	19.0610i	−0.257810	+	1.79311i	−0.548352	+	0.836247i	$0.684745\pi$
$114$	−1.51329			−0.141733
$115$	−0.119344	−	4.79435i	−0.0111289	−	0.447075i
$116$	5.86176			0.544250
$117$	0.411302	−	2.86067i	0.0380249	−	0.264469i
$118$	−1.28568	−	2.81524i	−0.118356	−	0.259164i
$119$	4.02438	+	1.18166i	0.368914	+	0.108323i
$120$	−0.654861	−	0.755750i	−0.0597803	−	0.0689902i
$121$	−2.13671	+	0.627396i	−0.194247	+	0.0570360i
$122$	6.30760	+	4.05365i	0.571063	+	0.367000i
$123$	−1.80642	+	3.95551i	−0.162880	+	0.356657i
$124$	−4.69671	+	5.42029i	−0.421777	+	0.486756i
$125$	−0.841254	+	0.540641i	−0.0752440	+	0.0483564i
$126$	0.212655	+	1.47905i	0.0189448	+	0.131764i
$127$	0.485364	+	3.37578i	0.0430691	+	0.299552i	0.999959	+	0.00909980i	$0.00289660\pi$
$127$	0.485364	+	3.37578i	0.0430691	+	0.299552i	−0.956890	+	0.290452i	$0.906194\pi$
$128$	0.841254	−	0.540641i	0.0743570	−	0.0477863i
$129$	0.914801	−	1.05574i	0.0805438	−	0.0929525i
$130$	1.20058	−	2.62891i	0.105298	−	0.230571i
$131$	6.13244	+	3.94108i	0.535794	+	0.344334i	0.780392	−	0.625291i	$-0.215020\pi$
$131$	6.13244	+	3.94108i	0.535794	+	0.344334i	−0.244598	+	0.969625i	$0.578656\pi$
$132$	3.48956	−	1.02463i	0.303728	−	0.0891825i
$133$	1.48080	+	1.70894i	0.128402	+	0.148184i
$134$	−2.21181	−	0.649446i	−0.191071	−	0.0561036i
$135$	0.415415	+	0.909632i	0.0357532	+	0.0782887i
$136$	−0.399467	+	2.77836i	−0.0342540	+	0.238242i
$137$	−15.4082			−1.31641			−0.658206	−	0.752838i	$-0.728684\pi$
$137$	−15.4082			−1.31641			−0.658206	+	0.752838i	$0.728684\pi$
$138$	−4.41067	−	1.88308i	−0.375461	−	0.160299i
$139$	13.3294			1.13059			0.565293	−	0.824890i	$-0.308763\pi$
$139$	13.3294			1.13059			0.565293	+	0.824890i	$0.308763\pi$
$140$	−0.212655	+	1.47905i	−0.0179727	+	0.125003i
$141$	2.15501	+	4.71882i	0.181485	+	0.397396i
$142$	−0.318250	−	0.0934466i	−0.0267069	−	0.00784186i
$143$	6.88318	+	7.94361i	0.575600	+	0.664278i
$144$	−0.959493	+	0.281733i	−0.0799577	+	0.0234777i
$145$	−4.93122	−	3.16910i	−0.409516	−	0.263180i
$146$	2.63556	−	5.77107i	0.218120	−	0.477617i
$147$	−3.12184	+	3.60280i	−0.257485	+	0.297154i
$148$	−0.751433	+	0.482917i	−0.0617674	+	0.0396955i
$149$	−0.113683	−	0.790685i	−0.00931330	−	0.0647754i	0.984635	−	0.174626i	$-0.0558717\pi$
$149$	−0.113683	−	0.790685i	−0.00931330	−	0.0647754i	−0.993948	+	0.109851i	$0.964963\pi$
$150$	0.142315	+	0.989821i	0.0116200	+	0.0808186i
$151$	15.7143	−	10.0989i	1.27881	−	0.821840i	0.288068	−	0.957610i	$-0.406987\pi$
$151$	15.7143	−	10.0989i	1.27881	−	0.821840i	0.990740	+	0.135770i	$0.0433508\pi$
$152$	−0.990995	+	1.14367i	−0.0803803	+	0.0927638i
$153$	1.16604	−	2.55327i	0.0942687	−	0.206420i
$154$	−4.57175	−	2.93808i	−0.368402	−	0.236758i
$155$	6.88155	−	2.02061i	0.552740	−	0.162299i
$156$	−1.89260	−	2.18418i	−0.151530	−	0.174874i
$157$	−15.5854	−	4.57630i	−1.24385	−	0.365228i	−0.407392	−	0.913253i	$-0.633562\pi$
$157$	−15.5854	−	4.57630i	−1.24385	−	0.365228i	−0.836462	+	0.548025i	$0.815380\pi$
$158$	0.803374	+	1.75914i	0.0639130	+	0.139950i
$159$	−1.07225	+	7.45769i	−0.0850353	+	0.591433i
$160$	−1.00000			−0.0790569
$161$	2.18944	+	6.82356i	0.172552	+	0.537772i
$162$	1.00000			0.0785674
$163$	−1.98247	+	13.7884i	−0.155279	+	1.07999i	0.751910	+	0.659266i	$0.229133\pi$
$163$	−1.98247	+	13.7884i	−0.155279	+	1.07999i	−0.907189	+	0.420723i	$0.861776\pi$
$164$	1.80642	+	3.95551i	0.141058	+	0.308874i
$165$	−3.48956	−	1.02463i	−0.271662	−	0.0797672i
$166$	7.84223	+	9.05042i	0.608675	+	0.702449i
$167$	−14.0235	+	4.11767i	−1.08517	+	0.318635i	−0.774946	−	0.632028i	$-0.782223\pi$
$167$	−14.0235	+	4.11767i	−1.08517	+	0.318635i	−0.310226	+	0.950663i	$0.600405\pi$
$168$	1.25705	+	0.807858i	0.0969836	+	0.0623276i
$169$	−1.93060	+	4.22743i	−0.148508	+	0.325187i
$170$	1.83815	−	2.12133i	0.140979	−	0.162699i
$171$	1.27306	−	0.818147i	0.0973535	−	0.0625653i
$172$	−0.198805	−	1.38272i	−0.0151588	−	0.105432i
$173$	−2.34872	−	16.3357i	−0.178570	−	1.24198i	−0.860075	−	0.510167i	$-0.829583\pi$
$173$	−2.34872	−	16.3357i	−0.178570	−	1.24198i	0.681505	−	0.731813i	$-0.261326\pi$
$174$	−4.93122	+	3.16910i	−0.373835	+	0.240249i
$175$	0.978532	−	1.12929i	0.0739701	−	0.0853660i
$176$	1.51082	−	3.30823i	0.113882	−	0.249367i
$177$	2.60361	+	1.67324i	0.195699	+	0.125768i
$178$	−6.50063	+	1.90876i	−0.487243	+	0.143067i
$179$	−1.75252	−	2.02251i	−0.130989	−	0.151170i	0.686466	−	0.727162i	$-0.259161\pi$
$179$	−1.75252	−	2.02251i	−0.130989	−	0.151170i	−0.817455	+	0.575992i	$0.804616\pi$
$180$	0.959493	+	0.281733i	0.0715164	+	0.0209991i
$181$	7.10681	+	15.5617i	0.528245	+	1.15670i	0.966222	+	0.257710i	$0.0829678\pi$
$181$	7.10681	+	15.5617i	0.528245	+	1.15670i	−0.437977	+	0.898986i	$0.644305\pi$
$182$	−0.614592	+	4.27458i	−0.0455566	+	0.316853i
$183$	−7.49785			−0.554257
$184$	−4.31151	+	2.10020i	−0.317849	+	0.154829i
$185$	0.893230			0.0656716
$186$	1.02069	−	7.09907i	0.0748408	−	0.520529i
$187$	4.24075	+	9.28594i	0.310114	+	0.679055i
$188$	4.97748	+	1.46152i	0.363020	+	0.106592i
$189$	−0.978532	−	1.12929i	−0.0711777	−	0.0821435i
$190$	1.45199	−	0.426343i	0.105339	−	0.0309302i
$191$	−18.8634	−	12.1228i	−1.36491	−	0.877173i	−0.366329	−	0.930485i	$-0.619386\pi$
$191$	−18.8634	−	12.1228i	−1.36491	−	0.877173i	−0.998578	+	0.0533127i	$0.983022\pi$
$192$	−0.415415	+	0.909632i	−0.0299800	+	0.0656470i
$193$	8.59742	−	9.92195i	0.618856	−	0.714198i	−0.356633	−	0.934244i	$-0.616075\pi$
$193$	8.59742	−	9.92195i	0.618856	−	0.714198i	0.975489	+	0.220047i	$0.0706209\pi$
$194$	−11.9619	+	7.68744i	−0.858813	+	0.551926i
$195$	0.411302	+	2.86067i	0.0294539	+	0.204857i
$196$	0.678442	+	4.71867i	0.0484601	+	0.337048i
$197$	−4.01327	+	2.57917i	−0.285934	+	0.183758i	−0.675743	−	0.737137i	$-0.736177\pi$
$197$	−4.01327	+	2.57917i	−0.285934	+	0.183758i	0.389810	+	0.920895i	$0.372541\pi$
$198$	−2.38165	+	2.74857i	−0.169257	+	0.195333i
$199$	0.193789	−	0.424340i	0.0137374	−	0.0300806i	−0.902639	−	0.430399i	$-0.858373\pi$
$199$	0.193789	−	0.424340i	0.0137374	−	0.0300806i	0.916376	+	0.400318i	$0.131100\pi$
$200$	0.841254	+	0.540641i	0.0594856	+	0.0382291i
$201$	2.21181	−	0.649446i	0.156009	−	0.0458084i
$202$	1.34957	+	1.55749i	0.0949555	+	0.109584i
$203$	8.40418	+	2.46769i	0.589858	+	0.173198i
$204$	−1.16604	−	2.55327i	−0.0816391	−	0.178765i
$205$	0.618853	−	4.30422i	0.0432225	−	0.300619i
$206$	−6.03781			−0.420674
$207$	4.72856	−	0.800436i	0.328658	−	0.0556342i
$208$	−2.89008			−0.200391
$209$	−0.783253	+	5.44764i	−0.0541787	+	0.376821i
$210$	−0.620738	−	1.35923i	−0.0428350	−	0.0937955i
$211$	−8.09053	−	2.37559i	−0.556975	−	0.163543i	−0.00888281	−	0.999961i	$-0.502828\pi$
$211$	−8.09053	−	2.37559i	−0.556975	−	0.163543i	−0.548092	+	0.836418i	$0.684646\pi$
$212$	4.93397	+	5.69410i	0.338866	+	0.391073i
$213$	0.318250	−	0.0934466i	0.0218061	−	0.00640286i
$214$	−6.73291	−	4.32698i	−0.460252	−	0.295786i
$215$	−0.580310	+	1.27070i	−0.0395768	+	0.0866611i
$216$	0.654861	−	0.755750i	0.0445576	−	0.0514222i
$217$	−9.01566	+	5.79401i	−0.612023	+	0.393323i
$218$	1.96474	+	13.6650i	0.133069	+	0.925513i
$219$	0.902902	+	6.27982i	0.0610125	+	0.424351i
$220$	−3.05954	+	1.96625i	−0.206274	+	0.132564i
$221$	5.31240	−	6.13083i	0.357350	−	0.412404i
$222$	0.371061	−	0.812511i	0.0249040	−	0.0545321i
$223$	5.58898	+	3.59182i	0.374266	+	0.240526i	0.714228	−	0.699913i	$-0.246778\pi$
$223$	5.58898	+	3.59182i	0.374266	+	0.240526i	−0.339962	+	0.940439i	$0.610414\pi$
$224$	1.43373	−	0.420982i	0.0957952	−	0.0281280i
$225$	−0.654861	−	0.755750i	−0.0436574	−	0.0503833i
$226$	−18.4770	−	5.42533i	−1.22907	−	0.360888i
$227$	−10.8436	−	23.7441i	−0.719712	−	1.57595i	−0.814307	−	0.580434i	$-0.802883\pi$
$227$	−10.8436	−	23.7441i	−0.719712	−	1.57595i	0.0945952	−	0.995516i	$-0.469844\pi$
$228$	0.215364	−	1.49789i	0.0142628	−	0.0992001i
$229$	−3.32466			−0.219700			−0.109850	−	0.993948i	$-0.535037\pi$
$229$	−3.32466			−0.219700			−0.109850	+	0.993948i	$0.535037\pi$
$230$	4.76253	+	0.564177i	0.314032	+	0.0372007i
$231$	5.43445			0.357560
$232$	−0.834215	+	5.80209i	−0.0547689	+	0.380926i
$233$	5.82149	+	12.7473i	0.381379	+	0.835103i	0.998824	+	0.0484888i	$0.0154405\pi$
$233$	5.82149	+	12.7473i	0.381379	+	0.835103i	−0.617445	+	0.786614i	$0.711832\pi$
$234$	2.77302	+	0.814231i	0.181278	+	0.0532279i
$235$	−3.39716	−	3.92054i	−0.221607	−	0.255748i
$236$	2.96955	−	0.871940i	0.193302	−	0.0567584i
$237$	−1.62691	−	1.04555i	−0.105679	−	0.0679157i
$238$	−1.74236	+	3.81525i	−0.112941	+	0.247306i
$239$	5.63445	−	6.50250i	0.364462	−	0.420612i	−0.543668	−	0.839301i	$-0.682965\pi$
$239$	5.63445	−	6.50250i	0.364462	−	0.420612i	0.908130	+	0.418689i	$0.137510\pi$
$240$	0.841254	−	0.540641i	0.0543027	−	0.0348982i
$241$	−1.85225	−	12.8827i	−0.119314	−	0.829847i	−0.958314	−	0.285716i	$-0.907769\pi$
$241$	−1.85225	−	12.8827i	−0.119314	−	0.829847i	0.839000	−	0.544131i	$-0.183141\pi$
$242$	−0.316924	−	2.20425i	−0.0203726	−	0.141695i
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$	−4.91005	+	5.66650i	−0.314334	+	0.362760i
$245$	1.98036	−	4.33639i	0.126521	−	0.277042i
$246$	−3.65817	−	2.35096i	−0.233236	−	0.149892i
$247$	4.19638	−	1.23217i	0.267009	−	0.0784010i
$248$	−4.69671	−	5.42029i	−0.298241	−	0.344189i
$249$	−11.4903	−	3.37386i	−0.728170	−	0.213810i
$250$	−0.415415	−	0.909632i	−0.0262732	−	0.0575302i
$251$	−1.60257	+	11.1461i	−0.101154	+	0.703538i	0.874629	+	0.484794i	$0.161105\pi$
$251$	−1.60257	+	11.1461i	−0.101154	+	0.703538i	−0.975782	+	0.218745i	$0.929804\pi$
$252$	−1.49426			−0.0941295
$253$	−9.06173	+	14.9032i	−0.569706	+	0.936954i
$254$	−3.41049			−0.213993
$255$	−0.399467	+	2.77836i	−0.0250156	+	0.173987i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	10.1519	+	2.98086i	0.633256	+	0.185941i	0.582579	−	0.812774i	$-0.302044\pi$
$257$	10.1519	+	2.98086i	0.633256	+	0.185941i	0.0506773	+	0.998715i	$0.483862\pi$
$258$	0.914801	+	1.05574i	0.0569530	+	0.0657273i
$259$	−1.28065	+	0.376033i	−0.0795758	+	0.0233656i
$260$	2.43129	+	1.56250i	0.150782	+	0.0969020i
$261$	2.43506	−	5.33204i	0.150727	−	0.330045i
$262$	−4.77370	+	5.50915i	−0.294920	+	0.340356i
$263$	17.1662	−	11.0320i	1.05851	−	0.680264i	0.109014	−	0.994040i	$-0.465231\pi$
$263$	17.1662	−	11.0320i	1.05851	−	0.680264i	0.949497	+	0.313776i	$0.101594\pi$
$264$	0.517582	+	3.59986i	0.0318550	+	0.221556i
$265$	−1.07225	−	7.45769i	−0.0658680	−	0.458122i
$266$	−1.90228	+	1.22252i	−0.116637	+	0.0749578i
$267$	4.43673	−	5.12026i	0.271523	−	0.313355i
$268$	0.957608	−	2.09687i	0.0584952	−	0.128087i
$269$	17.4844	+	11.2365i	1.06604	+	0.685103i	0.951292	−	0.308292i	$-0.0997572\pi$
$269$	17.4844	+	11.2365i	1.06604	+	0.685103i	0.114749	+	0.993395i	$0.463394\pi$
$270$	−0.959493	+	0.281733i	−0.0583929	+	0.0171457i
$271$	−5.90542	−	6.81522i	−0.358729	−	0.413995i	0.547485	−	0.836816i	$-0.315585\pi$
$271$	−5.90542	−	6.81522i	−0.358729	−	0.413995i	−0.906213	+	0.422821i	$0.861040\pi$
$272$	−2.69323	−	0.790802i	−0.163301	−	0.0479494i
$273$	−1.79398	−	3.92828i	−0.108577	−	0.237750i
$274$	2.19282	−	15.2514i	0.132473	−	0.921369i
$275$	3.63688			0.219312
$276$	2.49162	−	4.09778i	0.149978	−	0.246658i
$277$	16.7162			1.00438			0.502189	−	0.864758i	$-0.332528\pi$
$277$	16.7162			1.00438			0.502189	+	0.864758i	$0.332528\pi$
$278$	−1.89697	+	13.1937i	−0.113773	+	0.791307i
$279$	2.97939	+	6.52395i	0.178371	+	0.390578i
$280$	−1.43373	−	0.420982i	−0.0856818	−	0.0251585i
$281$	−4.02966	−	4.65047i	−0.240389	−	0.277424i	0.622716	−	0.782448i	$-0.286029\pi$
$281$	−4.02966	−	4.65047i	−0.240389	−	0.277424i	−0.863105	+	0.505024i	$0.831484\pi$
$282$	−4.97748	+	1.46152i	−0.296404	+	0.0870322i
$283$	6.11979	+	3.93295i	0.363784	+	0.233790i	0.709744	−	0.704459i	$-0.248810\pi$
$283$	6.11979	+	3.93295i	0.363784	+	0.233790i	−0.345960	+	0.938249i	$0.612447\pi$
$284$	0.137787	−	0.301712i	0.00817616	−	0.0179033i
$285$	−0.990995	+	1.14367i	−0.0587015	+	0.0677451i
$286$	−8.84233	+	5.68262i	−0.522858	+	0.336020i
$287$	0.924727	+	6.43161i	0.0545849	+	0.379646i
$288$	−0.142315	−	0.989821i	−0.00838598	−	0.0583258i
$289$	−7.67322	+	4.93128i	−0.451366	+	0.290075i
$290$	3.83863	−	4.43002i	0.225412	−	0.260140i
$291$	5.90684	−	12.9342i	0.346265	−	0.758214i
$292$	5.33725	+	3.43004i	0.312339	+	0.200728i
$293$	20.4343	−	6.00005i	1.19379	−	0.350527i	0.376312	−	0.926493i	$-0.377192\pi$
$293$	20.4343	−	6.00005i	1.19379	−	0.350527i	0.817473	+	0.575966i	$0.195374\pi$
$294$	−3.12184	−	3.60280i	−0.182070	−	0.210120i
$295$	−2.96955	−	0.871940i	−0.172894	−	0.0507663i
$296$	−0.371061	−	0.812511i	−0.0215675	−	0.0472262i
$297$	0.517582	−	3.59986i	0.0300332	−	0.208885i
$298$	0.798816			0.0462741
$299$	13.7641	+	1.63052i	0.796000	+	0.0942954i
$300$	−1.00000			−0.0577350
$301$	0.297067	−	2.06614i	0.0171226	−	0.119091i
$302$	7.75978	+	16.9915i	0.446525	+	0.977753i
$303$	−1.97737	−	0.580609i	−0.113597	−	0.0333551i
$304$	−0.990995	−	1.14367i	−0.0568375	−	0.0655939i
$305$	7.19414	−	2.11239i	0.411935	−	0.120955i
$306$	2.36134	+	1.51754i	0.134989	+	0.0867519i
$307$	5.94998	−	13.0286i	0.339583	−	0.743583i	−0.660390	−	0.750923i	$-0.729609\pi$
$307$	5.94998	−	13.0286i	0.339583	−	0.743583i	0.999973	+	0.00733967i	$0.00233631\pi$
$308$	3.55881	−	4.10708i	0.202782	−	0.234023i
$309$	5.07933	−	3.26429i	0.288953	−	0.185699i
$310$	1.02069	+	7.09907i	0.0579714	+	0.403200i
$311$	−4.76870	−	33.1671i	−0.270408	−	1.88073i	−0.444169	−	0.895943i	$-0.646501\pi$
$311$	−4.76870	−	33.1671i	−0.270408	−	1.88073i	0.173760	−	0.984788i	$-0.444408\pi$
$312$	2.43129	−	1.56250i	0.137645	−	0.0884590i
$313$	6.11049	−	7.05188i	0.345385	−	0.398596i	−0.556305	−	0.830978i	$-0.687781\pi$
$313$	6.11049	−	7.05188i	0.345385	−	0.398596i	0.901690	+	0.432382i	$0.142327\pi$
$314$	6.74776	−	14.7755i	0.380798	−	0.833831i
$315$	1.25705	+	0.807858i	0.0708268	+	0.0455176i
$316$	−1.85557	+	0.544844i	−0.104384	+	0.0306499i
$317$	−18.7173	−	21.6009i	−1.05127	−	1.21323i	−0.976386	−	0.216035i	$-0.930687\pi$
$317$	−18.7173	−	21.6009i	−1.05127	−	1.21323i	−0.0748823	−	0.997192i	$-0.523858\pi$
$318$	−7.22918	−	2.12268i	−0.405392	−	0.119034i
$319$	8.85603	+	19.3920i	0.495843	+	1.08574i
$320$	0.142315	−	0.989821i	0.00795564	−	0.0553327i
$321$	8.00343			0.446708
$322$	−7.06570	+	1.19606i	−0.393756	+	0.0666538i
$323$	4.24770			0.236348
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	−1.20058	−	2.62891i	−0.0665965	−	0.145826i
$326$	−13.3659	−	3.92458i	−0.740269	−	0.217362i
$327$	−9.04072	−	10.4335i	−0.499953	−	0.576976i
$328$	−4.17233	+	1.22511i	−0.230379	+	0.0676452i
$329$	6.52109	+	4.19085i	0.359520	+	0.231049i
$330$	1.51082	−	3.30823i	0.0831677	−	0.182112i
$331$	21.8461	−	25.2117i	1.20077	−	1.38576i	0.298603	−	0.954378i	$-0.403479\pi$
$331$	21.8461	−	25.2117i	1.20077	−	1.38576i	0.902168	−	0.431385i	$-0.141975\pi$
$332$	−10.0744	+	6.47440i	−0.552902	+	0.355329i
$333$	0.127120	+	0.884138i	0.00696613	+	0.0484505i
$334$	−2.08001	−	14.4668i	−0.113813	−	0.791586i
$335$	−1.93924	+	1.24628i	−0.105952	+	0.0680914i
$336$	−0.978532	+	1.12929i	−0.0533833	+	0.0616076i
$337$	1.16294	−	2.54647i	0.0633492	−	0.138715i	−0.875309	−	0.483563i	$-0.839342\pi$
$337$	1.16294	−	2.54647i	0.0633492	−	0.138715i	0.938659	+	0.344848i	$0.112070\pi$
$338$	−3.90965	−	2.51258i	−0.212657	−	0.136666i
$339$	18.4770	−	5.42533i	1.00353	−	0.294664i
$340$	1.83815	+	2.12133i	0.0996874	+	0.115045i
$341$	−25.0274	−	7.34871i	−1.35531	−	0.397955i
$342$	0.628644	+	1.37654i	0.0339932	+	0.0744347i
$343$	−2.50235	+	17.4043i	−0.135114	+	0.939742i
$344$	1.39694			0.0753180
$345$	−4.31151	+	2.10020i	−0.232124	+	0.113071i
$346$	16.5037			0.887244
$347$	1.30557	−	9.08047i	0.0700869	−	0.487465i	−0.924301	−	0.381666i	$-0.875351\pi$
$347$	1.30557	−	9.08047i	0.0700869	−	0.487465i	0.994387	−	0.105800i	$-0.0337403\pi$
$348$	−2.43506	−	5.33204i	−0.130533	−	0.285827i
$349$	−18.3987	−	5.40234i	−0.984858	−	0.289180i	−0.250630	−	0.968083i	$-0.580638\pi$
$349$	−18.3987	−	5.40234i	−0.984858	−	0.289180i	−0.734228	+	0.678903i	$0.762456\pi$
$350$	0.978532	+	1.12929i	0.0523047	+	0.0603629i
$351$	−2.77302	+	0.814231i	−0.148013	+	0.0434604i
$352$	3.05954	+	1.96625i	0.163074	+	0.104801i
$353$	2.19707	−	4.81091i	0.116938	−	0.256059i	−0.842108	−	0.539309i	$-0.818685\pi$
$353$	2.19707	−	4.81091i	0.116938	−	0.256059i	0.959046	+	0.283250i	$0.0914127\pi$
$354$	−2.02674	+	2.33898i	−0.107720	+	0.124316i
$355$	−0.279032	+	0.179323i	−0.0148095	+	0.00951746i
$356$	−0.964193	−	6.70611i	−0.0511021	−	0.355423i
$357$	−0.596908	−	4.15158i	−0.0315917	−	0.219725i
$358$	2.25134	−	1.44685i	0.118987	−	0.0764682i
$359$	5.74097	−	6.62543i	0.302997	−	0.349677i	−0.583749	−	0.811934i	$-0.698415\pi$
$359$	5.74097	−	6.62543i	0.302997	−	0.349677i	0.886746	+	0.462257i	$0.152960\pi$
$360$	−0.415415	+	0.909632i	−0.0218943	+	0.0479418i
$361$	−14.0573	−	9.03408i	−0.739858	−	0.475478i
$362$	−16.4148	+	4.81981i	−0.862741	+	0.253323i
$363$	1.45832	+	1.68299i	0.0765420	+	0.0883342i
$364$	−4.14361	−	1.21667i	−0.217184	−	0.0637710i
$365$	−2.63556	−	5.77107i	−0.137951	−	0.302072i
$366$	1.06706	−	7.42154i	0.0557759	−	0.387930i
$367$	−28.0025			−1.46172			−0.730859	−	0.682528i	$-0.760880\pi$
$367$	−28.0025			−1.46172			−0.730859	+	0.682528i	$0.760880\pi$
$368$	−1.46523	−	4.56652i	−0.0763806	−	0.238046i
$369$	4.34848			0.226373
$370$	−0.127120	+	0.884138i	−0.00660865	+	0.0459642i
$371$	4.67687	+	10.2409i	0.242811	+	0.531682i
$372$	6.88155	+	2.02061i	0.356792	+	0.104764i
$373$	−0.531162	−	0.612994i	−0.0275025	−	0.0317396i	0.741832	−	0.670586i	$-0.233957\pi$
$373$	−0.531162	−	0.612994i	−0.0275025	−	0.0317396i	−0.769334	+	0.638847i	$0.779412\pi$
$374$	−9.79495	+	2.87606i	−0.506485	+	0.148717i
$375$	0.841254	+	0.540641i	0.0434421	+	0.0279186i
$376$	−2.15501	+	4.71882i	−0.111136	+	0.243354i
$377$	11.0940	−	12.8031i	0.571369	−	0.659395i
$378$	1.25705	−	0.807858i	0.0646557	−	0.0415517i
$379$	2.23849	+	15.5691i	0.114984	+	0.799729i	0.962950	+	0.269679i	$0.0869177\pi$
$379$	2.23849	+	15.5691i	0.114984	+	0.799729i	−0.847966	+	0.530050i	$0.822173\pi$
$380$	0.215364	+	1.49789i	0.0110479	+	0.0768400i
$381$	2.86909	−	1.84385i	0.146988	−	0.0944634i
$382$	14.6839	−	16.9461i	0.751294	−	0.867040i
$383$	12.1078	−	26.5123i	0.618679	−	1.35472i	−0.297798	−	0.954629i	$-0.596252\pi$
$383$	12.1078	−	26.5123i	0.618679	−	1.35472i	0.916477	−	0.400088i	$-0.131021\pi$
$384$	−0.841254	−	0.540641i	−0.0429300	−	0.0275895i
$385$	−5.21431	+	1.53106i	−0.265746	+	0.0780301i
$386$	8.59742	+	9.92195i	0.437597	+	0.505014i
$387$	−1.34035	−	0.393564i	−0.0681341	−	0.0200060i
$388$	−5.90684	−	12.9342i	−0.299874	−	0.656633i
$389$	−0.451465	+	3.14000i	−0.0228902	+	0.159205i	−0.998060	−	0.0622516i	$-0.980172\pi$
$389$	−0.451465	+	3.14000i	−0.0228902	+	0.159205i	0.975170	+	0.221456i	$0.0710810\pi$
$390$	−2.89008			−0.146345
$391$	12.3804	+	5.28568i	0.626105	+	0.267308i
$392$	−4.76719			−0.240779
$393$	1.03742	−	7.21545i	0.0523312	−	0.363971i
$394$	−1.98177	−	4.33948i	−0.0998403	−	0.218620i
$395$	1.85557	+	0.544844i	0.0933639	+	0.0274141i
$396$	−2.38165	−	2.74857i	−0.119683	−	0.138121i
$397$	−35.0696	+	10.2974i	−1.76009	+	0.516810i	−0.992297	−	0.123884i	$-0.960465\pi$
$397$	−35.0696	+	10.2974i	−1.76009	+	0.516810i	−0.767796	+	0.640694i	$0.778647\pi$
$398$	0.392441	+	0.252207i	0.0196713	+	0.0126420i
$399$	0.939357	−	2.05691i	0.0470267	−	0.102974i
$400$	−0.654861	+	0.755750i	−0.0327430	+	0.0377875i
$401$	−27.9263	+	17.9471i	−1.39457	+	0.896237i	−0.999746	−	0.0225194i	$-0.992831\pi$
$401$	−27.9263	+	17.9471i	−1.39457	+	0.896237i	−0.394825	+	0.918756i	$0.629195\pi$
$402$	0.328062	+	2.28172i	0.0163622	+	0.113802i
$403$	2.94989	+	20.5169i	0.146944	+	1.02202i
$404$	−1.73370	+	1.11418i	−0.0862547	+	0.0554326i
$405$	0.654861	−	0.755750i	0.0325403	−	0.0375535i
$406$	−3.63861	+	7.96745i	−0.180581	+	0.395418i
$407$	−2.73287	−	1.75631i	−0.135464	−	0.0870571i
$408$	2.69323	−	0.790802i	0.133335	−	0.0391505i
$409$	−17.4609	−	20.1510i	−0.863388	−	0.996403i	−0.999983	−	0.00577612i	$-0.998161\pi$
$409$	−17.4609	−	20.1510i	−0.863388	−	0.996403i	0.136595	−	0.990627i	$-0.456384\pi$
$410$	4.17233	+	1.22511i	0.206057	+	0.0605037i
$411$	6.40080	+	14.0158i	0.315728	+	0.691348i
$412$	0.859270	−	5.97635i	0.0423332	−	0.294434i
$413$	4.62461			0.227562
$414$	0.119344	+	4.79435i	0.00586546	+	0.235629i
$415$	11.9754			0.587850
$416$	0.411302	−	2.86067i	0.0201657	−	0.140256i
$417$	−5.53724	−	12.1249i	−0.271160	−	0.593757i
$418$	−5.28073	−	1.55056i	−0.258289	−	0.0758404i
$419$	−3.52436	−	4.06733i	−0.172176	−	0.198702i	0.663103	−	0.748529i	$-0.269239\pi$
$419$	−3.52436	−	4.06733i	−0.172176	−	0.198702i	−0.835279	+	0.549826i	$0.814694\pi$
$420$	1.43373	−	0.420982i	0.0699589	−	0.0205418i
$421$	17.2392	+	11.0789i	0.840185	+	0.539954i	0.888499	−	0.458878i	$-0.151748\pi$
$421$	17.2392	+	11.0789i	0.840185	+	0.539954i	−0.0483140	+	0.998832i	$0.515385\pi$
$422$	3.50282	−	7.67010i	0.170514	−	0.373374i
$423$	3.39716	−	3.92054i	0.165176	−	0.190623i
$424$	−6.33832	+	4.07339i	−0.307816	+	0.197821i
$425$	−0.399467	−	2.77836i	−0.0193770	−	0.134770i
$426$	0.0472038	+	0.328309i	0.00228703	+	0.0159066i
$427$	−9.42519	+	6.05720i	−0.456117	+	0.293128i
$428$	5.24113	−	6.04859i	0.253340	−	0.292370i
$429$	4.36639	−	9.56105i	0.210811	−	0.461612i
$430$	−1.17518	−	0.755243i	−0.0566723	−	0.0364211i
$431$	−26.5723	+	7.80234i	−1.27994	+	0.375825i	−0.849881	−	0.526974i	$-0.823327\pi$
$431$	−26.5723	+	7.80234i	−1.27994	+	0.375825i	−0.430062	+	0.902799i	$0.641508\pi$
$432$	0.654861	+	0.755750i	0.0315070	+	0.0363610i
$433$	−24.8365	−	7.29267i	−1.19357	−	0.350463i	−0.376178	−	0.926548i	$-0.622762\pi$
$433$	−24.8365	−	7.29267i	−1.19357	−	0.350463i	−0.817390	+	0.576084i	$0.804580\pi$
$434$	−4.45198	−	9.74847i	−0.213702	−	0.467941i
$435$	−0.834215	+	5.80209i	−0.0399975	+	0.278189i
$436$	−13.8056			−0.661166
$437$	4.07441	+	6.00586i	0.194906	+	0.287299i
$438$	−6.34440			−0.303147
$439$	0.760199	−	5.28730i	0.0362823	−	0.252349i	−0.963605	−	0.267328i	$-0.913859\pi$
$439$	0.760199	−	5.28730i	0.0362823	−	0.252349i	0.999888	+	0.0149793i	$0.00476822\pi$
$440$	−1.51082	−	3.30823i	−0.0720253	−	0.157713i
$441$	4.57408	+	1.34307i	0.217814	+	0.0639558i
$442$	5.31240	+	6.13083i	0.252685	+	0.291614i
$443$	27.6715	−	8.12509i	1.31471	−	0.386035i	0.452132	−	0.891951i	$-0.350664\pi$
$443$	27.6715	−	8.12509i	1.31471	−	0.386035i	0.862583	+	0.505916i	$0.168846\pi$
$444$	0.751433	+	0.482917i	0.0356614	+	0.0229182i
$445$	−2.81447	+	6.16282i	−0.133419	+	0.292146i
$446$	−4.35066	+	5.02092i	−0.206010	+	0.237748i
$447$	−0.672006	+	0.431872i	−0.0317848	+	0.0204269i
$448$	0.212655	+	1.47905i	0.0100470	+	0.0698785i
$449$	0.452143	+	3.14472i	0.0213379	+	0.148409i	0.997705	−	0.0677101i	$-0.0215693\pi$
$449$	0.452143	+	3.14472i	0.0213379	+	0.148409i	−0.976367	+	0.216119i	$0.930660\pi$
$450$	0.841254	−	0.540641i	0.0396571	−	0.0254861i
$451$	−10.3566	+	11.9521i	−0.487671	+	0.562803i
$452$	7.99966	−	17.5168i	0.376272	−	0.823921i
$453$	−15.7143	−	10.0989i	−0.738320	−	0.474490i
$454$	25.0456	−	7.35405i	1.17545	−	0.345143i
$455$	2.82804	+	3.26373i	0.132581	+	0.153006i
$456$	1.45199	+	0.426343i	0.0679958	+	0.0199654i
$457$	10.2927	+	22.5378i	0.481471	+	1.05427i	0.982056	+	0.188588i	$0.0603909\pi$
$457$	10.2927	+	22.5378i	0.481471	+	1.05427i	−0.500585	+	0.865687i	$0.666882\pi$
$458$	0.473149	−	3.29082i	0.0221088	−	0.153770i
$459$	−2.80693			−0.131016
$460$	−1.23621	+	4.63376i	−0.0576387	+	0.216050i
$461$	−0.610036			−0.0284122			−0.0142061	−	0.999899i	$-0.504522\pi$
$461$	−0.610036			−0.0284122			−0.0142061	+	0.999899i	$0.504522\pi$
$462$	−0.773402	+	5.37913i	−0.0359819	+	0.250260i
$463$	−1.44340	−	3.16060i	−0.0670804	−	0.146886i	0.873122	−	0.487502i	$-0.162092\pi$
$463$	−1.44340	−	3.16060i	−0.0670804	−	0.146886i	−0.940203	+	0.340616i	$0.889364\pi$
$464$	−5.62431	−	1.65145i	−0.261102	−	0.0766665i
$465$	−4.69671	−	5.42029i	−0.217805	−	0.251360i
$466$	−13.4460	+	3.94811i	−0.622875	+	0.182893i
$467$	−2.60268	−	1.67264i	−0.120438	−	0.0774006i	0.479035	−	0.877796i	$-0.340987\pi$
$467$	−2.60268	−	1.67264i	−0.120438	−	0.0774006i	−0.599473	+	0.800395i	$0.704623\pi$
$468$	−1.20058	+	2.62891i	−0.0554970	+	0.121522i
$469$	2.25570	−	2.60321i	0.104158	−	0.120205i
$470$	4.36410	−	2.80464i	0.201301	−	0.129368i
$471$	2.31168	+	16.0781i	0.106517	+	0.740839i
$472$	0.440453	+	3.06342i	0.0202735	+	0.141005i
$473$	4.27400	−	2.74673i	0.196519	−	0.126295i
$474$	1.26644	−	1.46155i	0.0581695	−	0.0671312i
$475$	0.628644	−	1.37654i	0.0288442	−	0.0631599i
$476$	−3.52845	−	2.26760i	−0.161726	−	0.103935i
$477$	7.22918	−	2.12268i	0.331002	−	0.0971908i
$478$	5.63445	+	6.50250i	0.257714	+	0.297417i
$479$	−30.8190	−	9.04926i	−1.40815	−	0.413471i	−0.512678	−	0.858581i	$-0.671347\pi$
$479$	−30.8190	−	9.04926i	−1.40815	−	0.413471i	−0.895476	+	0.445109i	$0.853165\pi$
$480$	0.415415	+	0.909632i	0.0189610	+	0.0415188i
$481$	−0.367387	+	2.55523i	−0.0167514	+	0.116509i
$482$	13.0152			0.592825
$483$	5.29741	−	4.82619i	0.241040	−	0.219599i
$484$	2.22692			0.101224
$485$	−2.02359	+	14.0744i	−0.0918866	+	0.639085i
$486$	−0.415415	−	0.909632i	−0.0188436	−	0.0412617i
$487$	1.42253	+	0.417691i	0.0644608	+	0.0189274i	0.313804	−	0.949488i	$-0.398397\pi$
$487$	1.42253	+	0.417691i	0.0644608	+	0.0189274i	−0.249343	+	0.968415i	$0.580215\pi$
$488$	−4.91005	−	5.66650i	−0.222268	−	0.256510i
$489$	13.3659	−	3.92458i	0.604427	−	0.177476i
$490$	4.01041	+	2.57734i	0.181172	+	0.116432i
$491$	0.444508	−	0.973337i	0.0200604	−	0.0439261i	−0.899337	−	0.437257i	$-0.855950\pi$
$491$	0.444508	−	0.973337i	0.0200604	−	0.0439261i	0.919397	+	0.393331i	$0.128677\pi$
$492$	2.84765	−	3.28636i	0.128382	−	0.148161i
$493$	13.8416	−	8.89544i	0.623393	−	0.400630i
$494$	0.622420	+	4.32902i	0.0280040	+	0.194772i
$495$	0.517582	+	3.59986i	0.0232636	+	0.161802i
$496$	6.03353	−	3.87752i	0.270914	−	0.174106i
$497$	0.324565	−	0.374568i	0.0145587	−	0.0168017i
$498$	4.97477	−	10.8932i	0.222925	−	0.488137i
$499$	20.7231	+	13.3179i	0.927692	+	0.596192i	0.914880	−	0.403726i	$-0.132285\pi$
$499$	20.7231	+	13.3179i	0.927692	+	0.596192i	0.0128123	+	0.999918i	$0.495922\pi$
$500$	0.959493	−	0.281733i	0.0429098	−	0.0125995i
$501$	9.57114	+	11.0457i	0.427607	+	0.493485i
$502$	−10.8046	−	3.17252i	−0.482234	−	0.141597i
$503$	−0.828797	−	1.81481i	−0.0369542	−	0.0809185i	0.890255	−	0.455463i	$-0.150526\pi$
$503$	−0.828797	−	1.81481i	−0.0369542	−	0.0809185i	−0.927209	+	0.374545i	$0.877799\pi$
$504$	0.212655	−	1.47905i	0.00947242	−	0.0658821i
$505$	2.06085			0.0917067
$506$	−13.4618	−	11.0904i	−0.598452	−	0.493030i
$507$	4.64741			0.206399
$508$	0.485364	−	3.37578i	0.0215345	−	0.149776i
$509$	−3.02113	−	6.61535i	−0.133909	−	0.293220i	0.830785	−	0.556594i	$-0.187892\pi$
$509$	−3.02113	−	6.61535i	−0.133909	−	0.293220i	−0.964694	+	0.263374i	$0.915165\pi$
$510$	−2.69323	−	0.790802i	−0.119258	−	0.0350173i
$511$	6.20820	+	7.16464i	0.274635	+	0.316945i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	−1.27306	−	0.818147i	−0.0562070	−	0.0361221i
$514$	−4.39528	+	9.62431i	−0.193867	+	0.424510i
$515$	−3.95392	+	4.56307i	−0.174231	+	0.201073i
$516$	−1.17518	+	0.755243i	−0.0517345	+	0.0332477i
$517$	2.68502	+	18.6747i	0.118087	+	0.821313i
$518$	−0.189950	−	1.32113i	−0.00834593	−	0.0580472i
$519$	−13.8838	+	8.92257i	−0.609431	+	0.391657i
$520$	−1.89260	+	2.18418i	−0.0829961	+	0.0957826i
$521$	−12.0245	+	26.3299i	−0.526802	+	1.15353i	0.439998	+	0.897999i	$0.354979\pi$
$521$	−12.0245	+	26.3299i	−0.526802	+	1.15353i	−0.966800	+	0.255536i	$0.917748\pi$
$522$	4.93122	+	3.16910i	0.215834	+	0.138708i
$523$	−23.5446	+	6.91333i	−1.02954	+	0.302299i	−0.752522	−	0.658567i	$-0.771163\pi$
$523$	−23.5446	+	6.91333i	−1.02954	+	0.302299i	−0.277014	+	0.960866i	$0.589345\pi$
$524$	−4.77370	−	5.50915i	−0.208540	−	0.240668i
$525$	−1.43373	−	0.420982i	−0.0625732	−	0.0183731i
$526$	8.47673	+	18.5615i	0.369603	+	0.809318i
$527$	−2.86501	+	19.9266i	−0.124802	+	0.868015i
$528$	−3.63688			−0.158275
$529$	4.40190	+	22.5748i	0.191387	+	0.981515i
$530$	7.53438			0.327273
$531$	0.440453	−	3.06342i	0.0191140	−	0.132941i
$532$	−0.939357	−	2.05691i	−0.0407263	−	0.0891782i
$533$	12.0584	+	3.54066i	0.522307	+	0.153363i
$534$	4.43673	+	5.12026i	0.191996	+	0.221575i
$535$	−7.67923	+	2.25483i	−0.332002	+	0.0974847i
$536$	1.93924	+	1.24628i	0.0837626	+	0.0538310i
$537$	−1.11172	+	2.43433i	−0.0479743	+	0.105049i
$538$	−13.6104	+	15.7073i	−0.586788	+	0.677189i
$539$	−14.5854	+	9.37347i	−0.628238	+	0.403744i
$540$	−0.142315	−	0.989821i	−0.00612426	−	0.0425951i
$541$	0.610999	+	4.24959i	0.0262689	+	0.182704i	0.998731	−	0.0503553i	$-0.0160354\pi$
$541$	0.610999	+	4.24959i	0.0262689	+	0.182704i	−0.972462	+	0.233060i	$0.925126\pi$
$542$	7.58628	−	4.87540i	0.325859	−	0.209417i
$543$	11.2032	−	12.9292i	0.480775	−	0.554844i
$544$	1.16604	−	2.55327i	0.0499935	−	0.109471i
$545$	11.6140	+	7.46385i	0.497488	+	0.319716i
$546$	4.14361	−	1.21667i	0.177330	−	0.0520688i
$547$	−13.6641	−	15.7692i	−0.584234	−	0.674242i	0.384276	−	0.923218i	$-0.374451\pi$
$547$	−13.6641	−	15.7692i	−0.584234	−	0.674242i	−0.968510	+	0.248977i	$0.919906\pi$
$548$	14.7841	+	4.34099i	0.631544	+	0.185438i
$549$	3.11472	+	6.82029i	0.132933	+	0.291083i
$550$	−0.517582	+	3.59986i	−0.0220698	+	0.153499i
$551$	8.87054			0.377898
$552$	3.70148	+	3.04943i	0.157545	+	0.129793i
$553$	−2.88976			−0.122885
$554$	−2.37896	+	16.5460i	−0.101072	+	0.702973i
$555$	−0.371061	−	0.812511i	−0.0157507	−	0.0344892i
$556$	−12.7895	−	3.75533i	−0.542394	−	0.159261i
$557$	4.43159	+	5.11433i	0.187773	+	0.216701i	0.841828	−	0.539745i	$-0.181479\pi$
$557$	4.43159	+	5.11433i	0.187773	+	0.216701i	−0.654056	+	0.756446i	$0.726934\pi$
$558$	−6.88155	+	2.02061i	−0.291319	+	0.0855391i
$559$	−3.39637	−	2.18272i	−0.143651	−	0.0923191i
$560$	0.620738	−	1.35923i	0.0262310	−	0.0574378i
$561$	6.68512	−	7.71504i	0.282246	−	0.325729i
$562$	5.17662	−	3.32681i	0.218363	−	0.140333i
$563$	6.56375	+	45.6519i	0.276629	+	1.92400i	0.371349	+	0.928493i	$0.378895\pi$
$563$	6.56375	+	45.6519i	0.276629	+	1.92400i	−0.0947204	+	0.995504i	$0.530196\pi$
$564$	−0.738274	−	5.13481i	−0.0310870	−	0.216215i
$565$	−16.2000	+	10.4111i	−0.681541	+	0.438000i
$566$	−4.76386	+	5.49779i	−0.200240	+	0.231089i
$567$	−0.620738	+	1.35923i	−0.0260685	+	0.0570821i
$568$	0.279032	+	0.179323i	0.0117079	+	0.00752421i
$569$	−0.716928	+	0.210509i	−0.0300552	+	0.00882500i	−0.296726	−	0.954963i	$-0.595895\pi$
$569$	−0.716928	+	0.210509i	−0.0300552	+	0.00882500i	0.266670	+	0.963788i	$0.414076\pi$
$570$	−0.990995	−	1.14367i	−0.0415082	−	0.0479030i
$571$	8.40497	+	2.46792i	0.351737	+	0.103279i	0.452828	−	0.891598i	$-0.350415\pi$
$571$	8.40497	+	2.46792i	0.351737	+	0.103279i	−0.101091	+	0.994877i	$0.532233\pi$
$572$	−4.36639	−	9.56105i	−0.182568	−	0.399768i
$573$	−3.19112	+	22.1947i	−0.133311	+	0.927198i
$574$	−6.49775			−0.271211
$575$	3.54517	−	3.22982i	0.147844	−	0.134693i
$576$	1.00000			0.0416667
$577$	6.45012	−	44.8616i	0.268522	−	1.86761i	−0.193995	−	0.981003i	$-0.562145\pi$
$577$	6.45012	−	44.8616i	0.268522	−	1.86761i	0.462517	−	0.886610i	$-0.346946\pi$
$578$	−3.78907	−	8.29691i	−0.157605	−	0.345106i
$579$	−12.5968	−	3.69876i	−0.523506	−	0.153715i
$580$	3.83863	+	4.43002i	0.159391	+	0.183947i
$581$	−17.1695	+	5.04143i	−0.712312	+	0.209154i
$582$	11.9619	+	7.68744i	0.495836	+	0.318655i
$583$	−11.3831	+	24.9254i	−0.471438	+	1.03231i
$584$	−4.15470	+	4.79478i	−0.171923	+	0.198409i
$585$	2.43129	−	1.56250i	0.100522	−	0.0646013i
$586$	3.03088	+	21.0802i	0.125204	+	0.870816i
$587$	−5.84868	−	40.6785i	−0.241401	−	1.67898i	−0.645108	−	0.764091i	$-0.723188\pi$
$587$	−5.84868	−	40.6785i	−0.241401	−	1.67898i	0.403707	−	0.914888i	$-0.367721\pi$
$588$	4.01041	−	2.57734i	0.165387	−	0.106288i
$589$	−7.10749	+	8.20248i	−0.292859	+	0.337977i
$590$	1.28568	−	2.81524i	0.0529305	−	0.115902i
$591$	4.01327	+	2.57917i	0.165084	+	0.106093i
$592$	0.857048	−	0.251652i	0.0352245	−	0.0103428i
$593$	−22.0593	−	25.4578i	−0.905868	−	1.04543i	−0.998762	−	0.0497516i	$-0.984157\pi$
$593$	−22.0593	−	25.4578i	−0.905868	−	1.04543i	0.0928934	−	0.995676i	$-0.470388\pi$
$594$	3.48956	+	1.02463i	0.143179	+	0.0420410i
$595$	1.74236	+	3.81525i	0.0714300	+	0.156410i
$596$	−0.113683	+	0.790685i	−0.00465665	+	0.0323877i
$597$	−0.466496			−0.0190924
$598$	−3.57276	+	13.3920i	−0.146101	+	0.547639i
$599$	−33.3457			−1.36247			−0.681234	−	0.732066i	$-0.738556\pi$
$599$	−33.3457			−1.36247			−0.681234	+	0.732066i	$0.738556\pi$
$600$	0.142315	−	0.989821i	0.00580998	−	0.0404093i
$601$	−0.981676	−	2.14957i	−0.0400434	−	0.0876828i	0.888553	−	0.458774i	$-0.151711\pi$
$601$	−0.981676	−	2.14957i	−0.0400434	−	0.0876828i	−0.928597	+	0.371091i	$0.878984\pi$
$602$	2.00284	+	0.588086i	0.0816296	+	0.0239686i
$603$	−1.50958	−	1.74214i	−0.0614746	−	0.0709455i
$604$	−17.9229	+	5.26264i	−0.729273	+	0.214134i
$605$	−1.87340	−	1.20396i	−0.0761647	−	0.0489481i
$606$	0.856109	−	1.87462i	0.0347770	−	0.0761511i
$607$	3.42942	−	3.95776i	0.139196	−	0.160641i	−0.681871	−	0.731472i	$-0.738834\pi$
$607$	3.42942	−	3.95776i	0.139196	−	0.160641i	0.821067	+	0.570831i	$0.193379\pi$
$608$	1.27306	−	0.818147i	0.0516295	−	0.0331802i
$609$	−1.24653	−	8.66983i	−0.0505121	−	0.351319i
$610$	1.06706	+	7.42154i	0.0432038	+	0.300489i
$611$	12.6126	−	8.10563i	0.510252	−	0.327919i
$612$	−1.83815	+	2.12133i	−0.0743026	+	0.0857498i
$613$	18.0669	−	39.5610i	0.729716	−	1.59785i	−0.0700504	−	0.997543i	$-0.522316\pi$
$613$	18.0669	−	39.5610i	0.729716	−	1.59785i	0.799766	−	0.600311i	$-0.204957\pi$
$614$	12.0492	+	7.74358i	0.486268	+	0.312505i
$615$	−4.17233	+	1.22511i	−0.168245	+	0.0494011i
$616$	3.55881	+	4.10708i	0.143388	+	0.165479i
$617$	22.5259	+	6.61420i	0.906858	+	0.266278i	0.701718	−	0.712455i	$-0.252417\pi$
$617$	22.5259	+	6.61420i	0.906858	+	0.266278i	0.205140	+	0.978733i	$0.434235\pi$
$618$	2.50820	+	5.49218i	0.100894	+	0.220928i
$619$	1.34796	−	9.37525i	0.0541790	−	0.376823i	−0.944635	−	0.328124i	$-0.893584\pi$
$619$	1.34796	−	9.37525i	0.0541790	−	0.376823i	0.998814	−	0.0486986i	$-0.0155074\pi$
$620$	−7.17207			−0.288037
$621$	−2.69242	−	3.96874i	−0.108043	−	0.159260i
$622$	33.5081			1.34355
$623$	1.44076	−	10.0207i	0.0577226	−	0.401470i
$624$	1.20058	+	2.62891i	0.0480618	+	0.105241i
$625$	−0.959493	−	0.281733i	−0.0383797	−	0.0112693i
$626$	6.11049	+	7.05188i	0.244224	+	0.281850i
$627$	5.28073	−	1.55056i	0.210892	−	0.0619235i
$628$	13.6648	+	8.78185i	0.545286	+	0.350434i
$629$	−1.04154	+	2.28066i	−0.0415290	+	0.0909357i
$630$	−0.978532	+	1.12929i	−0.0389856	+	0.0449918i
$631$	−13.6782	+	8.79044i	−0.544520	+	0.349942i	−0.783804	−	0.621008i	$-0.786724\pi$
$631$	−13.6782	+	8.79044i	−0.544520	+	0.349942i	0.239284	+	0.970950i	$0.423087\pi$
$632$	−0.275224	−	1.91422i	−0.0109478	−	0.0761437i
$633$	1.20001	+	8.34626i	0.0476962	+	0.331734i
$634$	24.0448	−	15.4526i	0.954941	−	0.613703i
$635$	−2.23340	+	2.57748i	−0.0886297	+	0.102284i
$636$	3.12989	−	6.85351i	0.124108	−	0.271759i
$637$	11.5904	+	7.44872i	0.459230	+	0.295129i
$638$	−20.4550	+	6.00612i	−0.809820	+	0.237785i
$639$	−0.217208	−	0.250671i	−0.00859261	−	0.00991640i
$640$	0.959493	+	0.281733i	0.0379273	+	0.0111365i
$641$	8.91308	+	19.5169i	0.352046	+	0.770872i	0.999958	+	0.00915758i	$0.00291499\pi$
$641$	8.91308	+	19.5169i	0.352046	+	0.770872i	−0.647912	+	0.761715i	$0.724358\pi$
$642$	−1.13901	+	7.92197i	−0.0449530	+	0.312655i
$643$	28.3638			1.11856			0.559279	−	0.828979i	$-0.311078\pi$
$643$	28.3638			1.11856			0.559279	+	0.828979i	$0.311078\pi$
$644$	−0.178331	−	7.16400i	−0.00702724	−	0.282301i
$645$	1.39694			0.0550045
$646$	−0.604510	+	4.20446i	−0.0237841	+	0.165422i
$647$	−5.10342	−	11.1749i	−0.200636	−	0.439332i	0.782392	−	0.622786i	$-0.213999\pi$
$647$	−5.10342	−	11.1749i	−0.200636	−	0.439332i	−0.983028	+	0.183454i	$0.941272\pi$
$648$	−0.959493	−	0.281733i	−0.0376924	−	0.0110675i
$649$	7.37102	+	8.50661i	0.289338	+	0.333914i
$650$	2.77302	−	0.814231i	0.108767	−	0.0319368i
$651$	9.01566	+	5.79401i	0.353352	+	0.227085i
$652$	5.78680	−	12.6713i	0.226629	−	0.496247i
$653$	10.2478	−	11.8266i	0.401029	−	0.462812i	−0.518936	−	0.854813i	$-0.673672\pi$
$653$	10.2478	−	11.8266i	0.401029	−	0.462812i	0.919965	+	0.392001i	$0.128217\pi$
$654$	11.6140	−	7.46385i	0.454142	−	0.291860i
$655$	1.03742	+	7.21545i	0.0405355	+	0.281931i
$656$	−0.618853	−	4.30422i	−0.0241621	−	0.168051i
$657$	5.33725	−	3.43004i	0.208226	−	0.133819i
$658$	−5.07624	+	5.85830i	−0.197893	+	0.228380i
$659$	16.1166	−	35.2903i	0.627812	−	1.37472i	−0.281887	−	0.959448i	$-0.590960\pi$
$659$	16.1166	−	35.2903i	0.627812	−	1.37472i	0.909699	−	0.415268i	$-0.136312\pi$
$660$	3.05954	+	1.96625i	0.119092	+	0.0765361i
$661$	−9.87654	+	2.90001i	−0.384153	+	0.112797i	−0.468106	−	0.883672i	$-0.655063\pi$
$661$	−9.87654	+	2.90001i	−0.384153	+	0.112797i	0.0839534	+	0.996470i	$0.473245\pi$
$662$	21.8461	+	25.2117i	0.849073	+	0.979882i
$663$	−7.78365	−	2.28549i	−0.302292	−	0.0887609i
$664$	−4.97477	−	10.8932i	−0.193058	−	0.422739i
$665$	−0.321809	+	2.23823i	−0.0124792	+	0.0867950i
$666$	−0.893230			−0.0346120
$667$	25.8543	+	11.0382i	1.00108	+	0.427400i
$668$	14.6155			0.565492
$669$	0.945488	−	6.57601i	0.0365547	−	0.254243i
$670$	−0.957608	−	2.09687i	−0.0369956	−	0.0810092i
$671$	−26.1642	−	7.68251i	−1.01006	−	0.296580i
$672$	−0.978532	−	1.12929i	−0.0377477	−	0.0435632i
$673$	−33.6887	+	9.89190i	−1.29860	+	0.381305i	−0.856727	−	0.515771i	$-0.827506\pi$
$673$	−33.6887	+	9.89190i	−1.29860	+	0.381305i	−0.441878	+	0.897075i	$0.645687\pi$
$674$	2.35505	+	1.51350i	0.0907132	+	0.0582978i
$675$	−0.415415	+	0.909632i	−0.0159893	+	0.0350118i
$676$	3.04341	−	3.51228i	0.117054	−	0.135088i
$677$	6.28750	−	4.04073i	0.241648	−	0.155298i	−0.414211	−	0.910181i	$-0.635943\pi$
$677$	6.28750	−	4.04073i	0.241648	−	0.155298i	0.655860	+	0.754883i	$0.272306\pi$
$678$	2.74056	+	19.0610i	0.105251	+	0.732034i
$679$	−3.02377	−	21.0308i	−0.116042	−	0.807088i
$680$	−2.36134	+	1.51754i	−0.0905531	+	0.0581949i
$681$	−17.0938	+	19.7273i	−0.655036	+	0.755951i
$682$	10.8357	−	23.7268i	0.414920	−	0.908547i
$683$	40.4673	+	26.0067i	1.54844	+	0.995120i	0.985705	+	0.168480i	$0.0538859\pi$
$683$	40.4673	+	26.0067i	1.54844	+	0.995120i	0.562731	+	0.826640i	$0.309751\pi$
$684$	−1.45199	+	0.426343i	−0.0555183	+	0.0163016i
$685$	−10.0902	−	11.6447i	−0.385528	−	0.444923i
$686$	−16.8710	−	4.95377i	−0.644137	−	0.189136i
$687$	1.38112	+	3.02422i	0.0526928	+	0.115381i
$688$	−0.198805	+	1.38272i	−0.00757938	+	0.0527158i
$689$	21.7750			0.829561
$690$	−1.46523	−	4.56652i	−0.0557805	−	0.173844i
$691$	−7.44477			−0.283212			−0.141606	−	0.989923i	$-0.545227\pi$
$691$	−7.44477			−0.283212			−0.141606	+	0.989923i	$0.545227\pi$
$692$	−2.34872	+	16.3357i	−0.0892849	+	0.620990i
$693$	−2.25755	−	4.94335i	−0.0857573	−	0.187782i
$694$	8.80224	+	2.58457i	0.334129	+	0.0981090i
$695$	8.72890	+	10.0737i	0.331106	+	0.382117i
$696$	5.62431	−	1.65145i	0.213189	−	0.0625980i
$697$	10.2682	+	6.59898i	0.388936	+	0.249954i
$698$	7.96575	−	17.4426i	0.301508	−	0.660211i
$699$	9.17701	−	10.5908i	0.347106	−	0.400582i
$700$	−1.25705	+	0.807858i	−0.0475121	+	0.0305341i
$701$	2.81107	+	19.5514i	0.106173	+	0.738447i	0.971466	+	0.237180i	$0.0762232\pi$
$701$	2.81107	+	19.5514i	0.106173	+	0.738447i	−0.865293	+	0.501266i	$0.832868\pi$
$702$	−0.411302	−	2.86067i	−0.0155236	−	0.107969i
$703$	−1.13714	+	0.730794i	−0.0428879	+	0.0275624i
$704$	−2.38165	+	2.74857i	−0.0897619	+	0.103591i
$705$	−2.15501	+	4.71882i	−0.0811625	+	0.177721i
$706$	4.44926	+	2.85937i	0.167450	+	0.107614i
$707$	−2.95471	+	0.867581i	−0.111123	+	0.0326287i
$708$	−2.02674	−	2.33898i	−0.0761696	−	0.0879044i
$709$	41.3606	+	12.1446i	1.55333	+	0.456099i	0.942094	−	0.335348i	$-0.108854\pi$
$709$	41.3606	+	12.1446i	1.55333	+	0.456099i	0.611237	+	0.791448i	$0.290672\pi$
$710$	−0.137787	−	0.301712i	−0.00517106	−	0.0113230i
$711$	−0.275224	+	1.91422i	−0.0103217	+	0.0717889i
$712$	6.77507			0.253907
$713$	−30.9225	+	15.0628i	−1.15806	+	0.564107i
$714$	4.19428			0.156967
$715$	−1.49586	+	10.4039i	−0.0559419	+	0.389084i
$716$	1.11172	+	2.43433i	0.0415469	+	0.0909751i
$717$	−8.25551	−	2.42404i	−0.308308	−	0.0905273i
$718$	5.74097	+	6.62543i	0.214251	+	0.247259i
$719$	−30.4891	+	8.95242i	−1.13705	+	0.333869i	−0.795476	−	0.605985i	$-0.792779\pi$
$719$	−30.4891	+	8.95242i	−1.13705	+	0.333869i	−0.341577	+	0.939854i	$0.610961\pi$
$720$	−0.841254	−	0.540641i	−0.0313517	−	0.0201485i
$721$	3.74790	−	8.20675i	0.139579	−	0.305635i
$722$	10.9427	−	12.6285i	0.407245	−	0.469985i
$723$	−10.9491	+	7.03653i	−0.407200	+	0.261691i
$724$	−2.43469	−	16.9336i	−0.0904844	−	0.629333i
$725$	−0.834215	−	5.80209i	−0.0309820	−	0.215484i
$726$	−1.87340	+	1.20396i	−0.0695285	+	0.0446833i
$727$	−5.32417	+	6.14442i	−0.197463	+	0.227884i	−0.845842	−	0.533433i	$-0.820902\pi$
$727$	−5.32417	+	6.14442i	−0.197463	+	0.227884i	0.648380	+	0.761317i	$0.275447\pi$
$728$	1.79398	−	3.92828i	0.0664895	−	0.145592i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	6.08741	−	1.78742i	0.225305	−	0.0661555i
$731$	−2.56778	−	2.96338i	−0.0949728	−	0.109604i
$732$	7.19414	+	2.11239i	0.265903	+	0.0780762i
$733$	−2.58787	−	5.66664i	−0.0955850	−	0.209302i	0.855800	−	0.517308i	$-0.173066\pi$
$733$	−2.58787	−	5.66664i	−0.0955850	−	0.209302i	−0.951385	+	0.308006i	$0.900338\pi$
$734$	3.98517	−	27.7175i	0.147095	−	1.02307i
$735$	−4.76719			−0.175840
$736$	4.72856	−	0.800436i	0.174297	−	0.0295045i
$737$	8.38369			0.308817
$738$	−0.618853	+	4.30422i	−0.0227803	+	0.158440i
$739$	1.24793	+	2.73260i	0.0459060	+	0.100520i	0.931195	−	0.364520i	$-0.118767\pi$
$739$	1.24793	+	2.73260i	0.0459060	+	0.100520i	−0.885289	+	0.465041i	$0.846040\pi$
$740$	−0.857048	−	0.251652i	−0.0315057	−	0.00925091i
$741$	−2.86406	−	3.30530i	−0.105214	−	0.121423i
$742$	−10.8023	+	3.17183i	−0.396564	+	0.116442i
$743$	−4.44263	−	2.85510i	−0.162984	−	0.104744i	0.456606	−	0.889669i	$-0.349065\pi$
$743$	−4.44263	−	2.85510i	−0.162984	−	0.104744i	−0.619590	+	0.784925i	$0.712701\pi$
$744$	−2.97939	+	6.52395i	−0.109230	+	0.239179i
$745$	0.523113	−	0.603704i	0.0191654	−	0.0221180i
$746$	0.682347	−	0.438518i	0.0249825	−	0.0160553i
$747$	1.70428	+	11.8535i	0.0623563	+	0.433698i
$748$	−1.45282	−	10.1046i	−0.0531202	−	0.369459i
$749$	10.0607	−	6.46563i	0.367611	−	0.236249i
$750$	−0.654861	+	0.755750i	−0.0239121	+	0.0275961i
$751$	−11.5705	+	25.3358i	−0.422212	+	0.924516i	0.572315	+	0.820034i	$0.306046\pi$
$751$	−11.5705	+	25.3358i	−0.422212	+	0.924516i	−0.994527	+	0.104482i	$0.966682\pi$
$752$	−4.36410	−	2.80464i	−0.159142	−	0.102275i
$753$	10.8046	−	3.17252i	0.393742	−	0.115613i
$754$	11.0940	+	12.8031i	0.404019	+	0.466263i
$755$	17.9229	+	5.26264i	0.652282	+	0.191527i
$756$	0.620738	+	1.35923i	0.0225760	+	0.0494346i
$757$	−3.48847	+	24.2628i	−0.126791	+	0.881848i	0.822795	+	0.568339i	$0.192414\pi$
$757$	−3.48847	+	24.2628i	−0.126791	+	0.881848i	−0.949585	+	0.313509i	$0.898495\pi$
$758$	−15.7292			−0.571309
$759$	17.3208	+	2.05185i	0.628704	+	0.0744773i
$760$	−1.51329			−0.0548928
$761$	−7.34835	+	51.1089i	−0.266377	+	1.85270i	0.215560	+	0.976491i	$0.430842\pi$
$761$	−7.34835	+	51.1089i	−0.266377	+	1.85270i	−0.481938	+	0.876205i	$0.660067\pi$
$762$	1.41677	+	3.10229i	0.0513241	+	0.112384i
$763$	−19.7935	−	5.81189i	−0.716572	−	0.210404i
$764$	14.6839	+	16.9461i	0.531245	+	0.613090i
$765$	2.69323	−	0.790802i	0.0973738	−	0.0285915i
$766$	24.5194	+	15.7576i	0.885921	+	0.569347i
$767$	3.71571	−	8.13628i	0.134167	−	0.293784i
$768$	0.654861	−	0.755750i	0.0236303	−	0.0272708i
$769$	−28.3630	+	18.2278i	−1.02279	+	0.657310i	−0.940674	−	0.339312i	$-0.889806\pi$
$769$	−28.3630	+	18.2278i	−1.02279	+	0.657310i	−0.0821209	+	0.996622i	$0.526169\pi$
$770$	−0.773402	−	5.37913i	−0.0278715	−	0.193850i
$771$	−1.50575	−	10.4728i	−0.0542284	−	0.377167i
$772$	−11.0445	+	7.09787i	−0.397500	+	0.255458i
$773$	4.44403	−	5.12868i	0.159841	−	0.184466i	−0.670180	−	0.742199i	$-0.733783\pi$
$773$	4.44403	−	5.12868i	0.159841	−	0.184466i	0.830021	+	0.557733i	$0.188329\pi$
$774$	0.580310	−	1.27070i	0.0208588	−	0.0456744i
$775$	6.03353	+	3.87752i	0.216731	+	0.139284i
$776$	13.6431	−	4.00599i	0.489760	−	0.143807i
$777$	0.874054	+	1.00871i	0.0313565	+	0.0361873i
$778$	−3.04379	−	0.893739i	−0.109125	−	0.0320421i
$779$	2.73364	+	5.98584i	0.0979429	+	0.214465i
$780$	0.411302	−	2.86067i	0.0147270	−	0.102428i
$781$	1.20630			0.0431649
$782$	−6.99379	+	11.5022i	−0.250098	+	0.411317i
$783$	−5.86176			−0.209482
$784$	0.678442	−	4.71867i	0.0242301	−	0.168524i
$785$	−6.74776	−	14.7755i	−0.240838	−	0.527361i
$786$	6.99436	+	2.05373i	0.249481	+	0.0732541i
$787$	12.7815	+	14.7507i	0.455612	+	0.525804i	0.936354	−	0.351058i	$-0.114178\pi$
$787$	12.7815	+	14.7507i	0.455612	+	0.525804i	−0.480742	+	0.876862i	$0.659633\pi$
$788$	4.57734	−	1.34403i	0.163061	−	0.0478791i
$789$	−17.1662	−	11.0320i	−0.611132	−	0.392750i
$790$	−0.803374	+	1.75914i	−0.0285828	+	0.0625875i
$791$	18.8436	−	21.7467i	0.670002	−	0.773223i
$792$	3.05954	−	1.96625i	0.108716	−	0.0698676i
$793$	3.08388	+	21.4489i	0.109512	+	0.761672i
$794$	−5.20163	−	36.1781i	−0.184599	−	1.28391i
$795$	−6.33832	+	4.07339i	−0.224797	+	0.144468i
$796$	−0.305490	+	0.352554i	−0.0108278	+	0.0124959i
$797$	3.85252	−	8.43584i	0.136463	−	0.298813i	−0.829046	−	0.559180i	$-0.811116\pi$
$797$	3.85252	−	8.43584i	0.136463	−	0.298813i	0.965510	+	0.260367i	$0.0838435\pi$
$798$	1.90228	+	1.22252i	0.0673401	+	0.0432769i
$799$	13.9714	−	4.10238i	0.494273	−	0.145132i
$800$	−0.654861	−	0.755750i	−0.0231528	−	0.0267198i
$801$	−6.50063	−	1.90876i	−0.229689	−	0.0674427i
$802$	−13.7901	−	30.1962i	−0.486946	−	1.06626i
$803$	−3.28375	+	22.8390i	−0.115881	+	0.805970i
$804$	−2.30518			−0.0812976
$805$	−3.72313	+	6.12315i	−0.131223	+	0.215813i
$806$	−20.7279			−0.730109
$807$	2.95783	−	20.5722i	0.104121	−	0.724174i
$808$	−0.856109	−	1.87462i	−0.0301178	−	0.0659488i
$809$	42.5773	+	12.5018i	1.49694	+	0.439541i	0.924748	−	0.380580i	$-0.124276\pi$
$809$	42.5773	+	12.5018i	1.49694	+	0.439541i	0.572191	+	0.820121i	$0.306094\pi$
$810$	0.654861	+	0.755750i	0.0230095	+	0.0265543i
$811$	−4.61369	+	1.35470i	−0.162009	+	0.0475701i	−0.361731	−	0.932282i	$-0.617814\pi$
$811$	−4.61369	+	1.35470i	−0.162009	+	0.0475701i	0.199722	+	0.979853i	$0.435996\pi$
$812$	−7.36853	−	4.73546i	−0.258585	−	0.166182i
$813$	−3.74614	+	8.20290i	−0.131383	+	0.287688i
$814$	2.12736	−	2.45511i	0.0745640	−	0.0860515i
$815$	−11.7188	+	7.53122i	−0.410492	+	0.263807i
$816$	0.399467	+	2.77836i	0.0139841	+	0.0972619i
$817$	−0.300850	−	2.09246i	−0.0105254	−	0.0732059i
$818$	22.4308	−	14.4154i	0.784276	−	0.504024i
$819$	−2.82804	+	3.26373i	−0.0988197	+	0.114044i
$820$	−1.80642	+	3.95551i	−0.0630830	+	0.138133i
$821$	46.4653	+	29.8614i	1.62165	+	1.04217i	0.954917	+	0.296874i	$0.0959442\pi$
$821$	46.4653	+	29.8614i	1.62165	+	1.04217i	0.666733	+	0.745297i	$0.267692\pi$
$822$	−14.7841	+	4.34099i	−0.515653	+	0.151410i
$823$	−27.7450	−	32.0195i	−0.967131	−	1.11613i	−0.993194	−	0.116469i	$-0.962843\pi$
$823$	−27.7450	−	32.0195i	−0.967131	−	1.11613i	0.0260631	−	0.999660i	$-0.491703\pi$
$824$	5.79324	+	1.70105i	0.201817	+	0.0592588i
$825$	−1.51082	−	3.30823i	−0.0525999	−	0.115178i
$826$	−0.658151	+	4.57754i	−0.0229000	+	0.159273i
$827$	−25.4443			−0.884785			−0.442393	−	0.896822i	$-0.645870\pi$
$827$	−25.4443			−0.884785			−0.442393	+	0.896822i	$0.645870\pi$
$828$	−4.76253	−	0.564177i	−0.165509	−	0.0196065i
$829$	−16.1446			−0.560724			−0.280362	−	0.959894i	$-0.590455\pi$
$829$	−16.1446			−0.560724			−0.280362	+	0.959894i	$0.590455\pi$
$830$	−1.70428	+	11.8535i	−0.0591564	+	0.411442i
$831$	−6.94415	−	15.2056i	−0.240890	−	0.527475i
$832$	2.77302	+	0.814231i	0.0961370	+	0.0282284i
$833$	8.76279	+	10.1128i	0.303613	+	0.350388i
$834$	12.7895	−	3.75533i	0.442863	−	0.130036i
$835$	−12.2954	−	7.90175i	−0.425499	−	0.273451i
$836$	2.28630	−	5.00631i	0.0790735	−	0.173147i
$837$	4.69671	−	5.42029i	0.162342	−	0.187353i
$838$	4.52750	−	2.90965i	0.156400	−	0.100512i
$839$	−5.51843	−	38.3816i	−0.190518	−	1.32508i	−0.830642	−	0.556807i	$-0.812026\pi$
$839$	−5.51843	−	38.3816i	−0.190518	−	1.32508i	0.640124	−	0.768271i	$-0.278883\pi$
$840$	0.212655	+	1.47905i	0.00733730	+	0.0510321i
$841$	4.50927	−	2.89793i	0.155492	−	0.0999287i
$842$	−13.4196	+	15.4870i	−0.462468	+	0.533717i
$843$	−2.55624	+	5.59738i	−0.0880416	+	0.192784i
$844$	7.09352	+	4.55873i	0.244169	+	0.156918i
$845$	−4.45916	+	1.30933i	−0.153400	+	0.0450422i
$846$	3.39716	+	3.92054i	0.116797	+	0.134791i
$847$	3.19280	+	0.937492i	0.109706	+	0.0322126i
$848$	−3.12989	−	6.85351i	−0.107481	−	0.235351i
$849$	1.03529	−	7.20057i	0.0355309	−	0.247123i
$850$	2.80693			0.0962768
$851$	−4.22369	+	0.714974i	−0.144786	+	0.0245090i
$852$	−0.331685			−0.0113634
$853$	7.53247	−	52.3895i	0.257907	−	1.79378i	−0.289774	−	0.957095i	$-0.593580\pi$
$853$	7.53247	−	52.3895i	0.257907	−	1.79378i	0.547681	−	0.836687i	$-0.315511\pi$
$854$	−4.65420	−	10.1913i	−0.159263	−	0.348738i
$855$	1.45199	+	0.426343i	0.0496571	+	0.0145806i
$856$	5.24113	+	6.04859i	0.179138	+	0.206737i
$857$	4.34726	−	1.27647i	0.148500	−	0.0436034i	−0.206638	−	0.978417i	$-0.566252\pi$
$857$	4.34726	−	1.27647i	0.148500	−	0.0436034i	0.355137	+	0.934814i	$0.384434\pi$
$858$	8.84233	+	5.68262i	0.301872	+	0.194002i
$859$	16.9599	−	37.1370i	0.578664	−	1.26710i	−0.363390	−	0.931637i	$-0.618381\pi$
$859$	16.9599	−	37.1370i	0.578664	−	1.26710i	0.942054	−	0.335461i	$-0.108892\pi$
$860$	0.914801	−	1.05574i	0.0311945	−	0.0360003i
$861$	5.46626	−	3.51295i	0.186290	−	0.119721i
$862$	−3.94128	−	27.4122i	−0.134241	−	0.933665i
$863$	−0.114690	−	0.797684i	−0.00390408	−	0.0271535i	0.987776	−	0.155878i	$-0.0498207\pi$
$863$	−0.114690	−	0.797684i	−0.00390408	−	0.0271535i	−0.991680	+	0.128725i	$0.958912\pi$
$864$	−0.841254	+	0.540641i	−0.0286200	+	0.0183930i
$865$	10.8076	−	12.4727i	0.367470	−	0.424083i
$866$	10.7530	−	23.5459i	0.365403	−	0.800122i
$867$	7.67322	+	4.93128i	0.260596	+	0.167475i
$868$	10.2828	−	3.01931i	0.349022	−	0.102482i
$869$	−4.60589	−	5.31548i	−0.156244	−	0.180315i
$870$	−5.62431	−	1.65145i	−0.190682	−	0.0559893i
$871$	−2.76757	−	6.06013i	−0.0937755	−	0.205340i
$872$	1.96474	−	13.6650i	0.0665344	−	0.462757i
$873$	−14.2191			−0.481244
$874$	−6.52458	+	3.17822i	−0.220697	+	0.107505i
$875$	1.49426			0.0505152
$876$	0.902902	−	6.27982i	0.0305062	−	0.212176i
$877$	−6.30596	−	13.8081i	−0.212937	−	0.466267i	0.772781	−	0.634673i	$-0.218865\pi$
$877$	−6.30596	−	13.8081i	−0.212937	−	0.466267i	−0.985718	+	0.168406i	$0.946138\pi$
$878$	5.12530	+	1.50492i	0.172970	+	0.0507887i
$879$	−13.9466	−	16.0952i	−0.470406	−	0.542877i
$880$	3.48956	−	1.02463i	0.117633	−	0.0345402i
$881$	21.3379	+	13.7130i	0.718892	+	0.462004i	0.848251	−	0.529594i	$-0.177656\pi$
$881$	21.3379	+	13.7130i	0.718892	+	0.462004i	−0.129359	+	0.991598i	$0.541292\pi$
$882$	−1.98036	+	4.33639i	−0.0666822	+	0.146014i
$883$	−4.39721	+	5.07466i	−0.147978	+	0.170776i	−0.824899	−	0.565280i	$-0.808768\pi$
$883$	−4.39721	+	5.07466i	−0.147978	+	0.170776i	0.676921	+	0.736055i	$0.263314\pi$
$884$	−6.82446	+	4.38582i	−0.229531	+	0.147511i
$885$	0.440453	+	3.06342i	0.0148057	+	0.102976i
$886$	4.10432	+	28.5462i	0.137887	+	0.959028i
$887$	26.1533	−	16.8077i	0.878142	−	0.564348i	−0.0220908	−	0.999756i	$-0.507032\pi$
$887$	26.1533	−	16.8077i	0.878142	−	0.564348i	0.900233	+	0.435408i	$0.143396\pi$
$888$	−0.584941	+	0.675058i	−0.0196293	+	0.0226535i
$889$	2.11702	−	4.63563i	0.0710026	−	0.155474i
$890$	−5.69955	−	3.66288i	−0.191049	−	0.122780i
$891$	−3.48956	+	1.02463i	−0.116905	+	0.0343263i
$892$	−4.35066	−	5.02092i	−0.145671	−	0.168113i
$893$	7.53237	+	2.21170i	0.252061	+	0.0740119i
$894$	−0.331840	−	0.726628i	−0.0110984	−	0.0243021i
$895$	0.380858	−	2.64893i	0.0127307	−	0.0885439i
$896$	−1.49426			−0.0499197
$897$	−4.23465	−	13.1976i	−0.141391	−	0.440656i
$898$	−3.17706			−0.106020
$899$	−5.98305	+	41.6130i	−0.199546	+	1.38787i
$900$	0.415415	+	0.909632i	0.0138472	+	0.0303211i
$901$	20.2918	+	5.95820i	0.676017	+	0.198497i
$902$	−10.3566	−	11.9521i	−0.344836	−	0.397962i
$903$	−2.00284	+	0.588086i	−0.0666503	+	0.0195703i
$904$	16.2000	+	10.4111i	0.538805	+	0.346269i
$905$	−7.10681	+	15.5617i	−0.236238	+	0.517290i
$906$	12.2325	−	14.1171i	0.406398	−	0.469009i
$907$	7.47207	−	4.80201i	0.248106	−	0.159448i	−0.410677	−	0.911781i	$-0.634708\pi$
$907$	7.47207	−	4.80201i	0.248106	−	0.159448i	0.658783	+	0.752333i	$0.271071\pi$
$908$	3.71484	+	25.8373i	0.123281	+	0.857440i
$909$	0.293290	+	2.03988i	0.00972781	+	0.0676584i
$910$	−3.63298	+	2.33478i	−0.120432	+	0.0773971i
$911$	−31.5666	+	36.4298i	−1.04585	+	1.20697i	−0.0679924	+	0.997686i	$0.521659\pi$
$911$	−31.5666	+	36.4298i	−1.04585	+	1.20697i	−0.977854	+	0.209286i	$0.932886\pi$
$912$	−0.628644	+	1.37654i	−0.0208165	+	0.0455817i
$913$	−36.6393	−	23.5466i	−1.21258	−	0.779280i
$914$	−23.7732	+	6.98045i	−0.786348	+	0.230893i
$915$	−4.91005	−	5.66650i	−0.162321	−	0.187329i
$916$	3.18999	+	0.936666i	0.105400	+	0.0309483i
$917$	−4.52496	−	9.90828i	−0.149427	−	0.327200i
$918$	0.399467	−	2.77836i	0.0131844	−	0.0916994i
$919$	−42.5665			−1.40414			−0.702069	−	0.712109i	$-0.747740\pi$
$919$	−42.5665			−1.40414			−0.702069	+	0.712109i	$0.747740\pi$
$920$	−4.41067	−	1.88308i	−0.145415	−	0.0620834i
$921$	−14.3230			−0.471958
$922$	0.0868171	−	0.603826i	0.00285917	−	0.0198860i
$923$	−0.398216	−	0.871972i	−0.0131075	−	0.0287013i
$924$	−5.21431	−	1.53106i	−0.171538	−	0.0503682i
$925$	0.584941	+	0.675058i	0.0192327	+	0.0221958i
$926$	3.33385	−	0.978906i	0.109557	−	0.0321688i
$927$	−5.07933	−	3.26429i	−0.166827	−	0.107213i
$928$	2.43506	−	5.33204i	0.0799348	−	0.175033i
$929$	−16.6547	+	19.2206i	−0.546423	+	0.630606i	−0.960046	−	0.279842i	$-0.909718\pi$
$929$	−16.6547	+	19.2206i	−0.546423	+	0.630606i	0.413623	+	0.910448i	$0.364263\pi$
$930$	6.03353	−	3.87752i	0.197847	−	0.127149i
$931$	1.02668	+	7.14072i	0.0336481	+	0.234028i
$932$	−1.99435	−	13.8710i	−0.0653273	−	0.454361i
$933$	−28.1888	+	18.1159i	−0.922861	+	0.593087i
$934$	2.02602	−	2.33815i	0.0662933	−	0.0765065i
$935$	−4.24075	+	9.28594i	−0.138687	+	0.303683i
$936$	−2.43129	−	1.56250i	−0.0794693	−	0.0510718i
$937$	23.8990	−	7.01739i	0.780748	−	0.229248i	0.133013	−	0.991114i	$-0.457535\pi$
$937$	23.8990	−	7.01739i	0.780748	−	0.229248i	0.647735	+	0.761866i	$0.275717\pi$
$938$	2.25570	+	2.60321i	0.0736511	+	0.0849979i
$939$	−8.95300	−	2.62884i	−0.292170	−	0.0857889i
$940$	2.15501	+	4.71882i	0.0702887	+	0.153911i
$941$	−2.63400	+	18.3199i	−0.0858659	+	0.597210i	0.900773	+	0.434290i	$0.143001\pi$
$941$	−2.63400	+	18.3199i	−0.0858659	+	0.597210i	−0.986639	+	0.162921i	$0.947909\pi$
$942$	−16.2434			−0.529239
$943$	0.518966	+	20.8481i	0.0168999	+	0.678908i
$944$	−3.09492			−0.100731
$945$	0.212655	−	1.47905i	0.00691768	−	0.0481135i
$946$	2.11052	+	4.62139i	0.0686189	+	0.150254i
$947$	−34.0798	−	10.0067i	−1.10744	−	0.325175i	−0.323638	−	0.946181i	$-0.604906\pi$
$947$	−34.0798	−	10.0067i	−1.10744	−	0.325175i	−0.783806	+	0.621006i	$0.786724\pi$
$948$	1.26644	+	1.46155i	0.0411320	+	0.0474689i
$949$	17.5931	−	5.16581i	0.571097	−	0.167689i
$950$	1.27306	+	0.818147i	0.0413036	+	0.0265442i
$951$	−11.8734	+	25.9992i	−0.385022	+	0.843081i
$952$	2.74667	−	3.16982i	0.0890200	−	0.102735i
$953$	−8.32765	+	5.35185i	−0.269759	+	0.173364i	−0.668526	−	0.743689i	$-0.733075\pi$
$953$	−8.32765	+	5.35185i	−0.269759	+	0.173364i	0.398767	+	0.917052i	$0.369438\pi$
$954$	1.07225	+	7.45769i	0.0347155	+	0.241452i
$955$	−3.19112	−	22.1947i	−0.103262	−	0.718204i
$956$	−7.23818	+	4.65169i	−0.234099	+	0.150447i
$957$	13.9607	−	16.1115i	0.451284	−	0.520810i
$958$	13.3432	−	29.2174i	0.431098	−	0.943972i
$959$	19.3689	+	12.4476i	0.625454	+	0.401955i
$960$	−0.959493	+	0.281733i	−0.0309675	+	0.00909288i
$961$	−13.3845	−	15.4465i	−0.431757	−	0.498274i
$962$	−2.47694	−	0.727296i	−0.0798598	−	0.0234489i
$963$	−3.32474	−	7.28018i	−0.107138	−	0.234600i
$964$	−1.85225	+	12.8827i	−0.0596570	+	0.414924i
$965$	13.1286			0.422625
$966$	4.02317	+	5.93032i	0.129443	+	0.190805i
$967$	−43.7203			−1.40595			−0.702974	−	0.711215i	$-0.748145\pi$
$967$	−43.7203			−1.40595			−0.702974	+	0.711215i	$0.748145\pi$
$968$	−0.316924	+	2.20425i	−0.0101863	+	0.0708473i
$969$	−1.76456	−	3.86384i	−0.0566857	−	0.124124i
$970$	−13.6431	−	4.00599i	−0.438055	−	0.128625i
$971$	−1.02172	−	1.17913i	−0.0327885	−	0.0378400i	0.739118	−	0.673575i	$-0.235242\pi$
$971$	−1.02172	−	1.17913i	−0.0327885	−	0.0378400i	−0.771907	+	0.635735i	$0.780697\pi$
$972$	0.959493	−	0.281733i	0.0307758	−	0.00903658i
$973$	−16.7557	−	10.7683i	−0.537164	−	0.345215i
$974$	−0.615887	+	1.34860i	−0.0197343	+	0.0432120i
$975$	−1.89260	+	2.18418i	−0.0606118	+	0.0699498i
$976$	6.30760	−	4.05365i	0.201901	−	0.129754i
$977$	1.17345	+	8.16152i	0.0375420	+	0.261110i	0.999945	−	0.0105163i	$-0.00334751\pi$
$977$	1.17345	+	8.16152i	0.0375420	+	0.261110i	−0.962403	+	0.271627i	$0.912438\pi$
$978$	1.98247	+	13.7884i	0.0633924	+	0.440904i
$979$	20.7286	−	13.3215i	0.662489	−	0.425756i
$980$	−3.12184	+	3.60280i	−0.0997237	+	0.115087i
$981$	−5.73504	+	12.5580i	−0.183106	+	0.400945i
$982$	0.900170	+	0.578504i	0.0287256	+	0.0184608i
$983$	−37.4788	+	11.0048i	−1.19539	+	0.350998i	−0.818088	−	0.575093i	$-0.804966\pi$
$983$	−37.4788	+	11.0048i	−1.19539	+	0.350998i	−0.377301	+	0.926091i	$0.623148\pi$
$984$	2.84765	+	3.28636i	0.0907797	+	0.104765i
$985$	−4.57734	−	1.34403i	−0.145846	−	0.0428243i
$986$	6.83504	+	14.9666i	0.217672	+	0.476635i
$987$	1.10317	−	7.67274i	0.0351144	−	0.244226i
$988$	−4.37354			−0.139141
$989$	1.72692	−	6.47309i	0.0549127	−	0.205832i
$990$	−3.63688			−0.115588
$991$	4.52849	−	31.4964i	0.143852	−	1.00051i	−0.782175	−	0.623059i	$-0.785890\pi$
$991$	4.52849	−	31.4964i	0.143852	−	1.00051i	0.926028	−	0.377456i	$-0.123201\pi$
$992$	2.97939	+	6.52395i	0.0945956	+	0.207136i
$993$	−32.0086	−	9.39858i	−1.01576	−	0.298255i
$994$	0.324565	+	0.374568i	0.0102946	+	0.0118806i
$995$	0.447600	−	0.131427i	0.0141899	−	0.00416652i
$996$	10.0744	+	6.47440i	0.319218	+	0.205149i
$997$	9.60740	−	21.0373i	0.304270	−	0.666257i	−0.694302	−	0.719684i	$-0.744287\pi$
$997$	9.60740	−	21.0373i	0.304270	−	0.666257i	0.998572	+	0.0534261i	$0.0170142\pi$
$998$	−16.1316	+	18.6168i	−0.510635	+	0.589305i
$999$	0.751433	−	0.482917i	0.0237743	−	0.0152788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.d.31.2	✓	20
23.3	even	11	inner	690.2.m.d.601.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.d.31.2	✓	20	1.1	even	1	trivial
690.2.m.d.601.2	yes	20	23.3	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-1.25705 - 0.807858i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-1.25705 - 0.807858i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.841254 + 0.540641i) q^{10} +(-0.517582 - 3.59986i) q^{11} +(0.142315 + 0.989821i) q^{12} +(-2.43129 + 1.56250i) q^{13} +(0.978532 - 1.12929i) q^{14} +(0.415415 - 0.909632i) q^{15} +(0.841254 + 0.540641i) q^{16} +(-2.69323 + 0.790802i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(-1.45199 - 0.426343i) q^{19} +(-0.415415 - 0.909632i) q^{20} +(-0.212655 + 1.47905i) q^{21} +3.63688 q^{22} +(-3.70148 - 3.04943i) q^{23} -1.00000 q^{24} +(-0.142315 + 0.989821i) q^{25} +(-1.20058 - 2.62891i) q^{26} +(0.959493 + 0.281733i) q^{27} +(0.978532 + 1.12929i) q^{28} +(-5.62431 + 1.65145i) q^{29} +(0.841254 + 0.540641i) q^{30} +(2.97939 - 6.52395i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-3.05954 + 1.96625i) q^{33} +(-0.399467 - 2.77836i) q^{34} +(-0.212655 - 1.47905i) q^{35} +(0.841254 - 0.540641i) q^{36} +(0.584941 - 0.675058i) q^{37} +(0.628644 - 1.37654i) q^{38} +(2.43129 + 1.56250i) q^{39} +(0.959493 - 0.281733i) q^{40} +(-2.84765 - 3.28636i) q^{41} +(-1.43373 - 0.420982i) q^{42} +(0.580310 + 1.27070i) q^{43} +(-0.517582 + 3.59986i) q^{44} -1.00000 q^{45} +(3.54517 - 3.22982i) q^{46} -5.18761 q^{47} +(0.142315 - 0.989821i) q^{48} +(-1.98036 - 4.33639i) q^{49} +(-0.959493 - 0.281733i) q^{50} +(1.83815 + 2.12133i) q^{51} +(2.77302 - 0.814231i) q^{52} +(-6.33832 - 4.07339i) q^{53} +(-0.415415 + 0.909632i) q^{54} +(2.38165 - 2.74857i) q^{55} +(-1.25705 + 0.807858i) q^{56} +(0.215364 + 1.49789i) q^{57} +(-0.834215 - 5.80209i) q^{58} +(-2.60361 + 1.67324i) q^{59} +(-0.654861 + 0.755750i) q^{60} +(3.11472 - 6.82029i) q^{61} +(6.03353 + 3.87752i) q^{62} +(1.43373 - 0.420982i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-2.77302 - 0.814231i) q^{65} +(-1.51082 - 3.30823i) q^{66} +(-0.328062 + 2.28172i) q^{67} +2.80693 q^{68} +(-1.23621 + 4.63376i) q^{69} +1.49426 q^{70} +(-0.0472038 + 0.328309i) q^{71} +(0.415415 + 0.909632i) q^{72} +(-6.08741 - 1.78742i) q^{73} +(0.584941 + 0.675058i) q^{74} +(0.959493 - 0.281733i) q^{75} +(1.27306 + 0.818147i) q^{76} +(-2.25755 + 4.94335i) q^{77} +(-1.89260 + 2.18418i) q^{78} +(1.62691 - 1.04555i) q^{79} +(0.142315 + 0.989821i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(3.65817 - 2.35096i) q^{82} +(7.84223 - 9.05042i) q^{83} +(0.620738 - 1.35923i) q^{84} +(-2.36134 - 1.51754i) q^{85} +(-1.34035 + 0.393564i) q^{86} +(3.83863 + 4.43002i) q^{87} +(-3.48956 - 1.02463i) q^{88} +(2.81447 + 6.16282i) q^{89} +(0.142315 - 0.989821i) q^{90} +4.31854 q^{91} +(2.69242 + 3.96874i) q^{92} -7.17207 q^{93} +(0.738274 - 5.13481i) q^{94} +(-0.628644 - 1.37654i) q^{95} +(0.959493 + 0.281733i) q^{96} +(9.31155 + 10.7461i) q^{97} +(4.57408 - 1.34307i) q^{98} +(3.05954 + 1.96625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{12} - 11 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 24 q^{17} - 2 q^{18} + 22 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} - 22 q^{23} - 20 q^{24} - 2 q^{25} + 11 q^{26} + 2 q^{27} + 2 q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} - 2 q^{32} - 2 q^{33} - 9 q^{34} - 2 q^{35} - 2 q^{36} + 20 q^{37} + 11 q^{39} + 2 q^{40} - 21 q^{41} - 13 q^{42} + 34 q^{43} + 2 q^{44} - 20 q^{45} + 14 q^{47} + 2 q^{48} + 10 q^{49} - 2 q^{50} + 31 q^{51} + 2 q^{54} - 2 q^{55} + 2 q^{56} + 11 q^{57} - 19 q^{58} - 40 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 13 q^{63} - 2 q^{64} + 9 q^{66} + 18 q^{67} - 20 q^{68} - 22 q^{69} + 20 q^{70} - 85 q^{71} - 2 q^{72} + 39 q^{73} + 20 q^{74} + 2 q^{75} - 48 q^{77} - 11 q^{78} - 28 q^{79} + 2 q^{80} - 2 q^{81} + q^{82} + 49 q^{83} + 9 q^{84} - 13 q^{85} - 32 q^{86} + 8 q^{87} + 2 q^{88} + 3 q^{89} + 2 q^{90} - 34 q^{91} - 11 q^{92} - 36 q^{93} + 3 q^{94} + 2 q^{96} + 43 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 + 2 * q^10 + 2 * q^11 + 2 * q^12 - 11 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 24 * q^17 - 2 * q^18 + 22 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 - 22 * q^23 - 20 * q^24 - 2 * q^25 + 11 * q^26 + 2 * q^27 + 2 * q^28 + 14 * q^29 - 2 * q^30 - 8 * q^31 - 2 * q^32 - 2 * q^33 - 9 * q^34 - 2 * q^35 - 2 * q^36 + 20 * q^37 + 11 * q^39 + 2 * q^40 - 21 * q^41 - 13 * q^42 + 34 * q^43 + 2 * q^44 - 20 * q^45 + 14 * q^47 + 2 * q^48 + 10 * q^49 - 2 * q^50 + 31 * q^51 + 2 * q^54 - 2 * q^55 + 2 * q^56 + 11 * q^57 - 19 * q^58 - 40 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 13 * q^63 - 2 * q^64 + 9 * q^66 + 18 * q^67 - 20 * q^68 - 22 * q^69 + 20 * q^70 - 85 * q^71 - 2 * q^72 + 39 * q^73 + 20 * q^74 + 2 * q^75 - 48 * q^77 - 11 * q^78 - 28 * q^79 + 2 * q^80 - 2 * q^81 + q^82 + 49 * q^83 + 9 * q^84 - 13 * q^85 - 32 * q^86 + 8 * q^87 + 2 * q^88 + 3 * q^89 + 2 * q^90 - 34 * q^91 - 11 * q^92 - 36 * q^93 + 3 * q^94 + 2 * q^96 + 43 * q^97 + 10 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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