LMFDB - Embedded newform 750.2.o.b.469.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, degree $20$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$14$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			469.6
Character	$\chi$	$=$	750.469
Dual form			750.2.o.b.379.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.08543 + 1.95495i) q^{5} +(0.876307 - 0.481754i) q^{6} +(0.161189 + 0.221857i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})$	\(q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.08543 + 1.95495i) q^{5} +(0.876307 - 0.481754i) q^{6} +(0.161189 + 0.221857i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(-1.20605 - 1.88294i) q^{10} +(-0.316853 - 5.03624i) q^{11} +(-0.844328 + 0.535827i) q^{12} +(-4.85464 - 4.01611i) q^{13} +(-0.174801 - 0.211298i) q^{14} +(-1.81451 - 1.30674i) q^{15} +(0.968583 - 0.248690i) q^{16} +(0.721548 - 5.71164i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(-3.03381 + 6.44718i) q^{19} +(1.32190 + 1.80349i) q^{20} +(-0.240310 - 0.132112i) q^{21} +(0.632456 + 5.00640i) q^{22} +(-0.824684 - 2.08291i) q^{23} +(0.809017 - 0.587785i) q^{24} +(-2.64366 + 4.24394i) q^{25} +(5.09723 + 3.70336i) q^{26} +(-0.248690 + 0.968583i) q^{27} +(0.187724 + 0.199905i) q^{28} +(6.57603 - 6.17530i) q^{29} +(1.89298 + 1.19022i) q^{30} +(8.18321 + 1.03378i) q^{31} +(-0.951057 + 0.309017i) q^{32} +(2.43102 + 4.42201i) q^{33} +(-0.361487 + 5.74567i) q^{34} +(-0.258760 + 0.555927i) q^{35} +(0.535827 - 0.844328i) q^{36} +(-1.32526 - 5.16153i) q^{37} +(2.62301 - 6.62495i) q^{38} +(6.10258 + 1.56688i) q^{39} +(-1.43253 - 1.71693i) q^{40} +(-6.58326 - 2.60650i) q^{41} +(0.248131 + 0.116762i) q^{42} +(1.60042 + 0.520009i) q^{43} +(-0.945563 - 4.95681i) q^{44} +(2.19820 + 0.409790i) q^{45} +(0.953844 + 2.02702i) q^{46} +(-8.74786 - 1.66874i) q^{47} +(-0.770513 + 0.637424i) q^{48} +(2.13988 - 6.58587i) q^{49} +(2.37197 - 4.40156i) q^{50} +(1.77902 + 5.47526i) q^{51} +(-5.31971 - 3.37599i) q^{52} +(-2.13940 + 3.89155i) q^{53} +(0.187381 - 0.982287i) q^{54} +(9.50167 - 6.08594i) q^{55} +(-0.199905 - 0.187724i) q^{56} -7.12532i q^{57} +(-6.17530 + 6.57603i) q^{58} +(1.46867 + 2.31425i) q^{59} +(-1.96398 - 1.06901i) q^{60} +(-0.525542 + 0.208077i) q^{61} +(-8.23198 - 0.517912i) q^{62} +(0.273689 + 0.0172191i) q^{63} +(0.929776 - 0.368125i) q^{64} +(2.58190 - 13.8498i) q^{65} +(-2.70389 - 4.26064i) q^{66} +(2.18155 - 2.32311i) q^{67} -5.75703i q^{68} +(1.63306 + 1.53354i) q^{69} +(0.223342 - 0.571078i) q^{70} +(2.95927 - 15.5130i) q^{71} +(-0.481754 + 0.876307i) q^{72} +(-0.955496 - 0.606376i) q^{73} +(1.64674 + 5.06813i) q^{74} +(0.585075 - 4.96565i) q^{75} +(-2.20184 + 6.77658i) q^{76} +(1.06625 - 0.882081i) q^{77} +(-6.18893 - 1.18060i) q^{78} +(0.844319 + 1.79427i) q^{79} +(1.53751 + 1.62360i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(6.73393 + 2.18799i) q^{82} +(11.0962 + 5.22148i) q^{83} +(-0.254973 - 0.100951i) q^{84} +(11.9492 - 4.78902i) q^{85} +(-1.62992 - 0.418491i) q^{86} +(-3.32085 + 8.38752i) q^{87} +(1.25494 + 4.88766i) q^{88} +(1.18147 - 1.86169i) q^{89} +(-2.21959 - 0.270956i) q^{90} +(0.108489 - 1.72439i) q^{91} +(-1.07924 - 1.96313i) q^{92} +(-7.84456 + 2.54885i) q^{93} +(8.83538 + 1.11617i) q^{94} +(-15.8969 + 1.06704i) q^{95} +(0.728969 - 0.684547i) q^{96} +(-5.44913 - 5.80274i) q^{97} +(-1.72213 + 6.70724i) q^{98} +(-4.08246 - 2.96608i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q+O(q^{10}) $ 280 * q	$ 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) $ 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{49}{50}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.998027	+	0.0627905i	−0.705711	+	0.0443996i
$2$	−0.998027	+	0.0627905i	−0.705711	+	0.0443996i
$3$	−0.904827	+	0.425779i	−0.522402	+	0.245824i
$3$	−0.904827	+	0.425779i	−0.522402	+	0.245824i
$4$	0.992115	−	0.125333i	0.496057	−	0.0626666i
$5$	1.08543	+	1.95495i	0.485421	+	0.874280i
$5$	1.08543	+	1.95495i	0.485421	+	0.874280i
$6$	0.876307	−	0.481754i	0.357751	−	0.196675i
$7$	0.161189	+	0.221857i	0.0609236	+	0.0838541i	0.838392	−	0.545068i	$-0.183496\pi$
$7$	0.161189	+	0.221857i	0.0609236	+	0.0838541i	−0.777468	+	0.628922i	$0.783496\pi$
$8$	−0.982287	+	0.187381i	−0.347291	+	0.0662493i
$9$	0.637424	−	0.770513i	0.212475	−	0.256838i
$10$	−1.20605	−	1.88294i	−0.381385	−	0.595437i
$11$	−0.316853	−	5.03624i	−0.0955348	−	1.51848i	−0.695540	−	0.718487i	$-0.744835\pi$
$11$	−0.316853	−	5.03624i	−0.0955348	−	1.51848i	0.600006	−	0.799996i	$-0.295165\pi$
$12$	−0.844328	+	0.535827i	−0.243736	+	0.154680i
$13$	−4.85464	−	4.01611i	−1.34643	−	1.11387i	−0.983272	−	0.182142i	$-0.941697\pi$
$13$	−4.85464	−	4.01611i	−1.34643	−	1.11387i	−0.363162	−	0.931726i	$-0.618303\pi$
$14$	−0.174801	−	0.211298i	−0.0467176	−	0.0564718i
$15$	−1.81451	−	1.30674i	−0.468504	−	0.337398i
$16$	0.968583	−	0.248690i	0.242146	−	0.0621725i
$17$	0.721548	−	5.71164i	0.175001	−	1.38528i	−0.622812	−	0.782371i	$-0.714010\pi$
$17$	0.721548	−	5.71164i	0.175001	−	1.38528i	0.797813	−	0.602904i	$-0.205990\pi$
$18$	−0.587785	+	0.809017i	−0.138542	+	0.190687i
$19$	−3.03381	+	6.44718i	−0.696005	+	1.47909i	0.173331	+	0.984864i	$0.444547\pi$
$19$	−3.03381	+	6.44718i	−0.696005	+	1.47909i	−0.869336	+	0.494221i	$0.835453\pi$
$20$	1.32190	+	1.80349i	0.295585	+	0.403274i
$21$	−0.240310	−	0.132112i	−0.0524400	−	0.0288291i
$22$	0.632456	+	5.00640i	0.134840	+	1.06737i
$23$	−0.824684	−	2.08291i	−0.171959	−	0.434318i	0.818082	−	0.575102i	$-0.195038\pi$
$23$	−0.824684	−	2.08291i	−0.171959	−	0.434318i	−0.990040	+	0.140784i	$0.955038\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	−2.64366	+	4.24394i	−0.528733	+	0.848788i
$26$	5.09723	+	3.70336i	0.999650	+	0.726288i
$27$	−0.248690	+	0.968583i	−0.0478604	+	0.186404i
$28$	0.187724	+	0.199905i	0.0354765	+	0.0377786i
$29$	6.57603	−	6.17530i	1.22114	−	1.14672i	0.236590	−	0.971610i	$-0.423970\pi$
$29$	6.57603	−	6.17530i	1.22114	−	1.14672i	0.984548	−	0.175115i	$-0.0560297\pi$
$30$	1.89298	+	1.19022i	0.345609	+	0.217304i
$31$	8.18321	+	1.03378i	1.46975	+	0.185672i	0.819076	−	0.573686i	$-0.194487\pi$
$31$	8.18321	+	1.03378i	1.46975	+	0.185672i	0.650673	+	0.759358i	$0.274487\pi$
$32$	−0.951057	+	0.309017i	−0.168125	+	0.0546270i
$33$	2.43102	+	4.42201i	0.423187	+	0.769774i
$34$	−0.361487	+	5.74567i	−0.0619945	+	0.985375i
$35$	−0.258760	+	0.555927i	−0.0437384	+	0.0939689i
$36$	0.535827	−	0.844328i	0.0893045	−	0.140721i
$37$	−1.32526	−	5.16153i	−0.217871	−	0.848550i	−0.979650	−	0.200714i	$-0.935674\pi$
$37$	−1.32526	−	5.16153i	−0.217871	−	0.848550i	0.761779	−	0.647837i	$-0.224326\pi$
$38$	2.62301	−	6.62495i	0.425508	−	1.07471i
$39$	6.10258	+	1.56688i	0.977196	+	0.250901i
$40$	−1.43253	−	1.71693i	−0.226503	−	0.271471i
$41$	−6.58326	−	2.60650i	−1.02813	−	0.407066i	−0.207325	−	0.978272i	$-0.566476\pi$
$41$	−6.58326	−	2.60650i	−1.02813	−	0.407066i	−0.820807	+	0.571206i	$0.806476\pi$
$42$	0.248131	+	0.116762i	0.0382875	+	0.0180167i
$43$	1.60042	+	0.520009i	0.244062	+	0.0793006i	0.428494	−	0.903545i	$-0.359044\pi$
$43$	1.60042	+	0.520009i	0.244062	+	0.0793006i	−0.184432	+	0.982845i	$0.559044\pi$
$44$	−0.945563	−	4.95681i	−0.142549	−	0.747268i
$45$	2.19820	+	0.409790i	0.327688	+	0.0610880i
$46$	0.953844	+	2.02702i	0.140637	+	0.298868i
$47$	−8.74786	−	1.66874i	−1.27601	−	0.243411i	−0.495527	−	0.868593i	$-0.665025\pi$
$47$	−8.74786	−	1.66874i	−1.27601	−	0.243411i	−0.780479	+	0.625181i	$0.785025\pi$
$48$	−0.770513	+	0.637424i	−0.111214	+	0.0920042i
$49$	2.13988	−	6.58587i	0.305697	−	0.940839i
$50$	2.37197	−	4.40156i	0.335447	−	0.622475i
$51$	1.77902	+	5.47526i	0.249113	+	0.766690i
$52$	−5.31971	−	3.37599i	−0.737711	−	0.468166i
$53$	−2.13940	+	3.89155i	−0.293869	+	0.534545i	−0.981487	−	0.191527i	$-0.938656\pi$
$53$	−2.13940	+	3.89155i	−0.293869	+	0.534545i	0.687619	+	0.726072i	$0.258656\pi$
$54$	0.187381	−	0.982287i	0.0254994	−	0.133672i
$55$	9.50167	−	6.08594i	1.28121	−	0.820628i
$56$	−0.199905	−	0.187724i	−0.0267135	−	0.0250856i
$57$		−	7.12532i		−	0.943772i
$58$	−6.17530	+	6.57603i	−0.810857	+	0.863475i
$59$	1.46867	+	2.31425i	0.191204	+	0.301289i	0.926382	−	0.376584i	$-0.122902\pi$
$59$	1.46867	+	2.31425i	0.191204	+	0.301289i	−0.735178	+	0.677874i	$0.762902\pi$
$60$	−1.96398	−	1.06901i	−0.253548	−	0.138009i
$61$	−0.525542	+	0.208077i	−0.0672888	+	0.0266415i	−0.401528	−	0.915847i	$-0.631521\pi$
$61$	−0.525542	+	0.208077i	−0.0672888	+	0.0266415i	0.334239	+	0.942488i	$0.391521\pi$
$62$	−8.23198	−	0.517912i	−1.04546	−	0.0657749i
$63$	0.273689	+	0.0172191i	0.0344816	+	0.00216940i
$64$	0.929776	−	0.368125i	0.116222	−	0.0460156i
$65$	2.58190	−	13.8498i	0.320245	−	1.71786i
$66$	−2.70389	−	4.26064i	−0.332825	−	0.524449i
$67$	2.18155	−	2.32311i	0.266519	−	0.283813i	−0.581764	−	0.813358i	$-0.697637\pi$
$67$	2.18155	−	2.32311i	0.266519	−	0.283813i	0.848282	+	0.529544i	$0.177637\pi$
$68$		−	5.75703i		−	0.698143i
$69$	1.63306	+	1.53354i	0.196597	+	0.184617i
$70$	0.223342	−	0.571078i	0.0266945	−	0.0682569i
$71$	2.95927	−	15.5130i	0.351201	−	1.84106i	−0.167203	−	0.985923i	$-0.553474\pi$
$71$	2.95927	−	15.5130i	0.351201	−	1.84106i	0.518404	−	0.855136i	$-0.326526\pi$
$72$	−0.481754	+	0.876307i	−0.0567752	+	0.103274i
$73$	−0.955496	−	0.606376i	−0.111832	−	0.0709709i	0.478734	−	0.877960i	$-0.341096\pi$
$73$	−0.955496	−	0.606376i	−0.111832	−	0.0709709i	−0.590567	+	0.806989i	$0.701096\pi$
$74$	1.64674	+	5.06813i	0.191429	+	0.589158i
$75$	0.585075	−	4.96565i	0.0675586	−	0.573384i
$76$	−2.20184	+	6.77658i	−0.252569	+	0.777327i
$77$	1.06625	−	0.882081i	0.121511	−	0.100522i
$78$	−6.18893	−	1.18060i	−0.700758	−	0.133677i
$79$	0.844319	+	1.79427i	0.0949934	+	0.201871i	0.946676	−	0.322186i	$-0.104418\pi$
$79$	0.844319	+	1.79427i	0.0949934	+	0.201871i	−0.851683	+	0.524057i	$0.824418\pi$
$80$	1.53751	+	1.62360i	0.171899	+	0.181523i
$81$	−0.187381	−	0.982287i	−0.0208201	−	0.109143i
$82$	6.73393	+	2.18799i	0.743638	+	0.241623i
$83$	11.0962	+	5.22148i	1.21797	+	0.573132i	0.923893	−	0.382651i	$-0.124989\pi$
$83$	11.0962	+	5.22148i	1.21797	+	0.573132i	0.294074	+	0.955783i	$0.404989\pi$
$84$	−0.254973	−	0.100951i	−0.0278199	−	0.0110147i
$85$	11.9492	−	4.78902i	1.29607	−	0.519442i
$86$	−1.62992	−	0.418491i	−0.175758	−	0.0451271i
$87$	−3.32085	+	8.38752i	−0.356033	+	0.899236i
$88$	1.25494	+	4.88766i	0.133777	+	0.521026i
$89$	1.18147	−	1.86169i	0.125235	−	0.197339i	−0.775925	−	0.630825i	$-0.782717\pi$
$89$	1.18147	−	1.86169i	0.125235	−	0.197339i	0.901160	+	0.433486i	$0.142717\pi$
$90$	−2.21959	−	0.270956i	−0.233965	−	0.0285613i
$91$	0.108489	−	1.72439i	0.0113728	−	0.180765i
$92$	−1.07924	−	1.96313i	−0.112519	−	0.204670i
$93$	−7.84456	+	2.54885i	−0.813443	+	0.264303i
$94$	8.83538	+	1.11617i	0.911300	+	0.115124i
$95$	−15.8969	+	1.06704i	−1.63099	+	0.109476i
$96$	0.728969	−	0.684547i	0.0744000	−	0.0698663i
$97$	−5.44913	−	5.80274i	−0.553276	−	0.589179i	0.390155	−	0.920749i	$-0.372421\pi$
$97$	−5.44913	−	5.80274i	−0.553276	−	0.589179i	−0.943430	+	0.331571i	$0.892421\pi$
$98$	−1.72213	+	6.70724i	−0.173961	+	0.677534i
$99$	−4.08246	−	2.96608i	−0.410302	−	0.298102i
$100$	−2.09091	+	4.54182i	−0.209091	+	0.454182i
$101$	11.2698	−	8.18798i	1.12139	−	0.814734i	0.136967	−	0.990576i	$-0.456265\pi$
$101$	11.2698	−	8.18798i	1.12139	−	0.814734i	0.984419	+	0.175841i	$0.0562645\pi$
$102$	−2.11931	−	5.35275i	−0.209843	−	0.530002i
$103$	1.80954	+	14.3240i	0.178299	+	1.41139i	0.786494	+	0.617598i	$0.211894\pi$
$103$	1.80954	+	14.3240i	0.178299	+	1.41139i	−0.608195	+	0.793788i	$0.708106\pi$
$104$	5.52119	+	3.03530i	0.541398	+	0.297636i
$105$	−0.00256931	−	0.613193i	−0.000250739	−	0.0598415i
$106$	1.89082	−	4.01820i	0.183653	−	0.390282i
$107$	−4.84248	+	6.66511i	−0.468140	+	0.644340i	−0.976172	−	0.216998i	$-0.930373\pi$
$107$	−4.84248	+	6.66511i	−0.468140	+	0.644340i	0.508032	+	0.861338i	$0.330373\pi$
$108$	−0.125333	+	0.992115i	−0.0120602	+	0.0954663i
$109$	−9.32008	+	2.39299i	−0.892702	+	0.229207i	−0.667061	−	0.745004i	$-0.732448\pi$
$109$	−9.32008	+	2.39299i	−0.892702	+	0.229207i	−0.225641	+	0.974210i	$0.572448\pi$
$110$	−9.10078	+	6.67055i	−0.867726	+	0.636012i
$111$	3.39680	+	4.10602i	0.322410	+	0.389727i
$112$	0.211298	+	0.174801i	0.0199658	+	0.0165172i
$113$	10.1687	−	6.45326i	0.956592	−	0.607072i	0.0367350	−	0.999325i	$-0.488304\pi$
$113$	10.1687	−	6.45326i	0.956592	−	0.607072i	0.919857	+	0.392253i	$0.128304\pi$
$114$	0.447403	+	7.11126i	0.0419031	+	0.666030i
$115$	3.17685	−	3.87309i	0.296243	−	0.361167i
$116$	5.75020	−	6.95080i	0.533893	−	0.645366i
$117$	−6.18893	+	1.18060i	−0.572166	+	0.109147i
$118$	−1.61108	−	2.21746i	−0.148312	−	0.204134i
$119$	1.38347	−	0.760571i	0.126823	−	0.0697214i
$120$	2.02723	+	0.943586i	0.185060	+	0.0861372i
$121$	−14.3500	+	1.81283i	−1.30455	+	0.164803i
$122$	0.511440	−	0.240665i	0.0463036	−	0.0217888i
$123$	7.06650	−	0.444586i	0.637165	−	0.0400870i
$124$	8.24825			0.740715
$125$	−11.1662	−	0.561707i	−0.998737	−	0.0502406i
$126$	−0.274231			−0.0244304
$127$	−0.599636	+	0.0377259i	−0.0532091	+	0.00334763i	−0.0893727	−	0.995998i	$-0.528486\pi$
$127$	−0.599636	+	0.0377259i	−0.0532091	+	0.00334763i	0.0361637	+	0.999346i	$0.488486\pi$
$128$	−0.904827	+	0.425779i	−0.0799762	+	0.0376339i
$129$	−1.66951	+	0.210909i	−0.146993	+	0.0185695i
$130$	−1.70716	+	13.9846i	−0.149728	+	1.22653i
$131$	−0.225371	+	0.123899i	−0.0196907	+	0.0108251i	−0.491569	−	0.870839i	$-0.663576\pi$
$131$	−0.225371	+	0.123899i	−0.0196907	+	0.0108251i	0.471878	+	0.881664i	$0.343576\pi$
$132$	2.96608	+	4.08246i	0.258164	+	0.355332i
$133$	−1.91937	+	0.366139i	−0.166431	+	0.0317483i
$134$	−2.03137	+	2.45551i	−0.175484	+	0.212124i
$135$	−2.16347	+	0.565157i	−0.186202	+	0.0486410i
$136$	0.361487	+	5.74567i	0.0309973	+	0.492687i
$137$	17.4698	−	11.0867i	1.49255	−	0.947199i	0.495646	−	0.868524i	$-0.334931\pi$
$137$	17.4698	−	11.0867i	1.49255	−	0.947199i	0.996900	−	0.0786744i	$-0.0250687\pi$
$138$	−1.72613	−	1.42798i	−0.146938	−	0.121558i
$139$	−5.42260	−	6.55480i	−0.459939	−	0.555971i	0.488651	−	0.872480i	$-0.337489\pi$
$139$	−5.42260	−	6.55480i	−0.459939	−	0.555971i	−0.948590	+	0.316509i	$0.897489\pi$
$140$	−0.187043	+	0.583975i	−0.0158081	+	0.0493549i
$141$	8.62581	−	2.21473i	0.726425	−	0.186514i
$142$	−1.97936	+	15.6682i	−0.166104	+	1.31485i
$143$	−18.6879	+	25.7216i	−1.56276	+	2.15095i
$144$	0.425779	−	0.904827i	0.0354816	−	0.0754023i
$145$	19.2103	+	6.15292i	1.59533	+	0.510972i
$146$	0.991685	+	0.545183i	0.0820724	+	0.0451197i
$147$	0.867907	+	6.87019i	0.0715838	+	0.566644i
$148$	−1.96172	−	4.95473i	−0.161252	−	0.407276i
$149$	−11.7220	+	8.51650i	−0.960300	+	0.697699i	−0.953220	−	0.302276i	$-0.902254\pi$
$149$	−11.7220	+	8.51650i	−0.960300	+	0.697699i	−0.00707964	+	0.999975i	$0.502254\pi$
$150$	−0.272125	+	4.99259i	−0.0222189	+	0.407643i
$151$	−5.92124	−	4.30203i	−0.481863	−	0.350094i	0.320183	−	0.947356i	$-0.396256\pi$
$151$	−5.92124	−	4.30203i	−0.481863	−	0.350094i	−0.802047	+	0.597261i	$0.796256\pi$
$152$	1.77200	−	6.90146i	0.143728	−	0.559783i
$153$	−3.94096	−	4.19670i	−0.318608	−	0.339283i
$154$	−1.00876	+	0.947291i	−0.0812884	+	0.0763349i
$155$	6.86136	+	17.1199i	0.551117	+	1.37510i
$156$	6.25085	+	0.789665i	0.500468	+	0.0632238i
$157$	3.25519	−	1.05768i	0.259793	−	0.0844117i	−0.176225	−	0.984350i	$-0.556389\pi$
$157$	3.25519	−	1.05768i	0.259793	−	0.0844117i	0.436017	+	0.899938i	$0.356389\pi$
$158$	−0.955316	−	1.73771i	−0.0760009	−	0.138245i
$159$	0.278843	−	4.43209i	0.0221137	−	0.351488i
$160$	−1.63642	−	1.52385i	−0.129371	−	0.120471i
$161$	0.329180	−	0.518704i	0.0259430	−	0.0408796i
$162$	0.248690	+	0.968583i	0.0195389	+	0.0760991i
$163$	−4.73418	+	11.9572i	−0.370810	+	0.936559i	0.617838	+	0.786306i	$0.288009\pi$
$163$	−4.73418	+	11.9572i	−0.370810	+	0.936559i	−0.988648	+	0.150253i	$0.951991\pi$
$164$	−6.85803	−	1.76084i	−0.535522	−	0.137499i
$165$	−6.00610	+	9.55234i	−0.467574	+	0.743649i
$166$	−11.4022	−	4.51444i	−0.884980	−	0.350388i
$167$	−17.0827	−	8.03853i	−1.32190	−	0.622040i	−0.370168	−	0.928965i	$-0.620700\pi$
$167$	−17.0827	−	8.03853i	−1.32190	−	0.622040i	−0.951734	+	0.306925i	$0.900700\pi$
$168$	0.260809	+	0.0847419i	0.0201218	+	0.00653798i
$169$	5.00245	+	26.2238i	0.384804	+	2.01721i
$170$	−11.6249	+	5.52986i	−0.891587	+	0.424121i
$171$	3.03381	+	6.44718i	0.232002	+	0.493028i
$172$	1.65298	+	0.315322i	0.126038	+	0.0240431i
$173$	−13.3530	+	11.0466i	−1.01521	+	0.839858i	−0.987158	−	0.159749i	$-0.948932\pi$
$173$	−13.3530	+	11.0466i	−1.01521	+	0.839858i	−0.0280557	+	0.999606i	$0.508932\pi$
$174$	2.78764	−	8.57948i	0.211331	−	0.650409i
$175$	−1.36768	+	0.0975599i	−0.103387	+	0.00737483i
$176$	−1.55936	−	4.79922i	−0.117541	−	0.361755i
$177$	−2.31425	−	1.46867i	−0.173950	−	0.110392i
$178$	−1.06224	+	1.93221i	−0.0796182	+	0.144825i
$179$	−0.934468	+	4.89865i	−0.0698454	+	0.366142i	−0.999999	−	0.00102701i	$-0.999673\pi$
$179$	−0.934468	+	4.89865i	−0.0698454	+	0.366142i	0.930154	+	0.367169i	$0.119673\pi$
$180$	2.23222	+	0.131052i	0.166380	+	0.00976804i
$181$	7.95102	+	7.46650i	0.590994	+	0.554981i	0.921280	−	0.388900i	$-0.127145\pi$
$181$	7.95102	+	7.46650i	0.590994	+	0.554981i	−0.330285	+	0.943881i	$0.607145\pi$
$182$			1.72780i			0.128073i
$183$	0.386930	−	0.412038i	0.0286027	−	0.0304588i
$184$	1.20038	+	1.89149i	0.0884929	+	0.139443i
$185$	8.65205	−	8.19331i	0.636112	−	0.602384i
$186$	7.66903	−	3.03638i	0.562321	−	0.222639i
$187$	−28.9938	−	1.82413i	−2.12024	−	0.133394i
$188$	−8.88803	−	0.559187i	−0.648226	−	0.0407829i
$189$	−0.254973	+	0.100951i	−0.0185466	+	0.00734311i
$190$	15.7986	−	2.06311i	1.14615	−	0.149674i
$191$	6.63984	+	10.4627i	0.480442	+	0.757055i	0.994944	−	0.100434i	$-0.0320232\pi$
$191$	6.63984	+	10.4627i	0.480442	+	0.757055i	−0.514502	+	0.857489i	$0.672023\pi$
$192$	−0.684547	+	0.728969i	−0.0494029	+	0.0526088i
$193$		−	20.4711i		−	1.47354i	−0.676141	−	0.736772i	$-0.736349\pi$
$193$		−	20.4711i		−	1.47354i	0.676141	−	0.736772i	$-0.263651\pi$
$194$	5.80274	+	5.44913i	0.416612	+	0.391225i
$195$	3.56079	+	13.6310i	0.254993	+	0.976136i
$196$	1.29758	−	6.80214i	0.0926841	−	0.485867i
$197$	10.6265	−	19.3295i	0.757107	−	1.37717i	−0.163445	−	0.986553i	$-0.552260\pi$
$197$	10.6265	−	19.3295i	0.757107	−	1.37717i	0.920552	−	0.390620i	$-0.127740\pi$
$198$	4.26064	+	2.70389i	0.302791	+	0.192157i
$199$	5.41884	+	16.6775i	0.384131	+	1.18223i	0.937108	+	0.349038i	$0.113492\pi$
$199$	5.41884	+	16.6775i	0.384131	+	1.18223i	−0.552977	+	0.833196i	$0.686508\pi$
$200$	1.80160	−	4.66414i	0.127392	−	0.329805i
$201$	−0.984791	+	3.03087i	−0.0694618	+	0.213781i
$202$	−10.7334	+	8.87946i	−0.755201	+	0.624756i
$203$	2.43002	+	0.463550i	0.170554	+	0.0325349i
$204$	2.45123	+	5.20912i	0.171620	+	0.364711i
$205$	−2.05013	−	15.6991i	−0.143187	−	1.09647i
$206$	−2.70538	−	14.1821i	−0.188493	−	0.988114i
$207$	−2.13059	−	0.692270i	−0.148086	−	0.0481161i
$208$	−5.70089	−	2.68263i	−0.395285	−	0.186007i
$209$	33.4308	+	13.2362i	2.31246	+	0.915567i
$210$	0.0410669	+	0.611822i	0.00283389	+	0.0422197i
$211$	−13.5636	−	3.48253i	−0.933754	−	0.239747i	−0.248985	−	0.968507i	$-0.580097\pi$
$211$	−13.5636	−	3.48253i	−0.933754	−	0.239747i	−0.684769	+	0.728760i	$0.740097\pi$
$212$	−1.63479	+	4.12900i	−0.112278	+	0.283581i
$213$	3.92750	+	15.2966i	0.269108	+	1.04811i
$214$	4.41442	−	6.95602i	0.301764	−	0.475503i
$215$	0.720563	+	3.69318i	0.0491420	+	0.251873i
$216$	0.0627905	−	0.998027i	0.00427235	−	0.0679071i
$217$	1.08969	+	1.98214i	0.0739730	+	0.134556i
$218$	9.15143	−	2.97348i	0.619813	−	0.201390i
$219$	1.12274	+	0.141835i	0.0758678	+	0.00958433i
$220$	8.66398	−	7.22883i	0.584125	−	0.487367i
$221$	−26.4414	+	24.8301i	−1.77864	+	1.67026i
$222$	−3.64792	−	3.88464i	−0.244832	−	0.260720i
$223$	−1.77282	+	6.90467i	−0.118717	+	0.462371i	−0.999947	−	0.0103166i	$-0.996716\pi$
$223$	−1.77282	+	6.90467i	−0.118717	+	0.462371i	0.881230	+	0.472688i	$0.156716\pi$
$224$	−0.221857	−	0.161189i	−0.0148235	−	0.0107699i
$225$	1.58488	+	4.74217i	0.105659	+	0.316145i
$226$	−9.74345	+	7.07903i	−0.648124	+	0.470890i
$227$	−6.60271	−	16.6766i	−0.438237	−	1.10686i	−0.966246	−	0.257622i	$-0.917061\pi$
$227$	−6.60271	−	16.6766i	−0.438237	−	1.10686i	0.528008	−	0.849239i	$-0.322939\pi$
$228$	−0.893039	−	7.06913i	−0.0591430	−	0.468165i
$229$	−13.1938	−	7.25337i	−0.871873	−	0.479316i	−0.0180246	−	0.999838i	$-0.505738\pi$
$229$	−13.1938	−	7.25337i	−0.871873	−	0.479316i	−0.853849	+	0.520521i	$0.825738\pi$
$230$	−2.92739	+	4.06492i	−0.193027	+	0.268033i
$231$	−0.589202	+	1.25212i	−0.0387667	+	0.0823834i
$232$	−5.30241	+	7.29814i	−0.348120	+	0.479147i
$233$	0.460790	−	3.64753i	0.0301874	−	0.238958i	−0.969800	−	0.243900i	$-0.921573\pi$
$233$	0.460790	−	3.64753i	0.0301874	−	0.238958i	0.999988	+	0.00494230i	$0.00157319\pi$
$234$	6.10258	−	1.56688i	0.398938	−	0.102430i
$235$	−6.23292	−	18.9129i	−0.406591	−	1.23374i
$236$	1.74714	+	2.11193i	0.113729	+	0.137475i
$237$	−1.52793	−	1.26401i	−0.0992495	−	0.0821063i
$238$	−1.33299	+	0.845939i	−0.0864047	+	0.0548341i
$239$	−0.485293	−	7.71351i	−0.0313910	−	0.498946i	−0.982039	−	0.188676i	$-0.939581\pi$
$239$	−0.485293	−	7.71351i	−0.0313910	−	0.498946i	0.950648	−	0.310270i	$-0.100419\pi$
$240$	−2.08247	−	0.814433i	−0.134423	−	0.0525714i
$241$	9.94710	−	12.0240i	0.640749	−	0.774532i	−0.345745	−	0.938328i	$-0.612374\pi$
$241$	9.94710	−	12.0240i	0.640749	−	0.774532i	0.986494	+	0.163796i	$0.0523739\pi$
$242$	14.2079	−	2.71030i	0.913318	−	0.174225i
$243$	0.587785	+	0.809017i	0.0377064	+	0.0518985i
$244$	−0.495319	+	0.272304i	−0.0317096	+	0.0174325i
$245$	15.1978	−	2.96518i	0.970949	−	0.189438i
$246$	−7.02464	+	0.887418i	−0.447875	+	0.0565797i
$247$	40.6206	−	19.1146i	2.58463	−	1.21623i
$248$	−8.23198	+	0.517912i	−0.522731	+	0.0328875i
$249$	−12.2633			−0.777158
$250$	11.1795	−	0.140534i	0.707051	−	0.00888814i
$251$	3.66335			0.231228			0.115614	−	0.993294i	$-0.463116\pi$
$251$	3.66335			0.231228			0.115614	+	0.993294i	$0.463116\pi$
$252$	0.273689	−	0.0172191i	0.0172408	−	0.00108470i
$253$	−10.2288	+	4.81328i	−0.643076	+	0.302609i
$254$	0.596084	−	0.0753029i	0.0374016	−	0.00472492i
$255$	−8.77286	+	9.42094i	−0.549378	+	0.589962i
$256$	0.876307	−	0.481754i	0.0547692	−	0.0301096i
$257$	1.70185	+	2.34240i	0.106159	+	0.146115i	0.858791	−	0.512326i	$-0.171216\pi$
$257$	1.70185	+	2.34240i	0.106159	+	0.146115i	−0.752632	+	0.658441i	$0.771216\pi$
$258$	1.65298	−	0.315322i	0.102910	−	0.0196311i
$259$	0.931506	−	1.12600i	0.0578810	−	0.0699661i
$260$	0.825696	−	14.0642i	0.0512075	−	0.872224i
$261$	−0.566433	−	9.00320i	−0.0350614	−	0.557284i
$262$	0.217147	−	0.137805i	0.0134154	−	0.00851364i
$263$	6.89457	+	5.70368i	0.425137	+	0.351704i	0.825256	−	0.564759i	$-0.191031\pi$
$263$	6.89457	+	5.70368i	0.425137	+	0.351704i	−0.400118	+	0.916463i	$0.631031\pi$
$264$	−3.21657	−	3.88816i	−0.197966	−	0.239300i
$265$	−9.92996	+	0.0416070i	−0.609993	+	0.00255590i
$266$	1.89259	−	0.485935i	0.116042	−	0.0297946i
$267$	−0.276353	+	2.18756i	−0.0169125	+	0.133876i
$268$	1.87318	−	2.57822i	0.114423	−	0.157490i
$269$	−13.3312	+	28.3301i	−0.812815	+	1.72732i	−0.136585	+	0.990628i	$0.543613\pi$
$269$	−13.3312	+	28.3301i	−0.812815	+	1.72732i	−0.676229	+	0.736691i	$0.736387\pi$
$270$	2.12371	−	0.699888i	0.129245	−	0.0425938i
$271$	−25.2353	−	13.8732i	−1.53294	−	0.842739i	−0.532942	−	0.846152i	$-0.678913\pi$
$271$	−25.2353	−	13.8732i	−1.53294	−	0.842739i	−0.999994	+	0.00341341i	$0.998913\pi$
$272$	−0.721548	−	5.71164i	−0.0437503	−	0.346319i
$273$	0.636045	+	1.60647i	0.0384952	+	0.0972277i
$274$	−16.7392	+	12.1617i	−1.01125	+	0.734718i
$275$	22.2112	+	11.9694i	1.33938	+	0.721782i
$276$	1.81239	+	1.31678i	0.109093	+	0.0792606i
$277$	−2.03525	+	7.92678i	−0.122286	+	0.476274i	−0.999996	−	0.00291939i	$-0.999071\pi$
$277$	−2.03525	+	7.92678i	−0.122286	+	0.476274i	0.877709	+	0.479193i	$0.159071\pi$
$278$	5.82348	+	6.20137i	0.349269	+	0.371934i
$279$	6.01272	−	5.64632i	0.359972	−	0.338036i
$280$	0.150006	−	0.594567i	0.00896459	−	0.0355322i
$281$	1.07034	+	0.135216i	0.0638513	+	0.00806629i	0.157194	−	0.987568i	$-0.449755\pi$
$281$	1.07034	+	0.135216i	0.0638513	+	0.00806629i	−0.0933427	+	0.995634i	$0.529755\pi$
$282$	−8.46973	+	2.75198i	−0.504365	+	0.163878i
$283$	−2.74443	−	4.99210i	−0.163139	−	0.296750i	0.782084	−	0.623173i	$-0.214157\pi$
$283$	−2.74443	−	4.99210i	−0.163139	−	0.296750i	−0.945224	+	0.326423i	$0.894157\pi$
$284$	0.991636	−	15.7616i	0.0588428	−	0.935279i
$285$	13.9296	−	7.73407i	0.825121	−	0.458127i
$286$	17.0359	−	26.8443i	1.00735	−	1.58734i
$287$	−0.482877	−	1.88068i	−0.0285033	−	0.111013i
$288$	−0.368125	+	0.929776i	−0.0216919	+	0.0547876i
$289$	−15.6363	−	4.01471i	−0.919780	−	0.236159i
$290$	−19.5587	−	4.93456i	−1.14853	−	0.289767i
$291$	7.40121	+	2.93035i	0.433867	+	0.171780i
$292$	−1.02396	−	0.481839i	−0.0599228	−	0.0281975i
$293$	−5.14148	−	1.67057i	−0.300369	−	0.0975957i	0.154955	−	0.987921i	$-0.450477\pi$
$293$	−5.14148	−	1.67057i	−0.300369	−	0.0975957i	−0.455324	+	0.890326i	$0.650477\pi$
$294$	−1.29758	−	6.80214i	−0.0756763	−	0.396709i
$295$	−2.93010	+	5.38314i	−0.170597	+	0.313418i
$296$	2.26896	+	4.82178i	0.131880	+	0.280260i
$297$	4.95681	+	0.945563i	0.287623	+	0.0548671i
$298$	11.1641	−	9.23572i	0.646717	−	0.535011i
$299$	−4.36166	+	13.4238i	−0.252242	+	0.776320i
$300$	−0.0418997	−	4.99982i	−0.00241908	−	0.288665i
$301$	0.142602	+	0.438885i	0.00821946	+	0.0252969i
$302$	6.17968	+	3.92174i	0.355601	+	0.225671i
$303$	−6.71094	+	12.2071i	−0.385533	+	0.701282i
$304$	−1.33515	+	6.99911i	−0.0765762	+	0.401427i
$305$	−0.977222	−	0.801555i	−0.0559555	−	0.0458969i
$306$	4.19670	+	3.94096i	0.239909	+	0.225290i
$307$			12.3199i			0.703136i	0.936162	+	0.351568i	$0.114351\pi$
$307$			12.3199i			0.703136i	−0.936162	+	0.351568i	$0.885649\pi$
$308$	0.947291	−	1.00876i	0.0539769	−	0.0574796i
$309$	−7.73618	−	12.1903i	−0.440096	−	0.693481i
$310$	−7.92278	−	16.6553i	−0.449984	−	0.945956i
$311$	−18.3742	+	7.27485i	−1.04190	+	0.412519i	−0.825866	−	0.563866i	$-0.809313\pi$
$311$	−18.3742	+	7.27485i	−1.04190	+	0.412519i	−0.216038	+	0.976385i	$0.569313\pi$
$312$	−6.28809	−	0.395613i	−0.355993	−	0.0223972i
$313$	15.6886	+	0.987044i	0.886773	+	0.0557910i	0.499640	−	0.866233i	$-0.333466\pi$
$313$	15.6886	+	0.987044i	0.886773	+	0.0557910i	0.387133	+	0.922024i	$0.373466\pi$
$314$	−3.18236	+	1.25998i	−0.179591	+	0.0711050i
$315$	0.263410	+	0.553740i	0.0148414	+	0.0311997i
$316$	1.06254	+	1.67430i	0.0597727	+	0.0941868i
$317$	−5.80421	+	6.18085i	−0.325997	+	0.347151i	−0.871000	−	0.491282i	$-0.836528\pi$
$317$	−5.80421	+	6.18085i	−0.325997	+	0.347151i	0.545004	+	0.838434i	$0.316528\pi$
$318$			4.44085i			0.249031i
$319$	−33.1839	−	31.1618i	−1.85794	−	1.74472i
$320$	1.72888	+	1.41809i	0.0966472	+	0.0792737i
$321$	1.54375	−	8.09260i	0.0861635	−	0.451685i
$322$	−0.295961	+	0.538350i	−0.0164932	+	0.0300011i
$323$	34.6349	+	21.9800i	1.92714	+	1.22300i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	29.8782	−	9.98558i	1.65734	−	0.553900i
$326$	3.97404	−	12.2308i	0.220102	−	0.677404i
$327$	7.41418	−	6.13354i	0.410005	−	0.339186i
$328$	6.95506	+	1.32675i	0.384029	+	0.0732574i
$329$	−1.03983	−	2.20976i	−0.0573279	−	0.121828i
$330$	5.39445	−	9.91062i	0.296955	−	0.545561i
$331$	3.54124	+	18.5638i	0.194644	+	1.02036i	0.936729	+	0.350055i	$0.113837\pi$
$331$	3.54124	+	18.5638i	0.194644	+	1.02036i	−0.742085	+	0.670306i	$0.766163\pi$
$332$	11.6631	+	3.78958i	0.640098	+	0.207980i
$333$	−4.82178	−	2.26896i	−0.264232	−	0.124338i
$334$	17.5538	+	6.95003i	0.960500	+	0.380289i
$335$	6.90950	+	1.74323i	0.377506	+	0.0952429i
$336$	−0.265615	−	0.0681984i	−0.0144905	−	0.00372053i
$337$	−5.12979	+	12.9564i	−0.279437	+	0.705778i	0.720487	+	0.693469i	$0.243918\pi$
$337$	−5.12979	+	12.9564i	−0.279437	+	0.705778i	−0.999924	+	0.0123097i	$0.996082\pi$
$338$	−6.63918	−	25.8579i	−0.361124	−	1.40648i
$339$	−6.45326	+	10.1687i	−0.350493	+	0.552289i
$340$	11.2547	−	6.24888i	0.610373	−	0.338893i
$341$	2.61349	−	41.5402i	0.141528	−	2.24953i
$342$	−3.43265	−	6.24397i	−0.185616	−	0.337635i
$343$	3.63171	−	1.18001i	0.196094	−	0.0637148i
$344$	−1.66951	−	0.210909i	−0.0900142	−	0.0113714i
$345$	−1.22542	+	4.85711i	−0.0659746	+	0.261498i
$346$	12.6331	−	11.8632i	0.679158	−	0.637772i
$347$	−8.47306	−	9.02289i	−0.454858	−	0.484374i	0.460133	−	0.887850i	$-0.347802\pi$
$347$	−8.47306	−	9.02289i	−0.454858	−	0.484374i	−0.914990	+	0.403476i	$0.867802\pi$
$348$	−2.24343	+	8.73759i	−0.120261	+	0.468384i
$349$	28.7065	+	20.8565i	1.53663	+	1.11642i	0.952407	+	0.304828i	$0.0985989\pi$
$349$	28.7065	+	20.8565i	1.53663	+	1.11642i	0.584219	+	0.811596i	$0.301401\pi$
$350$	1.35885	−	0.183245i	0.0726338	−	0.00979483i
$351$	5.09723	−	3.70336i	0.272070	−	0.197671i
$352$	1.85763	+	4.69183i	0.0990119	+	0.250076i
$353$	2.54062	+	20.1111i	0.135223	+	1.07040i	0.902986	+	0.429670i	$0.141370\pi$
$353$	2.54062	+	20.1111i	0.135223	+	1.07040i	−0.767763	+	0.640734i	$0.778630\pi$
$354$	2.40190	+	1.32046i	0.127660	+	0.0701814i
$355$	33.5393	−	11.0532i	1.78008	−	0.586641i
$356$	0.938819	−	1.99509i	0.0497573	−	0.105740i
$357$	−0.927969	+	1.27724i	−0.0491133	+	0.0675987i
$358$	0.625035	−	4.94766i	0.0330341	−	0.261492i
$359$	28.2903	−	7.26373i	1.49311	−	0.383365i	0.588110	−	0.808781i	$-0.299872\pi$
$359$	28.2903	−	7.26373i	1.49311	−	0.383365i	0.904998	+	0.425417i	$0.139872\pi$
$360$	−2.23605	+	0.00936915i	−0.117850	+	0.000493797i
$361$	−20.2511	−	24.4793i	−1.06585	−	1.28839i
$362$	−8.40415	−	6.95252i	−0.441713	−	0.365416i
$363$	12.2124	−	7.75024i	0.640986	−	0.406782i
$364$	−0.108489	−	1.72439i	−0.00568638	−	0.0903825i
$365$	0.148307	−	2.52613i	0.00776273	−	0.132224i
$366$	−0.360294	+	0.435521i	−0.0188329	+	0.0227650i
$367$	30.8658	−	5.88797i	1.61118	−	0.307350i	0.698374	−	0.715733i	$-0.253907\pi$
$367$	30.8658	−	5.88797i	1.61118	−	0.307350i	0.912810	+	0.408384i	$0.133907\pi$
$368$	−1.31678	−	1.81239i	−0.0686417	−	0.0944771i
$369$	−6.20466	+	3.41104i	−0.323002	+	0.177572i
$370$	−8.12052	+	8.72041i	−0.422166	+	0.453353i
$371$	−1.20821	+	0.152633i	−0.0627274	+	0.00792431i
$372$	−7.46324	+	3.51194i	−0.386951	+	0.182085i
$373$	11.7395	−	0.738589i	0.607850	−	0.0382427i	0.244117	−	0.969746i	$-0.421502\pi$
$373$	11.7395	−	0.738589i	0.607850	−	0.0382427i	0.363733	+	0.931503i	$0.381502\pi$
$374$	29.0511			1.50220
$375$	10.3427	−	4.24610i	0.534093	−	0.219268i
$376$	8.90560			0.459271
$377$	−56.7249	+	3.56883i	−2.92148	+	0.183804i
$378$	0.248131	−	0.116762i	0.0127625	−	0.00600557i
$379$	−10.4054	+	1.31450i	−0.534487	+	0.0675214i	−0.387944	−	0.921683i	$-0.626815\pi$
$379$	−10.4054	+	1.31450i	−0.534487	+	0.0675214i	−0.146543	+	0.989204i	$0.546815\pi$
$380$	−15.6378	+	3.05104i	−0.802204	+	0.156515i
$381$	0.526504	−	0.289448i	0.0269736	−	0.0148289i
$382$	−7.28369	−	10.0251i	−0.372666	−	0.512931i
$383$	2.51988	−	0.480693i	0.128760	−	0.0245623i	−0.122598	−	0.992456i	$-0.539123\pi$
$383$	2.51988	−	0.480693i	0.128760	−	0.0245623i	0.251358	+	0.967894i	$0.419123\pi$
$384$	0.637424	−	0.770513i	0.0325284	−	0.0393201i
$385$	2.88177	+	1.12703i	0.146869	+	0.0574387i
$386$	1.28539	+	20.4307i	0.0654248	+	1.03990i
$387$	1.42082	−	0.901681i	0.0722244	−	0.0458350i
$388$	−6.13344	−	5.07402i	−0.311378	−	0.257595i
$389$	−15.0125	−	18.1470i	−0.761164	−	0.920090i	0.237519	−	0.971383i	$-0.423666\pi$
$389$	−15.0125	−	18.1470i	−0.761164	−	0.920090i	−0.998684	+	0.0512931i	$0.983666\pi$
$390$	−4.40966	−	13.3805i	−0.223292	−	0.677549i
$391$	−12.4919	+	3.20738i	−0.631743	+	0.162204i
$392$	−0.867907	+	6.87019i	−0.0438359	+	0.346997i
$393$	0.151168	−	0.208065i	0.00762543	−	0.0104955i
$394$	−9.39183	+	19.9586i	−0.473153	+	1.00550i
$395$	−2.59126	+	3.59817i	−0.130380	+	0.181043i
$396$	−4.42201	−	2.43102i	−0.222215	−	0.122164i
$397$	−1.81981	−	14.4053i	−0.0913338	−	0.722981i	−0.969580	−	0.244773i	$-0.921286\pi$
$397$	−1.81981	−	14.4053i	−0.0913338	−	0.722981i	0.878247	−	0.478208i	$-0.158714\pi$
$398$	−6.45533	−	16.3043i	−0.323577	−	0.817261i
$399$	1.58080	−	1.14852i	0.0791392	−	0.0574980i
$400$	−1.50518	+	4.76806i	−0.0752591	+	0.238403i
$401$	−16.4133	−	11.9250i	−0.819641	−	0.595504i	0.0969683	−	0.995287i	$-0.469085\pi$
$401$	−16.4133	−	11.9250i	−0.819641	−	0.595504i	−0.916610	+	0.399783i	$0.869085\pi$
$402$	0.792537	−	3.08673i	0.0395282	−	0.153952i
$403$	−35.5748	−	37.8833i	−1.77211	−	1.88710i
$404$	10.1547	−	9.53589i	0.505215	−	0.474428i
$405$	1.71693	−	1.43253i	0.0853151	−	0.0711830i
$406$	−2.45433	−	0.310054i	−0.121806	−	0.0153877i
$407$	−25.5748	+	8.30975i	−1.26769	+	0.411899i
$408$	−2.77347	−	5.04493i	−0.137307	−	0.249761i
$409$	0.491950	−	7.81932i	0.0243254	−	0.386640i	−0.966962	−	0.254921i	$-0.917950\pi$
$409$	0.491950	−	7.81932i	0.0243254	−	0.386640i	0.991287	−	0.131719i	$-0.0420496\pi$
$410$	3.03184	+	15.5394i	0.149732	+	0.767437i
$411$	−11.0867	+	17.4698i	−0.546866	+	0.861722i
$412$	3.59055	+	13.9843i	0.176893	+	0.688955i
$413$	−0.276700	+	0.698865i	−0.0136155	+	0.0343889i
$414$	2.16985	+	0.557123i	0.106642	+	0.0273811i
$415$	1.83648	+	27.3601i	0.0901491	+	1.34306i
$416$	5.85808	+	2.31938i	0.287216	+	0.113717i
$417$	7.69741	+	3.62213i	0.376944	+	0.177376i
$418$	−34.1960	−	11.1109i	−1.67258	−	0.543454i
$419$	−0.998745	−	5.23560i	−0.0487919	−	0.255776i	0.949531	−	0.313674i	$-0.101560\pi$
$419$	−0.998745	−	5.23560i	−0.0487919	−	0.255776i	−0.998322	+	0.0578984i	$0.981560\pi$
$420$	−0.0794025	−	0.608036i	−0.00387444	−	0.0296691i
$421$	2.53322	+	5.38337i	0.123462	+	0.262369i	0.956998	−	0.290096i	$-0.0936872\pi$
$421$	2.53322	+	5.38337i	0.123462	+	0.262369i	−0.833536	+	0.552465i	$0.813687\pi$
$422$	13.7555	+	2.62399i	0.669605	+	0.127734i
$423$	−6.86188	+	5.67664i	−0.333636	+	0.276008i
$424$	1.37230	−	4.22350i	0.0666447	−	0.205111i
$425$	22.3323	+	18.1619i	1.08328	+	0.880979i
$426$	−4.88023	−	15.0198i	−0.236448	−	0.727712i
$427$	−0.130875	−	0.0830557i	−0.00633348	−	0.00401935i
$428$	−3.96894	+	7.21947i	−0.191846	+	0.348966i
$429$	5.95754	−	31.2305i	0.287633	−	1.50782i
$430$	−0.951038	−	3.64065i	−0.0458631	−	0.175568i
$431$	2.69690	+	2.53256i	0.129905	+	0.121989i	0.746777	−	0.665075i	$-0.231600\pi$
$431$	2.69690	+	2.53256i	0.129905	+	0.121989i	−0.616872	+	0.787064i	$0.711600\pi$
$432$			1.00000i			0.0481125i
$433$	11.3452	−	12.0815i	0.545218	−	0.580598i	−0.396063	−	0.918223i	$-0.629624\pi$
$433$	11.3452	−	12.0815i	0.545218	−	0.580598i	0.941281	+	0.337626i	$0.109624\pi$
$434$	−1.21200	−	1.90981i	−0.0581778	−	0.0916736i
$435$	−20.0017	+	2.61200i	−0.959010	+	0.125236i
$436$	−8.94667	+	3.54224i	−0.428468	+	0.169642i
$437$	15.9309	+	1.00229i	0.762077	+	0.0479458i
$438$	−1.12943	−	0.0710578i	−0.0539663	−	0.00339527i
$439$	15.1910	−	6.01455i	0.725027	−	0.287059i	0.0235225	−	0.999723i	$-0.492512\pi$
$439$	15.1910	−	6.01455i	0.725027	−	0.287059i	0.701505	+	0.712665i	$0.252512\pi$
$440$	−8.19298	+	7.75858i	−0.390585	+	0.369876i
$441$	−3.71049	−	5.84680i	−0.176690	−	0.278419i
$442$	24.8301	−	26.4414i	1.18105	−	1.25769i
$443$			2.06317i			0.0980240i	0.998798	+	0.0490120i	$0.0156073\pi$
$443$			2.06317i			0.0980240i	−0.998798	+	0.0490120i	$0.984393\pi$
$444$	3.88464	+	3.64792i	0.184357	+	0.173122i
$445$	4.92193	+	0.288962i	0.233322	+	0.0136981i
$446$	1.33577	−	7.00236i	0.0632506	−	0.331571i
$447$	6.98019	−	12.6969i	0.330152	−	0.600544i
$448$	0.231541	+	0.146940i	0.0109393	+	0.00694227i
$449$	−1.39685	−	4.29907i	−0.0659215	−	0.202886i	0.912670	−	0.408697i	$-0.134017\pi$
$449$	−1.39685	−	4.29907i	−0.0659215	−	0.202886i	−0.978592	+	0.205811i	$0.934017\pi$
$450$	−1.87952	−	4.63329i	−0.0886012	−	0.218416i
$451$	−11.0410	+	33.9807i	−0.519901	+	1.60009i
$452$	9.27972	−	7.67686i	0.436482	−	0.361089i
$453$	7.18941	+	1.37145i	0.337788	+	0.0644365i
$454$	7.63681	+	16.2291i	0.358413	+	0.761667i
$455$	3.48885	−	1.65962i	0.163560	−	0.0778041i
$456$	1.33515	+	6.99911i	0.0625242	+	0.327763i
$457$	13.3262	+	4.32996i	0.623375	+	0.202547i	0.603638	−	0.797258i	$-0.293717\pi$
$457$	13.3262	+	4.32996i	0.623375	+	0.202547i	0.0197369	+	0.999805i	$0.493717\pi$
$458$	13.6232	+	6.41061i	0.636572	+	0.299548i
$459$	5.35275	+	2.11931i	0.249845	+	0.0989207i
$460$	2.66638	−	4.24071i	0.124320	−	0.197724i
$461$	0.559581	+	0.143676i	0.0260623	+	0.00669166i	0.261699	−	0.965150i	$-0.415717\pi$
$461$	0.559581	+	0.143676i	0.0260623	+	0.00669166i	−0.235636	+	0.971841i	$0.575717\pi$
$462$	0.509419	−	1.28664i	0.0237003	−	0.0598601i
$463$	−8.83174	−	34.3974i	−0.410446	−	1.59858i	−0.752295	−	0.658826i	$-0.771053\pi$
$463$	−8.83174	−	34.3974i	−0.410446	−	1.59858i	0.341849	−	0.939755i	$-0.388947\pi$
$464$	4.83370	−	7.61668i	0.224399	−	0.353596i
$465$	−13.4976	−	12.5691i	−0.625938	−	0.582878i
$466$	−0.230851	+	3.66926i	−0.0106939	+	0.169975i
$467$	14.6830	+	26.7083i	0.679450	+	1.23591i	0.961048	+	0.276382i	$0.0891356\pi$
$467$	14.6830	+	26.7083i	0.679450	+	1.23591i	−0.281598	+	0.959533i	$0.590864\pi$
$468$	−5.99216	+	1.94697i	−0.276988	+	0.0899987i
$469$	0.867040	+	0.109533i	0.0400362	+	0.00505775i
$470$	7.40817	+	18.4843i	0.341714	+	0.852615i
$471$	−2.49505	+	2.34301i	−0.114966	+	0.107960i
$472$	−1.87630	−	1.99806i	−0.0863637	−	0.0919680i
$473$	2.11179	−	8.22487i	0.0971001	−	0.378180i
$474$	1.60428	+	1.16558i	0.0736870	+	0.0535367i
$475$	−19.3411	−	29.9195i	−0.887430	−	1.37280i
$476$	1.27724	−	0.927969i	0.0585422	−	0.0425334i
$477$	1.63479	+	4.12900i	0.0748518	+	0.189054i
$478$	0.968671	+	7.66782i	0.0443060	+	0.350718i
$479$	−6.45357	−	3.54788i	−0.294871	−	0.162107i	0.327451	−	0.944868i	$-0.393810\pi$
$479$	−6.45357	−	3.54788i	−0.294871	−	0.162107i	−0.622322	+	0.782761i	$0.713810\pi$
$480$	2.12950	+	0.682066i	0.0971981	+	0.0311319i
$481$	−14.2956	+	30.3797i	−0.651824	+	1.38520i
$482$	−9.17248	+	12.6248i	−0.417795	+	0.575045i
$483$	−0.0769972	+	0.609496i	−0.00350350	+	0.0277330i
$484$	−14.0097	+	3.59707i	−0.636803	+	0.163503i
$485$	5.42939	−	16.9513i	0.246536	−	0.769718i
$486$	−0.637424	−	0.770513i	−0.0289141	−	0.0349512i
$487$	32.3039	+	26.7241i	1.46383	+	1.21098i	0.931135	+	0.364675i	$0.118820\pi$
$487$	32.3039	+	26.7241i	1.46383	+	1.21098i	0.532693	+	0.846309i	$0.321180\pi$
$488$	0.477244	−	0.302868i	0.0216038	−	0.0137102i
$489$	−0.807503	−	12.8349i	−0.0365166	−	0.580414i
$490$	−14.9816	+	3.91360i	−0.676799	+	0.176798i
$491$	23.5521	−	28.4696i	1.06289	−	1.28482i	0.106003	−	0.994366i	$-0.466195\pi$
$491$	23.5521	−	28.4696i	1.06289	−	1.28482i	0.956890	−	0.290451i	$-0.0938054\pi$
$492$	6.95506	−	1.32675i	0.313558	−	0.0598144i
$493$	−30.5262	−	42.0157i	−1.37483	−	1.89229i
$494$	−39.3403	+	21.6275i	−1.77000	+	0.973067i
$495$	1.36730	−	11.2005i	0.0614554	−	0.503424i
$496$	8.18321	−	1.03378i	0.367437	−	0.0464181i
$497$	3.91868	−	1.84399i	0.175777	−	0.0827143i
$498$	12.2391	−	0.770022i	0.548449	−	0.0345055i
$499$	−10.4715			−0.468769			−0.234384	−	0.972144i	$-0.575307\pi$
$499$	−10.4715			−0.468769			−0.234384	+	0.972144i	$0.575307\pi$
$500$	−11.1486	+	0.842220i	−0.498579	+	0.0376652i
$501$	18.8796			0.843476
$502$	−3.65612	+	0.230023i	−0.163180	+	0.0102664i
$503$	−8.42857	+	3.96619i	−0.375812	+	0.176843i	−0.604403	−	0.796679i	$-0.706588\pi$
$503$	−8.42857	+	3.96619i	−0.375812	+	0.176843i	0.228591	+	0.973523i	$0.426588\pi$
$504$	−0.272068	+	0.0343702i	−0.0121189	+	0.00153097i
$505$	28.2397	+	13.1444i	1.25665	+	0.584916i
$506$	9.90634	−	5.44606i	0.440390	−	0.242107i
$507$	−15.6919	−	21.5980i	−0.696901	−	0.959202i
$508$	−0.590179	+	0.112583i	−0.0261850	+	0.00499505i
$509$	−14.2169	+	17.1853i	−0.630155	+	0.761726i	−0.984879	−	0.173245i	$-0.944575\pi$
$509$	−14.2169	+	17.1853i	−0.630155	+	0.761726i	0.354724	+	0.934971i	$0.384575\pi$
$510$	8.16400	−	9.95320i	0.361508	−	0.440735i
$511$	−0.0194862	−	0.309725i	−0.000862020	−	0.0137014i
$512$	−0.844328	+	0.535827i	−0.0373144	+	0.0236804i
$513$	−5.49015	−	4.54185i	−0.242396	−	0.200528i
$514$	−1.84558	−	2.23092i	−0.0814049	−	0.0984016i
$515$	−26.0386	+	19.0853i	−1.14740	+	0.841000i
$516$	−1.62992	+	0.418491i	−0.0717530	+	0.0184231i
$517$	−5.63240	+	44.5850i	−0.247713	+	1.96085i
$518$	−0.858966	+	1.18227i	−0.0377408	+	0.0519458i
$519$	7.37878	−	15.6807i	0.323893	−	0.688307i
$520$	0.0590305	+	14.0883i	0.00258866	+	0.617812i
$521$	−15.3550	−	8.44151i	−0.672717	−	0.369829i	0.108494	−	0.994097i	$-0.465397\pi$
$521$	−15.3550	−	8.44151i	−0.672717	−	0.369829i	−0.781210	+	0.624268i	$0.785397\pi$
$522$	1.13063	+	8.94987i	0.0494864	+	0.391725i
$523$	2.42729	+	6.13062i	0.106138	+	0.268073i	0.973133	−	0.230243i	$-0.0739519\pi$
$523$	2.42729	+	6.13062i	0.106138	+	0.268073i	−0.866995	+	0.498316i	$0.833952\pi$
$524$	−0.208065	+	0.151168i	−0.00908937	+	0.00660381i
$525$	1.19597	−	0.670604i	0.0521965	−	0.0292675i
$526$	−7.23910	−	5.25952i	−0.315640	−	0.229326i
$527$	11.8092	−	45.9936i	0.514415	−	2.00351i
$528$	3.45436	+	3.67852i	0.150332	+	0.160087i
$529$	13.1078	−	12.3091i	0.569906	−	0.535178i
$530$	9.90776	−	0.665032i	0.430365	−	0.0288872i
$531$	2.71932	+	0.343530i	0.118009	+	0.0149079i
$532$	−1.85835	+	0.603813i	−0.0805695	+	0.0261786i
$533$	21.4914	+	39.0927i	0.930894	+	1.69329i
$534$	0.138449	−	2.20059i	0.00599130	−	0.0952289i
$535$	−18.2861	−	2.23228i	−0.790579	−	0.0965097i
$536$	−1.70760	+	2.69075i	−0.0737571	+	0.116223i
$537$	−1.24021	−	4.83031i	−0.0535191	−	0.208443i
$538$	11.5260	−	29.1113i	0.496920	−	1.25508i
$539$	−33.8461	−	8.69019i	−1.45785	−	0.374313i
$540$	−2.07558	+	0.831856i	−0.0893186	+	0.0357974i
$541$	19.0711	+	7.55077i	0.819929	+	0.324633i	0.740372	−	0.672197i	$-0.234649\pi$
$541$	19.0711	+	7.55077i	0.819929	+	0.324633i	0.0795573	+	0.996830i	$0.474649\pi$
$542$	26.0566	+	12.2613i	1.11923	+	0.526669i
$543$	−10.3734	−	3.37051i	−0.445164	−	0.144643i
$544$	1.07876	+	5.65506i	0.0462515	+	0.242459i
$545$	−14.7945	−	15.6229i	−0.633728	−	0.669210i
$546$	−0.735660	−	1.56336i	−0.0314834	−	0.0669055i
$547$	7.66839	+	1.46282i	0.327877	+	0.0625458i	0.348692	−	0.937238i	$-0.386626\pi$
$547$	7.66839	+	1.46282i	0.327877	+	0.0625458i	−0.0208149	+	0.999783i	$0.506626\pi$
$548$	15.9425	−	13.1888i	0.681031	−	0.563398i
$549$	−0.174667	+	0.537570i	−0.00745461	+	0.0229429i
$550$	−22.9189	−	10.5511i	−0.977265	−	0.449902i
$551$	19.8628	+	61.1316i	0.846186	+	2.60429i
$552$	−1.89149	−	1.20038i	−0.0805072	−	0.0510914i
$553$	−0.261977	+	0.476534i	−0.0111404	+	0.0202643i
$554$	1.53351	−	8.03893i	0.0651525	−	0.341541i
$555$	−4.34007	+	11.0974i	−0.184226	+	0.471058i
$556$	−6.20137	−	5.82348i	−0.262997	−	0.246970i
$557$			1.69797i			0.0719454i	0.999353	+	0.0359727i	$0.0114529\pi$
$557$			1.69797i			0.0719454i	−0.999353	+	0.0359727i	$0.988547\pi$
$558$	−5.64632	+	6.01272i	−0.239028	+	0.254539i
$559$	−5.68106	−	8.95192i	−0.240283	−	0.378626i
$560$	−0.112377	+	0.602813i	−0.00474880	+	0.0254735i
$561$	27.0110	−	10.6944i	1.14041	−	0.451519i
$562$	−1.07672	−	0.0677415i	−0.0454187	−	0.00285750i
$563$	−20.4500	−	1.28660i	−0.861863	−	0.0542238i	−0.374296	−	0.927309i	$-0.622116\pi$
$563$	−20.4500	−	1.28660i	−0.861863	−	0.0542238i	−0.487567	+	0.873086i	$0.662116\pi$
$564$	8.28022	−	3.27837i	0.348660	−	0.138044i
$565$	23.6533	+	12.8747i	0.995101	+	0.541644i
$566$	3.05247	+	4.80993i	0.128305	+	0.202176i
$567$	0.187724	−	0.199905i	0.00788366	−	0.00839524i
$568$			15.7928i			0.662650i
$569$	15.7226	+	14.7645i	0.659126	+	0.618961i	0.940158	−	0.340737i	$-0.110677\pi$
$569$	15.7226	+	14.7645i	0.659126	+	0.618961i	−0.281032	+	0.959698i	$0.590677\pi$
$570$	−13.4165	+	8.59346i	−0.561957	+	0.359940i
$571$	1.68499	−	8.83303i	0.0705147	−	0.369651i	−0.929485	−	0.368860i	$-0.879748\pi$
$571$	1.68499	−	8.83303i	0.0705147	−	0.369651i	1.00000		0.000791032i	$-0.000251793\pi$
$572$	−15.3167	+	27.8610i	−0.640424	+	1.16493i
$573$	−10.4627	−	6.63984i	−0.437086	−	0.277383i
$574$	0.600013	+	1.84665i	0.0250440	+	0.0770776i
$575$	11.0200	+	2.00661i	0.459564	+	0.0836815i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	27.5646	−	22.8034i	1.14753	−	0.949317i	0.148313	−	0.988941i	$-0.452616\pi$
$577$	27.5646	−	22.8034i	1.14753	−	0.949317i	0.999215	+	0.0396233i	$0.0126158\pi$
$578$	15.8575	+	3.02498i	0.659585	+	0.125823i
$579$	8.71618	+	18.5228i	0.362232	+	0.769783i
$580$	19.8299	+	3.69672i	0.823394	+	0.153498i
$581$	0.630161	+	3.30342i	0.0261435	+	0.137049i
$582$	−7.57060	−	2.45984i	−0.313812	−	0.101964i
$583$	20.2766	+	9.54146i	0.839773	+	0.395167i
$584$	1.05219	+	0.416593i	0.0435401	+	0.0172388i
$585$	−9.02569	−	10.8176i	−0.373166	−	0.447252i
$586$	5.23623	+	1.34444i	0.216307	+	0.0555381i
$587$	−15.4289	+	38.9689i	−0.636818	+	1.60842i	0.148208	+	0.988956i	$0.452649\pi$
$587$	−15.4289	+	38.9689i	−0.636818	+	1.60842i	−0.785026	+	0.619463i	$0.787351\pi$
$588$	1.72213	+	6.70724i	0.0710193	+	0.276602i
$589$	−31.4913	+	49.6224i	−1.29758	+	2.04465i
$590$	2.58631	−	5.55650i	0.106477	−	0.228757i
$591$	−1.38503	+	22.0144i	−0.0569726	+	0.905553i
$592$	−2.56724	−	4.66979i	−0.105513	−	0.191927i
$593$	18.7190	−	6.08216i	0.768696	−	0.249765i	0.101689	−	0.994816i	$-0.467575\pi$
$593$	18.7190	−	6.08216i	0.768696	−	0.249765i	0.667007	+	0.745052i	$0.267575\pi$
$594$	−5.00640	−	0.632456i	−0.205415	−	0.0259500i
$595$	2.98855	+	1.87907i	0.122519	+	0.0770344i
$596$	−10.5621	+	9.91849i	−0.432641	+	0.406277i
$597$	−12.0040	−	12.7830i	−0.491292	−	0.523173i
$598$	3.51017	−	13.6712i	0.143541	−	0.559057i
$599$	4.37796	+	3.18078i	0.178879	+	0.129963i	0.673622	−	0.739076i	$-0.264738\pi$
$599$	4.37796	+	3.18078i	0.178879	+	0.129963i	−0.494743	+	0.869039i	$0.664738\pi$
$600$	0.355759	+	4.98733i	0.0145238	+	0.203607i
$601$	−29.9508	+	21.7605i	−1.22172	+	0.887630i	−0.996242	−	0.0866189i	$-0.972394\pi$
$601$	−29.9508	+	21.7605i	−1.22172	+	0.887630i	−0.225476	+	0.974249i	$0.572394\pi$
$602$	−0.169879	−	0.429065i	−0.00692374	−	0.0174874i
$603$	−0.399418	−	3.16172i	−0.0162656	−	0.128755i
$604$	−6.41373	−	3.52598i	−0.260971	−	0.143470i
$605$	−19.1200	−	26.0859i	−0.777339	−	1.06054i
$606$	5.93120	−	12.6044i	0.240939	−	0.512020i
$607$	12.3973	−	17.0635i	0.503192	−	0.692584i	−0.479561	−	0.877509i	$-0.659204\pi$
$607$	12.3973	−	17.0635i	0.503192	−	0.692584i	0.982753	+	0.184924i	$0.0592040\pi$
$608$	0.893039	−	7.06913i	0.0362175	−	0.286691i
$609$	−2.39611	+	0.615218i	−0.0970955	+	0.0249299i
$610$	1.02562	+	0.738613i	0.0415263	+	0.0299056i
$611$	35.7658	+	43.2335i	1.44693	+	1.74904i
$612$	−4.43587	−	3.66967i	−0.179309	−	0.148338i
$613$	6.54466	−	4.15337i	0.264336	−	0.167753i	−0.397053	−	0.917796i	$-0.629967\pi$
$613$	6.54466	−	4.15337i	0.264336	−	0.167753i	0.661389	+	0.750043i	$0.269967\pi$
$614$	−0.773575	−	12.2956i	−0.0312189	−	0.496211i
$615$	8.53937	+	13.3321i	0.344341	+	0.537602i
$616$	−0.882081	+	1.06625i	−0.0355400	+	0.0429605i
$617$	20.4494	−	3.90092i	0.823260	−	0.157045i	0.241495	−	0.970402i	$-0.422362\pi$
$617$	20.4494	−	3.90092i	0.823260	−	0.157045i	0.581765	+	0.813357i	$0.302362\pi$
$618$	8.48635	+	11.6805i	0.341371	+	0.469857i
$619$	13.0248	−	7.16043i	0.523510	−	0.287802i	−0.198005	−	0.980201i	$-0.563446\pi$
$619$	13.0248	−	7.16043i	0.523510	−	0.287802i	0.721515	+	0.692399i	$0.243446\pi$
$620$	8.95294	+	16.1249i	0.359559	+	0.647593i
$621$	2.22257	−	0.280775i	0.0891885	−	0.0112671i
$622$	17.8811	−	8.41422i	0.716968	−	0.337379i
$623$	0.603470	−	0.0379671i	0.0241775	−	0.00152112i
$624$	6.30053			0.252223
$625$	−11.0221	−	22.4391i	−0.440884	−	0.897564i
$626$	−15.7196			−0.628283
$627$	−35.8848	+	2.25768i	−1.43310	+	0.0901631i
$628$	3.09696	−	1.45732i	0.123582	−	0.0581534i
$629$	−30.4370	+	3.84509i	−1.21360	+	0.153314i
$630$	−0.297659	−	0.536107i	−0.0118590	−	0.0213590i
$631$	18.9314	−	10.4076i	0.753646	−	0.414320i	−0.0581154	−	0.998310i	$-0.518509\pi$
$631$	18.9314	−	10.4076i	0.753646	−	0.414320i	0.811761	+	0.583990i	$0.198509\pi$
$632$	−1.16558	−	1.60428i	−0.0463642	−	0.0638148i
$633$	13.7555	−	2.62399i	0.546730	−	0.104294i
$634$	5.40466	−	6.53311i	0.214646	−	0.259463i
$635$	−0.724618	−	1.13131i	−0.0287556	−	0.0448946i
$636$	−0.278843	−	4.43209i	−0.0110569	−	0.175744i
$637$	−36.8379	+	23.3781i	−1.45957	+	0.926272i
$638$	35.0751	+	29.0167i	1.38864	+	1.14878i
$639$	−10.0667	−	12.1685i	−0.398232	−	0.481380i
$640$	−1.81451	−	1.30674i	−0.0717247	−	0.0516533i
$641$	−17.0956	+	4.38941i	−0.675237	+	0.173371i	−0.570711	−	0.821151i	$-0.693332\pi$
$641$	−17.0956	+	4.38941i	−0.675237	+	0.173371i	−0.104526	+	0.994522i	$0.533332\pi$
$642$	−1.03256	+	8.17356i	−0.0407519	+	0.322585i
$643$	6.94186	−	9.55465i	0.273760	−	0.376799i	−0.649894	−	0.760025i	$-0.725187\pi$
$643$	6.94186	−	9.55465i	0.273760	−	0.376799i	0.923655	+	0.383226i	$0.125187\pi$
$644$	0.261573	−	0.555872i	0.0103074	−	0.0219044i
$645$	−2.22446	−	3.03489i	−0.0875882	−	0.119499i
$646$	−35.9467	−	19.7619i	−1.41430	−	0.777521i
$647$	4.65876	+	36.8779i	0.183155	+	1.44982i	0.768923	+	0.639341i	$0.220793\pi$
$647$	4.65876	+	36.8779i	0.183155	+	1.44982i	−0.585768	+	0.810479i	$0.699207\pi$
$648$	0.368125	+	0.929776i	0.0144613	+	0.0365251i
$649$	11.1898	−	8.12983i	0.439236	−	0.319124i
$650$	−29.1922	+	11.8419i	−1.14501	+	0.464479i
$651$	−1.82993	−	1.32953i	−0.0717208	−	0.0521082i
$652$	−3.19822	+	12.4562i	−0.125252	+	0.487824i
$653$	8.41966	+	8.96603i	0.329487	+	0.350868i	0.872287	−	0.488994i	$-0.162636\pi$
$653$	8.41966	+	8.96603i	0.329487	+	0.350868i	−0.542800	+	0.839862i	$0.682636\pi$
$654$	−7.01442	+	6.58698i	−0.274285	+	0.257571i
$655$	−0.486841	−	0.306105i	−0.0190225	−	0.0119605i
$656$	−7.02464	−	0.887418i	−0.274266	−	0.0346479i
$657$	−1.07628	+	0.349703i	−0.0419896	+	0.0136432i
$658$	1.17653	+	2.14011i	0.0458660	+	0.0834300i
$659$	0.133359	−	2.11968i	0.00519494	−	0.0825711i	−0.994575	−	0.104022i	$-0.966829\pi$
$659$	0.133359	−	2.11968i	0.00519494	−	0.0825711i	0.999770	+	0.0214512i	$0.00682865\pi$
$660$	−4.76152	+	10.2298i	−0.185342	+	0.398194i
$661$	−4.88474	+	7.69711i	−0.189994	+	0.299383i	−0.925950	−	0.377647i	$-0.876733\pi$
$661$	−4.88474	+	7.69711i	−0.189994	+	0.299383i	0.735955	+	0.677030i	$0.236733\pi$
$662$	−4.69989	−	18.3048i	−0.182666	−	0.711438i
$663$	13.3527	−	33.7252i	0.518577	−	1.30978i
$664$	−11.8781	−	3.04977i	−0.460959	−	0.118354i
$665$	−2.79914	−	3.35485i	−0.108546	−	0.130096i
$666$	4.95473	+	1.96172i	0.191992	+	0.0760150i
$667$	−18.2858	−	8.60463i	−0.708028	−	0.333173i
$668$	−17.9555	−	5.83410i	−0.694720	−	0.225728i
$669$	−1.33577	−	7.00236i	−0.0516439	−	0.270727i
$670$	−7.00532	−	1.30594i	−0.270639	−	0.0504529i
$671$	1.21444	+	2.58083i	0.0468831	+	0.0996317i
$672$	0.269373	+	0.0513857i	0.0103913	+	0.00198225i
$673$	−9.66284	+	7.99380i	−0.372475	+	0.308138i	−0.804762	−	0.593598i	$-0.797707\pi$
$673$	−9.66284	+	7.99380i	−0.372475	+	0.308138i	0.432287	+	0.901736i	$0.357707\pi$
$674$	4.30613	−	13.2529i	0.165866	−	0.510483i
$675$	−3.45316	−	3.61603i	−0.132912	−	0.139181i
$676$	8.24971	+	25.3900i	0.317297	+	0.976539i
$677$	−22.7947	−	14.4659i	−0.876071	−	0.555972i	0.0200412	−	0.999799i	$-0.493620\pi$
$677$	−22.7947	−	14.4659i	−0.876071	−	0.555972i	−0.896112	+	0.443828i	$0.853620\pi$
$678$	5.80203	−	10.5539i	0.222826	−	0.405318i
$679$	0.409040	−	2.14426i	0.0156975	−	0.0822893i
$680$	−10.8401	+	6.94324i	−0.415700	+	0.266261i
$681$	13.0748	+	12.2781i	0.501029	+	0.470498i
$682$			41.6223i			1.59380i
$683$	22.1413	−	23.5781i	0.847214	−	0.902192i	−0.149025	−	0.988833i	$-0.547614\pi$
$683$	22.1413	−	23.5781i	0.847214	−	0.902192i	0.996240	+	0.0866416i	$0.0276135\pi$
$684$	3.81794	+	6.01611i	0.145982	+	0.230032i
$685$	40.6362	+	22.1187i	1.55263	+	0.845114i
$686$	−3.55045	+	1.40572i	−0.135557	+	0.0536707i
$687$	15.0265	+	0.945386i	0.573296	+	0.0360687i
$688$	1.67946	+	0.105663i	0.0640289	+	0.00402836i
$689$	26.0149	−	10.3000i	0.991088	−	0.392399i
$690$	0.918026	−	4.92447i	0.0349486	−	0.187471i
$691$	5.33211	+	8.40206i	0.202843	+	0.319630i	0.930487	−	0.366326i	$-0.119384\pi$
$691$	5.33211	+	8.40206i	0.202843	+	0.319630i	−0.727644	+	0.685955i	$0.759384\pi$
$692$	−11.8632	+	12.6331i	−0.450973	+	0.480237i
$693$		−	1.38382i		−	0.0525670i
$694$	9.02289	+	8.47306i	0.342504	+	0.321633i
$695$	6.92842	−	17.7157i	0.262810	−	0.671995i
$696$	1.69037	−	8.86122i	0.0640732	−	0.335884i
$697$	−19.6375	+	35.7205i	−0.743823	+	1.35301i
$698$	−29.9595	−	19.0129i	−1.13398	−	0.719648i
$699$	1.13611	+	3.49658i	0.0429715	+	0.132253i
$700$	−1.34467	+	0.268206i	−0.0508236	+	0.0101372i
$701$	0.106902	−	0.329009i	0.00403761	−	0.0124265i	−0.949017	−	0.315224i	$-0.897920\pi$
$701$	0.106902	−	0.329009i	0.00403761	−	0.0124265i	0.953055	+	0.302797i	$0.0979205\pi$
$702$	−4.85464	+	4.01611i	−0.183227	+	0.151578i
$703$	37.2979	+	7.11495i	1.40672	+	0.268346i
$704$	−2.14857	−	4.56593i	−0.0809771	−	0.172085i
$705$	13.6925	+	14.4591i	0.515688	+	0.544561i
$706$	−3.79839	−	19.9119i	−0.142954	−	0.749393i
$707$	3.63312	+	1.18047i	0.136638	+	0.0443963i
$708$	−2.48007	−	1.16703i	−0.0932068	−	0.0438598i
$709$	−39.5298	−	15.6510i	−1.48457	−	0.587784i	−0.520603	−	0.853799i	$-0.674293\pi$
$709$	−39.5298	−	15.6510i	−1.48457	−	0.587784i	−0.963969	+	0.266015i	$0.914293\pi$
$710$	−32.7791	+	13.1373i	−1.23018	+	0.493034i
$711$	1.92070	+	0.493152i	0.0720318	+	0.0184946i
$712$	−0.811694	+	2.05010i	−0.0304195	+	0.0768309i
$713$	−4.59529	−	17.8975i	−0.172095	−	0.670266i
$714$	0.845939	−	1.33299i	0.0316585	−	0.0498858i
$715$	−70.5690	−	8.61469i	−2.63913	−	0.322171i
$716$	−0.313135	+	4.97714i	−0.0117024	+	0.186005i
$717$	3.72336	+	6.77277i	0.139051	+	0.252934i
$718$	−27.7784	+	9.02576i	−1.03668	+	0.336838i
$719$	−10.7502	−	1.35807i	−0.400917	−	0.0506475i	−0.0777101	−	0.996976i	$-0.524761\pi$
$719$	−10.7502	−	1.35807i	−0.400917	−	0.0506475i	−0.323207	+	0.946328i	$0.604761\pi$
$720$	2.23105	−	0.149753i	0.0831462	−	0.00558098i
$721$	−2.88620	+	2.71033i	−0.107488	+	0.100938i
$722$	21.7482	+	23.1595i	0.809384	+	0.861906i
$723$	−3.88084	+	15.1149i	−0.144330	+	0.562129i
$724$	8.82412	+	6.41110i	0.327946	+	0.238267i
$725$	8.82282	+	44.2337i	0.327671	+	1.64280i
$726$	−11.7017	+	8.50178i	−0.434291	+	0.315531i
$727$	6.53342	+	16.5015i	0.242311	+	0.612008i	0.999134	−	0.0416121i	$-0.0132494\pi$
$727$	6.53342	+	16.5015i	0.242311	+	0.612008i	−0.756823	+	0.653620i	$0.773249\pi$
$728$	0.216550	+	1.71417i	0.00802589	+	0.0635315i
$729$	−0.876307	−	0.481754i	−0.0324558	−	0.0178427i
$730$	0.0106027	+	2.53046i	0.000392425	+	0.0936564i
$731$	4.12488	−	8.76582i	0.152564	−	0.324216i
$732$	0.332237	−	0.457285i	0.0122798	−	0.0169017i
$733$	−3.71717	+	29.4244i	−0.137297	+	1.08682i	0.761411	+	0.648269i	$0.224507\pi$
$733$	−3.71717	+	29.4244i	−0.137297	+	1.08682i	−0.898708	+	0.438547i	$0.855493\pi$
$734$	−30.4352	+	7.81444i	−1.12338	+	0.288436i
$735$	−12.4888	+	9.15386i	−0.460657	+	0.337645i
$736$	1.42798	+	1.72613i	0.0526359	+	0.0636259i
$737$	−12.3910	−	10.2507i	−0.456428	−	0.377590i
$738$	5.97824	−	3.79391i	0.220062	−	0.139656i
$739$	−1.14354	−	18.1761i	−0.0420660	−	0.668620i	−0.961402	−	0.275147i	$-0.911274\pi$
$739$	−1.14354	−	18.1761i	−0.0420660	−	0.668620i	0.919336	−	0.393473i	$-0.128726\pi$
$740$	7.55694	−	9.21309i	0.277799	−	0.338680i
$741$	−28.6160	+	34.5909i	−1.05124	+	1.27073i
$742$	1.19625	−	0.228196i	0.0439156	−	0.00837735i
$743$	12.8990	+	17.7540i	0.473219	+	0.651330i	0.977184	−	0.212394i	$-0.0681259\pi$
$743$	12.8990	+	17.7540i	0.473219	+	0.651330i	−0.503965	+	0.863724i	$0.668126\pi$
$744$	7.22800	−	3.97363i	0.264991	−	0.145680i
$745$	−29.3728	−	13.6717i	−1.07613	−	0.500894i
$746$	−11.6700	+	1.47426i	−0.427269	+	0.0539766i
$747$	11.0962	−	5.22148i	0.405989	−	0.191044i
$748$	−28.9938	+	1.82413i	−1.06012	+	0.0666970i
$749$	−2.25925			−0.0825514
$750$	−10.0556	+	4.88714i	−0.367180	+	0.178453i
$751$	16.9646			0.619048			0.309524	−	0.950892i	$-0.399830\pi$
$751$	16.9646			0.619048			0.309524	+	0.950892i	$0.399830\pi$
$752$	−8.88803	+	0.559187i	−0.324113	+	0.0203915i
$753$	−3.31469	+	1.55978i	−0.120794	+	0.0568414i
$754$	56.3889	−	7.12357i	2.05356	−	0.259425i
$755$	1.98314	−	16.2453i	0.0721739	−	0.591227i
$756$	−0.240310	+	0.132112i	−0.00873999	+	0.00480485i
$757$	16.4618	+	22.6578i	0.598316	+	0.823511i	0.995553	−	0.0942052i	$-0.0300310\pi$
$757$	16.4618	+	22.6578i	0.598316	+	0.823511i	−0.397237	+	0.917716i	$0.630031\pi$
$758$	10.3023	−	1.96527i	0.374196	−	0.0713817i
$759$	7.20585	−	8.71038i	0.261556	−	0.316167i
$760$	15.4154	−	4.02693i	0.559176	−	0.146072i
$761$	−2.98304	−	47.4141i	−0.108135	−	1.71876i	−0.561536	−	0.827452i	$-0.689789\pi$
$761$	−2.98304	−	47.4141i	−0.108135	−	1.71876i	0.453401	−	0.891307i	$-0.350211\pi$
$762$	−0.507290	+	0.321936i	−0.0183772	+	0.0116625i
$763$	−2.03319	−	1.68200i	−0.0736066	−	0.0608926i
$764$	7.89880	+	9.54801i	0.285769	+	0.345435i
$765$	3.92668	−	12.2596i	0.141969	−	0.443248i
$766$	−2.48473	+	0.637970i	−0.0897769	+	0.0230508i
$767$	2.16442	−	17.1332i	0.0781527	−	0.618643i
$768$	−0.587785	+	0.809017i	−0.0212099	+	0.0291929i
$769$	0.297251	−	0.631690i	0.0107191	−	0.0227793i	−0.899396	−	0.437135i	$-0.855993\pi$
$769$	0.297251	−	0.631690i	0.0107191	−	0.0227793i	0.910115	+	0.414356i	$0.135993\pi$
$770$	−2.94685	−	0.943858i	−0.106197	−	0.0340143i
$771$	−2.53723	−	1.39485i	−0.0913761	−	0.0502344i
$772$	−2.56571	−	20.3097i	−0.0923420	−	0.730962i
$773$	−4.00419	−	10.1134i	−0.144021	−	0.363755i	0.839804	−	0.542890i	$-0.182670\pi$
$773$	−4.00419	−	10.1134i	−0.144021	−	0.363755i	−0.983824	+	0.179135i	$0.942670\pi$
$774$	−1.36140	+	0.989115i	−0.0489345	+	0.0355530i
$775$	−26.0210	+	31.9961i	−0.934701	+	1.14933i
$776$	6.43994	+	4.67889i	0.231180	+	0.167962i
$777$	−0.363426	+	1.41545i	−0.0130378	+	0.0507790i
$778$	16.1223	+	17.1686i	0.578014	+	0.615522i
$779$	36.7769	−	34.5358i	1.31767	−	1.23737i
$780$	5.24113	+	13.0772i	0.187662	+	0.468240i
$781$	−79.0650	−	9.98823i	−2.82917	−	0.357407i
$782$	12.2659	−	3.98542i	0.438626	−	0.142518i
$783$	4.34590	+	7.90517i	0.155310	+	0.282508i
$784$	0.434812	−	6.91113i	0.0155290	−	0.246826i
$785$	5.60100	+	5.21570i	0.199908	+	0.186156i
$786$	−0.137805	+	0.217147i	−0.00491535	+	0.00774536i
$787$	−3.13073	−	12.1934i	−0.111598	−	0.434647i	0.888088	−	0.459673i	$-0.152033\pi$
$787$	−3.13073	−	12.1934i	−0.111598	−	0.434647i	−0.999687	+	0.0250255i	$0.992033\pi$
$788$	8.12008	−	20.5090i	0.289266	−	0.730602i
$789$	−8.66690	−	2.22528i	−0.308550	−	0.0792222i
$790$	2.36021	−	3.75377i	0.0839726	−	0.133553i
$791$	3.07079	+	1.21581i	0.109185	+	0.0432292i
$792$	4.56593	+	2.14857i	0.162243	+	0.0763459i
$793$	3.38698	+	1.10050i	0.120275	+	0.0390797i
$794$	2.72074	+	14.2626i	0.0965554	+	0.506161i
$795$	8.96718	−	4.26562i	0.318033	−	0.151286i
$796$	7.46635	+	15.8668i	0.264638	+	0.562384i
$797$	37.7197	+	7.19541i	1.33610	+	0.254875i	0.805423	−	0.592700i	$-0.201938\pi$
$797$	37.7197	+	7.19541i	1.33610	+	0.254875i	0.530676	+	0.847575i	$0.321938\pi$
$798$	−1.50557	+	1.24551i	−0.0532965	+	0.0440907i
$799$	−15.8433	+	48.7605i	−0.560494	+	1.72502i
$800$	1.20282	−	4.85317i	0.0425262	−	0.171585i
$801$	−0.681365	−	2.09703i	−0.0240748	−	0.0740947i
$802$	17.1297	+	10.8708i	0.604871	+	0.383862i
$803$	−2.75110	+	5.00424i	−0.0970843	+	0.176596i
$804$	−0.597156	+	3.13040i	−0.0210601	+	0.110401i
$805$	1.37134	+	0.0805105i	0.0483336	+	0.00283762i
$806$	37.8833	+	35.5748i	1.33438	+	1.25307i
$807$		−	31.3100i		−	1.10216i
$808$	−9.53589	+	10.1547i	−0.335472	+	0.357241i
$809$	−3.29054	−	5.18506i	−0.115689	−	0.182297i	0.781549	−	0.623844i	$-0.214430\pi$
$809$	−3.29054	−	5.18506i	−0.115689	−	0.182297i	−0.897238	+	0.441547i	$0.854430\pi$
$810$	−1.62360	+	1.53751i	−0.0570473	+	0.0540226i
$811$	4.93811	−	1.95513i	0.173400	−	0.0686541i	−0.279820	−	0.960052i	$-0.590275\pi$
$811$	4.93811	−	1.95513i	0.173400	−	0.0686541i	0.453221	+	0.891398i	$0.350275\pi$
$812$	2.46895	+	0.155333i	0.0866433	+	0.00545113i
$813$	28.7405	+	1.80820i	1.00797	+	0.0634164i
$814$	25.0025	−	9.89920i	0.876338	−	0.346967i
$815$	−28.5143	+	3.72365i	−0.998814	+	0.130434i
$816$	3.08477	+	4.86082i	0.107989	+	0.170163i
$817$	−8.20797	+	8.74060i	−0.287161	+	0.305795i
$818$			7.83478i			0.273937i
$819$	−1.25951	−	1.18276i	−0.0440108	−	0.0413289i
$820$	−4.00158	−	15.3184i	−0.139741	−	0.534941i
$821$	−9.67247	+	50.7049i	−0.337572	+	1.76961i	0.257837	+	0.966189i	$0.416990\pi$
$821$	−9.67247	+	50.7049i	−0.337572	+	1.76961i	−0.595408	+	0.803423i	$0.703010\pi$
$822$	9.96786	−	18.1315i	0.347669	−	0.632408i
$823$	−15.3177	−	9.72091i	−0.533942	−	0.338850i	0.241365	−	0.970434i	$-0.422405\pi$
$823$	−15.3177	−	9.72091i	−0.533942	−	0.338850i	−0.775307	+	0.631585i	$0.782405\pi$
$824$	−4.46154	−	13.7312i	−0.155425	−	0.478349i
$825$	−25.1936	−	1.37319i	−0.877128	−	0.0478085i
$826$	0.232272	−	0.714860i	0.00808178	−	0.0248732i
$827$	9.73055	−	8.04981i	0.338364	−	0.279919i	−0.452686	−	0.891670i	$-0.649534\pi$
$827$	9.73055	−	8.04981i	0.338364	−	0.279919i	0.791051	+	0.611750i	$0.209534\pi$
$828$	−2.20055	−	0.419778i	−0.0764744	−	0.0145883i
$829$	12.3064	+	26.1524i	0.427418	+	0.908309i	0.996304	+	0.0858932i	$0.0273744\pi$
$829$	12.3064	+	26.1524i	0.427418	+	0.908309i	−0.568886	+	0.822416i	$0.692626\pi$
$830$	−3.55081	−	27.1908i	−0.123250	−	0.943807i
$831$	−1.53351	−	8.03893i	−0.0531968	−	0.278867i
$832$	−5.99216	−	1.94697i	−0.207741	−	0.0674990i
$833$	−36.0721	−	16.9742i	−1.24982	−	0.588123i
$834$	−7.90966	−	3.13165i	−0.273889	−	0.108440i
$835$	−2.82728	−	42.1212i	−0.0978419	−	1.45766i
$836$	34.8261	+	8.94183i	1.20449	+	0.309260i
$837$	−3.03638	+	7.66903i	−0.104953	+	0.265081i
$838$	1.32552	+	5.16256i	0.0457893	+	0.178338i
$839$	10.0951	−	15.9073i	0.348520	−	0.549180i	−0.624170	−	0.781289i	$-0.714563\pi$
$839$	10.0951	−	15.9073i	0.348520	−	0.549180i	0.972690	+	0.232109i	$0.0745627\pi$
$840$	0.117425	+	0.601850i	0.00405154	+	0.0207658i
$841$	3.28887	−	52.2751i	0.113409	−	1.80259i
$842$	−2.86625	−	5.21368i	−0.0987774	−	0.179675i
$843$	−1.02605	+	0.333383i	−0.0353389	+	0.0114823i
$844$	−13.8931	−	1.75510i	−0.478219	−	0.0604132i
$845$	−45.8363	+	38.2437i	−1.57682	+	1.31562i
$846$	6.49190	−	6.09630i	0.223196	−	0.209595i
$847$	−2.71525	−	2.89145i	−0.0932972	−	0.0993514i
$848$	−1.10440	+	4.30134i	−0.0379251	+	0.147708i
$849$	4.60877	+	3.34847i	0.158173	+	0.114919i
$850$	−23.4287	−	16.7238i	−0.803596	−	0.573620i
$851$	−9.65811	+	7.01703i	−0.331076	+	0.240541i
$852$	5.81371	+	14.6837i	0.199174	+	0.503057i
$853$	−2.02906	−	16.0617i	−0.0694738	−	0.549942i	−0.987985	−	0.154548i	$-0.950608\pi$
$853$	−2.02906	−	16.0617i	−0.0694738	−	0.549942i	0.918512	−	0.395394i	$-0.129392\pi$
$854$	0.135832	+	0.0746741i	0.00464806	+	0.00255529i
$855$	−9.31092	+	12.9290i	−0.318427	+	0.442161i
$856$	3.50779	−	7.45444i	0.119894	−	0.254787i
$857$	−2.93025	+	4.03315i	−0.100096	+	0.137770i	−0.856127	−	0.516766i	$-0.827136\pi$
$857$	−2.93025	+	4.03315i	−0.100096	+	0.137770i	0.756031	+	0.654536i	$0.227136\pi$
$858$	−3.98481	+	31.5430i	−0.136039	+	1.07686i
$859$	35.0077	−	8.98846i	1.19445	−	0.306682i	0.401436	−	0.915887i	$-0.368511\pi$
$859$	35.0077	−	8.98846i	1.19445	−	0.306682i	0.793013	+	0.609205i	$0.208511\pi$
$860$	1.17776	+	3.57375i	0.0401613	+	0.121864i
$861$	1.23767	+	1.49609i	0.0421798	+	0.0509867i
$862$	−2.85060	−	2.35822i	−0.0970918	−	0.0803213i
$863$	−10.4125	+	6.60794i	−0.354444	+	0.224937i	−0.701112	−	0.713051i	$-0.747313\pi$
$863$	−10.4125	+	6.60794i	−0.354444	+	0.224937i	0.346668	+	0.937988i	$0.387313\pi$
$864$	−0.0627905	−	0.998027i	−0.00213618	−	0.0339536i
$865$	−36.0894	−	14.1142i	−1.22708	−	0.479897i
$866$	−10.5643	+	12.7700i	−0.358988	+	0.433942i
$867$	15.8575	−	3.02498i	0.538549	−	0.102734i
$868$	1.32953	+	1.82993i	0.0451270	+	0.0621120i
$869$	8.76885	−	4.82071i	0.297463	−	0.163532i
$870$	19.7983	−	3.86277i	0.671224	−	0.130960i
$871$	−19.9205	+	2.51654i	−0.674981	+	0.0852699i
$872$	8.70660	−	4.09701i	0.294843	−	0.138742i
$873$	−7.94449	+	0.499825i	−0.268880	+	0.0169165i
$874$	−15.9624			−0.539935
$875$	−1.67525	−	2.56785i	−0.0566338	−	0.0868091i
$876$	1.13166			0.0382354
$877$	13.8686	−	0.872541i	0.468311	−	0.0294636i	0.173117	−	0.984901i	$-0.444616\pi$
$877$	13.8686	−	0.872541i	0.468311	−	0.0294636i	0.295193	+	0.955438i	$0.404616\pi$
$878$	−14.7834	+	6.95653i	−0.498915	+	0.234771i
$879$	5.36344	−	0.677561i	0.180905	−	0.0228536i
$880$	7.68965	−	8.25771i	0.259218	−	0.278367i
$881$	31.7236	−	17.4402i	1.06880	−	0.587576i	0.152593	−	0.988289i	$-0.451238\pi$
$881$	31.7236	−	17.4402i	1.06880	−	0.587576i	0.916203	+	0.400714i	$0.131238\pi$
$882$	4.07029	+	5.60228i	0.137054	+	0.188639i
$883$	49.8196	−	9.50360i	1.67656	−	0.319821i	0.740607	−	0.671939i	$-0.234538\pi$
$883$	49.8196	−	9.50360i	1.67656	−	0.319821i	0.935956	+	0.352117i	$0.114538\pi$
$884$	−23.1209	+	27.9483i	−0.777639	+	0.940004i
$885$	0.359205	−	6.11838i	0.0120745	−	0.205667i
$886$	−0.129547	−	2.05909i	−0.00435222	−	0.0691766i
$887$	4.95595	−	3.14514i	0.166404	−	0.105603i	−0.450017	−	0.893020i	$-0.648582\pi$
$887$	4.95595	−	3.14514i	0.166404	−	0.105603i	0.616421	+	0.787417i	$0.288582\pi$
$888$	−4.10602	−	3.39680i	−0.137789	−	0.113989i
$889$	−0.105024	−	0.126953i	−0.00352240	−	0.00425785i
$890$	−4.93036	+	0.0206584i	−0.165266	+	0.000692472i
$891$	−4.88766	+	1.25494i	−0.163743	+	0.0420420i
$892$	−0.893454	+	7.07242i	−0.0299151	+	0.236802i
$893$	37.2981	−	51.3364i	1.24813	−	1.71791i
$894$	−6.16917	+	13.1102i	−0.206328	+	0.438469i
$895$	−10.5909	+	3.49033i	−0.354016	+	0.116669i
$896$	−0.240310	−	0.132112i	−0.00802820	−	0.00441354i
$897$	−1.76903	−	14.0033i	−0.0590663	−	0.467558i
$898$	1.66404	+	4.20288i	0.0555296	+	0.140252i
$899$	60.1969	−	43.7356i	2.00768	−	1.45867i
$900$	2.16673	+	4.50614i	0.0722245	+	0.150205i
$901$	20.6834	+	15.0274i	0.689065	+	0.500635i
$902$	8.88555	−	34.6069i	0.295856	−	1.15228i
$903$	−0.315898	−	0.336398i	−0.0105124	−	0.0111946i
$904$	−8.77938	+	8.24439i	−0.291998	+	0.274204i
$905$	−5.96633	+	23.6482i	−0.198328	+	0.786094i
$906$	−7.26134	−	0.917320i	−0.241242	−	0.0304759i
$907$	12.1363	−	3.94333i	0.402980	−	0.130936i	−0.100512	−	0.994936i	$-0.532048\pi$
$907$	12.1363	−	3.94333i	0.402980	−	0.130936i	0.503492	+	0.864000i	$0.332048\pi$
$908$	−8.64077	−	15.7175i	−0.286754	−	0.521604i
$909$	0.874686	−	13.9027i	0.0290115	−	0.461125i
$910$	−3.37776	+	1.87541i	−0.111972	+	0.0621693i
$911$	19.6867	−	31.0213i	0.652251	−	1.02778i	−0.343804	−	0.939041i	$-0.611716\pi$
$911$	19.6867	−	31.0213i	0.652251	−	1.02778i	0.996055	−	0.0887414i	$-0.0282845\pi$
$912$	−1.77200	−	6.90146i	−0.0586766	−	0.228530i
$913$	22.7807	−	57.5376i	0.753933	−	1.90422i
$914$	−13.5718	−	3.48465i	−0.448916	−	0.115262i
$915$	1.22550	+	0.309188i	0.0405138	+	0.0102214i
$916$	−13.9989	−	5.54255i	−0.462536	−	0.183131i
$917$	−0.0638151	−	0.0300291i	−0.00210736	−	0.000991648i
$918$	−5.47526	−	1.77902i	−0.180711	−	0.0587165i
$919$	6.26163	+	32.8246i	0.206552	+	1.08278i	0.922900	+	0.385040i	$0.125812\pi$
$919$	6.26163	+	32.8246i	0.206552	+	1.08278i	−0.716348	+	0.697743i	$0.754188\pi$
$920$	−2.39484	+	4.39977i	−0.0789555	+	0.145056i
$921$	−5.24557	−	11.1474i	−0.172848	−	0.367320i
$922$	−0.567498	−	0.108256i	−0.0186896	−	0.00356522i
$923$	−76.6682	+	63.4254i	−2.52356	+	2.08767i
$924$	−0.427624	+	1.31609i	−0.0140678	+	0.0432962i
$925$	25.4088	+	8.02103i	0.835435	+	0.263730i
$926$	10.9741	+	33.7749i	0.360633	+	1.10991i
$927$	12.1903	+	7.73618i	0.400381	+	0.254090i
$928$	−4.34590	+	7.90517i	−0.142661	+	0.259500i
$929$	0.407202	−	2.13463i	0.0133599	−	0.0700349i	−0.974983	−	0.222280i	$-0.928650\pi$
$929$	0.407202	−	2.13463i	0.0133599	−	0.0700349i	0.988343	+	0.152245i	$0.0486502\pi$
$930$	14.2602	+	11.6968i	0.467611	+	0.383553i
$931$	35.9683	+	33.7765i	1.17881	+	1.10698i
$932$		−	3.67652i		−	0.120428i
$933$	13.5280	−	14.4058i	0.442886	−	0.471626i
$934$	−16.3311	−	25.7337i	−0.534370	−	0.842032i
$935$	−27.9048	−	58.6614i	−0.912584	−	1.91843i
$936$	5.85808	−	2.31938i	0.191477	−	0.0758113i
$937$	54.2808	+	3.41506i	1.77328	+	0.111565i	0.915465	−	0.402398i	$-0.131823\pi$
$937$	54.2808	+	3.41506i	1.77328	+	0.111565i	0.857812	+	0.513963i	$0.171823\pi$
$938$	−0.872207	−	0.0548746i	−0.0284786	−	0.00179172i
$939$	−14.6157	+	5.78678i	−0.476967	+	0.188844i
$940$	−8.55419	−	17.9826i	−0.279007	−	0.586528i
$941$	−17.4527	−	27.5010i	−0.568941	−	0.896507i	0.431042	−	0.902332i	$-0.358146\pi$
$941$	−17.4527	−	27.5010i	−0.568941	−	0.896507i	−0.999983	+	0.00582460i	$0.998146\pi$
$942$	2.34301	−	2.49505i	0.0763393	−	0.0812931i
$943$			15.8619i			0.516534i
$944$	1.99806	+	1.87630i	0.0650312	+	0.0610683i
$945$	−0.474111	−	0.388884i	−0.0154228	−	0.0126504i
$946$	−1.59118	+	8.34124i	−0.0517336	+	0.271197i
$947$	10.6966	−	19.4571i	0.347593	−	0.632270i	−0.643499	−	0.765447i	$-0.722518\pi$
$947$	10.6966	−	19.4571i	0.347593	−	0.632270i	0.991092	+	0.133177i	$0.0425179\pi$
$948$	−1.67430	−	1.06254i	−0.0543788	−	0.0345098i
$949$	2.20332	+	6.78111i	0.0715227	+	0.220124i
$950$	21.1816	+	28.6460i	0.687221	+	0.929400i
$951$	2.62012	−	8.06391i	0.0849634	−	0.261490i
$952$	−1.21645	+	1.00634i	−0.0394254	+	0.0326155i
$953$	−30.9637	−	5.90664i	−1.00301	−	0.191335i	−0.340387	−	0.940286i	$-0.610558\pi$
$953$	−30.9637	−	5.90664i	−1.00301	−	0.191335i	−0.662626	+	0.748951i	$0.730558\pi$
$954$	−1.89082	−	4.01820i	−0.0612177	−	0.130094i
$955$	−13.2470	+	24.3371i	−0.428662	+	0.787531i
$956$	−1.44823	−	7.59187i	−0.0468390	−	0.245538i
$957$	43.2937	+	14.0670i	1.39949	+	0.454721i
$958$	6.66361	+	3.13566i	0.215291	+	0.101308i
$959$	5.27560	+	2.08876i	0.170358	+	0.0674494i
$960$	−2.16813	−	0.547008i	−0.0699761	−	0.0176546i
$961$	35.8702	+	9.20990i	1.15710	+	0.297094i
$962$	12.3598	−	31.2174i	0.398497	−	1.00649i
$963$	2.04884	+	7.97969i	0.0660229	+	0.257142i
$964$	8.36166	−	13.1759i	0.269311	−	0.424366i
$965$	40.0200	−	22.2201i	1.28829	−	0.715290i
$966$	0.0385747	−	0.613128i	0.00124112	−	0.0197271i
$967$	−9.94859	−	18.0964i	−0.319925	−	0.581942i	0.666626	−	0.745392i	$-0.267738\pi$
$967$	−9.94859	−	18.0964i	−0.319925	−	0.581942i	−0.986552	+	0.163450i	$0.947738\pi$
$968$	13.7562	−	4.46965i	0.442140	−	0.143660i
$969$	−40.6972	−	5.14126i	−1.30738	−	0.165161i
$970$	−4.35429	+	17.2587i	−0.139808	+	0.554145i
$971$	−12.5806	+	11.8140i	−0.403732	+	0.379129i	−0.859642	−	0.510896i	$-0.829314\pi$
$971$	−12.5806	+	11.8140i	−0.403732	+	0.379129i	0.455911	+	0.890026i	$0.349314\pi$
$972$	0.684547	+	0.728969i	0.0219569	+	0.0233817i
$973$	0.580167	−	2.25960i	0.0185993	−	0.0724395i
$974$	−33.9181	−	24.6430i	−1.08681	−	0.789612i
$975$	−22.7829	+	21.7567i	−0.729637	+	0.696773i
$976$	−0.457285	+	0.332237i	−0.0146373	+	0.0106346i
$977$	−6.90910	−	17.4504i	−0.221042	−	0.558288i	0.776363	−	0.630286i	$-0.217062\pi$
$977$	−6.90910	−	17.4504i	−0.221042	−	0.558288i	−0.997405	+	0.0719983i	$0.977062\pi$
$978$	1.61182	+	12.7589i	0.0515403	+	0.407984i
$979$	−9.75029	−	5.36027i	−0.311621	−	0.171315i
$980$	14.7063	−	4.84658i	0.469775	−	0.154818i
$981$	−4.09701	+	8.70660i	−0.130808	+	0.277980i
$982$	−21.7180	+	29.8923i	−0.693050	+	0.953902i
$983$	1.47067	−	11.6415i	0.0469069	−	0.371307i	−0.951136	−	0.308773i	$-0.900082\pi$
$983$	1.47067	−	11.6415i	0.0469069	−	0.371307i	0.998043	−	0.0625341i	$-0.0199182\pi$
$984$	−6.85803	+	1.76084i	−0.218626	+	0.0561336i
$985$	49.3227	−	0.206664i	1.57155	−	0.00658487i
$986$	33.1041	+	40.0160i	1.05425	+	1.27437i
$987$	1.88174	+	1.55671i	0.0598964	+	0.0495506i
$988$	37.9046	−	24.0550i	1.20591	−	0.765292i
$989$	−0.236709	−	3.76239i	−0.00752692	−	0.119637i
$990$	−0.661314	+	11.2642i	−0.0210179	+	0.358001i
$991$	6.67609	−	8.07000i	0.212073	−	0.256352i	−0.653741	−	0.756718i	$-0.726801\pi$
$991$	6.67609	−	8.07000i	0.212073	−	0.256352i	0.865814	+	0.500366i	$0.166801\pi$
$992$	−8.10215	+	1.54557i	−0.257244	+	0.0490719i
$993$	−11.1083	−	15.2893i	−0.352512	−	0.485190i
$994$	−3.79516	+	2.08641i	−0.120375	+	0.0661768i
$995$	−26.7218	+	28.6959i	−0.847139	+	0.909720i
$996$	−12.1666	+	1.53701i	−0.385515	+	0.0487019i
$997$	54.2002	−	25.5047i	1.71654	−	0.807742i	0.723450	−	0.690377i	$-0.242555\pi$
$997$	54.2002	−	25.5047i	1.71654	−	0.807742i	0.993089	−	0.117365i	$-0.0374447\pi$
$998$	10.4508	−	0.657511i	0.330816	−	0.0208132i
$999$	5.32895			0.168600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.b.469.6	yes	280
125.4	even	50	inner	750.2.o.b.379.6	✓	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.b.379.6	✓	280	125.4	even	50	inner
750.2.o.b.469.6	yes	280	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.08543 + 1.95495i) q^{5} +(0.876307 - 0.481754i) q^{6} +(0.161189 + 0.221857i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})\)	\(q+(-0.998027 + 0.0627905i) q^{2} +(-0.904827 + 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.08543 + 1.95495i) q^{5} +(0.876307 - 0.481754i) q^{6} +(0.161189 + 0.221857i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(-1.20605 - 1.88294i) q^{10} +(-0.316853 - 5.03624i) q^{11} +(-0.844328 + 0.535827i) q^{12} +(-4.85464 - 4.01611i) q^{13} +(-0.174801 - 0.211298i) q^{14} +(-1.81451 - 1.30674i) q^{15} +(0.968583 - 0.248690i) q^{16} +(0.721548 - 5.71164i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(-3.03381 + 6.44718i) q^{19} +(1.32190 + 1.80349i) q^{20} +(-0.240310 - 0.132112i) q^{21} +(0.632456 + 5.00640i) q^{22} +(-0.824684 - 2.08291i) q^{23} +(0.809017 - 0.587785i) q^{24} +(-2.64366 + 4.24394i) q^{25} +(5.09723 + 3.70336i) q^{26} +(-0.248690 + 0.968583i) q^{27} +(0.187724 + 0.199905i) q^{28} +(6.57603 - 6.17530i) q^{29} +(1.89298 + 1.19022i) q^{30} +(8.18321 + 1.03378i) q^{31} +(-0.951057 + 0.309017i) q^{32} +(2.43102 + 4.42201i) q^{33} +(-0.361487 + 5.74567i) q^{34} +(-0.258760 + 0.555927i) q^{35} +(0.535827 - 0.844328i) q^{36} +(-1.32526 - 5.16153i) q^{37} +(2.62301 - 6.62495i) q^{38} +(6.10258 + 1.56688i) q^{39} +(-1.43253 - 1.71693i) q^{40} +(-6.58326 - 2.60650i) q^{41} +(0.248131 + 0.116762i) q^{42} +(1.60042 + 0.520009i) q^{43} +(-0.945563 - 4.95681i) q^{44} +(2.19820 + 0.409790i) q^{45} +(0.953844 + 2.02702i) q^{46} +(-8.74786 - 1.66874i) q^{47} +(-0.770513 + 0.637424i) q^{48} +(2.13988 - 6.58587i) q^{49} +(2.37197 - 4.40156i) q^{50} +(1.77902 + 5.47526i) q^{51} +(-5.31971 - 3.37599i) q^{52} +(-2.13940 + 3.89155i) q^{53} +(0.187381 - 0.982287i) q^{54} +(9.50167 - 6.08594i) q^{55} +(-0.199905 - 0.187724i) q^{56} -7.12532i q^{57} +(-6.17530 + 6.57603i) q^{58} +(1.46867 + 2.31425i) q^{59} +(-1.96398 - 1.06901i) q^{60} +(-0.525542 + 0.208077i) q^{61} +(-8.23198 - 0.517912i) q^{62} +(0.273689 + 0.0172191i) q^{63} +(0.929776 - 0.368125i) q^{64} +(2.58190 - 13.8498i) q^{65} +(-2.70389 - 4.26064i) q^{66} +(2.18155 - 2.32311i) q^{67} -5.75703i q^{68} +(1.63306 + 1.53354i) q^{69} +(0.223342 - 0.571078i) q^{70} +(2.95927 - 15.5130i) q^{71} +(-0.481754 + 0.876307i) q^{72} +(-0.955496 - 0.606376i) q^{73} +(1.64674 + 5.06813i) q^{74} +(0.585075 - 4.96565i) q^{75} +(-2.20184 + 6.77658i) q^{76} +(1.06625 - 0.882081i) q^{77} +(-6.18893 - 1.18060i) q^{78} +(0.844319 + 1.79427i) q^{79} +(1.53751 + 1.62360i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(6.73393 + 2.18799i) q^{82} +(11.0962 + 5.22148i) q^{83} +(-0.254973 - 0.100951i) q^{84} +(11.9492 - 4.78902i) q^{85} +(-1.62992 - 0.418491i) q^{86} +(-3.32085 + 8.38752i) q^{87} +(1.25494 + 4.88766i) q^{88} +(1.18147 - 1.86169i) q^{89} +(-2.21959 - 0.270956i) q^{90} +(0.108489 - 1.72439i) q^{91} +(-1.07924 - 1.96313i) q^{92} +(-7.84456 + 2.54885i) q^{93} +(8.83538 + 1.11617i) q^{94} +(-15.8969 + 1.06704i) q^{95} +(0.728969 - 0.684547i) q^{96} +(-5.44913 - 5.80274i) q^{97} +(-1.72213 + 6.70724i) q^{98} +(-4.08246 - 2.96608i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q+O(q^{10}) \) 280 * q	\( 280 q - 10 q^{11} - 20 q^{13} + 30 q^{17} + 10 q^{19} + 20 q^{22} + 60 q^{23} + 70 q^{24} + 20 q^{25} + 20 q^{29} + 10 q^{30} + 20 q^{31} + 20 q^{33} - 10 q^{34} + 30 q^{35} - 20 q^{37} + 90 q^{38} - 40 q^{41} - 10 q^{46} - 100 q^{47} + 120 q^{49} - 20 q^{50} - 30 q^{51} + 80 q^{52} - 30 q^{53} - 10 q^{55} + 30 q^{58} + 20 q^{59} + 60 q^{61} - 50 q^{62} - 10 q^{63} + 20 q^{65} + 40 q^{66} + 50 q^{67} + 10 q^{69} + 20 q^{70} + 80 q^{71} - 20 q^{73} + 80 q^{75} - 30 q^{76} - 100 q^{77} - 100 q^{79} + 100 q^{82} + 30 q^{83} - 20 q^{86} - 10 q^{87} - 60 q^{89} - 10 q^{90} + 70 q^{91} - 120 q^{92} + 50 q^{93} + 30 q^{94} - 20 q^{95} + 10 q^{97} + 40 q^{98} + 20 q^{99}+O(q^{100}) \) 280 * q - 10 * q^11 - 20 * q^13 + 30 * q^17 + 10 * q^19 + 20 * q^22 + 60 * q^23 + 70 * q^24 + 20 * q^25 + 20 * q^29 + 10 * q^30 + 20 * q^31 + 20 * q^33 - 10 * q^34 + 30 * q^35 - 20 * q^37 + 90 * q^38 - 40 * q^41 - 10 * q^46 - 100 * q^47 + 120 * q^49 - 20 * q^50 - 30 * q^51 + 80 * q^52 - 30 * q^53 - 10 * q^55 + 30 * q^58 + 20 * q^59 + 60 * q^61 - 50 * q^62 - 10 * q^63 + 20 * q^65 + 40 * q^66 + 50 * q^67 + 10 * q^69 + 20 * q^70 + 80 * q^71 - 20 * q^73 + 80 * q^75 - 30 * q^76 - 100 * q^77 - 100 * q^79 + 100 * q^82 + 30 * q^83 - 20 * q^86 - 10 * q^87 - 60 * q^89 - 10 * q^90 + 70 * q^91 - 120 * q^92 + 50 * q^93 + 30 * q^94 - 20 * q^95 + 10 * q^97 + 40 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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