LMFDB - Embedded newform 750.2.o.b.469.14

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			469.14
Character	$\chi$	$=$	750.469
Dual form			750.2.o.b.379.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.998027 - 0.0627905i) q^{2} +(0.904827 - 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.84003 + 1.27055i) q^{5} +(0.876307 - 0.481754i) q^{6} +(1.37798 + 1.89663i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})$	\(q+(0.998027 - 0.0627905i) q^{2} +(0.904827 - 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.84003 + 1.27055i) q^{5} +(0.876307 - 0.481754i) q^{6} +(1.37798 + 1.89663i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(1.91617 + 1.15251i) q^{10} +(-0.0497016 - 0.789985i) q^{11} +(0.844328 - 0.535827i) q^{12} +(-2.53196 - 2.09462i) q^{13} +(1.49436 + 1.80637i) q^{14} +(2.20588 + 0.366183i) q^{15} +(0.968583 - 0.248690i) q^{16} +(-0.335537 + 2.65605i) q^{17} +(0.587785 - 0.809017i) q^{18} +(-0.671124 + 1.42621i) q^{19} +(1.98476 + 1.02992i) q^{20} +(2.05438 + 1.12941i) q^{21} +(-0.0992071 - 0.785305i) q^{22} +(-1.59367 - 4.02514i) q^{23} +(0.809017 - 0.587785i) q^{24} +(1.77140 + 4.67570i) q^{25} +(-2.65848 - 1.93150i) q^{26} +(0.248690 - 0.968583i) q^{27} +(1.60483 + 1.70897i) q^{28} +(-2.45714 + 2.30741i) q^{29} +(2.22452 + 0.226952i) q^{30} +(-1.68103 - 0.212363i) q^{31} +(0.951057 - 0.309017i) q^{32} +(-0.381331 - 0.693638i) q^{33} +(-0.168100 + 2.67188i) q^{34} +(0.125760 + 5.24066i) q^{35} +(0.535827 - 0.844328i) q^{36} +(-1.68919 - 6.57897i) q^{37} +(-0.580247 + 1.46554i) q^{38} +(-3.18283 - 0.817211i) q^{39} +(2.04551 + 0.903259i) q^{40} +(-3.05304 - 1.20879i) q^{41} +(2.12125 + 0.998183i) q^{42} +(4.17882 + 1.35778i) q^{43} +(-0.148321 - 0.777526i) q^{44} +(2.15185 - 0.607886i) q^{45} +(-1.84326 - 3.91713i) q^{46} +(1.75966 + 0.335674i) q^{47} +(0.770513 - 0.637424i) q^{48} +(0.464744 - 1.43034i) q^{49} +(2.06149 + 4.55524i) q^{50} +(0.827288 + 2.54613i) q^{51} +(-2.77452 - 1.76076i) q^{52} +(-0.0989713 + 0.180028i) q^{53} +(0.187381 - 0.982287i) q^{54} +(0.912264 - 1.51674i) q^{55} +(1.70897 + 1.60483i) q^{56} +1.57623i q^{57} +(-2.30741 + 2.45714i) q^{58} +(-4.24400 - 6.68748i) q^{59} +(2.23438 + 0.0868256i) q^{60} +(6.44037 - 2.54992i) q^{61} +(-1.69105 - 0.106392i) q^{62} +(2.33974 + 0.147204i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-1.99755 - 7.07113i) q^{65} +(-0.424132 - 0.668325i) q^{66} +(2.10679 - 2.24350i) q^{67} +2.67716i q^{68} +(-3.15581 - 2.96350i) q^{69} +(0.454576 + 5.22242i) q^{70} +(1.73475 - 9.09387i) q^{71} +(0.481754 - 0.876307i) q^{72} +(-5.42362 - 3.44193i) q^{73} +(-2.09896 - 6.45992i) q^{74} +(3.59363 + 3.47647i) q^{75} +(-0.487081 + 1.49908i) q^{76} +(1.42982 - 1.18285i) q^{77} +(-3.22786 - 0.615747i) q^{78} +(5.25607 + 11.1697i) q^{79} +(2.09819 + 0.773038i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(-3.12292 - 1.01470i) q^{82} +(-4.68106 - 2.20274i) q^{83} +(2.17974 + 0.863019i) q^{84} +(-3.99205 + 4.46089i) q^{85} +(4.25583 + 1.09271i) q^{86} +(-1.24084 + 3.13400i) q^{87} +(-0.196850 - 0.766679i) q^{88} +(-9.24572 + 14.5689i) q^{89} +(2.10944 - 0.741802i) q^{90} +(0.483722 - 7.68854i) q^{91} +(-2.08558 - 3.79366i) q^{92} +(-1.61146 + 0.523595i) q^{93} +(1.77727 + 0.224521i) q^{94} +(-3.04696 + 1.77157i) q^{95} +(0.728969 - 0.684547i) q^{96} +(-7.51246 - 7.99996i) q^{97} +(0.374016 - 1.45669i) q^{98} +(-0.640375 - 0.465260i) 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
$5$	1.84003	+	1.27055i	0.822885	+	0.568208i
$5$	1.84003	+	1.27055i	0.822885	+	0.568208i
$6$	0.876307	−	0.481754i	0.357751	−	0.196675i
$7$	1.37798	+	1.89663i	0.520829	+	0.716860i	0.985698	−	0.168520i	$-0.0538986\pi$
$7$	1.37798	+	1.89663i	0.520829	+	0.716860i	−0.464869	+	0.885379i	$0.653899\pi$
$8$	0.982287	−	0.187381i	0.347291	−	0.0662493i
$9$	0.637424	−	0.770513i	0.212475	−	0.256838i
$10$	1.91617	+	1.15251i	0.605948	+	0.364455i
$11$	−0.0497016	−	0.789985i	−0.0149856	−	0.238189i	−0.998388	−	0.0567529i	$-0.981925\pi$
$11$	−0.0497016	−	0.789985i	−0.0149856	−	0.238189i	0.983403	−	0.181437i	$-0.0580747\pi$
$12$	0.844328	−	0.535827i	0.243736	−	0.154680i
$13$	−2.53196	−	2.09462i	−0.702238	−	0.580942i	0.216275	−	0.976333i	$-0.430609\pi$
$13$	−2.53196	−	2.09462i	−0.702238	−	0.580942i	−0.918513	+	0.395391i	$0.870609\pi$
$14$	1.49436	+	1.80637i	0.399383	+	0.482772i
$15$	2.20588	+	0.366183i	0.569556	+	0.0945481i
$16$	0.968583	−	0.248690i	0.242146	−	0.0621725i
$17$	−0.335537	+	2.65605i	−0.0813797	+	0.644187i	0.897685	+	0.440638i	$0.145248\pi$
$17$	−0.335537	+	2.65605i	−0.0813797	+	0.644187i	−0.979065	+	0.203549i	$0.934752\pi$
$18$	0.587785	−	0.809017i	0.138542	−	0.190687i
$19$	−0.671124	+	1.42621i	−0.153966	+	0.327195i	−0.966898	−	0.255164i	$-0.917870\pi$
$19$	−0.671124	+	1.42621i	−0.153966	+	0.327195i	0.812931	+	0.582360i	$0.197870\pi$
$20$	1.98476	+	1.02992i	0.443806	+	0.230296i
$21$	2.05438	+	1.12941i	0.448303	+	0.246457i
$22$	−0.0992071	−	0.785305i	−0.0211510	−	0.167428i
$23$	−1.59367	−	4.02514i	−0.332302	−	0.839299i	−0.995837	−	0.0911539i	$-0.970944\pi$
$23$	−1.59367	−	4.02514i	−0.332302	−	0.839299i	0.663535	−	0.748146i	$-0.269056\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	1.77140	+	4.67570i	0.354280	+	0.935139i
$26$	−2.65848	−	1.93150i	−0.521371	−	0.378798i
$27$	0.248690	−	0.968583i	0.0478604	−	0.186404i
$28$	1.60483	+	1.70897i	0.303284	+	0.322965i
$29$	−2.45714	+	2.30741i	−0.456279	+	0.428475i	−0.878299	−	0.478112i	$-0.841321\pi$
$29$	−2.45714	+	2.30741i	−0.456279	+	0.428475i	0.422020	+	0.906587i	$0.361321\pi$
$30$	2.22452	+	0.226952i	0.406140	+	0.0414356i
$31$	−1.68103	−	0.212363i	−0.301922	−	0.0381416i	−0.0270870	−	0.999633i	$-0.508623\pi$
$31$	−1.68103	−	0.212363i	−0.301922	−	0.0381416i	−0.274835	+	0.961491i	$0.588623\pi$
$32$	0.951057	−	0.309017i	0.168125	−	0.0546270i
$33$	−0.381331	−	0.693638i	−0.0663811	−	0.120747i
$34$	−0.168100	+	2.67188i	−0.0288290	+	0.458223i
$35$	0.125760	+	5.24066i	0.0212574	+	0.885832i
$36$	0.535827	−	0.844328i	0.0893045	−	0.140721i
$37$	−1.68919	−	6.57897i	−0.277701	−	1.08158i	−0.942406	−	0.334470i	$-0.891443\pi$
$37$	−1.68919	−	6.57897i	−0.277701	−	1.08158i	0.664705	−	0.747106i	$-0.268557\pi$
$38$	−0.580247	+	1.46554i	−0.0941286	+	0.237742i
$39$	−3.18283	−	0.817211i	−0.509660	−	0.130858i
$40$	2.04551	+	0.903259i	0.323424	+	0.142818i
$41$	−3.05304	−	1.20879i	−0.476805	−	0.188781i	0.117415	−	0.993083i	$-0.462539\pi$
$41$	−3.05304	−	1.20879i	−0.476805	−	0.188781i	−0.594220	+	0.804302i	$0.702539\pi$
$42$	2.12125	+	0.998183i	0.327315	+	0.154023i
$43$	4.17882	+	1.35778i	0.637264	+	0.207060i	0.609790	−	0.792563i	$-0.291254\pi$
$43$	4.17882	+	1.35778i	0.637264	+	0.207060i	0.0274737	+	0.999623i	$0.491254\pi$
$44$	−0.148321	−	0.777526i	−0.0223602	−	0.117217i
$45$	2.15185	−	0.607886i	0.320779	−	0.0906183i
$46$	−1.84326	−	3.91713i	−0.271774	−	0.577549i
$47$	1.75966	+	0.335674i	0.256673	+	0.0489630i	0.314112	−	0.949386i	$-0.398293\pi$
$47$	1.75966	+	0.335674i	0.256673	+	0.0489630i	−0.0574386	+	0.998349i	$0.518293\pi$
$48$	0.770513	−	0.637424i	0.111214	−	0.0920042i
$49$	0.464744	−	1.43034i	0.0663920	−	0.204334i
$50$	2.06149	+	4.55524i	0.291539	+	0.644209i
$51$	0.827288	+	2.54613i	0.115844	+	0.356530i
$52$	−2.77452	−	1.76076i	−0.384756	−	0.244174i
$53$	−0.0989713	+	0.180028i	−0.0135948	+	0.0247288i	−0.883017	−	0.469341i	$-0.844491\pi$
$53$	−0.0989713	+	0.180028i	−0.0135948	+	0.0247288i	0.869422	+	0.494070i	$0.164491\pi$
$54$	0.187381	−	0.982287i	0.0254994	−	0.133672i
$55$	0.912264	−	1.51674i	0.123010	−	0.204518i
$56$	1.70897	+	1.60483i	0.228371	+	0.214454i
$57$			1.57623i			0.208776i
$58$	−2.30741	+	2.45714i	−0.302977	+	0.322638i
$59$	−4.24400	−	6.68748i	−0.552522	−	0.870635i	0.447195	−	0.894437i	$-0.352423\pi$
$59$	−4.24400	−	6.68748i	−0.552522	−	0.870635i	−0.999717	+	0.0238013i	$0.992423\pi$
$60$	2.23438	+	0.0868256i	0.288457	+	0.0112091i
$61$	6.44037	−	2.54992i	0.824605	−	0.326484i	0.0823512	−	0.996603i	$-0.473757\pi$
$61$	6.44037	−	2.54992i	0.824605	−	0.326484i	0.742253	+	0.670119i	$0.233757\pi$
$62$	−1.69105	−	0.106392i	−0.214763	−	0.0135117i
$63$	2.33974	+	0.147204i	0.294780	+	0.0185460i
$64$	0.929776	−	0.368125i	0.116222	−	0.0460156i
$65$	−1.99755	−	7.07113i	−0.247766	−	0.877066i
$66$	−0.424132	−	0.668325i	−0.0522070	−	0.0822651i
$67$	2.10679	−	2.24350i	0.257385	−	0.274088i	−0.587278	−	0.809385i	$-0.699801\pi$
$67$	2.10679	−	2.24350i	0.257385	−	0.274088i	0.844664	+	0.535298i	$0.179801\pi$
$68$			2.67716i			0.324654i
$69$	−3.15581	−	2.96350i	−0.379915	−	0.356764i
$70$	0.454576	+	5.22242i	0.0543322	+	0.624198i
$71$	1.73475	−	9.09387i	0.205877	−	1.07924i	−0.717852	−	0.696196i	$-0.754874\pi$
$71$	1.73475	−	9.09387i	0.205877	−	1.07924i	0.923728	−	0.383048i	$-0.125126\pi$
$72$	0.481754	−	0.876307i	0.0567752	−	0.103274i
$73$	−5.42362	−	3.44193i	−0.634787	−	0.402848i	0.179133	−	0.983825i	$-0.442671\pi$
$73$	−5.42362	−	3.44193i	−0.634787	−	0.402848i	−0.813920	+	0.580977i	$0.802671\pi$
$74$	−2.09896	−	6.45992i	−0.243999	−	0.750951i
$75$	3.59363	+	3.47647i	0.414956	+	0.401428i
$76$	−0.487081	+	1.49908i	−0.0558720	+	0.171956i
$77$	1.42982	−	1.18285i	0.162943	−	0.134799i
$78$	−3.22786	−	0.615747i	−0.365483	−	0.0697196i
$79$	5.25607	+	11.1697i	0.591354	+	1.25669i	0.946748	+	0.321975i	$0.104347\pi$
$79$	5.25607	+	11.1697i	0.591354	+	1.25669i	−0.355394	+	0.934717i	$0.615653\pi$
$80$	2.09819	+	0.773038i	0.234585	+	0.0864283i
$81$	−0.187381	−	0.982287i	−0.0208201	−	0.109143i
$82$	−3.12292	−	1.01470i	−0.344869	−	0.112055i
$83$	−4.68106	−	2.20274i	−0.513813	−	0.241782i	0.151350	−	0.988480i	$-0.451638\pi$
$83$	−4.68106	−	2.20274i	−0.513813	−	0.241782i	−0.665163	+	0.746698i	$0.731638\pi$
$84$	2.17974	+	0.863019i	0.237829	+	0.0941631i
$85$	−3.99205	+	4.46089i	−0.432998	+	0.483851i
$86$	4.25583	+	1.09271i	0.458918	+	0.117830i
$87$	−1.24084	+	3.13400i	−0.133032	+	0.336000i
$88$	−0.196850	−	0.766679i	−0.0209843	−	0.0817283i
$89$	−9.24572	+	14.5689i	−0.980044	+	1.54430i	−0.148449	+	0.988920i	$0.547428\pi$
$89$	−9.24572	+	14.5689i	−0.980044	+	1.54430i	−0.831595	+	0.555382i	$0.812572\pi$
$90$	2.10944	−	0.741802i	0.222354	−	0.0781928i
$91$	0.483722	−	7.68854i	0.0507078	−	0.805978i
$92$	−2.08558	−	3.79366i	−0.217437	−	0.395516i
$93$	−1.61146	+	0.523595i	−0.167101	+	0.0542943i
$94$	1.77727	+	0.224521i	0.183311	+	0.0231576i
$95$	−3.04696	+	1.77157i	−0.312612	+	0.181759i
$96$	0.728969	−	0.684547i	0.0744000	−	0.0698663i
$97$	−7.51246	−	7.99996i	−0.762775	−	0.812273i	0.223962	−	0.974598i	$-0.428101\pi$
$97$	−7.51246	−	7.99996i	−0.762775	−	0.812273i	−0.986737	+	0.162325i	$0.948101\pi$
$98$	0.374016	−	1.45669i	0.0377813	−	0.147148i
$99$	−0.640375	−	0.465260i	−0.0643601	−	0.0467604i
$100$	2.34345	+	4.41681i	0.234345	+	0.441681i
$101$	−4.61548	+	3.35334i	−0.459257	+	0.333670i	−0.793240	−	0.608909i	$-0.791607\pi$
$101$	−4.61548	+	3.35334i	−0.459257	+	0.333670i	0.333983	+	0.942579i	$0.391607\pi$
$102$	0.985529	+	2.48916i	0.0975819	+	0.246464i
$103$	0.850190	+	6.72995i	0.0837718	+	0.663122i	0.976958	+	0.213434i	$0.0684648\pi$
$103$	0.850190	+	6.72995i	0.0837718	+	0.663122i	−0.893186	+	0.449688i	$0.851535\pi$
$104$	−2.87960	−	1.58307i	−0.282368	−	0.155233i
$105$	2.34515	+	4.68834i	0.228864	+	0.457535i
$106$	−0.0874720	+	0.185887i	−0.00849603	+	0.0180550i
$107$	−1.42288	+	1.95843i	−0.137555	+	0.189329i	−0.872237	−	0.489083i	$-0.837331\pi$
$107$	−1.42288	+	1.95843i	−0.137555	+	0.189329i	0.734682	+	0.678412i	$0.237331\pi$
$108$	0.125333	−	0.992115i	0.0120602	−	0.0954663i
$109$	4.10242	−	1.05332i	0.392941	−	0.100890i	−0.0470497	−	0.998893i	$-0.514982\pi$
$109$	4.10242	−	1.05332i	0.392941	−	0.100890i	0.439990	+	0.898003i	$0.354982\pi$
$110$	0.815227	−	1.57103i	0.0777288	−	0.149792i
$111$	−4.32962	−	5.23361i	−0.410949	−	0.496752i
$112$	1.80637	+	1.49436i	0.170686	+	0.141203i
$113$	−9.37559	+	5.94993i	−0.881981	+	0.559722i	−0.897924	−	0.440150i	$-0.854925\pi$
$113$	−9.37559	+	5.94993i	−0.881981	+	0.559722i	0.0159426	+	0.999873i	$0.494925\pi$
$114$	0.0989720	+	1.57312i	0.00926958	+	0.147336i
$115$	2.18176	−	9.43120i	0.203450	−	0.879464i
$116$	−2.14857	+	2.59717i	−0.199490	+	0.241141i
$117$	−3.22786	+	0.615747i	−0.298416	+	0.0569258i
$118$	−4.65554	−	6.40780i	−0.428577	−	0.589886i
$119$	−5.49992	+	3.02361i	−0.504177	+	0.277173i
$120$	2.23542	−	0.0536437i	0.204065	−	0.00489697i
$121$	10.2917	−	1.30014i	0.935605	−	0.118194i
$122$	6.26755	−	2.94928i	0.567437	−	0.267016i
$123$	−3.27715	+	0.206181i	−0.295491	+	0.0185907i
$124$	−1.69439			−0.152161
$125$	−2.68128	+	10.8541i	−0.239821	+	0.970817i
$126$	2.34437			0.208853
$127$	−1.05684	+	0.0664907i	−0.0937793	+	0.00590009i	−0.109611	−	0.993975i	$-0.534960\pi$
$127$	−1.05684	+	0.0664907i	−0.0937793	+	0.00590009i	0.0158315	+	0.999875i	$0.494960\pi$
$128$	0.904827	−	0.425779i	0.0799762	−	0.0376339i
$129$	4.35922	−	0.550698i	0.383808	−	0.0484862i
$130$	−2.43761	−	6.93175i	−0.213793	−	0.607955i
$131$	11.2486	−	6.18398i	0.982797	−	0.540297i	0.0925172	−	0.995711i	$-0.470509\pi$
$131$	11.2486	−	6.18398i	0.982797	−	0.540297i	0.890280	+	0.455414i	$0.150509\pi$
$132$	−0.465260	−	0.640375i	−0.0404957	−	0.0557375i
$133$	−3.62980	+	0.692421i	−0.314743	+	0.0600405i
$134$	1.96176	−	2.37136i	0.169470	−	0.204855i
$135$	1.68823	−	1.46625i	0.145300	−	0.126194i
$136$	0.168100	+	2.67188i	0.0144145	+	0.229112i
$137$	−15.7573	+	9.99988i	−1.34624	+	0.854347i	−0.996588	−	0.0825344i	$-0.973699\pi$
$137$	−15.7573	+	9.99988i	−1.34624	+	0.854347i	−0.349647	+	0.936881i	$0.613699\pi$
$138$	−3.33566	−	2.75950i	−0.283951	−	0.234904i
$139$	−3.57046	−	4.31595i	−0.302843	−	0.366074i	0.597036	−	0.802215i	$-0.296345\pi$
$139$	−3.57046	−	4.31595i	−0.302843	−	0.366074i	−0.899879	+	0.436141i	$0.856345\pi$
$140$	0.781597	+	5.18357i	0.0660570	+	0.438092i
$141$	1.73511	−	0.445501i	0.146123	−	0.0375180i
$142$	1.16032	−	9.18486i	0.0973716	−	0.770776i
$143$	−1.52887	+	2.10431i	−0.127851	+	0.175971i
$144$	0.425779	−	0.904827i	0.0354816	−	0.0754023i
$145$	−7.45288	+	1.12377i	−0.618928	+	0.0933242i
$146$	−5.62904	−	3.09459i	−0.465863	−	0.256110i
$147$	−0.188494	−	1.49208i	−0.0155467	−	0.123065i
$148$	−2.50044	−	6.31538i	−0.205535	−	0.519121i
$149$	−18.5566	+	13.4822i	−1.52022	+	1.10450i	−0.558840	+	0.829276i	$0.688753\pi$
$149$	−18.5566	+	13.4822i	−1.52022	+	1.10450i	−0.961379	+	0.275228i	$0.911247\pi$
$150$	3.80482	+	3.24397i	0.310663	+	0.264869i
$151$	10.1112	+	7.34624i	0.822841	+	0.597829i	0.917525	−	0.397679i	$-0.130184\pi$
$151$	10.1112	+	7.34624i	0.822841	+	0.597829i	−0.0946842	+	0.995507i	$0.530184\pi$
$152$	−0.391991	+	1.52671i	−0.0317947	+	0.123832i
$153$	1.83264	+	1.95157i	0.148160	+	0.157775i
$154$	1.35273	−	1.27030i	0.109006	−	0.102364i
$155$	−2.82332	−	2.52659i	−0.226775	−	0.202940i
$156$	−3.26015	−	0.411853i	−0.261021	−	0.0329746i
$157$	−6.71218	+	2.18092i	−0.535690	+	0.174056i	−0.564354	−	0.825533i	$-0.690875\pi$
$157$	−6.71218	+	2.18092i	−0.535690	+	0.174056i	0.0286638	+	0.999589i	$0.490875\pi$
$158$	5.94705	+	10.8176i	0.473122	+	0.860606i
$159$	−0.0128997	+	0.205034i	−0.00102301	+	0.0162603i
$160$	2.14259	+	0.639766i	0.169387	+	0.0505779i
$161$	5.43816	−	8.56918i	0.428587	−	0.675346i
$162$	−0.248690	−	0.968583i	−0.0195389	−	0.0760991i
$163$	8.83176	−	22.3065i	0.691757	−	1.74718i	0.0275620	−	0.999620i	$-0.491226\pi$
$163$	8.83176	−	22.3065i	0.691757	−	1.74718i	0.664195	−	0.747559i	$-0.268774\pi$
$164$	−3.18047	−	0.816606i	−0.248353	−	0.0637662i
$165$	0.179643	−	1.76081i	0.0139852	−	0.137079i
$166$	−4.81013	−	1.90447i	−0.373339	−	0.147815i
$167$	−0.394765	−	0.185762i	−0.0305478	−	0.0143747i	0.410445	−	0.911885i	$-0.365373\pi$
$167$	−0.394765	−	0.185762i	−0.0305478	−	0.0143747i	−0.440993	+	0.897511i	$0.645373\pi$
$168$	2.22963	+	0.724449i	0.172019	+	0.0558925i
$169$	−0.412573	−	2.16278i	−0.0317364	−	0.166368i
$170$	−3.70407	+	4.70275i	−0.284089	+	0.360684i
$171$	0.671124	+	1.42621i	0.0513222	+	0.109065i
$172$	4.31604	+	0.823329i	0.329095	+	0.0627783i
$173$	−7.85992	+	6.50230i	−0.597579	+	0.494360i	−0.886336	−	0.463042i	$-0.846758\pi$
$173$	−7.85992	+	6.50230i	−0.597579	+	0.494360i	0.288757	+	0.957402i	$0.406758\pi$
$174$	−1.04161	+	3.20573i	−0.0789639	+	0.243026i
$175$	−6.42712	+	9.80273i	−0.485844	+	0.741017i
$176$	−0.244601	−	0.752806i	−0.0184375	−	0.0567449i
$177$	−6.68748	−	4.24400i	−0.502662	−	0.318999i
$178$	−8.31268	+	15.1207i	−0.623062	+	1.13335i
$179$	−2.20071	+	11.5365i	−0.164489	+	0.862281i	0.800369	+	0.599508i	$0.204637\pi$
$179$	−2.20071	+	11.5365i	−0.164489	+	0.862281i	−0.964858	+	0.262773i	$0.915363\pi$
$180$	2.05870	−	0.872791i	0.153446	−	0.0650540i
$181$	10.7526	+	10.0974i	0.799236	+	0.750533i	0.972139	−	0.234406i	$-0.0753146\pi$
$181$	10.7526	+	10.0974i	0.799236	+	0.750533i	−0.172903	+	0.984939i	$0.555315\pi$
$182$		−	7.70374i		−	0.571039i
$183$	4.74171	−	5.04941i	0.350518	−	0.373263i
$184$	−2.31967	−	3.65522i	−0.171009	−	0.269466i
$185$	5.25075	−	14.2517i	0.386043	−	1.04780i
$186$	−1.57540	+	0.623746i	−0.115514	+	0.0457353i
$187$	2.11492	+	0.133059i	0.154658	+	0.00973026i
$188$	1.78786	+	0.112482i	0.130393	+	0.00820363i
$189$	2.17974	−	0.863019i	0.158553	−	0.0627754i
$190$	−2.92971	+	1.95940i	−0.212544	+	0.142149i
$191$	−10.8910	−	17.1615i	−0.788047	−	1.24176i	−0.966209	−	0.257762i	$-0.917015\pi$
$191$	−10.8910	−	17.1615i	−0.788047	−	1.24176i	0.178162	−	0.984001i	$-0.442985\pi$
$192$	0.684547	−	0.728969i	0.0494029	−	0.0526088i
$193$			6.17946i			0.444808i	0.974955	+	0.222404i	$0.0713903\pi$
$193$			6.17946i			0.444808i	−0.974955	+	0.222404i	$0.928610\pi$
$194$	−7.99996	−	7.51246i	−0.574364	−	0.539363i
$195$	−4.81818	−	5.54763i	−0.345037	−	0.397274i
$196$	0.281811	−	1.47730i	0.0201294	−	0.105522i
$197$	6.68488	−	12.1597i	0.476278	−	0.866346i	−0.523619	−	0.851953i	$-0.675418\pi$
$197$	6.68488	−	12.1597i	0.476278	−	0.866346i	0.999896	−	0.0143933i	$-0.00458170\pi$
$198$	−0.668325	−	0.424132i	−0.0474958	−	0.0301418i
$199$	3.27101	+	10.0671i	0.231876	+	0.713640i	0.997521	+	0.0703762i	$0.0224200\pi$
$199$	3.27101	+	10.0671i	0.231876	+	0.713640i	−0.765645	+	0.643263i	$0.777580\pi$
$200$	2.61616	+	4.26095i	0.184991	+	0.301295i
$201$	0.951044	−	2.92701i	0.0670814	−	0.206455i
$202$	−4.39581	+	3.63653i	−0.309288	+	0.255865i
$203$	−7.76220	−	1.48072i	−0.544800	−	0.103926i
$204$	1.13988	+	2.42237i	0.0798076	+	0.169600i
$205$	−4.08186	−	6.10324i	−0.285089	−	0.426269i
$206$	1.27109	+	6.66329i	0.0885610	+	0.464253i
$207$	−4.11726	−	1.33778i	−0.286170	−	0.0929821i
$208$	−2.97332	−	1.39914i	−0.206163	−	0.0970128i
$209$	1.16004	+	0.459293i	0.0802418	+	0.0317700i
$210$	2.63491	+	4.53184i	0.181826	+	0.312726i
$211$	14.4134	+	3.70072i	0.992256	+	0.254768i	0.709717	−	0.704487i	$-0.248823\pi$
$211$	14.4134	+	3.70072i	0.992256	+	0.254768i	0.282540	+	0.959256i	$0.408823\pi$
$212$	−0.0756274	+	0.191013i	−0.00519411	+	0.0131188i
$213$	−2.30234	−	8.96700i	−0.157753	−	0.614409i
$214$	−1.29711	+	2.04391i	−0.0886683	+	0.139719i
$215$	5.96401	+	7.80775i	0.406742	+	0.532484i
$216$	0.0627905	−	0.998027i	0.00427235	−	0.0679071i
$217$	−1.91366	−	3.48093i	−0.129907	−	0.236301i
$218$	4.02819	−	1.30884i	0.272823	−	0.0886456i
$219$	−6.37294	−	0.805090i	−0.430644	−	0.0544029i
$220$	0.714972	−	1.61912i	0.0482034	−	0.109161i
$221$	6.41297	−	6.02218i	0.431383	−	0.405096i
$222$	−4.64969	−	4.95142i	−0.312067	−	0.332318i
$223$	0.107509	−	0.418722i	0.00719936	−	0.0280397i	−0.964882	−	0.262684i	$-0.915392\pi$
$223$	0.107509	−	0.418722i	0.00719936	−	0.0280397i	0.972081	+	0.234644i	$0.0753924\pi$
$224$	1.89663	+	1.37798i	0.126724	+	0.0920704i
$225$	4.73182	+	1.61551i	0.315455	+	0.107701i
$226$	−8.98349	+	6.52689i	−0.597573	+	0.434162i
$227$	2.39513	+	6.04942i	0.158971	+	0.401514i	0.987329	−	0.158684i	$-0.0507251\pi$
$227$	2.39513	+	6.04942i	0.158971	+	0.401514i	−0.828359	+	0.560198i	$0.810725\pi$
$228$	0.197553	+	1.56380i	0.0130833	+	0.103565i
$229$	5.65037	+	3.10632i	0.373387	+	0.205271i	0.657387	−	0.753553i	$-0.271662\pi$
$229$	5.65037	+	3.10632i	0.373387	+	0.205271i	−0.284000	+	0.958824i	$0.591662\pi$
$230$	1.58526	−	9.54958i	0.104529	−	0.629681i
$231$	0.790109	−	1.67907i	0.0519853	−	0.110474i
$232$	−1.98125	+	2.72696i	−0.130075	+	0.179034i
$233$	1.83271	−	14.5074i	0.120065	−	0.950412i	−0.810870	−	0.585227i	$-0.801006\pi$
$233$	1.83271	−	14.5074i	0.120065	−	0.950412i	0.930935	−	0.365186i	$-0.118994\pi$
$234$	−3.18283	+	0.817211i	−0.208068	+	0.0534227i
$235$	2.81134	+	2.85339i	0.183391	+	0.186135i
$236$	−5.04870	−	6.10283i	−0.328642	−	0.397260i
$237$	9.51167	+	7.86874i	0.617850	+	0.511130i
$238$	−5.29921	+	3.36298i	−0.343497	+	0.217990i
$239$	0.957751	+	15.2230i	0.0619517	+	0.984695i	0.899107	+	0.437729i	$0.144217\pi$
$239$	0.957751	+	15.2230i	0.0619517	+	0.984695i	−0.837155	+	0.546966i	$0.815783\pi$
$240$	2.22765	−	0.193901i	0.143794	−	0.0125163i
$241$	7.30229	−	8.82696i	0.470382	−	0.568594i	−0.480955	−	0.876745i	$-0.659710\pi$
$241$	7.30229	−	8.82696i	0.470382	−	0.568594i	0.951338	+	0.308151i	$0.0997101\pi$
$242$	10.1897	−	1.94379i	0.655019	−	0.124952i
$243$	−0.587785	−	0.809017i	−0.0377064	−	0.0518985i
$244$	6.06999	−	3.33701i	0.388591	−	0.213630i
$245$	2.67246	−	2.04138i	0.170737	−	0.130419i
$246$	−3.25774	+	0.411548i	−0.207706	+	0.0262393i
$247$	4.68662	−	2.20536i	0.298203	−	0.140324i
$248$	−1.69105	+	0.106392i	−0.107382	+	0.00675587i
$249$	−5.17343			−0.327853
$250$	−1.99446	+	11.0010i	−0.126141	+	0.695765i
$251$	−10.3001			−0.650139			−0.325070	−	0.945690i	$-0.605388\pi$
$251$	−10.3001			−0.650139			−0.325070	+	0.945690i	$0.605388\pi$
$252$	2.33974	−	0.147204i	0.147390	−	0.00927298i
$253$	−3.10059	+	1.45903i	−0.194933	+	0.0917283i
$254$	−1.05058	+	0.132719i	−0.0659191	+	0.00832752i
$255$	−1.71276	+	5.73606i	−0.107257	+	0.359206i
$256$	0.876307	−	0.481754i	0.0547692	−	0.0301096i
$257$	−12.6526	−	17.4149i	−0.789249	−	1.08631i	−0.994201	−	0.107536i	$-0.965704\pi$
$257$	−12.6526	−	17.4149i	−0.789249	−	1.08631i	0.204952	−	0.978772i	$-0.434296\pi$
$258$	4.31604	−	0.823329i	0.268705	−	0.0512582i
$259$	10.1502	−	12.2695i	0.630703	−	0.762389i
$260$	−2.86805	−	6.76501i	−0.177869	−	0.419548i
$261$	0.211648	+	3.36405i	0.0131007	+	0.208230i
$262$	10.8381	−	6.87809i	0.669582	−	0.424930i
$263$	15.7731	+	13.0487i	0.972612	+	0.804614i	0.980733	−	0.195353i	$-0.0625852\pi$
$263$	15.7731	+	13.0487i	0.972612	+	0.804614i	−0.00812151	+	0.999967i	$0.502585\pi$
$264$	−0.504551	−	0.609897i	−0.0310530	−	0.0375366i
$265$	−0.410845	+	0.205509i	−0.0252380	+	0.0126243i
$266$	−3.57916	+	0.918972i	−0.219452	+	0.0563458i
$267$	−2.16263	+	17.1190i	−0.132351	+	1.04766i
$268$	1.80899	−	2.48986i	0.110502	−	0.152093i
$269$	−10.2633	+	21.8106i	−0.625763	+	1.32981i	0.300805	+	0.953686i	$0.402745\pi$
$269$	−10.2633	+	21.8106i	−0.625763	+	1.32981i	−0.926568	+	0.376128i	$0.877255\pi$
$270$	1.59283	−	1.56936i	0.0969367	−	0.0955081i
$271$	12.3404	+	6.78419i	0.749625	+	0.412110i	0.810276	−	0.586049i	$-0.199317\pi$
$271$	12.3404	+	6.78419i	0.749625	+	0.412110i	−0.0606502	+	0.998159i	$0.519317\pi$
$272$	0.335537	+	2.65605i	0.0203449	+	0.161047i
$273$	−2.83594	−	7.16276i	−0.171639	−	0.433510i
$274$	−15.0983	+	10.9696i	−0.912121	+	0.662695i
$275$	3.60569	−	1.63177i	0.217431	−	0.0983994i
$276$	−3.50235	−	2.54461i	−0.210817	−	0.153167i
$277$	6.13863	−	23.9084i	0.368834	−	1.43651i	−0.465398	−	0.885102i	$-0.654089\pi$
$277$	6.13863	−	23.9084i	0.368834	−	1.43651i	0.834232	−	0.551413i	$-0.185911\pi$
$278$	−3.83442	−	4.08324i	−0.229973	−	0.244897i
$279$	−1.23516	+	1.15989i	−0.0739469	+	0.0694408i
$280$	1.10553	+	5.12426i	0.0660683	+	0.306233i
$281$	2.44776	+	0.309224i	0.146021	+	0.0184467i	0.198004	−	0.980201i	$-0.436554\pi$
$281$	2.44776	+	0.309224i	0.146021	+	0.0184467i	−0.0519829	+	0.998648i	$0.516554\pi$
$282$	1.70372	−	0.553571i	0.101455	−	0.0329647i
$283$	1.17829	+	2.14330i	0.0700420	+	0.127406i	0.909009	−	0.416776i	$-0.136840\pi$
$283$	1.17829	+	2.14330i	0.0700420	+	0.127406i	−0.838967	+	0.544182i	$0.816840\pi$
$284$	0.581306	−	9.23959i	0.0344941	−	0.548269i
$285$	−2.00268	+	2.90030i	−0.118628	+	0.171799i
$286$	−1.39373	+	2.19616i	−0.0824127	+	0.129862i
$287$	−1.91442	−	7.45619i	−0.113005	−	0.440125i
$288$	0.368125	−	0.929776i	0.0216919	−	0.0547876i
$289$	9.52389	+	2.44532i	0.560229	+	0.143842i
$290$	−7.36761	+	1.58952i	−0.432641	+	0.0933401i
$291$	−10.2037	−	4.03993i	−0.598151	−	0.236825i
$292$	−5.81224	−	2.73503i	−0.340136	−	0.160056i
$293$	−1.29163	−	0.419675i	−0.0754576	−	0.0245177i	0.271045	−	0.962567i	$-0.412631\pi$
$293$	−1.29163	−	0.419675i	−0.0754576	−	0.0245177i	−0.346503	+	0.938049i	$0.612631\pi$
$294$	−0.281811	−	1.47730i	−0.0164355	−	0.0861582i
$295$	0.687700	−	17.6974i	0.0400395	−	1.03038i
$296$	−2.89205	−	6.14591i	−0.168097	−	0.357224i
$297$	−0.777526	−	0.148321i	−0.0451167	−	0.00860646i
$298$	−17.6735	+	14.6208i	−1.02380	+	0.846958i
$299$	−4.39603	+	13.5296i	−0.254229	+	0.782436i
$300$	4.00101	+	2.99866i	0.230998	+	0.173128i
$301$	3.18314	+	9.79668i	0.183473	+	0.564671i
$302$	10.5526	+	6.69686i	0.607231	+	0.385361i
$303$	−2.74843	+	4.99937i	−0.157893	+	0.287206i
$304$	−0.295355	+	1.54831i	−0.0169398	+	0.0888015i
$305$	15.0903	+	3.49089i	0.864066	+	0.199888i
$306$	1.95157	+	1.83264i	0.111564	+	0.104765i
$307$		−	16.5452i		−	0.944282i	−0.881523	−	0.472141i	$-0.843481\pi$
$307$		−	16.5452i		−	0.944282i	0.881523	−	0.472141i	$-0.156519\pi$
$308$	1.27030	−	1.35273i	0.0723819	−	0.0770789i
$309$	3.63475	+	5.72745i	0.206774	+	0.325823i
$310$	−2.97640	−	2.34432i	−0.169048	−	0.133149i
$311$	22.1117	−	8.75466i	1.25384	−	0.496431i	0.355067	−	0.934841i	$-0.384458\pi$
$311$	22.1117	−	8.75466i	1.25384	−	0.496431i	0.898775	+	0.438410i	$0.144458\pi$
$312$	−3.27958	−	0.206334i	−0.185670	−	0.0116813i
$313$	−29.5592	−	1.85971i	−1.67079	−	0.105117i	−0.801038	−	0.598613i	$-0.795719\pi$
$313$	−29.5592	−	1.85971i	−1.67079	−	0.105117i	−0.869748	+	0.493496i	$0.835719\pi$
$314$	−6.56200	+	2.59808i	−0.370315	+	0.146618i
$315$	4.11816	+	3.24362i	0.232032	+	0.182757i
$316$	6.61456	+	10.4229i	0.372098	+	0.586333i
$317$	0.972495	−	1.03560i	0.0546208	−	0.0581652i	−0.701078	−	0.713085i	$-0.747297\pi$
$317$	0.972495	−	1.03560i	0.0546208	−	0.0581652i	0.755699	+	0.654919i	$0.227297\pi$
$318$			0.205440i			0.0115205i
$319$	1.94494	+	1.82642i	0.108896	+	0.102260i
$320$	2.17854	+	0.503969i	0.121784	+	0.0281727i
$321$	−0.453604	+	2.37788i	−0.0253177	+	0.132720i
$322$	4.88937	−	8.89373i	0.272474	−	0.495628i
$323$	−3.56290	−	2.26109i	−0.198245	−	0.125810i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	5.30868	−	15.5491i	0.294473	−	0.862507i
$326$	7.41370	−	22.8170i	0.410607	−	1.26372i
$327$	3.26350	−	2.69980i	0.180472	−	0.149299i
$328$	−3.22547	−	0.615291i	−0.178097	−	0.0339738i
$329$	1.78814	+	3.79999i	0.0985832	+	0.209500i
$330$	0.0687266	−	1.76862i	0.00378327	−	0.0973592i
$331$	2.93425	+	15.3819i	0.161281	+	0.845464i	0.967312	+	0.253591i	$0.0816116\pi$
$331$	2.93425	+	15.3819i	0.161281	+	0.845464i	−0.806031	+	0.591874i	$0.798388\pi$
$332$	−4.92022	−	1.59868i	−0.270032	−	0.0877388i
$333$	−6.14591	−	2.89205i	−0.336794	−	0.158483i
$334$	−0.405650	−	0.160608i	−0.0221962	−	0.00878809i
$335$	6.72704	−	1.45132i	0.367537	−	0.0792943i
$336$	2.27071	+	0.583020i	0.123878	+	0.0318064i
$337$	−13.1031	+	33.0947i	−0.713772	+	1.80278i	−0.128901	+	0.991657i	$0.541145\pi$
$337$	−13.1031	+	33.0947i	−0.713772	+	1.80278i	−0.584872	+	0.811126i	$0.698855\pi$
$338$	−0.547561	−	2.13261i	−0.0297834	−	0.115999i
$339$	−5.94993	+	9.37559i	−0.323156	+	0.509212i
$340$	−3.40147	+	4.92605i	−0.184471	+	0.267153i
$341$	−0.0842140	+	1.33854i	−0.00456044	+	0.0724861i
$342$	0.759353	+	1.38126i	0.0410611	+	0.0746898i
$343$	18.9606	−	6.16068i	1.02378	−	0.332645i
$344$	4.35922	+	0.550698i	0.235034	+	0.0296916i
$345$	−2.04150	−	9.46255i	−0.109910	−	0.509447i
$346$	−7.43613	+	6.98299i	−0.399769	+	0.375408i
$347$	−3.09932	−	3.30044i	−0.166380	−	0.177177i	0.640376	−	0.768062i	$-0.278779\pi$
$347$	−3.09932	−	3.30044i	−0.166380	−	0.177177i	−0.806756	+	0.590885i	$0.798779\pi$
$348$	−0.838260	+	3.26481i	−0.0449355	+	0.175012i
$349$	11.0969	+	8.06238i	0.594004	+	0.431570i	0.843746	−	0.536743i	$-0.180346\pi$
$349$	11.0969	+	8.06238i	0.594004	+	0.431570i	−0.249741	+	0.968313i	$0.580346\pi$
$350$	−5.79892	+	10.1870i	−0.309965	+	0.544515i
$351$	−2.65848	+	1.93150i	−0.141899	+	0.103096i
$352$	−0.291388	−	0.735962i	−0.0155310	−	0.0392269i
$353$	−0.107412	−	0.850253i	−0.00571696	−	0.0452544i	0.988998	−	0.147928i	$-0.0472603\pi$
$353$	−0.107412	−	0.850253i	−0.00571696	−	0.0452544i	−0.994715	+	0.102673i	$0.967260\pi$
$354$	−6.94076	−	3.81572i	−0.368897	−	0.202803i
$355$	14.7462	−	14.5289i	0.782648	−	0.771113i
$356$	−7.34684	+	15.6128i	−0.389382	+	0.827479i
$357$	−3.68909	+	5.07759i	−0.195247	+	0.268735i
$358$	−1.47198	+	11.6520i	−0.0777968	+	0.615825i
$359$	15.9175	−	4.08692i	0.840093	−	0.215699i	0.195959	−	0.980612i	$-0.437218\pi$
$359$	15.9175	−	4.08692i	0.840093	−	0.215699i	0.644134	+	0.764913i	$0.277218\pi$
$360$	1.99983	−	1.00034i	0.105400	−	0.0527223i
$361$	10.5274	+	12.7254i	0.554073	+	0.669759i
$362$	11.3654	+	9.40230i	0.597354	+	0.494174i
$363$	8.75860	−	5.55837i	0.459707	−	0.291739i
$364$	−0.483722	−	7.68854i	−0.0253539	−	0.402989i
$365$	−5.60646	−	13.2242i	−0.293455	−	0.692188i
$366$	4.41530	−	5.33718i	0.230792	−	0.278979i
$367$	9.88530	−	1.88572i	0.516009	−	0.0984339i	0.0772020	−	0.997015i	$-0.475401\pi$
$367$	9.88530	−	1.88572i	0.516009	−	0.0984339i	0.438807	+	0.898582i	$0.355401\pi$
$368$	−2.54461	−	3.50235i	−0.132647	−	0.182573i
$369$	−2.87747	+	1.58190i	−0.149795	+	0.0823505i
$370$	4.34552	−	14.5533i	0.225913	−	0.756588i
$371$	−0.477828	+	0.0603637i	−0.0248076	+	0.00313393i
$372$	−1.53313	+	0.721436i	−0.0794891	+	0.0374047i
$373$	−12.8135	+	0.806154i	−0.663455	+	0.0417411i	−0.390948	−	0.920413i	$-0.627853\pi$
$373$	−12.8135	+	0.806154i	−0.663455	+	0.0417411i	−0.272507	+	0.962154i	$0.587853\pi$
$374$	2.11910			0.109576
$375$	2.19534	+	10.9627i	0.113367	+	0.566111i
$376$	1.79139			0.0923840
$377$	11.0545	−	0.695490i	0.569336	−	0.0358196i
$378$	2.12125	−	0.998183i	0.109105	−	0.0513410i
$379$	15.4805	−	1.95565i	0.795182	−	0.100455i	0.282762	−	0.959190i	$-0.408749\pi$
$379$	15.4805	−	1.95565i	0.795182	−	0.100455i	0.512420	+	0.858735i	$0.328749\pi$
$380$	−2.80090	+	2.13949i	−0.143683	+	0.109753i
$381$	−0.927946	+	0.510143i	−0.0475401	+	0.0261354i
$382$	−11.9471	−	16.4438i	−0.611267	−	0.841337i
$383$	18.2263	−	3.47685i	0.931321	−	0.177659i	0.300672	−	0.953728i	$-0.402789\pi$
$383$	18.2263	−	3.47685i	0.931321	−	0.177659i	0.630649	+	0.776069i	$0.282789\pi$
$384$	0.637424	−	0.770513i	0.0325284	−	0.0393201i
$385$	4.13379	−	0.359818i	0.210677	−	0.0183380i
$386$	0.388012	+	6.16727i	0.0197493	+	0.313906i
$387$	3.70987	−	2.35435i	0.188583	−	0.119678i
$388$	−8.45589	−	6.99532i	−0.429283	−	0.355133i
$389$	13.1969	+	15.9523i	0.669109	+	0.808814i	0.990409	−	0.138163i	$-0.0441199\pi$
$389$	13.1969	+	15.9523i	0.669109	+	0.808814i	−0.321300	+	0.946977i	$0.604120\pi$
$390$	−5.15701	−	5.23415i	−0.261135	−	0.265041i
$391$	11.2257	−	2.88227i	0.567708	−	0.145763i
$392$	0.188494	−	1.49208i	0.00952039	−	0.0753617i
$393$	7.54505	−	10.3849i	0.380597	−	0.523847i
$394$	5.90817	−	12.5555i	0.297649	−	0.632537i
$395$	−4.52038	+	27.2307i	−0.227445	+	1.37013i
$396$	−0.693638	−	0.381331i	−0.0348566	−	0.0191626i
$397$	−0.187980	−	1.48801i	−0.00943444	−	0.0746813i	0.986695	−	0.162585i	$-0.0519832\pi$
$397$	−0.187980	−	1.48801i	−0.00943444	−	0.0746813i	−0.996129	+	0.0879038i	$0.971983\pi$
$398$	3.89667	+	9.84187i	0.195323	+	0.493328i
$399$	−2.98952	+	2.17201i	−0.149663	+	0.108737i
$400$	2.87855	+	4.08827i	0.143927	+	0.204414i
$401$	4.87241	+	3.54001i	0.243316	+	0.176780i	0.702760	−	0.711427i	$-0.251951\pi$
$401$	4.87241	+	3.54001i	0.243316	+	0.176780i	−0.459443	+	0.888207i	$0.651951\pi$
$402$	0.765378	−	2.98095i	0.0381736	−	0.148676i
$403$	3.81147	+	4.05880i	0.189863	+	0.202183i
$404$	−4.15880	+	3.90537i	−0.206908	+	0.194299i
$405$	0.903259	−	2.04551i	0.0448833	−	0.101642i
$406$	−7.83986	−	0.990405i	−0.389086	−	0.0491530i
$407$	−5.11333	+	1.66142i	−0.253458	+	0.0823536i
$408$	1.28973	+	2.34601i	0.0638513	+	0.116145i
$409$	1.68497	−	26.7818i	0.0833162	−	1.32427i	−0.705090	−	0.709118i	$-0.749093\pi$
$409$	1.68497	−	26.7818i	0.0833162	−	1.32427i	0.788406	−	0.615155i	$-0.210907\pi$
$410$	−4.45703	−	5.83490i	−0.220117	−	0.288165i
$411$	−9.99988	+	15.7573i	−0.493257	+	0.777249i
$412$	1.68697	+	6.57033i	0.0831112	+	0.323697i
$413$	6.83552	−	17.2646i	0.336354	−	0.849533i
$414$	−4.19314	−	1.07661i	−0.206082	−	0.0529127i
$415$	−5.81458	−	10.0006i	−0.285427	−	0.490911i
$416$	−3.05530	−	1.20968i	−0.149799	−	0.0593095i
$417$	−5.06829	−	2.38496i	−0.248195	−	0.116792i
$418$	1.18659	+	0.385547i	0.0580381	+	0.0188577i
$419$	−0.718558	−	3.76681i	−0.0351039	−	0.184021i	0.960417	−	0.278568i	$-0.0898597\pi$
$419$	−0.718558	−	3.76681i	−0.0351039	−	0.184021i	−0.995520	+	0.0945470i	$0.969860\pi$
$420$	2.91427	+	4.35745i	0.142202	+	0.212622i
$421$	6.35597	+	13.5071i	0.309771	+	0.658297i	0.997722	−	0.0674602i	$-0.0214896\pi$
$421$	6.35597	+	13.5071i	0.309771	+	0.658297i	−0.687951	+	0.725757i	$0.741490\pi$
$422$	14.6173	+	2.78840i	0.711558	+	0.135737i
$423$	1.38029	−	1.14188i	0.0671121	−	0.0555200i
$424$	−0.0634844	+	0.195385i	−0.00308307	+	0.00948872i
$425$	−13.0133	+	3.13606i	−0.631236	+	0.152121i
$426$	−2.86083	−	8.80474i	−0.138608	−	0.426591i
$427$	13.7110	+	8.70126i	0.663521	+	0.421083i
$428$	−1.16621	+	2.12132i	−0.0563708	+	0.102538i
$429$	−0.487393	+	2.55500i	−0.0235315	+	0.123357i
$430$	6.44250	+	7.41786i	0.310685	+	0.357721i
$431$	9.40826	+	8.83494i	0.453180	+	0.425564i	0.877227	−	0.480076i	$-0.159391\pi$
$431$	9.40826	+	8.83494i	0.453180	+	0.425564i	−0.424047	+	0.905640i	$0.639391\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−19.1894	+	20.4347i	−0.922185	+	0.982027i	−0.999888	−	0.0149495i	$-0.995241\pi$
$433$	−19.1894	+	20.4347i	−0.922185	+	0.982027i	0.0777035	+	0.996977i	$0.475241\pi$
$434$	−2.12845	−	3.35390i	−0.102169	−	0.160992i
$435$	−6.26509	+	4.19010i	−0.300388	+	0.200900i
$436$	3.93805	−	1.55919i	0.188599	−	0.0746715i
$437$	6.81025	+	0.428464i	0.325778	+	0.0204962i
$438$	−6.41092	−	0.403341i	−0.306326	−	0.0192724i
$439$	8.10737	−	3.20994i	0.386944	−	0.153202i	−0.166595	−	0.986025i	$-0.553277\pi$
$439$	8.10737	−	3.20994i	0.386944	−	0.153202i	0.553539	+	0.832824i	$0.313277\pi$
$440$	0.611896	−	1.66082i	0.0291710	−	0.0791764i
$441$	−0.805853	−	1.26982i	−0.0383740	−	0.0604677i
$442$	6.02218	−	6.41297i	0.286446	−	0.305034i
$443$		−	17.8694i		−	0.849001i	−0.905428	−	0.424501i	$-0.860450\pi$
$443$		−	17.8694i		−	0.849001i	0.905428	−	0.424501i	$-0.139550\pi$
$444$	−4.95142	−	4.64969i	−0.234984	−	0.220665i
$445$	−35.5229	+	15.0601i	−1.68395	+	0.713915i
$446$	0.0810055	−	0.424646i	0.00383572	−	0.0201076i
$447$	−11.0501	+	20.1001i	−0.522652	+	0.950701i
$448$	1.97941	+	1.25617i	0.0935185	+	0.0593487i
$449$	−2.91583	−	8.97399i	−0.137606	−	0.423509i	0.858380	−	0.513014i	$-0.171471\pi$
$449$	−2.91583	−	8.97399i	−0.137606	−	0.423509i	−0.995986	+	0.0895056i	$0.971471\pi$
$450$	4.82392	+	1.31521i	0.227402	+	0.0619997i
$451$	−0.803181	+	2.47194i	−0.0378203	+	0.116399i
$452$	−8.55594	+	7.07809i	−0.402437	+	0.332925i
$453$	12.2768	+	2.34192i	0.576814	+	0.110033i
$454$	2.77025	+	5.88709i	0.130014	+	0.276295i
$455$	10.6587	−	13.5325i	0.499689	−	0.634415i
$456$	0.295355	+	1.54831i	0.0138313	+	0.0725061i
$457$	−25.0968	−	8.15444i	−1.17398	−	0.381449i	−0.343852	−	0.939024i	$-0.611732\pi$
$457$	−25.0968	−	8.15444i	−1.17398	−	0.381449i	−0.830126	+	0.557575i	$0.811732\pi$
$458$	5.83427	+	2.74540i	0.272618	+	0.128284i
$459$	2.48916	+	0.985529i	0.116184	+	0.0460005i
$460$	0.982510	−	9.63028i	0.0458098	−	0.449014i
$461$	30.4881	+	7.82801i	1.41997	+	0.364587i	0.879148	−	0.476550i	$-0.158113\pi$
$461$	30.4881	+	7.82801i	1.41997	+	0.364587i	0.540823	+	0.841136i	$0.318113\pi$
$462$	0.683120	−	1.72536i	0.0317816	−	0.0802712i
$463$	4.65718	+	18.1385i	0.216437	+	0.842968i	0.980288	+	0.197575i	$0.0633064\pi$
$463$	4.65718	+	18.1385i	0.216437	+	0.842968i	−0.763851	+	0.645393i	$0.776694\pi$
$464$	−1.80611	+	2.84598i	−0.0838468	+	0.132121i
$465$	−3.63039	−	1.08401i	−0.168355	−	0.0502699i
$466$	0.918168	−	14.5939i	0.0425333	−	0.676048i
$467$	5.79530	+	10.5416i	0.268174	+	0.487807i	0.975767	−	0.218814i	$-0.0702186\pi$
$467$	5.79530	+	10.5416i	0.268174	+	0.487807i	−0.707592	+	0.706621i	$0.750219\pi$
$468$	−3.12523	+	1.01545i	−0.144464	+	0.0469392i
$469$	7.15823	+	0.904295i	0.330536	+	0.0417564i
$470$	2.98495	+	2.67123i	0.137686	+	0.123215i
$471$	−5.14477	+	4.83126i	−0.237059	+	0.222613i
$472$	−5.42194	−	5.77378i	−0.249565	−	0.265760i
$473$	0.864932	−	3.36869i	0.0397696	−	0.154892i
$474$	9.98699	+	7.25597i	0.458717	+	0.333278i
$475$	−7.85736	−	0.611581i	−0.360521	−	0.0280612i
$476$	−5.07759	+	3.68909i	−0.232731	+	0.169089i
$477$	0.0756274	+	0.191013i	0.00346274	+	0.00874588i
$478$	1.91172	+	15.1328i	0.0874401	+	0.692160i
$479$	29.2264	+	16.0673i	1.33539	+	0.734135i	0.979700	−	0.200470i	$-0.0642471\pi$
$479$	29.2264	+	16.0673i	1.33539	+	0.734135i	0.355687	+	0.934605i	$0.384247\pi$
$480$	2.21107	−	0.333394i	0.100921	−	0.0152173i
$481$	−9.50345	+	20.1959i	−0.433320	+	0.920852i
$482$	6.73364	−	9.26805i	0.306709	−	0.422148i
$483$	1.27202	−	10.0691i	0.0578789	−	0.458159i
$484$	10.0476	−	2.57977i	0.456707	−	0.117262i
$485$	−3.65878	−	24.2651i	−0.166137	−	1.10182i
$486$	−0.637424	−	0.770513i	−0.0289141	−	0.0349512i
$487$	−20.7623	−	17.1761i	−0.940830	−	0.778322i	0.0344246	−	0.999407i	$-0.489040\pi$
$487$	−20.7623	−	17.1761i	−0.940830	−	0.778322i	−0.975255	+	0.221085i	$0.929040\pi$
$488$	5.84848	−	3.71156i	0.264748	−	0.168014i
$489$	−1.50642	−	23.9439i	−0.0681228	−	1.08278i
$490$	2.53900	−	2.20515i	0.114700	−	0.0996186i
$491$	9.31617	−	11.2613i	0.420433	−	0.508216i	−0.517190	−	0.855871i	$-0.673022\pi$
$491$	9.31617	−	11.2613i	0.420433	−	0.508216i	0.937623	+	0.347655i	$0.113022\pi$
$492$	−3.22547	+	0.615291i	−0.145415	+	0.0277395i
$493$	−5.30413	−	7.30051i	−0.238886	−	0.328798i
$494$	4.53890	−	2.49528i	0.204215	−	0.112268i
$495$	−0.587171	−	1.66972i	−0.0263914	−	0.0750483i
$496$	−1.68103	+	0.212363i	−0.0754804	+	0.00953540i
$497$	19.6382	−	9.24103i	0.880893	−	0.414517i
$498$	−5.16322	+	0.324842i	−0.231369	+	0.0145565i
$499$	40.4736			1.81185			0.905924	−	0.423441i	$-0.139178\pi$
$499$	40.4736			1.81185			0.905924	+	0.423441i	$0.139178\pi$
$500$	−1.29977	+	11.1045i	−0.0581273	+	0.496610i
$501$	−0.436288			−0.0194919
$502$	−10.2798	+	0.646751i	−0.458811	+	0.0288659i
$503$	19.9210	−	9.37409i	0.888231	−	0.417970i	0.0731531	−	0.997321i	$-0.476694\pi$
$503$	19.9210	−	9.37409i	0.888231	−	0.417970i	0.815078	+	0.579351i	$0.196694\pi$
$504$	2.32588	−	0.293827i	0.103603	−	0.0130881i
$505$	−12.7532	+	0.306039i	−0.567510	+	0.0136186i
$506$	−3.00286	+	1.65084i	−0.133493	+	0.0733886i
$507$	−1.29418	−	1.78128i	−0.0574764	−	0.0791095i
$508$	−1.04017	+	0.198423i	−0.0461502	+	0.00880361i
$509$	14.9939	−	18.1246i	0.664595	−	0.803357i	−0.325232	−	0.945634i	$-0.605442\pi$
$509$	14.9939	−	18.1246i	0.664595	−	0.803357i	0.989827	+	0.142277i	$0.0454424\pi$
$510$	−1.34921	+	5.83229i	−0.0597439	+	0.258258i
$511$	−0.945579	−	15.0295i	−0.0418299	−	0.664868i
$512$	0.844328	−	0.535827i	0.0373144	−	0.0236804i
$513$	1.21450	+	1.00472i	0.0536216	+	0.0443597i
$514$	−13.7212	−	16.5860i	−0.605214	−	0.731578i
$515$	−6.98637	+	13.4635i	−0.307856	+	0.593273i
$516$	4.25583	−	1.09271i	0.187352	−	0.0481039i
$517$	0.177719	−	1.40679i	0.00781607	−	0.0618706i
$518$	9.35977	−	12.8826i	0.411245	−	0.566030i
$519$	−4.34333	+	9.23005i	−0.190651	+	0.405154i
$520$	−3.28717	−	6.57158i	−0.144152	−	0.288183i
$521$	0.0874594	+	0.0480812i	0.00383167	+	0.00210648i	0.483668	−	0.875251i	$-0.339304\pi$
$521$	0.0874594	+	0.0480812i	0.00383167	+	0.00210648i	−0.479837	+	0.877358i	$0.659304\pi$
$522$	0.422461	+	3.34413i	0.0184906	+	0.146368i
$523$	−2.65996	−	6.71830i	−0.116312	−	0.293771i	0.859945	−	0.510387i	$-0.170498\pi$
$523$	−2.65996	−	6.71830i	−0.116312	−	0.293771i	−0.976257	+	0.216616i	$0.930498\pi$
$524$	10.3849	−	7.54505i	0.453665	−	0.329607i
$525$	−1.64163	+	11.6063i	−0.0716465	+	0.506541i
$526$	16.5613	+	12.0325i	0.722108	+	0.524642i
$527$	1.12810	−	4.39364i	0.0491406	−	0.191390i
$528$	−0.541851	−	0.577013i	−0.0235810	−	0.0251113i
$529$	3.10431	−	2.91514i	0.134970	−	0.126745i
$530$	−0.397130	+	0.230900i	−0.0172502	+	0.0100297i
$531$	−7.85802	−	0.992699i	−0.341009	−	0.0430794i
$532$	−3.51439	+	1.14190i	−0.152368	+	0.0495075i
$533$	5.19823	+	9.45554i	0.225160	+	0.409565i
$534$	−1.08345	+	17.2210i	−0.0468856	+	0.745225i
$535$	−5.10643	+	1.79572i	−0.220770	+	0.0776358i
$536$	1.64908	−	2.59854i	0.0712295	−	0.112240i
$537$	2.92075	+	11.3756i	0.126040	+	0.490893i
$538$	−8.87353	+	22.4120i	−0.382565	+	0.966249i
$539$	−1.15304	−	0.296051i	−0.0496650	−	0.0127518i
$540$	1.49115	−	1.66628i	0.0641688	−	0.0717051i
$541$	−9.17921	−	3.63431i	−0.394645	−	0.156251i	0.162416	−	0.986722i	$-0.448071\pi$
$541$	−9.17921	−	3.63431i	−0.394645	−	0.156251i	−0.557061	+	0.830471i	$0.688071\pi$
$542$	12.7420	+	5.99594i	0.547317	+	0.257548i
$543$	14.0285	+	4.55814i	0.602022	+	0.195609i
$544$	0.501650	+	2.62974i	0.0215081	+	0.112749i
$545$	8.88686	+	3.27419i	0.380671	+	0.140251i
$546$	−3.28009	−	6.97055i	−0.140375	−	0.298312i
$547$	−6.67832	−	1.27396i	−0.285545	−	0.0544705i	0.0426192	−	0.999091i	$-0.486430\pi$
$547$	−6.67832	−	1.27396i	−0.285545	−	0.0544705i	−0.328164	+	0.944621i	$0.606430\pi$
$548$	−14.3797	+	11.8959i	−0.614271	+	0.508169i
$549$	2.14050	−	6.58777i	0.0913541	−	0.281159i
$550$	3.49611	−	1.85495i	0.149075	−	0.0790955i
$551$	−1.64181	−	5.05296i	−0.0699432	−	0.215263i
$552$	−3.65522	−	2.31967i	−0.155576	−	0.0987318i
$553$	−13.9421	+	25.3605i	−0.592877	+	1.07844i
$554$	4.62529	−	24.2466i	0.196510	−	1.03014i
$555$	−1.31705	−	15.1310i	−0.0559056	−	0.642274i
$556$	−4.08324	−	3.83442i	−0.173168	−	0.162616i
$557$		−	13.0012i		−	0.550877i	−0.961319	−	0.275439i	$-0.911177\pi$
$557$		−	13.0012i		−	0.550877i	0.961319	−	0.275439i	$-0.0888231\pi$
$558$	−1.15989	+	1.23516i	−0.0491020	+	0.0522884i
$559$	−7.73655	−	12.1909i	−0.327221	−	0.515618i
$560$	1.42511	+	5.04473i	0.0602218	+	0.213179i
$561$	1.97029	−	0.780092i	0.0831856	−	0.0329355i
$562$	2.46234	+	0.154917i	0.103868	+	0.00653480i
$563$	26.2066	+	1.64878i	1.10448	+	0.0694878i	0.604541	−	0.796574i	$-0.293357\pi$
$563$	26.2066	+	1.64878i	1.10448	+	0.0694878i	0.499937	+	0.866062i	$0.333357\pi$
$564$	1.66560	−	0.659456i	0.0701342	−	0.0277681i
$565$	−24.8110	−	0.964130i	−1.04381	−	0.0405612i
$566$	1.31054	+	2.06508i	0.0550862	+	0.0868020i
$567$	1.60483	−	1.70897i	0.0673965	−	0.0717700i
$568$		−	9.25786i		−	0.388451i
$569$	−0.896919	−	0.842263i	−0.0376008	−	0.0353095i	0.665519	−	0.746381i	$-0.268210\pi$
$569$	−0.896919	−	0.842263i	−0.0376008	−	0.0353095i	−0.703120	+	0.711071i	$0.748210\pi$
$570$	−1.81661	+	3.02032i	−0.0760895	+	0.126507i
$571$	−4.63446	+	24.2947i	−0.193946	+	1.01670i	0.743544	+	0.668687i	$0.233143\pi$
$571$	−4.63446	+	24.2947i	−0.193946	+	1.01670i	−0.937490	+	0.348013i	$0.886857\pi$
$572$	−1.25308	+	2.27934i	−0.0523938	+	0.0953039i
$573$	−17.1615	−	10.8910i	−0.716932	−	0.454979i
$574$	−2.37882	−	7.32127i	−0.0992902	−	0.305584i
$575$	15.9973	−	14.5816i	0.667134	−	0.608096i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	26.1849	−	21.6620i	1.09009	−	0.901802i	0.0944929	−	0.995526i	$-0.469877\pi$
$577$	26.1849	−	21.6620i	1.09009	−	0.901802i	0.995598	+	0.0937237i	$0.0298770\pi$
$578$	9.65864	+	1.84248i	0.401746	+	0.0766372i
$579$	2.63109	+	5.59135i	0.109344	+	0.232368i
$580$	−7.25327	+	2.04900i	−0.301175	+	0.0850803i
$581$	−2.27264	−	11.9136i	−0.0942849	−	0.494259i
$582$	−10.4372	−	3.39126i	−0.432637	−	0.140572i
$583$	0.147139	+	0.0692382i	0.00609386	+	0.00286755i
$584$	−5.97251	−	2.36468i	−0.247144	−	0.0978513i
$585$	−6.72169	−	2.96817i	−0.277908	−	0.122719i
$586$	−1.31543	−	0.337745i	−0.0543399	−	0.0139521i
$587$	−17.2684	+	43.6149i	−0.712742	+	1.80018i	−0.123299	+	0.992370i	$0.539347\pi$
$587$	−17.2684	+	43.6149i	−0.712742	+	1.80018i	−0.589442	+	0.807810i	$0.700653\pi$
$588$	−0.374016	−	1.45669i	−0.0154241	−	0.0600731i
$589$	1.43105	−	2.25498i	0.0589656	−	0.0929149i
$590$	−0.424883	−	17.7056i	−0.0174922	−	0.728929i
$591$	0.871290	−	13.8488i	0.0358401	−	0.569661i
$592$	−3.27225	−	5.95219i	−0.134488	−	0.244634i
$593$	−11.5828	+	3.76348i	−0.475649	+	0.154548i	−0.537024	−	0.843567i	$-0.680451\pi$
$593$	−11.5828	+	3.76348i	−0.475649	+	0.154548i	0.0613751	+	0.998115i	$0.480451\pi$
$594$	−0.785305	−	0.0992071i	−0.0322215	−	0.00407052i
$595$	−13.9616	−	1.42441i	−0.572372	−	0.0583951i
$596$	−16.7205	+	15.7016i	−0.684900	+	0.643164i
$597$	7.24607	+	7.71628i	0.296562	+	0.315806i
$598$	−3.53783	+	13.7789i	−0.144672	+	0.563462i
$599$	−17.0276	−	12.3713i	−0.695729	−	0.505477i	0.182809	−	0.983148i	$-0.441481\pi$
$599$	−17.0276	−	12.3713i	−0.695729	−	0.505477i	−0.878539	+	0.477672i	$0.841481\pi$
$600$	4.18140	+	2.74151i	0.170705	+	0.111922i
$601$	−37.4311	+	27.1953i	−1.52685	+	1.10932i	−0.568890	+	0.822414i	$0.692627\pi$
$601$	−37.4311	+	27.1953i	−1.52685	+	1.10932i	−0.957959	+	0.286907i	$0.907373\pi$
$602$	3.79199	+	9.57748i	0.154550	+	0.390349i
$603$	−0.385731	−	3.05337i	−0.0157082	−	0.124343i
$604$	10.9522	+	6.02104i	0.445640	+	0.244993i
$605$	20.5888	+	10.6838i	0.837055	+	0.434357i
$606$	−2.42909	+	5.16208i	−0.0986750	+	0.209695i
$607$	−15.3448	+	21.1204i	−0.622828	+	0.857249i	−0.997555	−	0.0698858i	$-0.977736\pi$
$607$	−15.3448	+	21.1204i	−0.622828	+	0.857249i	0.374727	+	0.927135i	$0.377736\pi$
$608$	−0.197553	+	1.56380i	−0.00801185	+	0.0634203i
$609$	−7.65391	+	1.96519i	−0.310152	+	0.0796335i
$610$	15.2797	+	2.53648i	0.618656	+	0.102699i
$611$	−3.75228	−	4.53573i	−0.151801	−	0.183496i
$612$	2.06279	+	1.70649i	0.0833833	+	0.0689806i
$613$	22.5727	−	14.3250i	0.911701	−	0.578583i	0.00482846	−	0.999988i	$-0.498463\pi$
$613$	22.5727	−	14.3250i	0.911701	−	0.578583i	0.906872	+	0.421405i	$0.138463\pi$
$614$	−1.03888	−	16.5125i	−0.0419257	−	0.666390i
$615$	−6.29201	−	3.78441i	−0.253718	−	0.152602i
$616$	1.18285	−	1.42982i	0.0476585	−	0.0576092i
$617$	29.4475	−	5.61741i	1.18551	−	0.226148i	0.443337	−	0.896355i	$-0.353795\pi$
$617$	29.4475	−	5.61741i	1.18551	−	0.226148i	0.742174	+	0.670207i	$0.233795\pi$
$618$	3.98721	+	5.48792i	0.160389	+	0.220756i
$619$	−35.7631	+	19.6609i	−1.43744	+	0.790240i	−0.994341	−	0.106233i	$-0.966121\pi$
$619$	−35.7631	+	19.6609i	−1.43744	+	0.790240i	−0.443099	+	0.896472i	$0.646121\pi$
$620$	−3.11772	−	2.15281i	−0.125211	−	0.0864589i
$621$	−4.29501	+	0.542586i	−0.172353	+	0.0217732i
$622$	21.5184	−	10.1258i	0.862809	−	0.406007i
$623$	−40.3723	+	2.54001i	−1.61748	+	0.101763i
$624$	−3.28606			−0.131548
$625$	−18.7243	+	16.5651i	−0.748971	+	0.662603i
$626$	−29.6177			−1.18376
$627$	1.24519	−	0.0783410i	0.0497283	−	0.00312864i
$628$	−6.38591	+	3.00498i	−0.254826	+	0.119912i
$629$	18.0409	−	2.27909i	0.719336	−	0.0908733i
$630$	4.31370	+	2.97864i	0.171862	+	0.118672i
$631$	−22.8027	+	12.5359i	−0.907760	+	0.499045i	−0.865978	−	0.500082i	$-0.833303\pi$
$631$	−22.8027	+	12.5359i	−0.907760	+	0.499045i	−0.0417814	+	0.999127i	$0.513303\pi$
$632$	7.25597	+	9.98699i	0.288627	+	0.397261i
$633$	14.6173	−	2.78840i	0.580985	−	0.110829i
$634$	0.905550	−	1.09462i	0.0359640	−	0.0434730i
$635$	−2.02909	−	1.22042i	−0.0805221	−	0.0484310i
$636$	0.0128997	+	0.205034i	0.000511505	+	0.00813014i
$637$	−4.17271	+	2.64809i	−0.165329	+	0.104921i
$638$	2.05578	+	1.70069i	0.0813893	+	0.0673311i
$639$	−5.90118	−	7.13330i	−0.233447	−	0.282189i
$640$	2.20588	+	0.366183i	0.0871951	+	0.0144747i
$641$	−45.3699	+	11.6490i	−1.79200	+	0.460108i	−0.990457	−	0.137825i	$-0.955989\pi$
$641$	−45.3699	+	11.6490i	−1.79200	+	0.460108i	−0.801546	+	0.597933i	$0.795989\pi$
$642$	−0.303401	+	2.40167i	−0.0119743	+	0.0947863i
$643$	−7.02219	+	9.66522i	−0.276928	+	0.381159i	−0.924713	−	0.380664i	$-0.875695\pi$
$643$	−7.02219	+	9.66522i	−0.276928	+	0.381159i	0.647785	+	0.761823i	$0.275695\pi$
$644$	4.32128	−	9.18319i	0.170282	−	0.361868i
$645$	8.72078	+	4.52532i	0.343380	+	0.178184i
$646$	−3.69785	−	2.03291i	−0.145490	−	0.0799838i
$647$	0.349370	+	2.76555i	0.0137351	+	0.108725i	0.997492	−	0.0707825i	$-0.0225496\pi$
$647$	0.349370	+	2.76555i	0.0137351	+	0.108725i	−0.983757	+	0.179507i	$0.942550\pi$
$648$	−0.368125	−	0.929776i	−0.0144613	−	0.0365251i
$649$	−5.07207	+	3.68508i	−0.199096	+	0.144652i
$650$	4.32187	−	15.8517i	0.169518	−	0.621755i
$651$	−3.21364	−	2.33484i	−0.125952	−	0.0915097i
$652$	5.96638	−	23.2375i	0.233661	−	0.910051i
$653$	28.2216	+	30.0530i	1.10440	+	1.17606i	0.983028	+	0.183457i	$0.0587288\pi$
$653$	28.2216	+	30.0530i	1.10440	+	1.17606i	0.121370	+	0.992607i	$0.461271\pi$
$654$	3.08754	−	2.89939i	0.120732	−	0.113375i
$655$	28.5548	+	2.91325i	1.11573	+	0.113830i
$656$	−3.25774	−	0.411548i	−0.127193	−	0.0160683i
$657$	−6.10920	+	1.98500i	−0.238343	+	0.0774422i
$658$	2.02321	+	3.68021i	0.0788730	+	0.143470i
$659$	1.34152	−	21.3229i	0.0522583	−	0.830622i	−0.881381	−	0.472407i	$-0.843385\pi$
$659$	1.34152	−	21.3229i	0.0522583	−	0.830622i	0.933639	−	0.358215i	$-0.116615\pi$
$660$	−0.0424615	−	1.76944i	−0.00165281	−	0.0688755i
$661$	−17.7556	+	27.9784i	−0.690613	+	1.08823i	0.300315	+	0.953840i	$0.402908\pi$
$661$	−17.7556	+	27.9784i	−0.690613	+	1.08823i	−0.990928	+	0.134392i	$0.957092\pi$
$662$	3.89429	+	15.1673i	0.151356	+	0.589493i
$663$	3.23851	−	8.17954i	0.125773	−	0.317667i
$664$	−5.01089	−	1.28658i	−0.194460	−	0.0499289i
$665$	−7.55868	−	3.33777i	−0.293113	−	0.129433i
$666$	−6.31538	−	2.50044i	−0.244716	−	0.0968899i
$667$	13.2035	+	6.21309i	0.511241	+	0.240572i
$668$	−0.414934	−	0.134820i	−0.0160543	−	0.00521636i
$669$	−0.0810055	−	0.424646i	−0.00313186	−	0.0164178i
$670$	6.62264	−	1.87085i	0.255855	−	0.0722774i
$671$	−2.33450	−	4.96106i	−0.0901223	−	0.191520i
$672$	2.30284	+	0.439291i	0.0888340	+	0.0169460i
$673$	4.27816	−	3.53920i	0.164911	−	0.136426i	−0.551308	−	0.834302i	$-0.685871\pi$
$673$	4.27816	−	3.53920i	0.164911	−	0.136426i	0.716219	+	0.697876i	$0.245871\pi$
$674$	−10.9992	+	33.8522i	−0.423675	+	1.30394i
$675$	4.96933	−	0.552951i	0.191270	−	0.0212831i
$676$	−0.680389	−	2.09402i	−0.0261688	−	0.0805393i
$677$	−15.0121	−	9.52696i	−0.576962	−	0.366151i	0.215100	−	0.976592i	$-0.430992\pi$
$677$	−15.0121	−	9.52696i	−0.576962	−	0.366151i	−0.792062	+	0.610441i	$0.790992\pi$
$678$	−5.34949	+	9.73069i	−0.205446	+	0.373705i
$679$	4.82093	−	25.2722i	0.185010	−	0.969858i
$680$	−3.08545	+	5.12991i	−0.118322	+	0.196723i
$681$	4.74290	+	4.45388i	0.181748	+	0.170673i
$682$			1.34119i			0.0513568i
$683$	3.58530	−	3.81796i	0.137188	−	0.146090i	−0.656706	−	0.754147i	$-0.728051\pi$
$683$	3.58530	−	3.81796i	0.137188	−	0.146090i	0.793894	+	0.608057i	$0.208051\pi$
$684$	0.844584	+	1.33085i	0.0322935	+	0.0508864i
$685$	−41.6992	−	1.62038i	−1.59324	−	0.0619117i
$686$	18.5364	−	7.33907i	0.707722	−	0.280207i
$687$	6.43522	+	0.404870i	0.245519	+	0.0154467i
$688$	4.38520	+	0.275893i	0.167184	+	0.0105183i
$689$	0.627681	−	0.248516i	0.0239127	−	0.00946772i
$690$	−2.63163	−	9.31569i	−0.100184	−	0.354642i
$691$	−23.3439	−	36.7841i	−0.888043	−	1.39933i	−0.916628	−	0.399740i	$-0.869100\pi$
$691$	−23.3439	−	36.7841i	−0.888043	−	1.39933i	0.0285855	−	0.999591i	$-0.490900\pi$
$692$	−6.98299	+	7.43613i	−0.265454	+	0.282679i
$693$		−	1.85568i		−	0.0704913i
$694$	−3.30044	−	3.09932i	−0.125283	−	0.117649i
$695$	−1.08612	−	12.4779i	−0.0411988	−	0.473315i
$696$	−0.631607	+	3.31100i	−0.0239410	+	0.125503i
$697$	4.23501	−	7.70345i	0.160412	−	0.291789i
$698$	11.5813	+	7.34969i	0.438357	+	0.278190i
$699$	−4.51867	−	13.9070i	−0.170912	−	0.526012i
$700$	−5.14783	+	10.5310i	−0.194570	+	0.398033i
$701$	8.23575	−	25.3470i	0.311060	−	0.957344i	−0.666286	−	0.745696i	$-0.732117\pi$
$701$	8.23575	−	25.3470i	0.311060	−	0.957344i	0.977346	−	0.211648i	$-0.0678829\pi$
$702$	−2.53196	+	2.09462i	−0.0955625	+	0.0790562i
$703$	10.5167	+	2.00616i	0.396643	+	0.0756638i
$704$	−0.337024	−	0.716213i	−0.0127021	−	0.0269933i
$705$	3.75869	+	1.38481i	0.141560	+	0.0521551i
$706$	−0.160588	−	0.841831i	−0.00604380	−	0.0316827i
$707$	−12.7201	−	4.13301i	−0.478389	−	0.155438i
$708$	−7.16666	−	3.37237i	−0.269340	−	0.126742i
$709$	14.9797	+	5.93087i	0.562573	+	0.222738i	0.632160	−	0.774837i	$-0.282168\pi$
$709$	14.9797	+	5.93087i	0.562573	+	0.222738i	−0.0695876	+	0.997576i	$0.522168\pi$
$710$	13.8048	−	15.4261i	0.518086	−	0.578933i
$711$	11.9568	+	3.06998i	0.448414	+	0.115133i
$712$	−6.35201	+	16.0433i	−0.238052	+	0.601249i
$713$	1.82421	+	7.10481i	0.0683170	+	0.266077i
$714$	−3.36298	+	5.29921i	−0.125856	+	0.198318i
$715$	−5.48680	+	1.92948i	−0.205195	+	0.0721586i
$716$	−0.737447	+	11.7214i	−0.0275597	+	0.438049i
$717$	7.34824	+	13.3664i	0.274425	+	0.499177i
$718$	15.6295	−	5.07832i	0.583286	−	0.189521i
$719$	−27.6748	−	3.49614i	−1.03210	−	0.130384i	−0.409004	−	0.912533i	$-0.634124\pi$
$719$	−27.6748	−	3.49614i	−1.03210	−	0.130384i	−0.623092	+	0.782149i	$0.714124\pi$
$720$	1.93307	−	1.12393i	0.0720414	−	0.0418865i
$721$	−11.5927	+	10.8863i	−0.431735	+	0.405426i
$722$	11.3056	+	12.0393i	0.420753	+	0.448056i
$723$	2.84898	−	11.0960i	0.105955	−	0.412666i
$724$	11.9334	+	8.67010i	0.443500	+	0.322222i
$725$	−15.1413	−	7.40149i	−0.562334	−	0.274885i
$726$	8.39230	−	6.09736i	0.311467	−	0.226294i
$727$	6.20501	+	15.6721i	0.230131	+	0.581245i	0.998255	−	0.0590568i	$-0.0188093\pi$
$727$	6.20501	+	15.6721i	0.230131	+	0.581245i	−0.768123	+	0.640302i	$0.778809\pi$
$728$	−0.965535	−	7.64299i	−0.0357851	−	0.283268i
$729$	−0.876307	−	0.481754i	−0.0324558	−	0.0178427i
$730$	−6.42575	−	12.8461i	−0.237828	−	0.475456i
$731$	−5.00848	+	10.6436i	−0.185245	+	0.393667i
$732$	4.07147	−	5.60389i	0.150486	−	0.207126i
$733$	0.200366	−	1.58606i	0.00740069	−	0.0585825i	−0.987982	−	0.154570i	$-0.950601\pi$
$733$	0.200366	−	1.58606i	0.00740069	−	0.0585825i	0.995383	+	0.0959874i	$0.0306008\pi$
$734$	9.74739	−	2.50270i	0.359783	−	0.0923765i
$735$	1.54894	−	2.98497i	0.0571333	−	0.110102i
$736$	−2.75950	−	3.33566i	−0.101717	−	0.122954i
$737$	−1.87705	−	1.55283i	−0.0691419	−	0.0571991i
$738$	−2.77246	+	1.75946i	−0.102056	+	0.0647665i
$739$	−3.19356	−	50.7602i	−0.117477	−	1.86724i	−0.411452	−	0.911431i	$-0.634978\pi$
$739$	−3.19356	−	50.7602i	−0.117477	−	1.86724i	0.293975	−	0.955813i	$-0.405022\pi$
$740$	3.42314	−	14.7974i	0.125837	−	0.543963i
$741$	3.30159	−	3.99093i	0.121287	−	0.146611i
$742$	−0.473095	+	0.0902477i	−0.0173679	+	0.00331310i
$743$	−18.1548	−	24.9879i	−0.666034	−	0.916717i	0.333629	−	0.942705i	$-0.391727\pi$
$743$	−18.1548	−	24.9879i	−0.666034	−	0.916717i	−0.999662	+	0.0259879i	$0.991727\pi$
$744$	−1.48481	+	0.816279i	−0.0544356	+	0.0299262i
$745$	−51.2745	+	1.23044i	−1.87855	+	0.0450798i
$746$	−12.7375	+	1.60913i	−0.466355	+	0.0589143i
$747$	−4.68106	+	2.20274i	−0.171271	+	0.0805940i
$748$	2.11492	−	0.133059i	0.0773290	−	0.00486513i
$749$	−5.67514			−0.207365
$750$	2.87936	+	10.8032i	0.105139	+	0.394477i
$751$	−43.6357			−1.59229			−0.796145	−	0.605106i	$-0.793131\pi$
$751$	−43.6357			−1.59229			−0.796145	+	0.605106i	$0.793131\pi$
$752$	1.78786	−	0.112482i	0.0651965	−	0.00410181i
$753$	−9.31984	+	4.38559i	−0.339634	+	0.159820i
$754$	10.9890	−	1.38824i	0.400196	−	0.0505565i
$755$	9.27117	+	26.3641i	0.337413	+	0.959489i
$756$	2.05438	−	1.12941i	0.0747172	−	0.0410761i
$757$	−2.25315	−	3.10119i	−0.0818920	−	0.112715i	0.766106	−	0.642715i	$-0.222192\pi$
$757$	−2.25315	−	3.10119i	−0.0818920	−	0.112715i	−0.847998	+	0.530000i	$0.822192\pi$
$758$	15.3272	−	2.92382i	0.556709	−	0.106198i
$759$	−2.18428	+	2.64034i	−0.0792842	+	0.0958381i
$760$	−2.66103	+	2.31114i	−0.0965258	+	0.0838337i
$761$	1.15018	+	18.2815i	0.0416938	+	0.662704i	0.962262	+	0.272123i	$0.0877258\pi$
$761$	1.15018	+	18.2815i	0.0416938	+	0.662704i	−0.920569	+	0.390581i	$0.872274\pi$
$762$	−0.894083	+	0.567402i	−0.0323892	+	0.0205548i
$763$	7.65084	+	6.32932i	0.276979	+	0.229137i
$764$	−12.9561	−	15.6612i	−0.468733	−	0.566601i
$765$	0.892549	+	5.91940i	0.0322702	+	0.214016i
$766$	17.9720	−	4.61443i	0.649356	−	0.166726i
$767$	−3.26207	+	25.8220i	−0.117787	+	0.932377i
$768$	0.587785	−	0.809017i	0.0212099	−	0.0291929i
$769$	−6.64700	+	14.1256i	−0.239697	+	0.509382i	−0.988091	−	0.153873i	$-0.950825\pi$
$769$	−6.64700	+	14.1256i	−0.239697	+	0.509382i	0.748394	+	0.663255i	$0.230825\pi$
$770$	4.10304	−	0.618671i	0.147863	−	0.0222953i
$771$	−18.8633	−	10.3702i	−0.679346	−	0.373474i
$772$	0.774492	+	6.13074i	0.0278746	+	0.220650i
$773$	−10.1757	−	25.7008i	−0.365993	−	0.924394i	−0.989755	−	0.142779i	$-0.954396\pi$
$773$	−10.1757	−	25.7008i	−0.365993	−	0.924394i	0.623761	−	0.781615i	$-0.285604\pi$
$774$	3.55472	−	2.58265i	0.127772	−	0.0928315i
$775$	−1.98483	−	8.23616i	−0.0712972	−	0.295852i
$776$	−8.87844	−	6.45056i	−0.318717	−	0.231562i
$777$	3.96009	−	15.4235i	0.142067	−	0.553316i
$778$	14.1725	+	15.0922i	0.508109	+	0.541081i
$779$	3.77296	−	3.54304i	0.135180	−	0.126943i
$780$	−5.47549	−	4.90001i	−0.196054	−	0.175449i
$781$	−7.27024	−	0.918445i	−0.260150	−	0.0328646i
$782$	11.0226	−	3.58145i	0.394167	−	0.128072i
$783$	1.62385	+	2.95377i	0.0580317	+	0.105559i
$784$	0.0944334	−	1.50098i	0.00337262	−	0.0536063i
$785$	−15.1216	−	4.51522i	−0.539712	−	0.161155i
$786$	6.87809	−	10.8381i	0.245333	−	0.386583i
$787$	−1.43472	−	5.58787i	−0.0511423	−	0.199186i	0.937878	−	0.346965i	$-0.112788\pi$
$787$	−1.43472	−	5.58787i	−0.0511423	−	0.199186i	−0.989020	+	0.147779i	$0.952788\pi$
$788$	5.10814	−	12.9017i	0.181970	−	0.459604i
$789$	19.8278	+	5.09091i	0.705888	+	0.181241i
$790$	−2.80163	+	27.4608i	−0.0996777	+	0.977012i
$791$	−24.2043	−	9.58314i	−0.860604	−	0.340737i
$792$	−0.716213	−	0.337024i	−0.0254495	−	0.0119756i
$793$	−21.6478	−	7.03381i	−0.768737	−	0.249778i
$794$	−0.281042	−	1.47327i	−0.00997381	−	0.0522845i
$795$	−0.284242	+	0.360879i	−0.0100810	+	0.0127991i
$796$	4.50696	+	9.57778i	0.159745	+	0.339475i
$797$	−34.2092	−	6.52575i	−1.21175	−	0.231154i	−0.458384	−	0.888754i	$-0.651572\pi$
$797$	−34.2092	−	6.52575i	−1.21175	−	0.231154i	−0.753367	+	0.657600i	$0.771572\pi$
$798$	−2.84724	+	2.35544i	−0.100791	+	0.0833817i
$799$	−1.48200	+	4.56112i	−0.0524293	+	0.161361i
$800$	3.12957	+	3.89946i	0.110647	+	0.137867i
$801$	5.33210	+	16.4105i	0.188401	+	0.579837i
$802$	5.08507	+	3.22708i	0.179560	+	0.113952i
$803$	−2.44951	+	4.45565i	−0.0864415	+	0.157236i
$804$	0.576693	−	3.02313i	0.0203384	−	0.106618i
$805$	20.8939	−	8.85805i	0.736415	−	0.312205i
$806$	4.05880	+	3.81147i	0.142965	+	0.134253i
$807$			24.1047i			0.848525i
$808$	−3.90537	+	4.15880i	−0.137390	+	0.146306i
$809$	−11.7057	−	18.4452i	−0.411549	−	0.648497i	0.573810	−	0.818988i	$-0.305465\pi$
$809$	−11.7057	−	18.4452i	−0.411549	−	0.648497i	−0.985359	+	0.170491i	$0.945465\pi$
$810$	0.773038	−	2.09819i	0.0271618	−	0.0737230i
$811$	48.1290	−	19.0556i	1.69004	−	0.669133i	0.691459	−	0.722416i	$-0.256968\pi$
$811$	48.1290	−	19.0556i	1.69004	−	0.669133i	0.998579	+	0.0532826i	$0.0169684\pi$
$812$	−7.88658	−	0.496181i	−0.276765	−	0.0174126i
$813$	14.0545	+	0.884233i	0.492912	+	0.0310114i
$814$	−4.99892	+	1.97921i	−0.175212	+	0.0693714i
$815$	44.5922	−	29.8233i	1.56200	−	1.04467i
$816$	1.43449	+	2.26040i	0.0502174	+	0.0791299i
$817$	−4.74099	+	5.04864i	−0.165866	+	0.176630i
$818$		−	26.8347i		−	0.938254i
$819$	−5.61578	−	5.27357i	−0.196231	−	0.184274i
$820$	−4.81461	−	5.54353i	−0.168134	−	0.193588i
$821$	10.1705	−	53.3158i	0.354954	−	1.86073i	−0.137653	−	0.990481i	$-0.543956\pi$
$821$	10.1705	−	53.3158i	0.354954	−	1.86073i	0.492607	−	0.870252i	$-0.336044\pi$
$822$	−8.99074	+	16.3541i	−0.313588	+	0.570414i
$823$	−21.5514	−	13.6769i	−0.751234	−	0.476748i	0.104266	−	0.994549i	$-0.466751\pi$
$823$	−21.5514	−	13.6769i	−0.751234	−	0.476748i	−0.855501	+	0.517802i	$0.826751\pi$
$824$	2.09620	+	6.45143i	0.0730245	+	0.224746i
$825$	2.56775	−	3.01170i	0.0893976	−	0.104854i
$826$	5.73798	−	17.6597i	0.199650	−	0.614459i
$827$	−35.2306	+	29.1453i	−1.22509	+	1.01348i	−0.225861	+	0.974159i	$0.572520\pi$
$827$	−35.2306	+	29.1453i	−1.22509	+	1.01348i	−0.999227	+	0.0393214i	$0.987480\pi$
$828$	−4.25247	−	0.811201i	−0.147783	−	0.0281912i
$829$	−9.29596	−	19.7549i	−0.322862	−	0.686117i	0.675840	−	0.737048i	$-0.263781\pi$
$829$	−9.29596	−	19.7549i	−0.322862	−	0.686117i	−0.998702	+	0.0509316i	$0.983781\pi$
$830$	−6.43105	−	9.61578i	−0.223225	−	0.333769i
$831$	−4.62529	−	24.2466i	−0.160450	−	0.841107i
$832$	−3.12523	−	1.01545i	−0.108348	−	0.0352044i
$833$	3.64311	+	1.71432i	0.126226	+	0.0593975i
$834$	−5.20805	−	2.06201i	−0.180340	−	0.0714016i
$835$	−0.490358	−	0.843377i	−0.0169695	−	0.0291863i
$836$	1.20846	+	0.310280i	0.0417954	+	0.0107312i
$837$	−0.623746	+	1.57540i	−0.0215598	+	0.0544539i
$838$	−0.953660	−	3.71426i	−0.0329436	−	0.128307i
$839$	0.0624642	−	0.0984278i	0.00215650	−	0.00339811i	−0.843248	−	0.537525i	$-0.819359\pi$
$839$	0.0624642	−	0.0984278i	0.00215650	−	0.00339811i	0.845404	+	0.534127i	$0.179359\pi$
$840$	3.18212	+	4.16586i	0.109794	+	0.143736i
$841$	−1.10752	+	17.6035i	−0.0381904	+	0.607019i
$842$	7.19155	+	13.0814i	0.247837	+	0.450814i
$843$	2.34646	−	0.762410i	0.0808163	−	0.0262588i
$844$	14.7635	+	1.86507i	0.508182	+	0.0641983i
$845$	1.98878	−	4.50378i	0.0684162	−	0.154935i
$846$	1.30587	−	1.22629i	0.0448967	−	0.0421608i
$847$	16.6476	+	17.7279i	0.572019	+	0.609139i
$848$	−0.0510908	+	0.198985i	−0.00175446	+	0.00683319i
$849$	1.97872	+	1.43762i	0.0679095	+	0.0493391i
$850$	−12.7907	+	3.94698i	−0.438716	+	0.135380i
$851$	−23.7893	+	17.2839i	−0.815485	+	0.592485i
$852$	−3.40804	−	8.60774i	−0.116758	−	0.294896i
$853$	3.24737	+	25.7055i	0.111188	+	0.880141i	0.944767	+	0.327742i	$0.106288\pi$
$853$	3.24737	+	25.7055i	0.111188	+	0.880141i	−0.833580	+	0.552399i	$0.813712\pi$
$854$	14.2303	+	7.82317i	0.486951	+	0.267703i
$855$	−0.577188	+	3.47697i	−0.0197394	+	0.118910i
$856$	−1.03071	+	2.19037i	−0.0352289	+	0.0748651i
$857$	−10.0823	+	13.8771i	−0.344405	+	0.474032i	−0.945721	−	0.324978i	$-0.894643\pi$
$857$	−10.0823	+	13.8771i	−0.344405	+	0.474032i	0.601317	+	0.799011i	$0.294643\pi$
$858$	−0.326001	+	2.58056i	−0.0111295	+	0.0880990i
$859$	−47.0207	+	12.0729i	−1.60433	+	0.411921i	−0.941543	−	0.336892i	$-0.890624\pi$
$859$	−47.0207	+	12.0729i	−1.60433	+	0.411921i	−0.662782	+	0.748812i	$0.730624\pi$
$860$	6.89555	+	6.99870i	0.235136	+	0.238654i
$861$	−4.90691	−	5.93144i	−0.167227	−	0.202143i
$862$	9.94444	+	8.22676i	0.338709	+	0.280204i
$863$	20.8620	−	13.2394i	0.710149	−	0.450674i	−0.131067	−	0.991374i	$-0.541840\pi$
$863$	20.8620	−	13.2394i	0.710149	−	0.450674i	0.841216	+	0.540699i	$0.181840\pi$
$864$	−0.0627905	−	0.998027i	−0.00213618	−	0.0339536i
$865$	−22.7240	+	1.97797i	−0.772638	+	0.0672529i
$866$	−17.8685	+	21.5992i	−0.607195	+	0.733972i
$867$	9.65864	−	1.84248i	0.328025	−	0.0625740i
$868$	−2.33484	−	3.21364i	−0.0792497	−	0.109078i
$869$	8.56268	−	4.70737i	0.290469	−	0.159687i
$870$	−5.98963	+	4.57522i	−0.203067	+	0.155115i
$871$	−10.0336	+	1.26754i	−0.339975	+	0.0429488i
$872$	3.83238	−	1.80338i	0.129781	−	0.0610702i
$873$	−10.9527	+	0.689085i	−0.370693	+	0.0233220i
$874$	6.82371			0.230816
$875$	−24.2809	+	9.87132i	−0.820846	+	0.333711i
$876$	−6.42359			−0.217033
$877$	21.1690	−	1.33184i	0.714827	−	0.0449731i	0.298788	−	0.954320i	$-0.403418\pi$
$877$	21.1690	−	1.33184i	0.714827	−	0.0449731i	0.416040	+	0.909347i	$0.363418\pi$
$878$	7.88982	−	3.71267i	0.266269	−	0.125296i
$879$	−1.34739	+	0.170215i	−0.0454462	+	0.00574119i
$880$	0.506405	−	1.69596i	0.0170709	−	0.0571709i
$881$	7.45881	−	4.10051i	0.251294	−	0.138150i	−0.351129	−	0.936327i	$-0.614202\pi$
$881$	7.45881	−	4.10051i	0.251294	−	0.138150i	0.602423	+	0.798177i	$0.294202\pi$
$882$	−0.883996	−	1.21672i	−0.0297657	−	0.0409690i
$883$	51.5899	−	9.84129i	1.73614	−	0.331186i	0.780372	−	0.625316i	$-0.215030\pi$
$883$	51.5899	−	9.84129i	1.73614	−	0.331186i	0.955766	+	0.294130i	$0.0950298\pi$
$884$	5.60762	−	6.77845i	0.188605	−	0.227984i
$885$	−6.91292	−	16.3059i	−0.232375	−	0.548115i
$886$	−1.12203	−	17.8341i	−0.0376953	−	0.599150i
$887$	−44.7109	+	28.3744i	−1.50124	+	0.952719i	−0.505281	+	0.862955i	$0.668611\pi$
$887$	−44.7109	+	28.3744i	−1.50124	+	0.952719i	−0.995963	+	0.0897641i	$0.971389\pi$
$888$	−5.23361	−	4.32962i	−0.175628	−	0.145292i
$889$	−1.58242	−	1.91281i	−0.0530725	−	0.0641536i
$890$	−34.5072	+	17.2608i	−1.15668	+	0.578585i
$891$	−0.766679	+	0.196850i	−0.0256847	+	0.00659471i
$892$	0.0541820	−	0.428894i	0.00181415	−	0.0143604i
$893$	−1.65969	+	2.28437i	−0.0555395	+	0.0764436i
$894$	−9.76621	+	20.7543i	−0.326631	+	0.694126i
$895$	−18.7071	+	18.4314i	−0.625310	+	0.616094i
$896$	2.05438	+	1.12941i	0.0686322	+	0.0377309i
$897$	1.78297	+	14.1137i	0.0595317	+	0.471242i
$898$	−3.47355	−	8.77320i	−0.115914	−	0.292765i
$899$	4.62053	−	3.35701i	0.154103	−	0.111963i
$900$	4.89699	+	1.00972i	0.163233	+	0.0336573i
$901$	−0.444955	−	0.323279i	−0.0148236	−	0.0107700i
$902$	−0.646382	+	2.51749i	−0.0215222	+	0.0838233i
$903$	7.05141	+	7.50899i	0.234656	+	0.249884i
$904$	−8.09462	+	7.60135i	−0.269223	+	0.252817i
$905$	6.95588	+	32.2412i	0.231221	+	1.07173i
$906$	12.3996	+	1.56644i	0.411950	+	0.0520414i
$907$	−7.08922	+	2.30343i	−0.235394	+	0.0764841i	−0.424338	−	0.905504i	$-0.639493\pi$
$907$	−7.08922	+	2.30343i	−0.235394	+	0.0764841i	0.188945	+	0.981988i	$0.439493\pi$
$908$	3.13444	+	5.70153i	0.104020	+	0.189212i
$909$	−0.358223	+	5.69378i	−0.0118815	+	0.188851i
$910$	9.78799	−	14.1751i	0.324469	−	0.469900i
$911$	7.37171	−	11.6160i	0.244236	−	0.384854i	−0.699990	−	0.714153i	$-0.746812\pi$
$911$	7.37171	−	11.6160i	0.244236	−	0.384854i	0.944226	+	0.329299i	$0.106812\pi$
$912$	0.391991	+	1.52671i	0.0129801	+	0.0505543i
$913$	−1.50747	+	3.80744i	−0.0498901	+	0.126008i
$914$	−25.5593	−	6.56251i	−0.845426	−	0.217069i
$915$	15.1404	−	3.26647i	0.500527	−	0.107986i
$916$	5.99514	+	2.37365i	0.198085	+	0.0784274i
$917$	27.2292	+	12.8131i	0.899187	+	0.423125i
$918$	2.54613	+	0.827288i	0.0840349	+	0.0273046i
$919$	−4.95518	−	25.9760i	−0.163456	−	0.856869i	−0.965658	−	0.259816i	$-0.916338\pi$
$919$	−4.95518	−	25.9760i	−0.163456	−	0.856869i	0.802202	−	0.597053i	$-0.203662\pi$
$920$	0.375881	−	9.67297i	0.0123924	−	0.318908i
$921$	−7.04458	−	14.9705i	−0.232127	−	0.493295i
$922$	30.9194	+	5.89820i	1.01828	+	0.194247i
$923$	−23.4405	+	19.3917i	−0.771553	+	0.638284i
$924$	0.573436	−	1.76485i	0.0188646	−	0.0580594i
$925$	27.7690	−	19.5521i	0.913040	−	0.642870i
$926$	5.78691	+	17.8103i	0.190170	+	0.585282i
$927$	5.72745	+	3.63475i	0.188114	+	0.119381i
$928$	−1.62385	+	2.95377i	−0.0533055	+	0.0969623i
$929$	−10.3302	+	54.1530i	−0.338924	+	1.77670i	0.249727	+	0.968316i	$0.419659\pi$
$929$	−10.3302	+	54.1530i	−0.338924	+	1.77670i	−0.588651	+	0.808387i	$0.700341\pi$
$930$	−3.69129	−	0.853920i	−0.121042	−	0.0280011i
$931$	1.72806	+	1.62276i	0.0566349	+	0.0531837i
$932$		−	14.6227i		−	0.478983i
$933$	16.2797	−	17.3362i	0.532975	−	0.567561i
$934$	6.44577	+	10.1569i	0.210912	+	0.332344i
$935$	3.72245	+	2.93194i	0.121737	+	0.0958848i
$936$	−3.05530	+	1.20968i	−0.0998658	+	0.0395397i
$937$	7.45215	+	0.468850i	0.243451	+	0.0153166i	0.184047	−	0.982917i	$-0.441080\pi$
$937$	7.45215	+	0.468850i	0.243451	+	0.0153166i	0.0594038	+	0.998234i	$0.481080\pi$
$938$	7.20088	+	0.453041i	0.235117	+	0.0147923i
$939$	−27.5378	+	10.9030i	−0.898662	+	0.355806i
$940$	3.14679	+	2.47854i	0.102637	+	0.0808409i
$941$	12.8298	+	20.2166i	0.418241	+	0.659042i	0.986491	−	0.163813i	$-0.0523795\pi$
$941$	12.8298	+	20.2166i	0.418241	+	0.659042i	−0.568250	+	0.822856i	$0.692379\pi$
$942$	−4.83126	+	5.14477i	−0.157411	+	0.167626i
$943$			14.2153i			0.462915i
$944$	−5.77378	−	5.42194i	−0.187920	−	0.176469i
$945$	5.10729	+	1.18149i	0.166140	+	0.0384338i
$946$	0.651704	−	3.41635i	0.0211887	−	0.111075i
$947$	−10.8949	+	19.8178i	−0.354037	+	0.643991i	−0.992023	−	0.126057i	$-0.959768\pi$
$947$	−10.8949	+	19.8178i	−0.354037	+	0.643991i	0.637986	+	0.770048i	$0.279768\pi$
$948$	10.4229	+	6.61456i	0.338520	+	0.214831i
$949$	6.52284	+	20.0752i	0.211740	+	0.651669i
$950$	−7.88026	−	0.117006i	−0.255669	−	0.00379618i
$951$	0.439002	−	1.35111i	0.0142356	−	0.0438127i
$952$	−4.83593	+	4.00063i	−0.156733	+	0.129661i
$953$	−21.1731	−	4.03899i	−0.685865	−	0.130836i	−0.167341	−	0.985899i	$-0.553518\pi$
$953$	−21.1731	−	4.03899i	−0.685865	−	0.130836i	−0.518524	+	0.855063i	$0.673518\pi$
$954$	0.0874720	+	0.185887i	0.00283201	+	0.00601833i
$955$	1.76479	−	45.4152i	0.0571072	−	1.46960i
$956$	2.85815	+	14.9829i	0.0924391	+	0.484583i
$957$	2.53749	+	0.824479i	0.0820253	+	0.0266516i
$958$	30.1776	+	14.2005i	0.974993	+	0.458797i
$959$	−40.6794	−	16.1061i	−1.31361	−	0.520093i
$960$	2.18578	−	0.471570i	0.0705457	−	0.0152199i
$961$	−27.2453	−	6.99541i	−0.878881	−	0.225658i
$962$	−8.21659	+	20.7527i	−0.264914	+	0.669095i
$963$	0.602017	+	2.34470i	0.0193997	+	0.0755570i
$964$	6.13840	−	9.67257i	0.197705	−	0.311533i
$965$	−7.85132	+	11.3704i	−0.252743	+	0.366026i
$966$	0.637268	−	10.1291i	0.0205038	−	0.325898i
$967$	0.502789	+	0.914570i	0.0161686	+	0.0294106i	0.884268	−	0.466981i	$-0.154658\pi$
$967$	0.502789	+	0.914570i	0.0161686	+	0.0294106i	−0.868099	+	0.496391i	$0.834658\pi$
$968$	9.86574	−	3.20557i	0.317097	−	0.103031i
$969$	−4.18654	−	0.528883i	−0.134491	−	0.0169902i
$970$	−5.17518	−	23.9875i	−0.166165	−	0.770192i
$971$	−8.57144	+	8.04912i	−0.275071	+	0.258309i	−0.809788	−	0.586722i	$-0.800418\pi$
$971$	−8.57144	+	8.04912i	−0.275071	+	0.258309i	0.534718	+	0.845031i	$0.320418\pi$
$972$	−0.684547	−	0.728969i	−0.0219569	−	0.0233817i
$973$	3.26573	−	12.7192i	0.104694	−	0.407758i
$974$	−21.7998	−	15.8385i	−0.698512	−	0.507498i
$975$	−1.81703	−	16.3295i	−0.0581916	−	0.522964i
$976$	5.60389	−	4.07147i	0.179376	−	0.130324i
$977$	−10.2129	−	25.7948i	−0.326738	−	0.825247i	−0.996572	−	0.0827355i	$-0.973634\pi$
$977$	−10.2129	−	25.7948i	−0.326738	−	0.825247i	0.669833	−	0.742512i	$-0.266366\pi$
$978$	−3.00690	−	23.8021i	−0.0961501	−	0.761106i
$979$	11.9688	+	6.57988i	0.382523	+	0.210294i
$980$	2.39553	−	2.36023i	0.0765224	−	0.0753946i
$981$	1.80338	−	3.83238i	0.0575775	−	0.122359i
$982$	8.59069	−	11.8241i	0.274140	−	0.377321i
$983$	−4.86981	+	38.5485i	−0.155323	+	1.22951i	0.701036	+	0.713126i	$0.252721\pi$
$983$	−4.86981	+	38.5485i	−0.155323	+	1.22951i	−0.856359	+	0.516381i	$0.827279\pi$
$984$	−3.18047	+	0.816606i	−0.101390	+	0.0260324i
$985$	27.7499	−	13.8808i	0.884186	−	0.442279i
$986$	−5.75206	−	6.95305i	−0.183183	−	0.221430i
$987$	3.23591	+	2.67698i	0.103000	+	0.0852092i
$988$	4.37326	−	2.77536i	0.139132	−	0.0882959i
$989$	−1.19438	−	18.9842i	−0.0379792	−	0.603662i
$990$	−0.690855	−	1.62956i	−0.0219568	−	0.0517907i
$991$	33.4068	−	40.3819i	1.06120	−	1.28277i	0.103620	−	0.994617i	$-0.466958\pi$
$991$	33.4068	−	40.3819i	1.06120	−	1.28277i	0.957583	−	0.288157i	$-0.0930424\pi$
$992$	−1.66438	+	0.317497i	−0.0528440	+	0.0100805i
$993$	9.20427	+	12.6686i	0.292089	+	0.402026i
$994$	19.0192	−	10.4559i	0.603252	−	0.331641i
$995$	−6.77205	+	22.6798i	−0.214688	+	0.718997i
$996$	−5.13263	+	0.648402i	−0.162634	+	0.0205454i
$997$	4.75740	−	2.23866i	0.150668	−	0.0708992i	−0.348967	−	0.937135i	$-0.613467\pi$
$997$	4.75740	−	2.23866i	0.150668	−	0.0708992i	0.499635	+	0.866236i	$0.333467\pi$
$998$	40.3937	−	2.54136i	1.27864	−	0.0804453i
$999$	−6.79236			−0.214901

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.b.469.14	yes	280
125.4	even	50	inner	750.2.o.b.379.14	✓	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.b.379.14	✓	280	125.4	even	50	inner
750.2.o.b.469.14	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)

\(f(q)\)	\(=\)	\(q+(0.998027 - 0.0627905i) q^{2} +(0.904827 - 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.84003 + 1.27055i) q^{5} +(0.876307 - 0.481754i) q^{6} +(1.37798 + 1.89663i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})\)	\(q+(0.998027 - 0.0627905i) q^{2} +(0.904827 - 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(1.84003 + 1.27055i) q^{5} +(0.876307 - 0.481754i) q^{6} +(1.37798 + 1.89663i) q^{7} +(0.982287 - 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(1.91617 + 1.15251i) q^{10} +(-0.0497016 - 0.789985i) q^{11} +(0.844328 - 0.535827i) q^{12} +(-2.53196 - 2.09462i) q^{13} +(1.49436 + 1.80637i) q^{14} +(2.20588 + 0.366183i) q^{15} +(0.968583 - 0.248690i) q^{16} +(-0.335537 + 2.65605i) q^{17} +(0.587785 - 0.809017i) q^{18} +(-0.671124 + 1.42621i) q^{19} +(1.98476 + 1.02992i) q^{20} +(2.05438 + 1.12941i) q^{21} +(-0.0992071 - 0.785305i) q^{22} +(-1.59367 - 4.02514i) q^{23} +(0.809017 - 0.587785i) q^{24} +(1.77140 + 4.67570i) q^{25} +(-2.65848 - 1.93150i) q^{26} +(0.248690 - 0.968583i) q^{27} +(1.60483 + 1.70897i) q^{28} +(-2.45714 + 2.30741i) q^{29} +(2.22452 + 0.226952i) q^{30} +(-1.68103 - 0.212363i) q^{31} +(0.951057 - 0.309017i) q^{32} +(-0.381331 - 0.693638i) q^{33} +(-0.168100 + 2.67188i) q^{34} +(0.125760 + 5.24066i) q^{35} +(0.535827 - 0.844328i) q^{36} +(-1.68919 - 6.57897i) q^{37} +(-0.580247 + 1.46554i) q^{38} +(-3.18283 - 0.817211i) q^{39} +(2.04551 + 0.903259i) q^{40} +(-3.05304 - 1.20879i) q^{41} +(2.12125 + 0.998183i) q^{42} +(4.17882 + 1.35778i) q^{43} +(-0.148321 - 0.777526i) q^{44} +(2.15185 - 0.607886i) q^{45} +(-1.84326 - 3.91713i) q^{46} +(1.75966 + 0.335674i) q^{47} +(0.770513 - 0.637424i) q^{48} +(0.464744 - 1.43034i) q^{49} +(2.06149 + 4.55524i) q^{50} +(0.827288 + 2.54613i) q^{51} +(-2.77452 - 1.76076i) q^{52} +(-0.0989713 + 0.180028i) q^{53} +(0.187381 - 0.982287i) q^{54} +(0.912264 - 1.51674i) q^{55} +(1.70897 + 1.60483i) q^{56} +1.57623i q^{57} +(-2.30741 + 2.45714i) q^{58} +(-4.24400 - 6.68748i) q^{59} +(2.23438 + 0.0868256i) q^{60} +(6.44037 - 2.54992i) q^{61} +(-1.69105 - 0.106392i) q^{62} +(2.33974 + 0.147204i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-1.99755 - 7.07113i) q^{65} +(-0.424132 - 0.668325i) q^{66} +(2.10679 - 2.24350i) q^{67} +2.67716i q^{68} +(-3.15581 - 2.96350i) q^{69} +(0.454576 + 5.22242i) q^{70} +(1.73475 - 9.09387i) q^{71} +(0.481754 - 0.876307i) q^{72} +(-5.42362 - 3.44193i) q^{73} +(-2.09896 - 6.45992i) q^{74} +(3.59363 + 3.47647i) q^{75} +(-0.487081 + 1.49908i) q^{76} +(1.42982 - 1.18285i) q^{77} +(-3.22786 - 0.615747i) q^{78} +(5.25607 + 11.1697i) q^{79} +(2.09819 + 0.773038i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(-3.12292 - 1.01470i) q^{82} +(-4.68106 - 2.20274i) q^{83} +(2.17974 + 0.863019i) q^{84} +(-3.99205 + 4.46089i) q^{85} +(4.25583 + 1.09271i) q^{86} +(-1.24084 + 3.13400i) q^{87} +(-0.196850 - 0.766679i) q^{88} +(-9.24572 + 14.5689i) q^{89} +(2.10944 - 0.741802i) q^{90} +(0.483722 - 7.68854i) q^{91} +(-2.08558 - 3.79366i) q^{92} +(-1.61146 + 0.523595i) q^{93} +(1.77727 + 0.224521i) q^{94} +(-3.04696 + 1.77157i) q^{95} +(0.728969 - 0.684547i) q^{96} +(-7.51246 - 7.99996i) q^{97} +(0.374016 - 1.45669i) q^{98} +(-0.640375 - 0.465260i) 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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