LMFDB - Embedded newform 960.2.cn.a.731.90

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(11,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8, 0]))

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

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

chi := DirichletCharacter("960.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.cn (of order $16$, degree $8$, 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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$128$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			731.90
Character	$\chi$	$=$	960.731
Dual form			960.2.cn.a.851.90

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.834066 - 1.14207i) q^{2} +(-0.116737 + 1.72811i) q^{3} +(-0.608666 - 1.90513i) q^{4} +(-0.980785 - 0.195090i) q^{5} +(1.87627 + 1.57468i) q^{6} +(-0.720445 - 0.298418i) q^{7} +(-2.68347 - 0.893864i) q^{8} +(-2.97274 - 0.403470i) q^{9} +O(q^{10})$	\(q+(0.834066 - 1.14207i) q^{2} +(-0.116737 + 1.72811i) q^{3} +(-0.608666 - 1.90513i) q^{4} +(-0.980785 - 0.195090i) q^{5} +(1.87627 + 1.57468i) q^{6} +(-0.720445 - 0.298418i) q^{7} +(-2.68347 - 0.893864i) q^{8} +(-2.97274 - 0.403470i) q^{9} +(-1.04085 + 0.957411i) q^{10} +(0.148890 - 0.0994854i) q^{11} +(3.36334 - 0.829444i) q^{12} +(0.940359 + 4.72750i) q^{13} +(-0.941715 + 0.573901i) q^{14} +(0.451632 - 1.67213i) q^{15} +(-3.25905 + 2.31918i) q^{16} +(0.808181 + 0.808181i) q^{17} +(-2.94026 + 3.05857i) q^{18} +(1.23490 + 6.20826i) q^{19} +(0.225298 + 1.98727i) q^{20} +(0.599803 - 1.21017i) q^{21} +(0.0105648 - 0.253021i) q^{22} +(-7.96433 + 3.29893i) q^{23} +(1.85796 - 4.53299i) q^{24} +(0.923880 + 0.382683i) q^{25} +(6.18348 + 2.86909i) q^{26} +(1.04427 - 5.09014i) q^{27} +(-0.130015 + 1.55418i) q^{28} +(-1.45040 + 2.17068i) q^{29} +(-1.53301 - 1.91047i) q^{30} +4.51094 q^{31} +(-0.0695920 + 5.65643i) q^{32} +(0.154541 + 0.268913i) q^{33} +(1.59708 - 0.248926i) q^{34} +(0.648384 + 0.433236i) q^{35} +(1.04075 + 5.90905i) q^{36} +(1.39564 + 0.277609i) q^{37} +(8.12028 + 3.76776i) q^{38} +(-8.27943 + 1.07317i) q^{39} +(2.45752 + 1.40021i) q^{40} +(0.198093 + 0.478238i) q^{41} +(-0.881833 - 1.69439i) q^{42} +(-1.37852 + 0.921099i) q^{43} +(-0.280157 - 0.223102i) q^{44} +(2.83691 + 0.975671i) q^{45} +(-2.87515 + 11.8474i) q^{46} +(-7.68827 + 7.68827i) q^{47} +(-3.62735 - 5.90274i) q^{48} +(-4.51976 - 4.51976i) q^{49} +(1.20763 - 0.735955i) q^{50} +(-1.49097 + 1.30228i) q^{51} +(8.43415 - 4.66898i) q^{52} +(0.142450 + 0.213192i) q^{53} +(-4.94232 - 5.43815i) q^{54} +(-0.165438 + 0.0685267i) q^{55} +(1.66655 + 1.44478i) q^{56} +(-10.8727 + 1.40931i) q^{57} +(1.26935 + 3.46696i) q^{58} +(0.0352382 - 0.177154i) q^{59} +(-3.46053 + 0.157352i) q^{60} +(0.464167 - 0.694675i) q^{61} +(3.76243 - 5.15183i) q^{62} +(2.02130 + 1.17780i) q^{63} +(6.40201 + 4.79731i) q^{64} -4.82012i q^{65} +(0.436016 + 0.0477942i) q^{66} +(-3.79345 - 2.53470i) q^{67} +(1.04778 - 2.03160i) q^{68} +(-4.77119 - 14.1484i) q^{69} +(1.03558 - 0.379155i) q^{70} +(-2.73285 + 6.59768i) q^{71} +(7.61662 + 3.73993i) q^{72} +(-0.219349 - 0.529556i) q^{73} +(1.48110 - 1.36238i) q^{74} +(-0.769171 + 1.55189i) q^{75} +(11.0759 - 6.13141i) q^{76} +(-0.136956 + 0.0272422i) q^{77} +(-5.67996 + 10.3508i) q^{78} +(0.529782 - 0.529782i) q^{79} +(3.64888 - 1.63881i) q^{80} +(8.67442 + 2.39883i) q^{81} +(0.711406 + 0.172646i) q^{82} +(-3.70815 + 0.737596i) q^{83} +(-2.67062 - 0.406111i) q^{84} +(-0.634984 - 0.950320i) q^{85} +(-0.0978158 + 2.34263i) q^{86} +(-3.58187 - 2.75986i) q^{87} +(-0.488469 + 0.133878i) q^{88} +(5.62039 - 13.5688i) q^{89} +(3.48046 - 2.42619i) q^{90} +(0.733296 - 3.68653i) q^{91} +(11.1325 + 13.1651i) q^{92} +(-0.526595 + 7.79542i) q^{93} +(2.36804 + 15.1931i) q^{94} -6.32989i q^{95} +(-9.76682 - 0.780578i) q^{96} -4.37891i q^{97} +(-8.93168 + 1.39212i) q^{98} +(-0.482753 + 0.235672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) $ 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{9}{16}\right)$

Coefficient data

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

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

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

$2$	0.834066	−	1.14207i	0.589774	−	0.807568i
$2$	0.834066	−	1.14207i	0.589774	−	0.807568i
$3$	−0.116737	+	1.72811i	−0.0673982	+	0.997726i
$3$	−0.116737	+	1.72811i	−0.0673982	+	0.997726i
$4$	−0.608666	−	1.90513i	−0.304333	−	0.952566i
$5$	−0.980785	−	0.195090i	−0.438621	−	0.0872470i
$5$	−0.980785	−	0.195090i	−0.438621	−	0.0872470i
$6$	1.87627	+	1.57468i	0.765982	+	0.642862i
$7$	−0.720445	−	0.298418i	−0.272303	−	0.112792i	0.242354	−	0.970188i	$-0.422081\pi$
$7$	−0.720445	−	0.298418i	−0.272303	−	0.112792i	−0.514657	+	0.857396i	$0.672081\pi$
$8$	−2.68347	−	0.893864i	−0.948750	−	0.316029i
$9$	−2.97274	−	0.403470i	−0.990915	−	0.134490i
$10$	−1.04085	+	0.957411i	−0.329145	+	0.302760i
$11$	0.148890	−	0.0994854i	0.0448922	−	0.0299960i	−0.532922	−	0.846165i	$-0.678906\pi$
$11$	0.148890	−	0.0994854i	0.0448922	−	0.0299960i	0.577814	+	0.816169i	$0.303906\pi$
$12$	3.36334	−	0.829444i	0.970911	−	0.239440i
$13$	0.940359	+	4.72750i	0.260809	+	1.31117i	0.859888	+	0.510484i	$0.170534\pi$
$13$	0.940359	+	4.72750i	0.260809	+	1.31117i	−0.599079	+	0.800690i	$0.704466\pi$
$14$	−0.941715	+	0.573901i	−0.251684	+	0.153382i
$15$	0.451632	−	1.67213i	0.116611	−	0.431743i
$16$	−3.25905	+	2.31918i	−0.814763	+	0.579795i
$17$	0.808181	+	0.808181i	0.196013	+	0.196013i	0.798288	−	0.602276i	$-0.205739\pi$
$17$	0.808181	+	0.808181i	0.196013	+	0.196013i	−0.602276	+	0.798288i	$0.705739\pi$
$18$	−2.94026	+	3.05857i	−0.693026	+	0.720913i
$19$	1.23490	+	6.20826i	0.283306	+	1.42427i	0.816042	+	0.577992i	$0.196164\pi$
$19$	1.23490	+	6.20826i	0.283306	+	1.42427i	−0.532737	+	0.846281i	$0.678836\pi$
$20$	0.225298	+	1.98727i	0.0503782	+	0.444367i
$21$	0.599803	−	1.21017i	0.130888	−	0.264082i
$22$	0.0105648	−	0.253021i	0.00225243	−	0.0539443i
$23$	−7.96433	+	3.29893i	−1.66068	+	0.687875i	−0.998129	−	0.0611447i	$-0.980525\pi$
$23$	−7.96433	+	3.29893i	−1.66068	+	0.687875i	−0.662548	+	0.749020i	$0.730525\pi$
$24$	1.85796	−	4.53299i	0.379254	−	0.925293i
$25$	0.923880	+	0.382683i	0.184776	+	0.0765367i
$26$	6.18348	+	2.86909i	1.21268	+	0.562675i
$27$	1.04427	−	5.09014i	0.200970	−	0.979597i
$28$	−0.130015	+	1.55418i	−0.0245706	+	0.293712i
$29$	−1.45040	+	2.17068i	−0.269333	+	0.403086i	−0.941340	−	0.337459i	$-0.890433\pi$
$29$	−1.45040	+	2.17068i	−0.269333	+	0.403086i	0.672007	+	0.740545i	$0.265433\pi$
$30$	−1.53301	−	1.91047i	−0.279888	−	0.348802i
$31$	4.51094			0.810190			0.405095	−	0.914275i	$-0.367239\pi$
$31$	4.51094			0.810190			0.405095	+	0.914275i	$0.367239\pi$
$32$	−0.0695920	+	5.65643i	−0.0123022	+	0.999924i
$33$	0.154541	+	0.268913i	0.0269021	+	0.0468118i
$34$	1.59708	−	0.248926i	0.273897	−	0.0426904i
$35$	0.648384	+	0.433236i	0.109597	+	0.0732303i
$36$	1.04075	+	5.90905i	0.173458	+	0.984841i
$37$	1.39564	+	0.277609i	0.229441	+	0.0456387i	0.308472	−	0.951233i	$-0.400182\pi$
$37$	1.39564	+	0.277609i	0.229441	+	0.0456387i	−0.0790305	+	0.996872i	$0.525182\pi$
$38$	8.12028	+	3.76776i	1.31728	+	0.611211i
$39$	−8.27943	+	1.07317i	−1.32577	+	0.171845i
$40$	2.45752	+	1.40021i	0.388568	+	0.221392i
$41$	0.198093	+	0.478238i	0.0309369	+	0.0746882i	0.938593	−	0.345027i	$-0.112130\pi$
$41$	0.198093	+	0.478238i	0.0309369	+	0.0746882i	−0.907656	+	0.419715i	$0.862130\pi$
$42$	−0.881833	−	1.69439i	−0.136070	−	0.261449i
$43$	−1.37852	+	0.921099i	−0.210223	+	0.140466i	−0.656224	−	0.754566i	$-0.727848\pi$
$43$	−1.37852	+	0.921099i	−0.210223	+	0.140466i	0.446002	+	0.895032i	$0.352848\pi$
$44$	−0.280157	−	0.223102i	−0.0422353	−	0.0336340i
$45$	2.83691	+	0.975671i	0.422902	+	0.145444i
$46$	−2.87515	+	11.8474i	−0.423918	+	1.74680i
$47$	−7.68827	+	7.68827i	−1.12145	+	1.12145i	−0.129925	+	0.991524i	$0.541474\pi$
$47$	−7.68827	+	7.68827i	−1.12145	+	1.12145i	−0.991524	+	0.129925i	$0.958526\pi$
$48$	−3.62735	−	5.90274i	−0.523563	−	0.851987i
$49$	−4.51976	−	4.51976i	−0.645680	−	0.645680i
$50$	1.20763	−	0.735955i	0.170785	−	0.104080i
$51$	−1.49097	+	1.30228i	−0.208778	+	0.182356i
$52$	8.43415	−	4.66898i	1.16961	−	0.647471i
$53$	0.142450	+	0.213192i	0.0195671	+	0.0292842i	0.841124	−	0.540842i	$-0.181894\pi$
$53$	0.142450	+	0.213192i	0.0195671	+	0.0292842i	−0.821557	+	0.570126i	$0.806894\pi$
$54$	−4.94232	−	5.43815i	−0.672565	−	0.740038i
$55$	−0.165438	+	0.0685267i	−0.0223077	+	0.00924014i
$56$	1.66655	+	1.44478i	0.222702	+	0.193066i
$57$	−10.8727	+	1.40931i	−1.44013	+	0.186668i
$58$	1.26935	+	3.46696i	0.166673	+	0.455235i
$59$	0.0352382	−	0.177154i	0.00458762	−	0.0230635i	−0.978424	−	0.206609i	$-0.933757\pi$
$59$	0.0352382	−	0.177154i	0.00458762	−	0.0230635i	0.983011	+	0.183545i	$0.0587573\pi$
$60$	−3.46053	+	0.157352i	−0.446752	+	0.0203141i
$61$	0.464167	−	0.694675i	0.0594305	−	0.0889440i	−0.800564	−	0.599247i	$-0.795467\pi$
$61$	0.464167	−	0.694675i	0.0594305	−	0.0889440i	0.859995	+	0.510303i	$0.170467\pi$
$62$	3.76243	−	5.15183i	0.477829	−	0.654283i
$63$	2.02130	+	1.17780i	0.254660	+	0.148389i
$64$	6.40201	+	4.79731i	0.800252	+	0.599664i
$65$		−	4.82012i		−	0.597862i
$66$	0.436016	+	0.0477942i	0.0536699	+	0.00588306i
$67$	−3.79345	−	2.53470i	−0.463444	−	0.309663i	0.301837	−	0.953359i	$-0.402400\pi$
$67$	−3.79345	−	2.53470i	−0.463444	−	0.309663i	−0.765281	+	0.643696i	$0.777400\pi$
$68$	1.04778	−	2.03160i	0.127062	−	0.246368i
$69$	−4.77119	−	14.1484i	−0.574384	−	1.70326i
$70$	1.03558	−	0.379155i	0.123776	−	0.0453176i
$71$	−2.73285	+	6.59768i	−0.324329	+	0.783000i	0.674663	+	0.738126i	$0.264289\pi$
$71$	−2.73285	+	6.59768i	−0.324329	+	0.783000i	−0.998993	+	0.0448746i	$0.985711\pi$
$72$	7.61662	+	3.73993i	0.897627	+	0.440755i
$73$	−0.219349	−	0.529556i	−0.0256729	−	0.0619798i	0.910523	−	0.413458i	$-0.135679\pi$
$73$	−0.219349	−	0.529556i	−0.0256729	−	0.0619798i	−0.936196	+	0.351478i	$0.885679\pi$
$74$	1.48110	−	1.36238i	0.172175	−	0.158373i
$75$	−0.769171	+	1.55189i	−0.0888162	+	0.179197i
$76$	11.0759	−	6.13141i	1.27049	−	0.703321i
$77$	−0.136956	+	0.0272422i	−0.0156076	+	0.00310454i
$78$	−5.67996	+	10.3508i	−0.643128	+	1.17200i
$79$	0.529782	−	0.529782i	0.0596051	−	0.0596051i	−0.676676	−	0.736281i	$-0.736580\pi$
$79$	0.529782	−	0.529782i	0.0596051	−	0.0596051i	0.736281	+	0.676676i	$0.236580\pi$
$80$	3.64888	−	1.63881i	0.407957	−	0.183224i
$81$	8.67442	+	2.39883i	0.963825	+	0.266536i
$82$	0.711406	+	0.172646i	0.0785616	+	0.0190655i
$83$	−3.70815	+	0.737596i	−0.407022	+	0.0809617i	−0.394355	−	0.918958i	$-0.629032\pi$
$83$	−3.70815	+	0.737596i	−0.407022	+	0.0809617i	−0.0126667	+	0.999920i	$0.504032\pi$
$84$	−2.67062	−	0.406111i	−0.291389	−	0.0443104i
$85$	−0.634984	−	0.950320i	−0.0688736	−	0.103077i
$86$	−0.0978158	+	2.34263i	−0.0105477	+	0.252612i
$87$	−3.58187	−	2.75986i	−0.384017	−	0.295888i
$88$	−0.488469	+	0.133878i	−0.0520710	+	0.0142715i
$89$	5.62039	−	13.5688i	0.595760	−	1.43829i	−0.282106	−	0.959383i	$-0.591033\pi$
$89$	5.62039	−	13.5688i	0.595760	−	1.43829i	0.877865	−	0.478908i	$-0.158967\pi$
$90$	3.48046	−	2.42619i	0.366873	−	0.255743i
$91$	0.733296	−	3.68653i	0.0768703	−	0.386453i
$92$	11.1325	+	13.1651i	1.16064	+	1.37256i
$93$	−0.526595	+	7.79542i	−0.0546053	+	0.808347i
$94$	2.36804	+	15.1931i	0.244245	+	1.56705i
$95$		−	6.32989i		−	0.649433i
$96$	−9.76682	−	0.780578i	−0.996822	−	0.0796674i
$97$		−	4.37891i		−	0.444611i	−0.974977	−	0.222306i	$-0.928642\pi$
$97$		−	4.37891i		−	0.444611i	0.974977	−	0.222306i	$-0.0713583\pi$
$98$	−8.93168	+	1.39212i	−0.902236	+	0.140625i
$99$	−0.482753	+	0.235672i	−0.0485185	+	0.0236859i
$100$	0.166728	−	1.99304i	0.0166728	−	0.199304i
$101$	2.38319	−	11.9811i	0.237137	−	1.19217i	−0.660293	−	0.751008i	$-0.729568\pi$
$101$	2.38319	−	11.9811i	0.237137	−	1.19217i	0.897429	−	0.441158i	$-0.145432\pi$
$102$	0.243733	+	2.78899i	0.0241332	+	0.276151i
$103$	−4.42394	+	10.6803i	−0.435904	+	1.05236i	0.541447	+	0.840735i	$0.317877\pi$
$103$	−4.42394	+	10.6803i	−0.435904	+	1.05236i	−0.977350	+	0.211629i	$0.932123\pi$
$104$	1.70232	−	13.5267i	0.166926	−	1.32640i
$105$	−0.824371	+	1.06991i	−0.0804504	+	0.104412i
$106$	0.362294	+	0.0151275i	0.0351891	+	0.00146931i
$107$	5.61443	+	8.40259i	0.542767	+	0.812309i	0.996904	−	0.0786230i	$-0.0250523\pi$
$107$	5.61443	+	8.40259i	0.542767	+	0.812309i	−0.454137	+	0.890932i	$0.650052\pi$
$108$	−10.3330	+	1.10872i	−0.994293	+	0.106687i
$109$	−0.586075	+	0.116577i	−0.0561358	+	0.0111661i	−0.223078	−	0.974801i	$-0.571611\pi$
$109$	−0.586075	+	0.116577i	−0.0561358	+	0.0111661i	0.166943	+	0.985967i	$0.446611\pi$
$110$	−0.0597238	+	0.246099i	−0.00569444	+	0.0234646i
$111$	−0.642663	+	2.37941i	−0.0609989	+	0.225844i
$112$	3.04005	−	0.698281i	0.287258	−	0.0659814i
$113$	2.35924	−	2.35924i	0.221938	−	0.221938i	−0.587376	−	0.809314i	$-0.699839\pi$
$113$	2.35924	−	2.35924i	0.221938	−	0.221938i	0.809314	+	0.587376i	$0.199839\pi$
$114$	−7.45904	+	13.5929i	−0.698604	+	1.27309i
$115$	8.45488	−	1.68178i	0.788422	−	0.156827i
$116$	5.01825	+	1.44199i	0.465933	+	0.133885i
$117$	−0.888042	−	14.4331i	−0.0820996	−	1.33434i
$118$	−0.172932	−	0.188003i	−0.0159197	−	0.0173071i
$119$	−0.341074	−	0.823426i	−0.0312662	−	0.0754833i
$120$	−2.70660	+	4.08342i	−0.247078	+	0.372763i
$121$	−4.19725	+	10.1331i	−0.381568	+	0.921186i
$122$	−0.406224	−	1.10952i	−0.0367778	−	0.100451i
$123$	−0.849574	+	0.286498i	−0.0766035	+	0.0258327i
$124$	−2.74566	−	8.59394i	−0.246567	−	0.771759i
$125$	−0.831470	−	0.555570i	−0.0743689	−	0.0496917i
$126$	3.03103	−	1.32611i	0.270026	−	0.118139i
$127$			12.5327i			1.11209i	0.831151	+	0.556047i	$0.187682\pi$
$127$			12.5327i			1.11209i	−0.831151	+	0.556047i	$0.812318\pi$
$128$	10.8186	−	3.31029i	0.956238	−	0.292591i
$129$	−1.43084	−	2.48977i	−0.125978	−	0.219212i
$130$	−5.50493	−	4.02030i	−0.482815	−	0.352604i
$131$	10.7387	−	16.0715i	0.938241	−	1.40418i	0.0236841	−	0.999719i	$-0.492460\pi$
$131$	10.7387	−	16.0715i	0.938241	−	1.40418i	0.914557	−	0.404457i	$-0.132540\pi$
$132$	0.418251	−	0.458099i	0.0364041	−	0.0398724i
$133$	0.962981	−	4.84123i	0.0835010	−	0.419788i
$134$	−6.05881	+	2.21829i	−0.523401	+	0.191631i
$135$	−2.01724	+	4.78860i	−0.173617	+	0.412137i
$136$	−1.44632	−	2.89113i	−0.124021	−	0.247913i
$137$	12.0482	−	4.99053i	1.02935	−	0.426370i	0.196871	−	0.980429i	$-0.436922\pi$
$137$	12.0482	−	4.99053i	1.02935	−	0.426370i	0.832477	+	0.554060i	$0.186922\pi$
$138$	−20.1380	−	6.35162i	−1.71426	−	0.540686i
$139$	9.62831	+	14.4098i	0.816662	+	1.22222i	0.972144	+	0.234383i	$0.0753070\pi$
$139$	9.62831	+	14.4098i	0.816662	+	1.22222i	−0.155482	+	0.987839i	$0.549693\pi$
$140$	0.430723	−	1.49895i	0.0364027	−	0.126685i
$141$	−12.3887	−	14.1837i	−1.04332	−	1.19448i
$142$	5.25566	+	8.62402i	0.441045	+	0.723711i
$143$	0.610328	+	0.610328i	0.0510382	+	0.0510382i
$144$	10.6240	−	5.57940i	0.885337	−	0.464950i
$145$	1.84601	−	1.84601i	0.153303	−	0.153303i
$146$	−0.787743	−	0.191172i	−0.0651941	−	0.0158215i
$147$	8.33828	−	7.28303i	0.687729	−	0.600694i
$148$	−0.320595	−	2.82784i	−0.0263527	−	0.232447i
$149$	4.29507	−	2.86987i	0.351866	−	0.235109i	−0.367058	−	0.930198i	$-0.619635\pi$
$149$	4.29507	−	2.86987i	0.351866	−	0.235109i	0.718924	+	0.695089i	$0.244635\pi$
$150$	1.13084	+	2.17283i	0.0923326	+	0.177411i
$151$	−3.81275	−	9.20479i	−0.310277	−	0.749076i	−0.999695	−	0.0247112i	$-0.992133\pi$
$151$	−3.81275	−	9.20479i	−0.310277	−	0.749076i	0.689417	−	0.724364i	$-0.257867\pi$
$152$	2.23553	−	17.7635i	0.181325	−	1.44081i
$153$	−2.07644	−	2.72859i	−0.167870	−	0.220594i
$154$	−0.0831176	+	0.179135i	−0.00669781	+	0.0144351i
$155$	−4.42427	−	0.880042i	−0.355366	−	0.0706866i
$156$	7.08394	+	15.1202i	0.567169	+	1.21059i
$157$	−19.6350	−	13.1197i	−1.56705	−	1.04707i	−0.969456	−	0.245267i	$-0.921124\pi$
$157$	−19.6350	−	13.1197i	−1.56705	−	1.04707i	−0.597591	−	0.801801i	$-0.703876\pi$
$158$	−0.163177	−	1.04692i	−0.0129817	−	0.0832888i
$159$	−0.385049	+	0.221283i	−0.0305364	+	0.0175489i
$160$	1.17177	−	5.53416i	0.0926365	−	0.437514i
$161$	6.72232			0.529793
$162$	9.97468	−	7.90605i	0.783685	−	0.621158i
$163$	12.4227	−	18.5919i	0.973020	−	1.45623i	0.0850224	−	0.996379i	$-0.472904\pi$
$163$	12.4227	−	18.5919i	0.973020	−	1.45623i	0.887998	−	0.459848i	$-0.152096\pi$
$164$	0.790534	−	0.668480i	0.0617303	−	0.0521995i
$165$	−0.0991091	−	0.293895i	−0.00771564	−	0.0228797i
$166$	−2.25045	+	4.85018i	−0.174669	+	0.376447i
$167$	10.3974	+	4.30674i	0.804574	+	0.333265i	0.746787	−	0.665064i	$-0.231596\pi$
$167$	10.3974	+	4.30674i	0.804574	+	0.333265i	0.0577869	+	0.998329i	$0.481596\pi$
$168$	−2.69128	+	2.71132i	−0.207637	+	0.209183i
$169$	−9.45458	+	3.91622i	−0.727275	+	0.301247i
$170$	−1.61495	−	0.0674319i	−0.123861	−	0.00517179i
$171$	−1.16620	−	18.9538i	−0.0891813	−	1.44944i
$172$	2.59387	+	2.06562i	0.197781	+	0.157502i
$173$	0.829577	+	4.17057i	0.0630716	+	0.317082i	0.999422	−	0.0339835i	$-0.0108194\pi$
$173$	0.829577	+	4.17057i	0.0630716	+	0.317082i	−0.936351	+	0.351066i	$0.885819\pi$
$174$	−6.13948	+	1.78885i	−0.465433	+	0.135612i
$175$	−0.551405	−	0.551405i	−0.0416823	−	0.0416823i
$176$	−0.254517	+	0.669531i	−0.0191850	+	0.0504678i
$177$	0.302029	+	0.0815760i	0.0227019	+	0.00613163i
$178$	−10.8088	−	17.7362i	−0.810155	−	1.32938i
$179$	−1.98775	−	9.99307i	−0.148571	−	0.746917i	−0.981186	−	0.193065i	$-0.938157\pi$
$179$	−1.98775	−	9.99307i	−0.148571	−	0.746917i	0.832615	−	0.553852i	$-0.186843\pi$
$180$	0.132049	−	5.99855i	0.00984237	−	0.447105i
$181$	−11.6451	+	7.78100i	−0.865573	+	0.578357i	−0.907164	−	0.420778i	$-0.861757\pi$
$181$	−11.6451	+	7.78100i	−0.865573	+	0.578357i	0.0415912	+	0.999135i	$0.486757\pi$
$182$	−3.59867	−	3.91229i	−0.266751	−	0.289998i
$183$	1.14629	+	0.883227i	0.0847362	+	0.0652900i
$184$	24.3208	−	1.73355i	1.79295	−	0.127799i
$185$	−1.31466	−	0.544550i	−0.0966558	−	0.0400361i
$186$	8.46373	+	7.10331i	0.620591	+	0.520840i
$187$	0.200733	+	0.0399282i	0.0146790	+	0.00291984i
$188$	19.3267	+	9.96757i	1.40955	+	0.726960i
$189$	−2.27133	+	3.35554i	−0.165215	+	0.244079i
$190$	−7.22920	−	5.27955i	−0.524461	−	0.383019i
$191$	−21.9966			−1.59162			−0.795808	−	0.605549i	$-0.792953\pi$
$191$	−21.9966			−1.59162			−0.795808	+	0.605549i	$0.792953\pi$
$192$	−9.03765	+	10.5034i	−0.652236	+	0.758016i
$193$	−7.12624			−0.512958			−0.256479	−	0.966550i	$-0.582562\pi$
$193$	−7.12624			−0.512958			−0.256479	+	0.966550i	$0.582562\pi$
$194$	−5.00104	−	3.65231i	−0.359054	−	0.262220i
$195$	8.32971	+	0.562687i	0.596503	+	0.0402949i
$196$	−5.85971	+	11.3618i	−0.418551	+	0.811554i
$197$	2.70934	+	0.538922i	0.193033	+	0.0383966i	0.290660	−	0.956826i	$-0.406125\pi$
$197$	2.70934	+	0.538922i	0.193033	+	0.0383966i	−0.0976270	+	0.995223i	$0.531125\pi$
$198$	−0.133493	+	0.747905i	−0.00948693	+	0.0531513i
$199$	−11.3741	−	4.71130i	−0.806287	−	0.333975i	−0.0588153	−	0.998269i	$-0.518732\pi$
$199$	−11.3741	−	4.71130i	−0.806287	−	0.333975i	−0.747471	+	0.664294i	$0.768732\pi$
$200$	−2.13714	−	1.85274i	−0.151118	−	0.131009i
$201$	4.82309	−	6.25962i	0.340194	−	0.441519i
$202$	−11.6956	−	12.7148i	−0.822899	−	0.894613i
$203$	1.69271	−	1.13103i	0.118805	−	0.0793829i
$204$	3.38852	+	2.04784i	0.237244	+	0.143378i
$205$	−0.100987	−	0.507695i	−0.00705322	−	0.0354589i
$206$	8.50787	+	13.9606i	0.592771	+	0.972679i
$207$	25.0069	−	6.59352i	1.73810	−	0.458281i
$208$	−14.0286	−	13.2263i	−0.972708	−	0.917080i
$209$	0.801496	+	0.801496i	0.0554407	+	0.0554407i
$210$	0.534331	+	1.83387i	0.0368723	+	0.126549i
$211$	3.01502	+	15.1575i	0.207562	+	1.04349i	0.934277	+	0.356547i	$0.116046\pi$
$211$	3.01502	+	15.1575i	0.207562	+	1.04349i	−0.726715	+	0.686939i	$0.758954\pi$
$212$	0.319454	−	0.401149i	0.0219402	−	0.0275510i
$213$	−11.0825	−	5.49286i	−0.759361	−	0.376365i
$214$	14.2792	+	0.596223i	0.976105	+	0.0407569i
$215$	1.53173	−	0.634464i	0.104463	−	0.0432701i
$216$	−7.35216	+	12.7258i	−0.500251	+	0.865880i
$217$	−3.24989	−	1.34615i	−0.220617	−	0.0913825i
$218$	−0.355685	+	0.766574i	−0.0240900	+	0.0519189i
$219$	0.940738	−	0.317241i	0.0635692	−	0.0214372i
$220$	0.231249	+	0.273472i	0.0155908	+	0.0184374i
$221$	−3.06070	+	4.58066i	−0.205885	+	0.308128i
$222$	2.18144	+	2.71855i	0.146409	+	0.182457i
$223$	21.1547			1.41662			0.708312	−	0.705899i	$-0.249457\pi$
$223$	21.1547			1.41662			0.708312	+	0.705899i	$0.249457\pi$
$224$	1.73812	−	4.05438i	0.116133	−	0.270895i
$225$	−2.59206	−	1.51038i	−0.172804	−	0.100692i
$226$	−0.726662	−	4.66218i	−0.0483369	−	0.310124i
$227$	15.5613	+	10.3977i	1.03284	+	0.690123i	0.951841	−	0.306592i	$-0.0991886\pi$
$227$	15.5613	+	10.3977i	1.03284	+	0.690123i	0.0810002	+	0.996714i	$0.474189\pi$
$228$	9.30279	+	19.8562i	0.616092	+	1.31501i
$229$	16.5108	+	3.28420i	1.09106	+	0.217026i	0.707659	−	0.706555i	$-0.249751\pi$
$229$	16.5108	+	3.28420i	1.09106	+	0.217026i	0.383405	+	0.923580i	$0.374751\pi$
$230$	5.13122	−	11.0588i	0.338342	−	0.729197i
$231$	−0.0310897	−	0.239855i	−0.00204555	−	0.0157813i
$232$	5.83241	−	4.52850i	0.382917	−	0.297310i
$233$	6.83747	+	16.5071i	0.447938	+	1.08142i	0.973093	+	0.230411i	$0.0740070\pi$
$233$	6.83747	+	16.5071i	0.447938	+	1.08142i	−0.525156	+	0.851006i	$0.675993\pi$
$234$	−17.2243	−	11.0239i	−1.12599	−	0.720657i
$235$	9.04044	−	6.04063i	0.589734	−	0.394047i
$236$	−0.358951	+	0.0406945i	−0.0233657	+	0.00264899i
$237$	0.853678	+	0.977368i	0.0554523	+	0.0634869i
$238$	−1.22489	−	0.297260i	−0.0793980	−	0.0192685i
$239$	−13.7268	+	13.7268i	−0.887913	+	0.887913i	−0.994322	−	0.106410i	$-0.966065\pi$
$239$	−13.7268	+	13.7268i	−0.887913	+	0.887913i	0.106410	+	0.994322i	$0.466065\pi$
$240$	2.40608	+	6.49698i	0.155312	+	0.419378i
$241$	−13.0412	−	13.0412i	−0.840055	−	0.840055i	0.148810	−	0.988866i	$-0.452456\pi$
$241$	−13.0412	−	13.0412i	−0.840055	−	0.840055i	−0.988866	+	0.148810i	$0.952456\pi$
$242$	8.07191	+	13.2452i	0.518882	+	0.851434i
$243$	−5.15807	+	14.7103i	−0.330890	+	0.943669i
$244$	−1.60597	−	0.461474i	−0.102812	−	0.0295428i
$245$	3.55115	+	5.31467i	0.226875	+	0.339542i
$246$	−0.381399	+	1.20923i	−0.0243171	+	0.0770980i
$247$	−28.1883	+	11.6760i	−1.79358	+	0.742925i
$248$	−12.1050	−	4.03217i	−0.768667	−	0.256043i
$249$	−0.841771	−	6.49420i	−0.0533450	−	0.411553i
$250$	−1.32800	+	0.486217i	−0.0839903	+	0.0307511i
$251$	−1.42494	+	7.16368i	−0.0899417	+	0.452167i	0.909401	+	0.415920i	$0.136540\pi$
$251$	−1.42494	+	7.16368i	−0.0899417	+	0.452167i	−0.999343	+	0.0362472i	$0.988460\pi$
$252$	1.01357	−	4.56772i	0.0638487	−	0.287740i
$253$	−0.857616	+	1.28351i	−0.0539179	+	0.0806938i
$254$	14.3132	+	10.4531i	0.898091	+	0.655884i
$255$	1.71639	−	0.986385i	0.107484	−	0.0617698i
$256$	5.24283	−	15.1166i	0.327677	−	0.944790i
$257$			19.6662i			1.22674i	0.789794	+	0.613372i	$0.210187\pi$
$257$			19.6662i			1.22674i	−0.789794	+	0.613372i	$0.789813\pi$
$258$	−4.03691	−	0.442509i	−0.251327	−	0.0275494i
$259$	−0.922637	−	0.616486i	−0.0573298	−	0.0383066i
$260$	−9.18296	+	2.93384i	−0.569503	+	0.181949i
$261$	5.18749	−	5.86769i	0.321097	−	0.363201i
$262$	−9.39813	−	25.6691i	−0.580619	−	1.58584i
$263$	−9.82305	+	23.7149i	−0.605715	+	1.46233i	0.261903	+	0.965094i	$0.415650\pi$
$263$	−9.82305	+	23.7149i	−0.605715	+	1.46233i	−0.867618	+	0.497231i	$0.834350\pi$
$264$	−0.174334	−	0.859759i	−0.0107295	−	0.0529145i
$265$	−0.0981215	−	0.236886i	−0.00602755	−	0.0145518i
$266$	−4.72585	−	5.13770i	−0.289761	−	0.315013i
$267$	22.7923	+	11.2966i	1.39487	+	0.691343i
$268$	−2.52000	+	8.76981i	−0.153933	+	0.535701i
$269$	23.6448	−	4.70325i	1.44165	−	0.286762i	0.588529	−	0.808476i	$-0.299707\pi$
$269$	23.6448	−	4.70325i	1.44165	−	0.286762i	0.853120	+	0.521714i	$0.174707\pi$
$270$	3.78643	+	6.29785i	0.230435	+	0.383275i
$271$	−10.3070	+	10.3070i	−0.626103	+	0.626103i	−0.947085	−	0.320982i	$-0.895987\pi$
$271$	−10.3070	+	10.3070i	−0.626103	+	0.626103i	0.320982	+	0.947085i	$0.395987\pi$
$272$	−4.50822	−	0.759587i	−0.273351	−	0.0460567i
$273$	6.28513	+	1.69757i	0.380394	+	0.102742i
$274$	4.34945	−	17.9224i	0.262760	−	1.08273i
$275$	0.175628	−	0.0349346i	0.0105908	−	0.00210664i
$276$	−24.0504	+	17.7014i	−1.44767	+	1.06550i
$277$	−14.9703	−	22.4047i	−0.899481	−	1.34617i	−0.937900	−	0.346907i	$-0.887232\pi$
$277$	−14.9703	−	22.4047i	−0.899481	−	1.34617i	0.0384188	−	0.999262i	$-0.487768\pi$
$278$	24.4877	+	1.02247i	1.46867	+	0.0613240i
$279$	−13.4099	−	1.82003i	−0.802829	−	0.108962i
$280$	−1.35266	−	1.74214i	−0.0808371	−	0.104113i
$281$	0.190775	−	0.460571i	0.0113807	−	0.0274753i	−0.918087	−	0.396379i	$-0.870267\pi$
$281$	0.190775	−	0.460571i	0.0113807	−	0.0274753i	0.929468	+	0.368903i	$0.120267\pi$
$282$	−26.5318	+	2.31865i	−1.57995	+	0.138073i
$283$	−5.16694	+	25.9760i	−0.307143	+	1.54411i	0.451301	+	0.892372i	$0.350960\pi$
$283$	−5.16694	+	25.9760i	−0.307143	+	1.54411i	−0.758443	+	0.651739i	$0.774040\pi$
$284$	14.2328	+	1.19065i	0.844563	+	0.0706521i
$285$	10.9388	+	0.738933i	0.647956	+	0.0437706i
$286$	1.20609	−	0.187986i	0.0713178	−	0.0111158i
$287$		−	0.403659i		−	0.0238272i
$288$	2.48908	−	16.7870i	0.146670	−	0.989185i
$289$		−	15.6937i		−	0.923158i
$290$	−0.568586	−	3.64798i	−0.0333885	−	0.214217i
$291$	7.56726	+	0.511182i	0.443600	+	0.0299660i
$292$	−0.875363	+	0.740211i	−0.0512267	+	0.0433176i
$293$	−1.89698	+	9.53675i	−0.110823	+	0.557143i	0.884981	+	0.465627i	$0.154171\pi$
$293$	−1.89698	+	9.53675i	−0.110823	+	0.557143i	−0.995804	+	0.0915158i	$0.970829\pi$
$294$	−1.36308	−	15.5975i	−0.0794965	−	0.909662i
$295$	−0.0691222	+	0.166876i	−0.00402445	+	0.00971588i
$296$	−3.49700	−	1.99247i	−0.203259	−	0.115810i
$297$	−0.350912	−	0.861763i	−0.0203620	−	0.0500045i
$298$	0.304765	−	7.29895i	0.0176546	−	0.422817i
$299$	−23.0850	−	34.5492i	−1.33504	−	1.99803i
$300$	3.42473	+	0.520786i	0.197727	+	0.0300676i
$301$	1.26802	−	0.252225i	0.0730876	−	0.0145380i
$302$	−13.6926	−	3.32297i	−0.787923	−	0.191215i
$303$	20.4265	+	5.51707i	1.17347	+	0.316947i
$304$	−18.4227	−	17.3691i	−1.05661	−	0.996186i
$305$	−0.590772	+	0.590772i	−0.0338275	+	0.0338275i
$306$	−4.84814	+	0.0956199i	−0.277150	+	0.00546622i
$307$	−1.87225	+	0.372414i	−0.106855	+	0.0212548i	−0.248228	−	0.968702i	$-0.579848\pi$
$307$	−1.87225	+	0.372414i	−0.106855	+	0.0212548i	0.141373	+	0.989956i	$0.454848\pi$
$308$	0.135260	+	0.244337i	0.00770717	+	0.0139224i
$309$	−17.9404	−	8.89185i	−1.02059	−	0.505840i
$310$	−4.69521	+	4.31883i	−0.266670	+	0.245293i
$311$	−12.5827	−	30.3774i	−0.713501	−	1.72254i	−0.691062	−	0.722796i	$-0.742857\pi$
$311$	−12.5827	−	30.3774i	−0.713501	−	1.72254i	−0.0224390	−	0.999748i	$-0.507143\pi$
$312$	23.1769	+	4.52087i	1.31213	+	0.255944i
$313$	−5.14781	+	12.4279i	−0.290972	+	0.702468i	−0.999996	−	0.00271593i	$-0.999135\pi$
$313$	−5.14781	+	12.4279i	−0.290972	+	0.702468i	0.709025	+	0.705184i	$0.249135\pi$
$314$	−31.3606	+	11.4820i	−1.76978	+	0.647964i
$315$	−1.75268	−	1.54950i	−0.0987524	−	0.0873047i
$316$	−1.33176	−	0.686844i	−0.0749176	−	0.0386380i
$317$	−20.7779	−	13.8833i	−1.16700	−	0.779765i	−0.187710	−	0.982224i	$-0.560107\pi$
$317$	−20.7779	−	13.8833i	−1.16700	−	0.779765i	−0.979291	+	0.202459i	$0.935107\pi$
$318$	−0.0684351	+	0.624319i	−0.00383765	+	0.0350101i
$319$			0.467488i			0.0261743i
$320$	−5.34309	−	5.95411i	−0.298688	−	0.332845i
$321$	−15.1760	+	8.72147i	−0.847043	+	0.486785i
$322$	5.60687	−	7.67739i	0.312458	−	0.427844i
$323$	−4.01938	+	6.01542i	−0.223644	+	0.334707i
$324$	−0.709752	−	17.9860i	−0.0394306	−	0.999222i
$325$	−0.940359	+	4.72750i	−0.0521617	+	0.262235i
$326$	−10.8719	−	29.6945i	−0.602141	−	1.64463i
$327$	−0.133042	−	1.02641i	−0.00735726	−	0.0567607i
$328$	−0.104096	−	1.46040i	−0.00574772	−	0.0806374i
$329$	7.83330	−	3.24466i	0.431864	−	0.178884i
$330$	−0.418314	−	0.131938i	−0.0230274	−	0.00726297i
$331$	−13.6847	−	20.4806i	−0.752178	−	1.12571i	−0.988081	−	0.153937i	$-0.950805\pi$
$331$	−13.6847	−	20.4806i	−0.752178	−	1.12571i	0.235902	−	0.971777i	$-0.424195\pi$
$332$	3.66224	+	6.61555i	0.200992	+	0.363076i
$333$	−4.03687	−	1.38836i	−0.221219	−	0.0760816i
$334$	13.5907	−	8.28248i	0.743651	−	0.453197i
$335$	3.22606	+	3.22606i	0.176259	+	0.176259i
$336$	0.851821	+	5.33507i	0.0464706	+	0.291052i
$337$	−18.7043	+	18.7043i	−1.01889	+	1.01889i	−0.0190720	+	0.999818i	$0.506071\pi$
$337$	−18.7043	+	18.7043i	−1.01889	+	1.01889i	−0.999818	+	0.0190720i	$0.993929\pi$
$338$	−3.41314	+	14.0642i	−0.185650	+	0.764992i
$339$	3.80161	+	4.35243i	0.206475	+	0.236392i
$340$	−1.42399	+	1.78815i	−0.0772268	+	0.0969763i
$341$	0.671636	−	0.448773i	0.0363712	−	0.0243024i
$342$	−22.6194	−	14.4769i	−1.22311	−	0.782819i
$343$	3.99639	+	9.64814i	0.215785	+	0.520950i
$344$	4.52256	−	1.23953i	0.243840	−	0.0668309i
$345$	1.91931	+	14.8073i	0.103332	+	0.797199i
$346$	5.45502	+	2.53109i	0.293264	+	0.136072i
$347$	9.86374	+	1.96202i	0.529513	+	0.105327i	0.452604	−	0.891711i	$-0.350495\pi$
$347$	9.86374	+	1.96202i	0.529513	+	0.105327i	0.0769088	+	0.997038i	$0.475495\pi$
$348$	−3.07773	+	8.50376i	−0.164984	+	0.455850i
$349$	15.9792	+	10.6769i	0.855345	+	0.571523i	0.904116	−	0.427287i	$-0.140531\pi$
$349$	15.9792	+	10.6769i	0.855345	+	0.571523i	−0.0487713	+	0.998810i	$0.515531\pi$
$350$	−1.08965	+	0.169837i	−0.0582445	+	0.00907817i
$351$	25.0456	+	0.150238i	1.33684	+	0.00801910i
$352$	0.552370	+	0.849111i	0.0294414	+	0.0452578i
$353$	21.8864			1.16490			0.582449	−	0.812867i	$-0.302095\pi$
$353$	21.8864			1.16490			0.582449	+	0.812867i	$0.302095\pi$
$354$	0.345078	−	0.276900i	0.0183407	−	0.0147170i
$355$	3.96748	−	5.93775i	0.210572	−	0.315143i
$356$	−29.2713	−	2.44870i	−1.55138	−	0.129781i
$357$	1.46279	−	0.493290i	0.0774190	−	0.0261077i
$358$	−13.0707	−	6.06473i	−0.690810	−	0.320531i
$359$	14.4057	+	5.96702i	0.760302	+	0.314928i	0.728937	−	0.684580i	$-0.240015\pi$
$359$	14.4057	+	5.96702i	0.760302	+	0.314928i	0.0313650	+	0.999508i	$0.490015\pi$
$360$	−6.74065	−	5.15400i	−0.355263	−	0.271639i
$361$	−19.4638	+	8.06218i	−1.02441	+	0.424325i
$362$	−0.826301	+	19.7894i	−0.0434294	+	1.04011i
$363$	−17.0211	−	8.43622i	−0.893375	−	0.442787i
$364$	−7.46965	+	0.846840i	−0.391516	+	0.0443865i
$365$	0.111823	+	0.562173i	0.00585309	+	0.0294255i
$366$	1.96479	−	0.572479i	0.102701	−	0.0299239i
$367$	−5.70029	−	5.70029i	−0.297553	−	0.297553i	0.542502	−	0.840055i	$-0.317477\pi$
$367$	−5.70029	−	5.70029i	−0.297553	−	0.297553i	−0.840055	+	0.542502i	$0.817477\pi$
$368$	18.3053	−	29.2221i	0.954231	−	1.52331i
$369$	−0.395924	−	1.50160i	−0.0206110	−	0.0781704i
$370$	−1.71843	+	1.04725i	−0.0893370	+	0.0544439i
$371$	−0.0390073	−	0.196103i	−0.00202516	−	0.0101812i
$372$	15.1718	−	3.74158i	0.786622	−	0.193992i
$373$	27.0233	−	18.0564i	1.39922	−	0.934926i	0.399380	−	0.916785i	$-0.369225\pi$
$373$	27.0233	−	18.0564i	1.39922	−	0.934926i	0.999835	−	0.0181405i	$-0.00577462\pi$
$374$	0.213025	−	0.195949i	0.0110153	−	0.0101323i
$375$	1.05715	−	1.37202i	0.0545911	−	0.0708507i
$376$	27.5035	−	13.7590i	1.41838	−	0.709564i
$377$	−11.6258	−	4.81557i	−0.598760	−	0.248014i
$378$	1.93783	+	5.39277i	0.0996713	+	0.277374i
$379$	24.3604	+	4.84559i	1.25131	+	0.248901i	0.775897	−	0.630860i	$-0.217298\pi$
$379$	24.3604	+	4.84559i	1.25131	+	0.248901i	0.475415	+	0.879762i	$0.342298\pi$
$380$	−12.0593	+	3.85279i	−0.618628	+	0.197644i
$381$	−21.6578	−	1.46303i	−1.10956	−	0.0749531i
$382$	−18.3466	+	25.1217i	−0.938694	+	1.28534i
$383$	6.66191			0.340408			0.170204	−	0.985409i	$-0.445557\pi$
$383$	6.66191			0.340408			0.170204	+	0.985409i	$0.445557\pi$
$384$	4.45763	+	19.0822i	0.227477	+	0.973783i
$385$	0.139639			0.00711665
$386$	−5.94375	+	8.13869i	−0.302529	+	0.414248i
$387$	4.46963	−	2.18200i	0.227204	−	0.110917i
$388$	−8.34241	+	2.66530i	−0.423522	+	0.135310i
$389$	21.9911	+	4.37431i	1.11499	+	0.221786i	0.718005	−	0.696038i	$-0.245055\pi$
$389$	21.9911	+	4.37431i	1.11499	+	0.221786i	0.396988	+	0.917824i	$0.370055\pi$
$390$	7.59016	−	9.04383i	0.384343	−	0.457952i
$391$	−9.10275	−	3.77048i	−0.460346	−	0.190681i
$392$	8.08858	+	16.1687i	0.408535	+	0.816642i
$393$	26.5198	+	20.4338i	1.33775	+	1.03075i
$394$	2.87526	−	2.64478i	0.144854	−	0.133242i
$395$	−0.622958	+	0.416247i	−0.0313444	+	0.0209437i
$396$	0.742821	+	0.776262i	0.0373282	+	0.0390086i
$397$	7.18367	+	36.1148i	0.360538	+	1.81255i	0.555246	+	0.831686i	$0.312624\pi$
$397$	7.18367	+	36.1148i	0.360538	+	1.81255i	−0.194707	+	0.980861i	$0.562376\pi$
$398$	−14.8674	+	9.06050i	−0.745234	+	0.454162i
$399$	8.25378	+	2.22929i	0.413206	+	0.111604i
$400$	−3.89848	+	0.895456i	−0.194924	+	0.0447728i
$401$	22.4392	+	22.4392i	1.12056	+	1.12056i	0.991657	+	0.128903i	$0.0411456\pi$
$401$	22.4392	+	22.4392i	1.12056	+	1.12056i	0.128903	+	0.991657i	$0.458854\pi$
$402$	−3.12617	−	10.7293i	−0.155919	−	0.535127i
$403$	4.24191	+	21.3255i	0.211304	+	1.06230i
$404$	−24.2762	+	2.75221i	−1.20779	+	0.136927i
$405$	−8.03976	−	4.04503i	−0.399499	−	0.200999i
$406$	0.120110	−	2.87655i	0.00596094	−	0.142761i
$407$	0.235415	−	0.0975121i	0.0116691	−	0.00483350i
$408$	5.16504	−	2.16191i	0.255708	−	0.107030i
$409$	−18.7706	−	7.77503i	−0.928145	−	0.384450i	−0.133171	−	0.991093i	$-0.542516\pi$
$409$	−18.7706	−	7.77503i	−0.928145	−	0.384450i	−0.794975	+	0.606643i	$0.792516\pi$
$410$	−0.664055	−	0.308117i	−0.0327953	−	0.0152168i
$411$	7.21772	+	21.4032i	0.356024	+	1.05574i
$412$	23.0401	+	1.92743i	1.13511	+	0.0949575i
$413$	−0.0782533	+	0.117114i	−0.00385059	+	0.00576282i
$414$	13.3272	−	34.0592i	0.654994	−	1.67392i
$415$	3.78079			0.185592
$416$	−26.8062	+	4.99007i	−1.31428	+	0.244659i
$417$	−26.0257	+	14.9566i	−1.27448	+	0.732430i
$418$	1.58387	−	0.246867i	0.0774696	−	0.0120747i
$419$	−2.59053	−	1.73093i	−0.126556	−	0.0845617i	0.490681	−	0.871339i	$-0.336748\pi$
$419$	−2.59053	−	1.73093i	−0.126556	−	0.0845617i	−0.617237	+	0.786777i	$0.711748\pi$
$420$	2.54008	+	0.919320i	0.123943	+	0.0448582i
$421$	−9.79501	−	1.94835i	−0.477380	−	0.0949567i	−0.0494649	−	0.998776i	$-0.515752\pi$
$421$	−9.79501	−	1.94835i	−0.477380	−	0.0949567i	−0.427915	+	0.903819i	$0.640752\pi$
$422$	19.8257	+	9.19900i	0.965101	+	0.447800i
$423$	25.9572	−	19.7533i	1.26208	−	0.960437i
$424$	−0.191696	−	0.699425i	−0.00930960	−	0.0339671i
$425$	0.437384	+	1.05594i	0.0212163	+	0.0512206i
$426$	−15.5168	+	8.07563i	−0.751791	+	0.391265i
$427$	−0.541711	+	0.361959i	−0.0262152	+	0.0175164i
$428$	12.5907	−	15.8106i	0.608595	−	0.764234i
$429$	−1.12596	+	0.983468i	−0.0543620	+	0.0474823i
$430$	0.552961	−	2.27854i	0.0266661	−	0.109881i
$431$	−2.94568	+	2.94568i	−0.141888	+	0.141888i	−0.774483	−	0.632595i	$-0.781990\pi$
$431$	−2.94568	+	2.94568i	−0.141888	+	0.141888i	0.632595	+	0.774483i	$0.281990\pi$
$432$	8.40160	+	19.0109i	0.404222	+	0.914661i
$433$	1.54051	+	1.54051i	0.0740323	+	0.0740323i	0.743153	−	0.669121i	$-0.233329\pi$
$433$	1.54051	+	1.54051i	0.0740323	+	0.0740323i	−0.669121	+	0.743153i	$0.733329\pi$
$434$	−4.24802	+	2.58884i	−0.203912	+	0.124268i
$435$	2.97462	+	3.40562i	0.142622	+	0.163287i
$436$	0.578819	+	1.04559i	0.0277204	+	0.0500748i
$437$	−30.3158	−	45.3708i	−1.45020	−	2.17038i
$438$	0.422325	−	1.33899i	0.0201795	−	0.0639795i
$439$	−2.47311	+	1.02440i	−0.118035	+	0.0488918i	−0.440919	−	0.897547i	$-0.645348\pi$
$439$	−2.47311	+	1.02440i	−0.118035	+	0.0488918i	0.322884	+	0.946438i	$0.395348\pi$
$440$	0.505202	−	0.0360101i	0.0240846	−	0.00171671i
$441$	11.6125	+	15.2597i	0.552976	+	0.726651i
$442$	2.67862	+	7.31612i	0.127409	+	0.347992i
$443$	−7.74973	+	38.9605i	−0.368201	+	1.85107i	0.140435	+	0.990090i	$0.455150\pi$
$443$	−7.74973	+	38.9605i	−0.368201	+	1.85107i	−0.508636	+	0.860982i	$0.669850\pi$
$444$	4.92426	−	0.223909i	0.233695	−	0.0106263i
$445$	−8.15954	+	12.2116i	−0.386799	+	0.578886i
$446$	17.6444	−	24.1603i	0.835489	−	1.14402i
$447$	4.45807	+	7.75738i	0.210859	+	0.366911i
$448$	−3.18069	−	5.36668i	−0.150274	−	0.253552i
$449$		−	10.2177i		−	0.482202i	−0.970500	−	0.241101i	$-0.922491\pi$
$449$		−	10.2177i		−	0.482202i	0.970500	−	0.241101i	$-0.0775085\pi$
$450$	−3.88691	+	1.70057i	−0.183231	+	0.0801654i
$451$	0.0770718	+	0.0514977i	0.00362917	+	0.00242493i
$452$	−5.93064	−	3.05867i	−0.278954	−	0.143868i
$453$	16.3520	−	5.51432i	0.768284	−	0.259085i
$454$	24.8542	−	9.09977i	1.16646	−	0.427074i
$455$	−1.43841	+	3.47263i	−0.0674338	+	0.162800i
$456$	30.4364	+	5.93690i	1.42531	+	0.278021i
$457$	3.51394	+	8.48340i	0.164375	+	0.396836i	0.984509	−	0.175335i	$-0.0561010\pi$
$457$	3.51394	+	8.48340i	0.164375	+	0.396836i	−0.820134	+	0.572172i	$0.806101\pi$
$458$	17.5219	−	16.1173i	0.818744	−	0.753112i
$459$	4.95771	−	3.26979i	0.231406	−	0.152621i
$460$	−8.35022	−	15.0840i	−0.389331	−	0.703296i
$461$	3.79394	−	0.754662i	0.176702	−	0.0351481i	−0.105946	−	0.994372i	$-0.533787\pi$
$461$	3.79394	−	0.754662i	0.176702	−	0.0351481i	0.282648	+	0.959224i	$0.408787\pi$
$462$	−0.299863	−	0.164548i	−0.0139509	−	0.00765548i
$463$	24.5067	−	24.5067i	1.13892	−	1.13892i	0.150282	−	0.988643i	$-0.451982\pi$
$463$	24.5067	−	24.5067i	1.13892	−	1.13892i	0.988643	−	0.150282i	$-0.0480181\pi$
$464$	−0.307260	−	10.4381i	−0.0142642	−	0.484577i
$465$	2.03729	−	7.54290i	0.0944769	−	0.349794i
$466$	24.5552	+	5.95913i	1.13750	+	0.276051i
$467$	6.38256	−	1.26957i	0.295349	−	0.0587487i	−0.0451915	−	0.998978i	$-0.514390\pi$
$467$	6.38256	−	1.26957i	0.295349	−	0.0587487i	0.340541	+	0.940230i	$0.389390\pi$
$468$	−26.9564	+	10.4768i	−1.24606	+	0.484288i
$469$	1.97657	+	2.95815i	0.0912697	+	0.136595i
$470$	0.641483	−	15.3631i	0.0295894	−	0.708649i
$471$	24.9645	−	32.4000i	1.15030	−	1.49291i
$472$	−0.252913	+	0.443890i	−0.0116412	+	0.0204317i
$473$	−0.113613	+	0.274286i	−0.00522392	+	0.0126117i
$474$	1.82825	−	0.159773i	0.0839743	−	0.00733862i
$475$	−1.23490	+	6.20826i	−0.0566611	+	0.284855i
$476$	−1.36113	+	1.15098i	−0.0623875	+	0.0527552i
$477$	−0.337452	−	0.691240i	−0.0154509	−	0.0316497i
$478$	4.22796	+	27.1261i	0.193382	+	1.24072i
$479$			32.8489i			1.50090i	0.660925	+	0.750452i	$0.270164\pi$
$479$			32.8489i			1.50090i	−0.660925	+	0.750452i	$0.729836\pi$
$480$	9.42687	+	2.67099i	0.430276	+	0.121913i
$481$			6.85893i			0.312740i
$482$	−25.7712	+	4.01678i	−1.17385	+	0.182959i
$483$	−0.784745	+	11.6169i	−0.0357071	+	0.528589i
$484$	21.8595	+	1.82866i	0.993614	+	0.0831210i
$485$	−0.854284	+	4.29477i	−0.0387910	+	0.195016i
$486$	12.4981	+	18.1603i	0.566927	+	0.823768i
$487$	−9.82817	+	23.7273i	−0.445357	+	1.07519i	0.528685	+	0.848818i	$0.322685\pi$
$487$	−9.82817	+	23.7273i	−0.445357	+	1.07519i	−0.974042	+	0.226369i	$0.927315\pi$
$488$	−1.86652	+	1.44924i	−0.0844935	+	0.0656038i
$489$	30.6786	+	23.6382i	1.38734	+	1.06895i
$490$	9.03165	+	0.377113i	0.408008	+	0.0170362i
$491$	−8.24464	−	12.3390i	−0.372076	−	0.556850i	0.597430	−	0.801921i	$-0.296189\pi$
$491$	−8.24464	−	12.3390i	−0.372076	−	0.556850i	−0.969505	+	0.245071i	$0.921189\pi$
$492$	1.06292	+	1.44417i	0.0479203	+	0.0651081i
$493$	−2.92649	+	0.582116i	−0.131803	+	0.0262172i
$494$	−10.1761	+	41.9317i	−0.457844	+	1.88660i
$495$	0.519454	−	0.136963i	0.0233477	−	0.00615604i
$496$	−14.7014	+	10.4617i	−0.660112	+	0.469743i
$497$	3.93774	−	3.93774i	0.176632	−	0.176632i
$498$	−8.11895	−	4.45523i	−0.363819	−	0.199644i
$499$	−1.54694	+	0.307705i	−0.0692504	+	0.0137748i	−0.229594	−	0.973287i	$-0.573740\pi$
$499$	−1.54694	+	0.307705i	−0.0692504	+	0.0137748i	0.160343	+	0.987061i	$0.448740\pi$
$500$	−0.552347	+	1.92222i	−0.0247017	+	0.0859641i
$501$	−8.65629	+	17.4651i	−0.386734	+	0.780283i
$502$	6.99295	+	7.60237i	0.312111	+	0.339311i
$503$	6.61667	+	15.9740i	0.295023	+	0.712248i	0.999995	+	0.00301334i	$0.000959178\pi$
$503$	6.61667	+	15.9740i	0.295023	+	0.712248i	−0.704973	+	0.709234i	$0.749041\pi$
$504$	−4.37130	−	4.96735i	−0.194713	−	0.221264i
$505$	−4.67480	+	11.2860i	−0.208026	+	0.502219i
$506$	0.750559	+	2.05000i	0.0333664	+	0.0911335i
$507$	−5.66396	−	16.7957i	−0.251545	−	0.745925i
$508$	23.8764	−	7.62820i	1.05934	−	0.338447i
$509$	−25.8817	−	17.2936i	−1.14718	−	0.766524i	−0.171388	−	0.985204i	$-0.554825\pi$
$509$	−25.8817	−	17.2936i	−1.14718	−	0.766524i	−0.975797	+	0.218680i	$0.929825\pi$
$510$	0.305055	−	2.78295i	0.0135081	−	0.123231i
$511$			0.446974i			0.0197730i
$512$	−12.8915	−	18.5960i	−0.569727	−	0.821834i
$513$	32.8905	+	0.197296i	1.45215	+	0.00871081i
$514$	22.4603	+	16.4029i	0.990679	+	0.723502i
$515$	6.42256	−	9.61204i	0.283012	−	0.423557i
$516$	−3.87243	+	4.24137i	−0.170474	+	0.186716i
$517$	−0.379839	+	1.90958i	−0.0167053	+	0.0839832i
$518$	−1.47361	+	0.539529i	−0.0647468	+	0.0237055i
$519$	−7.30405	+	0.946743i	−0.320612	+	0.0415574i
$520$	−4.30853	+	12.9346i	−0.188942	+	0.567222i
$521$	35.3313	−	14.6347i	1.54789	−	0.641158i	0.564958	−	0.825119i	$-0.308892\pi$
$521$	35.3313	−	14.6347i	1.54789	−	0.641158i	0.982933	+	0.183961i	$0.0588922\pi$
$522$	−2.37463	−	10.8185i	−0.103935	−	0.473515i
$523$	16.4305	+	24.5900i	0.718456	+	1.07525i	0.993502	+	0.113814i	$0.0363069\pi$
$523$	16.4305	+	24.5900i	0.718456	+	1.07525i	−0.275046	+	0.961431i	$0.588693\pi$
$524$	−37.1547	−	10.6764i	−1.62311	−	0.466399i
$525$	1.01726	−	0.888521i	0.0443968	−	0.0387782i
$526$	18.8911	+	30.9985i	0.823693	+	1.35160i
$527$	3.64566	+	3.64566i	0.158807	+	0.158807i
$528$	−1.12731	−	0.517993i	−0.0490600	−	0.0225428i
$529$	36.2841	−	36.2841i	1.57757	−	1.57757i
$530$	−0.352381	−	0.0855169i	−0.0153065	−	0.00371461i
$531$	−0.176231	+	0.512417i	−0.00764776	+	0.0222370i
$532$	−9.80932	+	1.11209i	−0.425288	+	0.0482152i
$533$	−2.07459	+	1.38620i	−0.0898606	+	0.0600429i
$534$	31.9119	−	16.6084i	1.38096	−	0.718714i
$535$	−3.86729	−	9.33646i	−0.167197	−	0.403650i
$536$	7.91393	+	10.1926i	0.341830	+	0.440254i
$537$	17.5012	−	2.26848i	0.755232	−	0.0978923i
$538$	14.3499	−	30.9269i	0.618668	−	1.33336i
$539$	−1.12260	−	0.223299i	−0.0483538	−	0.00961816i
$540$	10.3507	+	0.928449i	0.445425	+	0.0399541i
$541$	31.8262	+	21.2656i	1.36831	+	0.914278i	0.999882	−	0.0153773i	$-0.00489493\pi$
$541$	31.8262	+	21.2656i	1.36831	+	0.914278i	0.368431	+	0.929655i	$0.379895\pi$
$542$	3.17462	+	20.3680i	0.136362	+	0.874880i
$543$	−12.0870	−	21.0324i	−0.518704	−	0.902585i
$544$	−4.62766	+	4.51517i	−0.198409	+	0.193586i
$545$	0.597556			0.0255965
$546$	7.18097	−	5.76220i	0.307317	−	0.246599i
$547$	2.31494	−	3.46455i	0.0989796	−	0.148134i	−0.778674	−	0.627428i	$-0.784108\pi$
$547$	2.31494	−	3.46455i	0.0989796	−	0.148134i	0.877654	+	0.479295i	$0.159108\pi$
$548$	−16.8409	−	19.9158i	−0.719410	−	0.850763i
$549$	−1.66013	+	1.87781i	−0.0708526	+	0.0801431i
$550$	0.106588	−	0.229718i	0.00454491	−	0.00979522i
$551$	−15.2673	−	6.32391i	−0.650408	−	0.269408i
$552$	0.156635	+	42.2315i	0.00666682	+	1.79749i
$553$	−0.539776	+	0.223582i	−0.0229536	+	0.00950769i
$554$	−38.0741	−	1.58977i	−1.61761	−	0.0675429i
$555$	1.09451	−	2.20831i	0.0464595	−	0.0937377i
$556$	21.5921	−	27.1139i	0.915709	−	1.14989i
$557$	2.46929	+	12.4140i	0.104627	+	0.525996i	0.997180	+	0.0750525i	$0.0239124\pi$
$557$	2.46929	+	12.4140i	0.104627	+	0.525996i	−0.892552	+	0.450944i	$0.851088\pi$
$558$	−13.2633	+	13.7971i	−0.561482	+	0.584076i
$559$	−5.65080	−	5.65080i	−0.239003	−	0.239003i
$560$	−3.11787	+	0.0917787i	−0.131754	+	0.00387836i
$561$	−0.0924334	+	0.342227i	−0.00390254	+	0.0144489i
$562$	−0.366887	−	0.602025i	−0.0154762	−	0.0253949i
$563$	−3.89414	−	19.5771i	−0.164118	−	0.825078i	−0.971863	−	0.235546i	$-0.924312\pi$
$563$	−3.89414	−	19.5771i	−0.164118	−	0.825078i	0.807745	−	0.589532i	$-0.200688\pi$
$564$	−19.4812	+	32.2352i	−0.820308	+	1.35735i
$565$	−2.77417	+	1.85364i	−0.116710	+	0.0779832i
$566$	25.3569	+	27.5667i	1.06583	+	1.15872i
$567$	−5.53360	−	4.31683i	−0.232389	−	0.181290i
$568$	13.2309	−	15.2619i	0.555158	−	0.640374i
$569$	−5.12509	−	2.12288i	−0.214855	−	0.0889959i	0.272660	−	0.962110i	$-0.412097\pi$
$569$	−5.12509	−	2.12288i	−0.214855	−	0.0889959i	−0.487515	+	0.873115i	$0.662097\pi$
$570$	9.96757	−	11.8766i	0.417496	−	0.497454i
$571$	2.95229	+	0.587248i	0.123550	+	0.0245756i	0.256478	−	0.966550i	$-0.417438\pi$
$571$	2.95229	+	0.587248i	0.123550	+	0.0245756i	−0.132928	+	0.991126i	$0.542438\pi$
$572$	0.791269	−	1.53424i	0.0330846	−	0.0641499i
$573$	2.56782	−	38.0125i	0.107272	−	1.58800i
$574$	−0.461008	−	0.336678i	−0.0192421	−	0.0140527i
$575$	−8.62052			−0.359501
$576$	−17.0960	−	16.8442i	−0.712333	−	0.701842i
$577$	41.6401			1.73350			0.866751	−	0.498742i	$-0.166204\pi$
$577$	41.6401			1.73350			0.866751	+	0.498742i	$0.166204\pi$
$578$	−17.9234	−	13.0896i	−0.745513	−	0.544455i
$579$	0.831896	−	12.3149i	0.0345724	−	0.511791i
$580$	−4.64051	−	2.39329i	−0.192687	−	0.0993761i
$581$	2.89163	+	0.575181i	0.119965	+	0.0238625i
$582$	6.89540	−	8.21601i	0.285824	−	0.340564i
$583$	0.0424190	+	0.0175705i	0.00175681	+	0.000727696i
$584$	0.115266	+	1.61711i	0.00476973	+	0.0669167i
$585$	−1.94477	+	14.3290i	−0.0804065	+	0.592431i
$586$	9.30947	+	10.1208i	0.384571	+	0.418085i
$587$	−14.6755	+	9.80588i	−0.605724	+	0.404732i	−0.820266	−	0.571983i	$-0.806174\pi$
$587$	−14.6755	+	9.80588i	−0.605724	+	0.404732i	0.214541	+	0.976715i	$0.431174\pi$
$588$	−18.9504	−	11.4526i	−0.781499	−	0.472296i
$589$	5.57057	+	28.0051i	0.229531	+	1.15393i
$590$	0.132932	+	0.218128i	0.00547272	+	0.00898019i
$591$	−1.24760	+	4.61914i	−0.0513194	+	0.190006i
$592$	−5.19228	+	2.33199i	−0.213401	+	0.0958441i
$593$	25.9594	+	25.9594i	1.06603	+	1.06603i	0.997660	+	0.0683661i	$0.0217786\pi$
$593$	25.9594	+	25.9594i	1.06603	+	1.06603i	0.0683661	+	0.997660i	$0.478221\pi$
$594$	−1.27688	−	0.317999i	−0.0523911	−	0.0130477i
$595$	0.173878	+	0.874144i	0.00712831	+	0.0358364i
$596$	−8.08175	−	6.43587i	−0.331041	−	0.263624i
$597$	9.46942	−	19.1057i	0.387558	−	0.781944i
$598$	−58.7122	−	2.45151i	−2.40092	−	0.100250i
$599$	13.9506	−	5.77852i	0.570005	−	0.236104i	−0.0790170	−	0.996873i	$-0.525178\pi$
$599$	13.9506	−	5.77852i	0.570005	−	0.236104i	0.649022	+	0.760769i	$0.275178\pi$
$600$	3.45123	−	3.47693i	0.140896	−	0.141945i
$601$	4.28556	+	1.77514i	0.174812	+	0.0724094i	0.468373	−	0.883531i	$-0.344840\pi$
$601$	4.28556	+	1.77514i	0.174812	+	0.0724094i	−0.293561	+	0.955940i	$0.594840\pi$
$602$	0.769555	−	1.65855i	0.0313647	−	0.0675974i
$603$	10.2543	+	9.06557i	0.417587	+	0.369178i
$604$	−15.2157	+	12.8664i	−0.619116	+	0.523528i
$605$	6.09346	−	9.11950i	0.247734	−	0.370761i
$606$	23.3380	−	18.7270i	0.948040	−	0.760732i
$607$	−37.1970			−1.50978			−0.754890	−	0.655851i	$-0.772310\pi$
$607$	−37.1970			−1.50978			−0.754890	+	0.655851i	$0.772310\pi$
$608$	−35.2025	+	6.55308i	−1.42765	+	0.265762i
$609$	1.75695	+	3.05722i	0.0711951	+	0.123885i
$610$	0.181962	+	1.16745i	0.00736744	+	0.0472686i
$611$	−43.5760	−	29.1166i	−1.76290	−	1.17793i
$612$	−3.93447	+	5.61669i	−0.159041	+	0.227041i
$613$	9.13188	+	1.81644i	0.368833	+	0.0733655i	0.376027	−	0.926609i	$-0.377290\pi$
$613$	9.13188	+	1.81644i	0.368833	+	0.0733655i	−0.00719389	+	0.999974i	$0.502290\pi$
$614$	−1.13626	+	2.44887i	−0.0458557	+	0.0988283i
$615$	0.889142	−	0.115250i	0.0358537	−	0.00464731i
$616$	0.391867	+	0.0493163i	0.0157888	+	0.00198701i
$617$	−8.94514	−	21.5955i	−0.360118	−	0.869401i	−0.995282	−	0.0970242i	$-0.969068\pi$
$617$	−8.94514	−	21.5955i	−0.360118	−	0.869401i	0.635164	−	0.772377i	$-0.280932\pi$
$618$	−25.1186	+	13.0728i	−1.01042	+	0.525867i
$619$	−12.1021	+	8.08635i	−0.486423	+	0.325018i	−0.774483	−	0.632595i	$-0.781990\pi$
$619$	−12.1021	+	8.08635i	−0.486423	+	0.325018i	0.288060	+	0.957612i	$0.406990\pi$
$620$	1.01631	+	8.96446i	0.0408159	+	0.360021i
$621$	8.47510	+	43.9845i	0.340094	+	1.76504i
$622$	−45.1881	−	10.9664i	−1.81188	−	0.439711i
$623$	−8.09836	+	8.09836i	−0.324454	+	0.324454i
$624$	24.4942	−	22.6990i	0.980553	−	0.908687i
$625$	0.707107	+	0.707107i	0.0282843	+	0.0282843i
$626$	9.89999	+	16.2449i	0.395683	+	0.649277i
$627$	−1.47864	+	1.29151i	−0.0590512	+	0.0515780i
$628$	−13.0436	+	45.3929i	−0.520496	+	1.81137i
$629$	0.903568	+	1.35229i	0.0360276	+	0.0539191i
$630$	−3.23150	+	0.709303i	−0.128746	+	0.0282593i
$631$	−22.8666	+	9.47165i	−0.910305	+	0.377061i	−0.788173	−	0.615453i	$-0.788973\pi$
$631$	−22.8666	+	9.47165i	−0.910305	+	0.377061i	−0.122132	+	0.992514i	$0.538973\pi$
$632$	−1.89521	+	0.948100i	−0.0753873	+	0.0377134i
$633$	−26.5458	+	3.44084i	−1.05510	+	0.136761i
$634$	−33.1859	+	12.1502i	−1.31798	+	0.482548i
$635$	2.44500	−	12.2918i	0.0970268	−	0.487787i
$636$	0.655939	+	0.598881i	0.0260097	+	0.0237472i
$637$	17.1170	−	25.6174i	0.678200	−	1.01500i
$638$	0.533906	+	0.389916i	0.0211375	+	0.0154369i
$639$	10.7860	−	18.5106i	0.426688	−	0.732268i
$640$	−11.2565	+	1.13608i	−0.444953	+	0.0449077i
$641$			8.88590i			0.350972i	0.984482	+	0.175486i	$0.0561496\pi$
$641$			8.88590i			0.350972i	−0.984482	+	0.175486i	$0.943850\pi$
$642$	−2.69725	+	24.6064i	−0.106452	+	0.971139i
$643$	−31.7074	−	21.1862i	−1.25042	−	0.835502i	−0.258954	−	0.965890i	$-0.583378\pi$
$643$	−31.7074	−	21.1862i	−1.25042	−	0.835502i	−0.991463	+	0.130388i	$0.958378\pi$
$644$	−4.09165	−	12.8069i	−0.161234	−	0.504663i
$645$	0.917615	+	2.72107i	0.0361311	+	0.107142i
$646$	3.51763	+	9.60768i	0.138399	+	0.378009i
$647$	−0.195443	+	0.471841i	−0.00768366	+	0.0185500i	−0.927675	−	0.373389i	$-0.878196\pi$
$647$	−0.195443	+	0.471841i	−0.00768366	+	0.0185500i	0.919991	+	0.391939i	$0.128196\pi$
$648$	−21.1333	−	14.1909i	−0.830195	−	0.557472i
$649$	−0.0123776	−	0.0298823i	−0.000485865	−	0.00117298i
$650$	4.61484	+	5.01701i	0.181009	+	0.196783i
$651$	2.70568	−	5.45903i	0.106044	−	0.213956i
$652$	−42.9812	−	12.3506i	−1.68327	−	0.483687i
$653$	−8.56948	+	1.70458i	−0.335350	+	0.0667052i	−0.359893	−	0.932994i	$-0.617187\pi$
$653$	−8.56948	+	1.70458i	−0.335350	+	0.0667052i	0.0245434	+	0.999699i	$0.492187\pi$
$654$	−1.28320	−	0.704151i	−0.0501773	−	0.0275345i
$655$	−13.6677	+	13.6677i	−0.534042	+	0.534042i
$656$	−1.75471	−	1.09919i	−0.0685100	−	0.0429161i
$657$	0.438409	+	1.66273i	0.0171040	+	0.0648695i
$658$	2.82785	−	11.6525i	0.110241	−	0.454260i
$659$	49.2421	−	9.79487i	1.91820	−	0.381554i	0.918304	−	0.395877i	$-0.129559\pi$
$659$	49.2421	−	9.79487i	1.91820	−	0.381554i	0.999897	+	0.0143227i	$0.00455920\pi$
$660$	−0.499585	+	0.367700i	−0.0194463	+	0.0143127i
$661$	−17.1452	−	25.6596i	−0.666872	−	0.998044i	−0.998506	−	0.0546361i	$-0.982600\pi$
$661$	−17.1452	−	25.6596i	−0.666872	−	0.998044i	0.331635	−	0.943408i	$-0.392400\pi$
$662$	−34.8043	−	1.45324i	−1.35271	−	0.0564818i
$663$	−7.55859	−	5.82396i	−0.293551	−	0.226184i
$664$	10.6100	+	1.33526i	0.411748	+	0.0518183i
$665$	−1.88895	+	4.56034i	−0.0732505	+	0.176842i
$666$	−4.95262	+	3.45242i	−0.191910	+	0.133778i
$667$	4.39056	−	22.0728i	0.170003	−	0.854663i
$668$	1.87636	−	22.4297i	0.0725987	−	0.867833i
$669$	−2.46954	+	36.5577i	−0.0954780	+	1.41340i
$670$	6.37516	−	0.993652i	0.246294	−	0.0383881i
$671$		−	0.149608i		−	0.00577556i
$672$	6.80352	+	3.47696i	0.262451	+	0.134127i
$673$		−	3.54225i		−	0.136544i	−0.997667	−	0.0682719i	$-0.978251\pi$
$673$		−	3.54225i		−	0.136544i	0.997667	−	0.0682719i	$-0.0217485\pi$
$674$	5.76108	+	36.9624i	0.221908	+	1.42374i
$675$	2.91269	−	4.30305i	0.112110	−	0.165624i
$676$	13.2156	+	15.6286i	0.508292	+	0.601098i
$677$	0.719999	−	3.61968i	0.0276718	−	0.139116i	−0.964480	−	0.264157i	$-0.914906\pi$
$677$	0.719999	−	3.61968i	0.0276718	−	0.139116i	0.992152	+	0.125041i	$0.0399063\pi$
$678$	8.14160	−	0.711505i	0.312676	−	0.0273252i
$679$	−1.30675	+	3.15477i	−0.0501484	+	0.121069i
$680$	0.854502	+	3.11774i	0.0327686	+	0.119560i
$681$	−19.7851	+	25.6779i	−0.758165	+	0.983980i
$682$	0.0476573	−	1.14137i	0.00182489	−	0.0437051i
$683$	−8.95806	−	13.4067i	−0.342771	−	0.512992i	0.619533	−	0.784971i	$-0.287322\pi$
$683$	−8.95806	−	13.4067i	−0.342771	−	0.512992i	−0.962303	+	0.271978i	$0.912322\pi$
$684$	−35.3997	+	13.7583i	−1.35354	+	0.526062i
$685$	−12.7903	+	2.54415i	−0.488692	+	0.0972070i
$686$	14.3521	+	3.48302i	0.547967	+	0.132982i
$687$	−7.60289	+	28.1491i	−0.290068	+	1.07396i
$688$	2.35648	−	6.19895i	0.0898400	−	0.236333i
$689$	−0.873911	+	0.873911i	−0.0332934	+	0.0332934i
$690$	18.5119	+	10.1583i	0.704735	+	0.386720i
$691$	15.4080	−	3.06484i	0.586147	−	0.116592i	0.106897	−	0.994270i	$-0.465909\pi$
$691$	15.4080	−	3.06484i	0.586147	−	0.116592i	0.479251	+	0.877678i	$0.340909\pi$
$692$	7.44054	−	4.11894i	0.282847	−	0.156578i
$693$	0.418126	−	0.0257266i	0.0158833	−	0.000977272i
$694$	10.4678	−	9.62867i	0.397352	−	0.365499i
$695$	−6.63209	−	16.0113i	−0.251570	−	0.607343i
$696$	7.14489	+	10.6077i	0.270826	+	0.402084i
$697$	−0.226408	+	0.546597i	−0.00857582	+	0.0207039i
$698$	25.5215	−	9.34411i	0.966004	−	0.353680i
$699$	−29.3243	+	9.88892i	−1.10915	+	0.374033i
$700$	−0.714877	+	1.38612i	−0.0270198	+	0.0523904i
$701$	27.4011	+	18.3088i	1.03492	+	0.691514i	0.952330	−	0.305069i	$-0.0986797\pi$
$701$	27.4011	+	18.3088i	1.03492	+	0.691514i	0.0825935	+	0.996583i	$0.473680\pi$
$702$	21.0613	−	28.4787i	0.794908	−	1.07486i
$703$			9.00730i			0.339717i
$704$	1.43046	+	0.0773674i	0.0539125	+	0.00291589i
$705$	9.38354	+	16.3281i	0.353404	+	0.614951i
$706$	18.2548	−	24.9959i	0.687027	−	0.940735i
$707$	−5.29235	+	7.92056i	−0.199039	+	0.297883i
$708$	−0.0284218	−	0.625058i	−0.00106816	−	0.0234911i
$709$	−7.26807	+	36.5391i	−0.272958	+	1.37225i	0.564356	+	0.825532i	$0.309125\pi$
$709$	−7.26807	+	36.5391i	−0.272958	+	1.37225i	−0.837314	+	0.546722i	$0.815875\pi$
$710$	−3.47221	−	9.48364i	−0.130310	−	0.355915i
$711$	−1.78866	+	1.36116i	−0.0670799	+	0.0510473i
$712$	−27.2108	+	31.3876i	−1.01977	+	1.17630i
$713$	−35.9266	+	14.8813i	−1.34546	+	0.557309i
$714$	0.656689	−	2.08205i	0.0245760	−	0.0779188i
$715$	−0.479532	−	0.717670i	−0.0179335	−	0.0268393i
$716$	−17.8282	+	9.86936i	−0.666272	+	0.368835i
$717$	−22.1190	−	25.3239i	−0.826050	−	0.945738i
$718$	18.8301	−	11.4754i	0.702732	−	0.428260i
$719$	19.0181	+	19.0181i	0.709255	+	0.709255i	0.966379	−	0.257123i	$-0.0827747\pi$
$719$	19.0181	+	19.0181i	0.709255	+	0.709255i	−0.257123	+	0.966379i	$0.582775\pi$
$720$	−11.5084	+	3.39954i	−0.428892	+	0.126693i
$721$	6.37441	−	6.37441i	0.237395	−	0.237395i
$722$	−7.02652	+	28.9535i	−0.261500	+	1.07754i
$723$	24.0590	−	21.0142i	0.894764	−	0.781527i
$724$	21.9118	+	17.4494i	0.814346	+	0.648502i
$725$	−2.17068	+	1.45040i	−0.0806171	+	0.0538667i
$726$	−23.8315	+	12.4030i	−0.884470	+	0.460317i
$727$	−12.4300	−	30.0088i	−0.461005	−	1.11296i	−0.967985	−	0.251007i	$-0.919238\pi$
$727$	−12.4300	−	30.0088i	−0.461005	−	1.11296i	0.506980	−	0.861958i	$-0.330762\pi$
$728$	−5.26303	+	9.23722i	−0.195061	+	0.342354i
$729$	−24.8190	−	10.6310i	−0.919222	−	0.393739i
$730$	0.735311	+	0.341179i	0.0272151	+	0.0126276i
$731$	−1.85851	−	0.369680i	−0.0687394	−	0.0136731i
$732$	0.984955	−	2.72142i	0.0364050	−	0.100587i
$733$	21.6918	+	14.4940i	0.801205	+	0.535348i	0.887438	−	0.460927i	$-0.152483\pi$
$733$	21.6918	+	14.4940i	0.801205	+	0.535348i	−0.0862330	+	0.996275i	$0.527483\pi$
$734$	−11.2646	+	1.75573i	−0.415783	+	0.0648052i
$735$	−9.59891	+	5.51637i	−0.354061	+	0.203474i
$736$	−18.1059	−	45.2792i	−0.667393	−	1.66901i
$737$	−0.816975			−0.0300936
$738$	−2.04517	−	0.800263i	−0.0752837	−	0.0294581i
$739$	2.53667	−	3.79640i	0.0933131	−	0.139653i	−0.781876	−	0.623434i	$-0.785737\pi$
$739$	2.53667	−	3.79640i	0.0933131	−	0.139653i	0.875189	+	0.483781i	$0.160737\pi$
$740$	−0.237250	+	2.83605i	−0.00872150	+	0.104255i
$741$	−16.8868	−	50.0756i	−0.620352	−	1.83957i
$742$	−0.256499	−	0.119014i	−0.00941637	−	0.00436913i
$743$	−11.4335	−	4.73592i	−0.419455	−	0.173744i	0.162965	−	0.986632i	$-0.447894\pi$
$743$	−11.4335	−	4.73592i	−0.419455	−	0.173744i	−0.582420	+	0.812888i	$0.697894\pi$
$744$	8.38115	−	20.4481i	0.307268	−	0.749662i
$745$	−4.77242	+	1.97680i	−0.174848	+	0.0724244i
$746$	1.91750	−	45.9229i	0.0702045	−	1.68136i
$747$	11.3210	−	0.696560i	0.414213	−	0.0254858i
$748$	−0.0461107	−	0.406725i	−0.00168597	−	0.0148713i
$749$	−1.53740	−	7.72906i	−0.0561755	−	0.282414i
$750$	−0.685211	−	2.35170i	−0.0250204	−	0.0858719i
$751$	−18.4833	−	18.4833i	−0.674465	−	0.674465i	0.284278	−	0.958742i	$-0.408246\pi$
$751$	−18.4833	−	18.4833i	−0.674465	−	0.674465i	−0.958742	+	0.284278i	$0.908246\pi$
$752$	7.22599	−	42.8869i	0.263505	−	1.56392i
$753$	−12.2133	−	3.29873i	−0.445077	−	0.120212i
$754$	−15.1964	+	9.26103i	−0.553422	+	0.337267i
$755$	1.94372	+	9.77176i	0.0707393	+	0.355631i
$756$	7.77522	+	2.28478i	0.282782	+	0.0830967i
$757$	2.86070	−	1.91146i	0.103974	−	0.0694732i	−0.502496	−	0.864579i	$-0.667585\pi$
$757$	2.86070	−	1.91146i	0.103974	−	0.0694732i	0.606470	+	0.795106i	$0.292585\pi$
$758$	25.8523	−	23.7799i	0.938996	−	0.863724i
$759$	−2.11794	−	1.63189i	−0.0768764	−	0.0592339i
$760$	−5.65806	+	16.9861i	−0.205239	+	0.616149i
$761$	−28.9159	−	11.9773i	−1.04820	−	0.434178i	−0.208950	−	0.977926i	$-0.567005\pi$
$761$	−28.9159	−	11.9773i	−1.04820	−	0.434178i	−0.839249	+	0.543748i	$0.817005\pi$
$762$	−19.7350	+	23.5146i	−0.714922	+	0.851844i
$763$	0.457024	+	0.0909077i	0.0165454	+	0.00329108i
$764$	13.3886	+	41.9063i	0.484381	+	1.51612i
$765$	1.50422	+	3.08126i	0.0543851	+	0.111403i
$766$	5.55648	−	7.60840i	0.200764	−	0.274903i
$767$	0.870634			0.0314368
$768$	25.5112	+	10.8249i	0.920557	+	0.390609i
$769$	35.5966			1.28365			0.641824	−	0.766852i	$-0.278178\pi$
$769$	35.5966			1.28365			0.641824	+	0.766852i	$0.278178\pi$
$770$	0.116468	−	0.159478i	0.00419722	−	0.00574718i
$771$	−33.9854	−	2.29578i	−1.22395	−	0.0826803i
$772$	4.33750	+	13.5764i	0.156110	+	0.488626i
$773$	−21.0228	−	4.18169i	−0.756137	−	0.150405i	−0.198055	−	0.980191i	$-0.563462\pi$
$773$	−21.0228	−	4.18169i	−0.756137	−	0.150405i	−0.558082	+	0.829786i	$0.688462\pi$
$774$	1.23596	−	6.92458i	0.0444257	−	0.248899i
$775$	4.16757	+	1.72626i	0.149704	+	0.0620092i
$776$	−3.91416	+	11.7507i	−0.140510	+	0.421825i
$777$	1.17306	−	1.52245i	0.0420834	−	0.0546177i
$778$	23.3378	−	21.4670i	0.836702	−	0.769630i
$779$	−2.72440	+	1.82039i	−0.0976118	+	0.0652221i
$780$	−3.99802	−	16.2117i	−0.143152	−	0.580471i
$781$	0.249478	+	1.25421i	0.00892702	+	0.0448791i
$782$	−11.8985	+	7.25118i	−0.425488	+	0.259302i
$783$	9.53446	+	9.64954i	0.340734	+	0.344846i
$784$	25.2123	+	4.24800i	0.900438	+	0.151714i
$785$	16.6982	+	16.6982i	0.595985	+	0.595985i
$786$	45.4562	−	13.2445i	1.62137	−	0.472415i
$787$	−8.42290	−	42.3448i	−0.300244	−	1.50943i	−0.776498	−	0.630120i	$-0.783006\pi$
$787$	−8.42290	−	42.3448i	−0.300244	−	1.50943i	0.476254	−	0.879308i	$-0.341994\pi$
$788$	−0.622369	−	5.48968i	−0.0221710	−	0.195562i
$789$	−39.8354	−	19.7437i	−1.41818	−	0.702896i
$790$	−0.0442032	+	1.05864i	−0.00157268	+	0.0376648i
$791$	−2.40374	+	0.995662i	−0.0854671	+	0.0354016i
$792$	1.50611	−	0.200903i	0.0535173	−	0.00713878i
$793$	3.72056	+	1.54111i	0.132121	+	0.0547263i
$794$	47.2374	+	21.9178i	1.67639	+	0.777835i
$795$	0.420820	−	0.141912i	0.0149250	−	0.00503308i
$796$	−2.05262	+	24.5367i	−0.0727533	+	0.869681i
$797$	28.5915	−	42.7902i	1.01276	−	1.51571i	0.164326	−	0.986406i	$-0.447455\pi$
$797$	28.5915	−	42.7902i	1.01276	−	1.51571i	0.848435	−	0.529299i	$-0.177545\pi$
$798$	9.43021	−	7.56705i	0.333826	−	0.267871i
$799$	−12.4270			−0.439636
$800$	−2.22892	+	5.19922i	−0.0788041	+	0.183820i
$801$	−22.1826	+	38.0690i	−0.783783	+	1.34510i
$802$	44.3430	−	6.91144i	1.56581	−	0.244052i
$803$	−0.0853420	−	0.0570237i	−0.00301166	−	0.00201232i
$804$	−14.8610	−	5.37860i	−0.524108	−	0.189689i
$805$	−6.59316	−	1.31146i	−0.232378	−	0.0462229i
$806$	27.8933	+	12.9423i	0.982501	+	0.455874i
$807$	5.36751	+	41.4099i	0.188945	+	1.45770i
$808$	−17.1047	+	30.0207i	−0.601742	+	1.05613i
$809$	3.45259	+	8.33528i	0.121386	+	0.293053i	0.972879	−	0.231313i	$-0.0743023\pi$
$809$	3.45259	+	8.33528i	0.121386	+	0.293053i	−0.851493	+	0.524366i	$0.824302\pi$
$810$	−11.3254	+	5.80818i	−0.397935	+	0.204079i
$811$	−39.2545	+	26.2290i	−1.37841	+	0.921026i	−0.999989	−	0.00460591i	$-0.998534\pi$
$811$	−39.2545	+	26.2290i	−1.37841	+	0.921026i	−0.378424	+	0.925632i	$0.623534\pi$
$812$	−3.18506	−	2.53641i	−0.111774	−	0.0890106i
$813$	−16.6084	−	19.0148i	−0.582481	−	0.666878i
$814$	0.0849858	−	0.350193i	0.00297875	−	0.0122743i
$815$	−15.8111	+	15.8111i	−0.553838	+	0.553838i
$816$	1.83893	−	7.70203i	0.0643754	−	0.269625i
$817$	−7.42076	−	7.42076i	−0.259620	−	0.259620i
$818$	−24.5356	+	14.9525i	−0.857866	+	0.522802i
$819$	−3.66731	+	10.6632i	−0.128146	+	0.372604i
$820$	−0.905758	+	0.501410i	−0.0316304	+	0.0175100i
$821$	−0.220880	−	0.330570i	−0.00770875	−	0.0115370i	0.827595	−	0.561325i	$-0.189708\pi$
$821$	−0.220880	−	0.330570i	−0.00770875	−	0.0115370i	−0.835304	+	0.549788i	$0.814708\pi$
$822$	30.4641	+	9.60854i	1.06256	+	0.335136i
$823$	−5.07973	+	2.10409i	−0.177068	+	0.0733441i	−0.469456	−	0.882956i	$-0.655550\pi$
$823$	−5.07973	+	2.10409i	−0.177068	+	0.0733441i	0.292388	+	0.956300i	$0.405550\pi$
$824$	21.4183	−	24.7059i	0.746141	−	0.860672i
$825$	0.0398686	+	0.307584i	0.00138805	+	0.0107087i
$826$	0.0684848	+	0.187052i	0.00238289	+	0.00650838i
$827$	−11.0399	+	55.5014i	−0.383895	+	1.92997i	−0.0166118	+	0.999862i	$0.505288\pi$
$827$	−11.0399	+	55.5014i	−0.383895	+	1.92997i	−0.367283	+	0.930109i	$0.619712\pi$
$828$	−27.7824	−	43.6282i	−0.965505	−	1.51619i
$829$	5.69144	−	8.51784i	0.197672	−	0.295837i	−0.719371	−	0.694626i	$-0.755570\pi$
$829$	5.69144	−	8.51784i	0.197672	−	0.295837i	0.917042	+	0.398790i	$0.130570\pi$
$830$	3.15343	−	4.31794i	0.109457	−	0.149878i
$831$	40.4654	−	23.2550i	1.40373	−	0.806706i
$832$	−16.6591	+	34.7767i	−0.577551	+	1.20567i
$833$		−	7.30556i		−	0.253123i
$834$	−4.62557	+	42.1981i	−0.160171	+	1.46120i
$835$	−9.35740	−	6.25241i	−0.323826	−	0.216374i
$836$	1.03911	−	2.01480i	0.0359384	−	0.0696833i
$837$	4.71065	−	22.9613i	0.162824	−	0.793660i
$838$	−4.13753	+	1.51486i	−0.142928	+	0.0523299i
$839$	8.85111	−	21.3685i	0.305574	−	0.737721i	−0.694264	−	0.719721i	$-0.744270\pi$
$839$	8.85111	−	21.3685i	0.305574	−	0.737721i	0.999838	−	0.0180006i	$-0.00573008\pi$
$840$	3.16853	−	2.13418i	0.109325	−	0.0736363i
$841$	8.48963	+	20.4958i	0.292746	+	0.706751i
$842$	−10.3948	+	9.56157i	−0.358230	+	0.329514i
$843$	0.773648	+	0.383446i	0.0266458	+	0.0132066i
$844$	27.0419	−	14.9699i	0.930821	−	0.515284i
$845$	10.0369	−	1.99647i	0.345281	−	0.0686806i
$846$	−0.909637	−	46.1206i	−0.0312740	−	1.58566i
$847$	6.04777	−	6.04777i	0.207804	−	0.207804i
$848$	−0.958683	−	0.364436i	−0.0329213	−	0.0125148i
$849$	−44.2862	−	11.9614i	−1.51990	−	0.410515i
$850$	1.57077	+	0.381198i	0.0538769	+	0.0130750i
$851$	−12.0311	+	2.39314i	−0.412422	+	0.0820357i
$852$	−3.71908	+	24.4569i	−0.127413	+	0.837881i
$853$	9.69320	+	14.5069i	0.331889	+	0.496707i	0.959457	−	0.281855i	$-0.0909496\pi$
$853$	9.69320	+	14.5069i	0.331889	+	0.496707i	−0.627568	+	0.778562i	$0.715950\pi$
$854$	−0.0384382	+	0.920572i	−0.00131533	+	0.0315013i
$855$	−2.55392	+	18.8171i	−0.0873422	+	0.643533i
$856$	−7.55538	−	27.5666i	−0.258237	−	0.942208i
$857$	−10.0029	+	24.1491i	−0.341693	+	0.824919i	0.655852	+	0.754889i	$0.272309\pi$
$857$	−10.0029	+	24.1491i	−0.341693	+	0.824919i	−0.997545	+	0.0700296i	$0.977691\pi$
$858$	0.184064	+	2.10621i	0.00628385	+	0.0719049i
$859$	2.26471	−	11.3854i	0.0772708	−	0.388466i	−0.922725	−	0.385460i	$-0.874043\pi$
$859$	2.26471	−	11.3854i	0.0772708	−	0.388466i	0.999995	−	0.00300676i	$-0.000957083\pi$
$860$	−2.14105	−	2.53197i	−0.0730092	−	0.0863395i
$861$	0.697568	+	0.0471220i	0.0237730	+	0.00160591i
$862$	0.907291	+	5.82107i	0.0309025	+	0.198267i
$863$		−	24.8484i		−	0.845849i	−0.906165	−	0.422925i	$-0.861003\pi$
$863$		−	24.8484i		−	0.845849i	0.906165	−	0.422925i	$-0.138997\pi$
$864$	28.7193	+	6.26107i	0.977051	+	0.213006i
$865$		−	4.25227i		−	0.144582i
$866$	3.04427	−	0.474489i	0.103448	−	0.0161238i
$867$	27.1205	+	1.83204i	0.921059	+	0.0622192i
$868$	−0.586491	+	7.01082i	−0.0199068	+	0.237963i
$869$	0.0261739	−	0.131585i	0.000887889	−	0.00446372i
$870$	6.37050	−	0.556726i	0.215980	−	0.0188748i
$871$	8.41561	−	20.3171i	0.285152	−	0.688418i
$872$	1.67692	+	0.211039i	0.0567876	+	0.00714669i
$873$	−1.76676	+	13.0174i	−0.0597958	+	0.440572i
$874$	−77.1022	−	3.21937i	−2.60802	−	0.108897i
$875$	0.433236	+	0.648384i	0.0146461	+	0.0219194i
$876$	−1.17698	−	1.59914i	−0.0397665	−	0.0540298i
$877$	16.7688	−	3.33551i	0.566241	−	0.112632i	0.0963351	−	0.995349i	$-0.469288\pi$
$877$	16.7688	−	3.33551i	0.566241	−	0.112632i	0.469906	+	0.882717i	$0.344288\pi$
$878$	−0.892804	+	3.67889i	−0.0301307	+	0.124157i
$879$	−16.2591	−	4.39148i	−0.548407	−	0.148121i
$880$	0.380246	−	0.607013i	0.0128181	−	0.0204624i
$881$	−16.7358	+	16.7358i	−0.563842	+	0.563842i	−0.930397	−	0.366554i	$-0.880537\pi$
$881$	−16.7358	+	16.7358i	−0.563842	+	0.563842i	0.366554	+	0.930397i	$0.380537\pi$
$882$	27.1133	−	0.534755i	0.912952	−	0.0180061i
$883$	57.0999	−	11.3579i	1.92156	−	0.382223i	0.921582	−	0.388183i	$-0.126897\pi$
$883$	57.0999	−	11.3579i	1.92156	−	0.382223i	0.999982	+	0.00595994i	$0.00189712\pi$
$884$	10.5897	+	3.04294i	0.356170	+	0.102345i
$885$	−0.280311	−	0.138932i	−0.00942255	−	0.00467013i
$886$	38.0320	+	41.3465i	1.27771	+	1.38906i
$887$	−21.6108	−	52.1731i	−0.725619	−	1.75180i	−0.656668	−	0.754180i	$-0.728035\pi$
$887$	−21.6108	−	52.1731i	−0.725619	−	1.75180i	−0.0689512	−	0.997620i	$-0.521965\pi$
$888$	3.85144	−	5.81062i	0.129246	−	0.194992i
$889$	3.73997	−	9.02909i	0.125435	−	0.302826i
$890$	7.14097	+	19.5041i	0.239366	+	0.653778i
$891$	1.53019	−	0.505817i	0.0512632	−	0.0169455i
$892$	−12.8762	−	40.3025i	−0.431126	−	1.34943i
$893$	−57.2250	−	38.2365i	−1.91496	−	1.27954i
$894$	12.5778	+	1.37873i	0.420665	+	0.0461115i
$895$			10.1888i			0.340576i
$896$	−8.78206	−	0.843580i	−0.293388	−	0.0281820i
$897$	62.3998	−	35.8604i	2.08347	−	1.19734i
$898$	−11.6693	−	8.52222i	−0.389411	−	0.284390i
$899$	−6.54269	+	9.79183i	−0.218211	+	0.326576i
$900$	−1.29977	+	5.85752i	−0.0433257	+	0.195251i
$901$	−0.0571720	+	0.287423i	−0.00190468	+	0.00957546i
$902$	0.123097	−	0.0450692i	0.00409869	−	0.00150064i
$903$	0.287848	+	2.22073i	0.00957900	+	0.0739012i
$904$	−8.43977	+	4.22210i	−0.280703	+	0.140425i
$905$	12.9393	−	5.35965i	0.430118	−	0.178161i
$906$	7.34090	−	23.2745i	0.243885	−	0.773244i
$907$	7.65516	+	11.4568i	0.254186	+	0.380416i	0.936514	−	0.350630i	$-0.114033\pi$
$907$	7.65516	+	11.4568i	0.254186	+	0.380416i	−0.682328	+	0.731046i	$0.739033\pi$
$908$	10.3374	−	35.9751i	0.343059	−	1.19388i
$909$	−11.9186	+	34.6553i	−0.395317	+	1.14944i
$910$	2.76627	+	4.53918i	0.0917011	+	0.150472i
$911$	1.50750	+	1.50750i	0.0499457	+	0.0499457i	0.731639	−	0.681693i	$-0.238756\pi$
$911$	1.50750	+	1.50750i	0.0499457	+	0.0499457i	−0.681693	+	0.731639i	$0.738756\pi$
$912$	32.1663	−	29.8088i	1.06513	−	0.987069i
$913$	−0.478727	+	0.478727i	−0.0158436	+	0.0158436i
$914$	12.6195	+	3.06254i	0.417417	+	0.101300i
$915$	−0.951956	−	1.08989i	−0.0314707	−	0.0360305i
$916$	−3.79273	−	33.4542i	−0.125315	−	1.10536i
$917$	−12.5327	+	8.37406i	−0.413865	+	0.276536i
$918$	0.400716	−	8.38930i	0.0132256	−	0.276888i
$919$	−3.84230	−	9.27612i	−0.126746	−	0.305991i	0.847751	−	0.530395i	$-0.177956\pi$
$919$	−3.84230	−	9.27612i	−0.126746	−	0.305991i	−0.974496	+	0.224404i	$0.927956\pi$
$920$	−24.1917	−	3.04451i	−0.797577	−	0.100375i
$921$	−0.425012	−	3.27894i	−0.0140046	−	0.108045i
$922$	2.30252	−	4.96240i	0.0758295	−	0.163428i
$923$	−33.7604	−	6.71536i	−1.11124	−	0.221039i
$924$	−0.438032	+	0.205222i	−0.0144102	+	0.00675130i
$925$	1.18316	+	0.790565i	0.0389022	+	0.0259936i
$926$	−7.54826	−	48.4288i	−0.248051	−	1.59147i
$927$	17.4604	−	29.9650i	0.573476	−	0.984179i
$928$	−12.1774	−	8.35517i	−0.399742	−	0.274272i
$929$	20.6135			0.676308			0.338154	−	0.941091i	$-0.390197\pi$
$929$	20.6135			0.676308			0.338154	+	0.941091i	$0.390197\pi$
$930$	−6.91532	−	8.61801i	−0.226762	−	0.282596i
$931$	22.4784	−	33.6413i	0.736700	−	1.10255i
$932$	27.2865	−	23.0736i	0.893798	−	0.755801i
$933$	53.9644	−	18.1982i	1.76672	−	0.595782i
$934$	3.87353	−	8.34826i	0.126746	−	0.273163i
$935$	−0.189086	−	0.0783220i	−0.00618377	−	0.00256140i
$936$	−10.5182	+	39.5245i	−0.343797	+	1.29190i
$937$	13.4067	−	5.55324i	0.437978	−	0.181417i	−0.152788	−	0.988259i	$-0.548825\pi$
$937$	13.4067	−	5.55324i	0.437978	−	0.181417i	0.590767	+	0.806842i	$0.298825\pi$
$938$	5.02702	+	0.209901i	0.164138	+	0.00685353i
$939$	−20.8759	−	10.3468i	−0.681260	−	0.337655i
$940$	−17.0108	−	13.5465i	−0.554831	−	0.441838i
$941$	8.34014	+	41.9287i	0.271881	+	1.36684i	0.839417	+	0.543488i	$0.182897\pi$
$941$	8.34014	+	41.9287i	0.271881	+	1.36684i	−0.567536	+	0.823348i	$0.692103\pi$
$942$	−16.1812	−	55.5350i	−0.527211	−	1.80943i
$943$	−3.15535	−	3.15535i	−0.102752	−	0.102752i
$944$	0.296009	+	0.659079i	0.00963429	+	0.0214512i
$945$	2.88232	−	2.84795i	0.0937619	−	0.0926437i
$946$	0.218494	+	0.358527i	0.00710385	+	0.0116567i
$947$	−2.80734	−	14.1134i	−0.0912263	−	0.458625i	−0.999214	−	0.0396296i	$-0.987382\pi$
$947$	−2.80734	−	14.1134i	−0.0912263	−	0.458625i	0.907988	−	0.418996i	$-0.137618\pi$
$948$	1.34241	−	2.22126i	0.0435994	−	0.0721431i
$949$	2.29721	−	1.53495i	0.0745706	−	0.0498265i
$950$	6.06031	+	6.58845i	0.196622	+	0.213758i
$951$	26.4175	−	34.2858i	0.856646	−	1.11179i
$952$	0.179231	+	2.51451i	0.00580891	+	0.0814958i
$953$	−55.9779	−	23.1868i	−1.81330	−	0.751095i	−0.980210	−	0.197961i	$-0.936568\pi$
$953$	−55.9779	−	23.1868i	−1.81330	−	0.751095i	−0.833093	−	0.553133i	$-0.813432\pi$
$954$	−1.07090	−	0.191145i	−0.0346718	−	0.00618854i
$955$	21.5739	+	4.29132i	0.698115	+	0.138864i
$956$	34.5064	+	17.7963i	1.11602	+	0.575574i
$957$	−0.807872	−	0.0545732i	−0.0261148	−	0.00176410i
$958$	37.5158	+	27.3981i	1.21208	+	0.885194i
$959$	−10.1693			−0.328385
$960$	10.9131	−	8.53840i	0.352219	−	0.275576i
$961$	−10.6514			−0.343593
$962$	7.83341	+	5.72080i	0.252559	+	0.184446i
$963$	−13.3001	−	27.2440i	−0.428589	−	0.877926i
$964$	−16.9074	+	32.7829i	−0.544551	+	1.05586i
$965$	6.98931	+	1.39026i	0.224994	+	0.0447540i
$966$	12.6129	+	10.5855i	0.405812	+	0.340584i
$967$	−36.4955	−	15.1169i	−1.17361	−	0.486127i	−0.291229	−	0.956653i	$-0.594064\pi$
$967$	−36.4955	−	15.1169i	−1.17361	−	0.486127i	−0.882386	+	0.470526i	$0.844064\pi$
$968$	20.3208	−	23.4400i	0.653134	−	0.753389i
$969$	−9.92611	−	7.64816i	−0.318873	−	0.245694i
$970$	4.19242	+	4.55778i	0.134611	+	0.146342i
$971$	25.1364	−	16.7956i	0.806665	−	0.538996i	−0.0824958	−	0.996591i	$-0.526289\pi$
$971$	25.1364	−	16.7956i	0.806665	−	0.538996i	0.889161	+	0.457595i	$0.151289\pi$
$972$	31.1647	+	0.873104i	0.999608	+	0.0280048i
$973$	−2.63653	−	13.2547i	−0.0845232	−	0.424927i
$974$	18.9010	+	31.0147i	0.605627	+	0.993774i
$975$	−8.05988	−	2.17692i	−0.258123	−	0.0697173i
$976$	0.0983312	+	3.34047i	0.00314750	+	0.106926i
$977$	16.2660	+	16.2660i	0.520395	+	0.520395i	0.917691	−	0.397295i	$-0.130051\pi$
$977$	16.2660	+	16.2660i	0.520395	+	0.520395i	−0.397295	+	0.917691i	$0.630051\pi$
$978$	52.5846	−	15.3215i	1.68147	−	0.489927i
$979$	−0.513077	−	2.57941i	−0.0163980	−	0.0824384i
$980$	7.96369	−	10.0003i	0.254391	−	0.319447i
$981$	1.78929	−	0.110092i	0.0571275	−	0.00351496i
$982$	−20.9686	−	0.875537i	−0.669135	−	0.0279395i
$983$	−7.02614	+	2.91032i	−0.224099	+	0.0928248i	−0.491908	−	0.870647i	$-0.663700\pi$
$983$	−7.02614	+	2.91032i	−0.224099	+	0.0928248i	0.267809	+	0.963472i	$0.413700\pi$
$984$	2.53590	−	0.00940553i	0.0808414	−	0.000299837i
$985$	−2.55215	−	1.05713i	−0.0813182	−	0.0336831i
$986$	−1.77607	+	3.82779i	−0.0565616	+	0.121902i
$987$	4.69270	+	13.9156i	0.149370	+	0.442938i
$988$	39.4016	+	46.5957i	1.25353	+	1.48241i
$989$	7.94035	−	11.8836i	0.252489	−	0.377876i
$990$	0.276837	−	0.707491i	0.00879846	−	0.0224856i
$991$	32.0303			1.01748			0.508739	−	0.860921i	$-0.330112\pi$
$991$	32.0303			1.01748			0.508739	+	0.860921i	$0.330112\pi$
$992$	−0.313926	+	25.5158i	−0.00996715	+	0.810128i
$993$	36.9902	−	21.2578i	1.17385	−	0.674597i
$994$	−1.21285	−	7.78152i	−0.0384693	−	0.246815i
$995$	10.2364	+	6.83974i	0.324516	+	0.216834i
$996$	−11.8599	+	5.55648i	−0.375797	+	0.176064i
$997$	−32.0739	−	6.37989i	−1.01579	−	0.202053i	−0.341000	−	0.940063i	$-0.610766\pi$
$997$	−32.0739	−	6.37989i	−1.01579	−	0.202053i	−0.674790	+	0.738010i	$0.735766\pi$
$998$	−0.938827	+	2.02336i	−0.0297180	+	0.0640485i
$999$	2.87049	−	6.81408i	0.0908184	−	0.215588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.cn.a.731.90	yes	1024
3.2	odd	2	inner	960.2.cn.a.731.39	✓	1024
64.19	odd	16	inner	960.2.cn.a.851.39	yes	1024
192.83	even	16	inner	960.2.cn.a.851.90	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.cn.a.731.39	✓	1024	3.2	odd	2	inner
960.2.cn.a.731.90	yes	1024	1.1	even	1	trivial
960.2.cn.a.851.39	yes	1024	64.19	odd	16	inner
960.2.cn.a.851.90	yes	1024	192.83	even	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.cn (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.834066 - 1.14207i) q^{2} +(-0.116737 + 1.72811i) q^{3} +(-0.608666 - 1.90513i) q^{4} +(-0.980785 - 0.195090i) q^{5} +(1.87627 + 1.57468i) q^{6} +(-0.720445 - 0.298418i) q^{7} +(-2.68347 - 0.893864i) q^{8} +(-2.97274 - 0.403470i) q^{9} +O(q^{10})\)	\(q+(0.834066 - 1.14207i) q^{2} +(-0.116737 + 1.72811i) q^{3} +(-0.608666 - 1.90513i) q^{4} +(-0.980785 - 0.195090i) q^{5} +(1.87627 + 1.57468i) q^{6} +(-0.720445 - 0.298418i) q^{7} +(-2.68347 - 0.893864i) q^{8} +(-2.97274 - 0.403470i) q^{9} +(-1.04085 + 0.957411i) q^{10} +(0.148890 - 0.0994854i) q^{11} +(3.36334 - 0.829444i) q^{12} +(0.940359 + 4.72750i) q^{13} +(-0.941715 + 0.573901i) q^{14} +(0.451632 - 1.67213i) q^{15} +(-3.25905 + 2.31918i) q^{16} +(0.808181 + 0.808181i) q^{17} +(-2.94026 + 3.05857i) q^{18} +(1.23490 + 6.20826i) q^{19} +(0.225298 + 1.98727i) q^{20} +(0.599803 - 1.21017i) q^{21} +(0.0105648 - 0.253021i) q^{22} +(-7.96433 + 3.29893i) q^{23} +(1.85796 - 4.53299i) q^{24} +(0.923880 + 0.382683i) q^{25} +(6.18348 + 2.86909i) q^{26} +(1.04427 - 5.09014i) q^{27} +(-0.130015 + 1.55418i) q^{28} +(-1.45040 + 2.17068i) q^{29} +(-1.53301 - 1.91047i) q^{30} +4.51094 q^{31} +(-0.0695920 + 5.65643i) q^{32} +(0.154541 + 0.268913i) q^{33} +(1.59708 - 0.248926i) q^{34} +(0.648384 + 0.433236i) q^{35} +(1.04075 + 5.90905i) q^{36} +(1.39564 + 0.277609i) q^{37} +(8.12028 + 3.76776i) q^{38} +(-8.27943 + 1.07317i) q^{39} +(2.45752 + 1.40021i) q^{40} +(0.198093 + 0.478238i) q^{41} +(-0.881833 - 1.69439i) q^{42} +(-1.37852 + 0.921099i) q^{43} +(-0.280157 - 0.223102i) q^{44} +(2.83691 + 0.975671i) q^{45} +(-2.87515 + 11.8474i) q^{46} +(-7.68827 + 7.68827i) q^{47} +(-3.62735 - 5.90274i) q^{48} +(-4.51976 - 4.51976i) q^{49} +(1.20763 - 0.735955i) q^{50} +(-1.49097 + 1.30228i) q^{51} +(8.43415 - 4.66898i) q^{52} +(0.142450 + 0.213192i) q^{53} +(-4.94232 - 5.43815i) q^{54} +(-0.165438 + 0.0685267i) q^{55} +(1.66655 + 1.44478i) q^{56} +(-10.8727 + 1.40931i) q^{57} +(1.26935 + 3.46696i) q^{58} +(0.0352382 - 0.177154i) q^{59} +(-3.46053 + 0.157352i) q^{60} +(0.464167 - 0.694675i) q^{61} +(3.76243 - 5.15183i) q^{62} +(2.02130 + 1.17780i) q^{63} +(6.40201 + 4.79731i) q^{64} -4.82012i q^{65} +(0.436016 + 0.0477942i) q^{66} +(-3.79345 - 2.53470i) q^{67} +(1.04778 - 2.03160i) q^{68} +(-4.77119 - 14.1484i) q^{69} +(1.03558 - 0.379155i) q^{70} +(-2.73285 + 6.59768i) q^{71} +(7.61662 + 3.73993i) q^{72} +(-0.219349 - 0.529556i) q^{73} +(1.48110 - 1.36238i) q^{74} +(-0.769171 + 1.55189i) q^{75} +(11.0759 - 6.13141i) q^{76} +(-0.136956 + 0.0272422i) q^{77} +(-5.67996 + 10.3508i) q^{78} +(0.529782 - 0.529782i) q^{79} +(3.64888 - 1.63881i) q^{80} +(8.67442 + 2.39883i) q^{81} +(0.711406 + 0.172646i) q^{82} +(-3.70815 + 0.737596i) q^{83} +(-2.67062 - 0.406111i) q^{84} +(-0.634984 - 0.950320i) q^{85} +(-0.0978158 + 2.34263i) q^{86} +(-3.58187 - 2.75986i) q^{87} +(-0.488469 + 0.133878i) q^{88} +(5.62039 - 13.5688i) q^{89} +(3.48046 - 2.42619i) q^{90} +(0.733296 - 3.68653i) q^{91} +(11.1325 + 13.1651i) q^{92} +(-0.526595 + 7.79542i) q^{93} +(2.36804 + 15.1931i) q^{94} -6.32989i q^{95} +(-9.76682 - 0.780578i) q^{96} -4.37891i q^{97} +(-8.93168 + 1.39212i) q^{98} +(-0.482753 + 0.235672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) \) 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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