LMFDB - Embedded newform 768.2.z.a.421.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(13,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 47, 0]))

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

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

chi := DirichletCharacter("768.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.z (of order $64$, degree $32$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$2048$
Relative dimension:	$64$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			421.2
Character	$\chi$	$=$	768.421
Dual form			768.2.z.a.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41124 - 0.0916351i) q^{2} +(0.857729 + 0.514103i) q^{3} +(1.98321 + 0.258638i) q^{4} +(3.12088 - 1.11667i) q^{5} +(-1.16335 - 0.804121i) q^{6} +(0.222993 - 0.0676442i) q^{7} +(-2.77508 - 0.546733i) q^{8} +(0.471397 + 0.881921i) q^{9} +O(q^{10})$	\(q+(-1.41124 - 0.0916351i) q^{2} +(0.857729 + 0.514103i) q^{3} +(1.98321 + 0.258638i) q^{4} +(3.12088 - 1.11667i) q^{5} +(-1.16335 - 0.804121i) q^{6} +(0.222993 - 0.0676442i) q^{7} +(-2.77508 - 0.546733i) q^{8} +(0.471397 + 0.881921i) q^{9} +(-4.50664 + 1.28991i) q^{10} +(-1.22843 + 1.65635i) q^{11} +(1.56809 + 1.24141i) q^{12} +(3.87917 - 1.83471i) q^{13} +(-0.320896 + 0.0750284i) q^{14} +(3.25095 + 0.646654i) q^{15} +(3.86621 + 1.02587i) q^{16} +(0.901119 - 0.179244i) q^{17} +(-0.584440 - 1.28780i) q^{18} +(0.155885 + 3.17311i) q^{19} +(6.47816 - 1.40740i) q^{20} +(0.226044 + 0.0566210i) q^{21} +(1.88539 - 2.22494i) q^{22} +(0.0847228 + 0.860205i) q^{23} +(-2.09919 - 1.89563i) q^{24} +(4.62788 - 3.79800i) q^{25} +(-5.64257 + 2.23375i) q^{26} +(-0.0490677 + 0.998795i) q^{27} +(0.459737 - 0.0764778i) q^{28} +(0.395540 - 2.66652i) q^{29} +(-4.52862 - 1.21049i) q^{30} +(4.45297 + 1.84448i) q^{31} +(-5.36215 - 1.80203i) q^{32} +(-1.90519 + 0.789157i) q^{33} +(-1.28812 + 0.170382i) q^{34} +(0.620398 - 0.460119i) q^{35} +(0.706778 + 1.87095i) q^{36} +(1.02930 + 1.13565i) q^{37} +(0.0707769 - 4.49231i) q^{38} +(4.27050 + 0.420608i) q^{39} +(-9.27121 + 1.39256i) q^{40} +(-6.68989 - 5.49025i) q^{41} +(-0.313814 - 0.100619i) q^{42} +(-2.25376 - 3.76018i) q^{43} +(-2.86463 + 2.96716i) q^{44} +(2.45599 + 2.22598i) q^{45} +(-0.0407394 - 1.22172i) q^{46} +(-9.11903 - 6.09314i) q^{47} +(2.78876 + 2.86755i) q^{48} +(-5.77514 + 3.85882i) q^{49} +(-6.87909 + 4.93582i) q^{50} +(0.865065 + 0.309525i) q^{51} +(8.16772 - 2.63531i) q^{52} +(0.476160 + 3.21001i) q^{53} +(0.160771 - 1.40505i) q^{54} +(-1.98419 + 6.54101i) q^{55} +(-0.655808 + 0.0658007i) q^{56} +(-1.49760 + 2.80181i) q^{57} +(-0.802550 + 3.72686i) q^{58} +(4.73382 + 2.23893i) q^{59} +(6.28005 + 2.12327i) q^{60} +(13.8397 - 3.46665i) q^{61} +(-6.11520 - 3.01106i) q^{62} +(0.164775 + 0.164775i) q^{63} +(7.40217 + 3.03446i) q^{64} +(10.0577 - 10.0577i) q^{65} +(2.76100 - 0.939109i) q^{66} +(1.79654 + 7.17220i) q^{67} +(1.83346 - 0.122413i) q^{68} +(-0.369565 + 0.781379i) q^{69} +(-0.917695 + 0.592489i) q^{70} +(2.44375 + 1.30621i) q^{71} +(-0.825990 - 2.70513i) q^{72} +(7.33571 + 2.22526i) q^{73} +(-1.34852 - 1.69700i) q^{74} +(5.92203 - 0.878450i) q^{75} +(-0.511536 + 6.33325i) q^{76} +(-0.161889 + 0.452451i) q^{77} +(-5.98817 - 0.984907i) q^{78} +(-2.56345 - 3.83647i) q^{79} +(13.2115 - 1.11567i) q^{80} +(-0.555570 + 0.831470i) q^{81} +(8.93796 + 8.36110i) q^{82} +(-1.05011 + 1.15862i) q^{83} +(0.433647 + 0.170755i) q^{84} +(2.61213 - 1.56565i) q^{85} +(2.83604 + 5.51304i) q^{86} +(1.71013 - 2.08380i) q^{87} +(4.31458 - 3.92488i) q^{88} +(0.0248856 - 0.252668i) q^{89} +(-3.26201 - 3.36644i) q^{90} +(0.740921 - 0.671531i) q^{91} +(-0.0544594 + 1.72788i) q^{92} +(2.87119 + 3.87135i) q^{93} +(12.3108 + 9.43452i) q^{94} +(4.02981 + 9.72881i) q^{95} +(-3.67285 - 4.30235i) q^{96} +(2.08429 - 5.03192i) q^{97} +(8.50372 - 4.91653i) q^{98} +(-2.03985 - 0.302583i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2048 q+O(q^{10}) $ 2048 * q	$ 2048 q+O(q^{100}) $ 2048 * q

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{57}{64}\right)$

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 $

$2$	−1.41124	−	0.0916351i	−0.997899	−	0.0647958i
$2$	−1.41124	−	0.0916351i	−0.997899	−	0.0647958i
$3$	0.857729	+	0.514103i	0.495210	+	0.296817i
$3$	0.857729	+	0.514103i	0.495210	+	0.296817i
$4$	1.98321	+	0.258638i	0.991603	+	0.129319i
$5$	3.12088	−	1.11667i	1.39570	−	0.499389i	0.471692	−	0.881764i	$-0.343644\pi$
$5$	3.12088	−	1.11667i	1.39570	−	0.499389i	0.924007	+	0.382374i	$0.124894\pi$
$6$	−1.16335	−	0.804121i	−0.474937	−	0.328281i
$7$	0.222993	−	0.0676442i	0.0842835	−	0.0255671i	−0.247861	−	0.968796i	$-0.579728\pi$
$7$	0.222993	−	0.0676442i	0.0842835	−	0.0255671i	0.332145	+	0.943228i	$0.392228\pi$
$8$	−2.77508	−	0.546733i	−0.981140	−	0.193299i
$9$	0.471397	+	0.881921i	0.157132	+	0.293974i
$10$	−4.50664	+	1.28991i	−1.42512	+	0.407904i
$11$	−1.22843	+	1.65635i	−0.370386	+	0.499408i	−0.948600	−	0.316477i	$-0.897500\pi$
$11$	−1.22843	+	1.65635i	−0.370386	+	0.499408i	0.578214	+	0.815885i	$0.303750\pi$
$12$	1.56809	+	1.24141i	0.452667	+	0.358365i
$13$	3.87917	−	1.83471i	1.07589	−	0.508857i	0.194332	−	0.980936i	$-0.437746\pi$
$13$	3.87917	−	1.83471i	1.07589	−	0.508857i	0.881556	+	0.472079i	$0.156496\pi$
$14$	−0.320896	+	0.0750284i	−0.0857630	+	0.0200522i
$15$	3.25095	+	0.646654i	0.839391	+	0.166965i
$16$	3.86621	+	1.02587i	0.966553	+	0.256467i
$17$	0.901119	−	0.179244i	0.218553	−	0.0434730i	−0.0845989	−	0.996415i	$-0.526961\pi$
$17$	0.901119	−	0.179244i	0.218553	−	0.0434730i	0.303152	+	0.952942i	$0.401961\pi$
$18$	−0.584440	−	1.28780i	−0.137754	−	0.303537i
$19$	0.155885	+	3.17311i	0.0357624	+	0.727961i	0.947994	+	0.318287i	$0.103108\pi$
$19$	0.155885	+	3.17311i	0.0357624	+	0.727961i	−0.912232	+	0.409674i	$0.865642\pi$
$20$	6.47816	−	1.40740i	1.44856	−	0.314705i
$21$	0.226044	+	0.0566210i	0.0493268	+	0.0123557i
$22$	1.88539	−	2.22494i	0.401967	−	0.474359i
$23$	0.0847228	+	0.860205i	0.0176659	+	0.179365i	0.999969	−	0.00793573i	$-0.00252605\pi$
$23$	0.0847228	+	0.860205i	0.0176659	+	0.179365i	−0.982303	+	0.187301i	$0.940026\pi$
$24$	−2.09919	−	1.89563i	−0.428496	−	0.386943i
$25$	4.62788	−	3.79800i	0.925576	−	0.759601i
$26$	−5.64257	+	2.23375i	−1.10660	+	0.438075i
$27$	−0.0490677	+	0.998795i	−0.00944308	+	0.192218i
$28$	0.459737	−	0.0764778i	0.0868821	−	0.0144530i
$29$	0.395540	−	2.66652i	0.0734500	−	0.495160i	−0.920967	−	0.389640i	$-0.872599\pi$
$29$	0.395540	−	2.66652i	0.0734500	−	0.495160i	0.994417	−	0.105520i	$-0.0336506\pi$
$30$	−4.52862	−	1.21049i	−0.826809	−	0.221003i
$31$	4.45297	+	1.84448i	0.799777	+	0.331279i	0.744867	−	0.667213i	$-0.232513\pi$
$31$	4.45297	+	1.84448i	0.799777	+	0.331279i	0.0549100	+	0.998491i	$0.482513\pi$
$32$	−5.36215	−	1.80203i	−0.947904	−	0.318556i
$33$	−1.90519	+	0.789157i	−0.331652	+	0.137375i
$34$	−1.28812	+	0.170382i	−0.220911	+	0.0292203i
$35$	0.620398	−	0.460119i	0.104866	−	0.0777743i
$36$	0.706778	+	1.87095i	0.117796	+	0.311825i
$37$	1.02930	+	1.13565i	0.169215	+	0.186700i	0.819655	−	0.572858i	$-0.194165\pi$
$37$	1.02930	+	1.13565i	0.169215	+	0.186700i	−0.650439	+	0.759558i	$0.725415\pi$
$38$	0.0707769	−	4.49231i	0.0114815	−	0.728749i
$39$	4.27050	+	0.420608i	0.683828	+	0.0673512i
$40$	−9.27121	+	1.39256i	−1.46591	+	0.220183i
$41$	−6.68989	−	5.49025i	−1.04479	−	0.857433i	−0.0547853	−	0.998498i	$-0.517447\pi$
$41$	−6.68989	−	5.49025i	−1.04479	−	0.857433i	−0.990000	+	0.141065i	$0.954947\pi$
$42$	−0.313814	−	0.100619i	−0.0484225	−	0.0155259i
$43$	−2.25376	−	3.76018i	−0.343696	−	0.573422i	0.636543	−	0.771241i	$-0.280364\pi$
$43$	−2.25376	−	3.76018i	−0.343696	−	0.573422i	−0.980238	+	0.197820i	$0.936614\pi$
$44$	−2.86463	+	2.96716i	−0.431859	+	0.447316i
$45$	2.45599	+	2.22598i	0.366117	+	0.331829i
$46$	−0.0407394	−	1.22172i	−0.00600670	−	0.180133i
$47$	−9.11903	−	6.09314i	−1.33015	−	0.888776i	−0.331641	−	0.943406i	$-0.607602\pi$
$47$	−9.11903	−	6.09314i	−1.33015	−	0.888776i	−0.998507	+	0.0546293i	$0.982602\pi$
$48$	2.78876	+	2.86755i	0.402523	+	0.413895i
$49$	−5.77514	+	3.85882i	−0.825020	+	0.551260i
$50$	−6.87909	+	4.93582i	−0.972850	+	0.698031i
$51$	0.865065	+	0.309525i	0.121133	+	0.0433422i
$52$	8.16772	−	2.63531i	1.13266	−	0.365451i
$53$	0.476160	+	3.21001i	0.0654056	+	0.440929i	0.996998	+	0.0774247i	$0.0246697\pi$
$53$	0.476160	+	3.21001i	0.0654056	+	0.440929i	−0.931593	+	0.363504i	$0.881580\pi$
$54$	0.160771	−	1.40505i	0.0218782	−	0.191202i
$55$	−1.98419	+	6.54101i	−0.267549	+	0.881990i
$56$	−0.655808	+	0.0658007i	−0.0876360	+	0.00879299i
$57$	−1.49760	+	2.80181i	−0.198362	+	0.371108i
$58$	−0.802550	+	3.72686i	−0.105380	+	0.489360i
$59$	4.73382	+	2.23893i	0.616290	+	0.291484i	0.710094	−	0.704107i	$-0.248653\pi$
$59$	4.73382	+	2.23893i	0.616290	+	0.291484i	−0.0938035	+	0.995591i	$0.529903\pi$
$60$	6.28005	+	2.12327i	0.810751	+	0.274113i
$61$	13.8397	−	3.46665i	1.77199	−	0.443860i	0.787067	−	0.616868i	$-0.211599\pi$
$61$	13.8397	−	3.46665i	1.77199	−	0.443860i	0.984920	+	0.173008i	$0.0553487\pi$
$62$	−6.11520	−	3.01106i	−0.776631	−	0.382405i
$63$	0.164775	+	0.164775i	0.0207597	+	0.0207597i
$64$	7.40217	+	3.03446i	0.925271	+	0.379307i
$65$	10.0577	−	10.0577i	1.24750	−	1.24750i
$66$	2.76100	−	0.939109i	0.339856	−	0.115596i
$67$	1.79654	+	7.17220i	0.219483	+	0.876224i	0.975200	+	0.221326i	$0.0710384\pi$
$67$	1.79654	+	7.17220i	0.219483	+	0.876224i	−0.755717	+	0.654898i	$0.772712\pi$
$68$	1.83346	−	0.122413i	0.222340	−	0.0148448i
$69$	−0.369565	+	0.781379i	−0.0444904	+	0.0940670i
$70$	−0.917695	+	0.592489i	−0.109686	+	0.0708159i
$71$	2.44375	+	1.30621i	0.290020	+	0.155019i	0.609991	−	0.792409i	$-0.291173\pi$
$71$	2.44375	+	1.30621i	0.290020	+	0.155019i	−0.319971	+	0.947427i	$0.603673\pi$
$72$	−0.825990	−	2.70513i	−0.0973438	−	0.318803i
$73$	7.33571	+	2.22526i	0.858580	+	0.260447i	0.688726	−	0.725022i	$-0.258170\pi$
$73$	7.33571	+	2.22526i	0.858580	+	0.260447i	0.169854	+	0.985469i	$0.445670\pi$
$74$	−1.34852	−	1.69700i	−0.156762	−	0.197273i
$75$	5.92203	−	0.878450i	0.683817	−	0.101435i
$76$	−0.511536	+	6.33325i	−0.0586772	+	0.726473i
$77$	−0.161889	+	0.452451i	−0.0184490	+	0.0515616i
$78$	−5.98817	−	0.984907i	−0.678027	−	0.111519i
$79$	−2.56345	−	3.83647i	−0.288411	−	0.431637i	0.658767	−	0.752347i	$-0.271078\pi$
$79$	−2.56345	−	3.83647i	−0.288411	−	0.431637i	−0.947177	+	0.320710i	$0.896078\pi$
$80$	13.2115	−	1.11567i	1.47709	−	0.124736i
$81$	−0.555570	+	0.831470i	−0.0617300	+	0.0923855i
$82$	8.93796	+	8.36110i	0.987032	+	0.923329i
$83$	−1.05011	+	1.15862i	−0.115265	+	0.127175i	−0.795850	−	0.605494i	$-0.792976\pi$
$83$	−1.05011	+	1.15862i	−0.115265	+	0.127175i	0.680585	+	0.732669i	$0.261726\pi$
$84$	0.433647	+	0.170755i	0.0473148	+	0.0186309i
$85$	2.61213	−	1.56565i	0.283325	−	0.169818i
$86$	2.83604	+	5.51304i	0.305818	+	0.594487i
$87$	1.71013	−	2.08380i	0.183345	−	0.223407i
$88$	4.31458	−	3.92488i	0.459936	−	0.418394i
$89$	0.0248856	−	0.252668i	0.00263787	−	0.0267827i	−0.993776	−	0.111400i	$-0.964467\pi$
$89$	0.0248856	−	0.252668i	0.00263787	−	0.0267827i	0.996414	+	0.0846169i	$0.0269666\pi$
$90$	−3.26201	−	3.36644i	−0.343846	−	0.354854i
$91$	0.740921	−	0.671531i	0.0776696	−	0.0703956i
$92$	−0.0544594	+	1.72788i	−0.00567778	+	0.180144i
$93$	2.87119	+	3.87135i	0.297728	+	0.401440i
$94$	12.3108	+	9.43452i	1.26976	+	0.973097i
$95$	4.02981	+	9.72881i	0.413449	+	0.998155i
$96$	−3.67285	−	4.30235i	−0.374858	−	0.439107i
$97$	2.08429	−	5.03192i	0.211628	−	0.510915i	−0.782046	−	0.623221i	$-0.785824\pi$
$97$	2.08429	−	5.03192i	0.211628	−	0.510915i	0.993674	+	0.112306i	$0.0358238\pi$
$98$	8.50372	−	4.91653i	0.859005	−	0.496644i
$99$	−2.03985	−	0.302583i	−0.205012	−	0.0304107i
$100$	10.1603	−	6.33527i	1.01603	−	0.633527i
$101$	−13.5321	−	0.664790i	−1.34650	−	0.0661491i	−0.637003	−	0.770862i	$-0.719826\pi$
$101$	−13.5321	−	0.664790i	−1.34650	−	0.0661491i	−0.709493	+	0.704712i	$0.751076\pi$
$102$	−1.19245	−	0.516085i	−0.118070	−	0.0511000i
$103$	3.35653	+	4.08995i	0.330729	+	0.402995i	0.911651	−	0.410964i	$-0.134808\pi$
$103$	3.35653	+	4.08995i	0.330729	+	0.402995i	−0.580922	+	0.813959i	$0.697308\pi$
$104$	−11.7681	+	2.97060i	−1.15396	+	0.291292i
$105$	0.768682	−	0.0757085i	0.0750157	−	0.00738840i
$106$	−0.377827	−	4.57373i	−0.0366978	−	0.444240i
$107$	3.26223	−	13.0236i	0.315372	−	1.25903i	−0.580331	−	0.814381i	$-0.697077\pi$
$107$	3.26223	−	13.0236i	0.315372	−	1.25903i	0.895703	−	0.444654i	$-0.146673\pi$
$108$	−0.355638	+	1.96813i	−0.0342213	+	0.189383i
$109$	−11.5958	+	0.569667i	−1.11068	+	0.0545642i	−0.596124	−	0.802892i	$-0.703293\pi$
$109$	−11.5958	+	0.569667i	−1.11068	+	0.0545642i	−0.514557	+	0.857456i	$0.672043\pi$
$110$	3.39956	−	9.04913i	0.324136	−	0.862801i
$111$	0.299015	+	1.50325i	0.0283812	+	0.142682i
$112$	0.931533	−	0.0327657i	0.0880216	−	0.00309607i
$113$	1.51954	−	7.63922i	0.142946	−	0.718638i	−0.841122	−	0.540845i	$-0.818104\pi$
$113$	1.51954	−	7.63922i	0.142946	−	0.718638i	0.984068	−	0.177792i	$-0.0568956\pi$
$114$	2.37022	−	3.81679i	0.221991	−	0.357476i
$115$	1.22497	+	2.58999i	0.114229	+	0.241518i
$116$	1.47410	−	5.18595i	0.136867	−	0.481504i
$117$	3.44670	+	2.55625i	0.318647	+	0.236325i
$118$	−6.47539	−	3.59345i	−0.596108	−	0.330804i
$119$	0.188819	−	0.100926i	0.0173090	−	0.00925184i
$120$	−8.66810	−	3.57192i	−0.791286	−	0.326070i
$121$	1.95869	+	6.45692i	0.178062	+	0.586993i
$122$	−19.8488	+	3.62409i	−1.79702	+	0.328110i
$123$	−2.91556	−	8.14844i	−0.262887	−	0.734720i
$124$	8.35410	+	4.80970i	0.750221	+	0.431923i
$125$	1.68162	−	2.80561i	0.150408	−	0.250941i
$126$	−0.217438	−	0.247637i	−0.0193710	−	0.0220612i
$127$			6.38876i			0.566911i	0.958985	+	0.283455i	$0.0914807\pi$
$127$			6.38876i			0.566911i	−0.958985	+	0.283455i	$0.908519\pi$
$128$	−10.1682	−	4.96065i	−0.898749	−	0.438464i
$129$		−	4.38388i		−	0.385979i
$130$	−15.1154	+	13.2721i	−1.32571	+	1.16404i
$131$	0.173735	−	0.289859i	0.0151793	−	0.0253251i	−0.850045	−	0.526709i	$-0.823426\pi$
$131$	0.173735	−	0.289859i	0.0151793	−	0.0253251i	0.865225	+	0.501384i	$0.167176\pi$
$132$	−3.98250	+	1.07231i	−0.346632	+	0.0933322i
$133$	0.249404	+	0.697037i	0.0216261	+	0.0604408i
$134$	−1.87813	−	10.2863i	−0.162246	−	0.888604i
$135$	0.962189	+	3.17191i	0.0828120	+	0.272995i
$136$	−2.59868	+	0.00474494i	−0.222835	+	0.000406875i
$137$	5.62449	−	3.00635i	0.480532	−	0.256850i	−0.213300	−	0.976987i	$-0.568421\pi$
$137$	5.62449	−	3.00635i	0.480532	−	0.256850i	0.693832	+	0.720137i	$0.255921\pi$
$138$	0.593147	−	1.06885i	0.0504920	−	0.0909865i
$139$	−12.8496	−	9.52990i	−1.08989	−	0.808316i	−0.107321	−	0.994224i	$-0.534227\pi$
$139$	−12.8496	−	9.52990i	−1.08989	−	0.808316i	−0.982567	+	0.185909i	$0.940477\pi$
$140$	1.34938	−	0.752051i	0.114044	−	0.0635599i
$141$	−4.68915	−	9.91438i	−0.394898	−	0.834942i
$142$	−3.32903	−	2.06731i	−0.279366	−	0.173485i
$143$	−1.72638	+	8.67907i	−0.144367	+	0.725781i
$144$	0.917786	+	3.89329i	0.0764822	+	0.324440i
$145$	−1.74318	−	8.76356i	−0.144763	−	0.727774i
$146$	−10.1485	−	3.81259i	−0.839899	−	0.315532i
$147$	−6.93733	+	0.340809i	−0.572181	+	0.0281095i
$148$	1.74758	+	2.51845i	0.143651	+	0.207016i
$149$	−5.77821	+	23.0679i	−0.473370	+	1.88980i	−0.0173063	+	0.999850i	$0.505509\pi$
$149$	−5.77821	+	23.0679i	−0.473370	+	1.88980i	−0.456063	+	0.889947i	$0.650741\pi$
$150$	−8.43791	+	0.697040i	−0.688953	+	0.0569131i
$151$	−4.96332	+	0.488844i	−0.403909	+	0.0397816i	−0.297932	−	0.954587i	$-0.596297\pi$
$151$	−4.96332	+	0.488844i	−0.403909	+	0.0397816i	−0.105977	+	0.994369i	$0.533797\pi$
$152$	1.30225	−	8.89087i	0.105626	−	0.721145i
$153$	0.582863	+	0.710221i	0.0471217	+	0.0574180i
$154$	0.269926	−	0.623683i	0.0217512	−	0.0502578i
$155$	15.9569	+	0.783910i	1.28169	+	0.0629652i
$156$	8.36050	+	1.93867i	0.669376	+	0.155218i
$157$	0.500303	+	0.0742129i	0.0399285	+	0.00592283i	0.166665	−	0.986014i	$-0.446700\pi$
$157$	0.500303	+	0.0742129i	0.0399285	+	0.00592283i	−0.126736	+	0.991936i	$0.540450\pi$
$158$	3.26609	+	5.64909i	0.259836	+	0.449418i
$159$	−1.24186	+	2.99811i	−0.0984858	+	0.237766i
$160$	−18.7469	+	0.363841i	−1.48207	+	0.0287642i
$161$	0.0770805	+	0.186089i	0.00607480	+	0.0146659i
$162$	0.860236	−	1.12249i	0.0675865	−	0.0881915i
$163$	−2.58536	−	3.48595i	−0.202501	−	0.273041i	0.690270	−	0.723552i	$-0.257492\pi$
$163$	−2.58536	−	3.48595i	−0.202501	−	0.273041i	−0.892771	+	0.450511i	$0.851242\pi$
$164$	−11.8474	−	12.6186i	−0.925130	−	0.985344i
$165$	−5.06465	+	4.59033i	−0.394283	+	0.357357i
$166$	1.58813	−	1.53887i	0.123263	−	0.119439i
$167$	−2.31198	+	23.4739i	−0.178906	+	1.81647i	0.317370	+	0.948302i	$0.397200\pi$
$167$	−2.31198	+	23.4739i	−0.178906	+	1.81647i	−0.496277	+	0.868164i	$0.665300\pi$
$168$	−0.596333	−	0.280713i	−0.0460081	−	0.0216575i
$169$	3.43468	−	4.18517i	0.264206	−	0.321936i
$170$	−3.82981	+	1.97015i	−0.293733	+	0.151103i
$171$	−2.72495	+	1.63327i	−0.208382	+	0.124899i
$172$	−3.49715	−	8.04012i	−0.266655	−	0.613053i
$173$	12.8652	−	14.1945i	0.978122	−	1.07919i	−0.0187233	−	0.999825i	$-0.505960\pi$
$173$	12.8652	−	14.1945i	0.978122	−	1.07919i	0.996845	−	0.0793668i	$-0.0252898\pi$
$174$	−2.60436	+	2.78404i	−0.197436	+	0.211057i
$175$	0.775073	−	1.15998i	0.0585900	−	0.0876861i
$176$	−6.44857	+	5.14359i	−0.486079	+	0.387713i
$177$	2.90929	+	4.35406i	0.218676	+	0.327271i
$178$	−0.0582728	+	0.354295i	−0.00436773	+	0.0265555i
$179$	−6.96804	+	19.4744i	−0.520816	+	1.45558i	0.336941	+	0.941526i	$0.390608\pi$
$179$	−6.96804	+	19.4744i	−0.520816	+	1.45558i	−0.857756	+	0.514056i	$0.828142\pi$
$180$	4.29500	+	5.04978i	0.320131	+	0.376388i
$181$	−20.3714	+	3.02181i	−1.51419	+	0.224610i	−0.851530	−	0.524306i	$-0.824325\pi$
$181$	−20.3714	+	3.02181i	−1.51419	+	0.224610i	−0.662665	+	0.748916i	$0.730575\pi$
$182$	−1.10715	+	0.879799i	−0.0820677	+	0.0652150i
$183$	13.6529	+	4.14156i	1.00925	+	0.306153i
$184$	0.235189	−	2.43346i	0.0173384	−	0.179397i
$185$	4.48046	+	2.39486i	0.329410	+	0.176073i
$186$	−3.69719	−	5.72651i	−0.271091	−	0.419888i
$187$	−0.810073	+	1.71276i	−0.0592384	+	0.125249i
$188$	−16.5090	−	14.4425i	−1.20404	−	1.05333i
$189$	0.0566210	+	0.226044i	0.00411857	+	0.0164423i
$190$	−4.79553	−	14.0990i	−0.347904	−	1.02285i
$191$	−9.67003	+	9.67003i	−0.699699	+	0.699699i	−0.964345	−	0.264647i	$-0.914745\pi$
$191$	−9.67003	+	9.67003i	−0.699699	+	0.699699i	0.264647	+	0.964345i	$0.414745\pi$
$192$	4.78903	+	6.40821i	0.345618	+	0.462473i
$193$	−16.7452	−	16.7452i	−1.20534	−	1.20534i	−0.972519	−	0.232825i	$-0.925203\pi$
$193$	−16.7452	−	16.7452i	−1.20534	−	1.20534i	−0.232825	−	0.972519i	$-0.574797\pi$
$194$	−3.40254	+	6.91027i	−0.244288	+	0.496128i
$195$	13.7974	−	3.45607i	0.988052	−	0.247494i
$196$	−12.4513	+	6.15917i	−0.889380	+	0.439941i
$197$	1.01530	+	0.480200i	0.0723370	+	0.0342128i	0.463381	−	0.886159i	$-0.346636\pi$
$197$	1.01530	+	0.480200i	0.0723370	+	0.0342128i	−0.391044	+	0.920372i	$0.627886\pi$
$198$	2.85099	+	0.613939i	0.202611	+	0.0436308i
$199$	0.0901921	−	0.168738i	0.00639355	−	0.0119615i	−0.878704	−	0.477367i	$-0.841591\pi$
$199$	0.0901921	−	0.168738i	0.00639355	−	0.0119615i	0.885098	+	0.465405i	$0.154091\pi$
$200$	−14.9192	+	8.00956i	−1.05495	+	0.566361i
$201$	−2.14630	+	7.07541i	−0.151388	+	0.499061i
$202$	19.0362	+	2.17820i	1.33938	+	0.153257i
$203$	−0.0921717	−	0.621371i	−0.00646919	−	0.0436117i
$204$	1.63555	+	0.837591i	0.114511	+	0.0586431i
$205$	−27.0091	−	9.66402i	−1.88640	−	0.674964i
$206$	−4.36210	−	6.07948i	−0.303922	−	0.423578i
$207$	−0.718695	+	0.480217i	−0.0499528	+	0.0333774i
$208$	16.8799	−	3.11387i	1.17041	−	0.215908i
$209$	−5.44727	−	3.63975i	−0.376795	−	0.251767i
$210$	−1.09173	+	0.0364048i	−0.0753368	+	0.00251217i
$211$	−15.3099	−	13.8761i	−1.05398	−	0.955269i	−0.0549116	−	0.998491i	$-0.517488\pi$
$211$	−15.3099	−	13.8761i	−1.05398	−	0.955269i	−0.999065	+	0.0432221i	$0.986238\pi$
$212$	0.114091	+	6.48926i	0.00783582	+	0.445685i
$213$	1.42455	+	2.37671i	0.0976084	+	0.162850i
$214$	−5.79721	+	18.0804i	−0.396289	+	1.23595i
$215$	−11.2326	−	9.21835i	−0.766056	−	0.628686i
$216$	0.682241	−	2.74491i	0.0464206	−	0.186768i
$217$	1.11775	+	0.110089i	0.0758779	+	0.00747332i
$218$	16.4167	+	0.258648i	1.11188	+	0.0175179i
$219$	5.14803	+	5.67998i	0.347872	+	0.383817i
$220$	−5.62682	+	12.4590i	−0.379360	+	0.839985i
$221$	3.16673	−	2.34861i	0.213017	−	0.157984i
$222$	−0.284232	−	2.14885i	−0.0190764	−	0.144221i
$223$	15.3228	−	6.34691i	1.02609	−	0.425021i	0.194791	−	0.980845i	$-0.437597\pi$
$223$	15.3228	−	6.34691i	1.02609	−	0.425021i	0.831300	+	0.555824i	$0.187597\pi$
$224$	−1.31762	−	0.0391208i	−0.0880372	−	0.00261387i
$225$	5.53111	+	2.29106i	0.368740	+	0.152737i
$226$	−2.84445	+	10.6415i	−0.189210	+	0.707865i
$227$	0.278369	−	1.87661i	0.0184760	−	0.124555i	−0.977976	−	0.208717i	$-0.933071\pi$
$227$	0.278369	−	1.87661i	0.0184760	−	0.124555i	0.996452	+	0.0841617i	$0.0268212\pi$
$228$	−3.69470	+	5.16922i	−0.244687	+	0.342340i
$229$	1.15655	−	23.5421i	0.0764268	−	1.55570i	−0.588316	−	0.808631i	$-0.700209\pi$
$229$	1.15655	−	23.5421i	0.0764268	−	1.55570i	0.664743	−	0.747072i	$-0.268541\pi$
$230$	−1.49140	−	3.76735i	−0.0983400	−	0.248412i
$231$	−0.371463	+	0.304852i	−0.0244405	+	0.0200578i
$232$	−2.55553	+	7.18355i	−0.167779	+	0.471623i
$233$	−1.21088	−	12.2942i	−0.0793271	−	0.805422i	−0.949728	−	0.313077i	$-0.898640\pi$
$233$	−1.21088	−	12.2942i	−0.0793271	−	0.805422i	0.870400	−	0.492344i	$-0.163860\pi$
$234$	−4.62988	−	3.92332i	−0.302665	−	0.256475i
$235$	−35.2634	−	8.83302i	−2.30033	−	0.576203i
$236$	8.80906	+	5.66460i	0.573421	+	0.368734i
$237$	−0.226403	−	4.60853i	−0.0147064	−	0.299356i
$238$	−0.275717	+	0.125128i	−0.0178721	+	0.00811085i
$239$	−22.5194	+	4.47939i	−1.45666	+	0.289748i	−0.858989	−	0.511994i	$-0.828907\pi$
$239$	−22.5194	+	4.47939i	−1.45666	+	0.289748i	−0.597671	+	0.801741i	$0.703907\pi$
$240$	11.9055	+	5.83514i	0.768495	+	0.376657i
$241$	−1.49554	−	0.297482i	−0.0963363	−	0.0191625i	0.146687	−	0.989183i	$-0.453139\pi$
$241$	−1.49554	−	0.297482i	−0.0963363	−	0.0191625i	−0.243023	+	0.970021i	$0.578139\pi$
$242$	−2.17250	−	9.29176i	−0.139653	−	0.597297i
$243$	−0.903989	+	0.427555i	−0.0579909	+	0.0274277i
$244$	28.3435	−	3.29562i	1.81451	−	0.210981i
$245$	−13.7145	+	18.4918i	−0.876186	+	1.18140i
$246$	3.36787	+	11.7666i	0.214728	+	0.750210i
$247$	6.42644	+	12.0230i	0.408905	+	0.765007i
$248$	−11.3489	−	7.55317i	−0.720657	−	0.479627i
$249$	−1.49636	+	0.453917i	−0.0948281	+	0.0287658i
$250$	−2.63026	+	3.80530i	−0.166352	+	0.240668i
$251$	−9.02986	+	3.23093i	−0.569959	+	0.203935i	−0.606068	−	0.795413i	$-0.707254\pi$
$251$	−9.02986	+	3.23093i	−0.569959	+	0.203935i	0.0361082	+	0.999348i	$0.488504\pi$
$252$	0.284166	+	0.369400i	0.0179008	+	0.0232700i
$253$	−1.52888	−	0.916373i	−0.0961196	−	0.0576119i
$254$	0.585434	−	9.01608i	0.0367334	−	0.565719i
$255$	3.04540			0.190710
$256$	13.8952	+	7.93244i	0.868450	+	0.495777i
$257$	9.63184			0.600818			0.300409	−	0.953810i	$-0.402877\pi$
$257$	9.63184			0.600818			0.300409	+	0.953810i	$0.402877\pi$
$258$	−0.401717	+	6.18671i	−0.0250098	+	0.385168i
$259$	0.306347	+	0.183617i	0.0190355	+	0.0114094i
$260$	22.5477	−	17.3451i	1.39835	−	1.07570i
$261$	2.53811	−	0.908152i	0.157105	−	0.0562132i
$262$	−0.271743	+	0.393141i	−0.0167884	+	0.0242883i
$263$	16.5490	−	5.02010i	1.02046	−	0.309552i	0.264649	−	0.964345i	$-0.414744\pi$
$263$	16.5490	−	5.02010i	1.02046	−	0.309552i	0.755809	+	0.654792i	$0.227244\pi$
$264$	5.71853	−	1.14835i	0.351951	−	0.0706757i
$265$	5.07055	+	9.48634i	0.311482	+	0.582741i
$266$	−0.288096	−	1.00654i	−0.0176643	−	0.0617150i
$267$	0.151242	−	0.203927i	0.00925587	−	0.0124801i
$268$	1.70791	+	14.6886i	0.104327	+	0.897249i
$269$	2.34758	−	1.11032i	0.143134	−	0.0676976i	−0.354646	−	0.935001i	$-0.615399\pi$
$269$	2.34758	−	1.11032i	0.143134	−	0.0676976i	0.497780	+	0.867303i	$0.334149\pi$
$270$	−1.06722	−	4.56450i	−0.0649491	−	0.277787i
$271$	10.5853	+	2.10555i	0.643012	+	0.127903i	0.505817	−	0.862641i	$-0.331191\pi$
$271$	10.5853	+	2.10555i	0.643012	+	0.127903i	0.137195	+	0.990544i	$0.456191\pi$
$272$	3.66780	+	0.231434i	0.222393	+	0.0140327i
$273$	0.980745	−	0.195082i	0.0593574	−	0.0118069i
$274$	−8.21300	+	3.72729i	−0.496165	+	0.225174i
$275$	0.605782	+	12.3310i	0.0365300	+	0.743586i
$276$	−0.935018	+	1.45405i	−0.0562814	+	0.0875236i
$277$	−29.8503	−	7.47710i	−1.79353	−	0.449256i	−0.804127	−	0.594458i	$-0.797367\pi$
$277$	−29.8503	−	7.47710i	−1.79353	−	0.449256i	−0.989402	+	0.145202i	$0.953617\pi$
$278$	17.2606	+	14.6265i	1.03522	+	0.877237i
$279$	0.472429	+	4.79665i	0.0282836	+	0.287168i
$280$	−1.97322	+	0.937676i	−0.117922	+	0.0560368i
$281$	18.9397	−	15.5434i	1.12985	−	0.927240i	0.131897	−	0.991263i	$-0.457893\pi$
$281$	18.9397	−	15.5434i	1.12985	−	0.927240i	0.997948	+	0.0640234i	$0.0203932\pi$
$282$	5.70902	+	14.4213i	0.339967	+	0.858775i
$283$	1.36117	−	27.7073i	0.0809132	−	1.64703i	−0.524715	−	0.851278i	$-0.675828\pi$
$283$	1.36117	−	27.7073i	0.0809132	−	1.64703i	0.605628	−	0.795748i	$-0.292922\pi$
$284$	4.50862	+	3.22253i	0.267538	+	0.191222i
$285$	−1.54513	+	10.4164i	−0.0915256	+	0.617015i
$286$	3.23164	−	12.0901i	0.191091	−	0.714901i
$287$	−1.86318	−	0.771756i	−0.109980	−	0.0455553i
$288$	−0.938456	−	5.57847i	−0.0552991	−	0.328714i
$289$	−14.9261	+	6.18258i	−0.878004	+	0.363681i
$290$	1.65700	+	12.5272i	0.0973024	+	0.735625i
$291$	4.37468	−	3.24449i	0.256448	−	0.190195i
$292$	13.9727	+	6.31045i	0.817689	+	0.369291i
$293$	3.93475	+	4.34133i	0.229871	+	0.253623i	0.844954	−	0.534839i	$-0.179628\pi$
$293$	3.93475	+	4.34133i	0.229871	+	0.253623i	−0.615083	+	0.788462i	$0.710878\pi$
$294$	9.82148	+	0.154739i	0.572800	+	0.00902455i
$295$	17.2738	+	1.70132i	1.00572	+	0.0990547i
$296$	−2.23549	−	3.71429i	−0.129935	−	0.215889i
$297$	−1.59408	−	1.30823i	−0.0924977	−	0.0759109i
$298$	10.2683	−	32.0249i	0.594826	−	1.85515i
$299$	1.90688	+	3.18144i	0.110278	+	0.183987i
$300$	11.9718	−	0.210483i	0.691192	−	0.0121522i
$301$	−0.756928	−	0.686040i	−0.0436286	−	0.0395427i
$302$	7.04923	−	0.235063i	0.405638	−	0.0135264i
$303$	−11.2651	−	7.52711i	−0.647164	−	0.432421i
$304$	−2.65250	+	12.4278i	−0.152131	+	0.712785i
$305$	39.3208	−	26.2733i	2.25150	−	1.50441i
$306$	−0.757480	−	1.05570i	−0.0433022	−	0.0603506i
$307$	0.467967	+	0.167441i	0.0267083	+	0.00955637i	0.350210	−	0.936671i	$-0.386110\pi$
$307$	0.467967	+	0.167441i	0.0267083	+	0.00955637i	−0.323502	+	0.946228i	$0.604860\pi$
$308$	−0.438081	+	0.855432i	−0.0249620	+	0.0487428i
$309$	0.776341	+	5.23367i	0.0441645	+	0.297733i
$310$	−22.4471	−	2.56849i	−1.27491	−	0.145881i
$311$	−4.10346	+	13.5273i	−0.232686	+	0.767062i	0.760377	+	0.649481i	$0.225014\pi$
$311$	−4.10346	+	13.5273i	−0.232686	+	0.767062i	−0.993063	+	0.117581i	$0.962486\pi$
$312$	−11.6210	−	3.50205i	−0.657912	−	0.198264i
$313$	−8.16048	+	15.2672i	−0.461258	+	0.862952i	0.538535	+	0.842603i	$0.318978\pi$
$313$	−8.16048	+	15.2672i	−0.461258	+	0.862952i	−0.999793	+	0.0203493i	$0.993522\pi$
$314$	−0.699248	−	0.150578i	−0.0394608	−	0.00849759i
$315$	0.698242	+	0.330244i	0.0393415	+	0.0186071i
$316$	−4.09159	−	8.27152i	−0.230170	−	0.465310i
$317$	−17.8173	+	4.46300i	−1.00072	+	0.250667i	−0.708520	−	0.705691i	$-0.750637\pi$
$317$	−17.8173	+	4.46300i	−1.00072	+	0.250667i	−0.292198	+	0.956358i	$0.594387\pi$
$318$	2.02730	−	4.11726i	0.113685	−	0.230885i
$319$	3.93079	+	3.93079i	0.220082	+	0.220082i
$320$	26.4897	+	1.20441i	1.48082	+	0.0673283i
$321$	9.49355	−	9.49355i	0.529878	−	0.529878i
$322$	−0.0917270	−	0.269680i	−0.00511175	−	0.0150287i
$323$	0.709230	+	2.83141i	0.0394626	+	0.157544i
$324$	−1.31686	+	1.50528i	−0.0731589	+	0.0836269i
$325$	10.9841	−	23.2239i	0.609288	−	1.28823i
$326$	3.32913	+	5.15643i	0.184383	+	0.285588i
$327$	−10.2390	−	5.47284i	−0.566216	−	0.302649i
$328$	15.5633	+	18.8935i	0.859340	+	1.04322i
$329$	−2.44565	−	0.741879i	−0.134833	−	0.0409011i
$330$	7.56809	−	6.01397i	0.416609	−	0.331058i
$331$	−35.9147	+	5.32745i	−1.97405	+	0.292823i	−0.977357	+	0.211596i	$0.932134\pi$
$331$	−35.9147	+	5.32745i	−1.97405	+	0.292823i	−0.996696	+	0.0812275i	$0.974116\pi$
$332$	−2.38225	+	2.02619i	−0.130743	+	0.111201i
$333$	−0.516351	+	1.44310i	−0.0282958	+	0.0790816i
$334$	5.41379	−	32.9155i	0.296230	−	1.80106i
$335$	13.6158	+	20.3774i	0.743908	+	1.11334i
$336$	0.815847	+	0.450800i	0.0445081	+	0.0245931i
$337$	−1.31844	+	1.97319i	−0.0718203	+	0.107487i	−0.865641	−	0.500665i	$-0.833089\pi$
$337$	−1.31844	+	1.97319i	−0.0718203	+	0.107487i	0.793821	+	0.608152i	$0.208089\pi$
$338$	−5.23067	+	5.59155i	−0.284511	+	0.304140i
$339$	5.23070	−	5.77118i	0.284092	−	0.313448i
$340$	5.58532	−	2.42941i	0.302907	−	0.131753i
$341$	−8.52528	+	5.10985i	−0.461670	+	0.276714i
$342$	3.99523	−	2.05524i	0.216037	−	0.111135i
$343$	−2.06161	+	2.51207i	−0.111316	+	0.135639i
$344$	4.19857	+	11.6670i	0.226372	+	0.629043i
$345$	−0.280826	+	2.85127i	−0.0151191	+	0.153507i
$346$	−19.4566	+	18.8530i	−1.04599	+	1.01355i
$347$	−12.2220	+	11.0774i	−0.656113	+	0.594666i	−0.930206	−	0.367037i	$-0.880372\pi$
$347$	−12.2220	+	11.0774i	−0.656113	+	0.594666i	0.274093	+	0.961703i	$0.411622\pi$
$348$	3.93049	−	3.69030i	0.210696	−	0.197821i
$349$	3.18531	+	4.29489i	0.170506	+	0.229900i	0.880192	−	0.474617i	$-0.157414\pi$
$349$	3.18531	+	4.29489i	0.170506	+	0.229900i	−0.709687	+	0.704517i	$0.751164\pi$
$350$	−1.20011	+	1.56599i	−0.0641486	+	0.0837055i
$351$	1.64216	+	3.96452i	0.0876519	+	0.211610i
$352$	9.57183	−	6.66793i	0.510180	−	0.355402i
$353$	9.54291	−	23.0386i	0.507918	−	1.22622i	−0.437162	−	0.899383i	$-0.644016\pi$
$353$	9.54291	−	23.0386i	0.507918	−	1.22622i	0.945080	−	0.326839i	$-0.105984\pi$
$354$	−3.70673	−	6.41122i	−0.197010	−	0.340753i
$355$	9.08525	+	1.34767i	0.482195	+	0.0715269i
$356$	0.114703	−	0.494656i	0.00607924	−	0.0262167i
$357$	0.213841	+	0.0105053i	0.0113177	+	0.000556002i
$358$	11.6181	−	26.8445i	0.614037	−	1.41878i
$359$	−14.4321	−	17.5855i	−0.761695	−	0.928128i	0.237367	−	0.971420i	$-0.423715\pi$
$359$	−14.4321	−	17.5855i	−0.761695	−	0.928128i	−0.999062	+	0.0432919i	$0.986215\pi$
$360$	−5.59855	−	7.52003i	−0.295069	−	0.396340i
$361$	8.86419	−	0.873047i	0.466536	−	0.0459498i
$362$	29.0259	−	2.39777i	1.52557	−	0.126024i
$363$	−1.63950	+	6.54525i	−0.0860514	+	0.343537i
$364$	1.64308	−	1.14015i	0.0861209	−	0.0597603i
$365$	25.3787	−	1.24678i	1.32838	−	0.0652593i
$366$	−18.8880	−	7.09582i	−0.987292	−	0.370905i
$367$	1.12637	+	5.66266i	0.0587962	+	0.295588i	0.998984	−	0.0450685i	$-0.0143506\pi$
$367$	1.12637	+	5.66266i	0.0587962	+	0.295588i	−0.940188	+	0.340657i	$0.889351\pi$
$368$	−0.554900	+	3.41265i	−0.0289261	+	0.177897i
$369$	1.68838	−	8.48805i	0.0878934	−	0.441870i
$370$	−6.10356	−	3.79029i	−0.317309	−	0.197048i
$371$	0.323319	+	0.683601i	0.0167859	+	0.0354908i
$372$	4.69288	+	8.42028i	0.243314	+	0.436571i
$373$	−0.406205	−	0.301262i	−0.0210325	−	0.0155988i	0.585132	−	0.810938i	$-0.301043\pi$
$373$	−0.406205	−	0.301262i	−0.0210325	−	0.0155988i	−0.606164	+	0.795339i	$0.707293\pi$
$374$	1.30016	−	2.34288i	0.0672295	−	0.121147i
$375$	2.88474	−	1.54193i	0.148967	−	0.0796248i
$376$	21.9748	+	21.8947i	1.13326	+	1.12913i
$377$	−3.35792	−	11.0696i	−0.172942	−	0.570112i
$378$	−0.0591924	−	0.324191i	−0.00304453	−	0.0166746i
$379$	−10.0507	−	28.0899i	−0.516270	−	1.44288i	−0.863139	−	0.504966i	$-0.831505\pi$
$379$	−10.0507	−	28.0899i	−0.516270	−	1.44288i	0.346869	−	0.937914i	$-0.387245\pi$
$380$	5.47569	+	20.3365i	0.280897	+	1.04324i
$381$	−3.28448	+	5.47982i	−0.168269	+	0.280740i
$382$	14.5329	−	12.7606i	0.743566	−	0.652891i
$383$			30.4079i			1.55377i	0.629640	+	0.776887i	$0.283202\pi$
$383$			30.4079i			1.55377i	−0.629640	+	0.776887i	$0.716798\pi$
$384$	−6.17126	−	9.48238i	−0.314926	−	0.483896i
$385$			1.59282i			0.0811777i
$386$	22.0970	+	25.1659i	1.12471	+	1.28091i
$387$	2.25376	−	3.76018i	0.114565	−	0.191141i
$388$	5.43503	−	9.44027i	0.275922	−	0.479257i
$389$	−4.07435	−	11.3870i	−0.206578	−	0.577346i	0.792910	−	0.609338i	$-0.208565\pi$
$389$	−4.07435	−	11.3870i	−0.206578	−	0.577346i	−0.999488	+	0.0319922i	$0.989815\pi$
$390$	−19.7882	+	3.61302i	−1.00201	+	0.182953i
$391$	0.230532	+	0.759961i	0.0116585	+	0.0384329i
$392$	18.1362	−	7.55110i	0.916018	−	0.381388i
$393$	0.298035	−	0.159303i	0.0150339	−	0.00803577i
$394$	−1.38883	−	0.770715i	−0.0699681	−	0.0388281i
$395$	−12.2843	−	9.11064i	−0.618089	−	0.458406i
$396$	−3.96718	−	1.12767i	−0.199358	−	0.0566674i
$397$	2.60624	+	5.51043i	0.130803	+	0.276560i	0.958752	−	0.284243i	$-0.0917423\pi$
$397$	2.60624	+	5.51043i	0.130803	+	0.276560i	−0.827949	+	0.560804i	$0.810492\pi$
$398$	−0.142745	+	0.229865i	−0.00715517	+	0.0115221i
$399$	−0.144428	+	0.726088i	−0.00723043	+	0.0363499i
$400$	21.7886	−	9.93630i	1.08943	−	0.496815i
$401$	0.256322	+	1.28862i	0.0128001	+	0.0643504i	0.986657	−	0.162810i	$-0.0520558\pi$
$401$	0.256322	+	1.28862i	0.0128001	+	0.0643504i	−0.973857	+	0.227161i	$0.927056\pi$
$402$	3.67731	−	9.78843i	0.183407	−	0.488203i
$403$	20.6579	−	1.01486i	1.02904	−	0.0505537i
$404$	−26.6650	−	4.81834i	−1.32663	−	0.239721i
$405$	−0.805391	+	3.21530i	−0.0400202	+	0.159770i
$406$	0.0731372	+	0.885351i	0.00362974	+	0.0439392i
$407$	−3.14546	+	0.309801i	−0.155915	+	0.0153563i
$408$	−2.23140	−	1.33192i	−0.110471	−	0.0659397i
$409$	20.1192	+	24.5153i	0.994832	+	1.21221i	0.977191	+	0.212361i	$0.0681154\pi$
$409$	20.1192	+	24.5153i	0.994832	+	1.21221i	0.0176404	+	0.999844i	$0.494385\pi$
$410$	37.2308	+	16.1133i	1.83870	+	0.795777i
$411$	6.36986	+	0.312931i	0.314202	+	0.0154357i
$412$	5.59888	+	8.97934i	0.275837	+	0.442380i
$413$	1.20706	+	0.179050i	0.0593955	+	0.00881049i
$414$	1.05826	−	0.611844i	0.0520105	−	0.0300705i
$415$	−1.98348	+	4.78854i	−0.0973652	+	0.235060i
$416$	−24.1069	+	2.84763i	−1.18194	+	0.139617i
$417$	−6.12211	−	14.7801i	−0.299801	−	0.723784i
$418$	7.35388	+	5.63573i	0.359690	+	0.275652i
$419$	−14.1540	−	19.0845i	−0.691470	−	0.932340i	0.308350	−	0.951273i	$-0.400223\pi$
$419$	−14.1540	−	19.0845i	−0.691470	−	0.932340i	−0.999821	+	0.0189329i	$0.993973\pi$
$420$	1.54404	+	0.0486650i	0.0753412	+	0.00237461i
$421$	−28.9119	+	26.2042i	−1.40908	+	1.27711i	−0.496605	+	0.867977i	$0.665420\pi$
$421$	−28.9119	+	26.2042i	−1.40908	+	1.27711i	−0.912473	+	0.409137i	$0.865830\pi$
$422$	20.3344	+	20.9854i	0.989865	+	1.02155i
$423$	1.07499	−	10.9146i	0.0522678	−	0.530684i
$424$	0.433634	−	9.16838i	0.0210591	−	0.445256i
$425$	3.48950	−	4.25197i	0.169266	−	0.206251i
$426$	−1.79259	−	3.48466i	−0.0868513	−	0.168832i
$427$	2.85165	−	1.70921i	0.138001	−	0.0827147i
$428$	9.83807	−	24.9846i	0.475541	−	1.20768i
$429$	−5.94270	+	6.55676i	−0.286916	+	0.316563i
$430$	15.0072	+	14.0386i	0.723710	+	0.677002i
$431$	−3.26583	+	4.88766i	−0.157309	+	0.235430i	−0.901749	−	0.432259i	$-0.857717\pi$
$431$	−3.26583	+	4.88766i	−0.157309	+	0.235430i	0.744440	+	0.667689i	$0.232717\pi$
$432$	−1.21434	+	3.81122i	−0.0584248	+	0.183367i
$433$	8.62401	+	12.9067i	0.414443	+	0.620259i	0.978689	−	0.205349i	$-0.0658328\pi$
$433$	8.62401	+	12.9067i	0.414443	+	0.620259i	−0.564245	+	0.825607i	$0.690833\pi$
$434$	−1.56733	−	0.257787i	−0.0752342	−	0.0123742i
$435$	3.01020	−	8.41293i	0.144328	−	0.403369i
$436$	−23.1443	−	1.86936i	−1.10841	−	0.0895263i
$437$	−2.71632	+	0.402928i	−0.129939	+	0.0192746i
$438$	−6.74463	−	8.48756i	−0.322271	−	0.405551i
$439$	16.6421	+	5.04832i	0.794283	+	0.240943i	0.661247	−	0.750168i	$-0.270027\pi$
$439$	16.6421	+	5.04832i	0.794283	+	0.240943i	0.133036	+	0.991111i	$0.457527\pi$
$440$	9.08249	−	17.0670i	0.432991	−	0.813639i
$441$	−6.12556	−	3.27418i	−0.291693	−	0.155913i
$442$	−4.68424	+	3.02427i	−0.222807	+	0.143850i
$443$	4.94630	−	10.4581i	0.235006	−	0.496878i	−0.751678	−	0.659531i	$-0.770755\pi$
$443$	4.94630	−	10.4581i	0.235006	−	0.496878i	0.986683	+	0.162653i	$0.0520051\pi$
$444$	0.204210	+	3.05859i	0.00969137	+	0.145154i
$445$	−0.204481	−	0.816334i	−0.00969333	−	0.0386979i
$446$	−22.2058	+	7.55292i	−1.05147	+	0.357641i
$447$	−16.8154	+	16.8154i	−0.795342	+	0.795342i
$448$	1.85590	+	0.175949i	0.0876829	+	0.00831282i
$449$	17.9166	+	17.9166i	0.845538	+	0.845538i	0.989573	−	0.144034i	$-0.0460076\pi$
$449$	17.9166	+	17.9166i	0.845538	+	0.845538i	−0.144034	+	0.989573i	$0.546008\pi$
$450$	−7.59579	−	3.74008i	−0.358069	−	0.176309i
$451$	17.3119	−	4.33639i	0.815183	−	0.204193i
$452$	4.98935	−	14.7571i	0.234679	−	0.694118i
$453$	−4.50849	−	2.13236i	−0.211828	−	0.100187i
$454$	−0.564810	+	2.62285i	−0.0265079	+	0.123096i
$455$	1.56245	−	2.92313i	0.0732486	−	0.137038i
$456$	5.68780	−	6.95646i	0.266355	−	0.325766i
$457$	−7.95946	+	26.2388i	−0.372328	+	1.22740i	0.548075	+	0.836429i	$0.315361\pi$
$457$	−7.95946	+	26.2388i	−0.372328	+	1.22740i	−0.920403	+	0.390971i	$0.872139\pi$
$458$	−3.78945	+	33.1176i	−0.177069	+	1.54748i
$459$	0.134812	+	0.908828i	0.00629248	+	0.0424205i
$460$	1.75950	+	5.45331i	0.0820373	+	0.254262i
$461$	−4.15940	−	1.48826i	−0.193723	−	0.0693150i	0.238241	−	0.971206i	$-0.423429\pi$
$461$	−4.15940	−	1.48826i	−0.193723	−	0.0693150i	−0.431964	+	0.901891i	$0.642179\pi$
$462$	0.552160	−	0.396181i	0.0256888	−	0.0184320i
$463$	17.3007	−	11.5600i	0.804031	−	0.537237i	−0.0842996	−	0.996440i	$-0.526865\pi$
$463$	17.3007	−	11.5600i	0.804031	−	0.537237i	0.888331	+	0.459204i	$0.151865\pi$
$464$	4.26474	−	9.90355i	0.197985	−	0.459761i
$465$	13.2836	+	8.87584i	0.616014	+	0.411607i
$466$	0.582256	+	17.4611i	0.0269725	+	0.808869i
$467$	15.9449	+	14.4516i	0.737842	+	0.668741i	0.951319	−	0.308207i	$-0.0997290\pi$
$467$	15.9449	+	14.4516i	0.737842	+	0.668741i	−0.213478	+	0.976948i	$0.568479\pi$
$468$	6.17437	+	5.96101i	0.285410	+	0.275548i
$469$	0.885775	+	1.47783i	0.0409013	+	0.0682397i
$470$	48.9558	+	15.6969i	2.25816	+	0.724044i
$471$	0.390971	+	0.320862i	0.0180150	+	0.0147845i
$472$	−11.9126	−	8.80134i	−0.548323	−	0.405115i
$473$	8.99676	+	0.886103i	0.413671	+	0.0407431i
$474$	−0.102794	+	6.52449i	−0.00472150	+	0.299680i
$475$	12.7729	+	14.0927i	0.586061	+	0.646618i
$476$	0.400569	−	0.151321i	0.0183601	−	0.00693577i
$477$	−2.60652	+	1.93312i	−0.119344	+	0.0885117i
$478$	32.1908	−	4.25794i	1.47237	−	0.194753i
$479$	20.3420	−	8.42593i	0.929450	−	0.384991i	0.133980	−	0.990984i	$-0.457224\pi$
$479$	20.3420	−	8.42593i	0.929450	−	0.384991i	0.795470	+	0.605993i	$0.207224\pi$
$480$	−16.2668	−	9.32575i	−0.742474	−	0.425660i
$481$	6.07642	+	2.51693i	0.277061	+	0.114762i
$482$	2.08331	+	0.556863i	0.0948922	+	0.0253644i
$483$	−0.0295546	+	0.199241i	−0.00134478	+	0.00906578i
$484$	2.21447	+	13.3120i	0.100658	+	0.605091i
$485$	0.885830	−	18.0315i	0.0402235	−	0.818768i
$486$	1.31493	−	0.520546i	0.0596463	−	0.0236125i
$487$	15.4919	−	12.7139i	0.702007	−	0.576122i	−0.214218	−	0.976786i	$-0.568720\pi$
$487$	15.4919	−	12.7139i	0.702007	−	0.576122i	0.916225	+	0.400663i	$0.131220\pi$
$488$	−40.3015	+	2.05366i	−1.82436	+	0.0929648i
$489$	−0.425398	−	4.31914i	−0.0192372	−	0.195318i
$490$	21.0489	−	24.8397i	0.950894	−	1.12214i
$491$	−39.8755	−	9.98828i	−1.79955	−	0.450765i	−0.808991	−	0.587821i	$-0.799986\pi$
$491$	−39.8755	−	9.98828i	−1.79955	−	0.450765i	−0.990563	+	0.137056i	$0.956236\pi$
$492$	−3.67465	−	16.9141i	−0.165666	−	0.762547i
$493$	−0.121527	−	2.47375i	−0.00547332	−	0.111412i
$494$	−7.96753	−	17.5563i	−0.358476	−	0.789894i
$495$	−6.70400	+	1.33351i	−0.301322	+	0.0599368i
$496$	15.3239	+	11.6993i	0.688065	+	0.525315i
$497$	0.633297	+	0.125971i	0.0284073	+	0.00565056i
$498$	2.15332	−	0.503467i	0.0964928	−	0.0225609i
$499$	−14.9705	+	7.08052i	−0.670172	+	0.316968i	−0.732183	−	0.681108i	$-0.761498\pi$
$499$	−14.9705	+	7.08052i	−0.670172	+	0.316968i	0.0620114	+	0.998075i	$0.480248\pi$
$500$	4.06063	−	5.12917i	0.181597	−	0.229383i
$501$	−14.0511	+	18.9457i	−0.627755	+	0.846429i
$502$	13.0394	−	3.73218i	0.581976	−	0.166575i
$503$	−19.6088	−	36.6855i	−0.874313	−	1.63573i	−0.767135	−	0.641485i	$-0.778319\pi$
$503$	−19.6088	−	36.6855i	−0.874313	−	1.63573i	−0.107178	−	0.994240i	$-0.534181\pi$
$504$	−0.367177	−	0.547353i	−0.0163554	−	0.0243810i
$505$	−42.9744	+	13.0362i	−1.91234	+	0.580101i
$506$	2.07364	+	1.43332i	0.0921846	+	0.0637190i
$507$	5.09763	−	1.82396i	0.226394	−	0.0810049i
$508$	−1.65238	+	12.6702i	−0.0733124	+	0.562150i
$509$	29.9047	+	17.9242i	1.32550	+	0.794475i	0.989100	−	0.147243i	$-0.0470399\pi$
$509$	29.9047	+	17.9242i	1.32550	+	0.794475i	0.336402	+	0.941719i	$0.390790\pi$
$510$	−4.29779	−	0.279065i	−0.190310	−	0.0123572i
$511$	1.78634			0.0790230
$512$	−18.8826	−	12.4679i	−0.834500	−	0.551007i
$513$	−3.17694			−0.140265
$514$	−13.5929	−	0.882615i	−0.599555	−	0.0389305i
$515$	15.0424	+	9.01610i	0.662849	+	0.397297i
$516$	1.13384	−	8.69413i	0.0499145	−	0.382738i
$517$	21.2945	−	7.61929i	0.936530	−	0.335096i
$518$	−0.415504	−	0.287200i	−0.0182562	−	0.0126189i
$519$	18.3323	−	5.56104i	0.804698	−	0.244103i
$520$	−33.4097	+	22.4120i	−1.46511	+	0.982830i
$521$	3.08109	+	5.76432i	0.134985	+	0.252539i	0.940328	−	0.340270i	$-0.110519\pi$
$521$	3.08109	+	5.76432i	0.134985	+	0.252539i	−0.805343	+	0.592810i	$0.798019\pi$
$522$	−3.66511	+	1.04904i	−0.160418	+	0.0459153i
$523$	−2.78681	+	3.75758i	−0.121859	+	0.164308i	−0.859924	−	0.510421i	$-0.829489\pi$
$523$	−2.78681	+	3.75758i	−0.121859	+	0.164308i	0.738066	+	0.674729i	$0.235739\pi$
$524$	0.419521	−	0.529916i	0.0183269	−	0.0231495i
$525$	1.26115	−	0.596480i	0.0550411	−	0.0260325i
$526$	−23.8147	+	5.56810i	−1.03837	+	0.242781i
$527$	4.34327	+	0.863930i	0.189196	+	0.0376334i
$528$	−8.17546	+	1.09657i	−0.355791	+	0.0477223i
$529$	21.8253	−	4.34132i	0.948925	−	0.188753i
$530$	−6.28649	−	13.8522i	−0.273068	−	0.601699i
$531$	0.256947	+	5.23028i	0.0111505	+	0.226975i
$532$	0.314339	+	1.44687i	0.0136283	+	0.0627299i
$533$	−36.0242	−	9.02360i	−1.56038	−	0.390856i
$534$	−0.232126	+	0.273931i	−0.0100451	+	0.0118541i
$535$	−4.36196	−	44.2877i	−0.188584	−	1.91473i
$536$	−1.06428	−	20.8857i	−0.0459698	−	0.902124i
$537$	−15.9885	+	13.1214i	−0.689955	+	0.566232i
$538$	−3.41475	+	1.35181i	−0.147220	+	0.0582808i
$539$	0.702806	−	14.3059i	0.0302720	−	0.616201i
$540$	1.08784	+	6.53941i	0.0468132	+	0.281411i
$541$	−6.15790	+	41.5132i	−0.264749	+	1.78479i	0.294356	+	0.955696i	$0.404895\pi$
$541$	−6.15790	+	41.5132i	−0.264749	+	1.78479i	−0.559105	+	0.829097i	$0.688855\pi$
$542$	−14.7455	−	3.94143i	−0.633374	−	0.169299i
$543$	−19.0267	−	7.88110i	−0.816512	−	0.338210i
$544$	−5.15494	−	0.662708i	−0.221016	−	0.0284134i
$545$	−35.5531	+	14.7266i	−1.52293	+	0.630817i
$546$	−1.40194	+	0.185438i	−0.0599977	+	0.00793600i
$547$	16.7238	−	12.4032i	0.715059	−	0.530324i	−0.175900	−	0.984408i	$-0.556283\pi$
$547$	16.7238	−	12.4032i	0.715059	−	0.530324i	0.890959	+	0.454084i	$0.150033\pi$
$548$	11.9321	−	4.50750i	0.509713	−	0.192551i
$549$	9.58129	+	10.5713i	0.408919	+	0.451173i
$550$	0.275045	−	17.4575i	0.0117280	−	0.744390i
$551$	8.52281	+	0.839423i	0.363084	+	0.0357606i
$552$	1.45278	−	1.96634i	0.0618343	−	0.0836929i
$553$	−0.831147	−	0.682105i	−0.0353440	−	0.0290060i
$554$	41.4408	+	13.2873i	1.76065	+	0.564525i
$555$	2.61182	+	4.35755i	0.110865	+	0.184968i
$556$	−23.0186	−	22.2232i	−0.976205	−	0.942472i
$557$	26.3843	+	23.9133i	1.11794	+	1.01324i	0.999795	+	0.0202442i	$0.00644438\pi$
$557$	26.3843	+	23.9133i	1.11794	+	1.01324i	0.118144	+	0.992996i	$0.462306\pi$
$558$	−0.227170	−	6.81253i	−0.00961687	−	0.288397i
$559$	−15.6416	−	10.4514i	−0.661568	−	0.442045i
$560$	2.87061	−	1.14247i	0.121306	−	0.0482782i
$561$	−1.57536	+	1.05262i	−0.0665115	+	0.0444416i
$562$	−28.1528	+	20.1999i	−1.18755	+	0.852082i
$563$	38.1687	+	13.6570i	1.60862	+	0.575574i	0.979449	−	0.201692i	$-0.0646441\pi$
$563$	38.1687	+	13.6570i	1.60862	+	0.575574i	0.629172	+	0.777266i	$0.283394\pi$
$564$	−6.73532	−	20.8751i	−0.283608	−	0.878999i
$565$	−3.78819	−	25.5379i	−0.159370	−	1.07439i
$566$	−4.45990	+	38.9769i	−0.187463	+	1.63832i
$567$	−0.0676442	+	0.222993i	−0.00284079	+	0.00936483i
$568$	−6.06746	−	4.96092i	−0.254585	−	0.208156i
$569$	−6.74395	+	12.6170i	−0.282721	+	0.528934i	−0.982694	−	0.185235i	$-0.940695\pi$
$569$	−6.74395	+	12.6170i	−0.282721	+	0.528934i	0.699973	+	0.714169i	$0.253195\pi$
$570$	3.13506	−	14.5585i	0.131313	−	0.609788i
$571$	−15.6151	−	7.38537i	−0.653470	−	0.309068i	0.0719162	−	0.997411i	$-0.477089\pi$
$571$	−15.6151	−	7.38537i	−0.653470	−	0.309068i	−0.725386	+	0.688343i	$0.758339\pi$
$572$	−5.66850	+	16.7659i	−0.237012	+	0.701017i
$573$	−13.2656	+	3.32287i	−0.554180	+	0.138815i
$574$	2.55868	+	1.25987i	0.106797	+	0.0525859i
$575$	3.65915	+	3.65915i	0.152597	+	0.152597i
$576$	0.813206	+	7.95856i	0.0338836	+	0.331607i
$577$	−6.94599	+	6.94599i	−0.289165	+	0.289165i	−0.836750	−	0.547585i	$-0.815547\pi$
$577$	−6.94599	+	6.94599i	−0.289165	+	0.289165i	0.547585	+	0.836750i	$0.315547\pi$
$578$	21.6308	−	7.35736i	0.899724	−	0.306026i
$579$	−5.75407	−	22.9715i	−0.239131	−	0.954665i
$580$	−1.19049	−	17.8308i	−0.0494325	−	0.740384i
$581$	−0.155794	+	0.329399i	−0.00646343	+	0.0136658i
$582$	−6.47104	+	4.17788i	−0.268233	+	0.173179i
$583$	−5.90183	−	3.15459i	−0.244429	−	0.130650i
$584$	−19.1406	−	10.1860i	−0.792042	−	0.421498i
$585$	13.6112	+	4.12891i	0.562754	+	0.170710i
$586$	−5.15507	−	6.48723i	−0.212954	−	0.267985i
$587$	−24.8637	+	3.68818i	−1.02624	+	0.152228i	−0.638563	−	0.769569i	$-0.720471\pi$
$587$	−24.8637	+	3.68818i	−1.02624	+	0.152228i	−0.387673	+	0.921797i	$0.626721\pi$
$588$	−13.8463	−	1.11837i	−0.571012	−	0.0461206i
$589$	−5.15859	+	14.4173i	−0.212556	+	0.594054i
$590$	−24.2216	−	3.98386i	−0.997188	−	0.164013i
$591$	0.623978	+	0.933849i	0.0256670	+	0.0384134i
$592$	2.81445	+	5.44660i	0.115673	+	0.223854i
$593$	−7.25005	+	10.8505i	−0.297724	+	0.445575i	−0.949928	−	0.312468i	$-0.898844\pi$
$593$	−7.25005	+	10.8505i	−0.297724	+	0.445575i	0.652204	+	0.758043i	$0.273844\pi$
$594$	2.12975	+	1.99230i	0.0873847	+	0.0817449i
$595$	0.476579	−	0.525824i	0.0195378	−	0.0215567i
$596$	−17.4256	+	44.2540i	−0.713782	+	1.81271i
$597$	0.164109	−	0.0983630i	0.00671653	−	0.00402573i
$598$	−2.39954	−	4.66452i	−0.0981245	−	0.190746i
$599$	18.3876	−	22.4053i	0.751296	−	0.915456i	−0.247273	−	0.968946i	$-0.579534\pi$
$599$	18.3876	−	22.4053i	0.751296	−	0.915456i	0.998568	+	0.0534896i	$0.0170344\pi$
$600$	−16.9144	−	0.799995i	−0.690527	−	0.0326597i
$601$	2.23481	−	22.6904i	0.0911598	−	0.925561i	−0.835457	−	0.549555i	$-0.814797\pi$
$601$	2.23481	−	22.6904i	0.0911598	−	0.925561i	0.926617	−	0.376006i	$-0.122703\pi$
$602$	1.00534	+	1.03753i	0.0409747	+	0.0422865i
$603$	−5.47843	+	4.96536i	−0.223099	+	0.202205i
$604$	−9.96971	−	0.314226i	−0.405662	−	0.0127857i
$605$	13.3231	+	17.9641i	0.541659	+	0.730343i
$606$	15.2080	+	11.6548i	0.617785	+	0.473446i
$607$	−7.32179	−	17.6764i	−0.297182	−	0.717462i	−0.999982	−	0.00607332i	$-0.998067\pi$
$607$	−7.32179	−	17.6764i	−0.297182	−	0.717462i	0.702799	−	0.711388i	$-0.251933\pi$
$608$	4.88215	−	17.2956i	0.197997	−	0.701430i
$609$	0.240390	−	0.580354i	0.00974111	−	0.0235171i
$610$	−57.8987	+	33.4748i	−2.34425	+	1.35536i
$611$	−46.5534	−	6.90555i	−1.88335	−	0.279369i
$612$	0.972247	+	1.55927i	0.0393008	+	0.0630296i
$613$	−30.1377	−	1.48057i	−1.21725	−	0.0597997i	−0.569720	−	0.821839i	$-0.692948\pi$
$613$	−30.1377	−	1.48057i	−1.21725	−	0.0597997i	−0.647531	+	0.762039i	$0.724198\pi$
$614$	−0.645071	−	0.279182i	−0.0260329	−	0.0112669i
$615$	−18.1982	−	22.1746i	−0.733822	−	0.894165i
$616$	0.696626	−	1.16708i	0.0280679	−	0.0470229i
$617$	−27.8136	+	2.73940i	−1.11973	+	0.110284i	−0.640902	−	0.767623i	$-0.721439\pi$
$617$	−27.8136	+	2.73940i	−1.11973	+	0.110284i	−0.478831	+	0.877907i	$0.658939\pi$
$618$	−0.616018	−	7.45711i	−0.0247799	−	0.299969i
$619$	−0.641994	+	2.56299i	−0.0258039	+	0.103015i	−0.981565	−	0.191130i	$-0.938785\pi$
$619$	−0.641994	+	2.56299i	−0.0258039	+	0.103015i	0.955761	+	0.294145i	$0.0950348\pi$
$620$	31.4430	+	5.68171i	1.26278	+	0.228183i
$621$	−0.863326	+	0.0424125i	−0.0346441	+	0.00170195i
$622$	7.03055	−	18.7143i	0.281899	−	0.750373i
$623$	−0.0115422	−	0.0580265i	−0.000462428	−	0.00232478i
$624$	16.0792	+	6.00713i	0.643683	+	0.240478i
$625$	−3.72467	+	18.7252i	−0.148987	+	0.749007i
$626$	12.9154	−	20.7979i	0.516204	−	0.831251i
$627$	−2.80107	−	5.92237i	−0.111864	−	0.236517i
$628$	0.973009	+	0.276577i	0.0388273	+	0.0110366i
$629$	1.13108	+	0.838865i	0.0450990	+	0.0334477i
$630$	−0.955127	−	0.530038i	−0.0380532	−	0.0211172i
$631$	36.0714	−	19.2806i	1.43598	−	0.767548i	0.444252	−	0.895902i	$-0.353469\pi$
$631$	36.0714	−	19.2806i	1.43598	−	0.767548i	0.991728	+	0.128354i	$0.0409693\pi$
$632$	5.01626	+	12.0481i	0.199536	+	0.479246i
$633$	−5.99801	−	19.7728i	−0.238399	−	0.785897i
$634$	25.5535	−	4.66568i	1.01486	−	0.185298i
$635$	7.13412	+	19.9385i	0.283109	+	0.791237i
$636$	−3.23829	+	5.62468i	−0.128407	+	0.223033i
$637$	−15.3229	+	25.5647i	−0.607116	+	1.01291i
$638$	−5.18709	−	5.90749i	−0.205359	−	0.233880i
$639$			2.77094i			0.109617i
$640$	−37.2731	−	4.12710i	−1.47335	−	0.163138i
$641$			16.1166i			0.636568i	0.947995	+	0.318284i	$0.103107\pi$
$641$			16.1166i			0.636568i	−0.947995	+	0.318284i	$0.896893\pi$
$642$	−14.2676	+	12.5278i	−0.563099	+	0.494431i
$643$	2.73101	−	4.55642i	0.107701	−	0.179688i	−0.799160	−	0.601119i	$-0.794722\pi$
$643$	2.73101	−	4.55642i	0.107701	−	0.179688i	0.906861	+	0.421431i	$0.138472\pi$
$644$	0.104737	+	0.388989i	0.00412721	+	0.0153283i
$645$	−4.89534	−	13.6815i	−0.192754	−	0.538710i
$646$	−0.741439	−	4.06079i	−0.0291715	−	0.159770i
$647$	0.514479	+	1.69601i	0.0202262	+	0.0666770i	0.966473	−	0.256770i	$-0.0826583\pi$
$647$	0.514479	+	1.69601i	0.0202262	+	0.0666770i	−0.946246	+	0.323447i	$0.895158\pi$
$648$	1.99634	−	2.00365i	0.0784238	−	0.0787107i
$649$	−9.52362	+	5.09048i	−0.373835	+	0.199819i
$650$	−17.6293	+	31.7680i	−0.691479	+	1.24604i
$651$	0.902130	+	0.669065i	0.0353573	+	0.0262227i
$652$	−4.22570	−	7.58204i	−0.165491	−	0.296935i
$653$	−0.0419002	−	0.0885906i	−0.00163968	−	0.00346682i	0.903168	−	0.429288i	$-0.141235\pi$
$653$	−0.0419002	−	0.0885906i	−0.00163968	−	0.00346682i	−0.904807	+	0.425821i	$0.859985\pi$
$654$	13.9481	+	8.66174i	0.545415	+	0.338701i
$655$	0.218529	−	1.09862i	0.00853863	−	0.0429266i
$656$	−20.2323	−	28.0894i	−0.789938	−	1.09671i
$657$	1.49552	+	7.51850i	0.0583459	+	0.293325i
$658$	3.38342	+	1.27108i	0.131899	+	0.0495518i
$659$	29.1709	−	1.43308i	1.13634	−	0.0558247i	0.527814	−	0.849360i	$-0.323012\pi$
$659$	29.1709	−	1.43308i	1.13634	−	0.0558247i	0.608524	+	0.793535i	$0.291762\pi$
$660$	−11.2315	+	7.79366i	−0.437185	+	0.303368i
$661$	1.20283	−	4.80195i	0.0467845	−	0.186774i	−0.942133	−	0.335239i	$-0.891183\pi$
$661$	1.20283	−	4.80195i	0.0467845	−	0.186774i	0.988918	+	0.148464i	$0.0474330\pi$
$662$	51.1726	−	4.22727i	1.98888	−	0.164297i
$663$	3.92362	−	0.386443i	0.152381	−	0.0150082i
$664$	3.54761	−	2.64114i	0.137674	−	0.102496i
$665$	1.55672	+	1.89687i	0.0603669	+	0.0735573i
$666$	0.860934	−	1.98925i	0.0333605	−	0.0770819i
$667$	2.32726	+	0.114331i	0.0901120	+	0.00442692i
$668$	−10.6564	+	45.9556i	−0.412308	+	1.77808i
$669$	16.4058	+	2.43357i	0.634284	+	0.0940871i
$670$	−17.3478	−	30.0051i	−0.670205	−	1.15920i
$671$	−11.2591	+	27.1819i	−0.434652	+	1.04934i
$672$	−1.11005	−	0.710947i	−0.0428211	−	0.0274254i
$673$	2.12516	+	5.13059i	0.0819188	+	0.197770i	0.959532	−	0.281600i	$-0.0908652\pi$
$673$	2.12516	+	5.13059i	0.0819188	+	0.197770i	−0.877613	+	0.479370i	$0.840865\pi$
$674$	2.04146	−	2.66384i	0.0786340	−	0.102607i
$675$	3.56635	+	4.80866i	0.137269	+	0.185086i
$676$	7.89412	−	7.41171i	0.303620	−	0.285066i
$677$	10.5285	−	9.54248i	0.404643	−	0.366747i	−0.443717	−	0.896167i	$-0.646340\pi$
$677$	10.5285	−	9.54248i	0.404643	−	0.366747i	0.848360	+	0.529420i	$0.177590\pi$
$678$	−7.91062	+	7.66522i	−0.303805	+	0.294381i
$679$	0.124402	−	1.26308i	0.00477411	−	0.0484724i
$680$	−8.10486	+	2.91667i	−0.310807	+	0.111849i
$681$	1.20354	−	1.46652i	0.0461197	−	0.0561970i
$682$	12.4995	−	6.43002i	0.478629	−	0.246218i
$683$	37.8052	−	22.6595i	1.44657	−	0.867044i	0.446953	−	0.894557i	$-0.352509\pi$
$683$	37.8052	−	22.6595i	1.44657	−	0.867044i	0.999621	+	0.0275137i	$0.00875898\pi$
$684$	−5.82656	+	2.53434i	−0.222784	+	0.0969028i
$685$	14.1962	−	15.6631i	0.542411	−	0.598458i
$686$	3.13962	−	3.35623i	0.119871	−	0.128141i
$687$	13.0950	−	19.5981i	0.499607	−	0.747715i
$688$	−4.85609	−	16.8497i	−0.185137	−	0.642389i
$689$	7.73654	+	11.5786i	0.294739	+	0.441108i
$690$	0.657589	−	3.99810i	0.0250340	−	0.152205i
$691$	−11.1318	+	31.1113i	−0.423474	+	1.18353i	0.520601	+	0.853800i	$0.325708\pi$
$691$	−11.1318	+	31.1113i	−0.423474	+	1.18353i	−0.944075	+	0.329731i	$0.893042\pi$
$692$	29.1856	−	24.8233i	1.10947	−	0.943640i
$693$	−0.475340	+	0.0705101i	−0.0180567	+	0.00267846i
$694$	18.2633	−	14.5129i	0.693266	−	0.550903i
$695$	−50.7437	−	15.3929i	−1.92482	−	0.583888i
$696$	−5.88503	+	4.84773i	−0.223072	+	0.183753i
$697$	−7.01248	−	3.74825i	−0.265617	−	0.141975i
$698$	−4.10168	−	6.35301i	−0.155251	−	0.240465i
$699$	5.28190	−	11.1676i	0.199780	−	0.422399i
$700$	1.83714	−	2.10001i	0.0694375	−	0.0793730i
$701$	−6.82255	−	27.2372i	−0.257684	−	1.02873i	−0.951270	−	0.308359i	$-0.900220\pi$
$701$	−6.82255	−	27.2372i	−0.257684	−	1.02873i	0.693586	−	0.720374i	$-0.256030\pi$
$702$	−1.95419	−	5.74538i	−0.0737563	−	0.216845i
$703$	−3.44310	+	3.44310i	−0.129859	+	0.129859i
$704$	−14.1192	+	8.53295i	−0.532136	+	0.321598i
$705$	−25.7054	−	25.7054i	−0.968120	−	0.968120i
$706$	−15.5785	+	31.6386i	−0.586305	+	1.19073i
$707$	−3.06254	+	0.767126i	−0.115179	+	0.0288507i
$708$	4.64359	+	9.38745i	0.174517	+	0.352802i
$709$	32.1789	+	15.2195i	1.20851	+	0.571580i	0.922258	−	0.386575i	$-0.126342\pi$
$709$	32.1789	+	15.2195i	1.20851	+	0.571580i	0.286248	+	0.958156i	$0.407592\pi$
$710$	−12.6980	−	2.73442i	−0.476547	−	0.102621i
$711$	2.17507	−	4.06926i	0.0815713	−	0.152609i
$712$	−0.207201	+	0.687568i	−0.00776519	+	0.0257677i
$713$	−1.20936	+	3.98674i	−0.0452910	+	0.149305i
$714$	−0.300819	−	0.0344209i	−0.0112579	−	0.00128817i
$715$	4.30384	+	29.0141i	0.160954	+	1.08507i
$716$	−18.8559	+	36.8195i	−0.704677	+	1.37601i
$717$	−21.6184	−	7.73520i	−0.807355	−	0.288876i
$718$	18.7557	+	26.1399i	0.699956	+	0.975532i
$719$	26.4018	−	17.6411i	0.984621	−	0.657903i	0.0445950	−	0.999005i	$-0.485800\pi$
$719$	26.4018	−	17.6411i	0.984621	−	0.657903i	0.940026	+	0.341102i	$0.110800\pi$
$720$	7.21181	+	11.1256i	0.268768	+	0.414627i
$721$	1.02515	+	0.684980i	0.0381784	+	0.0255100i
$722$	−12.5895	+	0.419809i	−0.468533	+	0.0156237i
$723$	−1.12983	−	1.02402i	−0.0420189	−	0.0380837i
$724$	−41.1823	+	0.724048i	−1.53053	+	0.0269090i
$725$	−8.29693	−	13.8426i	−0.308140	−	0.514101i
$726$	2.91351	−	9.08670i	0.108130	−	0.337239i
$727$	−31.1080	−	25.5297i	−1.15373	−	0.946844i	−0.154579	−	0.987980i	$-0.549402\pi$
$727$	−31.1080	−	25.5297i	−1.15373	−	0.946844i	−0.999154	+	0.0411364i	$0.986902\pi$
$728$	−2.42326	+	1.45847i	−0.0898121	+	0.0540545i
$729$	−0.995185	−	0.0980171i	−0.0368587	−	0.00363026i
$730$	−35.9298	−	0.566078i	−1.32982	−	0.0209515i
$731$	−2.70490	−	2.98439i	−0.100044	−	0.110382i
$732$	26.0053	+	11.7447i	0.961185	+	0.434098i
$733$	21.3489	−	15.8334i	0.788538	−	0.584820i	−0.124724	−	0.992191i	$-0.539805\pi$
$733$	21.3489	−	15.8334i	0.788538	−	0.584820i	0.913262	+	0.407372i	$0.133555\pi$
$734$	−1.07069	−	8.09459i	−0.0395197	−	0.298777i
$735$	−21.2700	+	8.81032i	−0.784556	+	0.324974i
$736$	1.09582	−	4.76523i	0.0403923	−	0.175649i
$737$	−14.0866	−	5.83486i	−0.518886	−	0.214930i
$738$	−3.16051	+	11.8240i	−0.116340	+	0.435246i
$739$	2.94628	−	19.8622i	0.108381	−	0.730643i	−0.865054	−	0.501679i	$-0.832716\pi$
$739$	2.94628	−	19.8622i	0.108381	−	0.730643i	0.973435	−	0.228965i	$-0.0735340\pi$
$740$	8.26628	+	5.90831i	0.303874	+	0.217194i
$741$	−0.668928	+	13.6163i	−0.0245737	+	0.500209i
$742$	−0.393640	−	0.994353i	−0.0144510	−	0.0365039i
$743$	−7.76098	+	6.36927i	−0.284723	+	0.233666i	−0.765904	−	0.642956i	$-0.777708\pi$
$743$	−7.76098	+	6.36927i	−0.284723	+	0.233666i	0.481181	+	0.876621i	$0.340208\pi$
$744$	−5.85119	−	12.3131i	−0.214515	−	0.451420i
$745$	7.72611	+	78.4445i	0.283063	+	2.87398i
$746$	0.545647	+	0.462376i	0.0199776	+	0.0169288i
$747$	−1.51683	−	0.379947i	−0.0554980	−	0.0139015i
$748$	−2.04953	+	3.18723i	−0.0749381	+	0.116537i
$749$	−0.153513	−	3.12483i	−0.00560925	−	0.114179i
$750$	−4.21236	+	1.91169i	−0.153814	+	0.0698050i
$751$	0.987720	−	0.196470i	0.0360424	−	0.00716928i	−0.177036	−	0.984204i	$-0.556651\pi$
$751$	0.987720	−	0.196470i	0.0360424	−	0.00716928i	0.213079	+	0.977035i	$0.431651\pi$
$752$	−29.0054	−	32.9123i	−1.05772	−	1.20019i
$753$	−9.40620	−	1.87101i	−0.342781	−	0.0681834i
$754$	3.72447	+	15.9295i	0.135637	+	0.580120i
$755$	−14.9440	+	7.06800i	−0.543869	+	0.257231i
$756$	0.0538275	+	0.462936i	0.00195769	+	0.0168368i
$757$	3.84715	−	5.18728i	0.139827	−	0.188535i	−0.727743	−	0.685850i	$-0.759431\pi$
$757$	3.84715	−	5.18728i	0.139827	−	0.188535i	0.867570	+	0.497315i	$0.165681\pi$
$758$	11.6100	+	40.5626i	0.421693	+	1.47330i
$759$	−0.840251	−	1.57200i	−0.0304992	−	0.0570599i
$760$	−5.86399	−	29.2015i	−0.212709	−	1.05925i
$761$	2.64382	−	0.801995i	0.0958385	−	0.0290723i	−0.242001	−	0.970276i	$-0.577804\pi$
$761$	2.64382	−	0.801995i	0.0958385	−	0.0290723i	0.337840	+	0.941204i	$0.390304\pi$
$762$	5.13734	−	7.43238i	0.186106	−	0.269247i
$763$	−2.54726	+	0.911424i	−0.0922170	+	0.0329958i
$764$	−21.6787	+	16.6766i	−0.784308	+	0.603339i
$765$	2.61213	+	1.56565i	0.0944416	+	0.0566061i
$766$	2.78643	−	42.9130i	0.100678	−	1.55051i
$767$	22.4711			0.811383
$768$	7.84022	+	13.9474i	0.282909	+	0.503285i
$769$	−26.4245			−0.952891			−0.476446	−	0.879204i	$-0.658075\pi$
$769$	−26.4245			−0.952891			−0.476446	+	0.879204i	$0.658075\pi$
$770$	0.145958	−	2.24785i	0.00525997	−	0.0810071i
$771$	8.26151	+	4.95176i	0.297531	+	0.178333i
$772$	−28.8782	−	37.5401i	−1.03935	−	1.35110i
$773$	41.5360	−	14.8618i	1.49394	−	0.534542i	0.541885	−	0.840453i	$-0.317711\pi$
$773$	41.5360	−	14.8618i	1.49394	−	0.534542i	0.952060	+	0.305911i	$0.0989610\pi$
$774$	−3.52517	+	5.09999i	−0.126710	+	0.183316i
$775$	27.6132	−	8.37636i	0.991894	−	0.300888i
$776$	−8.53520	+	12.8245i	−0.306396	+	0.460371i
$777$	0.168364	+	0.314987i	0.00604004	+	0.0113001i
$778$	4.70644	+	16.4432i	0.168734	+	0.589518i
$779$	16.3783	−	22.0836i	0.586814	−	0.791227i
$780$	28.2570	−	3.28556i	1.01176	−	0.117642i
$781$	−5.16552	+	2.44311i	−0.184837	+	0.0874214i
$782$	−0.255697	−	1.09361i	−0.00914370	−	0.0391075i
$783$	2.64390	+	0.525904i	0.0944852	+	0.0187943i
$784$	−26.2865	+	8.99451i	−0.938805	+	0.321232i
$785$	1.64426	−	0.327063i	0.0586860	−	0.0116734i
$786$	−0.435197	+	0.197504i	−0.0155230	+	0.00704475i
$787$	−2.08282	−	42.3969i	−0.0742447	−	1.51128i	−0.690266	−	0.723555i	$-0.742507\pi$
$787$	−2.08282	−	42.3969i	−0.0742447	−	1.51128i	0.616022	−	0.787729i	$-0.288743\pi$
$788$	1.88935	+	1.21493i	0.0673052	+	0.0432801i
$789$	16.7754	+	4.20203i	0.597221	+	0.149596i
$790$	16.5012	+	13.9830i	0.587087	+	0.497492i
$791$	−0.177903	−	1.80628i	−0.00632551	−	0.0642240i
$792$	5.49531	+	1.95494i	0.195267	+	0.0694659i
$793$	47.3261	−	38.8395i	1.68060	−	1.37923i
$794$	−3.17308	−	8.01537i	−0.112609	−	0.284455i
$795$	−0.527794	+	10.7435i	−0.0187189	+	0.381032i
$796$	0.222512	−	0.311314i	0.00788671	−	0.0110342i
$797$	−0.767607	+	5.17479i	−0.0271900	+	0.183300i	−0.998517	−	0.0544491i	$-0.982660\pi$
$797$	−0.767607	+	5.17479i	−0.0271900	+	0.183300i	0.971327	+	0.237749i	$0.0764097\pi$
$798$	0.270358	−	1.01145i	0.00957056	−	0.0358050i
$799$	−9.30949	−	3.85612i	−0.329346	−	0.136420i
$800$	−31.6595	+	12.0259i	−1.11933	+	0.425180i
$801$	0.234564	−	0.0971596i	0.00828791	−	0.00343297i
$802$	−0.243649	−	1.84204i	−0.00860356	−	0.0650446i
$803$	−12.6972	+	9.41691i	−0.448075	+	0.332315i
$804$	−6.08653	+	13.4769i	−0.214655	+	0.475293i
$805$	0.448358	+	0.494687i	0.0158026	+	0.0174354i
$806$	−29.2463	−	0.460779i	−1.03016	−	0.0162303i
$807$	2.58441	+	0.254542i	0.0909754	+	0.00896029i
$808$	37.1893	+	9.24330i	1.30831	+	0.325178i
$809$	22.6405	+	18.5806i	0.795997	+	0.653258i	0.941844	−	0.336049i	$-0.109091\pi$
$809$	22.6405	+	18.5806i	0.795997	+	0.653258i	−0.145847	+	0.989307i	$0.546591\pi$
$810$	1.43124	−	4.46377i	0.0502885	−	0.156841i
$811$	24.3619	+	40.6454i	0.855463	+	1.42725i	0.903584	+	0.428412i	$0.140927\pi$
$811$	24.3619	+	40.6454i	0.855463	+	1.42725i	−0.0481210	+	0.998842i	$0.515323\pi$
$812$	−0.0220850	−	1.25615i	−0.000775031	−	0.0440821i
$813$	7.99686	+	7.24793i	0.280462	+	0.254196i
$814$	4.46740	−	0.148969i	0.156582	−	0.00522137i
$815$	−11.9612	−	7.99225i	−0.418984	−	0.279956i
$816$	3.02699	+	2.08413i	0.105966	+	0.0729592i
$817$	11.5801	−	7.73759i	0.405137	−	0.270704i
$818$	−26.1466	−	36.4407i	−0.914195	−	1.27412i
$819$	0.941505	+	0.336876i	0.0328989	+	0.0117714i
$820$	−51.0652	−	26.1513i	−1.78327	−	0.913245i
$821$	7.63112	+	51.4448i	0.266328	+	1.79544i	0.548581	+	0.836097i	$0.315168\pi$
$821$	7.63112	+	51.4448i	0.266328	+	1.79544i	−0.282253	+	0.959340i	$0.591082\pi$
$822$	−8.96073	−	1.02532i	−0.312541	−	0.0357623i
$823$	−1.82418	+	6.01350i	−0.0635868	+	0.209618i	−0.982977	−	0.183730i	$-0.941183\pi$
$823$	−1.82418	+	6.01350i	−0.0635868	+	0.209618i	0.919390	+	0.393347i	$0.128683\pi$
$824$	−7.07855	−	13.1851i	−0.246593	−	0.459324i
$825$	−5.81979	+	10.8881i	−0.202619	+	0.379074i
$826$	−1.68704	−	0.363292i	−0.0586998	−	0.0126406i
$827$	−7.38491	−	3.49280i	−0.256799	−	0.121457i	0.294821	−	0.955552i	$-0.404740\pi$
$827$	−7.38491	−	3.49280i	−0.256799	−	0.121457i	−0.551620	+	0.834096i	$0.685990\pi$
$828$	−1.54952	+	0.766487i	−0.0538497	+	0.0266373i
$829$	23.4618	−	5.87687i	0.814861	−	0.204112i	0.186922	−	0.982375i	$-0.440149\pi$
$829$	23.4618	−	5.87687i	0.814861	−	0.204112i	0.627939	+	0.778263i	$0.283899\pi$
$830$	3.23797	−	6.57604i	0.112392	−	0.228258i
$831$	−21.7594	−	21.7594i	−0.754826	−	0.754826i
$832$	34.2816	−	1.80966i	1.18850	−	0.0627387i
$833$	−4.51241	+	4.51241i	−0.156346	+	0.156346i
$834$	7.28540	+	21.4193i	0.252273	+	0.741688i
$835$	18.9972	+	75.8409i	0.657424	+	2.62458i
$836$	−9.86168	−	8.62724i	−0.341073	−	0.298379i
$837$	−2.06076	+	4.35710i	−0.0712302	+	0.150604i
$838$	18.2260	+	28.2299i	0.629606	+	0.975185i
$839$	28.8907	+	15.4424i	0.997417	+	0.533130i	0.887499	−	0.460810i	$-0.152441\pi$
$839$	28.8907	+	15.4424i	0.997417	+	0.533130i	0.109918	+	0.993941i	$0.464941\pi$
$840$	−2.17455	−	0.210166i	−0.0750290	−	0.00725141i
$841$	20.7974	+	6.30882i	0.717152	+	0.217546i
$842$	43.2028	−	34.3311i	1.48887	−	1.18313i
$843$	24.2360	−	3.59507i	0.834731	−	0.123821i
$844$	−26.7738	−	31.4789i	−0.921592	−	1.08355i
$845$	6.04577	−	16.8968i	0.207981	−	0.581267i
$846$	−2.51723	+	15.3046i	−0.0865441	+	0.526182i
$847$	0.873547	+	1.30736i	0.0300154	+	0.0449213i
$848$	−1.45211	+	12.8991i	−0.0498656	+	0.442955i
$849$	15.4119	−	23.0655i	0.528935	−	0.791607i
$850$	−5.31416	+	5.68080i	−0.182274	+	0.194850i
$851$	−0.889691	+	0.981623i	−0.0304982	+	0.0336496i
$852$	2.21046	+	5.08196i	0.0757292	+	0.174105i
$853$	20.5869	−	12.3393i	0.704883	−	0.422491i	−0.116256	−	0.993219i	$-0.537089\pi$
$853$	20.5869	−	12.3393i	0.704883	−	0.422491i	0.821139	+	0.570729i	$0.193339\pi$
$854$	−4.18099	+	2.15080i	−0.143071	+	0.0735989i
$855$	−6.68041	+	8.14010i	−0.228465	+	0.278386i
$856$	−16.1734	+	34.3579i	−0.552794	+	1.17433i
$857$	0.0322925	−	0.327871i	0.00110309	−	0.0111999i	−0.994617	−	0.103616i	$-0.966959\pi$
$857$	0.0322925	−	0.327871i	0.00110309	−	0.0111999i	0.995721	+	0.0924157i	$0.0294589\pi$
$858$	8.98741	−	8.70861i	0.306825	−	0.297307i
$859$	35.2444	−	31.9437i	1.20252	−	1.08990i	0.208811	−	0.977956i	$-0.433041\pi$
$859$	35.2444	−	31.9437i	1.20252	−	1.08990i	0.993714	−	0.111949i	$-0.0357092\pi$
$860$	−19.8923	−	21.1871i	−0.678322	−	0.722473i
$861$	−1.20134	−	1.61983i	−0.0409417	−	0.0552035i
$862$	5.05675	−	6.59840i	0.172234	−	0.224742i
$863$	1.97862	+	4.77682i	0.0673531	+	0.162605i	0.953972	−	0.299896i	$-0.0969521\pi$
$863$	1.97862	+	4.77682i	0.0673531	+	0.162605i	−0.886619	+	0.462501i	$0.846952\pi$
$864$	2.06296	−	5.26727i	0.0701835	−	0.179196i
$865$	24.3001	−	58.6656i	0.826228	−	1.99469i
$866$	−10.9879	−	19.0048i	−0.373382	−	0.645809i
$867$	−15.9810	−	2.37056i	−0.542743	−	0.0805083i
$868$	2.18826	+	0.507422i	0.0742743	+	0.0172230i
$869$	9.50356	+	0.466880i	0.322386	+	0.0158378i
$870$	−5.01903	+	11.5968i	−0.170161	+	0.393170i
$871$	20.1280	+	24.5260i	0.682011	+	0.831033i
$872$	32.4909	+	4.75895i	1.10028	+	0.161159i
$873$	5.42029	−	0.533852i	0.183449	−	0.0180682i
$874$	3.87030	−	0.319718i	0.130915	−	0.0108146i
$875$	0.185206	−	0.739384i	0.00626110	−	0.0249957i
$876$	8.74055	+	12.5960i	0.295316	+	0.425581i
$877$	19.7927	−	0.972351i	0.668350	−	0.0328340i	0.287935	−	0.957650i	$-0.407031\pi$
$877$	19.7927	−	0.972351i	0.668350	−	0.0328340i	0.380415	+	0.924816i	$0.375781\pi$
$878$	−23.0234	−	8.64940i	−0.777002	−	0.291903i
$879$	1.14306	+	5.74655i	0.0385545	+	0.193826i
$880$	−14.3815	+	23.2534i	−0.484801	+	0.783873i
$881$	3.25376	−	16.3577i	0.109622	−	0.551106i	−0.886470	−	0.462785i	$-0.846850\pi$
$881$	3.25376	−	16.3577i	0.109622	−	0.551106i	0.996092	−	0.0883205i	$-0.0281500\pi$
$882$	8.34461	+	5.18197i	0.280978	+	0.174486i
$883$	4.66991	+	9.87370i	0.157155	+	0.332276i	0.967169	−	0.254134i	$-0.0817905\pi$
$883$	4.66991	+	9.87370i	0.157155	+	0.332276i	−0.810014	+	0.586411i	$0.800541\pi$
$884$	6.88772	−	3.83874i	0.231659	−	0.129111i
$885$	13.9416	+	10.3398i	0.468641	+	0.347568i
$886$	−7.93875	+	14.3056i	−0.266707	+	0.480606i
$887$	17.4615	−	9.33337i	0.586300	−	0.313384i	−0.151443	−	0.988466i	$-0.548392\pi$
$887$	17.4615	−	9.33337i	0.586300	−	0.313384i	0.737742	+	0.675082i	$0.235892\pi$
$888$	−0.00791551	−	4.33512i	−0.000265627	−	0.145477i
$889$	0.432163	+	1.42465i	0.0144943	+	0.0477812i
$890$	0.213767	+	1.17078i	0.00716550	+	0.0392447i
$891$	−0.694723	−	1.94162i	−0.0232741	−	0.0650468i
$892$	32.0298	−	8.62417i	1.07244	−	0.288759i
$893$	17.9127	−	29.8855i	0.599425	−	1.00008i
$894$	25.2715	−	22.1897i	0.845205	−	0.742136i
$895$			68.5581i			2.29164i
$896$	−2.60299	−	0.418372i	−0.0869600	−	0.0139768i
$897$			3.70915i			0.123845i
$898$	−23.6429	−	26.9265i	−0.788974	−	0.898549i
$899$	6.67967	−	11.1444i	0.222779	−	0.371685i
$900$	10.3768	+	5.97420i	0.345892	+	0.199140i
$901$	1.00445	+	2.80725i	0.0334631	+	0.0935231i
$902$	−24.8286	+	4.53333i	−0.826701	+	0.150943i
$903$	−0.296544	−	0.977575i	−0.00986837	−	0.0325316i
$904$	−8.39345	+	20.3687i	−0.279162	+	0.677453i
$905$	−60.2023	+	32.1788i	−2.00119	+	1.06966i
$906$	6.16718	+	3.42241i	0.204891	+	0.113702i
$907$	−15.6047	−	11.5732i	−0.518145	−	0.384283i	0.304788	−	0.952420i	$-0.401414\pi$
$907$	−15.6047	−	11.5732i	−0.518145	−	0.384283i	−0.822934	+	0.568137i	$0.807664\pi$
$908$	1.03743	−	3.64972i	0.0344283	−	0.121120i
$909$	−5.79270	−	12.2476i	−0.192132	−	0.406229i
$910$	−2.47285	+	3.98207i	−0.0819742	+	0.132004i
$911$	−2.13369	+	10.7268i	−0.0706924	+	0.355395i	−0.999900	−	0.0141643i	$-0.995491\pi$
$911$	−2.13369	+	10.7268i	−0.0706924	+	0.355395i	0.929207	+	0.369559i	$0.120491\pi$
$912$	−8.66431	+	9.29605i	−0.286904	+	0.307823i
$913$	−0.629088	−	3.16264i	−0.0208198	−	0.104668i
$914$	13.6371	−	36.3000i	0.451076	−	1.20070i
$915$	47.2338	−	2.32045i	1.56150	−	0.0767116i
$916$	8.38256	−	46.3896i	0.276968	−	1.53276i
$917$	0.0191344	−	0.0763888i	0.000631873	−	0.00252258i
$918$	−0.106972	−	1.29493i	−0.00353059	−	0.0427391i
$919$	46.5769	−	4.58743i	1.53643	−	0.151325i	0.705906	−	0.708306i	$-0.250540\pi$
$919$	46.5769	−	4.58743i	1.53643	−	0.151325i	0.830526	+	0.556981i	$0.188040\pi$
$920$	−1.98337	−	7.85716i	−0.0653898	−	0.259043i
$921$	0.315306	+	0.384202i	0.0103897	+	0.0126599i
$922$	5.73354	+	2.48144i	0.188824	+	0.0817218i
$923$	11.8762	+	0.583442i	0.390911	+	0.0192042i
$924$	−0.815535	+	0.508510i	−0.0268291	+	0.0167287i
$925$	9.07669	+	1.34640i	0.298440	+	0.0442693i
$926$	−25.4748	+	14.7285i	−0.837152	+	0.484010i
$927$	−2.02475	+	4.88819i	−0.0665016	+	0.160549i
$928$	−6.92608	+	13.5855i	−0.227360	+	0.445966i
$929$	−10.4420	−	25.2093i	−0.342592	−	0.827090i	−0.997452	−	0.0713398i	$-0.977273\pi$
$929$	−10.4420	−	25.2093i	−0.342592	−	0.827090i	0.654860	−	0.755750i	$-0.272727\pi$
$930$	−17.9331	−	13.7432i	−0.588049	−	0.450658i
$931$	−13.1447	−	17.7236i	−0.430801	−	0.580868i
$932$	0.778345	−	24.6952i	0.0254955	−	0.808917i
$933$	−10.4741	+	9.49315i	−0.342906	+	0.310792i
$934$	−21.1778	−	21.8558i	−0.692959	−	0.715144i
$935$	−0.615560	+	6.24988i	−0.0201310	+	0.204393i
$936$	−8.16729	−	8.97821i	−0.266956	−	0.293462i
$937$	−14.6015	+	17.7920i	−0.477011	+	0.581240i	−0.954805	−	0.297232i	$-0.903937\pi$
$937$	−14.6015	+	17.7920i	−0.477011	+	0.581240i	0.477794	+	0.878472i	$0.341437\pi$
$938$	−1.11462	−	2.16674i	−0.0363937	−	0.0707465i
$939$	−14.8484	+	8.89977i	−0.484558	+	0.290433i
$940$	−67.6501	−	26.6382i	−2.20650	−	0.868842i
$941$	7.77514	−	8.57855i	0.253462	−	0.279653i	−0.600907	−	0.799319i	$-0.705194\pi$
$941$	7.77514	−	8.57855i	0.253462	−	0.279653i	0.854369	+	0.519666i	$0.173944\pi$
$942$	−0.522352	−	0.488640i	−0.0170192	−	0.0159207i
$943$	4.15596	−	6.21983i	0.135337	−	0.202546i
$944$	16.0051	+	13.5124i	0.520921	+	0.439792i
$945$	0.429123	+	0.642228i	0.0139594	+	0.0208917i
$946$	−12.6154	−	2.07492i	−0.410162	−	0.0674616i
$947$	−1.13273	+	3.16578i	−0.0368089	+	0.102874i	−0.958542	−	0.284950i	$-0.908023\pi$
$947$	−1.13273	+	3.16578i	−0.0368089	+	0.102874i	0.921734	+	0.387824i	$0.126773\pi$
$948$	0.742940	−	9.19822i	0.0241296	−	0.298744i
$949$	32.5392	−	4.82673i	1.05627	−	0.156682i
$950$	−16.7343	−	21.0587i	−0.542931	−	0.683234i
$951$	−17.5768	−	5.33187i	−0.569968	−	0.172898i
$952$	−0.579166	+	0.176844i	−0.0187709	+	0.00573154i
$953$	−7.60747	−	4.06628i	−0.246430	−	0.131720i	0.343558	−	0.939131i	$-0.388368\pi$
$953$	−7.60747	−	4.06628i	−0.246430	−	0.131720i	−0.589988	+	0.807412i	$0.700868\pi$
$954$	3.85557	−	2.48926i	0.124829	−	0.0805927i
$955$	−19.3808	+	40.9772i	−0.627147	+	1.32599i
$956$	−45.8192	+	3.05917i	−1.48190	+	0.0989405i
$957$	1.35072	+	5.39238i	0.0436626	+	0.174311i
$958$	−29.4796	+	10.0270i	−0.952442	+	0.323957i
$959$	1.05086	−	1.05086i	0.0339340	−	0.0339340i
$960$	22.1018	+	14.6515i	0.713333	+	0.472875i
$961$	−5.49347	−	5.49347i	−0.177209	−	0.177209i
$962$	−8.34465	−	4.10882i	−0.269042	−	0.132474i
$963$	13.0236	−	3.26223i	0.419678	−	0.105124i
$964$	−2.88903	−	0.976772i	−0.0930493	−	0.0314597i
$965$	−70.9584	−	33.5608i	−2.28423	−	1.08036i
$966$	0.0599662	−	0.278469i	0.00192938	−	0.00895960i
$967$	−20.6884	+	38.7053i	−0.665295	+	1.24468i	0.292235	+	0.956346i	$0.405601\pi$
$967$	−20.6884	+	38.7053i	−0.665295	+	1.24468i	−0.957530	+	0.288333i	$0.906899\pi$
$968$	−1.90530	−	18.9894i	−0.0612388	−	0.610341i
$969$	−0.847307	+	2.79320i	−0.0272194	+	0.0897304i
$970$	−2.90244	+	25.3656i	−0.0931916	+	0.814441i
$971$	−4.99203	−	33.6536i	−0.160202	−	1.07999i	−0.908879	−	0.417059i	$-0.863061\pi$
$971$	−4.99203	−	33.6536i	−0.160202	−	1.07999i	0.748677	−	0.662935i	$-0.230689\pi$
$972$	−1.90338	+	0.614123i	−0.0610509	+	0.0196980i
$973$	−3.51001	−	1.25590i	−0.112526	−	0.0402624i
$974$	−23.0279	+	16.5228i	−0.737862	+	0.529425i
$975$	21.3609	−	14.2729i	0.684095	−	0.457097i
$976$	57.0634	+	0.794826i	1.82655	+	0.0254418i
$977$	39.3829	+	26.3148i	1.25997	+	0.841886i	0.992567	−	0.121699i	$-0.0388342\pi$
$977$	39.3829	+	26.3148i	1.25997	+	0.841886i	0.267404	+	0.963585i	$0.413834\pi$
$978$	0.204555	+	6.13433i	0.00654095	+	0.196154i
$979$	0.387936	+	0.351604i	0.0123985	+	0.0112373i
$980$	−31.9813	+	33.1260i	−1.02161	+	1.05817i
$981$	−5.96865	−	9.95809i	−0.190564	−	0.317937i
$982$	55.3586	+	17.7499i	1.76656	+	0.566421i
$983$	11.5889	+	9.51079i	0.369629	+	0.303347i	0.800810	−	0.598919i	$-0.204403\pi$
$983$	11.5889	+	9.51079i	0.369629	+	0.303347i	−0.431180	+	0.902266i	$0.641903\pi$
$984$	3.63590	+	24.2066i	0.115908	+	0.771679i
$985$	3.70485	+	0.364895i	0.118046	+	0.0116265i
$986$	−0.0551775	+	3.50219i	−0.00175721	+	0.111532i
$987$	−1.71630	−	1.89365i	−0.0546304	−	0.0602754i
$988$	9.63534	+	25.5063i	0.306541	+	0.811462i
$989$	3.04358	−	2.25727i	0.0967802	−	0.0717771i
$990$	9.58316	−	1.26758i	0.304573	−	0.0402864i
$991$	−6.59603	+	2.73217i	−0.209530	+	0.0867901i	−0.484980	−	0.874525i	$-0.661173\pi$
$991$	−6.59603	+	2.73217i	−0.209530	+	0.0867901i	0.275450	+	0.961315i	$0.411173\pi$
$992$	−20.5537	−	17.9148i	−0.652581	−	0.568794i
$993$	−33.5440	−	13.8944i	−1.06449	−	0.440924i
$994$	−0.882192	−	0.235807i	−0.0279814	−	0.00747935i
$995$	0.0930547	−	0.627324i	0.00295003	−	0.0198875i
$996$	−3.08500	+	0.513193i	−0.0977518	+	0.0162611i
$997$	−1.11868	+	22.7713i	−0.0354290	+	0.721174i	0.913719	+	0.406346i	$0.133197\pi$
$997$	−1.11868	+	22.7713i	−0.0354290	+	0.721174i	−0.949149	+	0.314829i	$0.898053\pi$
$998$	21.7758	−	8.62050i	0.689302	−	0.272877i
$999$	−1.18479	+	0.972334i	−0.0374852	+	0.0307633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.z.a.421.2	yes	2048
256.45	even	64	inner	768.2.z.a.301.2	✓	2048

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
768.2.z.a.301.2	✓	2048	256.45	even	64	inner
768.2.z.a.421.2	yes	2048	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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.z (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41124 - 0.0916351i) q^{2} +(0.857729 + 0.514103i) q^{3} +(1.98321 + 0.258638i) q^{4} +(3.12088 - 1.11667i) q^{5} +(-1.16335 - 0.804121i) q^{6} +(0.222993 - 0.0676442i) q^{7} +(-2.77508 - 0.546733i) q^{8} +(0.471397 + 0.881921i) q^{9} +O(q^{10})\)	\(q+(-1.41124 - 0.0916351i) q^{2} +(0.857729 + 0.514103i) q^{3} +(1.98321 + 0.258638i) q^{4} +(3.12088 - 1.11667i) q^{5} +(-1.16335 - 0.804121i) q^{6} +(0.222993 - 0.0676442i) q^{7} +(-2.77508 - 0.546733i) q^{8} +(0.471397 + 0.881921i) q^{9} +(-4.50664 + 1.28991i) q^{10} +(-1.22843 + 1.65635i) q^{11} +(1.56809 + 1.24141i) q^{12} +(3.87917 - 1.83471i) q^{13} +(-0.320896 + 0.0750284i) q^{14} +(3.25095 + 0.646654i) q^{15} +(3.86621 + 1.02587i) q^{16} +(0.901119 - 0.179244i) q^{17} +(-0.584440 - 1.28780i) q^{18} +(0.155885 + 3.17311i) q^{19} +(6.47816 - 1.40740i) q^{20} +(0.226044 + 0.0566210i) q^{21} +(1.88539 - 2.22494i) q^{22} +(0.0847228 + 0.860205i) q^{23} +(-2.09919 - 1.89563i) q^{24} +(4.62788 - 3.79800i) q^{25} +(-5.64257 + 2.23375i) q^{26} +(-0.0490677 + 0.998795i) q^{27} +(0.459737 - 0.0764778i) q^{28} +(0.395540 - 2.66652i) q^{29} +(-4.52862 - 1.21049i) q^{30} +(4.45297 + 1.84448i) q^{31} +(-5.36215 - 1.80203i) q^{32} +(-1.90519 + 0.789157i) q^{33} +(-1.28812 + 0.170382i) q^{34} +(0.620398 - 0.460119i) q^{35} +(0.706778 + 1.87095i) q^{36} +(1.02930 + 1.13565i) q^{37} +(0.0707769 - 4.49231i) q^{38} +(4.27050 + 0.420608i) q^{39} +(-9.27121 + 1.39256i) q^{40} +(-6.68989 - 5.49025i) q^{41} +(-0.313814 - 0.100619i) q^{42} +(-2.25376 - 3.76018i) q^{43} +(-2.86463 + 2.96716i) q^{44} +(2.45599 + 2.22598i) q^{45} +(-0.0407394 - 1.22172i) q^{46} +(-9.11903 - 6.09314i) q^{47} +(2.78876 + 2.86755i) q^{48} +(-5.77514 + 3.85882i) q^{49} +(-6.87909 + 4.93582i) q^{50} +(0.865065 + 0.309525i) q^{51} +(8.16772 - 2.63531i) q^{52} +(0.476160 + 3.21001i) q^{53} +(0.160771 - 1.40505i) q^{54} +(-1.98419 + 6.54101i) q^{55} +(-0.655808 + 0.0658007i) q^{56} +(-1.49760 + 2.80181i) q^{57} +(-0.802550 + 3.72686i) q^{58} +(4.73382 + 2.23893i) q^{59} +(6.28005 + 2.12327i) q^{60} +(13.8397 - 3.46665i) q^{61} +(-6.11520 - 3.01106i) q^{62} +(0.164775 + 0.164775i) q^{63} +(7.40217 + 3.03446i) q^{64} +(10.0577 - 10.0577i) q^{65} +(2.76100 - 0.939109i) q^{66} +(1.79654 + 7.17220i) q^{67} +(1.83346 - 0.122413i) q^{68} +(-0.369565 + 0.781379i) q^{69} +(-0.917695 + 0.592489i) q^{70} +(2.44375 + 1.30621i) q^{71} +(-0.825990 - 2.70513i) q^{72} +(7.33571 + 2.22526i) q^{73} +(-1.34852 - 1.69700i) q^{74} +(5.92203 - 0.878450i) q^{75} +(-0.511536 + 6.33325i) q^{76} +(-0.161889 + 0.452451i) q^{77} +(-5.98817 - 0.984907i) q^{78} +(-2.56345 - 3.83647i) q^{79} +(13.2115 - 1.11567i) q^{80} +(-0.555570 + 0.831470i) q^{81} +(8.93796 + 8.36110i) q^{82} +(-1.05011 + 1.15862i) q^{83} +(0.433647 + 0.170755i) q^{84} +(2.61213 - 1.56565i) q^{85} +(2.83604 + 5.51304i) q^{86} +(1.71013 - 2.08380i) q^{87} +(4.31458 - 3.92488i) q^{88} +(0.0248856 - 0.252668i) q^{89} +(-3.26201 - 3.36644i) q^{90} +(0.740921 - 0.671531i) q^{91} +(-0.0544594 + 1.72788i) q^{92} +(2.87119 + 3.87135i) q^{93} +(12.3108 + 9.43452i) q^{94} +(4.02981 + 9.72881i) q^{95} +(-3.67285 - 4.30235i) q^{96} +(2.08429 - 5.03192i) q^{97} +(8.50372 - 4.91653i) q^{98} +(-2.03985 - 0.302583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2048 q+O(q^{10}) \) 2048 * q	\( 2048 q+O(q^{100}) \) 2048 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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