LMFDB - Embedded newform 768.2.z.a.421.6

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			421.6
Character	$\chi$	$=$	768.421
Dual form			768.2.z.a.301.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33145 + 0.476688i) q^{2} +(0.857729 + 0.514103i) q^{3} +(1.54554 - 1.26938i) q^{4} +(0.980766 - 0.350924i) q^{5} +(-1.38709 - 0.275635i) q^{6} +(-3.01316 + 0.914034i) q^{7} +(-1.45272 + 2.42685i) q^{8} +(0.471397 + 0.881921i) q^{9} +O(q^{10})$	\(q+(-1.33145 + 0.476688i) q^{2} +(0.857729 + 0.514103i) q^{3} +(1.54554 - 1.26938i) q^{4} +(0.980766 - 0.350924i) q^{5} +(-1.38709 - 0.275635i) q^{6} +(-3.01316 + 0.914034i) q^{7} +(-1.45272 + 2.42685i) q^{8} +(0.471397 + 0.881921i) q^{9} +(-1.13856 + 0.934758i) q^{10} +(-1.95587 + 2.63719i) q^{11} +(1.97824 - 0.294214i) q^{12} +(-2.88055 + 1.36240i) q^{13} +(3.57618 - 2.65333i) q^{14} +(1.02164 + 0.203217i) q^{15} +(0.777373 - 3.92373i) q^{16} +(-3.62602 + 0.721261i) q^{17} +(-1.04804 - 0.949528i) q^{18} +(-0.341829 - 6.95809i) q^{19} +(1.07036 - 1.78733i) q^{20} +(-3.05438 - 0.765084i) q^{21} +(1.34704 - 4.44363i) q^{22} +(-0.675249 - 6.85592i) q^{23} +(-2.49369 + 1.33474i) q^{24} +(-3.02630 + 2.48362i) q^{25} +(3.18588 - 3.18709i) q^{26} +(-0.0490677 + 0.998795i) q^{27} +(-3.49671 + 5.23751i) q^{28} +(-1.55512 + 10.4838i) q^{29} +(-1.45714 + 0.216430i) q^{30} +(-1.34305 - 0.556311i) q^{31} +(0.835360 + 5.59483i) q^{32} +(-3.03339 + 1.25647i) q^{33} +(4.48406 - 2.68881i) q^{34} +(-2.63445 + 1.95384i) q^{35} +(1.84805 + 0.764663i) q^{36} +(-3.93281 - 4.33918i) q^{37} +(3.77196 + 9.10142i) q^{38} +(-3.17114 - 0.312330i) q^{39} +(-0.573135 + 2.88997i) q^{40} +(8.25918 + 6.77814i) q^{41} +(4.43148 - 0.437314i) q^{42} +(-3.03969 - 5.07141i) q^{43} +(0.324708 + 6.55861i) q^{44} +(0.771817 + 0.699534i) q^{45} +(4.16719 + 8.80645i) q^{46} +(-4.93394 - 3.29675i) q^{47} +(2.68398 - 2.96585i) q^{48} +(2.42342 - 1.61928i) q^{49} +(2.84546 - 4.74942i) q^{50} +(-3.48094 - 1.24550i) q^{51} +(-2.72260 + 5.76214i) q^{52} +(-0.0297550 - 0.200592i) q^{53} +(-0.410782 - 1.35324i) q^{54} +(-0.992801 + 3.27283i) q^{55} +(2.15905 - 8.64034i) q^{56} +(3.28397 - 6.14388i) q^{57} +(-2.92691 - 14.7000i) q^{58} +(12.4227 + 5.87550i) q^{59} +(1.83695 - 0.982768i) q^{60} +(-10.5999 + 2.65514i) q^{61} +(2.05340 + 0.100485i) q^{62} +(-2.22650 - 2.22650i) q^{63} +(-3.77923 - 7.05106i) q^{64} +(-2.34705 + 2.34705i) q^{65} +(3.43988 - 3.11892i) q^{66} +(1.59031 + 6.34889i) q^{67} +(-4.68860 + 5.71752i) q^{68} +(2.94547 - 6.22766i) q^{69} +(2.57628 - 3.85727i) q^{70} +(-2.83692 - 1.51636i) q^{71} +(-2.82510 - 0.137171i) q^{72} +(-1.52485 - 0.462559i) q^{73} +(7.30478 + 3.90270i) q^{74} +(-3.87258 + 0.574442i) q^{75} +(-9.36073 - 10.3201i) q^{76} +(3.48289 - 9.73401i) q^{77} +(4.37111 - 1.09579i) q^{78} +(3.04210 + 4.55283i) q^{79} +(-0.614511 - 4.12107i) q^{80} +(-0.555570 + 0.831470i) q^{81} +(-14.2278 - 5.08772i) q^{82} +(-10.6759 + 11.7791i) q^{83} +(-5.69184 + 2.69470i) q^{84} +(-3.30317 + 1.97985i) q^{85} +(6.46469 + 5.30337i) q^{86} +(-6.72360 + 8.19273i) q^{87} +(-3.55874 - 8.57770i) q^{88} +(-1.10106 + 11.1793i) q^{89} +(-1.36110 - 0.563482i) q^{90} +(7.43429 - 6.73805i) q^{91} +(-9.74635 - 9.73893i) q^{92} +(-0.865974 - 1.16763i) q^{93} +(8.14084 + 2.03753i) q^{94} +(-2.77701 - 6.70430i) q^{95} +(-2.15981 + 5.22831i) q^{96} +(7.01508 - 16.9359i) q^{97} +(-2.45478 + 3.31121i) q^{98} +(-3.24778 - 0.481763i) 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 $

$2$	−1.33145	+	0.476688i	−0.941480	+	0.337069i
$2$	−1.33145	+	0.476688i	−0.941480	+	0.337069i
$3$	0.857729	+	0.514103i	0.495210	+	0.296817i
$3$	0.857729	+	0.514103i	0.495210	+	0.296817i
$4$	1.54554	−	1.26938i	0.772769	−	0.634688i
$5$	0.980766	−	0.350924i	0.438612	−	0.156938i	−0.108318	−	0.994116i	$-0.534546\pi$
$5$	0.980766	−	0.350924i	0.438612	−	0.156938i	0.546930	+	0.837178i	$0.315796\pi$
$6$	−1.38709	−	0.275635i	−0.566278	−	0.112528i
$7$	−3.01316	+	0.914034i	−1.13887	+	0.345472i	−0.802732	−	0.596341i	$-0.796621\pi$
$7$	−3.01316	+	0.914034i	−1.13887	+	0.345472i	−0.336138	+	0.941813i	$0.609121\pi$
$8$	−1.45272	+	2.42685i	−0.513613	+	0.858022i
$9$	0.471397	+	0.881921i	0.157132	+	0.293974i
$10$	−1.13856	+	0.934758i	−0.360046	+	0.295596i
$11$	−1.95587	+	2.63719i	−0.589718	+	0.795142i	−0.992770	−	0.120035i	$-0.961699\pi$
$11$	−1.95587	+	2.63719i	−0.589718	+	0.795142i	0.403052	+	0.915177i	$0.367949\pi$
$12$	1.97824	−	0.294214i	0.571069	−	0.0849324i
$13$	−2.88055	+	1.36240i	−0.798921	+	0.377861i	−0.783008	−	0.622012i	$-0.786316\pi$
$13$	−2.88055	+	1.36240i	−0.798921	+	0.377861i	−0.0159132	+	0.999873i	$0.505066\pi$
$14$	3.57618	−	2.65333i	0.955775	−	0.709133i
$15$	1.02164	+	0.203217i	0.263787	+	0.0524705i
$16$	0.777373	−	3.92373i	0.194343	−	0.980934i
$17$	−3.62602	+	0.721261i	−0.879440	+	0.174931i	−0.614104	−	0.789225i	$-0.710483\pi$
$17$	−3.62602	+	0.721261i	−0.879440	+	0.174931i	−0.265335	+	0.964156i	$0.585483\pi$
$18$	−1.04804	−	0.949528i	−0.247026	−	0.223806i
$19$	−0.341829	−	6.95809i	−0.0784209	−	1.59629i	−0.639672	−	0.768648i	$-0.720930\pi$
$19$	−0.341829	−	6.95809i	−0.0784209	−	1.59629i	0.561251	−	0.827646i	$-0.310320\pi$
$20$	1.07036	−	1.78733i	0.239339	−	0.399658i
$21$	−3.05438	−	0.765084i	−0.666521	−	0.166955i
$22$	1.34704	−	4.44363i	0.287189	−	0.947386i
$23$	−0.675249	−	6.85592i	−0.140799	−	1.42956i	−0.762847	−	0.646579i	$-0.776199\pi$
$23$	−0.675249	−	6.85592i	−0.140799	−	1.42956i	0.622048	−	0.782979i	$-0.286301\pi$
$24$	−2.49369	+	1.33474i	−0.509022	+	0.272452i
$25$	−3.02630	+	2.48362i	−0.605259	+	0.496724i
$26$	3.18588	−	3.18709i	0.624803	−	0.625041i
$27$	−0.0490677	+	0.998795i	−0.00944308	+	0.192218i
$28$	−3.49671	+	5.23751i	−0.660816	+	0.989796i
$29$	−1.55512	+	10.4838i	−0.288778	+	1.94679i	0.0316113	+	0.999500i	$0.489936\pi$
$29$	−1.55512	+	10.4838i	−0.288778	+	1.94679i	−0.320390	+	0.947286i	$0.603814\pi$
$30$	−1.45714	+	0.216430i	−0.266036	+	0.0395145i
$31$	−1.34305	−	0.556311i	−0.241219	−	0.0999164i	0.258799	−	0.965931i	$-0.416673\pi$
$31$	−1.34305	−	0.556311i	−0.241219	−	0.0999164i	−0.500018	+	0.866015i	$0.666673\pi$
$32$	0.835360	+	5.59483i	0.147672	+	0.989036i
$33$	−3.03339	+	1.25647i	−0.528046	+	0.218724i
$34$	4.48406	−	2.68881i	0.769011	−	0.461126i
$35$	−2.63445	+	1.95384i	−0.445304	+	0.330260i
$36$	1.84805	+	0.764663i	0.308008	+	0.127444i
$37$	−3.93281	−	4.33918i	−0.646549	−	0.713357i	0.326178	−	0.945308i	$-0.394239\pi$
$37$	−3.93281	−	4.33918i	−0.646549	−	0.713357i	−0.972727	+	0.231951i	$0.925489\pi$
$38$	3.77196	+	9.10142i	0.611893	+	1.47645i
$39$	−3.17114	−	0.312330i	−0.507789	−	0.0500129i
$40$	−0.573135	+	2.88997i	−0.0906205	+	0.456944i
$41$	8.25918	+	6.77814i	1.28987	+	1.05857i	0.994668	+	0.103131i	$0.0328862\pi$
$41$	8.25918	+	6.77814i	1.28987	+	1.05857i	0.295200	+	0.955436i	$0.404614\pi$
$42$	4.43148	−	0.437314i	0.683792	−	0.0674791i
$43$	−3.03969	−	5.07141i	−0.463548	−	0.773383i	0.533842	−	0.845584i	$-0.320748\pi$
$43$	−3.03969	−	5.07141i	−0.463548	−	0.773383i	−0.997390	+	0.0722008i	$0.976998\pi$
$44$	0.324708	+	6.55861i	0.0489515	+	0.988747i
$45$	0.771817	+	0.699534i	0.115056	+	0.104280i
$46$	4.16719	+	8.80645i	0.614419	+	1.29844i
$47$	−4.93394	−	3.29675i	−0.719689	−	0.480881i	0.141001	−	0.990009i	$-0.454968\pi$
$47$	−4.93394	−	3.29675i	−0.719689	−	0.480881i	−0.860691	+	0.509128i	$0.829968\pi$
$48$	2.68398	−	2.96585i	0.387399	−	0.428084i
$49$	2.42342	−	1.61928i	0.346203	−	0.231325i
$50$	2.84546	−	4.74942i	0.402409	−	0.671669i
$51$	−3.48094	−	1.24550i	−0.487430	−	0.174405i
$52$	−2.72260	+	5.76214i	−0.377557	+	0.799065i
$53$	−0.0297550	−	0.200592i	−0.00408716	−	0.0275534i	0.987037	−	0.160493i	$-0.0513084\pi$
$53$	−0.0297550	−	0.200592i	−0.00408716	−	0.0275534i	−0.991124	+	0.132940i	$0.957558\pi$
$54$	−0.410782	−	1.35324i	−0.0559004	−	0.184153i
$55$	−0.992801	+	3.27283i	−0.133869	+	0.441308i
$56$	2.15905	−	8.64034i	0.288515	−	1.15461i
$57$	3.28397	−	6.14388i	0.434973	−	0.813777i
$58$	−2.92691	−	14.7000i	−0.384322	−	1.93020i
$59$	12.4227	+	5.87550i	1.61730	+	0.764926i	0.999766	−	0.0216194i	$-0.00688221\pi$
$59$	12.4227	+	5.87550i	1.61730	+	0.764926i	0.617533	+	0.786545i	$0.288132\pi$
$60$	1.83695	−	0.982768i	0.237149	−	0.126875i
$61$	−10.5999	+	2.65514i	−1.35718	+	0.339956i	−0.852218	−	0.523187i	$-0.824743\pi$
$61$	−10.5999	+	2.65514i	−1.35718	+	0.339956i	−0.504961	+	0.863142i	$0.668493\pi$
$62$	2.05340	+	0.100485i	0.260782	+	0.0127616i
$63$	−2.22650	−	2.22650i	−0.280513	−	0.280513i
$64$	−3.77923	−	7.05106i	−0.472404	−	0.881382i
$65$	−2.34705	+	2.34705i	−0.291116	+	0.291116i
$66$	3.43988	−	3.11892i	0.423420	−	0.383912i
$67$	1.59031	+	6.34889i	0.194288	+	0.775640i	0.986276	+	0.165104i	$0.0527959\pi$
$67$	1.59031	+	6.34889i	0.194288	+	0.775640i	−0.791989	+	0.610536i	$0.790954\pi$
$68$	−4.68860	+	5.71752i	−0.568577	+	0.693351i
$69$	2.94547	−	6.22766i	0.354592	−	0.749723i
$70$	2.57628	−	3.85727i	0.307924	−	0.461031i
$71$	−2.83692	−	1.51636i	−0.336680	−	0.179959i	0.294389	−	0.955686i	$-0.404884\pi$
$71$	−2.83692	−	1.51636i	−0.336680	−	0.179959i	−0.631070	+	0.775726i	$0.717384\pi$
$72$	−2.82510	−	0.137171i	−0.332941	−	0.0161657i
$73$	−1.52485	−	0.462559i	−0.178470	−	0.0541384i	0.199785	−	0.979840i	$-0.435976\pi$
$73$	−1.52485	−	0.462559i	−0.178470	−	0.0541384i	−0.378255	+	0.925701i	$0.623476\pi$
$74$	7.30478	+	3.90270i	0.849164	+	0.453680i
$75$	−3.87258	+	0.574442i	−0.447167	+	0.0663309i
$76$	−9.36073	−	10.3201i	−1.07375	−	1.18379i
$77$	3.48289	−	9.73401i	0.396912	−	1.10929i
$78$	4.37111	−	1.09579i	0.494931	−	0.124074i
$79$	3.04210	+	4.55283i	0.342263	+	0.512233i	0.962173	−	0.272440i	$-0.0878306\pi$
$79$	3.04210	+	4.55283i	0.342263	+	0.512233i	−0.619909	+	0.784673i	$0.712831\pi$
$80$	−0.614511	−	4.12107i	−0.0687044	−	0.460749i
$81$	−0.555570	+	0.831470i	−0.0617300	+	0.0923855i
$82$	−14.2278	−	5.08772i	−1.57119	−	0.561845i
$83$	−10.6759	+	11.7791i	−1.17184	+	1.29292i	−0.223847	+	0.974624i	$0.571862\pi$
$83$	−10.6759	+	11.7791i	−1.17184	+	1.29292i	−0.947990	+	0.318299i	$0.896888\pi$
$84$	−5.69184	+	2.69470i	−0.621031	+	0.294015i
$85$	−3.30317	+	1.97985i	−0.358279	+	0.214744i
$86$	6.46469	+	5.30337i	0.697105	+	0.571877i
$87$	−6.72360	+	8.19273i	−0.720846	+	0.878353i
$88$	−3.55874	−	8.57770i	−0.379363	−	0.914386i
$89$	−1.10106	+	11.1793i	−0.116712	+	1.18500i	0.741230	+	0.671251i	$0.234243\pi$
$89$	−1.10106	+	11.1793i	−0.116712	+	1.18500i	−0.857942	+	0.513747i	$0.828257\pi$
$90$	−1.36110	−	0.563482i	−0.143472	−	0.0593962i
$91$	7.43429	−	6.73805i	0.779326	−	0.706340i
$92$	−9.74635	−	9.73893i	−1.01613	−	1.01535i
$93$	−0.865974	−	1.16763i	−0.0897973	−	0.121078i
$94$	8.14084	+	2.03753i	0.839663	+	0.210155i
$95$	−2.77701	−	6.70430i	−0.284915	−	0.687847i
$96$	−2.15981	+	5.22831i	−0.220434	+	0.533612i
$97$	7.01508	−	16.9359i	0.712274	−	1.71958i	0.0180332	−	0.999837i	$-0.494260\pi$
$97$	7.01508	−	16.9359i	0.712274	−	1.71958i	0.694240	−	0.719743i	$-0.255740\pi$
$98$	−2.45478	+	3.31121i	−0.247970	+	0.334482i
$99$	−3.24778	−	0.481763i	−0.326415	−	0.0484190i
$100$	−1.52461	+	7.68003i	−0.152461	+	0.768003i
$101$	−11.9159	−	0.585393i	−1.18568	−	0.0582488i	−0.553351	−	0.832948i	$-0.686651\pi$
$101$	−11.9159	−	0.585393i	−1.18568	−	0.0582488i	−0.632330	+	0.774699i	$0.717901\pi$
$102$	5.22843		0.000995567i	0.517692		9.85758e-5i
$103$	−9.68236	−	11.7980i	−0.954032	−	1.16249i	−0.986622	−	0.163022i	$-0.947876\pi$
$103$	−9.68236	−	11.7980i	−0.954032	−	1.16249i	0.0325908	−	0.999469i	$-0.489624\pi$
$104$	0.878280	−	8.96985i	0.0861224	−	0.879566i
$105$	−3.26412	+	0.321488i	−0.318546	+	0.0313740i
$106$	0.135237	+	0.252895i	0.0131354	+	0.0245633i
$107$	4.45940	−	17.8029i	0.431107	−	1.72107i	−0.232147	−	0.972681i	$-0.574575\pi$
$107$	4.45940	−	17.8029i	0.431107	−	1.72107i	0.663254	−	0.748394i	$-0.269175\pi$
$108$	1.19201	+	1.60596i	0.114701	+	0.154534i
$109$	10.7834	−	0.529756i	1.03287	−	0.0507414i	0.474433	−	0.880291i	$-0.342653\pi$
$109$	10.7834	−	0.529756i	1.03287	−	0.0507414i	0.558432	+	0.829550i	$0.311403\pi$
$110$	−0.238248	−	4.83087i	−0.0227160	−	0.460606i
$111$	−1.14249	−	5.74371i	−0.108441	−	0.545169i
$112$	1.24407	+	12.5334i	0.117554	+	1.18430i
$113$	−0.637445	+	3.20465i	−0.0599658	+	0.301468i	−0.999116	−	0.0420384i	$-0.986615\pi$
$113$	−0.637445	+	3.20465i	−0.0599658	+	0.301468i	0.939150	+	0.343507i	$0.111615\pi$
$114$	−1.44375	+	9.74573i	−0.135219	+	0.912771i
$115$	−3.06817	−	6.48709i	−0.286108	−	0.604924i
$116$	10.9043	+	18.1771i	1.01244	+	1.68770i
$117$	−2.55941	−	1.89819i	−0.236618	−	0.175488i
$118$	−19.3410	−	1.90121i	−1.78049	−	0.175020i
$119$	10.2665	−	5.48758i	0.941133	−	0.503046i
$120$	−1.97733	+	2.18416i	−0.180505	+	0.199386i
$121$	0.0638063	+	0.210341i	0.00580058	+	0.0191219i
$122$	12.8476	−	8.58804i	1.16317	−	0.777524i
$123$	3.59948	+	10.0599i	0.324554	+	0.907068i
$124$	−2.78191	+	0.845039i	−0.249823	+	0.0758867i
$125$	−4.77412	+	7.96515i	−0.427011	+	0.712424i
$126$	4.02583	+	1.90314i	0.358649	+	0.169545i
$127$			15.8909i			1.41009i	0.709161	+	0.705046i	$0.249074\pi$
$127$			15.8909i			1.41009i	−0.709161	+	0.705046i	$0.750926\pi$
$128$	8.39302	+	7.58664i	0.741846	+	0.670571i
$129$		−	5.91261i		−	0.520576i
$130$	2.00618	−	4.24380i	0.175953	−	0.372206i
$131$	0.610603	−	1.01873i	0.0533486	−	0.0890068i	−0.829899	−	0.557914i	$-0.811602\pi$
$131$	0.610603	−	1.01873i	0.0533486	−	0.0890068i	0.883248	+	0.468907i	$0.155352\pi$
$132$	−3.09329	+	5.79244i	−0.269236	+	0.504167i
$133$	7.38991	+	20.6534i	0.640786	+	1.79088i
$134$	−5.14386	−	7.69516i	−0.444362	−	0.664761i
$135$	0.302377	+	0.996804i	0.0260245	+	0.0857912i
$136$	3.51719	−	9.84761i	0.301596	−	0.844426i
$137$	−3.51990	+	1.88143i	−0.300725	+	0.160741i	−0.614858	−	0.788638i	$-0.710787\pi$
$137$	−3.51990	+	1.88143i	−0.300725	+	0.160741i	0.314132	+	0.949379i	$0.398287\pi$
$138$	−0.953100	+	9.69591i	−0.0811333	+	0.825371i
$139$	5.69959	+	4.22710i	0.483433	+	0.358538i	0.809801	−	0.586705i	$-0.199575\pi$
$139$	5.69959	+	4.22710i	0.483433	+	0.358538i	−0.326368	+	0.945243i	$0.605825\pi$
$140$	−1.59149	+	6.36385i	−0.134505	+	0.537844i
$141$	−2.53711	−	5.36427i	−0.213663	−	0.451753i
$142$	4.50006	+	0.666645i	0.377637	+	0.0559436i
$143$	2.04109	−	10.2612i	0.170684	−	0.858087i
$144$	3.82688	−	1.16405i	0.318906	−	0.0970045i
$145$	2.15379	+	10.8279i	0.178863	+	0.899204i
$146$	2.25076	−	0.111003i	0.186275	−	0.00918664i
$147$	2.91111	−	0.143014i	0.240104	−	0.0117956i
$148$	−11.5864	−	1.71416i	−0.952392	−	0.140903i
$149$	4.51670	−	18.0317i	0.370023	−	1.47721i	−0.443814	−	0.896119i	$-0.646375\pi$
$149$	4.51670	−	18.0317i	0.370023	−	1.47721i	0.813837	−	0.581094i	$-0.197375\pi$
$150$	4.88233	−	2.61085i	0.398640	−	0.213175i
$151$	−3.86758	+	0.380923i	−0.314739	+	0.0309991i	−0.254153	−	0.967164i	$-0.581797\pi$
$151$	−3.86758	+	0.380923i	−0.314739	+	0.0309991i	−0.0605855	+	0.998163i	$0.519297\pi$
$152$	17.3828	+	9.27855i	1.40993	+	0.752590i
$153$	−2.34539	−	2.85787i	−0.189614	−	0.231045i
$154$	0.00278397	+	14.6206i	0.000224339	+	1.17816i
$155$	−1.51244	−	0.0743016i	−0.121482	−	0.00596805i
$156$	−5.29759	+	3.54265i	−0.424146	+	0.283639i
$157$	16.5534	+	2.45546i	1.32110	+	0.195967i	0.769772	−	0.638319i	$-0.220370\pi$
$157$	16.5534	+	2.45546i	1.32110	+	0.195967i	0.551332	+	0.834286i	$0.314120\pi$
$158$	−6.22070	−	4.61175i	−0.494892	−	0.366891i
$159$	0.0776032	−	0.187351i	0.00615433	−	0.0148579i
$160$	2.78265	+	5.19408i	0.219988	+	0.410628i
$161$	8.30117	+	20.0408i	0.654224	+	1.57944i
$162$	0.343365	−	1.37190i	0.0269773	−	0.107786i
$163$	6.73172	+	9.07668i	0.527269	+	0.710940i	0.983901	−	0.178716i	$-0.0571942\pi$
$163$	6.73172	+	9.07668i	0.527269	+	0.710940i	−0.456631	+	0.889656i	$0.650944\pi$
$164$	21.3689	−	0.00813787i	1.66863	−	0.000635461i
$165$	−2.53412	+	2.29680i	−0.197281	+	0.178805i
$166$	8.59958	−	20.7724i	0.667457	−	1.61225i
$167$	0.121508	−	1.23369i	0.00940258	−	0.0954660i	−0.989338	−	0.145637i	$-0.953477\pi$
$167$	0.121508	−	1.23369i	0.00940258	−	0.0954660i	0.998741	+	0.0501713i	$0.0159767\pi$
$168$	6.29390	−	6.30109i	0.485585	−	0.486140i
$169$	−1.80567	+	2.20022i	−0.138898	+	0.169248i
$170$	3.45425	−	4.21066i	0.264929	−	0.322942i
$171$	5.97535	−	3.58148i	0.456946	−	0.273883i
$172$	−11.1355	−	3.97956i	−0.849073	−	0.303438i
$173$	−4.84992	+	5.35106i	−0.368733	+	0.406834i	−0.896848	−	0.442339i	$-0.854149\pi$
$173$	−4.84992	+	5.35106i	−0.368733	+	0.406834i	0.528115	+	0.849173i	$0.322899\pi$
$174$	5.04679	−	14.1133i	0.382596	−	1.06993i
$175$	6.84862	−	10.2497i	0.517707	−	0.774804i
$176$	8.82718	+	9.72440i	0.665374	+	0.733004i
$177$	7.63470	+	11.4261i	0.573859	+	0.858841i
$178$	−3.86300	−	15.4095i	−0.289544	−	1.15499i
$179$	−2.44543	+	6.83453i	−0.182780	+	0.510837i	−0.997628	−	0.0688387i	$-0.978071\pi$
$179$	−2.44543	+	6.83453i	−0.182780	+	0.510837i	0.814848	+	0.579675i	$0.196821\pi$
$180$	2.08084	+	0.101431i	0.155097	+	0.00756022i
$181$	12.8913	−	1.91225i	0.958205	−	0.142136i	0.350731	−	0.936476i	$-0.385933\pi$
$181$	12.8913	−	1.91225i	0.958205	−	0.142136i	0.607474	+	0.794340i	$0.292183\pi$
$182$	−6.68647	+	12.5152i	−0.495634	+	0.927691i
$183$	−10.4569	−	3.17205i	−0.772993	−	0.234485i
$184$	17.6192	+	8.32097i	1.29891	+	0.613430i
$185$	−5.37989	−	2.87561i	−0.395537	−	0.211419i
$186$	1.70960	+	1.14185i	0.125354	+	0.0837243i
$187$	5.18993	−	10.9732i	0.379526	−	0.802439i
$188$	−11.8104	+	1.16777i	−0.861363	+	0.0851680i
$189$	−0.765084	−	3.05438i	−0.0556516	−	0.222174i
$190$	6.89332	+	7.60270i	0.500094	+	0.551558i
$191$	−8.43972	+	8.43972i	−0.610677	+	0.610677i	−0.943122	−	0.332446i	$-0.892126\pi$
$191$	−8.43972	+	8.43972i	−0.610677	+	0.610677i	0.332446	+	0.943122i	$0.392126\pi$
$192$	0.383412	−	7.99081i	0.0276704	−	0.576687i
$193$	18.0527	+	18.0527i	1.29946	+	1.29946i	0.928747	+	0.370715i	$0.120887\pi$
$193$	18.0527	+	18.0527i	1.29946	+	1.29946i	0.370715	+	0.928747i	$0.379113\pi$
$194$	−1.26712	+	25.8934i	−0.0909737	+	1.85904i
$195$	−3.21976	+	0.806507i	−0.230571	+	0.0577551i
$196$	1.69001	−	5.57888i	0.120715	−	0.398491i
$197$	11.2458	+	5.31888i	0.801232	+	0.378955i	0.783894	−	0.620895i	$-0.213231\pi$
$197$	11.2458	+	5.31888i	0.801232	+	0.378955i	0.0173385	+	0.999850i	$0.494481\pi$
$198$	4.55392	−	0.906733i	0.323633	−	0.0644387i
$199$	−7.55421	+	14.1329i	−0.535504	+	1.00186i	0.458096	+	0.888903i	$0.348532\pi$
$199$	−7.55421	+	14.1329i	−0.535504	+	1.00186i	−0.993600	+	0.112955i	$0.963968\pi$
$200$	−1.63103	−	10.9524i	−0.115331	−	0.774449i
$201$	−1.89992	+	6.26321i	−0.134010	+	0.441772i
$202$	16.1446	−	4.90076i	1.13593	−	0.344817i
$203$	−4.89668	−	33.0107i	−0.343680	−	2.31690i
$204$	−6.96094	+	2.49366i	−0.487363	+	0.174591i
$205$	10.4789	+	3.74942i	0.731881	+	0.261871i
$206$	18.5156	+	11.0930i	1.29004	+	0.772887i
$207$	5.72807	−	3.82737i	0.398128	−	0.266021i
$208$	3.10643	+	12.3616i	0.215392	+	0.857123i
$209$	19.0184	+	12.7077i	1.31553	+	0.879007i
$210$	4.19278	−	1.98401i	0.289329	−	0.136910i
$211$	0.171493	+	0.155432i	0.0118061	+	0.0107004i	0.677441	−	0.735577i	$-0.263089\pi$
$211$	0.171493	+	0.155432i	0.0118061	+	0.0107004i	−0.665635	+	0.746278i	$0.731839\pi$
$212$	−0.300614	−	0.272252i	−0.0206463	−	0.0186984i
$213$	−1.65374	−	2.75910i	−0.113312	−	0.189050i
$214$	2.54895	+	25.8295i	0.174243	+	1.76567i
$215$	−4.76091	−	3.90717i	−0.324691	−	0.266467i
$216$	−2.35265	−	1.57005i	−0.160077	−	0.106828i
$217$	4.55533	+	0.448660i	0.309236	+	0.0304571i
$218$	−14.1051	+	5.84568i	−0.955319	+	0.395919i
$219$	−1.07011	−	1.18068i	−0.0723111	−	0.0797830i
$220$	2.62003	+	6.31852i	0.176643	+	0.425994i
$221$	9.46229	−	7.01772i	0.636503	−	0.472063i
$222$	4.25913	+	7.10287i	0.285854	+	0.476713i
$223$	−7.31331	+	3.02927i	−0.489735	+	0.202855i	−0.613865	−	0.789411i	$-0.710386\pi$
$223$	−7.31331	+	3.02927i	−0.489735	+	0.202855i	0.124130	+	0.992266i	$0.460386\pi$
$224$	−7.63094	−	16.0946i	−0.509864	−	1.07537i
$225$	−3.61694	−	1.49819i	−0.241129	−	0.0998791i
$226$	−0.678890	−	4.57071i	−0.0451591	−	0.304039i
$227$	2.53365	−	17.0805i	0.168164	−	1.13367i	−0.726576	−	0.687086i	$-0.758890\pi$
$227$	2.53365	−	17.0805i	0.168164	−	1.13367i	0.894741	−	0.446586i	$-0.147360\pi$
$228$	−2.72339	−	13.6642i	−0.180361	−	0.904934i
$229$	1.45653	−	29.6484i	0.0962505	−	1.95922i	−0.146688	−	0.989183i	$-0.546861\pi$
$229$	1.45653	−	29.6484i	0.0962505	−	1.95922i	0.242939	−	0.970042i	$-0.421889\pi$
$230$	7.17744	+	7.17471i	0.473266	+	0.473086i
$231$	7.99165	−	6.55858i	0.525812	−	0.431523i
$232$	−23.1834	−	19.0040i	−1.52207	−	1.24767i
$233$	0.531480	+	5.39621i	0.0348184	+	0.353518i	0.996771	+	0.0803001i	$0.0255879\pi$
$233$	0.531480	+	5.39621i	0.0348184	+	0.353518i	−0.961952	+	0.273217i	$0.911912\pi$
$234$	4.31258	+	1.30731i	0.281922	+	0.0854615i
$235$	−5.99595	−	1.50191i	−0.391133	−	0.0979737i
$236$	26.6580	−	6.68827i	1.73529	−	0.435369i
$237$	0.268677	+	5.46905i	0.0174524	+	0.355253i
$238$	−11.0536	+	12.2004i	−0.716496	+	0.790834i
$239$	−12.9273	+	2.57140i	−0.836196	+	0.166330i	−0.594574	−	0.804041i	$-0.702679\pi$
$239$	−12.9273	+	2.57140i	−0.836196	+	0.166330i	−0.241622	+	0.970370i	$0.577679\pi$
$240$	1.59157	−	3.85068i	0.102735	−	0.248560i
$241$	−11.4734	−	2.28221i	−0.739070	−	0.147010i	−0.188822	−	0.982011i	$-0.560467\pi$
$241$	−11.4734	−	2.28221i	−0.739070	−	0.147010i	−0.550248	+	0.835001i	$0.685467\pi$
$242$	−0.185222	−	0.249644i	−0.0119065	−	0.0160477i
$243$	−0.903989	+	0.427555i	−0.0579909	+	0.0274277i
$244$	−13.0122	+	17.5589i	−0.833020	+	1.12409i
$245$	1.80856	−	2.43857i	0.115545	−	0.155794i
$246$	−9.58796	−	11.6784i	−0.611306	−	0.744589i
$247$	10.4643	+	19.5774i	0.665830	+	1.24568i
$248$	3.30116	−	2.45123i	0.209624	−	0.155653i
$249$	−15.2127	+	4.61473i	−0.964068	+	0.292447i
$250$	2.55964	−	12.8810i	0.161886	−	0.814665i
$251$	21.5917	−	7.72565i	1.36286	−	0.487639i	0.448950	−	0.893557i	$-0.351798\pi$
$251$	21.5917	−	7.72565i	1.36286	−	0.487639i	0.913909	+	0.405918i	$0.133048\pi$
$252$	−6.26741	−	0.614876i	−0.394810	−	0.0387335i
$253$	19.4010	+	11.6285i	1.21973	+	0.731080i
$254$	−7.57501	−	21.1580i	−0.475299	−	1.32757i
$255$	−3.85107			−0.241163
$256$	−14.7914	−	6.10041i	−0.924461	−	0.381276i
$257$	−6.18206			−0.385626			−0.192813	−	0.981235i	$-0.561761\pi$
$257$	−6.18206			−0.385626			−0.192813	+	0.981235i	$0.561761\pi$
$258$	2.81847	+	7.87237i	0.175470	+	0.490112i
$259$	15.8164	+	9.47996i	0.982780	+	0.589056i
$260$	−0.648167	+	6.60674i	−0.0401976	+	0.409732i
$261$	−9.97893	+	3.57052i	−0.617680	+	0.221010i
$262$	−0.327374	+	1.64746i	−0.0202252	+	0.101780i
$263$	−11.3596	+	3.44590i	−0.700464	+	0.212484i	−0.620376	−	0.784304i	$-0.713020\pi$
$263$	−11.3596	+	3.44590i	−0.700464	+	0.212484i	−0.0800880	+	0.996788i	$0.525520\pi$
$264$	1.35738	−	9.18690i	0.0835412	−	0.565414i
$265$	−0.0995752	−	0.186292i	−0.00611686	−	0.0114438i
$266$	−19.6846	−	23.9764i	−1.20694	−	1.47009i
$267$	−6.69169	+	9.02271i	−0.409525	+	0.552181i
$268$	10.5170	+	7.79374i	0.642428	+	0.476078i
$269$	−13.9518	+	6.59870i	−0.850655	+	0.402330i	−0.802602	−	0.596515i	$-0.796552\pi$
$269$	−13.9518	+	6.59870i	−0.850655	+	0.402330i	−0.0480528	+	0.998845i	$0.515302\pi$
$270$	−0.877766	−	1.18306i	−0.0534191	−	0.0719987i
$271$	0.580550	+	0.115479i	0.0352659	+	0.00701483i	0.212692	−	0.977119i	$-0.431777\pi$
$271$	0.580550	+	0.115479i	0.0352659	+	0.00701483i	−0.177426	+	0.984134i	$0.556777\pi$
$272$	0.0112636	+	14.7882i	0.000682953	+	0.896668i
$273$	9.84066	−	1.95743i	0.595584	−	0.118469i
$274$	3.78973	−	4.18293i	0.228946	−	0.252700i
$275$	−0.630718	−	12.8386i	−0.0380337	−	0.774194i
$276$	−3.35291	−	13.3640i	−0.201822	−	0.804418i
$277$	−13.8672	−	3.47354i	−0.833196	−	0.208705i	−0.197167	−	0.980370i	$-0.563174\pi$
$277$	−13.8672	−	3.47354i	−0.833196	−	0.208705i	−0.636029	+	0.771665i	$0.719424\pi$
$278$	−9.60374	−	2.91127i	−0.575994	−	0.174606i
$279$	−0.142488	−	1.44671i	−0.00853056	−	0.0866123i
$280$	−0.914580	−	9.23182i	−0.0546566	−	0.551707i
$281$	0.765153	−	0.627945i	0.0456452	−	0.0374600i	−0.611294	−	0.791403i	$-0.709351\pi$
$281$	0.765153	−	0.627945i	0.0456452	−	0.0374600i	0.656939	+	0.753943i	$0.271851\pi$
$282$	5.93513	+	5.93287i	0.353432	+	0.353297i
$283$	−0.0429207	+	0.873672i	−0.00255137	+	0.0519344i	−0.999734	−	0.0230839i	$-0.992652\pi$
$283$	−0.0429207	+	0.873672i	−0.00255137	+	0.0519344i	0.997182	+	0.0750183i	$0.0239015\pi$
$284$	−6.30940	+	1.25752i	−0.374394	+	0.0746199i
$285$	1.06478	−	7.17814i	0.0630719	−	0.425196i
$286$	2.17379	+	14.6353i	0.128539	+	0.865404i
$287$	−31.0817	−	12.8745i	−1.83470	−	0.759956i
$288$	−4.54042	+	3.37411i	−0.267547	+	0.198821i
$289$	−3.07813	+	1.27500i	−0.181067	+	0.0750003i
$290$	−8.02918	−	13.3901i	−0.471490	−	0.786294i
$291$	14.7238	−	10.9199i	0.863126	−	0.640138i
$292$	−2.94388	+	1.22071i	−0.172277	+	0.0714365i
$293$	5.36621	+	5.92070i	0.313497	+	0.345891i	0.877234	−	0.480064i	$-0.159386\pi$
$293$	5.36621	+	5.92070i	0.313497	+	0.345891i	−0.563736	+	0.825955i	$0.690636\pi$
$294$	−3.80783	+	1.57811i	−0.222077	+	0.0920370i
$295$	14.2456	+	1.40307i	0.829413	+	0.0816900i
$296$	16.2438	−	3.24074i	0.944152	−	0.188364i
$297$	−2.53804	−	2.08292i	−0.147272	−	0.120863i
$298$	2.58170	+	26.1614i	0.149554	+	1.51549i
$299$	11.2856	+	18.8289i	0.652662	+	1.08890i
$300$	−5.25603	+	5.80357i	−0.303457	+	0.335070i
$301$	13.7945	+	12.5026i	0.795103	+	0.720640i
$302$	4.96792	−	2.35081i	0.285871	−	0.135274i
$303$	−9.91970	−	6.62813i	−0.569872	−	0.380776i
$304$	−27.5674	−	4.06778i	−1.58110	−	0.233303i
$305$	−9.46428	+	6.32383i	−0.541923	+	0.362101i
$306$	4.48509	+	2.68710i	0.256395	+	0.153611i
$307$	7.10167	+	2.54102i	0.405314	+	0.145024i	0.531650	−	0.846964i	$-0.321572\pi$
$307$	7.10167	+	2.54102i	0.405314	+	0.145024i	−0.126337	+	0.991987i	$0.540322\pi$
$308$	−6.97319	−	19.4654i	−0.397334	−	1.10914i
$309$	−2.23946	−	15.0972i	−0.127398	−	0.858850i
$310$	2.04917	−	0.622034i	0.116385	−	0.0353292i
$311$	0.445970	−	1.47017i	0.0252886	−	0.0833655i	−0.943388	−	0.331692i	$-0.892381\pi$
$311$	0.445970	−	1.47017i	0.0252886	−	0.0833655i	0.968676	+	0.248326i	$0.0798806\pi$
$312$	5.36475	−	7.24217i	0.303719	−	0.410007i
$313$	−7.72565	+	14.4537i	−0.436680	+	0.816970i	−0.999957	−	0.00929783i	$-0.997040\pi$
$313$	−7.72565	+	14.4537i	−0.436680	+	0.816970i	0.563277	+	0.826268i	$0.309540\pi$
$314$	−23.2106	+	4.62146i	−1.30985	+	0.260804i
$315$	−2.96501	−	1.40235i	−0.167059	−	0.0790132i
$316$	10.4809	+	3.17500i	0.589599	+	0.178608i
$317$	18.1128	−	4.53702i	1.01732	−	0.254824i	0.301763	−	0.953383i	$-0.402425\pi$
$317$	18.1128	−	4.53702i	1.01732	−	0.254824i	0.715553	+	0.698559i	$0.246175\pi$
$318$	−0.0140173	+	0.286441i	−0.000786050	+	0.0160628i
$319$	−24.6060	−	24.6060i	−1.37767	−	1.37767i
$320$	−6.18093	−	5.58922i	−0.345524	−	0.312447i
$321$	12.9775	−	12.9775i	0.724333	−	0.724333i
$322$	−20.6058	−	22.7263i	−1.14832	−	1.26649i
$323$	6.25807	+	24.9836i	0.348208	+	1.39013i
$324$	0.196792	+	1.99029i	0.0109329	+	0.110572i
$325$	5.33372	−	11.2772i	0.295862	−	0.625547i
$326$	−13.2897	−	8.87625i	−0.736049	−	0.491610i
$327$	9.52161	+	5.08941i	0.526546	+	0.281445i
$328$	−28.4478	+	10.1971i	−1.57077	+	0.563042i
$329$	17.8801	+	5.42388i	0.985763	+	0.299028i
$330$	2.27921	−	4.26606i	0.125467	−	0.234839i
$331$	23.2753	−	3.45256i	1.27933	−	0.189770i	0.527740	−	0.849406i	$-0.323039\pi$
$331$	23.2753	−	3.45256i	1.27933	−	0.189770i	0.751586	+	0.659636i	$0.229289\pi$
$332$	−1.54799	+	31.7568i	−0.0849570	+	1.74288i
$333$	1.97291	−	5.51390i	0.108115	−	0.302160i
$334$	0.426304	+	1.70053i	0.0233263	+	0.0930487i
$335$	3.78770	+	5.66870i	0.206944	+	0.309714i
$336$	−5.37638	+	11.3898i	−0.293306	+	0.621367i
$337$	3.57139	−	5.34496i	0.194546	−	0.291159i	−0.721353	−	0.692568i	$-0.756479\pi$
$337$	3.57139	−	5.34496i	0.194546	−	0.291159i	0.915899	+	0.401409i	$0.131479\pi$
$338$	1.35535	−	3.79023i	0.0737215	−	0.206161i
$339$	−2.19428	+	2.42101i	−0.119177	+	0.131491i
$340$	−2.59201	+	7.25289i	−0.140572	+	0.393343i
$341$	4.09393	−	2.45381i	0.221699	−	0.132881i
$342$	−6.24865	+	7.61696i	−0.337888	+	0.411878i
$343$	8.16073	−	9.94388i	0.440638	−	0.536919i
$344$	16.7234	−	0.00955310i	0.901664	−	0.000515069i
$345$	0.703378	−	7.14152i	0.0378686	−	0.384486i
$346$	3.90666	−	9.43659i	0.210023	−	0.507314i
$347$	−2.97151	+	2.69322i	−0.159519	+	0.144580i	−0.747416	−	0.664356i	$-0.768706\pi$
$347$	−2.97151	+	2.69322i	−0.159519	+	0.144580i	0.587897	+	0.808936i	$0.299956\pi$
$348$	0.00807239	+	21.1970i	0.000432726	+	1.13628i
$349$	−6.31010	−	8.50818i	−0.337772	−	0.455432i	0.601366	−	0.798974i	$-0.294623\pi$
$349$	−6.31010	−	8.50818i	−0.337772	−	0.455432i	−0.939138	+	0.343541i	$0.888373\pi$
$350$	−4.23272	+	16.9116i	−0.226249	+	0.903965i
$351$	−1.21942	−	2.94393i	−0.0650876	−	0.157135i
$352$	−16.3885	−	8.73978i	−0.873509	−	0.465832i
$353$	−1.55067	+	3.74364i	−0.0825337	+	0.199254i	−0.959759	−	0.280825i	$-0.909392\pi$
$353$	−1.55067	+	3.74364i	−0.0825337	+	0.199254i	0.877225	+	0.480079i	$0.159392\pi$
$354$	−15.6120	−	11.5740i	−0.829766	−	0.615151i
$355$	−3.31448	−	0.491657i	−0.175915	−	0.0260945i
$356$	12.4889	+	18.6756i	0.661912	+	0.989806i
$357$	11.6271	+	0.571202i	0.615371	+	0.0302312i
$358$	−0.00195471	−	10.2656i	−0.000103310	−	0.542552i
$359$	−1.40737	−	1.71489i	−0.0742783	−	0.0905084i	0.734546	−	0.678559i	$-0.237395\pi$
$359$	−1.40737	−	1.71489i	−0.0742783	−	0.0905084i	−0.808824	+	0.588051i	$0.799895\pi$
$360$	−2.81890	+	0.856862i	−0.148569	+	0.0451606i
$361$	−29.3896	+	2.89462i	−1.54682	+	0.152349i
$362$	−16.2527	+	8.69121i	−0.854221	+	0.456800i
$363$	−0.0534085	+	0.213219i	−0.00280322	+	0.0111911i
$364$	2.93687	−	19.8508i	0.153934	−	1.04047i
$365$	−1.65785	+	0.0814447i	−0.0867756	+	0.00426301i
$366$	15.4349	−	0.761214i	0.806795	−	0.0397893i
$367$	0.906444	+	4.55700i	0.0473160	+	0.237874i	0.997205	−	0.0747137i	$-0.0238043\pi$
$367$	0.906444	+	4.55700i	0.0473160	+	0.237874i	−0.949889	+	0.312587i	$0.898804\pi$
$368$	−27.4257	−	2.68011i	−1.42966	−	0.139710i
$369$	−2.08443	+	10.4791i	−0.108511	+	0.545522i
$370$	8.53384	+	1.26421i	0.443653	+	0.0657234i
$371$	0.273005	+	0.577220i	0.0141737	+	0.0299677i
$372$	−2.82056	−	0.705371i	−0.146239	−	0.0365718i
$373$	−1.18378	−	0.877954i	−0.0612940	−	0.0454587i	0.564619	−	0.825352i	$-0.309023\pi$
$373$	−1.18378	−	0.877954i	−0.0612940	−	0.0454587i	−0.625913	+	0.779893i	$0.715273\pi$
$374$	−1.67937	+	17.0843i	−0.0868381	+	0.883407i
$375$	−8.18981	+	4.37754i	−0.422920	+	0.226055i
$376$	15.1684	−	7.18470i	0.782248	−	0.370523i
$377$	−9.80347	−	32.3177i	−0.504904	−	1.66445i
$378$	2.47466	+	3.70207i	0.127283	+	0.190414i
$379$	−4.46109	−	12.4679i	−0.229151	−	0.640433i	−0.999994	−	0.00340869i	$-0.998915\pi$
$379$	−4.46109	−	12.4679i	−0.229151	−	0.640433i	0.770844	−	0.637025i	$-0.219835\pi$
$380$	−12.8023	−	6.83668i	−0.656742	−	0.350714i
$381$	−8.16957	+	13.6301i	−0.418540	+	0.698292i
$382$	7.21399	−	15.2602i	0.369100	−	0.780780i
$383$			1.10454i			0.0564396i	0.999602	+	0.0282198i	$0.00898383\pi$
$383$			1.10454i			0.0564396i	−0.999602	+	0.0282198i	$0.991016\pi$
$384$	3.29862	+	10.8222i	0.168332	+	0.552266i
$385$		−	10.7690i		−	0.548840i
$386$	−32.6418	−	15.4308i	−1.66143	−	0.785409i
$387$	3.03969	−	5.07141i	0.154516	−	0.257794i
$388$	−10.6559	−	35.0798i	−0.540974	−	1.78091i
$389$	−0.277201	−	0.774725i	−0.0140546	−	0.0392801i	0.934312	−	0.356457i	$-0.116015\pi$
$389$	−0.277201	−	0.774725i	−0.0140546	−	0.0392801i	−0.948367	+	0.317177i	$0.897265\pi$
$390$	3.90250	−	2.60864i	0.197611	−	0.132094i
$391$	7.39337	+	24.3727i	0.373899	+	1.23258i
$392$	0.409207	+	8.23363i	0.0206681	+	0.415861i
$393$	1.04746	−	0.559881i	0.0528375	−	0.0282423i
$394$	−17.5087	−	1.72109i	−0.882078	−	0.0867075i
$395$	4.58129	+	3.39772i	0.230510	+	0.170958i
$396$	−5.63111	+	3.37807i	−0.282974	+	0.169755i
$397$	−14.3456	−	30.3311i	−0.719983	−	1.52228i	−0.847706	−	0.530467i	$-0.822017\pi$
$397$	−14.3456	−	30.3311i	−0.719983	−	1.52228i	0.127723	−	0.991810i	$-0.459233\pi$
$398$	3.32109	−	22.4184i	0.166471	−	1.12373i
$399$	−4.27944	+	21.5142i	−0.214240	+	1.07706i
$400$	7.39249	+	13.8051i	0.369625	+	0.690254i
$401$	5.40105	+	27.1529i	0.269716	+	1.35595i	0.843581	+	0.537002i	$0.180443\pi$
$401$	5.40105	+	27.1529i	0.269716	+	1.35595i	−0.573865	+	0.818950i	$0.694557\pi$
$402$	−0.455934	−	9.24484i	−0.0227399	−	0.461091i
$403$	4.62665	−	0.227293i	0.230470	−	0.0113223i
$404$	−19.1596	+	14.2211i	−0.953227	+	0.707524i
$405$	−0.253102	+	1.01044i	−0.0125767	+	0.0502092i
$406$	22.2555	+	41.6181i	1.10452	+	2.06547i
$407$	19.1353	−	1.88466i	0.948502	−	0.0934193i
$408$	8.07947	−	6.63838i	0.399994	−	0.328649i
$409$	12.6001	+	15.3533i	0.623036	+	0.759171i	0.984912	−	0.173055i	$-0.0553638\pi$
$409$	12.6001	+	15.3533i	0.623036	+	0.759171i	−0.361877	+	0.932226i	$0.617864\pi$
$410$	−15.7395	+	0.00299703i	−0.777320	+	0.000148013i
$411$	−3.98637	−	0.195838i	−0.196633	−	0.00965996i
$412$	−29.9405	−	5.94369i	−1.47506	−	0.292825i
$413$	−42.8021	−	6.34909i	−2.10615	−	0.312418i
$414$	−5.80220	+	7.82647i	−0.285162	+	0.384650i
$415$	−6.33705	+	15.2990i	−0.311073	+	0.750998i
$416$	−10.0287	−	14.9781i	−0.491697	−	0.734362i
$417$	2.71553	+	6.55588i	0.132980	+	0.321043i
$418$	−31.3796	−	7.85384i	−1.53483	−	0.384144i
$419$	−19.3159	−	26.0444i	−0.943642	−	1.27235i	−0.962148	−	0.272526i	$-0.912141\pi$
$419$	−19.3159	−	26.0444i	−0.943642	−	1.27235i	0.0185061	−	0.999829i	$-0.494109\pi$
$420$	−4.63674	+	4.64027i	−0.226250	+	0.226422i
$421$	3.59548	−	3.25875i	0.175233	−	0.158822i	−0.579231	−	0.815164i	$-0.696647\pi$
$421$	3.59548	−	3.25875i	0.175233	−	0.158822i	0.754464	+	0.656342i	$0.227897\pi$
$422$	−0.302428	−	0.125202i	−0.0147220	−	0.00609475i
$423$	0.581634	−	5.90543i	0.0282800	−	0.287132i
$424$	0.530033	+	0.219192i	0.0257407	+	0.0106449i
$425$	9.18208	−	11.1884i	0.445396	−	0.542717i
$426$	3.51711	+	2.88529i	0.170404	+	0.139793i
$427$	29.5124	−	17.6890i	1.42820	−	0.856032i
$428$	−15.7064	−	33.1758i	−0.759199	−	1.60361i
$429$	7.02602	−	7.75202i	0.339220	−	0.374271i
$430$	8.20143	+	2.93276i	0.395508	+	0.141430i
$431$	11.1433	−	16.6771i	0.536752	−	0.803306i	−0.459646	−	0.888102i	$-0.652024\pi$
$431$	11.1433	−	16.6771i	0.536752	−	0.803306i	0.996398	+	0.0847958i	$0.0270238\pi$
$432$	3.88086	+	0.968965i	0.186718	+	0.0466194i
$433$	−4.94903	−	7.40675i	−0.237835	−	0.355946i	0.693281	−	0.720667i	$-0.256164\pi$
$433$	−4.94903	−	7.40675i	−0.237835	−	0.355946i	−0.931117	+	0.364721i	$0.881164\pi$
$434$	−6.27908	+	1.57410i	−0.301405	+	0.0755591i
$435$	−3.71926	+	10.3946i	−0.178325	+	0.498384i
$436$	15.9937	−	14.5070i	0.765961	−	0.694758i
$437$	−47.4732	+	7.04199i	−2.27095	+	0.336864i
$438$	1.98761	+	1.06191i	0.0949718	+	0.0507402i
$439$	5.87668	+	1.78267i	0.280479	+	0.0850823i	0.427390	−	0.904067i	$-0.359433\pi$
$439$	5.87668	+	1.78267i	0.280479	+	0.0850823i	−0.146911	+	0.989150i	$0.546933\pi$
$440$	−6.50041	−	7.16387i	−0.309895	−	0.341524i
$441$	2.57047	+	1.37394i	0.122403	+	0.0654258i
$442$	−9.25335	+	13.8543i	−0.440137	+	0.658983i
$443$	−0.909325	+	1.92261i	−0.0432033	+	0.0913458i	−0.924436	−	0.381336i	$-0.875464\pi$
$443$	−0.909325	+	1.92261i	−0.0432033	+	0.0913458i	0.881233	+	0.472682i	$0.156714\pi$
$444$	−9.05669	−	7.42686i	−0.429811	−	0.352463i
$445$	2.84318	+	11.3506i	0.134780	+	0.538071i
$446$	8.29332	−	7.51950i	0.392700	−	0.356059i
$447$	13.1442	−	13.1442i	0.621701	−	0.621701i
$448$	17.8324	+	17.7917i	0.842499	+	0.840577i
$449$	−7.57157	−	7.57157i	−0.357325	−	0.357325i	0.505501	−	0.862826i	$-0.331308\pi$
$449$	−7.57157	−	7.57157i	−0.357325	−	0.357325i	−0.862826	+	0.505501i	$0.831308\pi$
$450$	5.52996	+	0.270614i	0.260685	+	0.0127569i
$451$	−34.0291	+	8.52385i	−1.60237	+	0.401372i
$452$	3.08271	+	5.76207i	0.144999	+	0.271025i
$453$	−3.51316	−	1.66160i	−0.165063	−	0.0780689i
$454$	4.76862	+	23.9496i	0.223803	+	1.12401i
$455$	4.92676	−	9.21733i	0.230970	−	0.432115i
$456$	10.1396	+	16.8950i	0.474831	+	0.791183i
$457$	−0.0813797	+	0.268273i	−0.00380678	+	0.0125493i	−0.958823	−	0.284004i	$-0.908337\pi$
$457$	−0.0813797	+	0.268273i	−0.00380678	+	0.0125493i	0.955016	+	0.296553i	$0.0958372\pi$
$458$	12.1937	+	40.1698i	0.569776	+	1.87701i
$459$	−0.542471	−	3.65704i	−0.0253204	−	0.170696i
$460$	−12.9765	−	6.13139i	−0.605033	−	0.285878i
$461$	1.75398	+	0.627583i	0.0816908	+	0.0292294i	0.377418	−	0.926043i	$-0.376812\pi$
$461$	1.75398	+	0.627583i	0.0816908	+	0.0292294i	−0.295727	+	0.955272i	$0.595562\pi$
$462$	−7.51412	+	12.5420i	−0.349589	+	0.583505i
$463$	−7.61452	+	5.08786i	−0.353877	+	0.236453i	−0.719784	−	0.694199i	$-0.755759\pi$
$463$	−7.61452	+	5.08786i	−0.353877	+	0.236453i	0.365907	+	0.930652i	$0.380759\pi$
$464$	39.9266	+	14.2517i	1.85355	+	0.661617i
$465$	−1.25907	−	0.841282i	−0.0583879	−	0.0390135i
$466$	−3.27995	−	6.93146i	−0.151941	−	0.321093i
$467$	14.7631	+	13.3805i	0.683154	+	0.619175i	0.937519	−	0.347934i	$-0.113117\pi$
$467$	14.7631	+	13.3805i	0.683154	+	0.619175i	−0.254365	+	0.967108i	$0.581867\pi$
$468$	−6.36518	+	0.315131i	−0.294230	+	0.0145669i
$469$	−10.5950	−	17.6766i	−0.489230	−	0.816231i
$470$	8.69927	−	0.858476i	0.401268	−	0.0395986i
$471$	12.9360	+	10.6163i	0.596057	+	0.489171i
$472$	−32.3057	+	21.6127i	−1.48699	+	0.994803i
$473$	19.3195	+	1.90281i	0.888312	+	0.0874911i
$474$	−2.96476	−	7.15371i	−0.136176	−	0.328581i
$475$	18.3157	+	20.2083i	0.840382	+	0.927219i
$476$	8.90153	−	21.5134i	0.408001	−	0.986063i
$477$	0.162880	−	0.120800i	0.00745776	−	0.00553105i
$478$	15.9863	−	9.58597i	0.731197	−	0.438452i
$479$	−10.1516	+	4.20492i	−0.463837	+	0.192128i	−0.602349	−	0.798233i	$-0.705768\pi$
$479$	−10.1516	+	4.20492i	−0.463837	+	0.192128i	0.138511	+	0.990361i	$0.455768\pi$
$480$	−0.283528	+	5.88568i	−0.0129412	+	0.268643i
$481$	17.2403	+	7.14118i	0.786092	+	0.325610i
$482$	16.3643	−	2.43059i	0.745372	−	0.110711i
$483$	−3.18288	+	21.4572i	−0.144826	+	0.976338i
$484$	0.365617	+	0.244096i	0.0166190	+	0.0110953i
$485$	0.936944	−	19.0719i	0.0425444	−	0.866012i
$486$	0.999810	−	1.00019i	0.0453523	−	0.0453696i
$487$	−30.7292	+	25.2188i	−1.39247	+	1.14277i	−0.420605	+	0.907244i	$0.638182\pi$
$487$	−30.7292	+	25.2188i	−1.39247	+	1.14277i	−0.971867	+	0.235528i	$0.924318\pi$
$488$	8.95502	−	29.5816i	0.405375	−	1.33909i
$489$	1.10765	+	11.2461i	0.0500895	+	0.508567i
$490$	−1.24558	+	4.10896i	−0.0562698	+	0.185624i
$491$	−22.9779	−	5.75567i	−1.03698	−	0.259750i	−0.313132	−	0.949710i	$-0.601378\pi$
$491$	−22.9779	−	5.75567i	−1.03698	−	0.259750i	−0.723848	+	0.689960i	$0.757628\pi$
$492$	18.3329	+	10.9788i	0.826510	+	0.494963i
$493$	−1.92263	−	39.1360i	−0.0865908	−	1.76260i
$494$	−23.2651	−	21.0782i	−1.04675	−	0.948352i
$495$	−3.35438	+	0.667228i	−0.150768	+	0.0299896i
$496$	−3.22687	+	4.83732i	−0.144891	+	0.217202i
$497$	9.93411	+	1.97602i	0.445606	+	0.0886365i
$498$	18.0553	−	13.3960i	0.809075	−	0.600290i
$499$	9.00063	−	4.25698i	0.402924	−	0.190569i	−0.215341	−	0.976539i	$-0.569086\pi$
$499$	9.00063	−	4.25698i	0.402924	−	0.190569i	0.618264	+	0.785970i	$0.287836\pi$
$500$	2.73217	+	18.3706i	0.122186	+	0.821558i
$501$	0.738466	−	0.995706i	0.0329922	−	0.0444849i
$502$	−25.0657	+	20.5789i	−1.11874	+	0.918480i
$503$	−6.57413	−	12.2993i	−0.293126	−	0.548400i	0.691649	−	0.722234i	$-0.256885\pi$
$503$	−6.57413	−	12.2993i	−0.293126	−	0.548400i	−0.984775	+	0.173834i	$0.944385\pi$
$504$	8.63787	−	2.16892i	0.384761	−	0.0966113i
$505$	−11.8922	+	3.60746i	−0.529196	+	0.160530i
$506$	−31.3748	−	6.23462i	−1.39478	−	0.277163i
$507$	−2.67992	+	0.958889i	−0.119019	+	0.0425858i
$508$	20.1716	+	24.5600i	0.894968	+	1.08968i
$509$	−1.68017	−	1.00706i	−0.0744724	−	0.0446370i	0.476382	−	0.879238i	$-0.341948\pi$
$509$	−1.68017	−	1.00706i	−0.0744724	−	0.0446370i	−0.550854	+	0.834601i	$0.685698\pi$
$510$	5.12752	−	1.83576i	0.227050	−	0.0812887i
$511$	5.01742			0.221958
$512$	22.6020	+	1.07154i	0.998878	+	0.0473559i
$513$	6.96648			0.307577
$514$	8.23113	−	2.94691i	0.363059	−	0.129983i
$515$	−13.6363	−	8.17330i	−0.600889	−	0.360159i
$516$	−7.50532	−	9.13816i	−0.330403	−	0.402285i
$517$	18.3443	−	6.56370i	0.806782	−	0.288671i
$518$	−25.5777	−	5.08266i	−1.12382	−	0.223319i
$519$	−6.91091	+	2.09640i	−0.303355	+	0.0920219i
$520$	−2.28635	−	9.10554i	−0.100263	−	0.399304i
$521$	−8.22454	−	15.3870i	−0.360324	−	0.674118i	0.634808	−	0.772670i	$-0.281079\pi$
$521$	−8.22454	−	15.3870i	−0.360324	−	0.674118i	−0.995132	+	0.0985516i	$0.968579\pi$
$522$	11.5845	−	9.51082i	0.507038	−	0.416277i
$523$	−19.1680	+	25.8450i	−0.838157	+	1.13012i	0.151752	+	0.988419i	$0.451508\pi$
$523$	−19.1680	+	25.8450i	−0.838157	+	1.13012i	−0.989909	+	0.141705i	$0.954742\pi$
$524$	−0.349440	−	2.34957i	−0.0152654	−	0.102641i
$525$	11.1437	−	5.27055i	0.486349	−	0.230026i
$526$	13.4822	−	10.0031i	0.587852	−	0.436154i
$527$	5.27118	+	1.04850i	0.229616	+	0.0456735i
$528$	2.57199	+	12.8790i	0.111931	+	0.560485i
$529$	−23.9896	+	4.77182i	−1.04303	+	0.207471i
$530$	0.221383	+	0.200573i	0.00961626	+	0.00871234i
$531$	0.674293	+	13.7255i	0.0292618	+	0.595638i
$532$	37.6383	+	22.5401i	1.63183	+	0.977236i
$533$	−33.0255	−	8.27246i	−1.43049	−	0.358320i
$534$	4.60867	−	15.2032i	0.199437	−	0.657905i
$535$	−1.87384	−	19.0254i	−0.0810132	−	0.822541i
$536$	−17.7181	−	5.36367i	−0.765305	−	0.231675i
$537$	−5.61117	+	4.60497i	−0.242140	+	0.198719i
$538$	15.4306	−	15.4365i	0.665261	−	0.665515i
$539$	−0.469560	+	9.55811i	−0.0202254	+	0.411697i
$540$	1.73265	+	1.15677i	0.0745615	+	0.0497794i
$541$	−1.24994	+	8.42639i	−0.0537390	+	0.362279i	0.945580	+	0.325389i	$0.105495\pi$
$541$	−1.24994	+	8.42639i	−0.0537390	+	0.362279i	−0.999319	+	0.0368901i	$0.988255\pi$
$542$	−0.828023	+	0.122987i	−0.0355666	+	0.00528273i
$543$	12.0404	+	4.98728i	0.516701	+	0.214025i
$544$	−7.06437	−	19.6845i	−0.302882	−	0.843965i
$545$	10.3901	−	4.30373i	0.445064	−	0.184352i
$546$	−12.1693	+	7.29715i	−0.520798	+	0.312289i
$547$	19.9973	−	14.8310i	0.855023	−	0.634128i	−0.0767983	−	0.997047i	$-0.524470\pi$
$547$	19.9973	−	14.8310i	0.855023	−	0.634128i	0.931821	+	0.362919i	$0.118220\pi$
$548$	−3.05190	+	7.37589i	−0.130371	+	0.315082i
$549$	−7.33838	−	8.09666i	−0.313195	−	0.345557i
$550$	6.95975	+	16.7933i	0.296765	+	0.716068i
$551$	73.4785	+	7.23700i	3.13029	+	0.308307i
$552$	10.8347	+	16.1952i	0.461155	+	0.689315i
$553$	−13.3278	−	10.9378i	−0.566756	−	0.465124i
$554$	20.1193	−	1.98544i	0.854786	−	0.0843534i
$555$	−3.13612	−	5.23231i	−0.133121	−	0.222099i
$556$	14.1747	−	0.701770i	0.601141	−	0.0297617i
$557$	28.2226	+	25.5795i	1.19583	+	1.08384i	0.994545	+	0.104306i	$0.0332623\pi$
$557$	28.2226	+	25.5795i	1.19583	+	1.08384i	0.201287	+	0.979532i	$0.435488\pi$
$558$	0.879346	+	1.85830i	0.0372257	+	0.0786683i
$559$	15.6653	+	10.4672i	0.662570	+	0.442715i
$560$	5.61841	+	11.8558i	0.237421	+	0.500998i
$561$	10.0929	−	6.74386i	0.426123	−	0.284726i
$562$	−0.719432	+	1.20082i	−0.0303474	+	0.0506535i
$563$	−41.1734	−	14.7321i	−1.73525	−	0.620883i	−0.736778	−	0.676135i	$-0.763654\pi$
$563$	−41.1734	−	14.7321i	−1.73525	−	0.620883i	−0.998472	+	0.0552523i	$0.982404\pi$
$564$	−10.7305	−	5.07014i	−0.451835	−	0.213491i
$565$	0.499404	+	3.36671i	0.0210101	+	0.141639i
$566$	−0.359322	−	1.18371i	−0.0151034	−	0.0497552i
$567$	0.914034	−	3.01316i	0.0383858	−	0.126541i
$568$	7.80123	−	4.68194i	0.327332	−	0.196450i
$569$	−11.1095	+	20.7844i	−0.465734	+	0.871328i	0.533933	+	0.845527i	$0.320714\pi$
$569$	−11.1095	+	20.7844i	−0.465734	+	0.871328i	−0.999667	+	0.0258007i	$0.991786\pi$
$570$	2.00403	+	10.0649i	0.0839396	+	0.421573i
$571$	−1.86627	−	0.882680i	−0.0781010	−	0.0369390i	0.388106	−	0.921615i	$-0.373130\pi$
$571$	−1.86627	−	0.882680i	−0.0781010	−	0.0369390i	−0.466206	+	0.884676i	$0.654380\pi$
$572$	−9.87078	−	18.4500i	−0.412718	−	0.771434i
$573$	−11.5779	+	2.90011i	−0.483673	+	0.121154i
$574$	47.5210	+	2.32549i	1.98349	+	0.0970639i
$575$	19.0710	+	19.0710i	0.795315	+	0.795315i
$576$	4.43696	−	6.65683i	0.184873	−	0.277368i
$577$	27.7004	−	27.7004i	1.15318	−	1.15318i	0.167272	−	0.985911i	$-0.446504\pi$
$577$	27.7004	−	27.7004i	1.15318	−	1.15318i	0.985911	−	0.167272i	$-0.0534958\pi$
$578$	3.49061	−	3.16492i	0.145190	−	0.131643i
$579$	6.20338	+	24.7653i	0.257803	+	1.02921i
$580$	17.0734	+	14.0009i	0.708933	+	0.581355i
$581$	21.4019	−	45.2505i	0.887901	−	1.87731i
$582$	−14.3987	+	21.5581i	−0.596845	+	0.893610i
$583$	0.587196	+	0.313863i	0.0243192	+	0.0129989i
$584$	3.33774	−	3.02862i	0.138117	−	0.125325i
$585$	−3.17630	−	0.963521i	−0.131324	−	0.0398367i
$586$	−9.96719	−	5.32513i	−0.411741	−	0.219979i
$587$	8.35604	−	1.23950i	0.344891	−	0.0511597i	0.0279618	−	0.999609i	$-0.491098\pi$
$587$	8.35604	−	1.23950i	0.344891	−	0.0511597i	0.316929	+	0.948449i	$0.397348\pi$
$588$	4.31769	−	3.91632i	0.178059	−	0.161506i
$589$	−3.41176	+	9.53524i	−0.140579	+	0.392893i
$590$	−19.6362	+	4.92259i	−0.808411	+	0.202660i
$591$	6.91142	+	10.3437i	0.284298	+	0.425482i
$592$	−20.0831	+	12.0581i	−0.825409	+	0.495586i
$593$	−15.5803	+	23.3175i	−0.639805	+	0.957536i	0.359894	+	0.932993i	$0.382813\pi$
$593$	−15.5803	+	23.3175i	−0.639805	+	0.957536i	−0.999699	+	0.0245427i	$0.992187\pi$
$594$	4.37218	+	1.56345i	0.179393	+	0.0641493i
$595$	8.14336	−	8.98481i	0.333845	−	0.368341i
$596$	−15.9082	−	33.6020i	−0.651627	−	1.37639i
$597$	−13.7452	+	8.23858i	−0.562555	+	0.337183i
$598$	−24.0017	−	19.6901i	−0.981503	−	0.805186i
$599$	8.17509	−	9.96138i	0.334025	−	0.407011i	−0.578729	−	0.815520i	$-0.696451\pi$
$599$	8.17509	−	9.96138i	0.334025	−	0.407011i	0.912754	+	0.408509i	$0.133951\pi$
$600$	4.23167	−	10.2327i	0.172757	−	0.417747i
$601$	2.14795	−	21.8085i	0.0876168	−	0.889588i	−0.846445	−	0.532476i	$-0.821262\pi$
$601$	2.14795	−	21.8085i	0.0876168	−	0.889588i	0.934062	−	0.357112i	$-0.116238\pi$
$602$	−24.3266	−	10.0710i	−0.991479	−	0.410463i
$603$	−4.84955	+	4.39538i	−0.197489	+	0.178994i
$604$	−5.49395	+	5.49814i	−0.223546	+	0.223716i
$605$	0.136393	+	0.183905i	0.00554516	+	0.00747678i
$606$	16.3672	+	4.09645i	0.664871	+	0.166407i
$607$	−3.54046	−	8.54743i	−0.143703	−	0.346929i	0.835597	−	0.549342i	$-0.185122\pi$
$607$	−3.54046	−	8.54743i	−0.143703	−	0.346929i	−0.979300	+	0.202413i	$0.935122\pi$
$608$	38.6438	−	7.72498i	1.56721	−	0.313289i
$609$	12.7709	−	30.8317i	0.517503	−	1.24936i
$610$	9.58676	−	12.9314i	0.388156	−	0.523577i
$611$	18.7040	+	2.77447i	0.756681	+	0.112243i
$612$	−7.25259	−	1.43976i	−0.293169	−	0.0581988i
$613$	41.3861	+	2.03317i	1.67157	+	0.0821188i	0.862649	−	0.505803i	$-0.168804\pi$
$613$	41.3861	+	2.03317i	1.67157	+	0.0821188i	0.808918	+	0.587922i	$0.200054\pi$
$614$	−10.6668	+	0.00203111i	−0.430477	+	8.19690e-5i
$615$	7.06050	+	8.60324i	0.284707	+	0.346916i
$616$	18.5634	+	22.5932i	0.747940	+	0.910306i
$617$	−39.3475	+	3.87540i	−1.58407	+	0.156018i	−0.851383	−	0.524545i	$-0.824235\pi$
$617$	−39.3475	+	3.87540i	−1.58407	+	0.156018i	−0.732690	+	0.680563i	$0.761735\pi$
$618$	10.1784	+	19.0337i	0.409435	+	0.765648i
$619$	5.24955	−	20.9574i	0.210997	−	0.842349i	−0.768328	−	0.640056i	$-0.778911\pi$
$619$	5.24955	−	20.9574i	0.210997	−	0.842349i	0.979325	−	0.202292i	$-0.0648391\pi$
$620$	−2.43186	+	1.80502i	−0.0976657	+	0.0724915i
$621$	6.88079	−	0.338032i	0.276117	−	0.0135647i
$622$	0.107022	+	2.17005i	0.00429118	+	0.0870109i
$623$	−6.90054	−	34.6913i	−0.276464	−	1.38988i
$624$	−3.69066	+	12.1999i	−0.147745	+	0.488388i
$625$	1.93170	−	9.71132i	0.0772681	−	0.388453i
$626$	3.39646	−	22.9271i	0.135750	−	0.916352i
$627$	9.77954	+	20.6771i	0.390557	+	0.825764i
$628$	28.7008	−	17.2174i	1.14529	−	0.687051i
$629$	17.3901	+	12.8974i	0.693390	+	0.514253i
$630$	4.61626	+	0.453774i	0.183916	+	0.0180788i
$631$	−6.37023	+	3.40496i	−0.253595	+	0.135549i	−0.593297	−	0.804984i	$-0.702174\pi$
$631$	−6.37023	+	3.40496i	−0.253595	+	0.135549i	0.339702	+	0.940533i	$0.389674\pi$
$632$	−15.4684	+	0.768770i	−0.615298	+	0.0305800i
$633$	0.0671864	+	0.221484i	0.00267042	+	0.00880320i
$634$	−21.9536	+	14.6750i	−0.871888	+	0.582817i
$635$	5.57651	+	15.5853i	0.221297	+	0.618483i
$636$	−0.117880	−	0.388065i	−0.00467423	−	0.0153878i
$637$	−4.77468	+	7.96607i	−0.189180	+	0.315627i
$638$	44.4912	+	21.0324i	1.76142	+	0.832681i
$639$		−	3.21675i		−	0.127253i
$640$	10.8939	+	4.49541i	0.430620	+	0.177697i
$641$		−	2.86984i		−	0.113352i	−0.998393	−	0.0566759i	$-0.981950\pi$
$641$		−	2.86984i		−	0.113352i	0.998393	−	0.0566759i	$-0.0180502\pi$
$642$	−11.0927	+	23.4651i	−0.437795	+	0.926096i
$643$	−15.1860	+	25.3364i	−0.598879	+	0.999169i	0.397779	+	0.917481i	$0.369781\pi$
$643$	−15.1860	+	25.3364i	−0.598879	+	0.999169i	−0.996658	+	0.0816878i	$0.973969\pi$
$644$	38.2691	+	20.4365i	1.50801	+	0.805312i
$645$	−2.07488	−	5.79889i	−0.0816982	−	0.228331i
$646$	−20.2417	−	30.2814i	−0.796400	−	1.19141i
$647$	2.53355	+	8.35201i	0.0996043	+	0.328351i	0.992554	−	0.121805i	$-0.0388683\pi$
$647$	2.53355	+	8.35201i	0.0996043	+	0.328351i	−0.892950	+	0.450156i	$0.851368\pi$
$648$	−1.21077	−	2.55618i	−0.0475635	−	0.100416i
$649$	−39.7920	+	21.2693i	−1.56197	+	0.834893i
$650$	−1.72590	+	17.5576i	−0.0676953	+	0.688666i
$651$	3.67658	+	2.72673i	0.144096	+	0.106869i
$652$	21.9258	+	5.48326i	0.858682	+	0.214741i
$653$	12.6478	+	26.7416i	0.494948	+	1.04648i	0.984642	+	0.174586i	$0.0558587\pi$
$653$	12.6478	+	26.7416i	0.494948	+	1.04648i	−0.489694	+	0.871895i	$0.662891\pi$
$654$	−15.1036	−	2.23747i	−0.590599	−	0.0874922i
$655$	0.241362	−	1.21341i	0.00943081	−	0.0474119i
$656$	33.0161	−	27.1377i	1.28906	−	1.05955i
$657$	−0.310870	−	1.56285i	−0.0121282	−	0.0609725i
$658$	−26.3920	+	1.30160i	−1.02887	+	0.0507415i
$659$	−26.0212	+	1.27834i	−1.01364	+	0.0497971i	−0.549103	−	0.835755i	$-0.685030\pi$
$659$	−26.0212	+	1.27834i	−1.01364	+	0.0497971i	−0.464540	+	0.885552i	$0.653780\pi$
$660$	−1.00109	+	6.76654i	−0.0389673	+	0.263387i
$661$	2.01264	−	8.03492i	0.0782827	−	0.312522i	−0.918221	−	0.396068i	$-0.870374\pi$
$661$	2.01264	−	8.03492i	0.0782827	−	0.312522i	0.996504	+	0.0835458i	$0.0266245\pi$
$662$	−29.3442	+	15.6920i	−1.14049	+	0.609886i
$663$	11.7239	−	1.15470i	0.455319	−	0.0448450i
$664$	−13.0770	−	43.0206i	−0.507486	−	1.66952i
$665$	14.4956	+	17.6629i	0.562113	+	0.684937i
$666$	0.00157700	+	8.28197i	6.11076e−5	+	0.320920i
$667$	72.9259	+	3.58262i	2.82370	+	0.138720i
$668$	−1.37822	−	2.06096i	−0.0533251	−	0.0797409i
$669$	−7.83019	−	1.16150i	−0.302733	−	0.0449062i
$670$	−7.74535	−	5.74205i	−0.299229	−	0.221835i
$671$	13.7300	−	33.1470i	0.530039	−	1.27963i
$672$	1.72901	−	17.7279i	0.0666978	−	0.683869i
$673$	−8.97277	−	21.6622i	−0.345875	−	0.835015i	−0.997098	−	0.0761292i	$-0.975744\pi$
$673$	−8.97277	−	21.6622i	−0.345875	−	0.835015i	0.651223	−	0.758886i	$-0.274256\pi$
$674$	−2.20726	+	8.81901i	−0.0850206	+	0.339696i
$675$	−2.33213	−	3.14452i	−0.0897638	−	0.121033i
$676$	0.00216790	+	5.69260i	8.33808e−5	+	0.218946i
$677$	−17.0008	+	15.4086i	−0.653394	+	0.592201i	−0.929454	−	0.368939i	$-0.879721\pi$
$677$	−17.0008	+	15.4086i	−0.653394	+	0.592201i	0.276060	+	0.961140i	$0.410971\pi$
$678$	1.76751	−	4.26945i	0.0678808	−	0.163967i
$679$	−5.65761	+	57.4427i	−0.217119	+	2.20445i
$680$	−0.00622224	−	10.8925i	−0.000238612	−	0.417707i
$681$	10.9543	−	13.3479i	0.419770	−	0.511492i
$682$	−4.28118	+	5.21866i	−0.163935	+	0.199833i
$683$	−15.8682	+	9.51104i	−0.607180	+	0.363930i	−0.784413	−	0.620239i	$-0.787036\pi$
$683$	−15.8682	+	9.51104i	−0.607180	+	0.363930i	0.177232	+	0.984169i	$0.443286\pi$
$684$	4.68887	−	13.1203i	0.179284	−	0.501666i
$685$	−2.79196	+	3.08046i	−0.106675	+	0.117698i
$686$	−6.12551	+	17.1299i	−0.233873	+	0.654024i
$687$	16.4917	−	24.6815i	0.629196	−	0.941658i
$688$	−22.2619	+	7.98455i	−0.848725	+	0.304408i
$689$	0.358997	+	0.537277i	0.0136767	+	0.0204686i
$690$	2.46776	+	9.84389i	0.0939460	+	0.374751i
$691$	−5.78729	+	16.1744i	−0.220159	+	0.615302i	−0.999942	−	0.0107468i	$-0.996579\pi$
$691$	−5.78729	+	16.1744i	−0.220159	+	0.615302i	0.779784	+	0.626049i	$0.215329\pi$
$692$	−0.703228	+	14.4266i	−0.0267327	+	0.548419i
$693$	10.2265	−	1.51695i	0.388471	−	0.0576242i
$694$	2.67261	−	5.00239i	0.101451	−	0.189888i
$695$	7.07335	+	2.14568i	0.268308	+	0.0813902i
$696$	−10.1151	−	28.2189i	−0.383411	−	1.06964i
$697$	−34.8368	−	18.6206i	−1.31954	−	0.705307i
$698$	12.4573	+	8.32030i	0.471517	+	0.314928i
$699$	−2.31834	+	4.90172i	−0.0876877	+	0.185400i
$700$	−2.42590	−	24.5347i	−0.0916903	−	0.927326i
$701$	−7.09162	−	28.3114i	−0.267847	−	1.06930i	−0.943311	−	0.331912i	$-0.892306\pi$
$701$	−7.09162	−	28.3114i	−0.267847	−	1.06930i	0.675464	−	0.737393i	$-0.263944\pi$
$702$	3.02693	+	3.33843i	0.114244	+	0.126001i
$703$	−28.8481	+	28.8481i	−1.08803	+	1.08803i
$704$	25.9867	+	3.82442i	0.979409	+	0.144138i
$705$	−4.37077	−	4.37077i	−0.164613	−	0.164613i
$706$	0.280093	−	5.72367i	0.0105415	−	0.215413i
$707$	36.4398	−	9.12769i	1.37046	−	0.343282i
$708$	26.3038	+	7.96823i	0.988556	+	0.299464i
$709$	21.0361	+	9.94935i	0.790029	+	0.373656i	0.779590	−	0.626290i	$-0.215427\pi$
$709$	21.0361	+	9.94935i	0.790029	+	0.373656i	0.0104385	+	0.999946i	$0.496677\pi$
$710$	4.64745	−	0.925355i	0.174416	−	0.0347280i
$711$	−2.58120	+	4.82908i	−0.0968025	+	0.181105i
$712$	−25.5309	−	18.9124i	−0.956810	−	0.708772i
$713$	−2.90713	+	9.58351i	−0.108873	+	0.358905i
$714$	−15.7532	+	4.78196i	−0.589549	+	0.178960i
$715$	−1.59908	−	10.7801i	−0.0598023	−	0.403154i
$716$	4.89607	+	13.6672i	0.182975	+	0.510767i
$717$	−12.4101	−	4.44039i	−0.463462	−	0.165829i
$718$	2.69132	+	1.61242i	0.100439	+	0.0601749i
$719$	−23.7821	+	15.8907i	−0.886924	+	0.592623i	−0.913417	−	0.407026i	$-0.866566\pi$
$719$	−23.7821	+	15.8907i	−0.886924	+	0.592623i	0.0264931	+	0.999649i	$0.491566\pi$
$720$	3.34478	−	2.48461i	0.124652	−	0.0925958i
$721$	39.9583	+	26.6993i	1.48813	+	0.994334i
$722$	37.7511	−	17.8637i	1.40495	−	0.664819i
$723$	−8.66781	−	7.85605i	−0.322359	−	0.292170i
$724$	17.4967	−	19.3194i	0.650259	−	0.717999i
$725$	−21.3314	−	35.5893i	−0.792229	−	1.32175i
$726$	−0.0305278	−	0.309350i	−0.00113299	−	0.0114811i
$727$	3.13130	+	2.56979i	0.116134	+	0.0953084i	0.690668	−	0.723172i	$-0.257317\pi$
$727$	3.13130	+	2.56979i	0.116134	+	0.0953084i	−0.574534	+	0.818481i	$0.694817\pi$
$728$	5.55234	+	27.8304i	0.205784	+	1.03146i
$729$	−0.995185	−	0.0980171i	−0.0368587	−	0.00363026i
$730$	2.16852	−	0.898715i	0.0802606	−	0.0332629i
$731$	14.6798	+	16.1967i	0.542952	+	0.599055i
$732$	−20.1880	+	8.37115i	−0.746169	+	0.309406i
$733$	−28.1301	+	20.8627i	−1.03901	+	0.770581i	−0.973826	−	0.227293i	$-0.927013\pi$
$733$	−28.1301	+	20.8627i	−1.03901	+	0.770581i	−0.0651814	+	0.997873i	$0.520763\pi$
$734$	−3.37916	−	5.63535i	−0.124727	−	0.208004i
$735$	2.80493	−	1.16184i	0.103461	−	0.0428551i
$736$	37.7936	−	9.50506i	1.39309	−	0.350361i
$737$	−19.8537	−	8.22365i	−0.731319	−	0.302922i
$738$	−2.21995	−	14.9461i	−0.0817177	−	0.550174i
$739$	2.69455	−	18.1652i	0.0991205	−	0.668216i	−0.881483	−	0.472215i	$-0.843454\pi$
$739$	2.69455	−	18.1652i	0.0991205	−	0.668216i	0.980604	−	0.196001i	$-0.0627955\pi$
$740$	−11.9650	+	2.38473i	−0.439844	+	0.0876645i
$741$	−1.08923	+	22.1719i	−0.0400140	+	0.814503i
$742$	−0.638646	−	0.638403i	−0.0234454	−	0.0234365i
$743$	−30.1805	+	24.7685i	−1.10721	+	0.908668i	−0.996366	−	0.0851698i	$-0.972857\pi$
$743$	−30.1805	+	24.7685i	−1.10721	+	0.908668i	−0.110848	+	0.993837i	$0.535357\pi$
$744$	4.09168	−	0.405356i	0.150008	−	0.0148611i
$745$	−1.89792	−	19.2699i	−0.0695343	−	0.705994i
$746$	1.99466	+	0.604660i	0.0730298	+	0.0221382i
$747$	−15.4208	−	3.86272i	−0.564219	−	0.141330i
$748$	−5.90786	−	23.5475i	−0.216013	−	0.860980i
$749$	2.83556	+	57.7192i	0.103609	+	2.10901i
$750$	8.81763	−	9.73248i	0.321974	−	0.355380i
$751$	−49.3548	+	9.81729i	−1.80098	+	0.358238i	−0.977800	−	0.209538i	$-0.932804\pi$
$751$	−49.3548	+	9.81729i	−1.80098	+	0.358238i	−0.823183	+	0.567776i	$0.807804\pi$
$752$	−16.7711	+	16.7967i	−0.611579	+	0.612511i
$753$	22.4916	+	4.47386i	0.819641	+	0.163037i
$754$	28.4583	+	38.3563i	1.03639	+	1.39686i
$755$	−3.65951	+	1.73082i	−0.133183	+	0.0629910i
$756$	−5.05963	−	3.74949i	−0.184017	−	0.136368i
$757$	6.01164	−	8.10576i	0.218497	−	0.294609i	−0.680336	−	0.732900i	$-0.738166\pi$
$757$	6.01164	−	8.10576i	0.218497	−	0.294609i	0.898833	+	0.438291i	$0.144416\pi$
$758$	11.8830	+	14.4739i	0.431611	+	0.525715i
$759$	10.6626	+	19.9483i	0.387027	+	0.724076i
$760$	20.3046	+	3.00004i	0.736524	+	0.108823i
$761$	33.7449	−	10.2364i	1.22325	−	0.371069i	0.388372	−	0.921503i	$-0.373038\pi$
$761$	33.7449	−	10.2364i	1.22325	−	0.371069i	0.834879	+	0.550434i	$0.185538\pi$
$762$	4.38010	−	22.0422i	0.158674	−	0.798504i
$763$	−32.0081	+	11.4527i	−1.15877	+	0.414614i
$764$	−2.33073	+	23.7571i	−0.0843230	+	0.859501i
$765$	−3.30317	−	1.97985i	−0.119426	−	0.0715815i
$766$	−0.526523	−	1.47065i	−0.0190240	−	0.0531367i
$767$	−43.7890			−1.58113
$768$	−9.55075	−	12.8368i	−0.344633	−	0.463208i
$769$	−48.8360			−1.76107			−0.880536	−	0.473979i	$-0.842817\pi$
$769$	−48.8360			−1.76107			−0.880536	+	0.473979i	$0.842817\pi$
$770$	5.13346	+	14.3385i	0.184997	+	0.516722i
$771$	−5.30253	−	3.17821i	−0.190966	−	0.114461i
$772$	50.8168	+	4.98548i	1.82894	+	0.179431i
$773$	4.92389	−	1.76179i	0.177100	−	0.0633673i	−0.246847	−	0.969055i	$-0.579394\pi$
$773$	4.92389	−	1.76179i	0.177100	−	0.0633673i	0.423947	+	0.905687i	$0.360644\pi$
$774$	−1.62972	+	8.20134i	−0.0585792	+	0.294791i
$775$	5.44614	−	1.65207i	0.195631	−	0.0593441i
$776$	30.9100	+	41.6276i	1.10961	+	1.49434i
$777$	8.69247	+	16.2625i	0.311841	+	0.583413i
$778$	0.738382	+	0.899372i	0.0264723	+	0.0322440i
$779$	44.3396	−	59.7851i	1.58863	−	2.14202i
$780$	−3.95249	+	5.33356i	−0.141522	+	0.190972i
$781$	9.54759	−	4.51567i	0.341640	−	0.161584i
$782$	−21.4621	−	28.9268i	−0.767483	−	1.03442i
$783$	−10.3948	−	2.06766i	−0.371481	−	0.0738921i
$784$	−4.46971	−	10.7676i	−0.159633	−	0.384558i
$785$	17.0967	−	3.40074i	0.610207	−	0.121378i
$786$	−1.12776	+	1.24477i	−0.0402259	+	0.0443994i
$787$	2.01712	+	41.0593i	0.0719024	+	1.46361i	0.715698	+	0.698410i	$0.246109\pi$
$787$	2.01712	+	41.0593i	0.0719024	+	1.46361i	−0.643796	+	0.765197i	$0.722641\pi$
$788$	24.1325	−	6.05465i	0.859685	−	0.215688i
$789$	−11.5150	−	2.88436i	−0.409946	−	0.102686i
$790$	−7.71942	−	2.34006i	−0.274645	−	0.0832555i
$791$	−1.00843	−	10.2388i	−0.0358558	−	0.364050i
$792$	5.88728	−	7.18203i	0.209195	−	0.255202i
$793$	26.9162	−	22.0896i	0.955822	−	0.784423i
$794$	33.5589	+	33.5462i	1.19096	+	1.19051i
$795$	0.0103648	−	0.210980i	0.000367601	−	0.00748269i
$796$	6.26468	+	31.4321i	0.222046	+	1.11408i
$797$	−3.56136	+	24.0087i	−0.126150	+	0.850433i	0.830044	+	0.557698i	$0.188315\pi$
$797$	−3.56136	+	24.0087i	−0.126150	+	0.850433i	−0.956194	+	0.292735i	$0.905435\pi$
$798$	−4.55768	−	30.6851i	−0.161340	−	1.08624i
$799$	20.2684	+	8.39544i	0.717044	+	0.297009i
$800$	−16.4235	−	14.8569i	−0.580658	−	0.525271i
$801$	−10.3783	+	4.29881i	−0.366698	+	0.151891i
$802$	−20.1347	−	33.5782i	−0.710981	−	1.18569i
$803$	4.20227	−	3.11661i	0.148295	−	0.109983i
$804$	5.01396	+	12.0917i	0.176829	+	0.426443i
$805$	15.1743	+	16.7423i	0.534824	+	0.590088i
$806$	−6.05182	+	2.50810i	−0.213166	+	0.0883439i
$807$	−15.3592	−	1.51275i	−0.540671	−	0.0532514i
$808$	18.7312	−	28.0679i	0.658960	−	0.987424i
$809$	−11.4028	−	9.35806i	−0.400902	−	0.329012i	0.412242	−	0.911074i	$-0.364746\pi$
$809$	−11.4028	−	9.35806i	−0.400902	−	0.329012i	−0.813144	+	0.582063i	$0.802246\pi$
$810$	−0.144671	−	1.46601i	−0.00508321	−	0.0515102i
$811$	−20.3006	−	33.8696i	−0.712852	−	1.18932i	−0.974550	−	0.224171i	$-0.928032\pi$
$811$	−20.3006	−	33.8696i	−0.712852	−	1.18932i	0.261698	−	0.965150i	$-0.415718\pi$
$812$	−49.4710	−	44.8036i	−1.73609	−	1.57230i
$813$	0.438587	+	0.397512i	0.0153819	+	0.0139413i
$814$	−24.5794	+	11.6309i	−0.861507	+	0.407663i
$815$	9.78747	+	6.53978i	0.342840	+	0.229078i
$816$	−7.59301	+	12.6901i	−0.265809	+	0.444242i
$817$	−34.2483	+	22.8840i	−1.19820	+	0.800609i
$818$	−24.0952	−	14.4359i	−0.842469	−	0.504738i
$819$	9.44693	+	3.38017i	0.330103	+	0.118113i
$820$	20.9550	−	7.50683i	0.731781	−	0.262150i
$821$	−2.80737	−	18.9258i	−0.0979780	−	0.660514i	−0.981405	−	0.191946i	$-0.938520\pi$
$821$	−2.80737	−	18.9258i	−0.0979780	−	0.660514i	0.883427	−	0.468568i	$-0.155230\pi$
$822$	5.40102	−	1.63950i	0.188382	−	0.0571842i
$823$	−1.35308	+	4.46049i	−0.0471652	+	0.155483i	−0.977360	−	0.211584i	$-0.932138\pi$
$823$	−1.35308	+	4.46049i	−0.0471652	+	0.155483i	0.930195	+	0.367067i	$0.119638\pi$
$824$	42.6977	−	6.35854i	1.48745	−	0.221510i
$825$	6.05935	−	11.3362i	0.210959	−	0.394677i
$826$	60.0155	−	11.9497i	2.08821	−	0.415784i
$827$	−13.3297	−	6.30446i	−0.463517	−	0.219227i	0.181507	−	0.983390i	$-0.441903\pi$
$827$	−13.3297	−	6.30446i	−0.463517	−	0.219227i	−0.645024	+	0.764162i	$0.723153\pi$
$828$	3.99457	−	13.1864i	0.138821	−	0.458260i
$829$	−15.0486	+	3.76947i	−0.522659	+	0.130919i	−0.495326	−	0.868707i	$-0.664951\pi$
$829$	−15.0486	+	3.76947i	−0.522659	+	0.130919i	−0.0273328	+	0.999626i	$0.508701\pi$
$830$	1.14465	−	23.3907i	0.0397312	−	0.811902i
$831$	−10.1085	−	10.1085i	−0.350660	−	0.350660i
$832$	20.4926	+	15.1621i	0.710454	+	0.525651i
$833$	−7.61945	+	7.61945i	−0.263998	+	0.263998i
$834$	−6.74071	−	7.43439i	−0.233412	−	0.257432i
$835$	−0.313761	−	1.25260i	−0.0108582	−	0.0433482i
$836$	45.5244	−	4.50126i	1.57449	−	0.155679i
$837$	0.621541	−	1.31414i	0.0214836	−	0.0454233i
$838$	38.1333	+	25.4693i	1.31729	+	0.879823i
$839$	−4.72006	−	2.52292i	−0.162954	−	0.0871010i	0.387903	−	0.921700i	$-0.373199\pi$
$839$	−4.72006	−	2.52292i	−0.162954	−	0.0871010i	−0.550858	+	0.834599i	$0.685699\pi$
$840$	3.96164	−	8.38858i	0.136690	−	0.289434i
$841$	−79.7396	−	24.1888i	−2.74964	−	0.834095i
$842$	−3.23381	+	6.05280i	−0.111444	+	0.208593i
$843$	0.979121	−	0.145239i	0.0337227	−	0.00500230i
$844$	0.462351	+	0.0225374i	0.0159148	+	0.000775768i
$845$	−0.998834	+	2.79155i	−0.0343609	+	0.0960324i
$846$	2.04063	+	8.14006i	0.0701582	+	0.279861i
$847$	−0.384518	−	0.575472i	−0.0132122	−	0.0197735i
$848$	−0.810200	−	0.0391840i	−0.0278224	−	0.00134559i
$849$	−0.485971	+	0.727307i	−0.0166785	+	0.0249611i
$850$	−6.89215	+	19.2738i	−0.236399	+	0.661087i
$851$	−27.0935	+	29.8930i	−0.928752	+	1.02472i
$852$	−6.05825	−	2.16507i	−0.207552	−	0.0741742i
$853$	10.6767	−	6.39937i	0.365563	−	0.219110i	−0.319512	−	0.947582i	$-0.603519\pi$
$853$	10.6767	−	6.39937i	0.365563	−	0.219110i	0.685076	+	0.728472i	$0.259769\pi$
$854$	−30.8622	+	37.6203i	−1.05608	+	1.28734i
$855$	4.60359	−	5.60949i	0.157439	−	0.191841i
$856$	36.7269	+	36.6849i	1.25530	+	1.25387i
$857$	−3.07127	+	31.1831i	−0.104913	+	1.06520i	0.788217	+	0.615397i	$0.211004\pi$
$857$	−3.07127	+	31.1831i	−0.104913	+	1.06520i	−0.893130	+	0.449799i	$0.851496\pi$
$858$	−5.65953	+	13.6707i	−0.193213	+	0.466709i
$859$	1.52874	−	1.38557i	0.0521601	−	0.0472751i	−0.645063	−	0.764130i	$-0.723169\pi$
$859$	1.52874	−	1.38557i	0.0521601	−	0.0472751i	0.697223	+	0.716854i	$0.254419\pi$
$860$	−12.3178	+	0.00469097i	−0.420034	+	0.000159961i
$861$	−20.0409	−	27.0220i	−0.682991	−	0.920907i
$862$	−6.88698	+	27.5166i	−0.234572	+	0.937219i
$863$	−0.430955	−	1.04042i	−0.0146699	−	0.0354162i	0.916375	−	0.400321i	$-0.131101\pi$
$863$	−0.430955	−	1.04042i	−0.0146699	−	0.0354162i	−0.931045	+	0.364905i	$0.881101\pi$
$864$	−5.62908	+	0.559828i	−0.191505	+	0.0190457i
$865$	−2.87882	+	6.95010i	−0.0978830	+	0.236310i
$866$	10.1201	+	7.50260i	0.343895	+	0.254949i
$867$	−3.29569	−	0.488869i	−0.111927	−	0.0166029i
$868$	7.60995	−	5.08900i	0.258298	−	0.172732i
$869$	−17.9566	−	0.882153i	−0.609137	−	0.0299250i
$870$	−0.00297291	−	15.6129i	−0.000100791	−	0.529327i
$871$	−13.2307	−	16.1216i	−0.448305	−	0.546261i
$872$	−14.3796	+	26.9394i	−0.486956	+	0.912283i
$873$	18.2430	−	1.79678i	0.617433	−	0.0608118i
$874$	59.8516	−	32.0060i	2.02451	−	1.08262i
$875$	7.10481	−	28.3640i	0.240187	−	0.958879i
$876$	−3.15261	−	0.466419i	−0.106517	−	0.0157588i
$877$	−21.6315	+	1.06269i	−0.730443	+	0.0358843i	−0.410891	−	0.911685i	$-0.634782\pi$
$877$	−21.6315	+	1.06269i	−0.730443	+	0.0358843i	−0.319552	+	0.947569i	$0.603532\pi$
$878$	−8.67431	+	0.427797i	−0.292744	+	0.0144375i
$879$	1.55890	+	7.83714i	0.0525805	+	0.264340i
$880$	12.0699	+	6.43970i	0.406877	+	0.217082i
$881$	2.01895	−	10.1499i	0.0680200	−	0.341960i	−0.931757	−	0.363083i	$-0.881724\pi$
$881$	2.01895	−	10.1499i	0.0680200	−	0.341960i	0.999777	+	0.0211231i	$0.00672419\pi$
$882$	−4.07740	−	0.604031i	−0.137293	−	0.0203388i
$883$	−0.143008	−	0.302366i	−0.00481261	−	0.0101754i	0.901569	−	0.432636i	$-0.142416\pi$
$883$	−0.143008	−	0.302366i	−0.00481261	−	0.0101754i	−0.906381	+	0.422461i	$0.861166\pi$
$884$	5.71622	−	22.8573i	0.192257	−	0.768776i
$885$	11.4976	+	8.52717i	0.386486	+	0.286638i
$886$	0.294241	−	2.99333i	0.00988523	−	0.100563i
$887$	−12.5010	+	6.68190i	−0.419741	+	0.224356i	−0.667725	−	0.744408i	$-0.732732\pi$
$887$	−12.5010	+	6.68190i	−0.419741	+	0.224356i	0.247984	+	0.968764i	$0.420232\pi$
$888$	15.5989	+	5.57131i	0.523463	+	0.186961i
$889$	−14.5248	−	47.8820i	−0.487148	−	1.60591i
$890$	−9.19627	−	13.7575i	−0.308260	−	0.461153i
$891$	−1.10612	−	3.09139i	−0.0370563	−	0.103565i
$892$	−7.45771	+	13.9652i	−0.249703	+	0.467589i
$893$	−21.2525	+	35.4577i	−0.711189	+	1.18655i
$894$	−11.2352	+	23.7666i	−0.375763	+	0.794875i
$895$			7.56124i			0.252744i
$896$	−32.2240	−	15.1883i	−1.07653	−	0.507405i
$897$			21.9520i			0.732956i
$898$	13.6905	+	6.47192i	0.456857	+	0.215971i
$899$	7.92084	−	13.2151i	0.264175	−	0.440749i
$900$	−7.49188	+	2.27575i	−0.249729	+	0.0758584i
$901$	0.252571	+	0.705890i	0.00841437	+	0.0235166i
$902$	41.2450	−	27.5704i	1.37331	−	0.917993i
$903$	5.40432	+	17.8157i	0.179845	+	0.592868i
$904$	−6.85119	−	6.20244i	−0.227867	−	0.206290i
$905$	11.9723	−	6.39934i	0.397974	−	0.212721i
$906$	5.46968	+	0.537665i	0.181718	+	0.0178627i
$907$	−30.4259	−	22.5654i	−1.01028	−	0.749272i	−0.0419910	−	0.999118i	$-0.513370\pi$
$907$	−30.4259	−	22.5654i	−1.01028	−	0.749272i	−0.968286	+	0.249846i	$0.919620\pi$
$908$	−17.7657	−	29.6147i	−0.589576	−	0.982798i
$909$	−5.10087	−	10.7849i	−0.169185	−	0.357712i
$910$	−2.16597	+	14.6210i	−0.0718012	+	0.484680i
$911$	−6.09720	+	30.6527i	−0.202009	+	1.01557i	0.738099	+	0.674693i	$0.235724\pi$
$911$	−6.09720	+	30.6527i	−0.202009	+	1.01557i	−0.940108	+	0.340877i	$0.889276\pi$
$912$	−21.5541	−	17.6615i	−0.713727	−	0.584832i
$913$	−10.1829	−	51.1929i	−0.337005	−	1.69424i
$914$	−0.0195291	−	0.395986i	−0.000645966	−	0.0130980i
$915$	−11.3689	+	0.558517i	−0.375844	+	0.0184640i
$916$	−35.3839	−	47.6717i	−1.16912	−	1.57512i
$917$	−0.908695	+	3.62771i	−0.0300077	+	0.119798i
$918$	2.46554	+	4.61060i	0.0813751	+	0.152172i
$919$	13.0174	−	1.28211i	0.429406	−	0.0422928i	0.118994	−	0.992895i	$-0.462033\pi$
$919$	13.0174	−	1.28211i	0.429406	−	0.0422928i	0.310412	+	0.950602i	$0.399533\pi$
$920$	20.2004	+	1.97791i	0.665987	+	0.0652099i
$921$	4.78496	+	5.83049i	0.157670	+	0.192121i
$922$	−2.63450		0.000501645i	−0.0867626		1.65208e-5i
$923$	10.2378	+	0.502950i	0.336981	+	0.0165548i
$924$	4.02610	−	20.2809i	0.132449	−	0.667194i
$925$	22.6787	+	3.36407i	0.745671	+	0.110610i
$926$	7.71306	−	10.4040i	0.253467	−	0.341897i
$927$	5.84067	−	14.1006i	0.191833	−	0.463125i
$928$	−59.9540	+	0.0570804i	−1.96809	+	0.00187376i
$929$	−16.0612	−	38.7752i	−0.526951	−	1.27217i	−0.933511	−	0.358548i	$-0.883272\pi$
$929$	−16.0612	−	38.7752i	−0.526951	−	1.27217i	0.406560	−	0.913624i	$-0.366728\pi$
$930$	2.07742	+	0.519946i	0.0681213	+	0.0170497i
$931$	−12.0955	−	16.3088i	−0.396413	−	0.534501i
$932$	7.67124	+	7.66540i	0.251280	+	0.251089i
$933$	1.13834	−	1.03173i	0.0372675	−	0.0337773i
$934$	−26.0347	−	10.7781i	−0.851880	−	0.352670i
$935$	1.23936	−	12.5834i	0.0405313	−	0.411522i
$936$	8.32472	−	3.45378i	0.272102	−	0.112890i
$937$	5.23993	−	6.38487i	0.171181	−	0.208585i	−0.680352	−	0.732885i	$-0.738173\pi$
$937$	5.23993	−	6.38487i	0.171181	−	0.208585i	0.851533	+	0.524301i	$0.175673\pi$
$938$	22.5329	+	18.4851i	0.735727	+	0.603561i
$939$	−14.0572	+	8.42555i	−0.458739	+	0.274958i
$940$	−11.1735	+	5.28986i	−0.364438	+	0.172536i
$941$	−2.51639	+	2.77641i	−0.0820320	+	0.0905084i	−0.780584	−	0.625051i	$-0.785078\pi$
$941$	−2.51639	+	2.77641i	−0.0820320	+	0.0905084i	0.698552	+	0.715559i	$0.253828\pi$
$942$	−22.2843	−	7.96865i	−0.726060	−	0.259633i
$943$	40.8933	−	61.2012i	1.33167	−	1.99299i
$944$	32.7110	−	44.1760i	1.06465	−	1.43781i
$945$	−1.82222	−	2.72715i	−0.0592770	−	0.0887143i
$946$	−26.6301	+	6.67588i	−0.865819	+	0.217051i
$947$	−0.780703	+	2.18192i	−0.0253694	+	0.0709028i	−0.953561	−	0.301200i	$-0.902613\pi$
$947$	−0.780703	+	2.18192i	−0.0253694	+	0.0709028i	0.928192	+	0.372102i	$0.121363\pi$
$948$	7.35752	+	8.11156i	0.238961	+	0.263451i
$949$	5.02260	−	0.745032i	0.163041	−	0.0241848i
$950$	−34.0195	−	18.1755i	−1.10374	−	0.589691i
$951$	17.8683	+	5.42030i	0.579421	+	0.175765i
$952$	−1.59682	+	32.8873i	−0.0517532	+	1.06588i
$953$	25.5564	+	13.6602i	0.827853	+	0.442497i	0.830177	−	0.557500i	$-0.188240\pi$
$953$	25.5564	+	13.6602i	0.827853	+	0.442497i	−0.00232322	+	0.999997i	$0.500740\pi$
$954$	−0.159283	+	0.238482i	−0.00515698	+	0.00772115i
$955$	−5.31570	+	11.2391i	−0.172012	+	0.363689i
$956$	−16.7155	+	20.3838i	−0.540619	+	0.659258i
$957$	−8.45527	−	33.7553i	−0.273320	−	1.09116i
$958$	11.5119	−	10.4378i	0.371933	−	0.337230i
$959$	8.88636	−	8.88636i	0.286955	−	0.286955i
$960$	−2.42813	−	7.97166i	−0.0783675	−	0.257284i
$961$	−20.4260	−	20.4260i	−0.658903	−	0.658903i
$962$	−26.3588	−	1.28990i	−0.849843	−	0.0415879i
$963$	17.8029	−	4.45940i	0.573692	−	0.143702i
$964$	−20.6296	+	11.0369i	−0.664435	+	0.355474i
$965$	24.0406	+	11.3704i	0.773895	+	0.366025i
$966$	−5.99054	−	30.0865i	−0.192743	−	0.968019i
$967$	−24.7937	+	46.3858i	−0.797313	+	1.49167i	0.0719993	+	0.997405i	$0.477062\pi$
$967$	−24.7937	+	46.3858i	−0.797313	+	1.49167i	−0.869312	+	0.494263i	$0.835438\pi$
$968$	−0.603160	−	0.150718i	−0.0193863	−	0.00484425i
$969$	−7.47642	+	24.6465i	−0.240177	+	0.791758i
$970$	7.84386	+	25.8400i	0.251851	+	0.829673i
$971$	8.15570	+	54.9813i	0.261729	+	1.76443i	0.578262	+	0.815851i	$0.303731\pi$
$971$	8.15570	+	54.9813i	0.261729	+	1.76443i	−0.316533	+	0.948582i	$0.602519\pi$
$972$	−0.854422	+	1.80830i	−0.0274056	+	0.0580014i
$973$	−21.0375	−	7.52734i	−0.674431	−	0.241315i
$974$	28.8930	−	48.2259i	0.925791	−	1.54526i
$975$	10.3725	−	6.93070i	0.332187	−	0.221960i
$976$	2.17798	+	43.6552i	0.0697153	+	1.39737i
$977$	−18.6991	−	12.4943i	−0.598236	−	0.399728i	0.219257	−	0.975667i	$-0.429637\pi$
$977$	−18.6991	−	12.4943i	−0.598236	−	0.399728i	−0.817493	+	0.575939i	$0.804637\pi$
$978$	−6.83567	−	14.4457i	−0.218581	−	0.461922i
$979$	−27.3283	−	24.7689i	−0.873415	−	0.791617i
$980$	−0.300252	−	6.06464i	−0.00959120	−	0.193728i
$981$	5.55048	+	9.26041i	0.177213	+	0.295662i
$982$	33.3377	−	3.28989i	1.06385	−	0.104985i
$983$	22.4243	+	18.4032i	0.715225	+	0.586970i	0.920037	−	0.391831i	$-0.128158\pi$
$983$	22.4243	+	18.4032i	0.715225	+	0.586970i	−0.204812	+	0.978801i	$0.565658\pi$
$984$	−29.6428	−	5.87873i	−0.944979	−	0.187407i
$985$	12.8961	+	1.27015i	0.410902	+	0.0404704i
$986$	21.2155	+	51.1913i	0.675641	+	1.63026i
$987$	12.5479	+	13.8444i	0.399403	+	0.440673i
$988$	41.0241	+	16.9744i	1.30515	+	0.540029i
$989$	−32.7167	+	24.2643i	−1.04033	+	0.771561i
$990$	4.14814	−	2.48737i	0.131837	−	0.0790539i
$991$	−17.5616	+	7.27423i	−0.557861	+	0.231074i	−0.643756	−	0.765231i	$-0.722625\pi$
$991$	−17.5616	+	7.27423i	−0.557861	+	0.231074i	0.0858952	+	0.996304i	$0.472625\pi$
$992$	1.99053	−	7.97888i	0.0631995	−	0.253330i
$993$	21.7389	+	9.00453i	0.689862	+	0.285750i
$994$	−14.1688	+	2.10449i	−0.449406	+	0.0667505i
$995$	−2.44933	+	16.5121i	−0.0776491	+	0.523468i
$996$	−17.6540	+	26.4429i	−0.559389	+	0.837875i
$997$	−1.10412	+	22.4748i	−0.0349678	+	0.711785i	0.915754	+	0.401740i	$0.131594\pi$
$997$	−1.10412	+	22.4748i	−0.0349678	+	0.711785i	−0.950722	+	0.310046i	$0.899656\pi$
$998$	−9.95467	+	9.95847i	−0.315110	+	0.315230i
$999$	4.52693	−	3.71516i	0.143226	−	0.117542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.z.a.421.6	yes	2048
256.45	even	64	inner	768.2.z.a.301.6	✓	2048

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
768.2.z.a.301.6	✓	2048	256.45	even	64	inner
768.2.z.a.421.6	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)

\(f(q)\)	\(=\)	\(q+(-1.33145 + 0.476688i) q^{2} +(0.857729 + 0.514103i) q^{3} +(1.54554 - 1.26938i) q^{4} +(0.980766 - 0.350924i) q^{5} +(-1.38709 - 0.275635i) q^{6} +(-3.01316 + 0.914034i) q^{7} +(-1.45272 + 2.42685i) q^{8} +(0.471397 + 0.881921i) q^{9} +O(q^{10})\)	\(q+(-1.33145 + 0.476688i) q^{2} +(0.857729 + 0.514103i) q^{3} +(1.54554 - 1.26938i) q^{4} +(0.980766 - 0.350924i) q^{5} +(-1.38709 - 0.275635i) q^{6} +(-3.01316 + 0.914034i) q^{7} +(-1.45272 + 2.42685i) q^{8} +(0.471397 + 0.881921i) q^{9} +(-1.13856 + 0.934758i) q^{10} +(-1.95587 + 2.63719i) q^{11} +(1.97824 - 0.294214i) q^{12} +(-2.88055 + 1.36240i) q^{13} +(3.57618 - 2.65333i) q^{14} +(1.02164 + 0.203217i) q^{15} +(0.777373 - 3.92373i) q^{16} +(-3.62602 + 0.721261i) q^{17} +(-1.04804 - 0.949528i) q^{18} +(-0.341829 - 6.95809i) q^{19} +(1.07036 - 1.78733i) q^{20} +(-3.05438 - 0.765084i) q^{21} +(1.34704 - 4.44363i) q^{22} +(-0.675249 - 6.85592i) q^{23} +(-2.49369 + 1.33474i) q^{24} +(-3.02630 + 2.48362i) q^{25} +(3.18588 - 3.18709i) q^{26} +(-0.0490677 + 0.998795i) q^{27} +(-3.49671 + 5.23751i) q^{28} +(-1.55512 + 10.4838i) q^{29} +(-1.45714 + 0.216430i) q^{30} +(-1.34305 - 0.556311i) q^{31} +(0.835360 + 5.59483i) q^{32} +(-3.03339 + 1.25647i) q^{33} +(4.48406 - 2.68881i) q^{34} +(-2.63445 + 1.95384i) q^{35} +(1.84805 + 0.764663i) q^{36} +(-3.93281 - 4.33918i) q^{37} +(3.77196 + 9.10142i) q^{38} +(-3.17114 - 0.312330i) q^{39} +(-0.573135 + 2.88997i) q^{40} +(8.25918 + 6.77814i) q^{41} +(4.43148 - 0.437314i) q^{42} +(-3.03969 - 5.07141i) q^{43} +(0.324708 + 6.55861i) q^{44} +(0.771817 + 0.699534i) q^{45} +(4.16719 + 8.80645i) q^{46} +(-4.93394 - 3.29675i) q^{47} +(2.68398 - 2.96585i) q^{48} +(2.42342 - 1.61928i) q^{49} +(2.84546 - 4.74942i) q^{50} +(-3.48094 - 1.24550i) q^{51} +(-2.72260 + 5.76214i) q^{52} +(-0.0297550 - 0.200592i) q^{53} +(-0.410782 - 1.35324i) q^{54} +(-0.992801 + 3.27283i) q^{55} +(2.15905 - 8.64034i) q^{56} +(3.28397 - 6.14388i) q^{57} +(-2.92691 - 14.7000i) q^{58} +(12.4227 + 5.87550i) q^{59} +(1.83695 - 0.982768i) q^{60} +(-10.5999 + 2.65514i) q^{61} +(2.05340 + 0.100485i) q^{62} +(-2.22650 - 2.22650i) q^{63} +(-3.77923 - 7.05106i) q^{64} +(-2.34705 + 2.34705i) q^{65} +(3.43988 - 3.11892i) q^{66} +(1.59031 + 6.34889i) q^{67} +(-4.68860 + 5.71752i) q^{68} +(2.94547 - 6.22766i) q^{69} +(2.57628 - 3.85727i) q^{70} +(-2.83692 - 1.51636i) q^{71} +(-2.82510 - 0.137171i) q^{72} +(-1.52485 - 0.462559i) q^{73} +(7.30478 + 3.90270i) q^{74} +(-3.87258 + 0.574442i) q^{75} +(-9.36073 - 10.3201i) q^{76} +(3.48289 - 9.73401i) q^{77} +(4.37111 - 1.09579i) q^{78} +(3.04210 + 4.55283i) q^{79} +(-0.614511 - 4.12107i) q^{80} +(-0.555570 + 0.831470i) q^{81} +(-14.2278 - 5.08772i) q^{82} +(-10.6759 + 11.7791i) q^{83} +(-5.69184 + 2.69470i) q^{84} +(-3.30317 + 1.97985i) q^{85} +(6.46469 + 5.30337i) q^{86} +(-6.72360 + 8.19273i) q^{87} +(-3.55874 - 8.57770i) q^{88} +(-1.10106 + 11.1793i) q^{89} +(-1.36110 - 0.563482i) q^{90} +(7.43429 - 6.73805i) q^{91} +(-9.74635 - 9.73893i) q^{92} +(-0.865974 - 1.16763i) q^{93} +(8.14084 + 2.03753i) q^{94} +(-2.77701 - 6.70430i) q^{95} +(-2.15981 + 5.22831i) q^{96} +(7.01508 - 16.9359i) q^{97} +(-2.45478 + 3.31121i) q^{98} +(-3.24778 - 0.481763i) 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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