LMFDB - Embedded newform 798.2.cc.b.737.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(317,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 6, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.317"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cc (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [162,0,0,0,0,0,0,81] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			737.19
Character	$\chi$	$=$	798.737
Dual form			798.2.cc.b.641.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.766044 + 0.642788i) q^{2} +(0.818331 + 1.52654i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.25611 - 0.221486i) q^{5} +(-1.60812 - 0.643387i) q^{6} +(-1.62661 + 2.08666i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.66067 + 2.49844i) q^{9} +(-0.819866 + 0.977079i) q^{10} +(-4.03555 - 2.32993i) q^{11} +(1.64545 - 0.540817i) q^{12} +(-2.55839 - 0.451112i) q^{13} +(-0.0952210 - 2.64404i) q^{14} +(1.36602 + 1.73625i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-4.31707 + 0.761217i) q^{17} +(-0.333818 - 2.98137i) q^{18} +(3.56024 + 2.51490i) q^{19} -1.27549i q^{20} +(-4.51648 - 0.775515i) q^{21} +(4.58906 - 0.809176i) q^{22} +(-1.39607 - 3.83567i) q^{23} +(-0.912860 + 1.47197i) q^{24} +(-3.16971 + 1.15368i) q^{25} +(2.24981 - 1.29893i) q^{26} +(-5.17295 - 0.490534i) q^{27} +(1.77250 + 1.96424i) q^{28} +(-2.24287 + 0.816338i) q^{29} +(-2.16248 - 0.451988i) q^{30} +3.38721i q^{31} +(0.939693 - 0.342020i) q^{32} +(0.254316 - 8.06710i) q^{33} +(2.81777 - 3.35809i) q^{34} +(-1.58103 + 2.98134i) q^{35} +(2.17211 + 2.06929i) q^{36} +(3.51420 + 2.02892i) q^{37} +(-4.34385 + 0.361949i) q^{38} +(-1.40496 - 4.27465i) q^{39} +(0.819866 + 0.977079i) q^{40} +(1.67805 + 9.51669i) q^{41} +(3.95831 - 2.30906i) q^{42} +(0.447459 - 0.375463i) q^{43} +(-2.99530 + 3.56966i) q^{44} +(-1.53261 + 3.50612i) q^{45} +(3.53497 + 2.04092i) q^{46} +(5.32530 + 0.938993i) q^{47} +(-0.246871 - 1.71437i) q^{48} +(-1.70827 - 6.78836i) q^{49} +(1.68657 - 2.92122i) q^{50} +(-4.69483 - 5.96727i) q^{51} +(-0.888518 + 2.44118i) q^{52} +(-1.35224 + 7.66894i) q^{53} +(4.27802 - 2.94934i) q^{54} +(-5.58514 - 2.03282i) q^{55} +(-2.62040 - 0.365358i) q^{56} +(-0.925653 + 7.49287i) q^{57} +(1.19341 - 2.06704i) q^{58} +(0.221701 + 1.25733i) q^{59} +(1.94708 - 1.04377i) q^{60} +(-9.72993 + 3.54140i) q^{61} +(-2.17726 - 2.59475i) q^{62} +(-2.51212 - 7.52923i) q^{63} +(-0.500000 + 0.866025i) q^{64} -3.31352 q^{65} +(4.99061 + 6.34323i) q^{66} +(5.67627 - 6.76472i) q^{67} +4.38367i q^{68} +(4.71286 - 5.27000i) q^{69} +(-0.705225 - 3.30011i) q^{70} +(0.0380509 - 0.0319285i) q^{71} +(-2.99404 - 0.188963i) q^{72} +(2.66717 - 2.23802i) q^{73} +(-3.99620 + 0.704638i) q^{74} +(-4.35502 - 3.89461i) q^{75} +(3.09492 - 3.06944i) q^{76} +(11.4260 - 4.63093i) q^{77} +(3.82395 + 2.37147i) q^{78} +(1.39629 - 3.83628i) q^{79} +(-1.25611 - 0.221486i) q^{80} +(-3.48436 - 8.29815i) q^{81} +(-7.40267 - 6.21158i) q^{82} +(-0.668209 - 0.385791i) q^{83} +(-1.54801 + 4.31320i) q^{84} +(-5.25411 + 1.91234i) q^{85} +(-0.101431 + 0.575243i) q^{86} +(-3.08159 - 2.75580i) q^{87} -4.65986i q^{88} +(4.22784 + 3.54758i) q^{89} +(-1.07964 - 3.67099i) q^{90} +(5.10281 - 4.60469i) q^{91} +(-4.01982 + 0.708802i) q^{92} +(-5.17072 + 2.77186i) q^{93} +(-4.68299 + 2.70372i) q^{94} +(5.02906 + 2.37045i) q^{95} +(1.29109 + 1.15460i) q^{96} +(2.07068 - 5.68915i) q^{97} +(5.67209 + 4.10213i) q^{98} +(12.5229 - 6.21333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 81 q^{8} + 15 q^{13} - 9 q^{14} + 3 q^{15} - 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} + 9 q^{27} - 12 q^{28} - 6 q^{29} - 12 q^{33} + 6 q^{34} + 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots + 39 q^{99}+O(q^{100}) $ 162 * q + 81 * q^8 + 15 * q^13 - 9 * q^14 + 3 * q^15 - 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 + 9 * q^27 - 12 * q^28 - 6 * q^29 - 12 * q^33 + 6 * q^34 + 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 - 6 * q^44 + 18 * q^45 - 18 * q^46 - 12 * q^47 + 24 * q^49 - 87 * q^50 + 24 * q^51 + 12 * q^52 + 36 * q^53 + 18 * q^54 - 18 * q^57 - 24 * q^59 - 27 * q^60 - 9 * q^61 - 36 * q^62 + 6 * q^63 - 81 * q^64 + 72 * q^65 + 12 * q^66 - 63 * q^67 - 9 * q^69 + 12 * q^70 - 12 * q^71 - 51 * q^73 + 42 * q^74 - 18 * q^78 + 21 * q^79 - 12 * q^81 + 3 * q^84 - 6 * q^85 - 36 * q^86 - 84 * q^87 + 54 * q^89 + 12 * q^90 + 75 * q^91 - 66 * q^93 + 72 * q^94 - 12 * q^97 - 12 * q^98 + 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	0.818331	+	1.52654i	0.472464	+	0.881350i
$3$	0.818331	+	1.52654i	0.472464	+	0.881350i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	1.25611	−	0.221486i	0.561749	−	0.0990515i	0.114439	−	0.993430i	$-0.463493\pi$
$5$	1.25611	−	0.221486i	0.561749	−	0.0990515i	0.447310	+	0.894379i	$0.352382\pi$
$6$	−1.60812	−	0.643387i	−0.656513	−	0.262662i
$7$	−1.62661	+	2.08666i	−0.614801	+	0.788682i
$7$	−1.62661	+	2.08666i	−0.614801	+	0.788682i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−1.66067	+	2.49844i	−0.553556	+	0.832812i
$10$	−0.819866	+	0.977079i	−0.259265	+	0.308979i
$11$	−4.03555	−	2.32993i	−1.21677	−	0.702500i	−0.252541	−	0.967586i	$-0.581266\pi$
$11$	−4.03555	−	2.32993i	−1.21677	−	0.702500i	−0.964225	+	0.265086i	$0.914599\pi$
$12$	1.64545	−	0.540817i	0.475001	−	0.156121i
$13$	−2.55839	−	0.451112i	−0.709568	−	0.125116i	−0.192796	−	0.981239i	$-0.561756\pi$
$13$	−2.55839	−	0.451112i	−0.709568	−	0.125116i	−0.516772	+	0.856123i	$0.672867\pi$
$14$	−0.0952210	−	2.64404i	−0.0254489	−	0.706649i
$15$	1.36602	+	1.73625i	0.352705	+	0.448299i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−4.31707	+	0.761217i	−1.04704	+	0.184622i	−0.670602	−	0.741818i	$-0.733964\pi$
$17$	−4.31707	+	0.761217i	−1.04704	+	0.184622i	−0.376443	+	0.926440i	$0.622853\pi$
$18$	−0.333818	−	2.98137i	−0.0786816	−	0.702716i
$19$	3.56024	+	2.51490i	0.816774	+	0.576958i
$19$	3.56024	+	2.51490i	0.816774	+	0.576958i
$20$		−	1.27549i		−	0.285207i
$21$	−4.51648	−	0.775515i	−0.985576	−	0.169231i
$22$	4.58906	−	0.809176i	0.978391	−	0.172517i
$23$	−1.39607	−	3.83567i	−0.291100	−	0.799792i	−0.995906	−	0.0903914i	$-0.971188\pi$
$23$	−1.39607	−	3.83567i	−0.291100	−	0.799792i	0.704806	−	0.709400i	$-0.251034\pi$
$24$	−0.912860	+	1.47197i	−0.186337	+	0.300464i
$25$	−3.16971	+	1.15368i	−0.633942	+	0.230736i
$26$	2.24981	−	1.29893i	0.441223	−	0.254740i
$27$	−5.17295	−	0.490534i	−0.995534	−	0.0944033i
$28$	1.77250	+	1.96424i	0.334971	+	0.371207i
$29$	−2.24287	+	0.816338i	−0.416491	+	0.151590i	−0.541761	−	0.840532i	$-0.682242\pi$
$29$	−2.24287	+	0.816338i	−0.416491	+	0.151590i	0.125271	+	0.992123i	$0.460020\pi$
$30$	−2.16248	−	0.451988i	−0.394812	−	0.0825213i
$31$			3.38721i			0.608361i	0.952614	+	0.304180i	$0.0983825\pi$
$31$			3.38721i			0.608361i	−0.952614	+	0.304180i	$0.901617\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	0.254316	−	8.06710i	0.0442708	−	1.40430i
$34$	2.81777	−	3.35809i	0.483244	−	0.575907i
$35$	−1.58103	+	2.98134i	−0.267244	+	0.503938i
$36$	2.17211	+	2.06929i	0.362018	+	0.344881i
$37$	3.51420	+	2.02892i	0.577731	+	0.333553i	0.760231	−	0.649653i	$-0.225086\pi$
$37$	3.51420	+	2.02892i	0.577731	+	0.333553i	−0.182500	+	0.983206i	$0.558419\pi$
$38$	−4.34385	+	0.361949i	−0.704665	+	0.0587159i
$39$	−1.40496	−	4.27465i	−0.224974	−	0.684491i
$40$	0.819866	+	0.977079i	0.129632	+	0.154490i
$41$	1.67805	+	9.51669i	0.262067	+	1.48626i	0.777258	+	0.629181i	$0.216610\pi$
$41$	1.67805	+	9.51669i	0.262067	+	1.48626i	−0.515191	+	0.857075i	$0.672279\pi$
$42$	3.95831	−	2.30906i	0.610781	−	0.356295i
$43$	0.447459	−	0.375463i	0.0682369	−	0.0572576i	−0.608031	−	0.793913i	$-0.708040\pi$
$43$	0.447459	−	0.375463i	0.0682369	−	0.0572576i	0.676268	+	0.736655i	$0.263596\pi$
$44$	−2.99530	+	3.56966i	−0.451558	+	0.538146i
$45$	−1.53261	+	3.50612i	−0.228468	+	0.522662i
$46$	3.53497	+	2.04092i	0.521203	+	0.300917i
$47$	5.32530	+	0.938993i	0.776774	+	0.136966i	0.547961	−	0.836504i	$-0.315404\pi$
$47$	5.32530	+	0.938993i	0.776774	+	0.136966i	0.228814	+	0.973470i	$0.426515\pi$
$48$	−0.246871	−	1.71437i	−0.0356328	−	0.247448i
$49$	−1.70827	−	6.78836i	−0.244039	−	0.969765i
$50$	1.68657	−	2.92122i	0.238517	−	0.413123i
$51$	−4.69483	−	5.96727i	−0.657407	−	0.835585i
$52$	−0.888518	+	2.44118i	−0.123215	+	0.338531i
$53$	−1.35224	+	7.66894i	−0.185744	+	1.05341i	0.739251	+	0.673430i	$0.235180\pi$
$53$	−1.35224	+	7.66894i	−0.185744	+	1.05341i	−0.924995	+	0.379979i	$0.875931\pi$
$54$	4.27802	−	2.94934i	0.582164	−	0.401354i
$55$	−5.58514	−	2.03282i	−0.753100	−	0.274106i
$56$	−2.62040	−	0.365358i	−0.350166	−	0.0488230i
$57$	−0.925653	+	7.49287i	−0.122606	+	0.992455i
$58$	1.19341	−	2.06704i	0.156702	−	0.271416i
$59$	0.221701	+	1.25733i	0.0288630	+	0.163690i	0.995832	−	0.0912024i	$-0.0290710\pi$
$59$	0.221701	+	1.25733i	0.0288630	+	0.163690i	−0.966969	+	0.254892i	$0.917960\pi$
$60$	1.94708	−	1.04377i	0.251367	−	0.134750i
$61$	−9.72993	+	3.54140i	−1.24579	+	0.453430i	−0.878977	−	0.476865i	$-0.841773\pi$
$61$	−9.72993	+	3.54140i	−1.24579	+	0.453430i	−0.366813	+	0.930295i	$0.619551\pi$
$62$	−2.17726	−	2.59475i	−0.276512	−	0.329534i
$63$	−2.51212	−	7.52923i	−0.316497	−	0.948594i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−3.31352			−0.410992
$66$	4.99061	+	6.34323i	0.614302	+	0.780798i
$67$	5.67627	−	6.76472i	0.693467	−	0.826442i	−0.298303	−	0.954471i	$-0.596421\pi$
$67$	5.67627	−	6.76472i	0.693467	−	0.826442i	0.991770	+	0.128029i	$0.0408652\pi$
$68$			4.38367i			0.531598i
$69$	4.71286	−	5.27000i	0.567362	−	0.634434i
$70$	−0.705225	−	3.30011i	−0.0842905	−	0.394438i
$71$	0.0380509	−	0.0319285i	0.00451581	−	0.00378922i	−0.640527	−	0.767936i	$-0.721284\pi$
$71$	0.0380509	−	0.0319285i	0.00451581	−	0.00378922i	0.645043	+	0.764147i	$0.276840\pi$
$72$	−2.99404	−	0.188963i	−0.352851	−	0.0222695i
$73$	2.66717	−	2.23802i	0.312169	−	0.261941i	−0.473219	−	0.880945i	$-0.656908\pi$
$73$	2.66717	−	2.23802i	0.312169	−	0.261941i	0.785388	+	0.619004i	$0.212464\pi$
$74$	−3.99620	+	0.704638i	−0.464549	+	0.0819125i
$75$	−4.35502	−	3.89461i	−0.502874	−	0.449711i
$76$	3.09492	−	3.06944i	0.355012	−	0.352089i
$77$	11.4260	−	4.63093i	1.30212	−	0.527744i
$78$	3.82395	+	2.37147i	0.432978	+	0.268517i
$79$	1.39629	−	3.83628i	0.157095	−	0.431615i	−0.836028	−	0.548686i	$-0.815128\pi$
$79$	1.39629	−	3.83628i	0.157095	−	0.431615i	0.993124	+	0.117071i	$0.0373505\pi$
$80$	−1.25611	−	0.221486i	−0.140437	−	0.0247629i
$81$	−3.48436	−	8.29815i	−0.387151	−	0.922016i
$82$	−7.40267	−	6.21158i	−0.817488	−	0.685954i
$83$	−0.668209	−	0.385791i	−0.0733455	−	0.0423461i	0.462879	−	0.886422i	$-0.346817\pi$
$83$	−0.668209	−	0.385791i	−0.0733455	−	0.0423461i	−0.536224	+	0.844076i	$0.680150\pi$
$84$	−1.54801	+	4.31320i	−0.168902	+	0.470608i
$85$	−5.25411	+	1.91234i	−0.569889	+	0.207423i
$86$	−0.101431	+	0.575243i	−0.0109376	+	0.0620300i
$87$	−3.08159	−	2.75580i	−0.330381	−	0.295453i
$88$		−	4.65986i		−	0.496742i
$89$	4.22784	+	3.54758i	0.448150	+	0.376042i	0.838749	−	0.544519i	$-0.183288\pi$
$89$	4.22784	+	3.54758i	0.448150	+	0.376042i	−0.390599	+	0.920561i	$0.627732\pi$
$90$	−1.07964	−	3.67099i	−0.113804	−	0.386956i
$91$	5.10281	−	4.60469i	0.534920	−	0.482703i
$92$	−4.01982	+	0.708802i	−0.419095	+	0.0738978i
$93$	−5.17072	+	2.77186i	−0.536179	+	0.287428i
$94$	−4.68299	+	2.70372i	−0.483013	+	0.278868i
$95$	5.02906	+	2.37045i	0.515970	+	0.243203i
$96$	1.29109	+	1.15460i	0.131771	+	0.117840i
$97$	2.07068	−	5.68915i	0.210246	−	0.577646i	−0.789082	−	0.614287i	$-0.789444\pi$
$97$	2.07068	−	5.68915i	0.210246	−	0.577646i	0.999328	+	0.0366411i	$0.0116658\pi$
$98$	5.67209	+	4.10213i	0.572967	+	0.414377i
$99$	12.5229	−	6.21333i	1.25860	−	0.624464i
$100$	0.585739	+	3.32189i	0.0585739	+	0.332189i
$101$	2.53924	+	6.97650i	0.252664	+	0.694188i	0.999572	+	0.0292605i	$0.00931522\pi$
$101$	2.53924	+	6.97650i	0.252664	+	0.694188i	−0.746908	+	0.664927i	$0.768463\pi$
$102$	7.43214	+	1.55342i	0.735891	+	0.153812i
$103$		−	13.4513i		−	1.32539i	−0.748887	−	0.662697i	$-0.769412\pi$
$103$		−	13.4513i		−	1.32539i	0.748887	−	0.662697i	$-0.230588\pi$
$104$	−0.888518	−	2.44118i	−0.0871264	−	0.239378i
$105$	−5.84495	+	0.0262045i	−0.570409	+	0.00255730i
$106$	−3.89362	−	6.74395i	−0.378182	−	0.655030i
$107$	−5.95820	−	10.3199i	−0.576001	−	0.997663i	−0.995932	−	0.0901071i	$-0.971279\pi$
$107$	−5.95820	−	10.3199i	−0.576001	−	0.997663i	0.419931	−	0.907556i	$-0.362054\pi$
$108$	−1.38135	+	5.00918i	−0.132921	+	0.482008i
$109$	−2.62517	+	7.21260i	−0.251446	+	0.690842i	0.748180	+	0.663496i	$0.230928\pi$
$109$	−2.62517	+	7.21260i	−0.251446	+	0.690842i	−0.999626	+	0.0273464i	$0.991294\pi$
$110$	5.58514	−	2.03282i	0.532522	−	0.193822i
$111$	−0.221461	+	7.02491i	−0.0210202	+	0.666775i
$112$	2.24219	−	1.40448i	0.211867	−	0.132711i
$113$	−17.0814			−1.60688			−0.803442	−	0.595383i	$-0.797000\pi$
$113$	−17.0814			−1.60688			−0.803442	+	0.595383i	$0.797000\pi$
$114$	−4.10724	−	6.33487i	−0.384678	−	0.593315i
$115$	−2.60316	−	4.50880i	−0.242746	−	0.420448i
$116$	0.414466	+	2.35055i	0.0384822	+	0.218243i
$117$	5.37570	−	5.64281i	0.496984	−	0.521678i
$118$	−0.978027	−	0.820662i	−0.0900347	−	0.0755480i
$119$	5.43380	−	10.2465i	0.498116	−	0.939291i
$120$	−0.820631	+	2.05114i	−0.0749130	+	0.187242i
$121$	5.35713	+	9.27882i	0.487012	+	0.843529i
$122$	5.17719	−	8.96715i	0.468720	−	0.811847i
$123$	−13.1544	+	10.3494i	−1.18610	+	0.933175i
$124$	3.33575	+	0.588183i	0.299559	+	0.0528204i
$125$	−9.24899	+	5.33991i	−0.827255	+	0.477616i
$126$	6.76409	+	4.15297i	0.602593	+	0.369976i
$127$	17.0830	+	3.01220i	1.51587	+	0.267289i	0.868809	−	0.495147i	$-0.164886\pi$
$127$	17.0830	+	3.01220i	1.51587	+	0.267289i	0.647064	+	0.762436i	$0.275997\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	0.939330	+	0.375813i	0.0827034	+	0.0330885i
$130$	2.53831	−	2.12989i	0.222624	−	0.186804i
$131$	14.1246	+	16.8330i	1.23407	+	1.47071i	0.831695	+	0.555232i	$0.187371\pi$
$131$	14.1246	+	16.8330i	1.23407	+	1.47071i	0.402375	+	0.915475i	$0.368185\pi$
$132$	−7.90038	−	1.65129i	−0.687640	−	0.143726i
$133$	−11.0389	+	3.33822i	−0.957190	+	0.289461i
$134$			8.83071i			0.762857i
$135$	−6.60643	+	0.529570i	−0.568591	+	0.0455782i
$136$	−2.81777	−	3.35809i	−0.241622	−	0.287954i
$137$	−3.86789	−	0.682013i	−0.330456	−	0.0582683i	0.00595877	−	0.999982i	$-0.498103\pi$
$137$	−3.86789	−	0.682013i	−0.330456	−	0.0582683i	−0.336415	+	0.941714i	$0.609214\pi$
$138$	−0.222770	+	7.06643i	−0.0189634	+	0.601534i
$139$	−2.96098	+	16.7926i	−0.251147	+	1.42433i	0.554625	+	0.832101i	$0.312862\pi$
$139$	−2.96098	+	16.7926i	−0.251147	+	1.42433i	−0.805772	+	0.592226i	$0.798249\pi$
$140$	2.66150	+	2.07472i	0.224938	+	0.175346i
$141$	2.92444	+	8.89770i	0.246282	+	0.749322i
$142$	−0.00862544	+	0.0489173i	−0.000723831	+	0.00410505i
$143$	9.27344	+	7.78134i	0.775484	+	0.650709i
$144$	2.41503	−	1.77978i	0.201253	−	0.148315i
$145$	−2.63648	+	1.52217i	−0.218948	+	0.126410i
$146$	−0.604599	+	3.42885i	−0.0500370	+	0.283774i
$147$	8.96479	−	8.16288i	0.739403	−	0.673263i
$148$	2.60834	−	3.10849i	0.214404	−	0.255517i
$149$	−4.99562	+	13.7253i	−0.409257	+	1.12442i	0.548326	+	0.836265i	$0.315265\pi$
$149$	−4.99562	+	13.7253i	−0.409257	+	1.12442i	−0.957583	+	0.288159i	$0.906957\pi$
$150$	5.83954	+	0.184092i	0.476797	+	0.0150311i
$151$	−17.0223	+	9.82780i	−1.38525	+	0.799775i	−0.992775	−	0.119987i	$-0.961715\pi$
$151$	−17.0223	+	9.82780i	−1.38525	+	0.799775i	−0.392476	+	0.919762i	$0.628381\pi$
$152$	−0.397850	+	4.34070i	−0.0322699	+	0.352078i
$153$	5.26738	−	12.0501i	0.425842	−	0.974190i
$154$	−5.77615	+	10.8920i	−0.465455	+	0.877703i
$155$	0.750219	+	4.25470i	0.0602590	+	0.341746i
$156$	−4.45367	+	0.641335i	−0.356579	+	0.0513479i
$157$	7.31509	+	2.66248i	0.583808	+	0.212489i	0.617004	−	0.786960i	$-0.288346\pi$
$157$	7.31509	+	2.66248i	0.583808	+	0.212489i	−0.0331960	+	0.999449i	$0.510569\pi$
$158$	1.39629	+	3.83628i	0.111083	+	0.305198i
$159$	−12.8135	+	4.21148i	−1.01618	+	0.333992i
$160$	1.10460	−	0.637743i	0.0873265	−	0.0504180i
$161$	10.2746	+	3.32602i	0.809750	+	0.262127i
$162$	8.00312	+	4.11704i	0.628785	+	0.323466i
$163$	21.7214			1.70135			0.850675	−	0.525692i	$-0.176194\pi$
$163$	21.7214			1.70135			0.850675	+	0.525692i	$0.176194\pi$
$164$	9.66350			0.754592
$165$	−1.46730	−	10.1895i	−0.114229	−	0.793250i
$166$	0.759860	−	0.133984i	0.0589766	−	0.0103992i
$167$	1.05217	+	0.882874i	0.0814192	+	0.0683188i	0.682589	−	0.730803i	$-0.260854\pi$
$167$	1.05217	+	0.882874i	0.0814192	+	0.0683188i	−0.601170	+	0.799121i	$0.705298\pi$
$168$	−1.58662	−	4.29914i	−0.122411	−	0.331686i
$169$	−5.87417	−	2.13802i	−0.451859	−	0.164463i
$170$	2.79566	−	4.84222i	0.214417	−	0.371381i
$171$	−12.1957	+	4.71860i	−0.932628	+	0.360841i
$172$	−0.292058	−	0.505860i	−0.0222692	−	0.0385714i
$173$	13.2349	−	11.1054i	1.00623	−	0.844326i	0.0183939	−	0.999831i	$-0.494145\pi$
$173$	13.2349	−	11.1054i	1.00623	−	0.844326i	0.987835	+	0.155504i	$0.0497003\pi$
$174$	4.13203	+	0.130263i	0.313248	+	0.00987520i
$175$	2.74855	−	8.49069i	0.207771	−	0.641836i
$176$	2.99530	+	3.56966i	0.225779	+	0.269073i
$177$	−1.73794	+	1.36735i	−0.130632	+	0.102776i
$178$	−5.51905			−0.413670
$179$	−10.8367	+	18.7697i	−0.809974	+	1.40292i	0.102907	+	0.994691i	$0.467186\pi$
$179$	−10.8367	+	18.7697i	−0.809974	+	1.40292i	−0.912881	+	0.408226i	$0.866148\pi$
$180$	3.18672	+	2.11816i	0.237524	+	0.157878i
$181$	−3.03649	−	8.34269i	−0.225701	−	0.620107i	0.774217	−	0.632920i	$-0.218144\pi$
$181$	−3.03649	−	8.34269i	−0.225701	−	0.620107i	−0.999918	+	0.0128125i	$0.995922\pi$
$182$	−0.949146	+	6.80742i	−0.0703554	+	0.504600i
$183$	−13.3684	−	11.9551i	−0.988221	−	0.883747i
$184$	2.62375	−	3.12686i	0.193425	−	0.230515i
$185$	4.86359	+	1.77020i	0.357579	+	0.130148i
$186$	2.17929	−	5.44704i	0.159793	−	0.399396i
$187$	19.1954	+	6.98654i	1.40370	+	0.510907i
$188$	1.84946	−	5.08134i	0.134885	−	0.370595i
$189$	9.43795	−	9.99626i	0.686510	−	0.727121i
$190$	−5.37617	+	1.41675i	−0.390029	+	0.102782i
$191$	2.38397	+	1.37639i	0.172498	+	0.0995920i	0.583763	−	0.811924i	$-0.301580\pi$
$191$	2.38397	+	1.37639i	0.172498	+	0.0995920i	−0.411265	+	0.911516i	$0.634913\pi$
$192$	−1.73119	−	0.0545760i	−0.124938	−	0.00393869i
$193$	7.65265	+	9.12008i	0.550850	+	0.656477i	0.967584	−	0.252551i	$-0.0812696\pi$
$193$	7.65265	+	9.12008i	0.550850	+	0.656477i	−0.416734	+	0.909029i	$0.636825\pi$
$194$	2.07068	+	5.68915i	0.148666	+	0.408458i
$195$	−2.71156	−	5.05824i	−0.194179	−	0.362228i
$196$	−6.98187	+	0.503536i	−0.498705	+	0.0359668i
$197$	8.32973	+	4.80917i	0.593469	+	0.342639i	0.766468	−	0.642283i	$-0.222012\pi$
$197$	8.32973	+	4.80917i	0.593469	+	0.342639i	−0.172999	+	0.984922i	$0.555346\pi$
$198$	−5.59924	+	12.8093i	−0.397920	+	0.910314i
$199$	12.9663	+	10.8800i	0.919155	+	0.771262i	0.973838	−	0.227241i	$-0.0729706\pi$
$199$	12.9663	+	10.8800i	0.919155	+	0.771262i	−0.0546838	+	0.998504i	$0.517415\pi$
$200$	−2.58397	−	2.16821i	−0.182714	−	0.153316i
$201$	14.9717	+	3.12929i	1.05602	+	0.220723i
$202$	−6.42958	−	3.71212i	−0.452383	−	0.261184i
$203$	1.94486	−	6.00797i	0.136502	−	0.421677i
$204$	−6.69187	+	3.58730i	−0.468524	+	0.251161i
$205$	4.21562	+	11.5823i	0.294432	+	0.808945i
$206$	8.64632	+	10.3043i	0.602418	+	0.717933i
$207$	11.9016	+	2.88178i	0.827216	+	0.200298i
$208$	2.24981	+	1.29893i	0.155996	+	0.0900643i
$209$	−8.50798	−	18.4441i	−0.588510	−	1.27581i
$210$	4.46065	−	3.77714i	0.307814	−	0.260647i
$211$	1.27357	−	3.49910i	0.0876761	−	0.240888i	−0.888104	−	0.459643i	$-0.847977\pi$
$211$	1.27357	−	3.49910i	0.0876761	−	0.240888i	0.975780	+	0.218755i	$0.0701995\pi$
$212$	7.31761	+	2.66339i	0.502576	+	0.182923i
$213$	0.0798785	+	0.0319583i	0.00547318	+	0.00218974i
$214$	11.1978	+	4.07565i	0.765463	+	0.278606i
$215$	0.478898	−	0.570728i	0.0326605	−	0.0389233i
$216$	−2.16166	−	4.72517i	−0.147082	−	0.321507i
$217$	−7.06794	−	5.50967i	−0.479803	−	0.374021i
$218$	−2.62517	−	7.21260i	−0.177799	−	0.488499i
$219$	5.59907	+	2.24011i	0.378350	+	0.151373i
$220$	−2.97179	+	5.14729i	−0.200358	+	0.347030i
$221$	11.3881			0.766049
$222$	−4.34588	−	5.52375i	−0.291676	−	0.370730i
$223$	−6.66654	−	7.94487i	−0.446424	−	0.532028i	0.495161	−	0.868801i	$-0.335109\pi$
$223$	−6.66654	−	7.94487i	−0.446424	−	0.532028i	−0.941586	+	0.336773i	$0.890664\pi$
$224$	−0.814835	+	2.51715i	−0.0544435	+	0.168184i
$225$	2.38144	−	9.83520i	0.158763	−	0.655680i
$226$	13.0851	−	10.9797i	0.870410	−	0.730360i
$227$	−6.48864	−	11.2387i	−0.430666	−	0.745936i	0.566265	−	0.824223i	$-0.308388\pi$
$227$	−6.48864	−	11.2387i	−0.430666	−	0.745936i	−0.996931	+	0.0782878i	$0.975055\pi$
$228$	7.21830	+	2.21271i	0.478044	+	0.146541i
$229$	−11.2692	+	19.5189i	−0.744693	+	1.28985i	0.205646	+	0.978626i	$0.434071\pi$
$229$	−11.2692	+	19.5189i	−0.744693	+	1.28985i	−0.950338	+	0.311219i	$0.899263\pi$
$230$	4.89234	+	1.78067i	0.322591	+	0.117414i
$231$	16.4196	+	13.6527i	1.08033	+	0.898282i
$232$	−1.82841	−	1.53421i	−0.120041	−	0.100726i
$233$	7.65566	−	1.34990i	0.501539	−	0.0884348i	0.0828453	−	0.996562i	$-0.473599\pi$
$233$	7.65566	−	1.34990i	0.501539	−	0.0884348i	0.418694	+	0.908128i	$0.362488\pi$
$234$	−0.490898	+	7.77808i	−0.0320910	+	0.508469i
$235$	6.89712			0.449919
$236$	1.27672			0.0831076
$237$	6.99888	−	1.00785i	0.454626	−	0.0654667i
$238$	2.42376	+	11.3420i	0.157109	+	0.735194i
$239$	−6.68292	+	3.85839i	−0.432282	+	0.249578i	−0.700319	−	0.713830i	$-0.746959\pi$
$239$	−6.68292	+	3.85839i	−0.432282	+	0.249578i	0.268036	+	0.963409i	$0.413625\pi$
$240$	−0.689805	−	2.09875i	−0.0445267	−	0.135474i
$241$	1.29233	+	3.55063i	0.0832460	+	0.228716i	0.974331	−	0.225120i	$-0.0722773\pi$
$241$	1.29233	+	3.55063i	0.0832460	+	0.228716i	−0.891085	+	0.453836i	$0.850055\pi$
$242$	−10.0681	−	3.66449i	−0.647203	−	0.235563i
$243$	9.81612	−	12.1097i	0.629704	−	0.776835i
$244$	1.79802	+	10.1971i	0.115106	+	0.652800i
$245$	−3.64930	−	8.14855i	−0.233145	−	0.520592i
$246$	3.42441	−	16.3836i	0.218332	−	1.04458i
$247$	−7.97395	−	8.04015i	−0.507370	−	0.511583i
$248$	−2.93341	+	1.69360i	−0.186272	+	0.107544i
$249$	0.0421099	−	1.33576i	0.00266860	−	0.0846501i
$250$	3.65271	−	10.0357i	0.231018	−	0.634716i
$251$	11.7944	−	14.0560i	0.744453	−	0.887205i	−0.252306	−	0.967647i	$-0.581189\pi$
$251$	11.7944	−	14.0560i	0.744453	−	0.887205i	0.996759	+	0.0804429i	$0.0256335\pi$
$252$	−7.85107	+	1.16652i	−0.494571	+	0.0734836i
$253$	−3.30292	+	18.7318i	−0.207653	+	1.17766i
$254$	−15.0226	+	8.67328i	−0.942599	+	0.544210i
$255$	−7.21888	−	6.45570i	−0.452064	−	0.404272i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−0.312636	+	1.77305i	−0.0195017	+	0.110600i	−0.993005	−	0.118074i	$-0.962328\pi$
$257$	−0.312636	+	1.77305i	−0.0195017	+	0.110600i	0.973503	+	0.228674i	$0.0734390\pi$
$258$	−0.961137	+	0.315900i	−0.0598377	+	0.0196671i
$259$	−9.94991	+	4.03266i	−0.618257	+	0.250577i
$260$	−0.575387	+	3.26318i	−0.0356840	+	0.202374i
$261$	1.68510	−	6.95934i	0.104305	−	0.430772i
$262$	−21.6401	−	3.81573i	−1.33693	−	0.235737i
$263$	10.8509	+	12.9317i	0.669098	+	0.797400i	0.988661	−	0.150165i	$-0.0479805\pi$
$263$	10.8509	+	12.9317i	0.669098	+	0.797400i	−0.319563	+	0.947565i	$0.603536\pi$
$264$	7.11347	−	3.81331i	0.437804	−	0.234693i
$265$			9.93252i			0.610150i
$266$	6.31048	−	9.65287i	0.386920	−	0.591855i
$267$	−1.95576	+	9.35707i	−0.119690	+	0.572643i
$268$	−5.67627	−	6.76472i	−0.346733	−	0.413221i
$269$	−9.20724	+	7.72579i	−0.561375	+	0.471050i	−0.878771	−	0.477243i	$-0.841636\pi$
$269$	−9.20724	+	7.72579i	−0.561375	+	0.471050i	0.317396	+	0.948293i	$0.397192\pi$
$270$	4.72042	−	4.65220i	0.287275	−	0.283124i
$271$	−3.12429	−	17.7187i	−0.189787	−	1.07633i	−0.919649	−	0.392741i	$-0.871527\pi$
$271$	−3.12429	−	17.7187i	−0.189787	−	1.07633i	0.729862	−	0.683594i	$-0.239584\pi$
$272$	4.31707	+	0.761217i	0.261761	+	0.0461555i
$273$	11.2050	+	4.02151i	0.678160	+	0.243393i
$274$	3.40136	−	1.96378i	0.205484	−	0.118636i
$275$	15.4795	+	2.72946i	0.933451	+	0.164593i
$276$	−4.37156	−	5.55639i	−0.263137	−	0.334455i
$277$	−6.59531	+	11.4234i	−0.396273	+	0.686366i	−0.993263	−	0.115883i	$-0.963030\pi$
$277$	−6.59531	+	11.4234i	−0.396273	+	0.686366i	0.596989	+	0.802249i	$0.296363\pi$
$278$	−8.52581	−	14.7671i	−0.511344	−	0.885674i
$279$	−8.46272	−	5.62503i	−0.506650	−	0.336762i
$280$	−3.37243	+	0.121453i	−0.201541	+	0.00725821i
$281$	19.9046	+	16.7020i	1.18741	+	0.996356i	0.999901	+	0.0140931i	$0.00448612\pi$
$281$	19.9046	+	16.7020i	1.18741	+	0.996356i	0.187510	+	0.982263i	$0.439958\pi$
$282$	−7.95959	−	4.93624i	−0.473986	−	0.293949i
$283$	−3.26457	−	18.5143i	−0.194058	−	1.10056i	−0.913754	−	0.406269i	$-0.866830\pi$
$283$	−3.26457	−	18.5143i	−0.194058	−	1.10056i	0.719695	−	0.694290i	$-0.244282\pi$
$284$	−0.0248360	−	0.0430172i	−0.00147374	−	0.00255260i
$285$	0.496844	+	9.61688i	0.0294305	+	0.569655i
$286$	−12.1056			−0.715820
$287$	−22.5876	−	11.9784i	−1.33330	−	0.707065i
$288$	−0.706002	+	2.91574i	−0.0416016	+	0.171812i
$289$	2.08291	−	0.758117i	0.122524	−	0.0445951i
$290$	1.04123	−	2.86075i	0.0611430	−	0.167989i
$291$	10.3792	−	1.49463i	0.608442	−	0.0876165i
$292$	−1.74087	−	3.01528i	−0.101877	−	0.176456i
$293$	−15.5152	−	26.8731i	−0.906407	−	1.56994i	−0.819017	−	0.573769i	$-0.805481\pi$
$293$	−15.5152	−	26.8731i	−0.906407	−	1.56994i	−0.0873902	−	0.996174i	$-0.527853\pi$
$294$	−1.62043	+	12.0156i	−0.0945053	+	0.700763i
$295$	0.556960	+	1.53024i	0.0324275	+	0.0890937i
$296$			4.05785i			0.235858i
$297$	19.7328	+	14.0322i	1.14501	+	0.814229i
$298$	−4.99562	−	13.7253i	−0.289388	−	0.795088i
$299$	1.84136	+	10.4429i	0.106489	+	0.603928i
$300$	−4.59168	+	3.61256i	−0.265101	+	0.208571i
$301$	0.0556202	+	1.54443i	0.00320589	+	0.0890192i
$302$	6.72261	−	18.4702i	0.386843	−	1.06284i
$303$	−8.57199	+	9.58534i	−0.492448	+	0.550664i
$304$	−2.48538	−	3.58091i	−0.142546	−	0.205379i
$305$	−11.4375	+	6.60343i	−0.654908	+	0.378111i
$306$	3.71059	+	12.6167i	0.212120	+	0.721248i
$307$	−16.0743	+	2.83433i	−0.917408	+	0.161764i	−0.612365	−	0.790575i	$-0.709782\pi$
$307$	−16.0743	+	2.83433i	−0.917408	+	0.161764i	−0.305043	+	0.952339i	$0.598671\pi$
$308$	−2.57647	−	12.0566i	−0.146808	−	0.686989i
$309$	20.5340	−	11.0076i	1.16814	−	0.626201i
$310$	−3.30957	−	2.77706i	−0.187971	−	0.157726i
$311$			8.03591i			0.455675i	0.973699	+	0.227837i	$0.0731655\pi$
$311$			8.03591i			0.455675i	−0.973699	+	0.227837i	$0.926835\pi$
$312$	2.99947	−	3.35406i	0.169812	−	0.189886i
$313$	−3.72311	+	21.1148i	−0.210443	+	1.19348i	0.678199	+	0.734878i	$0.262761\pi$
$313$	−3.72311	+	21.1148i	−0.210443	+	1.19348i	−0.888642	+	0.458602i	$0.848350\pi$
$314$	−7.31509	+	2.66248i	−0.412814	+	0.150252i
$315$	−4.82311	−	8.90113i	−0.271751	−	0.501522i
$316$	−3.53553	−	2.04124i	−0.198889	−	0.114829i
$317$	−3.39058	−	2.84504i	−0.190434	−	0.159793i	0.542586	−	0.840000i	$-0.317445\pi$
$317$	−3.39058	−	2.84504i	−0.190434	−	0.159793i	−0.733020	+	0.680207i	$0.761890\pi$
$318$	7.10866	−	11.4626i	0.398634	−	0.642789i
$319$	10.9532	+	1.93135i	0.613263	+	0.108135i
$320$	−0.436242	+	1.19856i	−0.0243867	+	0.0670018i
$321$	10.8780	−	17.5406i	0.607151	−	0.979018i
$322$	−10.0087	+	4.05649i	−0.557763	+	0.226059i
$323$	−17.2842	−	8.14690i	−0.961718	−	0.453306i
$324$	−8.77713	+	1.99047i	−0.487618	+	0.110582i
$325$	8.62978	−	1.52166i	0.478694	−	0.0844067i
$326$	−16.6395	+	13.9622i	−0.921579	+	0.773297i
$327$	−13.1586	+	1.89486i	−0.727673	+	0.104786i
$328$	−7.40267	+	6.21158i	−0.408744	+	0.342977i
$329$	−10.6215	+	9.58469i	−0.585585	+	0.528421i
$330$	7.67369	+	6.86243i	0.422423	+	0.377764i
$331$		−	29.4368i		−	1.61799i	−0.587814	−	0.808996i	$-0.700012\pi$
$331$		−	29.4368i		−	1.61799i	0.587814	−	0.808996i	$-0.299988\pi$
$332$	−0.495963	+	0.591066i	−0.0272195	+	0.0324390i
$333$	−10.9051	+	5.41063i	−0.597594	+	0.296501i
$334$	−1.37351			−0.0751550
$335$	5.63172	−	9.75443i	0.307694	−	0.532941i
$336$	3.97886	+	2.27347i	0.217065	+	0.124028i
$337$	14.7632	+	17.5940i	0.804200	+	0.958409i	0.999752	−	0.0222849i	$-0.00709408\pi$
$337$	14.7632	+	17.5940i	0.804200	+	0.958409i	−0.195551	+	0.980693i	$0.562650\pi$
$338$	5.87417	−	2.13802i	0.319513	−	0.116293i
$339$	−13.9783	−	26.0755i	−0.759195	−	1.41623i
$340$	0.970921	+	5.50637i	0.0526556	+	0.298625i
$341$	7.89195	−	13.6693i	0.427373	−	0.740232i
$342$	6.30938	−	11.4539i	0.341172	−	0.619356i
$343$	16.9437	+	7.47743i	0.914872	+	0.403743i
$344$	0.548890	+	0.199780i	0.0295942	+	0.0107714i
$345$	4.75264	−	7.66353i	0.255873	−	0.412590i
$346$	−3.00010	+	17.0144i	−0.161287	+	0.914701i
$347$	−6.09508	+	16.7461i	−0.327201	+	0.898978i	0.661616	+	0.749843i	$0.269871\pi$
$347$	−6.09508	+	16.7461i	−0.327201	+	0.898978i	−0.988817	+	0.149135i	$0.952351\pi$
$348$	−3.24905	+	2.55623i	−0.174167	+	0.137028i
$349$	12.6233	−	21.8642i	0.675711	−	1.17037i	−0.300549	−	0.953766i	$-0.597170\pi$
$349$	12.6233	−	21.8642i	0.675711	−	1.17037i	0.976261	−	0.216600i	$-0.0694966\pi$
$350$	3.35220	+	8.27098i	0.179182	+	0.442102i
$351$	13.0131	+	3.58856i	0.694588	+	0.191543i
$352$	−4.58906	−	0.809176i	−0.244598	−	0.0431292i
$353$	−14.6939	−	8.48352i	−0.782076	−	0.451532i	0.0550892	−	0.998481i	$-0.482456\pi$
$353$	−14.6939	−	8.48352i	−0.782076	−	0.451532i	−0.837166	+	0.546949i	$0.815789\pi$
$354$	0.452426	−	2.16457i	0.0240462	−	0.115046i
$355$	0.0407243	−	0.0485334i	0.00216142	−	0.00257588i
$356$	4.22784	−	3.54758i	0.224075	−	0.188021i
$357$	20.0883	−	0.0900613i	1.06319	−	0.00476655i
$358$	−3.76355	−	21.3442i	−0.198910	−	1.12807i
$359$	−9.44482	−	11.2559i	−0.498478	−	0.594063i	0.456874	−	0.889531i	$-0.348969\pi$
$359$	−9.44482	−	11.2559i	−0.498478	−	0.594063i	−0.955353	+	0.295468i	$0.904524\pi$
$360$	−3.80269	+	0.425780i	−0.200420	+	0.0224406i
$361$	6.35055	+	17.9073i	0.334239	+	0.942488i
$362$	7.68867	+	4.43905i	0.404107	+	0.233312i
$363$	−9.78062	+	15.7710i	−0.513349	+	0.827765i
$364$	−3.64864	−	5.82489i	−0.191241	−	0.305307i
$365$	2.85457	−	3.40194i	0.149415	−	0.178066i
$366$	17.9254	+	0.565100i	0.936975	+	0.0295383i
$367$	18.8071	−	6.84524i	0.981725	−	0.357319i	0.199214	−	0.979956i	$-0.436161\pi$
$367$	18.8071	−	6.84524i	0.981725	−	0.357319i	0.782510	+	0.622637i	$0.213939\pi$
$368$			4.08183i			0.212780i
$369$	−26.5635	−	11.6116i	−1.38284	−	0.604474i
$370$	−4.86359	+	1.77020i	−0.252846	+	0.0920285i
$371$	−13.8029	−	15.2960i	−0.716609	−	0.794131i
$372$	1.83186	+	5.57349i	0.0949776	+	0.288972i
$373$	−9.90211	+	5.71698i	−0.512712	+	0.296014i	−0.733948	−	0.679206i	$-0.762324\pi$
$373$	−9.90211	+	5.71698i	−0.512712	+	0.296014i	0.221236	+	0.975220i	$0.428991\pi$
$374$	−19.1954	+	6.98654i	−0.992569	+	0.361266i
$375$	−15.7203	−	9.74917i	−0.811795	−	0.503445i
$376$	1.84946	+	5.08134i	0.0953784	+	0.262050i
$377$	6.10639	−	1.07672i	0.314495	−	0.0554540i
$378$	−0.804417	+	13.7242i	−0.0413747	+	0.705895i
$379$		−	0.746950i		−	0.0383682i	−0.999816	−	0.0191841i	$-0.993893\pi$
$379$		−	0.746950i		−	0.0383682i	0.999816	−	0.0191841i	$-0.00610687\pi$
$380$	3.20772	−	4.54103i	0.164553	−	0.232950i
$381$	9.38132	+	28.5430i	0.480620	+	1.46230i
$382$	−2.71096	+	0.478015i	−0.138705	+	0.0244574i
$383$	−3.81936	−	1.39013i	−0.195160	−	0.0710325i	0.242591	−	0.970129i	$-0.422003\pi$
$383$	−3.81936	−	1.39013i	−0.195160	−	0.0710325i	−0.437751	+	0.899096i	$0.644225\pi$
$384$	1.36125	−	1.07098i	0.0694660	−	0.0546532i
$385$	13.3267	−	8.34766i	0.679189	−	0.425436i
$386$	−11.7245	−	2.06735i	−0.596764	−	0.105226i
$387$	0.194989	+	1.74147i	0.00991182	+	0.0885238i
$388$	−5.24315	−	3.02714i	−0.266181	−	0.153680i
$389$	−24.7290	+	29.4709i	−1.25381	+	1.49424i	−0.457674	+	0.889120i	$0.651317\pi$
$389$	−24.7290	+	29.4709i	−1.25381	+	1.49424i	−0.796138	+	0.605115i	$0.793127\pi$
$390$	5.32855	+	2.13188i	0.269822	+	0.107952i
$391$	8.94670	+	15.4961i	0.452454	+	0.783674i
$392$	5.02475	−	4.87359i	0.253788	−	0.246153i
$393$	−14.1377	+	35.3368i	−0.713155	+	1.78250i
$394$	−9.47222	+	1.67021i	−0.477203	+	0.0841438i
$395$	0.904212	−	5.12804i	0.0454958	−	0.258020i
$396$	−3.94436	−	13.4116i	−0.198212	−	0.673957i
$397$	5.98359	−	5.02083i	0.300308	−	0.251988i	−0.480164	−	0.877178i	$-0.659423\pi$
$397$	5.98359	−	5.02083i	0.300308	−	0.251988i	0.780472	+	0.625190i	$0.214979\pi$
$398$	−16.9263			−0.848437
$399$	−14.1294	−	14.1195i	−0.707354	−	0.706860i
$400$	3.37314			0.168657
$401$	23.3129	−	19.5619i	1.16419	−	0.976873i	0.164237	−	0.986421i	$-0.447484\pi$
$401$	23.3129	−	19.5619i	1.16419	−	0.976873i	0.999954	+	0.00954798i	$0.00303926\pi$
$402$	−13.4805	+	7.22645i	−0.672344	+	0.360422i
$403$	1.52801	−	8.66579i	0.0761157	−	0.431674i
$404$	7.31144	−	1.28921i	0.363758	−	0.0641403i
$405$	−6.21466	−	9.65163i	−0.308809	−	0.479594i
$406$	2.37200	+	5.85250i	0.117720	+	0.290455i
$407$	−9.45450	−	16.3757i	−0.468642	−	0.811712i
$408$	2.82040	−	7.04948i	0.139630	−	0.349001i
$409$	1.57243	−	1.87395i	0.0777516	−	0.0926608i	−0.725766	−	0.687941i	$-0.758515\pi$
$409$	1.57243	−	1.87395i	0.0777516	−	0.0926608i	0.803518	+	0.595281i	$0.202959\pi$
$410$	−10.6743	−	6.16283i	−0.527167	−	0.304360i
$411$	−2.12409	−	6.46261i	−0.104774	−	0.318777i
$412$	−13.2469	−	2.33579i	−0.652629	−	0.115076i
$413$	−2.98423	−	1.58257i	−0.146844	−	0.0778731i
$414$	−10.9695	+	5.44261i	−0.539122	+	0.267490i
$415$	−0.924791	−	0.336596i	−0.0453962	−	0.0165229i
$416$	−2.55839	+	0.451112i	−0.125435	+	0.0221176i
$417$	−28.0576	+	9.22181i	−1.37399	+	0.451594i
$418$	18.3731	+	8.66018i	0.898660	+	0.423583i
$419$			9.86310i			0.481844i	0.970545	+	0.240922i	$0.0774498\pi$
$419$			9.86310i			0.481844i	−0.970545	+	0.240922i	$0.922550\pi$
$420$	−0.989159	+	5.76070i	−0.0482660	+	0.281094i
$421$	2.04157	−	0.359983i	0.0994999	−	0.0175445i	−0.123677	−	0.992323i	$-0.539469\pi$
$421$	2.04157	−	0.359983i	0.0994999	−	0.0175445i	0.223176	+	0.974778i	$0.428357\pi$
$422$	1.27357	+	3.49910i	0.0619964	+	0.170334i
$423$	−11.1896	+	11.7456i	−0.544055	+	0.571088i
$424$	−7.31761	+	2.66339i	−0.355375	+	0.129346i
$425$	12.8057	−	7.39336i	0.621167	−	0.358631i
$426$	−0.0817328	+	0.0268634i	−0.00395997	+	0.00130154i
$427$	8.43711	−	26.0635i	0.408300	−	1.26130i
$428$	−11.1978	+	4.07565i	−0.541264	+	0.197004i
$429$	−4.28981	+	20.5240i	−0.207114	+	0.990909i
$430$			0.745032i			0.0359287i
$431$	−38.8192	+	14.1290i	−1.86986	+	0.680572i	−0.900530	+	0.434794i	$0.856821\pi$
$431$	−38.8192	+	14.1290i	−1.86986	+	0.680572i	−0.969326	+	0.245777i	$0.920957\pi$
$432$	4.69321	+	2.23020i	0.225802	+	0.107301i
$433$	11.7215	−	13.9692i	0.563300	−	0.671315i	−0.406941	−	0.913454i	$-0.633405\pi$
$433$	11.7215	−	13.9692i	0.563300	−	0.671315i	0.970241	+	0.242139i	$0.0778491\pi$
$434$	8.95591	−	0.322533i	0.429897	−	0.0154821i
$435$	−4.48118	−	2.77906i	−0.214856	−	0.133246i
$436$	6.64717	+	3.83775i	0.318342	+	0.183795i
$437$	4.67599	−	17.1668i	0.223683	−	0.821202i
$438$	−5.72905	+	1.88299i	−0.273745	+	0.0899727i
$439$	−19.3374	−	23.0454i	−0.922923	−	1.09990i	−0.994735	−	0.102479i	$-0.967323\pi$
$439$	−19.3374	−	23.0454i	−0.922923	−	1.09990i	0.0718121	−	0.997418i	$-0.477122\pi$
$440$	−1.03209	−	5.85328i	−0.0492031	−	0.279044i
$441$	19.7972	+	7.00520i	0.942722	+	0.333581i
$442$	−8.72382	+	7.32015i	−0.414950	+	0.348184i
$443$	−9.27941	+	11.0588i	−0.440878	+	0.525418i	−0.940028	−	0.341098i	$-0.889201\pi$
$443$	−9.27941	+	11.0588i	−0.440878	+	0.525418i	0.499150	+	0.866516i	$0.333646\pi$
$444$	6.87973	+	1.43796i	0.326498	+	0.0682426i
$445$	6.09636	+	3.51974i	0.288995	+	0.166851i
$446$	10.2137	+	1.80096i	0.483634	+	0.0852777i
$447$	−25.0404	+	3.60585i	−1.18437	+	0.170551i
$448$	−0.993792	−	2.45201i	−0.0469523	−	0.115847i
$449$	17.7125	−	30.6790i	0.835906	−	1.44783i	−0.0573850	−	0.998352i	$-0.518276\pi$
$449$	17.7125	−	30.6790i	0.835906	−	1.44783i	0.893291	−	0.449479i	$-0.148390\pi$
$450$	4.49765	+	9.06496i	0.212021	+	0.427326i
$451$	15.4013	−	42.3148i	0.725221	−	1.99253i
$452$	−2.96616	+	16.8219i	−0.139516	+	0.791236i
$453$	−28.9324	−	17.9428i	−1.35936	−	0.843027i
$454$	12.1947	+	4.43849i	0.572323	+	0.208309i
$455$	5.38981	−	6.91419i	0.252678	−	0.324142i
$456$	−6.95185	+	2.94480i	−0.325550	+	0.137903i
$457$	−9.37396	+	16.2362i	−0.438495	+	0.759496i	−0.997574	−	0.0696187i	$-0.977822\pi$
$457$	−9.37396	+	16.2362i	−0.438495	+	0.759496i	0.559078	+	0.829115i	$0.311155\pi$
$458$	−3.91377	−	22.1961i	−0.182878	−	1.03715i
$459$	22.7054	−	1.82006i	1.05980	−	0.0849532i
$460$	−4.89234	+	1.78067i	−0.228106	+	0.0830239i
$461$	−16.6219	−	19.8093i	−0.774161	−	0.922609i	0.224493	−	0.974476i	$-0.427927\pi$
$461$	−16.6219	−	19.8093i	−0.774161	−	0.922609i	−0.998654	+	0.0518663i	$0.983483\pi$
$462$	−21.3539	+	0.0957354i	−0.993475	+	0.00445402i
$463$	−19.0360	+	32.9713i	−0.884677	+	1.53231i	−0.0385946	+	0.999255i	$0.512288\pi$
$463$	−19.0360	+	32.9713i	−0.884677	+	1.53231i	−0.846083	+	0.533051i	$0.821045\pi$
$464$	2.38681			0.110805
$465$	−5.88106	+	4.62700i	−0.272727	+	0.214572i
$466$	−4.99688	+	5.95505i	−0.231476	+	0.275862i
$467$		−	16.7862i		−	0.776775i	−0.921496	−	0.388387i	$-0.873032\pi$
$467$		−	16.7862i		−	0.776775i	0.921496	−	0.388387i	$-0.126968\pi$
$468$	−4.62361	−	6.27390i	−0.213726	−	0.290011i
$469$	4.88256	+	22.8480i	0.225456	+	1.05502i
$470$	−5.28350	+	4.43339i	−0.243710	+	0.204497i
$471$	1.92178	+	13.3456i	0.0885511	+	0.614932i
$472$	−0.978027	+	0.820662i	−0.0450173	+	0.0377740i
$473$	−2.68055	+	0.472653i	−0.123252	+	0.0217326i
$474$	−4.71362	+	5.27085i	−0.216504	+	0.242098i
$475$	−14.1863	−	3.86413i	−0.650912	−	0.177299i
$476$	−9.14722	−	7.13053i	−0.419262	−	0.326827i
$477$	−16.9147	−	16.1140i	−0.774472	−	0.737811i
$478$	2.63929	−	7.25140i	0.120718	−	0.331671i
$479$	−33.0189	−	5.82212i	−1.50867	−	0.266019i	−0.642701	−	0.766117i	$-0.722186\pi$
$479$	−33.0189	−	5.82212i	−1.50867	−	0.266019i	−0.865969	+	0.500098i	$0.833297\pi$
$480$	1.87747	+	1.16434i	0.0856945	+	0.0531446i
$481$	−8.07541	−	6.77607i	−0.368207	−	0.308962i
$482$	−3.27228	−	1.88925i	−0.149048	−	0.0860531i
$483$	3.33069	+	18.4064i	0.151552	+	0.837519i
$484$	10.0681	−	3.66449i	0.457642	−	0.166568i
$485$	1.34094	−	7.60482i	0.0608887	−	0.345317i
$486$	0.264359	+	15.5862i	0.0119915	+	0.707005i
$487$			13.4789i			0.610788i	0.952226	+	0.305394i	$0.0987881\pi$
$487$			13.4789i			0.610788i	−0.952226	+	0.305394i	$0.901212\pi$
$488$	−7.93191	−	6.65566i	−0.359061	−	0.301288i
$489$	17.7753	+	33.1586i	0.803826	+	1.49948i
$490$	8.03332	+	3.89643i	0.362908	+	0.176023i
$491$	34.8454	−	6.14418i	1.57255	−	0.277283i	0.681717	−	0.731616i	$-0.261233\pi$
$491$	34.8454	−	6.14418i	1.57255	−	0.277283i	0.890832	+	0.454333i	$0.150122\pi$
$492$	7.90794	+	14.7517i	0.356517	+	0.665060i
$493$	9.06123	−	5.23150i	0.408097	−	0.235615i
$494$	11.2765	+	1.03356i	0.507354	+	0.0465019i
$495$	14.3539	−	10.5783i	0.645162	−	0.475458i
$496$	1.15849	−	3.18293i	0.0520179	−	0.142918i
$497$	0.00472981	+	0.131334i	0.000212161	+	0.00589115i
$498$	0.826349	+	1.05032i	0.0370296	+	0.0470658i
$499$	1.20206	+	6.81721i	0.0538115	+	0.305180i	0.999820	−	0.0189609i	$-0.00603581\pi$
$499$	1.20206	+	6.81721i	0.0538115	+	0.305180i	−0.946009	+	0.324141i	$0.894925\pi$
$500$	3.65271	+	10.0357i	0.163354	+	0.448812i
$501$	−0.486723	+	2.32866i	−0.0217452	+	0.104037i
$502$			18.3488i			0.818945i
$503$	8.05235	+	22.1237i	0.359037	+	0.986445i	0.979364	+	0.202102i	$0.0647774\pi$
$503$	8.05235	+	22.1237i	0.359037	+	0.986445i	−0.620328	+	0.784343i	$0.713000\pi$
$504$	5.26444	−	5.94017i	0.234497	−	0.264596i
$505$	4.73475	+	8.20083i	0.210694	+	0.364932i
$506$	−9.51037	−	16.4724i	−0.422788	−	0.732290i
$507$	−1.54323	−	10.7168i	−0.0685373	−	0.475949i
$508$	5.93287	−	16.3004i	0.263229	−	0.723215i
$509$	−8.58663	+	3.12528i	−0.380596	+	0.138526i	−0.525231	−	0.850959i	$-0.676021\pi$
$509$	−8.58663	+	3.12528i	−0.380596	+	0.138526i	0.144636	+	0.989485i	$0.453799\pi$
$510$	9.67963	+	0.305152i	0.428621	+	0.0135123i
$511$	0.331536	+	9.20587i	0.0146663	+	0.407244i
$512$	−1.00000			−0.0441942
$513$	−17.1833	−	14.7559i	−0.758660	−	0.651487i
$514$	−0.900200	−	1.55919i	−0.0397061	−	0.0687730i
$515$	−2.97927	−	16.8963i	−0.131282	−	0.744539i
$516$	0.533216	−	0.859800i	0.0234735	−	0.0378506i
$517$	−19.3027	−	16.1969i	−0.848933	−	0.712340i
$518$	5.02993	−	9.48487i	0.221002	−	0.416741i
$519$	27.7834	+	11.1157i	1.21955	+	0.487927i
$520$	−1.65676	−	2.86960i	−0.0726538	−	0.125840i
$521$	15.5510	−	26.9350i	0.681300	−	1.18005i	−0.293285	−	0.956025i	$-0.594748\pi$
$521$	15.5510	−	26.9350i	0.681300	−	1.18005i	0.974584	−	0.224020i	$-0.0719182\pi$
$522$	3.18252	+	6.41432i	0.139295	+	0.280747i
$523$	−24.9673	−	4.40242i	−1.09175	−	0.192504i	−0.401342	−	0.915928i	$-0.631456\pi$
$523$	−24.9673	−	4.40242i	−1.09175	−	0.192504i	−0.690404	+	0.723424i	$0.742567\pi$
$524$	19.0300	−	10.9870i	0.831329	−	0.479968i
$525$	15.2106	−	2.75241i	0.663846	−	0.120125i
$526$	−16.6246	−	2.93137i	−0.724868	−	0.127814i
$527$	−2.57840	−	14.6228i	−0.112317	−	0.636981i
$528$	−2.99809	+	7.49361i	−0.130475	+	0.326118i
$529$	4.85570	−	4.07441i	0.211117	−	0.177148i
$530$	−6.38450	−	7.60875i	−0.277325	−	0.330503i
$531$	−3.50952	−	1.53410i	−0.152300	−	0.0665742i
$532$	1.37063	+	11.4508i	0.0594245	+	0.496456i
$533$		−	25.1043i		−	1.08739i
$534$	−4.51641	−	8.42507i	−0.195444	−	0.364588i
$535$	−9.76986	−	11.6433i	−0.422388	−	0.503382i
$536$	8.69655	+	1.53344i	0.375634	+	0.0662344i
$537$	−37.5208	−	1.18285i	−1.61914	−	0.0510437i
$538$	2.08711	−	11.8366i	0.0899818	−	0.510312i
$539$	−8.92255	+	31.3749i	−0.384322	+	1.35141i
$540$	−0.625669	+	6.59802i	−0.0269245	+	0.283934i
$541$	−4.67939	+	26.5381i	−0.201183	+	1.14096i	0.702152	+	0.712027i	$0.252223\pi$
$541$	−4.67939	+	26.5381i	−0.201183	+	1.14096i	−0.903335	+	0.428936i	$0.858888\pi$
$542$	13.7827	+	11.5651i	0.592018	+	0.496762i
$543$	10.2506	−	11.4624i	0.439896	−	0.491900i
$544$	−3.79637	+	2.19184i	−0.162768	+	0.0939742i
$545$	−1.70001	+	9.64125i	−0.0728205	+	0.412986i
$546$	−11.1685	+	4.12181i	−0.477969	+	0.176397i
$547$	23.1593	−	27.6002i	0.990219	−	1.18010i	0.00657466	−	0.999978i	$-0.497907\pi$
$547$	23.1593	−	27.6002i	0.990219	−	1.18010i	0.983645	−	0.180119i	$-0.0576483\pi$
$548$	−1.34330	+	3.69069i	−0.0573831	+	0.157659i
$549$	7.31021	−	30.1907i	0.311992	−	1.28851i
$550$	−13.6125	+	7.85916i	−0.580438	+	0.335116i
$551$	−10.0382	−	2.73424i	−0.427640	−	0.116483i
$552$	6.92039	+	1.44646i	0.294551	+	0.0615653i
$553$	5.73378	+	9.15372i	0.243825	+	0.389256i
$554$	−2.29053	−	12.9902i	−0.0973151	−	0.551901i
$555$	1.27774	+	8.87310i	0.0542370	+	0.376642i
$556$	16.0233	+	5.83200i	0.679538	+	0.247332i
$557$	6.43508	+	17.6802i	0.272663	+	0.749135i	0.998144	+	0.0608934i	$0.0193950\pi$
$557$	6.43508	+	17.6802i	0.272663	+	0.749135i	−0.725481	+	0.688242i	$0.758383\pi$
$558$	10.0985	−	1.13071i	0.427504	−	0.0478668i
$559$	−1.31415	+	0.758724i	−0.0555826	+	0.0320906i
$560$	2.50536	−	2.26080i	0.105871	−	0.0955361i
$561$	5.04291	+	35.0199i	0.212912	+	1.47854i
$562$	−25.9836			−1.09605
$563$	43.1870			1.82012			0.910058	−	0.414481i	$-0.136037\pi$
$563$	43.1870			1.82012			0.910058	+	0.414481i	$0.136037\pi$
$564$	9.27035	−	1.33494i	0.390352	−	0.0562113i
$565$	−21.4561	+	3.78329i	−0.902665	+	0.159164i
$566$	14.4015	+	12.0843i	0.605342	+	0.507942i
$567$	22.9831	+	6.22719i	0.965199	+	0.261517i
$568$	0.0466763	+	0.0169888i	0.00195850	+	0.000712834i
$569$	−4.01376	+	6.95204i	−0.168266	+	0.291445i	−0.937810	−	0.347149i	$-0.887150\pi$
$569$	−4.01376	+	6.95204i	−0.168266	+	0.291445i	0.769545	+	0.638593i	$0.220483\pi$
$570$	−6.56222	−	7.04759i	−0.274861	−	0.295191i
$571$	−7.54116	−	13.0617i	−0.315588	−	0.546614i	0.663974	−	0.747755i	$-0.268868\pi$
$571$	−7.54116	−	13.0617i	−0.315588	−	0.546614i	−0.979562	+	0.201141i	$0.935535\pi$
$572$	9.27344	−	7.78134i	0.387742	−	0.325354i
$573$	−0.150236	+	4.76558i	−0.00627618	+	0.199085i
$574$	25.0027	−	5.34301i	1.04359	−	0.223013i
$575$	8.85026	+	10.5473i	0.369082	+	0.439854i
$576$	−1.33337	−	2.68740i	−0.0555573	−	0.111975i
$577$	14.8537			0.618370			0.309185	−	0.951002i	$-0.399944\pi$
$577$	14.8537			0.618370			0.309185	+	0.951002i	$0.399944\pi$
$578$	−1.10829	+	1.91962i	−0.0460989	+	0.0798456i
$579$	−7.65979	+	19.1453i	−0.318330	+	0.795653i
$580$	1.04123	+	2.86075i	0.0432346	+	0.118786i
$581$	1.89193	−	0.766792i	0.0784905	−	0.0318119i
$582$	−6.99024	+	7.81660i	−0.289755	+	0.324008i
$583$	23.3251	−	27.7978i	0.966027	−	1.15127i
$584$	3.27177	+	1.19083i	0.135387	+	0.0492768i
$585$	5.50266	−	8.27863i	0.227507	−	0.342279i
$586$	29.1590	+	10.6130i	1.20455	+	0.438420i
$587$	8.79349	−	24.1599i	0.362946	−	0.997186i	−0.615036	−	0.788499i	$-0.710859\pi$
$587$	8.79349	−	24.1599i	0.362946	−	0.997186i	0.977982	−	0.208688i	$-0.0669192\pi$
$588$	−6.48215	−	10.2461i	−0.267319	−	0.422540i
$589$	−8.51849	+	12.0593i	−0.350998	+	0.496893i
$590$	−1.41027	−	0.814221i	−0.0580600	−	0.0335210i
$591$	−0.524931	+	16.6512i	−0.0215928	+	0.684938i
$592$	−2.60834	−	3.10849i	−0.107202	−	0.127758i
$593$	4.86085	+	13.3551i	0.199611	+	0.548427i	0.998599	−	0.0529202i	$-0.0168529\pi$
$593$	4.86085	+	13.3551i	0.199611	+	0.548427i	−0.798987	+	0.601348i	$0.794631\pi$
$594$	−24.1359	+	1.93473i	−0.990308	+	0.0793830i
$595$	4.55600	−	14.0742i	0.186778	−	0.576985i
$596$	12.6493	+	7.30310i	0.518137	+	0.299147i
$597$	−5.99808	+	28.6970i	−0.245485	+	1.17449i
$598$	−8.12313	−	6.81612i	−0.332179	−	0.278732i
$599$	−1.41638	−	1.18849i	−0.0578718	−	0.0485602i	0.613393	−	0.789778i	$-0.289804\pi$
$599$	−1.41638	−	1.18849i	−0.0578718	−	0.0485602i	−0.671265	+	0.741218i	$0.734249\pi$
$600$	1.19532	−	5.71886i	0.0487988	−	0.233471i
$601$	18.7390	+	10.8190i	0.764381	+	0.441316i	0.830867	−	0.556472i	$-0.187845\pi$
$601$	18.7390	+	10.8190i	0.764381	+	0.441316i	−0.0664854	+	0.997787i	$0.521179\pi$
$602$	−1.03535	−	1.14735i	−0.0421975	−	0.0467624i
$603$	7.47481	+	25.4157i	0.304398	+	1.03501i
$604$	6.72261	+	18.4702i	0.273539	+	0.751543i
$605$	8.78427	+	10.4687i	0.357131	+	0.425612i
$606$	0.405185	−	12.8528i	0.0164595	−	0.522108i
$607$	34.3581	+	19.8367i	1.39455	+	0.805145i	0.993815	−	0.111048i	$-0.0354206\pi$
$607$	34.3581	+	19.8367i	1.39455	+	0.805145i	0.400738	+	0.916193i	$0.368754\pi$
$608$	4.20567	+	1.14556i	0.170563	+	0.0464587i
$609$	10.7630	−	1.94759i	0.436137	−	0.0789205i
$610$	4.51701	−	12.4104i	0.182888	−	0.502482i
$611$	−13.2006	−	4.80461i	−0.534038	−	0.194374i
$612$	−10.9523	−	7.27983i	−0.442721	−	0.294270i
$613$	−39.5271	−	14.3867i	−1.59648	−	0.581072i	−0.617779	−	0.786352i	$-0.711967\pi$
$613$	−39.5271	−	14.3867i	−1.59648	−	0.581072i	−0.978703	+	0.205280i	$0.934190\pi$
$614$	10.4917	−	12.5036i	0.423412	−	0.504603i
$615$	−14.2311	+	15.9135i	−0.573855	+	0.641694i
$616$	9.72352	+	7.57977i	0.391772	+	0.305398i
$617$	−7.69406	−	21.1392i	−0.309751	−	0.851034i	−0.992705	−	0.120572i	$-0.961527\pi$
$617$	−7.69406	−	21.1392i	−0.309751	−	0.851034i	0.682954	−	0.730462i	$-0.260695\pi$
$618$	−8.65438	+	21.6313i	−0.348130	+	0.870138i
$619$	9.01973	−	15.6226i	0.362533	−	0.627926i	−0.625844	−	0.779949i	$-0.715245\pi$
$619$	9.01973	−	15.6226i	0.362533	−	0.627926i	0.988377	+	0.152022i	$0.0485785\pi$
$620$	4.32034			0.173509
$621$	5.34026	+	20.5265i	0.214297	+	0.823701i
$622$	−5.16539	−	6.15587i	−0.207113	−	0.246828i
$623$	−14.2796	+	3.05152i	−0.572101	+	0.122257i
$624$	−0.141780	+	4.49738i	−0.00567576	+	0.180039i
$625$	2.48484	−	2.08503i	0.0993935	−	0.0834011i
$626$	−10.7203	−	18.5681i	−0.428468	−	0.742129i
$627$	21.1934	−	28.0812i	0.846382	−	1.12145i
$628$	3.89228	−	6.74162i	0.155319	−	0.269020i
$629$	−16.7155	−	6.08395i	−0.666491	−	0.242583i
$630$	9.41625	+	3.71842i	0.375152	+	0.148146i
$631$	−11.3744	−	9.54430i	−0.452810	−	0.379952i	0.387668	−	0.921799i	$-0.373281\pi$
$631$	−11.3744	−	9.54430i	−0.452810	−	0.379952i	−0.840477	+	0.541847i	$0.817725\pi$
$632$	4.02046	−	0.708916i	0.159925	−	0.0281992i
$633$	6.38373	−	0.919266i	0.253731	−	0.0365376i
$634$	4.42609			0.175783
$635$	22.1253			0.878015
$636$	1.92245	+	13.3502i	0.0762299	+	0.529369i
$637$	1.30811	+	18.1379i	0.0518293	+	0.718648i
$638$	−9.63211	+	5.56110i	−0.381339	+	0.220166i
$639$	0.0165814	+	0.148090i	0.000655949	+	0.00585837i
$640$	−0.436242	−	1.19856i	−0.0172440	−	0.0473774i
$641$	33.1090	+	12.0507i	1.30773	+	0.475974i	0.899506	−	0.436909i	$-0.143927\pi$
$641$	33.1090	+	12.0507i	1.30773	+	0.475974i	0.408221	+	0.912883i	$0.366149\pi$
$642$	2.94182	+	20.4291i	0.116104	+	0.806272i
$643$	2.41812	+	13.7139i	0.0953615	+	0.540822i	0.994636	+	0.103437i	$0.0329841\pi$
$643$	2.41812	+	13.7139i	0.0953615	+	0.540822i	−0.899275	+	0.437385i	$0.855905\pi$
$644$	5.05965	−	9.54093i	0.199378	−	0.375965i
$645$	1.26314	+	0.264013i	0.0497360	+	0.0103955i
$646$	18.4772	−	4.86917i	0.726975	−	0.191575i
$647$	18.4453	−	10.6494i	0.725160	−	0.418671i	−0.0914890	−	0.995806i	$-0.529163\pi$
$647$	18.4453	−	10.6494i	0.725160	−	0.418671i	0.816649	+	0.577135i	$0.195829\pi$
$648$	5.44422	−	7.16662i	0.213869	−	0.281531i
$649$	2.03480	−	5.59056i	0.0798728	−	0.219449i
$650$	−5.63269	+	6.71278i	−0.220932	+	0.263297i
$651$	2.62683	−	15.2983i	0.102954	−	0.599586i
$652$	3.77188	−	21.3914i	0.147718	−	0.837751i
$653$	29.6068	−	17.0935i	1.15860	−	0.668920i	0.207634	−	0.978207i	$-0.433424\pi$
$653$	29.6068	−	17.0935i	1.15860	−	0.668920i	0.950969	+	0.309287i	$0.100090\pi$
$654$	8.86209	−	9.90974i	0.346535	−	0.387501i
$655$	21.4703	+	18.0157i	0.838913	+	0.703932i
$656$	1.67805	−	9.51669i	0.0655168	−	0.371564i
$657$	1.16227	+	10.3804i	0.0453445	+	0.404977i
$658$	1.97565	−	14.1697i	0.0770190	−	0.552392i
$659$	−2.42072	+	13.7286i	−0.0942977	+	0.534789i	0.900663	+	0.434519i	$0.143082\pi$
$659$	−2.42072	+	13.7286i	−0.0942977	+	0.534789i	−0.994960	+	0.100270i	$0.968029\pi$
$660$	−10.2895	−	0.324377i	−0.400517	−	0.0126264i
$661$	−17.3979	−	3.06771i	−0.676698	−	0.119320i	−0.175271	−	0.984520i	$-0.556080\pi$
$661$	−17.3979	−	3.06771i	−0.676698	−	0.119320i	−0.501427	+	0.865200i	$0.667191\pi$
$662$	18.9216	+	22.5499i	0.735409	+	0.876426i
$663$	9.31927	+	17.3845i	0.361930	+	0.675157i
$664$		−	0.771582i		−	0.0299432i
$665$	−13.1266	+	6.63812i	−0.509029	+	0.257415i
$666$	4.87587	−	11.1544i	0.188936	−	0.432225i
$667$	6.26240	+	7.46324i	0.242481	+	0.288978i
$668$	1.05217	−	0.882874i	0.0407096	−	0.0341594i
$669$	6.67275	−	16.6783i	0.257983	−	0.644820i
$670$	1.95588	+	11.0923i	0.0755621	+	0.428534i
$671$	47.5169	+	8.37850i	1.83437	+	0.323449i
$672$	−4.50934	+	0.815981i	−0.173952	+	0.0314771i
$673$	−18.4063	+	10.6269i	−0.709510	+	0.409636i	−0.810880	−	0.585213i	$-0.801011\pi$
$673$	−18.4063	+	10.6269i	−0.709510	+	0.409636i	0.101369	+	0.994849i	$0.467678\pi$
$674$	−22.6185	−	3.98825i	−0.871231	−	0.153621i
$675$	16.9627	−	4.41308i	0.652893	−	0.169859i
$676$	−3.12558	+	5.41366i	−0.120215	+	0.208218i
$677$	11.6298	+	20.1433i	0.446968	+	0.774171i	0.998187	−	0.0601893i	$-0.0191704\pi$
$677$	11.6298	+	20.1433i	0.446968	+	0.774171i	−0.551219	+	0.834361i	$0.685837\pi$
$678$	27.4690	+	10.9900i	1.05494	+	0.422067i
$679$	8.50312	+	13.5748i	0.326320	+	0.520955i
$680$	−4.28319	−	3.59403i	−0.164253	−	0.137825i
$681$	11.8464	−	19.1021i	0.453956	−	0.731995i
$682$	2.74085	+	15.5441i	0.104952	+	0.595215i
$683$	−13.8249	−	23.9455i	−0.528997	−	0.916250i	−0.999428	−	0.0338129i	$-0.989235\pi$
$683$	−13.8249	−	23.9455i	−0.528997	−	0.916250i	0.470431	−	0.882437i	$-0.344098\pi$
$684$	2.52916	+	12.8298i	0.0967048	+	0.490559i
$685$	−5.00954			−0.191405
$686$	−17.7860	+	5.16314i	−0.679073	+	0.197129i
$687$	−39.0184	−	1.23006i	−1.48865	−	0.0469298i
$688$	−0.548890	+	0.199780i	−0.0209262	+	0.00761653i
$689$	6.91910	−	19.0101i	0.263597	−	0.724226i
$690$	1.28529	+	8.92554i	0.0489301	+	0.339789i
$691$	−15.8961	−	27.5329i	−0.604717	−	1.04740i	−0.992096	−	0.125480i	$-0.959953\pi$
$691$	−15.8961	−	27.5329i	−0.604717	−	1.04740i	0.387379	−	0.921921i	$-0.373380\pi$
$692$	−8.63845	−	14.9622i	−0.328385	−	0.568779i
$693$	−7.40477	+	36.2377i	−0.281284	+	1.37655i
$694$	−6.09508	−	16.7461i	−0.231366	−	0.635673i
$695$			21.7491i			0.824990i
$696$	0.845803	−	4.04663i	0.0320601	−	0.153387i
$697$	−14.4885	−	39.8069i	−0.548792	−	1.50779i
$698$	4.38403	+	24.8631i	0.165938	+	0.941082i
$699$	8.32554	+	10.5820i	0.314901	+	0.400249i
$700$	−7.88442	−	4.18119i	−0.298003	−	0.158034i
$701$	−6.65409	+	18.2820i	−0.251322	+	0.690500i	0.748310	+	0.663349i	$0.230866\pi$
$701$	−6.65409	+	18.2820i	−0.251322	+	0.690500i	−0.999631	+	0.0271509i	$0.991357\pi$
$702$	−12.2753	+	5.61567i	−0.463301	+	0.211950i
$703$	7.40884	+	16.0613i	0.279430	+	0.605764i
$704$	4.03555	−	2.32993i	0.152096	−	0.0878125i
$705$	5.64413	+	10.5288i	0.212570	+	0.396536i
$706$	16.7093	−	2.94629i	0.628862	−	0.110885i
$707$	−18.6879	−	6.04953i	−0.702831	−	0.227516i
$708$	1.04478	+	1.94897i	0.0392653	+	0.0732469i
$709$	−16.1976	−	13.5914i	−0.608315	−	0.510437i	0.285791	−	0.958292i	$-0.407744\pi$
$709$	−16.1976	−	13.5914i	−0.608315	−	0.510437i	−0.894106	+	0.447855i	$0.852188\pi$
$710$			0.0633558i			0.00237770i
$711$	7.26592	+	9.85933i	0.272493	+	0.369754i
$712$	−0.958373	+	5.43520i	−0.0359165	+	0.203693i
$713$	12.9922	−	4.72877i	0.486562	−	0.177094i
$714$	−15.3306	+	12.9815i	−0.573735	+	0.485821i
$715$	13.3719	+	7.72027i	0.500081	+	0.288722i
$716$	16.6028	+	13.9314i	0.620476	+	0.520641i
$717$	−11.3588	−	7.04433i	−0.424204	−	0.263075i
$718$	14.4703	+	2.55150i	0.540027	+	0.0952213i
$719$	3.23644	−	8.89205i	0.120699	−	0.331618i	−0.864599	−	0.502462i	$-0.832428\pi$
$719$	3.23644	−	8.89205i	0.120699	−	0.331618i	0.985298	+	0.170845i	$0.0546497\pi$
$720$	2.63935	−	2.77049i	0.0983627	−	0.103250i
$721$	28.0682	+	21.8800i	1.04531	+	0.814854i
$722$	−16.3754	−	9.63571i	−0.609428	−	0.358604i
$723$	−4.36265	+	4.87838i	−0.162249	+	0.181429i
$724$	−8.74323	+	1.54167i	−0.324940	+	0.0572956i
$725$	6.16746	−	5.17511i	0.229054	−	0.192199i
$726$	−2.64504	−	18.3682i	−0.0981668	−	0.681707i
$727$	−38.1734	+	32.0313i	−1.41577	+	1.18798i	−0.462216	+	0.886768i	$0.652945\pi$
$727$	−38.1734	+	32.0313i	−1.41577	+	1.18798i	−0.953558	+	0.301208i	$0.902610\pi$
$728$	6.53918	+	2.11682i	0.242358	+	0.0784547i
$729$	26.5188	+	5.07501i	0.982176	+	0.187963i
$730$			4.44092i			0.164366i
$731$	−1.64591	+	1.96151i	−0.0608760	+	0.0725492i
$732$	−14.0949	+	11.0893i	−0.520962	+	0.409873i
$733$	−14.2815			−0.527499			−0.263750	−	0.964591i	$-0.584959\pi$
$733$	−14.2815			−0.527499			−0.263750	+	0.964591i	$0.584959\pi$
$734$	−10.0071	+	17.3328i	−0.369368	+	0.639764i
$735$	9.45278	−	12.2390i	0.348671	−	0.451444i
$736$	−2.62375	−	3.12686i	−0.0967127	−	0.115258i
$737$	−38.6682	+	14.0741i	−1.42436	+	0.518425i
$738$	27.8126	−	8.17972i	1.02380	−	0.301100i
$739$	0.534168	+	3.02942i	0.0196497	+	0.111439i	0.993055	−	0.117651i	$-0.0375363\pi$
$739$	0.534168	+	3.02942i	0.0196497	+	0.111439i	−0.973405	+	0.229090i	$0.926425\pi$
$740$	2.58786	−	4.48231i	0.0951318	−	0.164773i
$741$	5.74831	−	18.7521i	0.211169	−	0.688875i
$742$	20.4057	+	2.84513i	0.749117	+	0.104448i
$743$	−40.7763	−	14.8414i	−1.49594	−	0.544477i	−0.540933	−	0.841066i	$-0.681929\pi$
$743$	−40.7763	−	14.8414i	−1.49594	−	0.544477i	−0.955005	+	0.296589i	$0.904151\pi$
$744$	−4.98586	−	3.09205i	−0.182790	−	0.113360i
$745$	−3.23507	+	18.3470i	−0.118524	+	0.672181i
$746$	3.91065	−	10.7444i	0.143179	−	0.393381i
$747$	2.07355	−	1.02881i	0.0758672	−	0.0376421i
$748$	10.2136	−	17.6905i	0.373448	−	0.646830i
$749$	31.2258	+	4.35375i	1.14097	+	0.159083i
$750$	18.3091	−	2.63654i	0.668555	−	0.0962728i
$751$	−52.6657	−	9.28638i	−1.92180	−	0.338865i	−0.922869	−	0.385115i	$-0.874162\pi$
$751$	−52.6657	−	9.28638i	−1.92180	−	0.338865i	−0.998930	+	0.0462499i	$0.985273\pi$
$752$	−4.68299	−	2.70372i	−0.170771	−	0.0985947i
$753$	31.1087	+	6.50216i	1.13366	+	0.236952i
$754$	−3.98566	+	4.74993i	−0.145149	+	0.172982i
$755$	−19.2051	+	16.1150i	−0.698944	+	0.586484i
$756$	−8.20551	−	11.0304i	−0.298431	−	0.401172i
$757$	−2.71304	−	15.3864i	−0.0986073	−	0.559230i	−0.993582	−	0.113113i	$-0.963918\pi$
$757$	−2.71304	−	15.3864i	−0.0986073	−	0.559230i	0.894975	−	0.446117i	$-0.147193\pi$
$758$	0.480130	+	0.572197i	0.0174391	+	0.0207831i
$759$	−31.2977	+	10.2867i	−1.13604	+	0.373385i
$760$	0.461661	+	5.54051i	0.0167462	+	0.200976i
$761$	25.3716	+	14.6483i	0.919719	+	0.531000i	0.883545	−	0.468346i	$-0.155150\pi$
$761$	25.3716	+	14.6483i	0.919719	+	0.531000i	0.0361733	+	0.999346i	$0.488483\pi$
$762$	−25.5336	−	15.8350i	−0.924983	−	0.573641i
$763$	−10.7801	−	17.2099i	−0.390266	−	0.623041i
$764$	1.76945	−	2.10875i	0.0640165	−	0.0762919i
$765$	3.94748	−	16.3028i	0.142721	−	0.589430i
$766$	3.81936	−	1.39013i	0.137999	−	0.0502276i
$767$		−	3.31674i		−	0.119761i
$768$	−0.354365	+	1.69541i	−0.0127870	+	0.0611779i
$769$	29.0847	−	10.5860i	1.04882	−	0.381740i	0.240604	−	0.970623i	$-0.422654\pi$
$769$	29.0847	−	10.5860i	1.04882	−	0.381740i	0.808218	+	0.588883i	$0.200432\pi$
$770$	−4.84304	+	14.9609i	−0.174531	+	0.539153i
$771$	−2.96247	+	0.973688i	−0.106691	+	0.0350665i
$772$	10.3104	−	5.95271i	0.371079	−	0.214243i
$773$	−46.9745	+	17.0973i	−1.68955	+	0.614948i	−0.994569	−	0.104076i	$-0.966811\pi$
$773$	−46.9745	+	17.0973i	−1.68955	+	0.614948i	−0.694985	+	0.719024i	$0.744589\pi$
$774$	−1.26876	−	1.20871i	−0.0456048	−	0.0434460i
$775$	−3.90776	−	10.7365i	−0.140371	−	0.385665i
$776$	5.96229	−	1.05131i	0.214034	−	0.0377399i
$777$	−14.2983	−	11.8889i	−0.512950	−	0.426512i
$778$		−	38.4716i		−	1.37927i
$779$	−17.9593	+	38.1018i	−0.643458	+	1.36514i
$780$	−5.45225	+	1.79201i	−0.195222	+	0.0641643i
$781$	−0.227948	+	0.0401933i	−0.00815661	+	0.00143823i
$782$	−16.8143	−	6.11991i	−0.601278	−	0.218847i
$783$	12.0027	−	3.12267i	0.428941	−	0.111595i
$784$	−0.716502	+	6.96323i	−0.0255894	+	0.248687i
$785$	9.77825	+	1.72417i	0.349001	+	0.0615382i
$786$	−11.8839	−	36.1571i	−0.423884	−	1.28968i
$787$	−4.54651	−	2.62493i	−0.162066	−	0.0935686i	0.416774	−	0.909010i	$-0.363161\pi$
$787$	−4.54651	−	2.62493i	−0.162066	−	0.0935686i	−0.578839	+	0.815442i	$0.696494\pi$
$788$	6.18255	−	7.36808i	0.220244	−	0.262477i
$789$	−10.8611	+	27.1468i	−0.386664	+	0.966452i
$790$	2.60357	+	4.50952i	0.0926310	+	0.160442i
$791$	27.7848	−	35.6431i	0.987914	−	1.26732i
$792$	11.6424	+	7.73848i	0.413693	+	0.274975i
$793$	26.4905	−	4.67098i	0.940704	−	0.165872i
$794$	−1.35637	+	7.69236i	−0.0481358	+	0.272992i
$795$	−15.1624	+	8.12809i	−0.537755	+	0.288274i
$796$	12.9663	−	10.8800i	0.459577	−	0.385631i
$797$	−14.7557			−0.522675			−0.261338	−	0.965247i	$-0.584164\pi$
$797$	−14.7557			−0.522675			−0.261338	+	0.965247i	$0.584164\pi$
$798$	19.8996	+	1.73398i	0.704438	+	0.0613823i
$799$	−23.7045			−0.838604
$800$	−2.58397	+	2.16821i	−0.0913572	+	0.0766578i
$801$	−15.8844	+	4.67163i	−0.561249	+	0.165064i
$802$	−5.28461	+	29.9705i	−0.186606	+	1.05830i
$803$	−15.9780	+	2.81735i	−0.563850	+	0.0994220i
$804$	5.68156	−	14.2009i	0.200373	−	0.500825i
$805$	13.6426	+	1.90217i	0.480840	+	0.0670426i
$806$	4.39973	+	7.62056i	0.154974	+	0.268423i
$807$	−19.3283	−	7.73299i	−0.680389	−	0.272214i
$808$	−4.77221	+	5.68729i	−0.167886	+	0.200078i
$809$	−44.6513	−	25.7795i	−1.56986	−	0.906358i	−0.996184	−	0.0872735i	$-0.972185\pi$
$809$	−44.6513	−	25.7795i	−1.56986	−	0.906358i	−0.573673	−	0.819084i	$-0.694482\pi$
$810$	10.9647	+	3.39888i	0.385259	+	0.119424i
$811$	44.4643	+	7.84026i	1.56135	+	0.275309i	0.886530	−	0.462670i	$-0.153109\pi$
$811$	44.4643	+	7.84026i	1.56135	+	0.275309i	0.674823	+	0.737979i	$0.264220\pi$
$812$	−5.57897	−	2.95859i	−0.195783	−	0.103826i
$813$	24.4917	−	19.2691i	0.858960	−	0.675798i
$814$	17.7686	+	6.46726i	0.622791	+	0.226677i
$815$	27.2844	−	4.81098i	0.955731	−	0.168521i
$816$	2.37077	+	7.21313i	0.0829934	+	0.252510i
$817$	2.53731	−	0.211421i	0.0887693	−	0.00739667i
$818$			2.44627i			0.0855317i
$819$	3.03044	+	20.3959i	0.105892	+	0.712691i
$820$	12.1384	−	2.14033i	0.423891	−	0.0747435i
$821$	18.9488	+	52.0615i	0.661319	+	1.81696i	0.570841	+	0.821061i	$0.306617\pi$
$821$	18.9488	+	52.0615i	0.661319	+	1.81696i	0.0904784	+	0.995898i	$0.471160\pi$
$822$	5.78123	+	3.58531i	0.201644	+	0.125052i
$823$	12.7863	−	4.65383i	0.445703	−	0.162222i	−0.109412	−	0.993997i	$-0.534897\pi$
$823$	12.7863	−	4.65383i	0.445703	−	0.162222i	0.555114	+	0.831774i	$0.312674\pi$
$824$	11.6492	−	6.72564i	0.405817	−	0.234299i
$825$	8.50075	+	25.8638i	0.295958	+	0.900461i
$826$	3.30331	−	0.705909i	0.114937	−	0.0245617i
$827$	6.48447	−	2.36015i	0.225487	−	0.0820705i	−0.226806	−	0.973940i	$-0.572828\pi$
$827$	6.48447	−	2.36015i	0.225487	−	0.0820705i	0.452293	+	0.891869i	$0.350606\pi$
$828$	4.90469	−	11.2203i	0.170450	−	0.389934i
$829$		−	24.9439i		−	0.866338i	−0.901313	−	0.433169i	$-0.857395\pi$
$829$		−	24.9439i		−	0.866338i	0.901313	−	0.433169i	$-0.142605\pi$
$830$	0.924791	−	0.336596i	0.0321000	−	0.0116834i
$831$	−22.8355	−	0.719891i	−0.792153	−	0.0249727i
$832$	1.66987	−	1.99007i	0.0578922	−	0.0689933i
$833$	12.5422	+	28.0055i	0.434560	+	0.970332i
$834$	15.5657	−	25.0994i	0.538997	−	0.869122i
$835$	1.51718	+	0.875945i	0.0525042	+	0.0303133i
$836$	−19.6413	+	5.17594i	−0.679309	+	0.179014i
$837$	1.66154	−	17.5218i	0.0574313	−	0.605644i
$838$	−6.33988	−	7.55557i	−0.219007	−	0.261003i
$839$	8.02514	+	45.5128i	0.277058	+	1.57128i	0.732346	+	0.680932i	$0.238425\pi$
$839$	8.02514	+	45.5128i	0.277058	+	1.57128i	−0.455288	+	0.890344i	$0.650464\pi$
$840$	−2.94517	−	5.04877i	−0.101618	−	0.174199i
$841$	−17.8512	+	14.9790i	−0.615560	+	0.516516i
$842$	−1.33254	+	1.58806i	−0.0459223	+	0.0547281i
$843$	−9.20770	+	44.0530i	−0.317130	+	1.51727i
$844$	−3.22479	−	1.86183i	−0.111002	−	0.0640870i
$845$	−7.85214	−	1.38454i	−0.270122	−	0.0476297i
$846$	1.02181	−	16.1901i	0.0351305	−	0.556628i
$847$	−28.0757	−	3.91454i	−0.964692	−	0.134505i
$848$	3.89362	−	6.74395i	0.133707	−	0.231588i
$849$	25.5913	−	20.1343i	0.878292	−	0.691007i
$850$	−5.05736	+	13.8950i	−0.173466	+	0.476594i
$851$	2.87621	−	16.3118i	0.0985953	−	0.559162i
$852$	0.0453435	−	0.0731154i	0.00155344	−	0.00250489i
$853$	−35.0338	−	12.7513i	−1.19954	−	0.436595i	−0.336474	−	0.941693i	$-0.609234\pi$
$853$	−35.0338	−	12.7513i	−1.19954	−	0.436595i	−0.863062	+	0.505098i	$0.831457\pi$
$854$	10.2901	+	25.3891i	0.352120	+	0.868796i
$855$	−14.2740	+	8.62825i	−0.488161	+	0.295080i
$856$	5.95820	−	10.3199i	0.203647	−	0.352727i
$857$	10.0124	+	56.7834i	0.342018	+	1.93968i	0.342048	+	0.939682i	$0.388879\pi$
$857$	10.0124	+	56.7834i	0.342018	+	1.93968i	−2.97074e−5		1.00000i	$0.500009\pi$
$858$	−9.90641	−	18.4798i	−0.338199	−	0.630888i
$859$	−38.7894	+	14.1182i	−1.32348	+	0.481706i	−0.904570	−	0.426324i	$-0.859808\pi$
$859$	−38.7894	+	14.1182i	−1.32348	+	0.481706i	−0.418905	+	0.908030i	$0.637586\pi$
$860$	−0.478898	−	0.570728i	−0.0163303	−	0.0194617i
$861$	−0.198534	−	44.2833i	−0.00676601	−	1.50917i
$862$	20.6553	−	35.7760i	0.703521	−	1.21853i
$863$	19.0777			0.649411			0.324706	−	0.945815i	$-0.394735\pi$
$863$	19.0777			0.649411			0.324706	+	0.945815i	$0.394735\pi$
$864$	−5.02875	+	1.30830i	−0.171082	+	0.0445093i
$865$	14.1648	−	16.8809i	0.481616	−	0.573968i
$866$			18.2354i			0.619665i
$867$	2.86181	+	2.55926i	0.0971921	+	0.0869170i
$868$	−6.65330	+	6.00382i	−0.225828	+	0.203783i
$869$	−14.5731	+	12.2283i	−0.494357	+	0.414815i
$870$	5.21913	−	0.751562i	0.176945	−	0.0254803i
$871$	−17.5737	+	14.7461i	−0.595463	+	0.499653i
$872$	−7.55888	+	1.33284i	−0.255976	+	0.0451355i
$873$	10.7753	+	14.6213i	0.364688	+	0.494855i
$874$	7.45262	+	16.1562i	0.252089	+	0.546493i
$875$	3.90195	−	27.9854i	0.131910	−	0.946080i
$876$	3.17835	−	5.12502i	0.107386	−	0.173158i
$877$	−8.92200	+	24.5130i	−0.301274	+	0.827745i	0.693005	+	0.720933i	$0.256286\pi$
$877$	−8.92200	+	24.5130i	−0.301274	+	0.827745i	−0.994279	+	0.106812i	$0.965936\pi$
$878$	29.6266	+	5.22397i	0.999849	+	0.176300i
$879$	28.3264	−	45.6757i	0.955425	−	1.54060i
$880$	4.55305	+	3.82046i	0.153483	+	0.128788i
$881$	48.9450	+	28.2584i	1.64900	+	0.952050i	0.977471	+	0.211071i	$0.0676951\pi$
$881$	48.9450	+	28.2584i	1.64900	+	0.952050i	0.671528	+	0.740979i	$0.265638\pi$
$882$	−19.6684	+	7.35907i	−0.662268	+	0.247793i
$883$	−20.1624	+	7.33853i	−0.678520	+	0.246961i	−0.658212	−	0.752833i	$-0.728687\pi$
$883$	−20.1624	+	7.33853i	−0.678520	+	0.246961i	−0.0203083	+	0.999794i	$0.506465\pi$
$884$	1.97753	−	11.2151i	0.0665115	−	0.377205i
$885$	−1.88019	+	2.10246i	−0.0632020	+	0.0706735i
$886$		−	14.4362i		−	0.484994i
$887$	1.47415	+	1.23696i	0.0494973	+	0.0415331i	0.667201	−	0.744878i	$-0.267492\pi$
$887$	1.47415	+	1.23696i	0.0494973	+	0.0415331i	−0.617703	+	0.786411i	$0.711937\pi$
$888$	−6.19448	+	3.32066i	−0.207873	+	0.111434i
$889$	−34.0729	+	30.7467i	−1.14277	+	1.03121i
$890$	−6.93253	+	1.22239i	−0.232379	+	0.0409746i
$891$	−5.27275	+	41.6059i	−0.176644	+	1.39385i
$892$	−8.98180	+	5.18565i	−0.300733	+	0.173628i
$893$	16.5978	+	16.7356i	0.555425	+	0.560036i
$894$	16.8643	−	18.8579i	0.564025	−	0.630703i
$895$	−9.45486	+	25.9770i	−0.316041	+	0.868316i
$896$	2.33741	+	1.23955i	0.0780875	+	0.0414106i
$897$	−14.4347	+	11.3567i	−0.481960	+	0.379188i
$898$	6.15150	+	34.8869i	0.205278	+	1.16419i
$899$	−2.76511	−	7.59707i	−0.0922215	−	0.253377i
$900$	−9.27225	−	4.05313i	−0.309075	−	0.135104i
$901$		−	34.1367i		−	1.13726i
$902$	15.4013	+	42.3148i	0.512809	+	1.40893i
$903$	−2.31212	+	1.34876i	−0.0769424	+	0.0448839i
$904$	−8.54071	−	14.7929i	−0.284060	−	0.492006i
$905$	−5.66195	−	9.80679i	−0.188210	−	0.325989i
$906$	33.6969	−	4.85240i	1.11951	−	0.161210i
$907$	0.505109	−	1.38777i	0.0167719	−	0.0460803i	−0.931024	−	0.364957i	$-0.881084\pi$
$907$	0.505109	−	1.38777i	0.0167719	−	0.0460803i	0.947796	+	0.318877i	$0.103306\pi$
$908$	−12.1947	+	4.43849i	−0.404694	+	0.147297i
$909$	−21.6472	−	5.24153i	−0.717991	−	0.173851i
$910$	0.315517	+	8.76108i	0.0104593	+	0.290427i
$911$	−37.2878			−1.23540			−0.617700	−	0.786414i	$-0.711935\pi$
$911$	−37.2878			−1.23540			−0.617700	+	0.786414i	$0.711935\pi$
$912$	3.43254	−	6.72441i	0.113663	−	0.222667i
$913$	1.79773	+	3.11376i	0.0594962	+	0.103050i
$914$	−3.25554	−	18.4631i	−0.107684	−	0.610705i
$915$	−19.4401	−	12.0560i	−0.642668	−	0.398559i
$916$	17.2655	+	14.4875i	0.570468	+	0.478679i
$917$	−58.0999	+	2.09238i	−1.91863	+	0.0690965i
$918$	−16.2234	+	15.9890i	−0.535453	+	0.527716i
$919$	2.44476	+	4.23446i	0.0806453	+	0.139682i	0.903527	−	0.428531i	$-0.140969\pi$
$919$	2.44476	+	4.23446i	0.0806453	+	0.139682i	−0.822882	+	0.568212i	$0.807635\pi$
$920$	2.60316	−	4.50880i	0.0858236	−	0.148651i
$921$	−17.4808	−	22.2187i	−0.576013	−	0.732130i
$922$	25.4663	+	4.49040i	0.838688	+	0.147883i
$923$	−0.111752	+	0.0645202i	−0.00367837	+	0.00212371i
$924$	16.2965	−	13.7994i	0.536116	−	0.453966i
$925$	−13.4797	−	2.37684i	−0.443211	−	0.0781500i
$926$	−6.61113	−	37.4936i	−0.217255	−	1.23212i
$927$	33.6072	+	22.3381i	1.10380	+	0.733680i
$928$	−1.82841	+	1.53421i	−0.0600203	+	0.0503630i
$929$	−25.3916	−	30.2605i	−0.833071	−	0.992815i	−0.999977	−	0.00684229i	$-0.997822\pi$
$929$	−25.3916	−	30.2605i	−0.833071	−	0.992815i	0.166906	−	0.985973i	$-0.446622\pi$
$930$	1.53098	−	7.32475i	0.0502027	−	0.240188i
$931$	10.9902	−	28.4643i	0.360189	−	0.932879i
$932$		−	7.77376i		−	0.254638i
$933$	−12.2672	+	6.57604i	−0.401609	+	0.215290i
$934$	10.7900	+	12.8590i	0.353059	+	0.420760i
$935$	25.6589	+	4.52435i	0.839135	+	0.147962i
$936$	7.57467	+	1.83409i	0.247586	+	0.0599491i
$937$	1.26826	−	7.19267i	0.0414323	−	0.234974i	−0.957058	−	0.289895i	$-0.906380\pi$
$937$	1.26826	−	7.19267i	0.0414323	−	0.234974i	0.998491	+	0.0549209i	$0.0174907\pi$
$938$	−18.4267	−	14.3641i	−0.601652	−	0.469005i
$939$	−35.2794	+	11.5954i	−1.15130	+	0.378402i
$940$	1.19767	−	6.79234i	0.0390638	−	0.221542i
$941$	−9.26344	−	7.77295i	−0.301980	−	0.253391i	0.479188	−	0.877712i	$-0.340931\pi$
$941$	−9.26344	−	7.77295i	−0.301980	−	0.253391i	−0.781168	+	0.624321i	$0.785376\pi$
$942$	−10.0506	−	8.98802i	−0.327465	−	0.292845i
$943$	34.1602	−	19.7224i	1.11241	−	0.642249i
$944$	0.221701	−	1.25733i	0.00721574	−	0.0409225i
$945$	9.64106	−	14.6468i	0.313624	−	0.476459i
$946$	1.74960	−	2.08510i	0.0568845	−	0.0677923i
$947$	8.22830	−	22.6071i	0.267384	−	0.734631i	−0.731237	−	0.682124i	$-0.761056\pi$
$947$	8.22830	−	22.6071i	0.267384	−	0.734631i	0.998621	−	0.0525074i	$-0.0167213\pi$
$948$	0.222806	−	7.06756i	0.00723639	−	0.229544i
$949$	−7.83326	+	4.52253i	−0.254278	+	0.146808i
$950$	13.3512	−	6.15868i	0.433169	−	0.199814i
$951$	1.56845	−	7.50406i	0.0508606	−	0.243336i
$952$	11.5906	−	0.417418i	0.375653	−	0.0135286i
$953$	−5.87027	−	33.2920i	−0.190157	−	1.07843i	−0.919149	−	0.393911i	$-0.871122\pi$
$953$	−5.87027	−	33.2920i	−0.190157	−	1.07843i	0.728992	−	0.684522i	$-0.239989\pi$
$954$	23.3153	+	1.47150i	0.754862	+	0.0476416i
$955$	3.29938	+	1.20088i	0.106765	+	0.0388594i
$956$	2.63929	+	7.25140i	0.0853608	+	0.234527i
$957$	6.01508	+	18.3011i	0.194440	+	0.591590i
$958$	29.0363	−	16.7641i	0.938120	−	0.541624i
$959$	7.71467	−	6.96158i	0.249120	−	0.224801i
$960$	−2.18665	+	0.314881i	−0.0705739	+	0.0101627i
$961$	19.5268			0.629897
$962$	10.5417			0.339878
$963$	35.6782	+	2.25176i	1.14971	+	0.0725619i
$964$	3.72110	−	0.656131i	0.119849	−	0.0211325i
$965$	11.6325	+	9.76085i	0.374464	+	0.314213i
$966$	−14.3828	−	11.9592i	−0.462761	−	0.384780i
$967$	38.6273	+	14.0592i	1.24217	+	0.452113i	0.877749	−	0.479121i	$-0.159045\pi$
$967$	38.6273	+	14.0592i	1.24217	+	0.452113i	0.364421	+	0.931234i	$0.381267\pi$
$968$	−5.35713	+	9.27882i	−0.172185	+	0.298233i
$969$	−1.70759	−	33.0519i	−0.0548556	−	1.06178i
$970$	3.86107	+	6.68757i	0.123971	+	0.214725i
$971$	10.4190	−	8.74261i	0.334363	−	0.280564i	−0.460112	−	0.887861i	$-0.652191\pi$
$971$	10.4190	−	8.74261i	0.334363	−	0.280564i	0.794475	+	0.607297i	$0.207746\pi$
$972$	−10.2211	−	11.7698i	−0.327843	−	0.377517i
$973$	−30.2240	−	33.4935i	−0.968935	−	1.07375i
$974$	−8.66408	−	10.3254i	−0.277615	−	0.330849i
$975$	9.38490	+	11.9285i	0.300557	+	0.382018i
$976$	10.3544			0.331435
$977$	6.19340	−	10.7273i	0.198144	−	0.343196i	−0.749782	−	0.661684i	$-0.769842\pi$
$977$	6.19340	−	10.7273i	0.198144	−	0.343196i	0.947927	+	0.318488i	$0.103175\pi$
$978$	−34.9306	−	13.9752i	−1.11696	−	0.446879i
$979$	−8.79607	−	24.1670i	−0.281124	−	0.772381i
$980$	−8.65845	+	2.17888i	−0.276584	+	0.0696018i
$981$	−13.6607	−	18.5366i	−0.436152	−	0.591827i
$982$	−22.7437	+	27.1049i	−0.725781	+	0.864952i
$983$	−1.22064	−	0.444276i	−0.0389323	−	0.0141702i	0.322481	−	0.946576i	$-0.395483\pi$
$983$	−1.22064	−	0.444276i	−0.0389323	−	0.0141702i	−0.361413	+	0.932406i	$0.617706\pi$
$984$	−15.5401	−	6.21737i	−0.495399	−	0.198202i
$985$	11.5282	+	4.19592i	0.367319	+	0.133693i
$986$	−3.57856	+	9.83201i	−0.113965	+	0.313115i
$987$	−23.3234	−	8.37079i	−0.742391	−	0.266445i
$988$	−9.30267	+	6.45665i	−0.295957	+	0.205413i
$989$	−2.06483	−	1.19213i	−0.0656579	−	0.0379076i
$990$	−4.19618	+	17.3300i	−0.133363	+	0.550782i
$991$	11.2456	+	13.4020i	0.357229	+	0.425729i	0.914490	−	0.404609i	$-0.132592\pi$
$991$	11.2456	+	13.4020i	0.357229	+	0.425729i	−0.557261	+	0.830337i	$0.688148\pi$
$992$	1.15849	+	3.18293i	0.0367822	+	0.101058i
$993$	44.9365	−	24.0890i	1.42602	−	0.764442i
$994$	−0.0880434	−	0.0975677i	−0.00279257	−	0.00309466i
$995$	18.6968	+	10.7946i	0.592729	+	0.342212i
$996$	−1.30815	−	0.273422i	−0.0414503	−	0.00866370i
$997$	−28.8651	−	24.2207i	−0.914168	−	0.767078i	0.0587393	−	0.998273i	$-0.481292\pi$
$997$	−28.8651	−	24.2207i	−0.914168	−	0.767078i	−0.972907	+	0.231195i	$0.925736\pi$
$998$	−5.30285	−	4.44962i	−0.167859	−	0.140850i
$999$	−17.1835	−	12.2194i	−0.543662	−	0.386603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.cc.b.737.19	yes	162
3.2	odd	2		798.2.cc.a.737.21	yes	162
7.4	even	3		798.2.bu.b.53.18	yes	162
19.14	odd	18		798.2.bu.a.527.15	yes	162
21.11	odd	6		798.2.bu.a.53.15	✓	162
57.14	even	18		798.2.bu.b.527.18	yes	162
133.109	odd	18		798.2.cc.a.641.21	yes	162
399.242	even	18	inner	798.2.cc.b.641.19	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.53.15	✓	162	21.11	odd	6
798.2.bu.a.527.15	yes	162	19.14	odd	18
798.2.bu.b.53.18	yes	162	7.4	even	3
798.2.bu.b.527.18	yes	162	57.14	even	18
798.2.cc.a.641.21	yes	162	133.109	odd	18
798.2.cc.a.737.21	yes	162	3.2	odd	2
798.2.cc.b.641.19	yes	162	399.242	even	18	inner
798.2.cc.b.737.19	yes	162	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.cc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.818331 + 1.52654i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.25611 - 0.221486i) q^{5} +(-1.60812 - 0.643387i) q^{6} +(-1.62661 + 2.08666i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.66067 + 2.49844i) q^{9} +(-0.819866 + 0.977079i) q^{10} +(-4.03555 - 2.32993i) q^{11} +(1.64545 - 0.540817i) q^{12} +(-2.55839 - 0.451112i) q^{13} +(-0.0952210 - 2.64404i) q^{14} +(1.36602 + 1.73625i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-4.31707 + 0.761217i) q^{17} +(-0.333818 - 2.98137i) q^{18} +(3.56024 + 2.51490i) q^{19} -1.27549i q^{20} +(-4.51648 - 0.775515i) q^{21} +(4.58906 - 0.809176i) q^{22} +(-1.39607 - 3.83567i) q^{23} +(-0.912860 + 1.47197i) q^{24} +(-3.16971 + 1.15368i) q^{25} +(2.24981 - 1.29893i) q^{26} +(-5.17295 - 0.490534i) q^{27} +(1.77250 + 1.96424i) q^{28} +(-2.24287 + 0.816338i) q^{29} +(-2.16248 - 0.451988i) q^{30} +3.38721i q^{31} +(0.939693 - 0.342020i) q^{32} +(0.254316 - 8.06710i) q^{33} +(2.81777 - 3.35809i) q^{34} +(-1.58103 + 2.98134i) q^{35} +(2.17211 + 2.06929i) q^{36} +(3.51420 + 2.02892i) q^{37} +(-4.34385 + 0.361949i) q^{38} +(-1.40496 - 4.27465i) q^{39} +(0.819866 + 0.977079i) q^{40} +(1.67805 + 9.51669i) q^{41} +(3.95831 - 2.30906i) q^{42} +(0.447459 - 0.375463i) q^{43} +(-2.99530 + 3.56966i) q^{44} +(-1.53261 + 3.50612i) q^{45} +(3.53497 + 2.04092i) q^{46} +(5.32530 + 0.938993i) q^{47} +(-0.246871 - 1.71437i) q^{48} +(-1.70827 - 6.78836i) q^{49} +(1.68657 - 2.92122i) q^{50} +(-4.69483 - 5.96727i) q^{51} +(-0.888518 + 2.44118i) q^{52} +(-1.35224 + 7.66894i) q^{53} +(4.27802 - 2.94934i) q^{54} +(-5.58514 - 2.03282i) q^{55} +(-2.62040 - 0.365358i) q^{56} +(-0.925653 + 7.49287i) q^{57} +(1.19341 - 2.06704i) q^{58} +(0.221701 + 1.25733i) q^{59} +(1.94708 - 1.04377i) q^{60} +(-9.72993 + 3.54140i) q^{61} +(-2.17726 - 2.59475i) q^{62} +(-2.51212 - 7.52923i) q^{63} +(-0.500000 + 0.866025i) q^{64} -3.31352 q^{65} +(4.99061 + 6.34323i) q^{66} +(5.67627 - 6.76472i) q^{67} +4.38367i q^{68} +(4.71286 - 5.27000i) q^{69} +(-0.705225 - 3.30011i) q^{70} +(0.0380509 - 0.0319285i) q^{71} +(-2.99404 - 0.188963i) q^{72} +(2.66717 - 2.23802i) q^{73} +(-3.99620 + 0.704638i) q^{74} +(-4.35502 - 3.89461i) q^{75} +(3.09492 - 3.06944i) q^{76} +(11.4260 - 4.63093i) q^{77} +(3.82395 + 2.37147i) q^{78} +(1.39629 - 3.83628i) q^{79} +(-1.25611 - 0.221486i) q^{80} +(-3.48436 - 8.29815i) q^{81} +(-7.40267 - 6.21158i) q^{82} +(-0.668209 - 0.385791i) q^{83} +(-1.54801 + 4.31320i) q^{84} +(-5.25411 + 1.91234i) q^{85} +(-0.101431 + 0.575243i) q^{86} +(-3.08159 - 2.75580i) q^{87} -4.65986i q^{88} +(4.22784 + 3.54758i) q^{89} +(-1.07964 - 3.67099i) q^{90} +(5.10281 - 4.60469i) q^{91} +(-4.01982 + 0.708802i) q^{92} +(-5.17072 + 2.77186i) q^{93} +(-4.68299 + 2.70372i) q^{94} +(5.02906 + 2.37045i) q^{95} +(1.29109 + 1.15460i) q^{96} +(2.07068 - 5.68915i) q^{97} +(5.67209 + 4.10213i) q^{98} +(12.5229 - 6.21333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 81 q^{8} + 15 q^{13} - 9 q^{14} + 3 q^{15} - 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} + 9 q^{27} - 12 q^{28} - 6 q^{29} - 12 q^{33} + 6 q^{34} + 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots + 39 q^{99}+O(q^{100}) \) 162 * q + 81 * q^8 + 15 * q^13 - 9 * q^14 + 3 * q^15 - 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 + 9 * q^27 - 12 * q^28 - 6 * q^29 - 12 * q^33 + 6 * q^34 + 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 - 6 * q^44 + 18 * q^45 - 18 * q^46 - 12 * q^47 + 24 * q^49 - 87 * q^50 + 24 * q^51 + 12 * q^52 + 36 * q^53 + 18 * q^54 - 18 * q^57 - 24 * q^59 - 27 * q^60 - 9 * q^61 - 36 * q^62 + 6 * q^63 - 81 * q^64 + 72 * q^65 + 12 * q^66 - 63 * q^67 - 9 * q^69 + 12 * q^70 - 12 * q^71 - 51 * q^73 + 42 * q^74 - 18 * q^78 + 21 * q^79 - 12 * q^81 + 3 * q^84 - 6 * q^85 - 36 * q^86 - 84 * q^87 + 54 * q^89 + 12 * q^90 + 75 * q^91 - 66 * q^93 + 72 * q^94 - 12 * q^97 - 12 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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