LMFDB - Embedded newform 196.2.j.a.83.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,2,Mod(27,196)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("196.27"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.j (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			83.13
Character	$\chi$	$=$	196.83
Dual form			196.2.j.a.111.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.143162 - 1.40695i) q^{2} +(-0.576591 + 0.723022i) q^{3} +(-1.95901 + 0.402843i) q^{4} +(2.88506 + 2.30076i) q^{5} +(1.09980 + 0.707724i) q^{6} +(-2.64328 - 0.114420i) q^{7} +(0.847234 + 2.69855i) q^{8} +(0.477259 + 2.09101i) q^{9} +(2.82402 - 4.38851i) q^{10} +(6.29614 + 1.43705i) q^{11} +(0.838282 - 1.64868i) q^{12} +(-3.30359 - 0.754023i) q^{13} +(0.217432 + 3.73533i) q^{14} +(-3.32699 + 0.759365i) q^{15} +(3.67544 - 1.57834i) q^{16} +(-1.32426 - 2.74986i) q^{17} +(2.87362 - 0.970832i) q^{18} +3.15336 q^{19} +(-6.57870 - 3.34498i) q^{20} +(1.60682 - 1.84517i) q^{21} +(1.12049 - 9.06407i) q^{22} +(0.0319146 - 0.0662714i) q^{23} +(-2.43962 - 0.943392i) q^{24} +(1.91747 + 8.40098i) q^{25} +(-0.587923 + 4.75593i) q^{26} +(-4.28662 - 2.06433i) q^{27} +(5.22430 - 0.840673i) q^{28} +(0.122716 - 0.0590968i) q^{29} +(1.54469 + 4.57220i) q^{30} -1.68084 q^{31} +(-2.74683 - 4.94519i) q^{32} +(-4.66931 + 3.72365i) q^{33} +(-3.67933 + 2.25685i) q^{34} +(-7.36275 - 6.41164i) q^{35} +(-1.77730 - 3.90405i) q^{36} +(3.94364 - 1.89916i) q^{37} +(-0.451440 - 4.43661i) q^{38} +(2.44999 - 1.95380i) q^{39} +(-3.76440 + 9.73476i) q^{40} +(-3.34485 - 2.66743i) q^{41} +(-2.82610 - 1.99655i) q^{42} +(-5.02623 + 4.00829i) q^{43} +(-12.9131 - 0.278847i) q^{44} +(-3.43398 + 7.13074i) q^{45} +(-0.0978094 - 0.0354147i) q^{46} +(-0.166245 + 0.728365i) q^{47} +(-0.978044 + 3.56748i) q^{48} +(6.97382 + 0.604889i) q^{49} +(11.5452 - 3.90048i) q^{50} +(2.75177 + 0.628073i) q^{51} +(6.77551 + 0.146311i) q^{52} +(1.78996 + 0.861998i) q^{53} +(-2.29072 + 6.32659i) q^{54} +(14.8584 + 18.6318i) q^{55} +(-1.93070 - 7.22996i) q^{56} +(-1.81820 + 2.27995i) q^{57} +(-0.100714 - 0.164195i) q^{58} +(-0.754424 - 0.946018i) q^{59} +(6.21171 - 2.82786i) q^{60} +(-4.12089 - 8.55712i) q^{61} +(0.240633 + 2.36486i) q^{62} +(-1.02227 - 5.58172i) q^{63} +(-6.56439 + 4.57261i) q^{64} +(-7.79622 - 9.77615i) q^{65} +(5.90746 + 6.03640i) q^{66} -7.13583i q^{67} +(3.70201 + 4.85354i) q^{68} +(0.0295140 + 0.0612864i) q^{69} +(-7.96679 + 11.2769i) q^{70} +(2.54779 - 5.29054i) q^{71} +(-5.23835 + 3.05948i) q^{72} +(13.2990 - 3.03541i) q^{73} +(-3.23659 - 5.27661i) q^{74} +(-7.17969 - 3.45756i) q^{75} +(-6.17746 + 1.27031i) q^{76} +(-16.4780 - 4.51893i) q^{77} +(-3.09965 - 3.16730i) q^{78} -16.0338i q^{79} +(14.2352 + 3.90267i) q^{80} +(-1.83297 + 0.882711i) q^{81} +(-3.27408 + 5.08791i) q^{82} +(-0.852941 - 3.73698i) q^{83} +(-2.40445 + 4.26200i) q^{84} +(2.50619 - 10.9803i) q^{85} +(6.35902 + 6.49782i) q^{86} +(-0.0280285 + 0.122801i) q^{87} +(1.45634 + 18.2080i) q^{88} +(5.47805 - 1.25033i) q^{89} +(10.5242 + 3.81059i) q^{90} +(8.64602 + 2.37109i) q^{91} +(-0.0358241 + 0.142683i) q^{92} +(0.969158 - 1.21529i) q^{93} +(1.04857 + 0.129624i) q^{94} +(9.09762 + 7.25511i) q^{95} +(5.15928 + 0.865331i) q^{96} -0.0207508i q^{97} +(-0.147336 - 9.89840i) q^{98} +13.8511i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26}+ \cdots + 105 q^{98}+O(q^{100}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{14}\right)$

Coefficient data

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

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

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

$2$	−0.143162	−	1.40695i	−0.101231	−	0.994863i
$2$	−0.143162	−	1.40695i	−0.101231	−	0.994863i
$3$	−0.576591	+	0.723022i	−0.332895	+	0.417437i	−0.919904	−	0.392143i	$-0.871734\pi$
$3$	−0.576591	+	0.723022i	−0.332895	+	0.417437i	0.587009	+	0.809580i	$0.300305\pi$
$4$	−1.95901	+	0.402843i	−0.979505	+	0.201421i
$5$	2.88506	+	2.30076i	1.29024	+	1.02893i	0.997348	+	0.0727829i	$0.0231880\pi$
$5$	2.88506	+	2.30076i	1.29024	+	1.02893i	0.292889	+	0.956146i	$0.405383\pi$
$6$	1.09980	+	0.707724i	0.448992	+	0.288927i
$7$	−2.64328	−	0.114420i	−0.999064	−	0.0432468i
$7$	−2.64328	−	0.114420i	−0.999064	−	0.0432468i
$8$	0.847234	+	2.69855i	0.299542	+	0.954083i
$9$	0.477259	+	2.09101i	0.159086	+	0.697003i
$10$	2.82402	−	4.38851i	0.893032	−	1.38777i
$11$	6.29614	+	1.43705i	1.89836	+	0.433287i	0.999982	−	0.00594367i	$-0.00189194\pi$
$11$	6.29614	+	1.43705i	1.89836	+	0.433287i	0.898374	+	0.439231i	$0.144749\pi$
$12$	0.838282	−	1.64868i	0.241991	−	0.475933i
$13$	−3.30359	−	0.754023i	−0.916251	−	0.209128i	−0.261703	−	0.965149i	$-0.584284\pi$
$13$	−3.30359	−	0.754023i	−0.916251	−	0.209128i	−0.654548	+	0.756020i	$0.727141\pi$
$14$	0.217432	+	3.73533i	0.0581113	+	0.998310i
$15$	−3.32699	+	0.759365i	−0.859026	+	0.196067i
$16$	3.67544	−	1.57834i	0.918859	−	0.394586i
$17$	−1.32426	−	2.74986i	−0.321181	−	0.666939i	0.676394	−	0.736540i	$-0.263542\pi$
$17$	−1.32426	−	2.74986i	−0.321181	−	0.666939i	−0.997575	+	0.0696007i	$0.977827\pi$
$18$	2.87362	−	0.970832i	0.677318	−	0.228827i
$19$	3.15336			0.723430			0.361715	−	0.932289i	$-0.382191\pi$
$19$	3.15336			0.723430			0.361715	+	0.932289i	$0.382191\pi$
$20$	−6.57870	−	3.34498i	−1.47104	−	0.747960i
$21$	1.60682	−	1.84517i	0.350636	−	0.402650i
$22$	1.12049	−	9.06407i	0.238890	−	1.93247i
$23$	0.0319146	−	0.0662714i	0.00665466	−	0.0138185i	−0.897615	−	0.440780i	$-0.854702\pi$
$23$	0.0319146	−	0.0662714i	0.00665466	−	0.0138185i	0.904270	+	0.426962i	$0.140416\pi$
$24$	−2.43962	−	0.943392i	−0.497985	−	0.192569i
$25$	1.91747	+	8.40098i	0.383494	+	1.68020i
$26$	−0.587923	+	4.75593i	−0.115301	+	0.932714i
$27$	−4.28662	−	2.06433i	−0.824960	−	0.397280i
$28$	5.22430	−	0.840673i	0.987299	−	0.158872i
$29$	0.122716	−	0.0590968i	0.0227878	−	0.0109740i	−0.422455	−	0.906384i	$-0.638832\pi$
$29$	0.122716	−	0.0590968i	0.0227878	−	0.0109740i	0.445243	+	0.895410i	$0.353117\pi$
$30$	1.54469	+	4.57220i	0.282020	+	0.834765i
$31$	−1.68084			−0.301888			−0.150944	−	0.988542i	$-0.548231\pi$
$31$	−1.68084			−0.301888			−0.150944	+	0.988542i	$0.548231\pi$
$32$	−2.74683	−	4.94519i	−0.485576	−	0.874195i
$33$	−4.66931	+	3.72365i	−0.812823	+	0.648205i
$34$	−3.67933	+	2.25685i	−0.631000	+	0.387046i
$35$	−7.36275	−	6.41164i	−1.24453	−	1.08377i
$36$	−1.77730	−	3.90405i	−0.296217	−	0.650674i
$37$	3.94364	−	1.89916i	0.648330	−	0.312219i	−0.0806620	−	0.996742i	$-0.525703\pi$
$37$	3.94364	−	1.89916i	0.648330	−	0.312219i	0.728992	+	0.684522i	$0.239989\pi$
$38$	−0.451440	−	4.43661i	−0.0732333	−	0.719714i
$39$	2.44999	−	1.95380i	0.392313	−	0.312859i
$40$	−3.76440	+	9.73476i	−0.595203	+	1.53920i
$41$	−3.34485	−	2.66743i	−0.522378	−	0.416583i	0.326479	−	0.945204i	$-0.394138\pi$
$41$	−3.34485	−	2.66743i	−0.522378	−	0.416583i	−0.848858	+	0.528622i	$0.822709\pi$
$42$	−2.82610	−	1.99655i	−0.436076	−	0.308074i
$43$	−5.02623	+	4.00829i	−0.766493	+	0.611258i	−0.926690	−	0.375827i	$-0.877359\pi$
$43$	−5.02623	+	4.00829i	−0.766493	+	0.611258i	0.160196	+	0.987085i	$0.448787\pi$
$44$	−12.9131	−	0.278847i	−1.94672	−	0.0420377i
$45$	−3.43398	+	7.13074i	−0.511908	+	1.06299i
$46$	−0.0978094	−	0.0354147i	−0.0144212	−	0.00522161i
$47$	−0.166245	+	0.728365i	−0.0242493	+	0.106243i	−0.985604	−	0.169069i	$-0.945924\pi$
$47$	−0.166245	+	0.728365i	−0.0242493	+	0.106243i	0.961355	+	0.275312i	$0.0887811\pi$
$48$	−0.978044	+	3.56748i	−0.141169	+	0.514921i
$49$	6.97382	+	0.604889i	0.996259	+	0.0864128i
$50$	11.5452	−	3.90048i	1.63274	−	0.551611i
$51$	2.75177	+	0.628073i	0.385325	+	0.0879478i
$52$	6.77551	+	0.146311i	0.939595	+	0.0202897i
$53$	1.78996	+	0.861998i	0.245870	+	0.118405i	0.552761	−	0.833340i	$-0.313574\pi$
$53$	1.78996	+	0.861998i	0.245870	+	0.118405i	−0.306891	+	0.951745i	$0.599289\pi$
$54$	−2.29072	+	6.32659i	−0.311728	+	0.860940i
$55$	14.8584	+	18.6318i	2.00351	+	2.51232i
$56$	−1.93070	−	7.22996i	−0.258001	−	0.966145i
$57$	−1.81820	+	2.27995i	−0.240826	+	0.301986i
$58$	−0.100714	−	0.164195i	−0.0132245	−	0.0215598i
$59$	−0.754424	−	0.946018i	−0.0982176	−	0.123161i	0.730294	−	0.683133i	$-0.239383\pi$
$59$	−0.754424	−	0.946018i	−0.0982176	−	0.123161i	−0.828511	+	0.559972i	$0.810812\pi$
$60$	6.21171	−	2.82786i	0.801928	−	0.365075i
$61$	−4.12089	−	8.55712i	−0.527626	−	1.09563i	−0.979107	−	0.203346i	$-0.934818\pi$
$61$	−4.12089	−	8.55712i	−0.527626	−	1.09563i	0.451481	−	0.892281i	$-0.350896\pi$
$62$	0.240633	+	2.36486i	0.0305604	+	0.300338i
$63$	−1.02227	−	5.58172i	−0.128794	−	0.703231i
$64$	−6.56439	+	4.57261i	−0.820549	+	0.571577i
$65$	−7.79622	−	9.77615i	−0.967002	−	1.21258i
$66$	5.90746	+	6.03640i	0.727157	+	0.743029i
$67$		−	7.13583i		−	0.871780i	−0.900000	−	0.435890i	$-0.856434\pi$
$67$		−	7.13583i		−	0.871780i	0.900000	−	0.435890i	$-0.143566\pi$
$68$	3.70201	+	4.85354i	0.448934	+	0.588578i
$69$	0.0295140	+	0.0612864i	0.00355307	+	0.00737802i
$70$	−7.96679	+	11.2769i	−0.952213	+	1.34785i
$71$	2.54779	−	5.29054i	0.302367	−	0.627871i	−0.693322	−	0.720628i	$-0.743854\pi$
$71$	2.54779	−	5.29054i	0.302367	−	0.627871i	0.995689	+	0.0927568i	$0.0295679\pi$
$72$	−5.23835	+	3.05948i	−0.617345	+	0.360564i
$73$	13.2990	−	3.03541i	1.55653	−	0.355268i	0.644243	−	0.764821i	$-0.277173\pi$
$73$	13.2990	−	3.03541i	1.55653	−	0.355268i	0.912286	+	0.409553i	$0.134315\pi$
$74$	−3.23659	−	5.27661i	−0.376246	−	0.613393i
$75$	−7.17969	−	3.45756i	−0.829039	−	0.399244i
$76$	−6.17746	+	1.27031i	−0.708603	+	0.145714i
$77$	−16.4780	−	4.51893i	−1.87784	−	0.514980i
$78$	−3.09965	−	3.16730i	−0.350966	−	0.358627i
$79$		−	16.0338i		−	1.80394i	−0.431794	−	0.901972i	$-0.642119\pi$
$79$		−	16.0338i		−	1.80394i	0.431794	−	0.901972i	$-0.357881\pi$
$80$	14.2352	+	3.90267i	1.59155	+	0.436331i
$81$	−1.83297	+	0.882711i	−0.203663	+	0.0980790i
$82$	−3.27408	+	5.08791i	−0.361562	+	0.561866i
$83$	−0.852941	−	3.73698i	−0.0936224	−	0.410187i	0.906300	−	0.422635i	$-0.138895\pi$
$83$	−0.852941	−	3.73698i	−0.0936224	−	0.410187i	−0.999923	+	0.0124481i	$0.996038\pi$
$84$	−2.40445	+	4.26200i	−0.262348	+	0.465023i
$85$	2.50619	−	10.9803i	0.271834	−	1.19098i
$86$	6.35902	+	6.49782i	0.685711	+	0.700678i
$87$	−0.0280285	+	0.122801i	−0.00300497	+	0.0131656i
$88$	1.45634	+	18.2080i	0.155246	+	1.94098i
$89$	5.47805	−	1.25033i	0.580672	−	0.132535i	0.0779116	−	0.996960i	$-0.475175\pi$
$89$	5.47805	−	1.25033i	0.580672	−	0.132535i	0.502761	+	0.864426i	$0.332318\pi$
$90$	10.5242	+	3.81059i	1.10935	+	0.401671i
$91$	8.64602	+	2.37109i	0.906349	+	0.248558i
$92$	−0.0358241	+	0.142683i	−0.00373492	+	0.0148757i
$93$	0.969158	−	1.21529i	0.100497	−	0.126019i
$94$	1.04857	+	0.129624i	0.108152	+	0.0133696i
$95$	9.09762	+	7.25511i	0.933396	+	0.744358i
$96$	5.15928	+	0.865331i	0.526567	+	0.0883175i
$97$		−	0.0207508i		−	0.00210693i	−0.999999	−	0.00105346i	$-0.999665\pi$
$97$		−	0.0207508i		−	0.00210693i	0.999999	−	0.00105346i	$-0.000335328\pi$
$98$	−0.147336	−	9.89840i	−0.0148831	−	0.999889i
$99$			13.8511i			1.39209i
$100$	−7.14062	−	15.6852i	−0.714062	−	1.56852i
$101$	−8.88336	−	7.08424i	−0.883927	−	0.704909i	0.0723471	−	0.997380i	$-0.476951\pi$
$101$	−8.88336	−	7.08424i	−0.883927	−	0.704909i	−0.956274	+	0.292471i	$0.905523\pi$
$102$	0.489719	−	3.96151i	0.0484894	−	0.392248i
$103$	−8.28982	+	10.3951i	−0.816820	+	1.02426i	0.182338	+	0.983236i	$0.441634\pi$
$103$	−8.28982	+	10.3951i	−0.816820	+	1.02426i	−0.999158	+	0.0410242i	$0.986938\pi$
$104$	−0.764142	−	9.55375i	−0.0749303	−	0.936822i
$105$	8.88105	−	1.62653i	0.866702	−	0.158733i
$106$	0.956533	−	2.64178i	0.0929067	−	0.256593i
$107$	11.7807	−	2.68886i	1.13888	−	0.259942i	0.388821	−	0.921313i	$-0.372882\pi$
$107$	11.7807	−	2.68886i	1.13888	−	0.259942i	0.750059	+	0.661371i	$0.230025\pi$
$108$	9.22913	+	2.31720i	0.888073	+	0.222973i
$109$	1.68605	−	7.38706i	0.161494	−	0.707552i	−0.827728	−	0.561129i	$-0.810367\pi$
$109$	1.68605	−	7.38706i	0.161494	−	0.707552i	0.989222	−	0.146422i	$-0.0467758\pi$
$110$	24.0869	−	23.5724i	2.29660	−	2.24754i
$111$	−0.900733	+	3.94637i	−0.0854938	+	0.374573i
$112$	−9.89579	+	3.75146i	−0.935064	+	0.354479i
$113$	0.424656	+	1.86054i	0.0399482	+	0.175025i	0.990966	−	0.134110i	$-0.0428177\pi$
$113$	0.424656	+	1.86054i	0.0399482	+	0.175025i	−0.951018	+	0.309135i	$0.899961\pi$
$114$	3.46806	+	2.23171i	0.324814	+	0.209019i
$115$	0.244550	−	0.117769i	0.0228044	−	0.0109820i
$116$	−0.216595	+	0.165206i	−0.0201103	+	0.0153390i
$117$		−	7.26770i		−	0.671899i
$118$	−1.22299	+	1.19687i	−0.112586	+	0.110181i
$119$	3.18575	+	7.42017i	0.292038	+	0.680206i
$120$	−4.86793	−	8.33471i	−0.444379	−	0.760852i
$121$	27.6656	+	13.3230i	2.51505	+	1.21118i
$122$	−11.4495	+	7.02293i	−1.03659	+	0.635827i
$123$	3.85722	−	0.880386i	0.347794	−	0.0793817i
$124$	3.29279	−	0.677115i	0.295701	−	0.0608067i
$125$	−5.79118	+	12.0255i	−0.517979	+	1.07559i
$126$	−7.70684	+	2.23738i	−0.686580	+	0.199321i
$127$	3.53156	+	7.33336i	0.313375	+	0.650731i	0.996856	−	0.0792382i	$-0.0252488\pi$
$127$	3.53156	+	7.33336i	0.313375	+	0.650731i	−0.683480	+	0.729969i	$0.739534\pi$
$128$	7.37320	+	8.58113i	0.651705	+	0.758472i
$129$		−	5.94522i		−	0.523447i
$130$	−12.6384	+	12.3685i	−1.10846	+	1.08478i
$131$	−2.41824	−	3.03237i	−0.211282	−	0.264940i	0.664886	−	0.746945i	$-0.268480\pi$
$131$	−2.41824	−	3.03237i	−0.211282	−	0.264940i	−0.876168	+	0.482005i	$0.839909\pi$
$132$	7.64718	−	9.17567i	0.665602	−	0.798639i
$133$	−8.33520	−	0.360809i	−0.722753	−	0.0312861i
$134$	−10.0397	+	1.02158i	−0.867302	+	0.0882509i
$135$	−7.61763	−	15.8182i	−0.655621	−	1.36141i
$136$	6.29869	−	5.90337i	0.540108	−	0.506210i
$137$	2.29764	+	2.88115i	0.196301	+	0.246153i	0.870234	−	0.492639i	$-0.163968\pi$
$137$	2.29764	+	2.88115i	0.196301	+	0.246153i	−0.673933	+	0.738792i	$0.735396\pi$
$138$	0.0820016	−	0.0502985i	0.00698044	−	0.00428170i
$139$	−10.7748	+	13.5112i	−0.913909	+	1.14601i	0.0749552	+	0.997187i	$0.476119\pi$
$139$	−10.7748	+	13.5112i	−0.913909	+	1.14601i	−0.988864	+	0.148819i	$0.952453\pi$
$140$	17.0066	+	9.59444i	1.43732	+	0.810878i
$141$	−0.430769	−	0.540167i	−0.0362773	−	0.0454903i
$142$	−7.80826	−	2.82720i	−0.655255	−	0.237254i
$143$	−19.7163	−	9.49486i	−1.64876	−	0.794000i
$144$	5.05447	+	6.93209i	0.421206	+	0.577674i
$145$	0.490010	+	0.111841i	0.0406931	+	0.00928793i
$146$	−6.17457	−	18.2764i	−0.511011	−	1.51257i
$147$	−4.45838	+	4.69345i	−0.367721	+	0.387109i
$148$	−6.96056	+	5.30913i	−0.572155	+	0.436408i
$149$	−3.60339	+	15.7875i	−0.295201	+	1.29336i	0.581980	+	0.813203i	$0.302278\pi$
$149$	−3.60339	+	15.7875i	−0.295201	+	1.29336i	−0.877182	+	0.480159i	$0.840579\pi$
$150$	−3.83675	+	10.5964i	−0.313269	+	0.865196i
$151$	−2.00329	+	4.15987i	−0.163025	+	0.338526i	−0.966439	−	0.256895i	$-0.917300\pi$
$151$	−2.00329	+	4.15987i	−0.163025	+	0.338526i	0.803414	+	0.595421i	$0.203015\pi$
$152$	2.67163	+	8.50951i	0.216698	+	0.690212i
$153$	5.11797	−	4.08144i	0.413763	−	0.329965i
$154$	−3.99889	+	23.8306i	−0.322239	+	1.92033i
$155$	−4.84933	−	3.86721i	−0.389507	−	0.310622i
$156$	−4.01248	+	4.81448i	−0.321256	+	0.385467i
$157$	−7.33426	+	5.84888i	−0.585338	+	0.466791i	−0.870826	−	0.491591i	$-0.836416\pi$
$157$	−7.33426	+	5.84888i	−0.585338	+	0.466791i	0.285488	+	0.958382i	$0.407844\pi$
$158$	−22.5588	+	2.29543i	−1.79468	+	0.182615i
$159$	−1.65532	+	0.797158i	−0.131275	+	0.0632187i
$160$	3.45291	−	20.5869i	0.272977	−	1.62754i
$161$	−0.0919419	+	0.171522i	−0.00724604	+	0.0135178i
$162$	1.50434	+	2.45252i	0.118192	+	0.192688i
$163$	10.9548	−	8.73616i	0.858046	−	0.684269i	−0.0922096	−	0.995740i	$-0.529393\pi$
$163$	10.9548	−	8.73616i	0.858046	−	0.684269i	0.950256	+	0.311471i	$0.100822\pi$
$164$	7.62715	+	3.87807i	0.595581	+	0.302827i
$165$	−22.0384			−1.71569
$166$	−5.13563	+	1.73504i	−0.398602	+	0.134665i
$167$	9.86284	−	4.74969i	0.763210	−	0.367542i	−0.0114388	−	0.999935i	$-0.503641\pi$
$167$	9.86284	−	4.74969i	0.763210	−	0.367542i	0.774648	+	0.632392i	$0.217927\pi$
$168$	6.34065	+	2.77279i	0.489192	+	0.213925i
$169$	−1.36745	−	0.658528i	−0.105188	−	0.0506560i
$170$	−15.8075	−	1.95411i	−1.21238	−	0.149874i
$171$	1.50497	+	6.59370i	0.115088	+	0.504233i
$172$	8.23173	−	9.87705i	0.627663	−	0.753118i
$173$	−4.61562	+	9.58444i	−0.350919	+	0.728692i	−0.999472	−	0.0324778i	$-0.989660\pi$
$173$	−4.61562	+	9.58444i	−0.350919	+	0.728692i	0.648553	+	0.761169i	$0.275374\pi$
$174$	0.176787	+	0.0218543i	0.0134022	+	0.00165677i
$175$	−4.10716	−	22.4255i	−0.310472	−	1.69521i
$176$	25.4092	−	4.65568i	1.91529	−	0.350935i
$177$	1.11899			0.0841081
$178$	−2.54340	−	7.52834i	−0.190636	−	0.564273i
$179$	2.88308	+	5.98677i	0.215491	+	0.447472i	0.980492	−	0.196557i	$-0.0629760\pi$
$179$	2.88308	+	5.98677i	0.215491	+	0.447472i	−0.765001	+	0.644029i	$0.777262\pi$
$180$	3.85464	−	15.3525i	0.287308	−	1.14431i
$181$	−14.3390	+	3.27279i	−1.06581	+	0.243265i	−0.719242	−	0.694760i	$-0.755511\pi$
$181$	−14.3390	+	3.27279i	−1.06581	+	0.243265i	−0.346570	+	0.938024i	$0.612654\pi$
$182$	2.09822	−	12.5040i	0.155530	−	0.926855i
$183$	8.56305	+	1.95446i	0.632999	+	0.144478i
$184$	0.205876	+	0.0299759i	0.0151774	+	0.00220986i
$185$	15.7471	+	3.59418i	1.15775	+	0.264249i
$186$	−1.84859	−	1.18957i	−0.135545	−	0.0872238i
$187$	−4.38605	−	19.2165i	−0.320740	−	1.40525i
$188$	0.0322582	−	1.49384i	0.00235267	−	0.108950i
$189$	11.0945	+	5.94706i	0.807008	+	0.432585i
$190$	8.90514	−	13.8385i	0.646046	−	1.00395i
$191$	1.35444	+	1.08013i	0.0980036	+	0.0781553i	0.671266	−	0.741217i	$-0.265751\pi$
$191$	1.35444	+	1.08013i	0.0980036	+	0.0781553i	−0.573262	+	0.819372i	$0.694322\pi$
$192$	0.478865	−	7.38272i	0.0345591	−	0.532802i
$193$	−0.440447	+	0.552303i	−0.0317040	+	0.0397556i	−0.797431	−	0.603410i	$-0.793808\pi$
$193$	−0.440447	+	0.552303i	−0.0317040	+	0.0397556i	0.765727	+	0.643166i	$0.222380\pi$
$194$	−0.0291954	+	0.00297073i	−0.00209610	+	0.000213286i
$195$	11.5636			0.828086
$196$	−13.9054	+	1.62437i	−0.993246	+	0.116026i
$197$	−14.5205			−1.03454			−0.517271	−	0.855822i	$-0.673052\pi$
$197$	−14.5205			−1.03454			−0.517271	+	0.855822i	$0.673052\pi$
$198$	19.4878	−	1.98295i	1.38494	−	0.140922i
$199$	−7.80846	+	9.79150i	−0.553527	+	0.694101i	−0.977346	−	0.211646i	$-0.932118\pi$
$199$	−7.80846	+	9.79150i	−0.553527	+	0.694101i	0.423819	+	0.905747i	$0.360689\pi$
$200$	−21.0460	+	12.2920i	−1.48817	+	0.869175i
$201$	5.15936	+	4.11445i	0.363913	+	0.290211i
$202$	−8.69541	+	13.5126i	−0.611807	+	0.950745i
$203$	−0.331134	+	0.142168i	−0.0232410	+	0.00997824i
$204$	−5.64375	−	0.121872i	−0.395142	−	0.00853273i
$205$	−3.51298	−	15.3914i	−0.245357	−	1.07498i
$206$	15.8122	+	10.1752i	1.10169	+	0.708938i
$207$	0.153806	+	0.0351051i	0.0106902	+	0.00243997i
$208$	−13.3322	+	2.44284i	−0.924424	+	0.169381i
$209$	19.8540	+	4.53154i	1.37333	+	0.313453i
$210$	−3.55988	−	12.2623i	−0.245655	−	0.846181i
$211$	−5.59063	+	1.27603i	−0.384875	+	0.0878452i	−0.410581	−	0.911824i	$-0.634674\pi$
$211$	−5.59063	+	1.27603i	−0.384875	+	0.0878452i	0.0257054	+	0.999670i	$0.491817\pi$
$212$	−3.85379	−	0.967591i	−0.264680	−	0.0664544i
$213$	2.35614	+	4.89258i	0.161440	+	0.335234i
$214$	−5.46963	−	16.1898i	−0.373896	−	1.10672i
$215$	−23.7231			−1.61790
$216$	1.93893	−	13.3166i	0.131927	−	0.906083i
$217$	4.44293	+	0.192323i	0.301606	+	0.0130557i
$218$	−10.6346	−	1.31464i	−0.720265	−	0.0890385i
$219$	−5.47341	+	11.3656i	−0.369859	+	0.768019i
$220$	−36.6135	−	30.5144i	−2.46848	−	2.05728i
$221$	2.30136	+	10.0829i	0.154807	+	0.678252i
$222$	5.68129	+	0.702316i	0.381303	+	0.0471364i
$223$	5.10312	+	2.45753i	0.341730	+	0.164568i	0.596875	−	0.802334i	$-0.296409\pi$
$223$	5.10312	+	2.45753i	0.341730	+	0.164568i	−0.255145	+	0.966903i	$0.582123\pi$
$224$	6.69480	+	13.3858i	0.447315	+	0.894376i
$225$	−16.6514	+	8.01889i	−1.11009	+	0.534593i
$226$	2.55689	−	0.863826i	0.170082	−	0.0574609i
$227$	14.0310			0.931268			0.465634	−	0.884977i	$-0.345826\pi$
$227$	14.0310			0.931268			0.465634	+	0.884977i	$0.345826\pi$
$228$	2.64341	−	5.19888i	0.175064	−	0.344305i
$229$	17.4379	−	13.9063i	1.15233	−	0.918954i	0.154716	−	0.987959i	$-0.450554\pi$
$229$	17.4379	−	13.9063i	1.15233	−	0.918954i	0.997616	+	0.0690049i	$0.0219824\pi$
$230$	−0.200705	−	0.327209i	−0.0132341	−	0.0215755i
$231$	12.7683	−	9.30838i	0.840095	−	0.612446i
$232$	0.263445	+	0.281087i	0.0172960	+	0.0184542i
$233$	−21.6283	+	10.4156i	−1.41692	+	0.682351i	−0.976515	−	0.215450i	$-0.930878\pi$
$233$	−21.6283	+	10.4156i	−1.41692	+	0.682351i	−0.440401	+	0.897801i	$0.645164\pi$
$234$	−10.2253	+	1.04046i	−0.668447	+	0.0680168i
$235$	−2.15541	+	1.71889i	−0.140604	+	0.112128i
$236$	1.85902	+	1.54934i	0.121012	+	0.100854i
$237$	11.5928	+	9.24494i	0.753033	+	0.600524i
$238$	9.98372	−	5.54448i	0.647148	−	0.359395i
$239$	−5.78128	+	4.61042i	−0.373960	+	0.298223i	−0.792377	−	0.610032i	$-0.791157\pi$
$239$	−5.78128	+	4.61042i	−0.373960	+	0.298223i	0.418417	+	0.908255i	$0.362585\pi$
$240$	−11.0296	+	8.04214i	−0.711958	+	0.519118i
$241$	−6.40816	+	13.3067i	−0.412786	+	0.857159i	0.586112	+	0.810230i	$0.300658\pi$
$241$	−6.40816	+	13.3067i	−0.412786	+	0.857159i	−0.998898	+	0.0469292i	$0.985056\pi$
$242$	14.7842	−	40.8314i	0.950362	−	2.62474i
$243$	3.59478	−	15.7497i	0.230605	−	1.01035i
$244$	11.5200	+	15.1034i	0.737495	+	0.966896i
$245$	18.7282	+	17.7902i	1.19650	+	1.13657i
$246$	−1.79086	−	5.30087i	−0.114181	−	0.337971i
$247$	−10.4174	−	2.37770i	−0.662843	−	0.151290i
$248$	−1.42407	−	4.53585i	−0.0904284	−	0.288027i
$249$	3.19371	+	1.53801i	0.202393	+	0.0974675i
$250$	17.7483	+	6.42630i	1.12250	+	0.406435i
$251$	−8.66048	−	10.8599i	−0.546645	−	0.685471i	0.429382	−	0.903123i	$-0.358731\pi$
$251$	−8.66048	−	10.8599i	−0.546645	−	0.685471i	−0.976026	+	0.217653i	$0.930160\pi$
$252$	4.25120	+	10.5228i	0.267800	+	0.662876i
$253$	0.296174	−	0.371391i	0.0186203	−	0.0233491i
$254$	9.81208	−	6.01858i	0.615665	−	0.377640i
$255$	6.49396	+	8.14317i	0.406668	+	0.509945i
$256$	11.0177	−	11.6022i	0.688603	−	0.725138i
$257$	−6.15132	−	12.7734i	−0.383709	−	0.796780i	−0.999957	−	0.00922816i	$-0.997063\pi$
$257$	−6.15132	−	12.7734i	−0.383709	−	0.796780i	0.616248	−	0.787552i	$-0.288652\pi$
$258$	−8.36461	+	0.851128i	−0.520758	+	0.0529889i
$259$	−10.6414	+	4.56876i	−0.661226	+	0.283889i
$260$	19.2111	+	16.0109i	1.19142	+	0.992955i
$261$	0.182139	+	0.228395i	0.0112741	+	0.0141373i
$262$	−3.92019	+	3.83645i	−0.242190	+	0.237017i
$263$		−	17.0275i		−	1.04996i	−0.851114	−	0.524981i	$-0.824072\pi$
$263$		−	17.0275i		−	1.04996i	0.851114	−	0.524981i	$-0.175928\pi$
$264$	−14.0045	−	9.44559i	−0.861916	−	0.581336i
$265$	3.18088	+	6.60517i	0.195400	+	0.405752i
$266$	0.685643	+	11.7788i	0.0420394	+	0.722208i
$267$	−2.25458	+	4.68168i	−0.137978	+	0.286514i
$268$	2.87461	+	13.9792i	0.175595	+	0.853913i
$269$	9.29869	−	2.12236i	0.566951	−	0.129403i	0.0705688	−	0.997507i	$-0.477519\pi$
$269$	9.29869	−	2.12236i	0.566951	−	0.129403i	0.496382	+	0.868104i	$0.334661\pi$
$270$	−21.1648	+	12.9822i	−1.28805	+	0.790070i
$271$	15.3410	+	7.38785i	0.931901	+	0.448780i	0.837305	−	0.546736i	$-0.184130\pi$
$271$	15.3410	+	7.38785i	0.931901	+	0.448780i	0.0945960	+	0.995516i	$0.469844\pi$
$272$	−9.20748	−	8.01680i	−0.558285	−	0.486090i
$273$	−6.69956	+	4.88411i	−0.405476	+	0.295600i
$274$	3.72469	−	3.64513i	0.225017	−	0.220210i
$275$			55.6492i			3.35578i
$276$	−0.0825069	−	0.108171i	−0.00496633	−	0.00651114i
$277$	16.6096	−	7.99876i	0.997973	−	0.480599i	0.137723	−	0.990471i	$-0.456022\pi$
$277$	16.6096	−	7.99876i	0.997973	−	0.480599i	0.860250	+	0.509872i	$0.170307\pi$
$278$	20.5521	+	13.2253i	1.23263	+	0.793204i
$279$	−0.802198	−	3.51466i	−0.0480263	−	0.210417i
$280$	11.0642	−	25.3009i	0.661212	−	1.51202i
$281$	0.889293	−	3.89625i	0.0530508	−	0.232431i	−0.941451	−	0.337150i	$-0.890537\pi$
$281$	0.889293	−	3.89625i	0.0530508	−	0.232431i	0.994502	+	0.104719i	$0.0333943\pi$
$282$	−0.698317	+	0.683401i	−0.0415842	+	0.0406959i
$283$	−4.24407	+	18.5945i	−0.252284	+	1.10533i	0.677007	+	0.735977i	$0.263277\pi$
$283$	−4.24407	+	18.5945i	−0.252284	+	1.10533i	−0.929290	+	0.369350i	$0.879580\pi$
$284$	−2.85989	+	11.3906i	−0.169703	+	0.675906i
$285$	−10.4912	+	2.39455i	−0.621445	+	0.141841i
$286$	−10.5362	+	29.0991i	−0.623016	+	1.72067i
$287$	8.53616	+	7.43348i	0.503874	+	0.438784i
$288$	9.02949	−	8.10379i	0.532068	−	0.477520i
$289$	4.79126	−	6.00805i	0.281839	−	0.353415i
$290$	0.0872046	−	0.705430i	0.00512083	−	0.0414243i
$291$	0.0150033	+	0.0119647i	0.000879509	+	0.000701385i
$292$	−24.8301	+	11.3038i	−1.45307	+	0.661504i
$293$		−	30.5428i		−	1.78433i	−0.451712	−	0.892164i	$-0.649187\pi$
$293$		−	30.5428i		−	1.78433i	0.451712	−	0.892164i	$-0.350813\pi$
$294$	7.24171	+	5.60080i	0.422345	+	0.326645i
$295$		−	4.46506i		−	0.259966i
$296$	8.46616	+	9.03309i	0.492085	+	0.525038i
$297$	−24.0226	−	19.1574i	−1.39393	−	1.11162i
$298$	22.7281	+	2.80962i	1.31660	+	0.162757i
$299$	−0.155403	+	0.194869i	−0.00898718	+	0.0112696i
$300$	15.4579	+	3.88110i	0.892464	+	0.224075i
$301$	13.7444	−	10.0199i	0.792211	−	0.577538i
$302$	6.13952	+	2.22299i	0.353290	+	0.127919i
$303$	10.2441	−	2.33815i	0.588510	−	0.134323i
$304$	11.5900	−	4.97709i	0.664730	−	0.285456i
$305$	7.79884	−	34.1689i	0.446560	−	1.95651i
$306$	−6.47508	−	6.61641i	−0.370156	−	0.378235i
$307$	5.68808	−	24.9211i	0.324636	−	1.42232i	−0.504566	−	0.863373i	$-0.668348\pi$
$307$	5.68808	−	24.9211i	0.324636	−	1.42232i	0.829202	−	0.558949i	$-0.188795\pi$
$308$	34.1010	+	2.21459i	1.94308	+	0.126188i
$309$	−2.73605	−	11.9874i	−0.155649	−	0.681942i
$310$	−4.74673	+	7.37639i	−0.269596	+	0.418951i
$311$	−26.2309	+	12.6321i	−1.48742	+	0.716302i	−0.988623	−	0.150418i	$-0.951938\pi$
$311$	−26.2309	+	12.6321i	−1.48742	+	0.716302i	−0.498795	+	0.866720i	$0.666224\pi$
$312$	7.34816	+	4.95611i	0.416008	+	0.280584i
$313$			31.8341i			1.79937i	0.436539	+	0.899685i	$0.356204\pi$
$313$			31.8341i			1.79937i	−0.436539	+	0.899685i	$0.643796\pi$
$314$	9.27906	+	9.48160i	0.523648	+	0.535077i
$315$	9.89286	−	18.4556i	0.557400	−	1.03985i
$316$	6.45910	+	31.4104i	0.363353	+	1.76697i
$317$	−13.1758	−	6.34511i	−0.740024	−	0.356377i	0.0255938	−	0.999672i	$-0.491852\pi$
$317$	−13.1758	−	6.34511i	−0.740024	−	0.356377i	−0.765618	+	0.643296i	$0.777567\pi$
$318$	1.35854	+	2.21482i	0.0761831	+	0.124201i
$319$	0.857561	−	0.195733i	0.0480142	−	0.0109589i
$320$	−29.4591	−	1.91081i	−1.64681	−	0.106817i
$321$	−4.84852	+	10.0680i	−0.270618	+	0.561944i
$322$	0.254485	+	0.104802i	0.0141819	+	0.00584040i
$323$	−4.17588	−	8.67130i	−0.232352	−	0.482484i
$324$	3.23521	−	2.46764i	0.179734	−	0.137091i
$325$		−	29.1992i		−	1.61968i
$326$	−13.8596	−	14.1622i	−0.767614	−	0.784369i
$327$	4.36884	+	5.47836i	0.241598	+	0.302954i
$328$	4.36433	−	11.2862i	0.240980	−	0.623176i
$329$	0.522770	−	1.90625i	0.0288212	−	0.105095i
$330$	3.15506	+	31.0070i	0.173681	+	1.70688i
$331$	6.88686	+	14.3007i	0.378536	+	0.786039i	0.999997	+	0.00259297i	$0.000825368\pi$
$331$	6.88686	+	14.3007i	0.378536	+	0.786039i	−0.621460	+	0.783446i	$0.713460\pi$
$332$	3.17633	+	6.97717i	0.174324	+	0.382922i
$333$	5.85329	+	7.33979i	0.320758	+	0.402218i
$334$	−8.09456	−	13.1965i	−0.442914	−	0.722082i
$335$	16.4178	−	20.5873i	0.897000	−	1.12480i
$336$	2.99343	−	9.31792i	0.163305	−	0.508334i
$337$	12.9483	+	16.2367i	0.705339	+	0.884467i	0.997410	−	0.0719296i	$-0.0229157\pi$
$337$	12.9483	+	16.2367i	0.705339	+	0.884467i	−0.292071	+	0.956397i	$0.594344\pi$
$338$	−0.730749	+	2.01820i	−0.0397475	+	0.109776i
$339$	−1.59006	−	0.765733i	−0.0863603	−	0.0415889i
$340$	−0.486302	+	22.5201i	−0.0263734	+	1.22133i
$341$	−10.5828	−	2.41546i	−0.573092	−	0.130804i
$342$	9.06154	−	3.06138i	0.489992	−	0.165540i
$343$	−18.3645	−	2.39684i	−0.991590	−	0.129417i
$344$	−15.0750	−	10.1676i	−0.812788	−	0.548200i
$345$	−0.0558556	+	0.244719i	−0.00300716	+	0.0131752i
$346$	14.1456	+	5.12182i	0.760472	+	0.275351i
$347$	−0.913487	+	1.89687i	−0.0490385	+	0.101830i	−0.924048	−	0.382276i	$-0.875141\pi$
$347$	−0.913487	+	1.89687i	−0.0490385	+	0.101830i	0.875010	+	0.484105i	$0.160855\pi$
$348$	0.00543867	−	0.251859i	0.000291543	−	0.0135011i
$349$	7.68260	−	6.12667i	0.411240	−	0.327953i	−0.395921	−	0.918285i	$-0.629574\pi$
$349$	7.68260	−	6.12667i	0.411240	−	0.327953i	0.807161	+	0.590332i	$0.201003\pi$
$350$	−30.9636	+	8.98904i	−1.65507	+	0.480484i
$351$	12.6047	+	10.0519i	0.672788	+	0.536531i
$352$	−10.1879	−	35.0829i	−0.543019	−	1.86993i
$353$	−12.6303	+	10.0724i	−0.672245	+	0.536097i	−0.899052	−	0.437842i	$-0.855743\pi$
$353$	−12.6303	+	10.0724i	−0.672245	+	0.536097i	0.226807	+	0.973940i	$0.427171\pi$
$354$	−0.160196	−	1.57435i	−0.00851432	−	0.0836760i
$355$	19.5227	−	9.40166i	1.03616	−	0.498988i
$356$	−10.2279	+	4.65620i	−0.542076	+	0.246778i
$357$	−7.20182	−	1.97503i	−0.381161	−	0.104530i
$358$	8.01033	−	4.91342i	0.423359	−	0.259682i
$359$	−1.72458	+	1.37531i	−0.0910199	+	0.0725859i	−0.667943	−	0.744213i	$-0.732825\pi$
$359$	−1.72458	+	1.37531i	−0.0910199	+	0.0725859i	0.576923	+	0.816799i	$0.304253\pi$
$360$	−22.1521	−	3.22538i	−1.16752	−	0.169993i
$361$	−9.05633			−0.476649
$362$	6.65745	+	19.7057i	0.349908	+	1.03571i
$363$	−25.5845	+	12.3209i	−1.34284	+	0.646678i
$364$	−17.8928	−	1.16200i	−0.937838	−	0.0609052i
$365$	45.3521	+	21.8404i	2.37384	+	1.14318i
$366$	1.52392	−	12.3276i	0.0796568	−	0.644373i
$367$	3.04611	+	13.3459i	0.159006	+	0.696649i	0.990082	+	0.140491i	$0.0448680\pi$
$367$	3.04611	+	13.3459i	0.159006	+	0.696649i	−0.831076	+	0.556158i	$0.812275\pi$
$368$	0.0127010	−	0.293948i	0.000662087	−	0.0153231i
$369$	3.98126	−	8.26717i	0.207256	−	0.430372i
$370$	2.80244	−	22.6699i	0.145692	−	1.17855i
$371$	−4.63272	−	2.48331i	−0.240519	−	0.128927i
$372$	−1.40902	+	2.77118i	−0.0730544	+	0.143679i
$373$	−26.6728			−1.38107			−0.690534	−	0.723300i	$-0.742624\pi$
$373$	−26.6728			−1.38107			−0.690534	+	0.723300i	$0.742624\pi$
$374$	−26.4088	+	8.92202i	−1.36557	+	0.461347i
$375$	−5.35556	−	11.1209i	−0.276560	−	0.574283i
$376$	−2.10638	+	0.168476i	−0.108628	+	0.00868847i
$377$	−0.449963	+	0.102701i	−0.0231743	+	0.00528938i
$378$	6.77890	−	16.4608i	0.348669	−	0.846653i
$379$	12.4333	+	2.83782i	0.638656	+	0.145769i	0.529574	−	0.848264i	$-0.322352\pi$
$379$	12.4333	+	2.83782i	0.638656	+	0.145769i	0.109082	+	0.994033i	$0.465209\pi$
$380$	−20.7450	−	10.5479i	−1.06420	−	0.541097i
$381$	−7.33845	−	1.67495i	−0.375960	−	0.0858104i
$382$	1.32578	−	2.06026i	0.0678328	−	0.105412i
$383$	2.28378	+	10.0059i	0.116696	+	0.511277i	0.999163	+	0.0409038i	$0.0130237\pi$
$383$	2.28378	+	10.0059i	0.116696	+	0.511277i	−0.882467	+	0.470374i	$0.844119\pi$
$384$	−10.4557	+	0.383185i	−0.533564	+	0.0195543i
$385$	−37.1430	−	50.9492i	−1.89298	−	2.59661i
$386$	0.840117	+	0.540617i	0.0427608	+	0.0275167i
$387$	−10.7802	−	8.59691i	−0.547987	−	0.437005i
$388$	0.00835932	+	0.0406511i	0.000424380	+	0.00206375i
$389$	−1.61330	+	2.02302i	−0.0817976	+	0.102571i	−0.821046	−	0.570861i	$-0.806609\pi$
$389$	−1.61330	+	2.02302i	−0.0817976	+	0.102571i	0.739249	+	0.673432i	$0.235181\pi$
$390$	−1.65546	−	16.2694i	−0.0838277	−	0.823832i
$391$	−0.224500			−0.0113535
$392$	4.27613	+	19.3317i	0.215977	+	0.976398i
$393$	3.58680			0.180930
$394$	2.07878	+	20.4296i	0.104727	+	1.02923i
$395$	36.8899	−	46.2585i	1.85613	−	2.32752i
$396$	−5.57982	−	27.1345i	−0.280397	−	1.36356i
$397$	11.5515	+	9.21205i	0.579756	+	0.462340i	0.868929	−	0.494937i	$-0.164809\pi$
$397$	11.5515	+	9.21205i	0.579756	+	0.462340i	−0.289173	+	0.957277i	$0.593380\pi$
$398$	14.8940	+	9.58433i	0.746569	+	0.480419i
$399$	5.06687	−	5.81849i	0.253661	−	0.291289i
$400$	20.3072	+	27.8509i	1.01536	+	1.39254i
$401$	1.51328	+	6.63010i	0.0755694	+	0.331091i	0.998555	−	0.0537439i	$-0.0171155\pi$
$401$	1.51328	+	6.63010i	0.0755694	+	0.331091i	−0.922985	+	0.384835i	$0.874258\pi$
$402$	5.05020	−	7.84798i	0.251881	−	0.391422i
$403$	5.55281	+	1.26739i	0.276605	+	0.0631334i
$404$	20.2564	+	10.2995i	1.00779	+	0.512419i
$405$	−7.31912	−	1.67054i	−0.363690	−	0.0830099i
$406$	0.247429	+	0.445535i	0.0122797	+	0.0221115i
$407$	27.5589	−	6.29013i	1.36604	−	0.311790i
$408$	0.636503	+	7.95792i	0.0315116	+	0.393976i
$409$	4.60703	+	9.56660i	0.227803	+	0.473038i	0.983271	−	0.182148i	$-0.0583048\pi$
$409$	4.60703	+	9.56660i	0.227803	+	0.473038i	−0.755468	+	0.655185i	$0.772591\pi$
$410$	−21.1520	+	7.14604i	−1.04462	+	0.352918i
$411$	−3.40793			−0.168101
$412$	12.0522	−	23.7036i	0.593771	−	1.16779i
$413$	1.88591	+	2.58691i	0.0927994	+	0.127293i
$414$	0.0273720	−	0.221422i	0.00134526	−	0.0108823i
$415$	6.13709	−	12.7438i	0.301258	−	0.625569i
$416$	5.34562	+	18.4080i	0.262090	+	0.902529i
$417$	−3.55623	−	15.5809i	−0.174149	−	0.762999i
$418$	3.53331	−	28.5823i	0.172820	−	1.39800i
$419$	−22.4529	−	10.8127i	−1.09690	−	0.528237i	−0.204215	−	0.978926i	$-0.565464\pi$
$419$	−22.4529	−	10.8127i	−1.09690	−	0.528237i	−0.892681	+	0.450689i	$0.851178\pi$
$420$	−16.7428	+	6.76406i	−0.816966	+	0.330052i
$421$	−28.7493	+	13.8449i	−1.40115	+	0.674761i	−0.973395	−	0.229132i	$-0.926411\pi$
$421$	−28.7493	+	13.8449i	−1.40115	+	0.674761i	−0.427759	+	0.903893i	$0.640697\pi$
$422$	2.59567	+	7.68306i	0.126355	+	0.374005i
$423$	−1.60236			−0.0779094
$424$	−0.809635	+	5.56061i	−0.0393194	+	0.270047i
$425$	20.5623	−	16.3979i	0.997419	−	0.795415i
$426$	6.54630	−	4.01540i	0.317169	−	0.194547i
$427$	9.91354	+	23.0903i	0.479750	+	1.11742i
$428$	−21.9952	+	10.0133i	−1.06318	+	0.484009i
$429$	18.2332	−	8.78065i	0.880307	−	0.423934i
$430$	3.39624	+	33.3771i	0.163781	+	1.60959i
$431$	−25.7001	+	20.4951i	−1.23793	+	0.987215i	−0.238056	+	0.971251i	$0.576510\pi$
$431$	−25.7001	+	20.4951i	−1.23793	+	0.987215i	−0.999873	+	0.0159637i	$0.994918\pi$
$432$	−19.0134	−	0.821538i	−0.914784	−	0.0395263i
$433$	−12.5837	−	10.0352i	−0.604734	−	0.482259i	0.272608	−	0.962125i	$-0.412114\pi$
$433$	−12.5837	−	10.0352i	−0.604734	−	0.482259i	−0.877342	+	0.479866i	$0.840685\pi$
$434$	−0.365470	−	6.27851i	−0.0175431	−	0.301378i
$435$	−0.363399	+	0.289801i	−0.0174236	+	0.0138949i
$436$	−0.327162	+	15.1505i	−0.0156682	+	0.725579i
$437$	0.100638	−	0.208977i	0.00481418	−	0.00999675i
$438$	16.7745	+	6.07368i	0.801515	+	0.290212i
$439$	7.01383	−	30.7296i	0.334752	−	1.46664i	−0.475059	−	0.879954i	$-0.657573\pi$
$439$	7.01383	−	30.7296i	0.334752	−	1.46664i	0.809811	−	0.586691i	$-0.199570\pi$
$440$	−37.6905	+	55.8817i	−1.79682	+	2.66406i
$441$	2.06349	+	14.8710i	0.0982613	+	0.708143i
$442$	13.8567	−	4.68139i	0.659096	−	0.222671i
$443$	−28.8464	−	6.58401i	−1.37054	−	0.312816i	−0.526989	−	0.849872i	$-0.676679\pi$
$443$	−28.8464	−	6.58401i	−1.37054	−	0.312816i	−0.843547	+	0.537056i	$0.819536\pi$
$444$	0.174779	−	8.09383i	0.00829464	−	0.384116i
$445$	18.6812	+	8.99639i	0.885574	+	0.426470i
$446$	2.72705	−	7.53165i	0.129130	−	0.356634i
$447$	−9.33702	−	11.7083i	−0.441626	−	0.553781i
$448$	17.8747	−	11.3356i	0.844500	−	0.535556i
$449$	2.38390	−	2.98932i	0.112503	−	0.141075i	−0.722391	−	0.691484i	$-0.756957\pi$
$449$	2.38390	−	2.98932i	0.112503	−	0.141075i	0.834895	+	0.550410i	$0.185528\pi$
$450$	13.6660	+	22.2797i	0.644222	+	1.05027i
$451$	−17.2264	−	21.6012i	−0.811160	−	1.01716i
$452$	−1.58141	−	3.47374i	−0.0743832	−	0.163391i
$453$	−1.85260	−	3.84696i	−0.0870428	−	0.180746i
$454$	−2.00870	−	19.7408i	−0.0942728	−	0.926484i
$455$	19.4890	+	26.7331i	0.913657	+	1.25327i
$456$	−7.69300	−	2.97485i	−0.360258	−	0.139310i
$457$	2.28262	+	2.86232i	0.106777	+	0.133894i	0.832348	−	0.554253i	$-0.186996\pi$
$457$	2.28262	+	2.86232i	0.106777	+	0.133894i	−0.725572	+	0.688147i	$0.758425\pi$
$458$	−22.0619	−	22.5434i	−1.03088	−	1.05339i
$459$			14.5213i			0.677798i
$460$	−0.431633	+	0.329226i	−0.0201250	+	0.0153502i
$461$	−5.12861	−	10.6497i	−0.238863	−	0.496005i	0.746732	−	0.665125i	$-0.231622\pi$
$461$	−5.12861	−	10.6497i	−0.238863	−	0.496005i	−0.985595	+	0.169120i	$0.945907\pi$
$462$	−14.9243	−	16.6318i	−0.694343	−	0.773781i
$463$	1.87583	−	3.89520i	0.0871771	−	0.181025i	−0.852822	−	0.522201i	$-0.825111\pi$
$463$	1.87583	−	3.89520i	0.0871771	−	0.181025i	0.939999	+	0.341176i	$0.110825\pi$
$464$	0.357759	−	0.410895i	0.0166085	−	0.0190753i
$465$	5.59215	−	1.27637i	0.259330	−	0.0591904i
$466$	17.7506	+	28.9388i	0.822281	+	1.34056i
$467$	19.3485	+	9.31777i	0.895344	+	0.431175i	0.824205	−	0.566292i	$-0.191622\pi$
$467$	19.3485	+	9.31777i	0.895344	+	0.431175i	0.0711387	+	0.997466i	$0.477337\pi$
$468$	2.92774	+	14.2375i	0.135335	+	0.658128i
$469$	−0.816484	+	18.8620i	−0.0377017	+	0.870964i
$470$	2.72696	+	2.78648i	0.125785	+	0.128531i
$471$		−	8.67524i		−	0.399734i
$472$	1.91371	−	2.83735i	0.0880855	−	0.130600i
$473$	−37.4060	+	18.0138i	−1.71993	+	0.828274i
$474$	11.3475	−	17.6340i	0.521209	−	0.809956i
$475$	6.04647	+	26.4913i	0.277431	+	1.21551i
$476$	−9.23008	−	13.2528i	−0.423060	−	0.607442i
$477$	−0.948172	+	4.15421i	−0.0434138	+	0.190208i
$478$	7.31428	+	7.47393i	0.334547	+	0.341850i
$479$	−0.301045	+	1.31896i	−0.0137551	+	0.0602650i	−0.981340	−	0.192282i	$-0.938411\pi$
$479$	−0.301045	+	1.31896i	−0.0137551	+	0.0602650i	0.967585	+	0.252547i	$0.0812683\pi$
$480$	12.8939	+	14.3668i	0.588523	+	0.655750i
$481$	−14.4602	+	3.30044i	−0.659327	+	0.150487i
$482$	19.6392	+	7.11095i	0.894543	+	0.323895i
$483$	−0.0710012	−	0.165374i	−0.00323067	−	0.00752477i
$484$	−59.5642	−	14.9551i	−2.70746	−	0.679776i
$485$	0.0477426	−	0.0598673i	0.00216788	−	0.00271843i
$486$	−22.6737	−	2.80290i	−1.02850	−	0.127142i
$487$	−19.1513	−	15.2727i	−0.867830	−	0.692071i	0.0847361	−	0.996403i	$-0.472995\pi$
$487$	−19.1513	−	15.2727i	−0.867830	−	0.692071i	−0.952566	+	0.304332i	$0.901567\pi$
$488$	19.6005	−	18.3703i	0.887272	−	0.831586i
$489$			12.9577i			0.585970i
$490$	22.3487	−	28.8964i	1.00961	−	1.30541i
$491$		−	35.9095i		−	1.62057i	−0.586035	−	0.810285i	$-0.699312\pi$
$491$		−	35.9095i		−	1.62057i	0.586035	−	0.810285i	$-0.300688\pi$
$492$	−7.20168	+	3.27854i	−0.324677	+	0.147808i
$493$	−0.325016	−	0.259192i	−0.0146380	−	0.0116734i
$494$	−1.85393	+	14.9971i	−0.0834124	+	0.674753i
$495$	−31.8681	+	39.9613i	−1.43236	+	1.79613i
$496$	−6.17783	+	2.65295i	−0.277393	+	0.119121i
$497$	−7.33985	+	13.6928i	−0.329237	+	0.614207i
$498$	1.70669	−	4.71358i	0.0764784	−	0.211220i
$499$	16.5536	−	3.77824i	0.741039	−	0.169137i	0.164695	−	0.986345i	$-0.447336\pi$
$499$	16.5536	−	3.77824i	0.741039	−	0.169137i	0.576344	+	0.817207i	$0.304479\pi$
$500$	6.50059	−	25.8910i	0.290715	−	1.15788i
$501$	−2.25269	+	9.86968i	−0.100643	+	0.440945i
$502$	−14.0395	+	13.7396i	−0.626612	+	0.613227i
$503$	−7.99820	+	35.0424i	−0.356622	+	1.56246i	0.404922	+	0.914351i	$0.367299\pi$
$503$	−7.99820	+	35.0424i	−0.356622	+	1.56246i	−0.761544	+	0.648113i	$0.775559\pi$
$504$	14.1965	−	7.48768i	0.632361	−	0.333528i
$505$	−9.32988	−	40.8769i	−0.415174	−	1.81900i
$506$	−0.564928	−	0.363533i	−0.0251141	−	0.0161610i
$507$	1.26459	−	0.608993i	0.0561623	−	0.0270463i
$508$	−9.87255	−	12.9435i	−0.438024	−	0.574273i
$509$		−	0.698915i		−	0.0309788i	−0.999880	−	0.0154894i	$-0.995069\pi$
$509$		−	0.698915i		−	0.0309788i	0.999880	−	0.0154894i	$-0.00493063\pi$
$510$	10.5273	−	10.3025i	0.466158	−	0.456201i
$511$	−35.5002	+	6.50175i	−1.57044	+	0.287620i
$512$	−17.9010	−	13.8403i	−0.791121	−	0.611660i
$513$	−13.5173	−	6.50957i	−0.596801	−	0.287404i
$514$	−17.0908	+	10.4833i	−0.753844	+	0.462396i
$515$	−47.8332	+	10.9176i	−2.10778	+	0.481088i
$516$	2.39499	+	11.6467i	0.105433	+	0.512719i
$517$	−2.09340	+	4.34698i	−0.0920675	+	0.191180i
$518$	7.95146	+	14.3179i	0.349367	+	0.629091i
$519$	−4.26843	−	8.86350i	−0.187363	−	0.389064i
$520$	19.7762	−	29.3212i	0.867246	−	1.28582i
$521$		−	15.8242i		−	0.693270i	−0.938000	−	0.346635i	$-0.887324\pi$
$521$		−	15.8242i		−	0.693270i	0.938000	−	0.346635i	$-0.112676\pi$
$522$	0.295265	−	0.288958i	0.0129234	−	0.0126474i
$523$	24.2933	+	30.4628i	1.06227	+	1.33205i	0.940616	+	0.339473i	$0.110249\pi$
$523$	24.2933	+	30.4628i	1.06227	+	1.33205i	0.121655	+	0.992572i	$0.461180\pi$
$524$	5.95892	+	4.96628i	0.260316	+	0.216953i
$525$	18.5823	+	9.96078i	0.810997	+	0.434724i
$526$	−23.9569	+	2.43769i	−1.04457	+	0.106288i
$527$	2.22588	+	4.62209i	0.0969608	+	0.201341i
$528$	−11.2846	+	21.0558i	−0.491097	+	0.916337i
$529$	14.3369	+	17.9779i	0.623343	+	0.781648i
$530$	8.83775	−	5.42094i	0.383887	−	0.235471i
$531$	1.61808	−	2.02900i	0.0702185	−	0.0880512i
$532$	16.4741	−	2.65095i	0.714242	−	0.114933i
$533$	9.03871	+	11.3342i	0.391510	+	0.490938i
$534$	6.90965	+	2.50184i	0.299010	+	0.108265i
$535$	40.1743	+	19.3469i	1.73689	+	0.836440i
$536$	19.2564	−	6.04572i	0.831750	−	0.261135i
$537$	−5.99092	−	1.36739i	−0.258527	−	0.0590071i
$538$	−4.31728	−	12.7789i	−0.186131	−	0.550939i
$539$	43.0388	+	13.8302i	1.85381	+	0.595709i
$540$	21.2952	+	27.9192i	0.916401	+	1.20145i
$541$	1.18246	−	5.18070i	0.0508379	−	0.222735i	−0.943127	−	0.332432i	$-0.892131\pi$
$541$	1.18246	−	5.18070i	0.0508379	−	0.222735i	0.993965	+	0.109697i	$0.0349879\pi$
$542$	8.19808	−	22.6417i	0.352138	−	0.972544i
$543$	5.90145	−	12.2545i	0.253255	−	0.525890i
$544$	−9.96106	+	14.1021i	−0.427077	+	0.604625i
$545$	21.8602	−	17.4329i	0.936386	−	0.746743i
$546$	7.83082	+	8.72672i	0.335128	+	0.373469i
$547$	−23.4023	−	18.6627i	−1.00061	−	0.797960i	−0.0211867	−	0.999776i	$-0.506744\pi$
$547$	−23.4023	−	18.6627i	−1.00061	−	0.797960i	−0.979424	+	0.201815i	$0.935316\pi$
$548$	−5.66175	−	4.71861i	−0.241858	−	0.201569i
$549$	15.9263	−	12.7008i	0.679717	−	0.542056i
$550$	78.2956	−	7.96685i	3.33854	−	0.339707i
$551$	0.386967	−	0.186354i	0.0164854	−	0.00793893i
$552$	−0.140379	+	0.131569i	−0.00597495	+	0.00559995i
$553$	−1.83459	+	42.3818i	−0.0780149	+	1.80226i
$554$	−13.6317	−	22.2237i	−0.579155	−	0.944196i
$555$	−11.6783	+	9.31314i	−0.495716	+	0.395321i
$556$	15.6651	−	30.8091i	0.664348	−	1.30660i
$557$	5.13577			0.217610			0.108805	−	0.994063i	$-0.465298\pi$
$557$	5.13577			0.217610			0.108805	+	0.994063i	$0.465298\pi$
$558$	−4.83010	+	1.63182i	−0.204474	+	0.0690803i
$559$	19.6269	−	9.45184i	0.830131	−	0.399770i
$560$	−37.1811	−	11.9446i	−1.57119	−	0.504753i
$561$	16.4229	+	7.90887i	0.693377	+	0.333913i
$562$	−5.60913	−	0.693396i	−0.236607	−	0.0292491i
$563$	−8.55628	−	37.4875i	−0.360604	−	1.57991i	−0.751664	−	0.659546i	$-0.770749\pi$
$563$	−8.55628	−	37.4875i	−0.360604	−	1.57991i	0.391060	−	0.920365i	$-0.372108\pi$
$564$	1.06148	+	0.884660i	0.0446965	+	0.0372509i
$565$	−3.05549	+	6.34478i	−0.128545	+	0.266927i
$566$	26.7691	+	3.30917i	1.12519	+	0.139095i
$567$	4.94604	−	2.12352i	0.207714	−	0.0891795i
$568$	16.4354	+	2.39302i	0.689613	+	0.100409i
$569$	38.1102			1.59766			0.798832	−	0.601554i	$-0.205452\pi$
$569$	38.1102			1.59766			0.798832	+	0.601554i	$0.205452\pi$
$570$	4.87095	+	14.4178i	0.204022	+	0.603894i
$571$	−14.1050	−	29.2893i	−0.590276	−	1.22572i	−0.955552	−	0.294822i	$-0.904740\pi$
$571$	−14.1050	−	29.2893i	−0.590276	−	1.22572i	0.365276	−	0.930899i	$-0.380975\pi$
$572$	42.4493	+	10.6580i	1.77489	+	0.445632i
$573$	−1.56191	+	0.356496i	−0.0652498	+	0.0148928i
$574$	9.23647	−	13.0741i	0.385523	−	0.545704i
$575$	0.617940	+	0.141041i	0.0257699	+	0.00588181i
$576$	−12.6943	−	11.5439i	−0.528929	−	0.480995i
$577$	12.4254	+	2.83602i	0.517276	+	0.118065i	0.473186	−	0.880963i	$-0.343104\pi$
$577$	12.4254	+	2.83602i	0.517276	+	0.118065i	0.0440903	+	0.999028i	$0.485961\pi$
$578$	−9.13894	−	5.88093i	−0.380130	−	0.244615i
$579$	−0.145369	−	0.636905i	−0.00604135	−	0.0264689i
$580$	−1.00499	−	0.0217018i	−0.0417299	−	0.000901119i
$581$	1.82697	+	9.97546i	0.0757956	+	0.413852i
$582$	0.0146859	−	0.0228218i	0.000608749	−	0.000945993i
$583$	10.0311	+	7.99952i	0.415445	+	0.331306i
$584$	19.4586	+	33.3163i	0.805201	+	1.37864i
$585$	16.7212	−	20.9677i	0.691336	−	0.866908i
$586$	−42.9721	+	4.37256i	−1.77516	+	0.180629i
$587$	−20.0395			−0.827119			−0.413559	−	0.910477i	$-0.635715\pi$
$587$	−20.0395			−0.827119			−0.413559	+	0.910477i	$0.635715\pi$
$588$	6.84330	−	10.9905i	0.282213	−	0.453242i
$589$	−5.30030			−0.218395
$590$	−6.28211	+	0.639226i	−0.258630	+	0.0263165i
$591$	8.37238	−	10.4986i	0.344394	−	0.431856i
$592$	11.4971	−	13.2046i	0.472526	−	0.542708i
$593$	5.56296	+	4.43631i	0.228443	+	0.182178i	0.731022	−	0.682354i	$-0.239044\pi$
$593$	5.56296	+	4.43631i	0.228443	+	0.182178i	−0.502578	+	0.864532i	$0.667615\pi$
$594$	−23.5143	+	36.5412i	−0.964805	+	1.49930i
$595$	−7.88091	+	28.7372i	−0.323086	+	1.17811i
$596$	0.699205	−	32.3794i	0.0286406	−	1.32631i
$597$	−2.57718	−	11.2914i	−0.105477	−	0.462125i
$598$	0.296418	+	0.190746i	0.0121215	+	0.00780019i
$599$	18.9146	+	4.31714i	0.772831	+	0.176394i	0.590711	−	0.806883i	$-0.298847\pi$
$599$	18.9146	+	4.31714i	0.772831	+	0.176394i	0.182119	+	0.983276i	$0.441704\pi$
$600$	3.24752	−	22.3041i	0.132580	−	0.910563i
$601$	−4.54718	−	1.03786i	−0.185483	−	0.0423354i	0.128770	−	0.991674i	$-0.458897\pi$
$601$	−4.54718	−	1.03786i	−0.185483	−	0.0423354i	−0.314254	+	0.949339i	$0.601754\pi$
$602$	−16.0652	−	17.9031i	−0.654767	−	0.729677i
$603$	14.9211	−	3.40564i	0.607633	−	0.138688i
$604$	2.24869	−	8.95624i	0.0914978	−	0.364424i
$605$	49.1637	+	102.089i	1.99879	+	4.15052i
$606$	−4.75623	−	14.0782i	−0.193209	−	0.571889i
$607$	−1.95223			−0.0792387			−0.0396193	−	0.999215i	$-0.512615\pi$
$607$	−1.95223			−0.0792387			−0.0396193	+	0.999215i	$0.512615\pi$
$608$	−8.66175	−	15.5940i	−0.351280	−	0.632419i
$609$	0.0881380	−	0.321390i	0.00357153	−	0.0130234i
$610$	−49.1904	−	6.08088i	−1.99166	−	0.246208i
$611$	1.09841	−	2.28087i	0.0444368	−	0.0922740i
$612$	−8.38197	+	10.0573i	−0.338821	+	0.406543i
$613$	0.0117640	+	0.0515413i	0.000475142	+	0.00208173i	0.975165	−	0.221480i	$-0.0710887\pi$
$613$	0.0117640	+	0.0515413i	0.000475142	+	0.00208173i	−0.974690	+	0.223562i	$0.928232\pi$
$614$	−35.8770	−	4.43508i	−1.44788	−	0.178985i
$615$	13.1539	+	6.33456i	0.530415	+	0.255434i
$616$	−1.76614	−	48.2954i	−0.0711598	−	1.94588i
$617$	−0.0762730	+	0.0367311i	−0.00307063	+	0.00147874i	−0.435418	−	0.900228i	$-0.643400\pi$
$617$	−0.0762730	+	0.0367311i	−0.00307063	+	0.00147874i	0.432348	+	0.901707i	$0.357685\pi$
$618$	−16.4740	+	5.56563i	−0.662682	+	0.223883i
$619$	8.46533			0.340250			0.170125	−	0.985422i	$-0.445583\pi$
$619$	8.46533			0.340250			0.170125	+	0.985422i	$0.445583\pi$
$620$	11.0578	+	5.62239i	0.444090	+	0.225800i
$621$	−0.273612	+	0.218198i	−0.0109797	+	0.00875598i
$622$	21.5280	+	35.0971i	0.863195	+	1.40726i
$623$	−14.6231	+	2.67817i	−0.585861	+	0.107298i
$624$	5.92101	−	11.0480i	0.237030	−	0.442275i
$625$	−5.55724	+	2.67623i	−0.222290	+	0.107049i
$626$	44.7890	−	4.55743i	1.79013	−	0.182152i
$627$	−14.7240	+	11.7420i	−0.588021	+	0.468931i
$628$	12.0117	−	14.4126i	0.479320	−	0.575124i
$629$	−10.4448	−	8.32948i	−0.416463	−	0.332118i
$630$	−27.3823	−	11.2766i	−1.09094	−	0.449271i
$631$	−7.63577	+	6.08932i	−0.303975	+	0.242412i	−0.763583	−	0.645710i	$-0.776562\pi$
$631$	−7.63577	+	6.08932i	−0.303975	+	0.242412i	0.459608	+	0.888122i	$0.347990\pi$
$632$	43.2681	−	13.5844i	1.72111	−	0.540358i
$633$	2.30091	−	4.77789i	0.0914531	−	0.189904i
$634$	−7.04098	+	19.4460i	−0.279633	+	0.772299i
$635$	−6.68352	+	29.2824i	−0.265228	+	1.16204i
$636$	2.92165	−	2.22847i	0.115851	−	0.0883647i
$637$	−22.5825	−	7.25672i	−0.894752	−	0.287522i
$638$	−0.398156	−	1.17852i	−0.0157631	−	0.0466582i
$639$	12.2785	+	2.80249i	0.485730	+	0.110865i
$640$	1.52901	+	41.7210i	0.0604396	+	1.64917i
$641$	−33.3571	−	16.0639i	−1.31753	−	0.634487i	−0.362771	−	0.931878i	$-0.618169\pi$
$641$	−33.3571	−	16.0639i	−1.31753	−	0.634487i	−0.954756	+	0.297391i	$0.903883\pi$
$642$	14.8593	+	5.38025i	0.586452	+	0.212342i
$643$	3.60642	+	4.52230i	0.142223	+	0.178342i	0.847841	−	0.530250i	$-0.177902\pi$
$643$	3.60642	+	4.52230i	0.142223	+	0.178342i	−0.705618	+	0.708592i	$0.749331\pi$
$644$	0.111019	−	0.373051i	0.00437475	−	0.0147003i
$645$	13.6785	−	17.1523i	0.538590	−	0.675371i
$646$	−11.6022	+	7.11665i	−0.456484	+	0.280001i
$647$	8.59670	+	10.7799i	0.337971	+	0.423802i	0.921553	−	0.388252i	$-0.126921\pi$
$647$	8.59670	+	10.7799i	0.337971	+	0.423802i	−0.583582	+	0.812054i	$0.698349\pi$
$648$	−3.93500	−	4.19850i	−0.154581	−	0.164933i
$649$	−3.39048	−	7.04040i	−0.133088	−	0.276360i
$650$	−41.0818	+	4.18021i	−1.61136	+	0.163961i
$651$	−2.70081	+	3.10145i	−0.105853	+	0.121555i
$652$	−17.9413	+	21.5273i	−0.702634	+	0.843073i
$653$	10.6189	+	13.3156i	0.415548	+	0.521081i	0.944917	−	0.327311i	$-0.106143\pi$
$653$	10.6189	+	13.3156i	0.415548	+	0.521081i	−0.529369	+	0.848392i	$0.677571\pi$
$654$	7.08231	−	6.93103i	0.276940	−	0.271025i
$655$		−	14.3123i		−	0.559229i
$656$	−16.5039	−	4.52464i	−0.644370	−	0.176658i
$657$	12.6941	+	26.3596i	0.495245	+	1.02839i
$658$	−2.75683	−	0.462609i	−0.107473	−	0.0180344i
$659$	−11.8943	+	24.6987i	−0.463335	+	0.962124i	0.530123	+	0.847921i	$0.322146\pi$
$659$	−11.8943	+	24.6987i	−0.463335	+	0.962124i	−0.993457	+	0.114203i	$0.963568\pi$
$660$	43.1735	−	8.87803i	1.68053	−	0.345577i
$661$	−20.6258	+	4.70770i	−0.802249	+	0.183108i	−0.603938	−	0.797031i	$-0.706403\pi$
$661$	−20.6258	+	4.70770i	−0.802249	+	0.183108i	−0.198311	+	0.980139i	$0.563546\pi$
$662$	19.1344	−	11.7368i	0.743681	−	0.456163i
$663$	−8.61713	−	4.14979i	−0.334662	−	0.161164i
$664$	9.36180	−	5.46780i	0.363308	−	0.212192i
$665$	−23.2174	−	20.2182i	−0.900332	−	0.784029i
$666$	9.48874	−	9.28605i	0.367681	−	0.359827i
$667$		−	0.0100186i		−	0.000387922i
$668$	−17.4080	+	13.2779i	−0.673536	+	0.513736i
$669$	−4.71926	+	2.27268i	−0.182457	+	0.0878667i
$670$	−31.3156	−	20.1517i	−1.20983	−	0.778528i
$671$	−13.6487	−	59.7987i	−0.526901	−	2.30850i
$672$	−13.5384	−	2.87764i	−0.522255	−	0.111007i
$673$	5.67225	−	24.8517i	0.218649	−	0.957965i	−0.739828	−	0.672796i	$-0.765093\pi$
$673$	5.67225	−	24.8517i	0.218649	−	0.957965i	0.958477	−	0.285169i	$-0.0920496\pi$
$674$	20.9904	−	20.5421i	0.808522	−	0.791251i
$675$	9.12292	−	39.9701i	0.351141	−	1.53845i
$676$	2.94413	+	0.739196i	0.113236	+	0.0284306i
$677$	−24.3338	+	5.55403i	−0.935223	+	0.213459i	−0.662866	−	0.748738i	$-0.730660\pi$
$677$	−24.3338	+	5.55403i	−0.935223	+	0.213459i	−0.272357	+	0.962196i	$0.587803\pi$
$678$	−0.849711	+	2.34676i	−0.0326330	+	0.0901267i
$679$	−0.00237432	+	0.0548502i	−9.11180e−5	+	0.00210496i
$680$	31.7543	−	2.53982i	1.21772	−	0.0973977i
$681$	−8.09012	+	10.1447i	−0.310014	+	0.388745i
$682$	−1.88337	+	15.2353i	−0.0721180	+	0.583389i
$683$	25.3873	+	20.2457i	0.971419	+	0.774681i	0.974286	−	0.225315i	$-0.0723411\pi$
$683$	25.3873	+	20.2457i	0.971419	+	0.774681i	−0.00286675	+	0.999996i	$0.500913\pi$
$684$	−5.60447	−	12.3109i	−0.214292	−	0.470717i
$685$			13.5986i			0.519575i
$686$	−0.743130	+	26.1811i	−0.0283728	+	0.999597i
$687$			20.6263i			0.786941i
$688$	−12.1471	+	22.6653i	−0.463105	+	0.864108i
$689$	−5.26332	−	4.19735i	−0.200516	−	0.159906i
$690$	0.352304	+	0.0435515i	0.0134120	+	0.00165798i
$691$	21.5649	−	27.0416i	0.820369	−	1.02871i	−0.178628	−	0.983917i	$-0.557166\pi$
$691$	21.5649	−	27.0416i	0.820369	−	1.02871i	0.998996	−	0.0447931i	$-0.0142629\pi$
$692$	5.18103	−	20.6354i	0.196953	−	0.784440i
$693$	1.58485	−	36.6123i	0.0602035	−	1.39079i
$694$	2.79958	+	1.01367i	0.106271	+	0.0384784i
$695$	−62.1720	+	14.1904i	−2.35832	+	0.538271i
$696$	−0.355132	+	0.0284047i	−0.0134612	+	0.00107668i
$697$	−2.90560	+	12.7303i	−0.110057	+	0.482193i
$698$	−9.71977	−	9.93192i	−0.367899	−	0.375929i
$699$	4.93994	−	21.6433i	0.186846	−	0.818624i
$700$	17.0799	+	42.2773i	0.645560	+	1.59793i
$701$	1.73982	+	7.62266i	0.0657121	+	0.287904i	0.997098	−	0.0761300i	$-0.0242564\pi$
$701$	1.73982	+	7.62266i	0.0657121	+	0.287904i	−0.931386	+	0.364034i	$0.881399\pi$
$702$	12.3380	−	19.1732i	0.465668	−	0.723645i
$703$	12.4357	−	5.98872i	0.469021	−	0.225869i
$704$	−47.9014	+	19.3564i	−1.80535	+	0.729523i
$705$		−	2.54951i		−	0.0960199i
$706$	15.9795	+	16.3283i	0.601395	+	0.614522i
$707$	22.6706	+	19.7420i	0.852615	+	0.742476i
$708$	−2.19210	+	0.450775i	−0.0823843	+	0.0169412i
$709$	−4.04001	−	1.94557i	−0.151726	−	0.0730673i	0.356480	−	0.934303i	$-0.383977\pi$
$709$	−4.04001	−	1.94557i	−0.151726	−	0.0730673i	−0.508206	+	0.861236i	$0.669691\pi$
$710$	−16.0226	−	26.1215i	−0.601316	−	0.980324i
$711$	33.5268	−	7.65228i	1.25735	−	0.286983i
$712$	8.01527	+	13.7235i	0.300385	+	0.514310i
$713$	−0.0536435	+	0.111392i	−0.00200896	+	0.00417166i
$714$	−1.74774	+	10.4153i	−0.0654075	+	0.389784i
$715$	−35.0372	−	72.7555i	−1.31032	−	2.72090i
$716$	−8.05970	−	10.5667i	−0.301205	−	0.394896i
$717$		−	6.83832i		−	0.255382i
$718$	2.18188	+	2.22950i	0.0814271	+	0.0832044i
$719$	8.63837	+	10.8322i	0.322157	+	0.403972i	0.916368	−	0.400337i	$-0.131107\pi$
$719$	8.63837	+	10.8322i	0.322157	+	0.403972i	−0.594211	+	0.804309i	$0.702536\pi$
$720$	−1.36662	+	31.6286i	−0.0509309	+	1.17873i
$721$	23.1017	−	26.5286i	0.860352	−	0.987977i
$722$	1.29652	+	12.7418i	0.0482515	+	0.474200i
$723$	−5.92614	−	12.3058i	−0.220395	−	0.457656i
$724$	26.7719	−	12.1878i	0.994969	−	0.452956i
$725$	0.731776	+	0.917618i	0.0271775	+	0.0340795i
$726$	20.9976	+	34.2323i	0.779292	+	1.27048i
$727$	−4.51607	+	5.66297i	−0.167492	+	0.210028i	−0.858493	−	0.512826i	$-0.828599\pi$
$727$	−4.51607	+	5.66297i	−0.167492	+	0.210028i	0.691001	+	0.722854i	$0.257170\pi$
$728$	0.926696	+	25.3406i	0.0343456	+	0.939186i
$729$	5.50933	+	6.90848i	0.204049	+	0.255870i
$730$	24.2357	−	66.9348i	0.897002	−	2.47737i
$731$	17.6783	+	8.51342i	0.653855	+	0.314880i
$732$	−17.5624	−	0.379245i	−0.649126	−	0.0140173i
$733$	17.8387	+	4.07158i	0.658889	+	0.150387i	0.538876	−	0.842385i	$-0.318849\pi$
$733$	17.8387	+	4.07158i	0.658889	+	0.150387i	0.120013	+	0.992772i	$0.461706\pi$
$734$	18.3409	−	6.19634i	0.676974	−	0.228711i
$735$	−23.6612	+	3.28321i	−0.872755	+	0.121103i
$736$	−0.415389	+	0.0242125i	−0.0153114	+	0.000892484i
$737$	10.2546	−	44.9281i	0.377731	−	1.65495i
$738$	−12.2015	−	4.41789i	−0.449142	−	0.162625i
$739$	−20.8029	+	43.1978i	−0.765249	+	1.58906i	0.0421941	+	0.999109i	$0.486565\pi$
$739$	−20.8029	+	43.1978i	−0.765249	+	1.58906i	−0.807443	+	0.589946i	$0.799149\pi$
$740$	−32.2966	−	0.697417i	−1.18725	−	0.0256375i
$741$	7.72571	−	6.16105i	0.283811	−	0.226332i
$742$	−2.83066	+	6.87351i	−0.103917	+	0.252335i
$743$	−18.3337	−	14.6206i	−0.672599	−	0.536379i	0.226563	−	0.973997i	$-0.427251\pi$
$743$	−18.3337	−	14.6206i	−0.672599	−	0.536379i	−0.899161	+	0.437617i	$0.855823\pi$
$744$	4.10062	+	1.58569i	0.150336	+	0.0581344i
$745$	−46.7192	+	37.2573i	−1.71166	+	1.36500i
$746$	3.81853	+	37.5273i	0.139806	+	1.37397i
$747$	7.40698	−	3.56701i	0.271007	−	0.130510i
$748$	16.3336	+	35.8785i	0.597214	+	1.31185i
$749$	−31.4472	+	5.75945i	−1.14906	+	0.210446i
$750$	−14.8799	+	9.12710i	−0.543336	+	0.333274i
$751$	−22.7595	+	18.1501i	−0.830504	+	0.662305i	−0.943530	−	0.331287i	$-0.892517\pi$
$751$	−22.7595	+	18.1501i	−0.830504	+	0.662305i	0.113026	+	0.993592i	$0.463946\pi$
$752$	0.538590	+	2.93945i	0.0196404	+	0.107191i
$753$	12.8455			0.468116
$754$	0.208913	+	0.618372i	0.00760815	+	0.0225198i
$755$	−15.3505	+	7.39239i	−0.558660	+	0.269037i
$756$	−24.1300	−	7.18101i	−0.877600	−	0.261171i
$757$	11.8143	+	5.68947i	0.429399	+	0.206787i	0.636084	−	0.771620i	$-0.280553\pi$
$757$	11.8143	+	5.68947i	0.429399	+	0.206787i	−0.206685	+	0.978408i	$0.566268\pi$
$758$	2.21269	−	17.8993i	0.0803686	−	0.650131i
$759$	0.0977523	+	0.428281i	0.00354818	+	0.0155456i
$760$	−11.8705	+	30.6972i	−0.430588	+	1.11350i
$761$	−17.8610	+	37.0887i	−0.647459	+	1.34446i	0.276145	+	0.961116i	$0.410943\pi$
$761$	−17.8610	+	37.0887i	−0.647459	+	1.34446i	−0.923604	+	0.383347i	$0.874771\pi$
$762$	−1.30599	+	10.5646i	−0.0473109	+	0.382715i
$763$	−5.30192	+	19.3331i	−0.191942	+	0.699906i
$764$	−3.08848	−	1.57035i	−0.111737	−	0.0568134i
$765$	24.1560			0.873363
$766$	13.7508	−	4.64562i	0.496838	−	0.167853i
$767$	1.77899	+	3.69411i	0.0642355	+	0.133386i
$768$	2.03597	+	14.6557i	0.0734669	+	0.528843i
$769$	−33.0195	+	7.53649i	−1.19071	+	0.271773i	−0.771569	−	0.636146i	$-0.780528\pi$
$769$	−33.0195	+	7.53649i	−1.19071	+	0.271773i	−0.419146	+	0.907919i	$0.637670\pi$
$770$	−66.3655	+	59.5523i	−2.39165	+	2.14612i
$771$	12.7822	+	2.91746i	0.460340	+	0.105070i
$772$	0.640348	−	1.25940i	0.0230466	−	0.0453267i
$773$	−40.7221	−	9.29456i	−1.46467	−	0.334302i	−0.585449	−	0.810709i	$-0.699082\pi$
$773$	−40.7221	−	9.29456i	−1.46467	−	0.334302i	−0.879225	+	0.476407i	$0.841939\pi$
$774$	−10.5521	+	16.3979i	−0.379287	+	0.589411i
$775$	−3.22297	−	14.1207i	−0.115772	−	0.507232i
$776$	0.0559972	−	0.0175808i	0.00201018	−	0.000631114i
$777$	2.83243	−	10.3283i	0.101613	−	0.370525i
$778$	3.07724	+	1.98021i	0.110324	+	0.0709941i
$779$	−10.5475	−	8.41137i	−0.377904	−	0.301368i
$780$	−22.6532	+	4.65831i	−0.811114	+	0.166794i
$781$	23.6440	−	29.6486i	0.846049	−	1.06091i
$782$	0.0321399	+	0.315861i	0.00114932	+	0.0112952i
$783$	−0.648032			−0.0231588
$784$	26.5865	−	8.78385i	0.949519	−	0.313709i
$785$	−34.6166			−1.23552
$786$	−0.513493	−	5.04645i	−0.0183157	−	0.180001i
$787$	−23.9800	+	30.0700i	−0.854794	+	1.07188i	0.141839	+	0.989890i	$0.454698\pi$
$787$	−23.9800	+	30.0700i	−0.854794	+	1.07188i	−0.996633	+	0.0819883i	$0.973873\pi$
$788$	28.4458	−	5.84947i	1.01334	−	0.208379i
$789$	12.3113	+	9.81791i	0.438293	+	0.349527i
$790$	−70.3645	−	45.2797i	−2.50346	−	1.61098i
$791$	−0.909598	−	4.96650i	−0.0323416	−	0.176589i
$792$	−37.3780	+	11.7351i	−1.32817	+	0.416990i
$793$	7.16147	+	31.3764i	0.254311	+	1.11421i
$794$	11.3071	−	17.5712i	0.401276	−	0.623580i
$795$	−6.60975	−	1.50863i	−0.234424	−	0.0535056i
$796$	11.3524	−	22.3272i	0.402376	−	0.791367i
$797$	51.6081	+	11.7792i	1.82805	+	0.417241i	0.991441	−	0.130556i	$-0.0416761\pi$
$797$	51.6081	+	11.7792i	1.82805	+	0.417241i	0.836611	+	0.547797i	$0.184533\pi$
$798$	−8.91170	−	6.29584i	−0.315471	−	0.222870i
$799$	2.22305	−	0.507398i	0.0786460	−	0.0179504i
$800$	36.2775	−	32.5583i	1.28260	−	1.15111i
$801$	5.22890	+	10.8579i	0.184754	+	0.383646i
$802$	9.11156	−	3.07828i	0.321740	−	0.108698i
$803$	88.0943			3.10878
$804$	−11.7647	−	5.98184i	−0.414909	−	0.210963i
$805$	−0.659888	+	0.283314i	−0.0232580	+	0.00998552i
$806$	0.988207	−	7.99397i	0.0348081	−	0.281575i
$807$	−3.82702	+	7.94689i	−0.134717	+	0.279744i
$808$	11.5909	−	29.9742i	0.407767	−	1.05449i
$809$	−4.89749	−	21.4573i	−0.172187	−	0.754399i	−0.985096	−	0.172008i	$-0.944974\pi$
$809$	−4.89749	−	21.4573i	−0.172187	−	0.754399i	0.812909	−	0.582391i	$-0.197883\pi$
$810$	−1.30255	+	10.5368i	−0.0457669	+	0.370225i
$811$	−19.6919	−	9.48313i	−0.691477	−	0.332998i	0.0549277	−	0.998490i	$-0.482507\pi$
$811$	−19.6919	−	9.48313i	−0.691477	−	0.332998i	−0.746404	+	0.665493i	$0.768221\pi$
$812$	0.591423	−	0.411903i	0.0207549	−	0.0144550i
$813$	−14.1871	+	6.83213i	−0.497562	+	0.239613i
$814$	−12.7953	−	37.8734i	−0.448474	−	1.32746i
$815$	51.7050			1.81115
$816$	11.1053	−	2.03480i	0.388762	−	0.0712321i
$817$	−15.8495	+	12.6396i	−0.554504	+	0.442202i
$818$	12.8002	−	7.85143i	0.447547	−	0.274519i
$819$	−0.831573	+	19.2105i	−0.0290575	+	0.671270i
$820$	13.0823	+	28.7367i	0.456853	+	1.00353i
$821$	21.0119	−	10.1188i	0.733321	−	0.353149i	−0.0296686	−	0.999560i	$-0.509445\pi$
$821$	21.0119	−	10.1188i	0.733321	−	0.353149i	0.762989	+	0.646411i	$0.223731\pi$
$822$	0.487885	+	4.79478i	0.0170170	+	0.167237i
$823$	23.1352	−	18.4497i	0.806443	−	0.643117i	−0.130950	−	0.991389i	$-0.541803\pi$
$823$	23.1352	−	18.4497i	0.806443	−	0.643117i	0.937394	+	0.348272i	$0.113231\pi$
$824$	−35.0752	−	13.5634i	−1.22190	−	0.472505i
$825$	−40.2356	−	32.0868i	−1.40082	−	1.11712i
$826$	3.36966	−	3.02372i	0.117245	−	0.105209i
$827$	14.0089	−	11.1717i	0.487137	−	0.388479i	−0.348893	−	0.937163i	$-0.613442\pi$
$827$	14.0089	−	11.1717i	0.487137	−	0.388479i	0.836030	+	0.548684i	$0.184871\pi$
$828$	−0.315448	−	0.00681182i	−0.0109626	−	0.000236727i
$829$	22.9695	−	47.6966i	0.797763	−	1.65657i	0.0443567	−	0.999016i	$-0.485876\pi$
$829$	22.9695	−	47.6966i	0.797763	−	1.65657i	0.753406	−	0.657556i	$-0.228410\pi$
$830$	−18.8085	−	6.81015i	−0.652852	−	0.236384i
$831$	−3.79366	+	16.6211i	−0.131601	+	0.576580i
$832$	25.1339	−	10.1563i	0.871361	−	0.352108i
$833$	−7.57181	−	19.9781i	−0.262348	−	0.692199i
$834$	−21.4124	+	7.23402i	−0.741450	+	0.250494i
$835$	39.3827	+	8.98885i	1.36290	+	0.311072i
$836$	−40.7196	−	0.879304i	−1.40832	−	0.0304114i
$837$	7.20514	+	3.46981i	0.249046	+	0.119934i
$838$	−11.9986	+	33.1380i	−0.414484	+	1.14473i
$839$	−8.93086	−	11.1990i	−0.308328	−	0.386631i	0.603391	−	0.797445i	$-0.293816\pi$
$839$	−8.93086	−	11.1990i	−0.308328	−	0.386631i	−0.911719	+	0.410815i	$0.865244\pi$
$840$	11.9136	+	22.5879i	0.411059	+	0.779358i
$841$	−18.0696	+	22.6586i	−0.623091	+	0.781331i
$842$	23.5949	+	38.4667i	0.813134	+	1.32565i
$843$	2.30431	+	2.88952i	0.0793648	+	0.0995203i
$844$	10.4381	−	4.75189i	0.359293	−	0.163567i
$845$	−2.43005	−	5.04605i	−0.0835963	−	0.173590i
$846$	0.229397	+	2.25444i	0.00788682	+	0.0775091i
$847$	−71.6033	−	38.3819i	−2.46032	−	1.31882i
$848$	7.93940	+	0.343048i	0.272640	+	0.0117803i
$849$	−10.9971	−	13.7900i	−0.377420	−	0.473270i
$850$	−26.0147	−	26.5826i	−0.892298	−	0.911774i
$851$		−	0.321961i		−	0.0110367i
$852$	−6.58664	−	8.63546i	−0.225655	−	0.295846i
$853$	17.9730	+	37.3214i	0.615385	+	1.27786i	0.942920	+	0.333020i	$0.108068\pi$
$853$	17.9730	+	37.3214i	0.615385	+	1.27786i	−0.327535	+	0.944839i	$0.606218\pi$
$854$	31.0677	−	17.2535i	1.06311	−	0.590403i
$855$	−10.8286	+	22.4858i	−0.370329	+	0.768997i
$856$	17.2370	+	29.5127i	0.589149	+	1.00872i
$857$	48.0746	−	10.9727i	1.64220	−	0.374821i	0.701128	−	0.713036i	$-0.252680\pi$
$857$	48.0746	−	10.9727i	1.64220	−	0.374821i	0.941069	+	0.338215i	$0.109823\pi$
$858$	−14.9642	−	24.3961i	−0.510870	−	0.832870i
$859$	−36.7574	−	17.7014i	−1.25415	−	0.603965i	−0.315526	−	0.948917i	$-0.602181\pi$
$859$	−36.7574	−	17.7014i	−1.25415	−	0.603965i	−0.938620	+	0.344952i	$0.887895\pi$
$860$	46.4737	−	9.55666i	1.58474	−	0.325879i
$861$	−10.2964	+	1.88576i	−0.350902	+	0.0642664i
$862$	32.5148	+	33.2246i	1.10746	+	1.13163i
$863$		−	51.6283i		−	1.75745i	−0.477329	−	0.878725i	$-0.658395\pi$
$863$		−	51.6283i		−	1.75745i	0.477329	−	0.878725i	$-0.341605\pi$
$864$	1.56613	+	26.8685i	0.0532809	+	0.914086i
$865$	−35.3678	+	17.0322i	−1.20254	+	0.579113i
$866$	−12.3175	+	19.1413i	−0.418564	+	0.650447i
$867$	1.58136	+	6.92837i	0.0537056	+	0.235300i
$868$	−8.78122	+	1.41304i	−0.298054	+	0.0479617i
$869$	23.0414	−	100.951i	0.781627	−	3.42453i
$870$	0.459760	+	0.469795i	0.0155873	+	0.0159275i
$871$	−5.38057	+	23.5738i	−0.182314	+	0.798769i
$872$	21.3628	−	1.70868i	0.723437	−	0.0578631i
$873$	0.0433902	−	0.00990352i	0.00146853	−	0.000335183i
$874$	−0.308428	−	0.111675i	−0.0104327	−	0.00377747i
$875$	16.6836	−	31.1241i	0.564010	−	1.05219i
$876$	6.14389	−	24.4703i	0.207583	−	0.826776i
$877$	−30.9616	+	38.8246i	−1.04550	+	1.31101i	−0.0966364	+	0.995320i	$0.530808\pi$
$877$	−30.9616	+	38.8246i	−1.04550	+	1.31101i	−0.948861	+	0.315693i	$0.897763\pi$
$878$	−44.2391	−	5.46880i	−1.49300	−	0.184563i
$879$	22.0831	+	17.6107i	0.744844	+	0.593993i
$880$	84.0186	+	45.0285i	2.83227	+	1.51791i
$881$		−	48.6937i		−	1.64053i	−0.571981	−	0.820267i	$-0.693825\pi$
$881$		−	48.6937i		−	1.64053i	0.571981	−	0.820267i	$-0.306175\pi$
$882$	20.6273	−	5.03218i	0.694558	−	0.169442i
$883$		−	22.8933i		−	0.770422i	−0.922829	−	0.385211i	$-0.874129\pi$
$883$		−	22.8933i		−	0.770422i	0.922829	−	0.385211i	$-0.125871\pi$
$884$	−8.57023	−	18.8255i	−0.288248	−	0.633169i
$885$	3.22834	+	2.57451i	0.108519	+	0.0865413i
$886$	−5.13366	+	41.5280i	−0.172469	+	1.39516i
$887$	20.6967	−	25.9529i	0.694928	−	0.871412i	−0.301706	−	0.953401i	$-0.597556\pi$
$887$	20.6967	−	25.9529i	0.694928	−	0.871412i	0.996633	+	0.0819895i	$0.0261274\pi$
$888$	−11.4126	+	0.912822i	−0.382983	+	0.0306323i
$889$	−8.49581	−	19.7882i	−0.284940	−	0.663675i
$890$	9.98302	−	27.5714i	0.334632	−	0.924196i
$891$	−12.8091	+	2.92360i	−0.429122	+	0.0979442i
$892$	−10.9871	−	2.75857i	−0.367874	−	0.0923639i
$893$	−0.524229	+	2.29680i	−0.0175426	+	0.0768593i
$894$	−15.1362	+	14.8129i	−0.506230	+	0.495417i
$895$	−5.45626	+	23.9054i	−0.182383	+	0.799070i
$896$	−18.5076	−	23.5260i	−0.618294	−	0.785947i
$897$	−0.0512907	−	0.224719i	−0.00171255	−	0.00750316i
$898$	−4.54710	−	2.92607i	−0.151739	−	0.0976443i
$899$	−0.206266	+	0.0993325i	−0.00687936	+	0.00331292i
$900$	29.3899	−	22.4170i	0.979663	−	0.747233i
$901$		−	6.06365i		−	0.202009i
$902$	−27.9257	+	27.3291i	−0.929823	+	0.909961i
$903$	−0.680254	+	15.7148i	−0.0226374	+	0.522957i
$904$	−4.66098	+	2.72227i	−0.155022	+	0.0905412i
$905$	−48.8988	−	23.5484i	−1.62545	−	0.782776i
$906$	−5.14726	+	3.15725i	−0.171006	+	0.104893i
$907$	7.64236	−	1.74432i	0.253760	−	0.0579192i	−0.0937482	−	0.995596i	$-0.529885\pi$
$907$	7.64236	−	1.74432i	0.253760	−	0.0579192i	0.347509	+	0.937677i	$0.387028\pi$
$908$	−27.4868	+	5.65227i	−0.912181	+	0.187577i
$909$	10.5735	−	21.9562i	0.350702	−	0.728241i
$910$	34.8220	−	31.2471i	1.15434	−	1.03583i
$911$	25.0671	+	52.0523i	0.830509	+	1.72457i	0.676424	+	0.736513i	$0.263529\pi$
$911$	25.0671	+	52.0523i	0.830509	+	1.72457i	0.154086	+	0.988057i	$0.450757\pi$
$912$	−3.08412	+	11.2495i	−0.102126	+	0.372509i
$913$		−	24.7542i		−	0.819246i
$914$	3.70035	−	3.62131i	0.122397	−	0.119782i
$915$	20.2081	+	25.3402i	0.668061	+	0.837722i
$916$	−28.5591	+	34.2673i	−0.943618	+	1.13222i
$917$	6.04510	+	8.29209i	0.199627	+	0.273829i
$918$	20.4308	−	2.07890i	0.674316	−	0.0686139i
$919$	2.53282	+	5.25945i	0.0835499	+	0.173493i	0.938558	−	0.345121i	$-0.112162\pi$
$919$	2.53282	+	5.25945i	0.0835499	+	0.173493i	−0.855008	+	0.518615i	$0.826448\pi$
$920$	0.524997	+	0.560153i	0.0173086	+	0.0184677i
$921$	14.7388	+	18.4819i	0.485660	+	0.608998i
$922$	−14.2493	+	8.74032i	−0.469277	+	0.287847i
$923$	−12.4060	+	15.5567i	−0.408349	+	0.512054i
$924$	−21.2635	+	23.3788i	−0.699518	+	0.769107i
$925$	23.5166	+	29.4889i	0.773220	+	0.969588i
$926$	−5.74889	−	2.08155i	−0.188920	−	0.0684040i
$927$	−25.6926	−	12.3729i	−0.843857	−	0.406380i
$928$	−0.629325	−	0.444524i	−0.0206586	−	0.0145922i
$929$	12.6295	+	2.88261i	0.414361	+	0.0945753i	0.424619	−	0.905372i	$-0.360408\pi$
$929$	12.6295	+	2.88261i	0.414361	+	0.0945753i	−0.0102577	+	0.999947i	$0.503265\pi$
$930$	−2.59637	−	7.68515i	−0.0851384	−	0.252006i
$931$	21.9909	+	1.90743i	0.720724	+	0.0625136i
$932$	38.1742	−	29.1171i	1.25044	−	0.953763i
$933$	5.99118	−	26.2491i	0.196142	−	0.859356i
$934$	10.3396	−	28.5564i	0.338324	−	0.934392i
$935$	31.5586	−	65.5320i	1.03208	−	2.14313i
$936$	19.6123	−	6.15744i	0.641047	−	0.201262i
$937$	11.7522	−	9.37206i	0.383927	−	0.306172i	−0.412440	−	0.910985i	$-0.635323\pi$
$937$	11.7522	−	9.37206i	0.383927	−	0.306172i	0.796368	+	0.604813i	$0.206752\pi$
$938$	26.6547	−	1.55156i	0.870307	−	0.0506602i
$939$	−23.0168	−	18.3553i	−0.751124	−	0.599001i
$940$	3.53004	−	4.23561i	0.115137	−	0.138150i
$941$	13.4249	−	10.7060i	0.437639	−	0.349006i	−0.379752	−	0.925088i	$-0.623991\pi$
$941$	13.4249	−	10.7060i	0.437639	−	0.349006i	0.817392	+	0.576082i	$0.195419\pi$
$942$	−12.2056	+	1.24196i	−0.397681	+	0.0404653i
$943$	−0.283524	+	0.136538i	−0.00923281	+	0.00444629i
$944$	−4.26598	−	2.28629i	−0.138846	−	0.0744123i
$945$	18.3256	+	42.6834i	0.596131	+	1.38849i
$946$	30.6995	+	50.0494i	0.998128	+	1.62725i
$947$	−11.8517	+	9.45145i	−0.385130	+	0.307131i	−0.796847	−	0.604181i	$-0.793501\pi$
$947$	−11.8517	+	9.45145i	−0.385130	+	0.307131i	0.411717	+	0.911312i	$0.364929\pi$
$948$	−26.4347	−	13.4409i	−0.858558	−	0.436539i
$949$	−46.2232			−1.50047
$950$	36.4063	−	12.2996i	1.18118	−	0.399052i
$951$	12.1847	−	5.86783i	0.395115	−	0.190277i
$952$	−17.3246	+	14.8835i	−0.561495	+	0.482379i
$953$	−12.9076	−	6.21599i	−0.418120	−	0.201356i	0.212982	−	0.977056i	$-0.431683\pi$
$953$	−12.9076	−	6.21599i	−0.418120	−	0.201356i	−0.631101	+	0.775700i	$0.717397\pi$
$954$	5.98051	+	0.739305i	0.193626	+	0.0239359i
$955$	1.42252	+	6.23246i	0.0460316	+	0.201678i
$956$	9.46831	−	11.3608i	0.306227	−	0.367435i
$957$	−0.352943	+	0.732893i	−0.0114090	+	0.0236911i
$958$	1.89881	+	0.234730i	0.0613479	+	0.00758377i
$959$	−5.74363	−	7.87857i	−0.185472	−	0.254412i
$960$	18.3674	−	20.1978i	0.592805	−	0.651882i
$961$	−28.1748			−0.908863
$962$	6.71369	+	19.8722i	0.216458	+	0.640706i
$963$	11.2449	+	23.3502i	0.362360	+	0.752449i
$964$	7.19315	−	28.6494i	0.231676	−	0.922735i
$965$	−2.54143	+	0.580064i	−0.0818114	+	0.0186729i
$966$	−0.222508	+	0.123570i	−0.00715908	+	0.00397581i
$967$	22.4883	+	5.13280i	0.723174	+	0.165060i	0.568238	−	0.822865i	$-0.307625\pi$
$967$	22.4883	+	5.13280i	0.723174	+	0.165060i	0.154937	+	0.987924i	$0.450483\pi$
$968$	−12.5137	+	85.9447i	−0.402206	+	2.76237i
$969$	8.67731	+	1.98054i	0.278755	+	0.0636241i
$970$	−0.0910652	−	0.0586007i	−0.00292393	−	0.00188155i
$971$	−0.700907	−	3.07088i	−0.0224932	−	0.0985491i	0.962435	−	0.271511i	$-0.0875234\pi$
$971$	−0.700907	−	3.07088i	−0.0224932	−	0.0985491i	−0.984929	+	0.172962i	$0.944666\pi$
$972$	−0.697533	+	32.3020i	−0.0223734	+	1.03609i
$973$	30.0268	−	34.4810i	0.962615	−	1.10541i
$974$	−18.7461	+	29.1314i	−0.600665	+	0.933431i
$975$	21.1117	+	16.8360i	0.676114	+	0.539183i
$976$	−28.6522	−	24.9470i	−0.917133	−	0.798532i
$977$	4.61173	−	5.78292i	0.147542	−	0.185012i	−0.702568	−	0.711616i	$-0.747964\pi$
$977$	4.61173	−	5.78292i	0.147542	−	0.185012i	0.850111	+	0.526604i	$0.176535\pi$
$978$	18.2309	−	1.85505i	0.582959	−	0.0593181i
$979$	36.2873			1.15975
$980$	−43.8553	−	27.3067i	−1.40091	−	0.872279i
$981$	16.2511			0.518857
$982$	−50.5228	+	5.14086i	−1.61225	+	0.164051i
$983$	10.3836	−	13.0206i	0.331184	−	0.415292i	−0.588161	−	0.808744i	$-0.700148\pi$
$983$	10.3836	−	13.0206i	0.331184	−	0.415292i	0.919345	+	0.393452i	$0.128719\pi$
$984$	5.64374	+	9.66303i	0.179916	+	0.308046i
$985$	−41.8924	−	33.4081i	−1.33480	−	1.06447i
$986$	−0.318140	+	0.494388i	−0.0101316	+	0.0157445i
$987$	1.07683	+	1.47710i	0.0342760	+	0.0470166i
$988$	21.3656	+	0.461371i	0.679731	+	0.0146782i
$989$	0.105224	+	0.461018i	0.00334594	+	0.0146595i
$990$	60.7857	+	39.1158i	1.93190	+	1.24318i
$991$	−1.39714	−	0.318889i	−0.0443818	−	0.0101298i	0.200272	−	0.979740i	$-0.435817\pi$
$991$	−1.39714	−	0.318889i	−0.0443818	−	0.0101298i	−0.244654	+	0.969610i	$0.578674\pi$
$992$	4.61699	+	8.31209i	0.146590	+	0.263909i
$993$	−14.3106	−	3.26631i	−0.454134	−	0.103653i
$994$	20.3159	+	8.36651i	0.644381	+	0.265369i
$995$	−45.0557	+	10.2837i	−1.42836	+	0.326014i
$996$	−6.87609	−	1.72642i	−0.217877	−	0.0547036i
$997$	17.8347	+	37.0342i	0.564831	+	1.17288i	0.966397	+	0.257054i	$0.0827518\pi$
$997$	17.8347	+	37.0342i	0.564831	+	1.17288i	−0.401566	+	0.915830i	$0.631534\pi$
$998$	−7.68563	−	22.7491i	−0.243284	−	0.720111i
$999$	−20.8254			−0.658885

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.2.j.a.83.13	✓	156
4.3	odd	2	inner	196.2.j.a.83.18	yes	156
49.13	odd	14	inner	196.2.j.a.111.18	yes	156
196.111	even	14	inner	196.2.j.a.111.13	yes	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.2.j.a.83.13	✓	156	1.1	even	1	trivial
196.2.j.a.83.18	yes	156	4.3	odd	2	inner
196.2.j.a.111.13	yes	156	196.111	even	14	inner
196.2.j.a.111.18	yes	156	49.13	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.143162 - 1.40695i) q^{2} +(-0.576591 + 0.723022i) q^{3} +(-1.95901 + 0.402843i) q^{4} +(2.88506 + 2.30076i) q^{5} +(1.09980 + 0.707724i) q^{6} +(-2.64328 - 0.114420i) q^{7} +(0.847234 + 2.69855i) q^{8} +(0.477259 + 2.09101i) q^{9} +(2.82402 - 4.38851i) q^{10} +(6.29614 + 1.43705i) q^{11} +(0.838282 - 1.64868i) q^{12} +(-3.30359 - 0.754023i) q^{13} +(0.217432 + 3.73533i) q^{14} +(-3.32699 + 0.759365i) q^{15} +(3.67544 - 1.57834i) q^{16} +(-1.32426 - 2.74986i) q^{17} +(2.87362 - 0.970832i) q^{18} +3.15336 q^{19} +(-6.57870 - 3.34498i) q^{20} +(1.60682 - 1.84517i) q^{21} +(1.12049 - 9.06407i) q^{22} +(0.0319146 - 0.0662714i) q^{23} +(-2.43962 - 0.943392i) q^{24} +(1.91747 + 8.40098i) q^{25} +(-0.587923 + 4.75593i) q^{26} +(-4.28662 - 2.06433i) q^{27} +(5.22430 - 0.840673i) q^{28} +(0.122716 - 0.0590968i) q^{29} +(1.54469 + 4.57220i) q^{30} -1.68084 q^{31} +(-2.74683 - 4.94519i) q^{32} +(-4.66931 + 3.72365i) q^{33} +(-3.67933 + 2.25685i) q^{34} +(-7.36275 - 6.41164i) q^{35} +(-1.77730 - 3.90405i) q^{36} +(3.94364 - 1.89916i) q^{37} +(-0.451440 - 4.43661i) q^{38} +(2.44999 - 1.95380i) q^{39} +(-3.76440 + 9.73476i) q^{40} +(-3.34485 - 2.66743i) q^{41} +(-2.82610 - 1.99655i) q^{42} +(-5.02623 + 4.00829i) q^{43} +(-12.9131 - 0.278847i) q^{44} +(-3.43398 + 7.13074i) q^{45} +(-0.0978094 - 0.0354147i) q^{46} +(-0.166245 + 0.728365i) q^{47} +(-0.978044 + 3.56748i) q^{48} +(6.97382 + 0.604889i) q^{49} +(11.5452 - 3.90048i) q^{50} +(2.75177 + 0.628073i) q^{51} +(6.77551 + 0.146311i) q^{52} +(1.78996 + 0.861998i) q^{53} +(-2.29072 + 6.32659i) q^{54} +(14.8584 + 18.6318i) q^{55} +(-1.93070 - 7.22996i) q^{56} +(-1.81820 + 2.27995i) q^{57} +(-0.100714 - 0.164195i) q^{58} +(-0.754424 - 0.946018i) q^{59} +(6.21171 - 2.82786i) q^{60} +(-4.12089 - 8.55712i) q^{61} +(0.240633 + 2.36486i) q^{62} +(-1.02227 - 5.58172i) q^{63} +(-6.56439 + 4.57261i) q^{64} +(-7.79622 - 9.77615i) q^{65} +(5.90746 + 6.03640i) q^{66} -7.13583i q^{67} +(3.70201 + 4.85354i) q^{68} +(0.0295140 + 0.0612864i) q^{69} +(-7.96679 + 11.2769i) q^{70} +(2.54779 - 5.29054i) q^{71} +(-5.23835 + 3.05948i) q^{72} +(13.2990 - 3.03541i) q^{73} +(-3.23659 - 5.27661i) q^{74} +(-7.17969 - 3.45756i) q^{75} +(-6.17746 + 1.27031i) q^{76} +(-16.4780 - 4.51893i) q^{77} +(-3.09965 - 3.16730i) q^{78} -16.0338i q^{79} +(14.2352 + 3.90267i) q^{80} +(-1.83297 + 0.882711i) q^{81} +(-3.27408 + 5.08791i) q^{82} +(-0.852941 - 3.73698i) q^{83} +(-2.40445 + 4.26200i) q^{84} +(2.50619 - 10.9803i) q^{85} +(6.35902 + 6.49782i) q^{86} +(-0.0280285 + 0.122801i) q^{87} +(1.45634 + 18.2080i) q^{88} +(5.47805 - 1.25033i) q^{89} +(10.5242 + 3.81059i) q^{90} +(8.64602 + 2.37109i) q^{91} +(-0.0358241 + 0.142683i) q^{92} +(0.969158 - 1.21529i) q^{93} +(1.04857 + 0.129624i) q^{94} +(9.09762 + 7.25511i) q^{95} +(5.15928 + 0.865331i) q^{96} -0.0207508i q^{97} +(-0.147336 - 9.89840i) q^{98} +13.8511i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26}+ \cdots + 105 q^{98}+O(q^{100}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Introduction

L-functions

Modular forms

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Database

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