LMFDB - Embedded newform 234.2.t.a.103.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(25,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("234.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.3
Character	$\chi$	$=$	234.103
Dual form			234.2.t.a.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.579434 + 1.63225i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.32246 - 1.91822i) q^{5} +(-0.314323 - 1.70329i) q^{6} +(2.91802 - 1.68472i) q^{7} +1.00000i q^{8} +(-2.32851 - 1.89157i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.579434 + 1.63225i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.32246 - 1.91822i) q^{5} +(-0.314323 - 1.70329i) q^{6} +(2.91802 - 1.68472i) q^{7} +1.00000i q^{8} +(-2.32851 - 1.89157i) q^{9} +3.83645 q^{10} +(1.72495 - 0.995899i) q^{11} +(1.12386 + 1.31793i) q^{12} +(-0.985326 - 3.46830i) q^{13} +(-1.68472 + 2.91802i) q^{14} +(5.05618 - 4.31162i) q^{15} +(-0.500000 - 0.866025i) q^{16} +2.60129 q^{17} +(2.96233 + 0.473890i) q^{18} +1.99180i q^{19} +(-3.32246 + 1.91822i) q^{20} +(1.05909 + 5.73914i) q^{21} +(-0.995899 + 1.72495i) q^{22} +(2.13620 - 3.70000i) q^{23} +(-1.63225 - 0.579434i) q^{24} +(4.85917 + 8.41632i) q^{25} +(2.58747 + 2.51098i) q^{26} +(4.43674 - 2.70469i) q^{27} -3.36944i q^{28} +(-4.37469 - 7.57719i) q^{29} +(-2.22297 + 6.26206i) q^{30} +(-4.57313 - 2.64030i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.626068 + 3.39261i) q^{33} +(-2.25278 + 1.30064i) q^{34} -12.9267 q^{35} +(-2.80240 + 1.07077i) q^{36} -5.08689i q^{37} +(-0.995899 - 1.72495i) q^{38} +(6.23209 + 0.401349i) q^{39} +(1.91822 - 3.32246i) q^{40} +(7.13885 + 4.12162i) q^{41} +(-3.78677 - 4.44070i) q^{42} +(-5.13184 - 8.88861i) q^{43} -1.99180i q^{44} +(4.10794 + 10.7513i) q^{45} +4.27239i q^{46} +(-4.22784 + 2.44094i) q^{47} +(1.70329 - 0.314323i) q^{48} +(2.17657 - 3.76993i) q^{49} +(-8.41632 - 4.85917i) q^{50} +(-1.50727 + 4.24596i) q^{51} +(-3.49630 - 0.880834i) q^{52} -9.16444 q^{53} +(-2.48999 + 4.56070i) q^{54} -7.64143 q^{55} +(1.68472 + 2.91802i) q^{56} +(-3.25112 - 1.15412i) q^{57} +(7.57719 + 4.37469i) q^{58} +(6.33329 + 3.65653i) q^{59} +(-1.20588 - 6.53459i) q^{60} +(5.63669 + 9.76304i) q^{61} +5.28060 q^{62} +(-9.98142 - 1.59674i) q^{63} -1.00000 q^{64} +(-3.37927 + 13.4134i) q^{65} +(-2.23850 - 2.62505i) q^{66} +(-4.90591 - 2.83243i) q^{67} +(1.30064 - 2.25278i) q^{68} +(4.80156 + 5.63073i) q^{69} +(11.1948 - 6.46335i) q^{70} -1.94505i q^{71} +(1.89157 - 2.32851i) q^{72} +8.41425i q^{73} +(2.54345 + 4.40538i) q^{74} +(-16.5531 + 3.05469i) q^{75} +(1.72495 + 0.995899i) q^{76} +(3.35563 - 5.81211i) q^{77} +(-5.59782 + 2.76847i) q^{78} +(2.97607 + 5.15470i) q^{79} +3.83645i q^{80} +(1.84394 + 8.80908i) q^{81} -8.24323 q^{82} +(2.03658 - 1.17582i) q^{83} +(5.49979 + 1.95237i) q^{84} +(-8.64268 - 4.98985i) q^{85} +(8.88861 + 5.13184i) q^{86} +(14.9028 - 2.75013i) q^{87} +(0.995899 + 1.72495i) q^{88} -6.28290i q^{89} +(-8.93322 - 7.25690i) q^{90} +(-8.71833 - 8.46059i) q^{91} +(-2.13620 - 3.70000i) q^{92} +(6.95947 - 5.93464i) q^{93} +(2.44094 - 4.22784i) q^{94} +(3.82072 - 6.61767i) q^{95} +(-1.31793 + 1.12386i) q^{96} +(8.92313 - 5.15177i) q^{97} +4.35315i q^{98} +(-5.90037 - 0.943893i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} - 16 q^{9}+O(q^{10}) $ 28 * q + 14 * q^4 - 16 * q^9	$ 28 q + 14 q^{4} - 16 q^{9} + 2 q^{13} + 8 q^{14} - 14 q^{16} + 16 q^{17} - 8 q^{23} + 14 q^{25} + 8 q^{26} + 18 q^{27} - 16 q^{29} - 8 q^{30} - 68 q^{35} - 8 q^{36} - 8 q^{39} - 10 q^{42} - 4 q^{43} + 10 q^{49} + 58 q^{51} - 2 q^{52} - 120 q^{53} - 8 q^{56} + 28 q^{61} + 68 q^{62} - 28 q^{64} - 8 q^{65} - 24 q^{66} + 8 q^{68} - 92 q^{69} + 16 q^{74} + 32 q^{75} - 24 q^{77} - 22 q^{78} + 28 q^{79} + 8 q^{81} - 48 q^{82} + 68 q^{87} - 50 q^{90} + 8 q^{92}+O(q^{100}) $ 28 * q + 14 * q^4 - 16 * q^9 + 2 * q^13 + 8 * q^14 - 14 * q^16 + 16 * q^17 - 8 * q^23 + 14 * q^25 + 8 * q^26 + 18 * q^27 - 16 * q^29 - 8 * q^30 - 68 * q^35 - 8 * q^36 - 8 * q^39 - 10 * q^42 - 4 * q^43 + 10 * q^49 + 58 * q^51 - 2 * q^52 - 120 * q^53 - 8 * q^56 + 28 * q^61 + 68 * q^62 - 28 * q^64 - 8 * q^65 - 24 * q^66 + 8 * q^68 - 92 * q^69 + 16 * q^74 + 32 * q^75 - 24 * q^77 - 22 * q^78 + 28 * q^79 + 8 * q^81 - 48 * q^82 + 68 * q^87 - 50 * q^90 + 8 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.579434	+	1.63225i	−0.334536	+	0.942383i
$3$	−0.579434	+	1.63225i	−0.334536	+	0.942383i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−3.32246	−	1.91822i	−1.48585	−	0.857856i	−0.485980	−	0.873970i	$-0.661537\pi$
$5$	−3.32246	−	1.91822i	−1.48585	−	0.857856i	−0.999870	+	0.0161143i	$0.994870\pi$
$6$	−0.314323	−	1.70329i	−0.128322	−	0.695366i
$7$	2.91802	−	1.68472i	1.10291	−	0.636765i	0.165926	−	0.986138i	$-0.446939\pi$
$7$	2.91802	−	1.68472i	1.10291	−	0.636765i	0.936984	+	0.349373i	$0.113606\pi$
$8$			1.00000i			0.353553i
$9$	−2.32851	−	1.89157i	−0.776171	−	0.630523i
$10$	3.83645			1.21319
$11$	1.72495	−	0.995899i	0.520091	−	0.300275i	−0.216881	−	0.976198i	$-0.569588\pi$
$11$	1.72495	−	0.995899i	0.520091	−	0.300275i	0.736972	+	0.675923i	$0.236255\pi$
$12$	1.12386	+	1.31793i	0.324430	+	0.380454i
$13$	−0.985326	−	3.46830i	−0.273280	−	0.961934i
$13$	−0.985326	−	3.46830i	−0.273280	−	0.961934i
$14$	−1.68472	+	2.91802i	−0.450261	+	0.779875i
$15$	5.05618	−	4.31162i	1.30550	−	1.11326i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.60129			0.630905			0.315452	−	0.948941i	$-0.397844\pi$
$17$	2.60129			0.630905			0.315452	+	0.948941i	$0.397844\pi$
$18$	2.96233	+	0.473890i	0.698229	+	0.111697i
$19$			1.99180i			0.456950i	0.973550	+	0.228475i	$0.0733739\pi$
$19$			1.99180i			0.456950i	−0.973550	+	0.228475i	$0.926626\pi$
$20$	−3.32246	+	1.91822i	−0.742925	+	0.428928i
$21$	1.05909	+	5.73914i	0.231113	+	1.25238i
$22$	−0.995899	+	1.72495i	−0.212326	+	0.367760i
$23$	2.13620	−	3.70000i	0.445428	−	0.771504i	−0.552654	−	0.833411i	$-0.686385\pi$
$23$	2.13620	−	3.70000i	0.445428	−	0.771504i	0.998082	+	0.0619070i	$0.0197182\pi$
$24$	−1.63225	−	0.579434i	−0.333183	−	0.118276i
$25$	4.85917	+	8.41632i	0.971833	+	1.68326i
$26$	2.58747	+	2.51098i	0.507445	+	0.492443i
$27$	4.43674	−	2.70469i	0.853851	−	0.520517i
$28$		−	3.36944i		−	0.636765i
$29$	−4.37469	−	7.57719i	−0.812360	−	1.40705i	−0.911208	−	0.411947i	$-0.864849\pi$
$29$	−4.37469	−	7.57719i	−0.812360	−	1.40705i	0.0988475	−	0.995103i	$-0.468484\pi$
$30$	−2.22297	+	6.26206i	−0.405857	+	1.14329i
$31$	−4.57313	−	2.64030i	−0.821359	−	0.474212i	0.0295262	−	0.999564i	$-0.490600\pi$
$31$	−4.57313	−	2.64030i	−0.821359	−	0.474212i	−0.850885	+	0.525352i	$0.823933\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	0.626068	+	3.39261i	0.108984	+	0.590578i
$34$	−2.25278	+	1.30064i	−0.386349	+	0.223059i
$35$	−12.9267			−2.18501
$36$	−2.80240	+	1.07077i	−0.467067	+	0.178461i
$37$		−	5.08689i		−	0.836280i	−0.908383	−	0.418140i	$-0.862682\pi$
$37$		−	5.08689i		−	0.836280i	0.908383	−	0.418140i	$-0.137318\pi$
$38$	−0.995899	−	1.72495i	−0.161556	−	0.279824i
$39$	6.23209	+	0.401349i	0.997933	+	0.0642673i
$40$	1.91822	−	3.32246i	0.303298	−	0.525327i
$41$	7.13885	+	4.12162i	1.11490	+	0.643688i	0.940094	−	0.340915i	$-0.110737\pi$
$41$	7.13885	+	4.12162i	1.11490	+	0.643688i	0.174806	+	0.984603i	$0.444070\pi$
$42$	−3.78677	−	4.44070i	−0.584312	−	0.685214i
$43$	−5.13184	−	8.88861i	−0.782598	−	1.35550i	−0.930423	−	0.366486i	$-0.880561\pi$
$43$	−5.13184	−	8.88861i	−0.782598	−	1.35550i	0.147825	−	0.989014i	$-0.452773\pi$
$44$		−	1.99180i		−	0.300275i
$45$	4.10794	+	10.7513i	0.612376	+	1.60270i
$46$			4.27239i			0.629930i
$47$	−4.22784	+	2.44094i	−0.616693	+	0.356048i	−0.775580	−	0.631249i	$-0.782543\pi$
$47$	−4.22784	+	2.44094i	−0.616693	+	0.356048i	0.158887	+	0.987297i	$0.449209\pi$
$48$	1.70329	−	0.314323i	0.245849	−	0.0453686i
$49$	2.17657	−	3.76993i	0.310939	−	0.538562i
$50$	−8.41632	−	4.85917i	−1.19025	−	0.687190i
$51$	−1.50727	+	4.24596i	−0.211061	+	0.594554i
$52$	−3.49630	−	0.880834i	−0.484850	−	0.122150i
$53$	−9.16444			−1.25883			−0.629416	−	0.777068i	$-0.716706\pi$
$53$	−9.16444			−1.25883			−0.629416	+	0.777068i	$0.716706\pi$
$54$	−2.48999	+	4.56070i	−0.338844	+	0.620632i
$55$	−7.64143			−1.03037
$56$	1.68472	+	2.91802i	0.225130	+	0.389937i
$57$	−3.25112	−	1.15412i	−0.430622	−	0.152866i
$58$	7.57719	+	4.37469i	0.994934	+	0.574426i
$59$	6.33329	+	3.65653i	0.824524	+	0.476039i	0.851974	−	0.523584i	$-0.175405\pi$
$59$	6.33329	+	3.65653i	0.824524	+	0.476039i	−0.0274501	+	0.999623i	$0.508739\pi$
$60$	−1.20588	−	6.53459i	−0.155679	−	0.843612i
$61$	5.63669	+	9.76304i	0.721705	+	1.25003i	0.960316	+	0.278914i	$0.0899744\pi$
$61$	5.63669	+	9.76304i	0.721705	+	1.25003i	−0.238612	+	0.971115i	$0.576692\pi$
$62$	5.28060			0.670636
$63$	−9.98142	−	1.59674i	−1.25754	−	0.201171i
$64$	−1.00000			−0.125000
$65$	−3.37927	+	13.4134i	−0.419147	+	1.66373i
$66$	−2.23850	−	2.62505i	−0.275540	−	0.323122i
$67$	−4.90591	−	2.83243i	−0.599353	−	0.346037i	0.169434	−	0.985542i	$-0.445806\pi$
$67$	−4.90591	−	2.83243i	−0.599353	−	0.346037i	−0.768787	+	0.639505i	$0.779139\pi$
$68$	1.30064	−	2.25278i	0.157726	−	0.273190i
$69$	4.80156	+	5.63073i	0.578040	+	0.677860i
$70$	11.1948	−	6.46335i	1.33804	−	0.772518i
$71$		−	1.94505i		−	0.230835i	−0.993317	−	0.115418i	$-0.963179\pi$
$71$		−	1.94505i		−	0.230835i	0.993317	−	0.115418i	$-0.0368206\pi$
$72$	1.89157	−	2.32851i	0.222923	−	0.274418i
$73$			8.41425i			0.984814i	0.870365	+	0.492407i	$0.163883\pi$
$73$			8.41425i			0.984814i	−0.870365	+	0.492407i	$0.836117\pi$
$74$	2.54345	+	4.40538i	0.295669	+	0.512115i
$75$	−16.5531	+	3.05469i	−1.91139	+	0.352726i
$76$	1.72495	+	0.995899i	0.197865	+	0.114237i
$77$	3.35563	−	5.81211i	0.382409	−	0.662352i
$78$	−5.59782	+	2.76847i	−0.633828	+	0.313467i
$79$	2.97607	+	5.15470i	0.334834	+	0.579949i	0.983453	−	0.181164i	$-0.0579866\pi$
$79$	2.97607	+	5.15470i	0.334834	+	0.579949i	−0.648619	+	0.761113i	$0.724653\pi$
$80$			3.83645i			0.428928i
$81$	1.84394	+	8.80908i	0.204882	+	0.978787i
$82$	−8.24323			−0.910313
$83$	2.03658	−	1.17582i	0.223544	−	0.129063i	−0.384046	−	0.923314i	$-0.625470\pi$
$83$	2.03658	−	1.17582i	0.223544	−	0.129063i	0.607590	+	0.794251i	$0.292136\pi$
$84$	5.49979	+	1.95237i	0.600076	+	0.213021i
$85$	−8.64268	−	4.98985i	−0.937430	−	0.541225i
$86$	8.88861	+	5.13184i	0.958483	+	0.553381i
$87$	14.9028	−	2.75013i	1.59774	−	0.294845i
$88$	0.995899	+	1.72495i	0.106163	+	0.183880i
$89$		−	6.28290i		−	0.665986i	−0.942929	−	0.332993i	$-0.891941\pi$
$89$		−	6.28290i		−	0.665986i	0.942929	−	0.332993i	$-0.108059\pi$
$90$	−8.93322	−	7.25690i	−0.941644	−	0.764945i
$91$	−8.71833	−	8.46059i	−0.913929	−	0.886911i
$92$	−2.13620	−	3.70000i	−0.222714	−	0.385752i
$93$	6.95947	−	5.93464i	0.721663	−	0.615393i
$94$	2.44094	−	4.22784i	0.251764	−	0.436068i
$95$	3.82072	−	6.61767i	0.391997	−	0.678959i
$96$	−1.31793	+	1.12386i	−0.134511	+	0.114703i
$97$	8.92313	−	5.15177i	0.906006	−	0.523083i	0.0268622	−	0.999639i	$-0.491448\pi$
$97$	8.92313	−	5.15177i	0.906006	−	0.523083i	0.879144	+	0.476556i	$0.158115\pi$
$98$			4.35315i			0.439734i
$99$	−5.90037	−	0.943893i	−0.593010	−	0.0948648i
$100$	9.71833			0.971833
$101$	1.27960	+	2.21634i	0.127325	+	0.220534i	0.922639	−	0.385664i	$-0.126027\pi$
$101$	1.27960	+	2.21634i	0.127325	+	0.220534i	−0.795314	+	0.606197i	$0.792694\pi$
$102$	−0.817644	−	4.43075i	−0.0809588	−	0.438710i
$103$	2.82072	−	4.88562i	0.277933	−	0.481395i	−0.692938	−	0.720998i	$-0.743684\pi$
$103$	2.82072	−	4.88562i	0.277933	−	0.481395i	0.970871	+	0.239603i	$0.0770172\pi$
$104$	3.46830	−	0.985326i	0.340095	−	0.0966192i
$105$	7.49016	−	21.0997i	0.730965	−	2.05912i
$106$	7.93663	−	4.58222i	0.770874	−	0.445064i
$107$	18.3051			1.76962			0.884812	−	0.465948i	$-0.154287\pi$
$107$	18.3051			1.76962			0.884812	+	0.465948i	$0.154287\pi$
$108$	−0.123958	−	5.19467i	−0.0119278	−	0.499858i
$109$			6.74904i			0.646441i	0.946324	+	0.323221i	$0.104766\pi$
$109$			6.74904i			0.646441i	−0.946324	+	0.323221i	$0.895234\pi$
$110$	6.61767	−	3.82072i	0.630970	−	0.364291i
$111$	8.30310	+	2.94752i	0.788096	+	0.279766i
$112$	−2.91802	−	1.68472i	−0.275727	−	0.159191i
$113$	2.97526	−	5.15330i	0.279889	−	0.484781i	−0.691468	−	0.722407i	$-0.743036\pi$
$113$	2.97526	−	5.15330i	0.279889	−	0.484781i	0.971357	+	0.237626i	$0.0763691\pi$
$114$	3.39261	−	0.626068i	0.317747	−	0.0586366i
$115$	−14.1949	+	8.19541i	−1.32368	+	0.764226i
$116$	−8.74939			−0.812360
$117$	−4.26619	+	9.93980i	−0.394409	+	0.918935i
$118$	−7.31305			−0.673221
$119$	7.59062	−	4.38244i	0.695831	−	0.401738i
$120$	4.31162	+	5.05618i	0.393595	+	0.461564i
$121$	−3.51637	+	6.09053i	−0.319670	+	0.553685i
$122$	−9.76304	−	5.63669i	−0.883904	−	0.510322i
$123$	−10.8640	+	9.26422i	−0.979576	+	0.835326i
$124$	−4.57313	+	2.64030i	−0.410679	+	0.237106i
$125$		−	18.1016i		−	1.61906i
$126$	9.44253	−	3.60789i	0.841208	−	0.321416i
$127$	−5.93126			−0.526314			−0.263157	−	0.964753i	$-0.584764\pi$
$127$	−5.93126			−0.526314			−0.263157	+	0.964753i	$0.584764\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	17.4820	−	3.22611i	1.53921	−	0.284043i
$130$	−3.78015	−	13.3060i	−0.331541	−	1.16701i
$131$	−6.88246	+	11.9208i	−0.601324	+	1.04152i	0.391297	+	0.920264i	$0.372026\pi$
$131$	−6.88246	+	11.9208i	−0.601324	+	1.04152i	−0.992621	+	0.121259i	$0.961307\pi$
$132$	3.25112	+	1.15412i	0.282974	+	0.100453i
$133$	3.35563	+	5.81211i	0.290970	+	0.503974i
$134$	5.66486			0.489370
$135$	−19.9291	+	0.475557i	−1.71522	+	0.0409294i
$136$			2.60129i			0.223059i
$137$	3.30808	−	1.90992i	0.282628	−	0.163175i	−0.351985	−	0.936006i	$-0.614493\pi$
$137$	3.30808	−	1.90992i	0.282628	−	0.163175i	0.634613	+	0.772830i	$0.281160\pi$
$138$	−6.97364	−	2.47557i	−0.593635	−	0.210735i
$139$	−6.80487	+	11.7864i	−0.577182	+	0.999708i	0.418619	+	0.908162i	$0.362514\pi$
$139$	−6.80487	+	11.7864i	−0.577182	+	0.999708i	−0.995801	+	0.0915462i	$0.970819\pi$
$140$	−6.46335	+	11.1948i	−0.546252	+	0.946137i
$141$	−1.53449	−	8.31527i	−0.129227	−	0.700272i
$142$	0.972526	+	1.68446i	0.0816125	+	0.141357i
$143$	−5.15372	−	5.00136i	−0.430976	−	0.418235i
$144$	−0.473890	+	2.96233i	−0.0394908	+	0.246861i
$145$			33.5666i			2.78755i
$146$	−4.20713	−	7.28696i	−0.348184	−	0.603073i
$147$	4.89231	+	5.73715i	0.403511	+	0.473192i
$148$	−4.40538	−	2.54345i	−0.362120	−	0.209070i
$149$	6.74717	+	3.89548i	0.552749	+	0.319130i	0.750230	−	0.661177i	$-0.229943\pi$
$149$	6.74717	+	3.89548i	0.552749	+	0.319130i	−0.197481	+	0.980307i	$0.563276\pi$
$150$	12.8081	−	10.9220i	1.04578	−	0.891779i
$151$	18.5033	−	10.6829i	1.50578	−	0.869363i	0.505804	−	0.862649i	$-0.331196\pi$
$151$	18.5033	−	10.6829i	1.50578	−	0.869363i	0.999977	−	0.00671434i	$-0.00213726\pi$
$152$	−1.99180			−0.161556
$153$	−6.05713	−	4.92051i	−0.489690	−	0.397800i
$154$			6.71125i			0.540808i
$155$	10.1294	+	17.5446i	0.813610	+	1.40921i
$156$	3.46362	−	5.19647i	0.277312	−	0.416051i
$157$	2.12572	−	3.68185i	0.169651	−	0.293844i	−0.768646	−	0.639674i	$-0.779069\pi$
$157$	2.12572	−	3.68185i	0.169651	−	0.293844i	0.938297	+	0.345830i	$0.112403\pi$
$158$	−5.15470	−	2.97607i	−0.410086	−	0.236763i
$159$	5.31019	−	14.9587i	0.421125	−	1.18630i
$160$	−1.91822	−	3.32246i	−0.151649	−	0.262664i
$161$		−	14.3956i		−	1.13453i
$162$	−6.00144	−	6.70692i	−0.471518	−	0.526945i
$163$		−	11.0533i		−	0.865764i	−0.901451	−	0.432882i	$-0.857497\pi$
$163$		−	11.0533i		−	0.865764i	0.901451	−	0.432882i	$-0.142503\pi$
$164$	7.13885	−	4.12162i	0.557450	−	0.321844i
$165$	4.42770	−	12.4728i	0.344696	−	0.971003i
$166$	−1.17582	+	2.03658i	−0.0912614	+	0.158069i
$167$	8.14388	+	4.70187i	0.630193	+	0.363842i	0.780827	−	0.624748i	$-0.214798\pi$
$167$	8.14388	+	4.70187i	0.630193	+	0.363842i	−0.150634	+	0.988590i	$0.548131\pi$
$168$	−5.73914	+	1.05909i	−0.442784	+	0.0817108i
$169$	−11.0583	+	6.83482i	−0.850636	+	0.525756i
$170$	9.97970			0.765408
$171$	3.76762	−	4.63793i	0.288117	−	0.354671i
$172$	−10.2637			−0.782598
$173$	−1.08885	−	1.88594i	−0.0827835	−	0.143385i	0.821661	−	0.569976i	$-0.193048\pi$
$173$	−1.08885	−	1.88594i	−0.0827835	−	0.143385i	−0.904445	+	0.426591i	$0.859714\pi$
$174$	−11.5311	+	9.83306i	−0.874170	+	0.745443i
$175$	28.3583	+	16.3727i	2.14369	+	1.23766i
$176$	−1.72495	−	0.995899i	−0.130023	−	0.0750687i
$177$	−9.63811	+	8.21883i	−0.724444	+	0.617765i
$178$	3.14145	+	5.44115i	0.235462	+	0.407831i
$179$	7.91152			0.591334			0.295667	−	0.955291i	$-0.404458\pi$
$179$	7.91152			0.591334			0.295667	+	0.955291i	$0.404458\pi$
$180$	11.3648	+	1.81805i	0.847085	+	0.135510i
$181$	−1.02195			−0.0759611			−0.0379806	−	0.999278i	$-0.512092\pi$
$181$	−1.02195			−0.0759611			−0.0379806	+	0.999278i	$0.512092\pi$
$182$	11.7806	+	2.96792i	0.873236	+	0.219997i
$183$	−19.2019	+	3.54348i	−1.41944	+	0.261942i
$184$	3.70000	+	2.13620i	0.272768	+	0.157483i
$185$	−9.75779	+	16.9010i	−0.717407	+	1.24259i
$186$	−3.05976	+	8.61928i	−0.224352	+	0.631996i
$187$	4.48708	−	2.59062i	0.328128	−	0.189445i
$188$			4.88188i			0.356048i
$189$	8.38987	−	15.3670i	0.610273	−	1.11779i
$190$			7.64143i			0.554368i
$191$	−2.03054	−	3.51700i	−0.146925	−	0.254481i	0.783165	−	0.621814i	$-0.213604\pi$
$191$	−2.03054	−	3.51700i	−0.146925	−	0.254481i	−0.930089	+	0.367333i	$0.880271\pi$
$192$	0.579434	−	1.63225i	0.0418170	−	0.117798i
$193$	−14.4121	−	8.32085i	−1.03741	−	0.598948i	−0.118310	−	0.992977i	$-0.537748\pi$
$193$	−14.4121	−	8.32085i	−1.03741	−	0.598948i	−0.919098	+	0.394029i	$0.871081\pi$
$194$	−5.15177	+	8.92313i	−0.369875	+	0.640643i
$195$	−19.9360	−	13.2880i	−1.42765	−	0.951574i
$196$	−2.17657	−	3.76993i	−0.155469	−	0.269281i
$197$			20.8461i			1.48522i	0.669723	+	0.742611i	$0.266413\pi$
$197$			20.8461i			1.48522i	−0.669723	+	0.742611i	$0.733587\pi$
$198$	5.58182	−	2.13275i	0.396683	−	0.151568i
$199$	15.4367			1.09428			0.547138	−	0.837042i	$-0.315717\pi$
$199$	15.4367			1.09428			0.547138	+	0.837042i	$0.315717\pi$
$200$	−8.41632	+	4.85917i	−0.595124	+	0.343595i
$201$	7.46590	−	6.36650i	0.526604	−	0.449058i
$202$	−2.21634	−	1.27960i	−0.155941	−	0.0900325i
$203$	−25.5309	−	14.7403i	−1.79192	−	1.03457i
$204$	2.92348	+	3.42832i	0.204684	+	0.240030i
$205$	−15.8124	−	27.3878i	−1.10438	−	1.91285i
$206$			5.64143i			0.393057i
$207$	−11.9730	+	4.57474i	−0.832179	+	0.317966i
$208$	−2.51098	+	2.58747i	−0.174105	+	0.179409i
$209$	1.98363	+	3.43575i	0.137211	+	0.237656i
$210$	4.06316	+	22.0179i	0.280384	+	1.51938i
$211$	1.86662	−	3.23307i	0.128503	−	0.222574i	−0.794594	−	0.607142i	$-0.792316\pi$
$211$	1.86662	−	3.23307i	0.128503	−	0.222574i	0.923097	+	0.384568i	$0.125649\pi$
$212$	−4.58222	+	7.93663i	−0.314708	+	0.545090i
$213$	3.17482	+	1.12703i	0.217535	+	0.0772227i
$214$	−15.8527	+	9.15257i	−1.08367	+	0.625657i
$215$			39.3761i			2.68543i
$216$	2.70469	+	4.43674i	0.184031	+	0.301882i
$217$	−17.7927			−1.20785
$218$	−3.37452	−	5.84484i	−0.228551	−	0.395863i
$219$	−13.7342	−	4.87550i	−0.928071	−	0.329456i
$220$	−3.82072	+	6.61767i	−0.257593	+	0.446163i
$221$	−2.56312	−	9.02205i	−0.172414	−	0.606889i
$222$	−8.66446	+	1.59893i	−0.581520	+	0.107313i
$223$	2.38417	−	1.37650i	0.159656	−	0.0921775i	−0.418043	−	0.908427i	$-0.637284\pi$
$223$	2.38417	−	1.37650i	0.159656	−	0.0921775i	0.577699	+	0.816250i	$0.303951\pi$
$224$	3.36944			0.225130
$225$	4.60542	−	28.7890i	0.307028	−	1.91926i
$226$			5.95051i			0.395822i
$227$	3.30960	−	1.91080i	0.219666	−	0.126824i	−0.386130	−	0.922444i	$-0.626188\pi$
$227$	3.30960	−	1.91080i	0.219666	−	0.126824i	0.605795	+	0.795620i	$0.292855\pi$
$228$	−2.62505	+	2.23850i	−0.173849	+	0.148248i
$229$	9.50393	+	5.48710i	0.628037	+	0.362597i	0.779992	−	0.625790i	$-0.215223\pi$
$229$	9.50393	+	5.48710i	0.628037	+	0.362597i	−0.151954	+	0.988388i	$0.548557\pi$
$230$	8.19541	−	14.1949i	0.540389	−	0.935982i
$231$	7.54249	+	8.84497i	0.496259	+	0.581956i
$232$	7.57719	−	4.37469i	0.497467	−	0.287213i
$233$	2.26098			0.148122			0.0740610	−	0.997254i	$-0.476404\pi$
$233$	2.26098			0.148122			0.0740610	+	0.997254i	$0.476404\pi$
$234$	−1.27527	−	10.7412i	−0.0833672	−	0.702175i
$235$	18.7291			1.22175
$236$	6.33329	−	3.65653i	0.412262	−	0.238020i
$237$	−10.1382	+	1.87089i	−0.658548	+	0.121527i
$238$	−4.38244	+	7.59062i	−0.284072	+	0.492027i
$239$	−5.46146	−	3.15318i	−0.353273	−	0.203962i	0.312853	−	0.949802i	$-0.398715\pi$
$239$	−5.46146	−	3.15318i	−0.353273	−	0.203962i	−0.666126	+	0.745839i	$0.732049\pi$
$240$	−6.26206	−	2.22297i	−0.404214	−	0.143492i
$241$	−17.1743	+	9.91557i	−1.10629	+	0.638718i	−0.937867	−	0.346996i	$-0.887202\pi$
$241$	−17.1743	+	9.91557i	−1.10629	+	0.638718i	−0.168426	+	0.985714i	$0.553868\pi$
$242$		−	7.03274i		−	0.452082i
$243$	−15.4471	−	2.09450i	−0.990932	−	0.134362i
$244$	11.2734			0.721705
$245$	−14.4632	+	8.35031i	−0.924017	+	0.533482i
$246$	4.77641	−	13.4551i	0.304533	−	0.857863i
$247$	6.90816	−	1.96257i	0.439556	−	0.124875i
$248$	2.64030	−	4.57313i	0.167659	−	0.290394i
$249$	0.739175	+	4.00553i	0.0468433	+	0.253840i
$250$	9.05082	+	15.6765i	0.572424	+	0.991467i
$251$	0.440795			0.0278227			0.0139114	−	0.999903i	$-0.495572\pi$
$251$	0.440795			0.0278227			0.0139114	+	0.999903i	$0.495572\pi$
$252$	−6.37353	+	7.84579i	−0.401495	+	0.494238i
$253$		−	8.50975i		−	0.535003i
$254$	5.13662	−	2.96563i	0.322300	−	0.186080i
$255$	13.1526	−	11.2158i	0.823646	−	0.702358i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.78781	+	11.7568i	−0.423412	+	0.733371i	−0.996271	−	0.0862832i	$-0.972501\pi$
$257$	−6.78781	+	11.7568i	−0.423412	+	0.733371i	0.572859	+	0.819654i	$0.305834\pi$
$258$	−13.5268	+	11.5349i	−0.842144	+	0.718132i
$259$	−8.56999	−	14.8437i	−0.532513	−	0.922340i
$260$	9.92669	+	9.63323i	0.615627	+	0.597427i
$261$	−4.14625	+	25.9186i	−0.256646	+	1.60432i
$262$		−	13.7649i		−	0.850400i
$263$	−11.1892	−	19.3803i	−0.689956	−	1.19504i	−0.971852	−	0.235594i	$-0.924296\pi$
$263$	−11.1892	−	19.3803i	−0.689956	−	1.19504i	0.281896	−	0.959445i	$-0.409037\pi$
$264$	−3.39261	+	0.626068i	−0.208801	+	0.0385318i
$265$	30.4485	+	17.5794i	1.87044	+	1.07990i
$266$	−5.81211	−	3.35563i	−0.356364	−	0.205747i
$267$	10.2553	+	3.64052i	0.627614	+	0.222796i
$268$	−4.90591	+	2.83243i	−0.299676	+	0.173018i
$269$	−30.4520			−1.85669			−0.928345	−	0.371719i	$-0.878768\pi$
$269$	−30.4520			−1.85669			−0.928345	+	0.371719i	$0.878768\pi$
$270$	17.0213	−	10.3764i	1.03588	−	0.631487i
$271$		−	2.03437i		−	0.123579i	−0.998089	−	0.0617897i	$-0.980319\pi$
$271$		−	2.03437i		−	0.123579i	0.998089	−	0.0617897i	$-0.0196808\pi$
$272$	−1.30064	−	2.25278i	−0.0788631	−	0.136595i
$273$	18.8615	−	9.32819i	1.14155	−	0.564567i
$274$	−1.90992	+	3.30808i	−0.115382	+	0.199848i
$275$	16.7636	+	9.67848i	1.01088	+	0.583634i
$276$	7.27713	−	1.34291i	0.438032	−	0.0808338i
$277$	14.4567	+	25.0398i	0.868621	+	1.50450i	0.863406	+	0.504510i	$0.168327\pi$
$277$	14.4567	+	25.0398i	0.868621	+	1.50450i	0.00521502	+	0.999986i	$0.498340\pi$
$278$		−	13.6097i		−	0.816258i
$279$	5.65429	+	14.7984i	0.338513	+	0.885954i
$280$		−	12.9267i		−	0.772518i
$281$	17.7630	−	10.2555i	1.05965	−	0.611791i	0.134316	−	0.990939i	$-0.457116\pi$
$281$	17.7630	−	10.2555i	1.05965	−	0.611791i	0.925336	+	0.379148i	$0.123783\pi$
$282$	5.48654	+	6.43399i	0.326719	+	0.383139i
$283$	0.819991	−	1.42027i	0.0487434	−	0.0844260i	−0.840624	−	0.541619i	$-0.817812\pi$
$283$	0.819991	−	1.42027i	0.0487434	−	0.0844260i	0.889368	+	0.457193i	$0.151145\pi$
$284$	−1.68446	−	0.972526i	−0.0999545	−	0.0577088i
$285$	8.58788	+	10.0709i	0.508702	+	0.596548i
$286$	6.96393	+	1.75444i	0.411786	+	0.103742i
$287$	27.7751			1.63951
$288$	−1.07077	−	2.80240i	−0.0630955	−	0.165133i
$289$	−10.2333			−0.601959
$290$	−16.7833	−	29.0695i	−0.985549	−	1.70702i
$291$	3.23864	+	17.5499i	0.189852	+	1.02879i
$292$	7.28696	+	4.20713i	0.426437	+	0.246203i
$293$	10.7578	+	6.21102i	0.628477	+	0.362852i	0.780162	−	0.625577i	$-0.215137\pi$
$293$	10.7578	+	6.21102i	0.628477	+	0.362852i	−0.151685	+	0.988429i	$0.548470\pi$
$294$	−7.10544	−	2.52236i	−0.414398	−	0.147107i
$295$	−14.0281	−	24.2973i	−0.816746	−	1.41465i
$296$	5.08689			0.295669
$297$	4.95955	−	9.08399i	0.287782	−	0.527107i
$298$	−7.79096			−0.451318
$299$	−14.9376	−	3.76327i	−0.863863	−	0.217636i
$300$	−5.63113	+	15.8628i	−0.325114	+	0.915839i
$301$	−29.9497	−	17.2914i	−1.72627	−	0.996662i
$302$	−10.6829	+	18.5033i	−0.614733	+	1.06475i
$303$	−4.35907	+	0.804417i	−0.250422	+	0.0462125i
$304$	1.72495	−	0.995899i	0.0989326	−	0.0571187i
$305$		−	43.2498i		−	2.47647i
$306$	7.70588	+	1.23272i	0.440516	+	0.0704701i
$307$		−	25.8780i		−	1.47693i	−0.674289	−	0.738467i	$-0.735550\pi$
$307$		−	25.8780i		−	1.47693i	0.674289	−	0.738467i	$-0.264450\pi$
$308$	−3.35563	−	5.81211i	−0.191205	−	0.331176i
$309$	6.34016	+	7.43502i	0.360679	+	0.422964i
$310$	−17.5446	−	10.1294i	−0.996465	−	0.575309i
$311$	12.6911	−	21.9816i	0.719645	−	1.24646i	−0.241495	−	0.970402i	$-0.577638\pi$
$311$	12.6911	−	21.9816i	0.719645	−	1.24646i	0.961140	−	0.276060i	$-0.0890289\pi$
$312$	−0.401349	+	6.23209i	−0.0227219	+	0.352822i
$313$	5.09998	+	8.83342i	0.288268	+	0.499294i	0.973396	−	0.229128i	$-0.0735874\pi$
$313$	5.09998	+	8.83342i	0.288268	+	0.499294i	−0.685129	+	0.728422i	$0.740254\pi$
$314$			4.25143i			0.239922i
$315$	30.1000	+	24.4517i	1.69594	+	1.37770i
$316$	5.95213			0.334834
$317$	10.5613	−	6.09759i	0.593184	−	0.342475i	−0.173171	−	0.984892i	$-0.555401\pi$
$317$	10.5613	−	6.09759i	0.593184	−	0.342475i	0.766356	+	0.642417i	$0.222068\pi$
$318$	2.88059	+	15.6097i	0.161536	+	0.875349i
$319$	−15.0922	−	8.71351i	−0.845003	−	0.487863i
$320$	3.32246	+	1.91822i	0.185731	+	0.107232i
$321$	−10.6066	+	29.8786i	−0.592004	+	1.66766i
$322$	7.19780	+	12.4669i	0.401117	+	0.694756i
$323$			5.18124i			0.288292i
$324$	8.55086	+	2.80764i	0.475048	+	0.155980i
$325$	24.4025	−	25.1459i	1.35361	−	1.39484i
$326$	5.52667	+	9.57247i	0.306094	+	0.530170i
$327$	−11.0162	−	3.91063i	−0.609195	−	0.216258i
$328$	−4.12162	+	7.13885i	−0.227578	+	0.394177i
$329$	−8.22461	+	14.2454i	−0.453438	+	0.785377i
$330$	2.40188	+	13.0156i	0.132219	+	0.716484i
$331$	19.4652	−	11.2383i	1.06991	−	0.617711i	0.141750	−	0.989902i	$-0.454727\pi$
$331$	19.4652	−	11.2383i	1.06991	−	0.617711i	0.928156	+	0.372192i	$0.121394\pi$
$332$		−	2.35164i		−	0.129063i
$333$	−9.62220	+	11.8449i	−0.527293	+	0.649096i
$334$	−9.40375			−0.514550
$335$	10.8665	+	18.8213i	0.593699	+	1.02832i
$336$	4.44070	−	3.78677i	0.242260	−	0.206585i
$337$	15.3975	−	26.6692i	0.838755	−	1.45277i	−0.0521819	−	0.998638i	$-0.516618\pi$
$337$	15.3975	−	26.6692i	0.838755	−	1.45277i	0.890936	−	0.454128i	$-0.150049\pi$
$338$	6.15933	−	11.4483i	0.335023	−	0.622703i
$339$	6.68753	+	7.84237i	0.363217	+	0.425939i
$340$	−8.64268	+	4.98985i	−0.468715	+	0.270613i
$341$	−10.5179			−0.569575
$342$	−0.943893	+	5.90037i	−0.0510399	+	0.319056i
$343$			8.91842i			0.481550i
$344$	8.88861	−	5.13184i	0.479242	−	0.276690i
$345$	−5.15201	−	27.9183i	−0.277375	−	1.50307i
$346$	1.88594	+	1.08885i	0.101389	+	0.0585368i
$347$	14.5235	−	25.1555i	0.779664	−	1.35042i	−0.152472	−	0.988308i	$-0.548723\pi$
$347$	14.5235	−	25.1555i	0.779664	−	1.35042i	0.932136	−	0.362109i	$-0.117943\pi$
$348$	5.06969	−	14.2812i	0.271764	−	0.765554i
$349$	10.7969	−	6.23358i	0.577943	−	0.333676i	−0.182372	−	0.983230i	$-0.558378\pi$
$349$	10.7969	−	6.23358i	0.577943	−	0.333676i	0.760316	+	0.649554i	$0.225044\pi$
$350$	−32.7454			−1.75031
$351$	−13.7523	−	12.7230i	−0.734044	−	0.679102i
$352$	1.99180			0.106163
$353$	−29.8167	+	17.2147i	−1.58698	+	0.916244i	−0.593180	+	0.805070i	$0.702128\pi$
$353$	−29.8167	+	17.2147i	−1.58698	+	0.916244i	−0.993801	+	0.111174i	$0.964539\pi$
$354$	4.23743	−	11.9368i	0.225217	−	0.634432i
$355$	−3.73104	+	6.46236i	−0.198023	+	0.342986i
$356$	−5.44115	−	3.14145i	−0.288380	−	0.166496i
$357$	2.75501	+	14.9292i	0.145810	+	0.790135i
$358$	−6.85157	+	3.95576i	−0.362117	+	0.209068i
$359$			34.2496i			1.80762i	0.427931	+	0.903812i	$0.359243\pi$
$359$			34.2496i			1.80762i	−0.427931	+	0.903812i	$0.640757\pi$
$360$	−10.7513	+	4.10794i	−0.566642	+	0.216508i
$361$	15.0327			0.791197
$362$	0.885037	−	0.510976i	0.0465165	−	0.0268563i
$363$	−7.90380	−	9.26867i	−0.414842	−	0.486479i
$364$	−11.6863	+	3.32000i	−0.612526	+	0.174015i
$365$	16.1404	−	27.9560i	0.844828	−	1.46329i
$366$	14.8576	−	12.6697i	0.776617	−	0.662255i
$367$	2.51806	+	4.36140i	0.131441	+	0.227663i	0.924232	−	0.381830i	$-0.124706\pi$
$367$	2.51806	+	4.36140i	0.131441	+	0.227663i	−0.792791	+	0.609494i	$0.791373\pi$
$368$	−4.27239			−0.222714
$369$	−8.82658	−	23.1008i	−0.459493	−	1.20258i
$370$		−	19.5156i		−	1.01457i
$371$	−26.7420	+	15.4395i	−1.38838	+	0.801580i
$372$	−1.65981	−	8.99439i	−0.0860573	−	0.466338i
$373$	−5.60706	+	9.71171i	−0.290322	+	0.502853i	−0.973886	−	0.227038i	$-0.927096\pi$
$373$	−5.60706	+	9.71171i	−0.290322	+	0.502853i	0.683563	+	0.729891i	$0.260429\pi$
$374$	−2.59062	+	4.48708i	−0.133958	+	0.232022i
$375$	29.5465	+	10.4887i	1.52577	+	0.541634i
$376$	−2.44094	−	4.22784i	−0.125882	−	0.218034i
$377$	−21.9695	+	22.6388i	−1.13149	+	1.16596i
$378$	0.417668	+	17.5032i	0.0214825	+	0.900265i
$379$		−	5.12623i		−	0.263317i	−0.991295	−	0.131658i	$-0.957970\pi$
$379$		−	5.12623i		−	0.263317i	0.991295	−	0.131658i	$-0.0420302\pi$
$380$	−3.82072	−	6.61767i	−0.195999	−	0.339479i
$381$	3.43677	−	9.68132i	0.176071	−	0.495989i
$382$	3.51700	+	2.03054i	0.179945	+	0.103891i
$383$	−16.4042	−	9.47098i	−0.838216	−	0.483944i	0.0184411	−	0.999830i	$-0.494130\pi$
$383$	−16.4042	−	9.47098i	−0.838216	−	0.483944i	−0.856658	+	0.515885i	$0.827463\pi$
$384$	0.314323	+	1.70329i	0.0160402	+	0.0869207i
$385$	−22.2979	+	12.8737i	−1.13640	+	0.656104i
$386$	16.6417			0.847041
$387$	−4.86385	+	30.4045i	−0.247243	+	1.54555i
$388$		−	10.3035i		−	0.523083i
$389$	10.4199	+	18.0477i	0.528308	+	0.915057i	0.999455	+	0.0330020i	$0.0105068\pi$
$389$	10.4199	+	18.0477i	0.528308	+	0.915057i	−0.471147	+	0.882055i	$0.656160\pi$
$390$	23.9091	+	1.53976i	1.21068	+	0.0779686i
$391$	5.55686	−	9.62477i	0.281023	−	0.486745i
$392$	3.76993	+	2.17657i	0.190410	+	0.109934i
$393$	−15.4698	−	18.1412i	−0.780349	−	0.915104i
$394$	−10.4230	−	18.0532i	−0.525105	−	0.909509i
$395$		−	22.8350i		−	1.14896i
$396$	−3.76762	+	4.63793i	−0.189330	+	0.233065i
$397$		−	2.17152i		−	0.108985i	−0.998514	−	0.0544927i	$-0.982646\pi$
$397$		−	2.17152i		−	0.108985i	0.998514	−	0.0544927i	$-0.0173541\pi$
$398$	−13.3685	+	7.71833i	−0.670104	+	0.386885i
$399$	−11.4312	+	2.10950i	−0.572277	+	0.105607i
$400$	4.85917	−	8.41632i	0.242958	−	0.420816i
$401$	−9.35590	−	5.40163i	−0.467211	−	0.269745i	0.247860	−	0.968796i	$-0.420273\pi$
$401$	−9.35590	−	5.40163i	−0.467211	−	0.269745i	−0.715072	+	0.699051i	$0.753606\pi$
$402$	−3.28241	+	9.24650i	−0.163712	+	0.461173i
$403$	−4.65133	+	18.4626i	−0.231699	+	0.919686i
$404$	2.55921			0.127325
$405$	10.7714	−	32.8049i	0.535233	−	1.63009i
$406$	29.4806			1.46310
$407$	−5.06603	−	8.77462i	−0.251114	−	0.434942i
$408$	−4.24596	−	1.50727i	−0.210207	−	0.0746212i
$409$	−1.34494	−	0.776503i	−0.0665031	−	0.0383956i	0.466380	−	0.884585i	$-0.345558\pi$
$409$	−1.34494	−	0.776503i	−0.0665031	−	0.0383956i	−0.532883	+	0.846189i	$0.678891\pi$
$410$	27.3878	+	15.8124i	1.35259	+	0.780917i
$411$	1.20066	+	6.50629i	0.0592243	+	0.320932i
$412$	−2.82072	−	4.88562i	−0.138967	−	0.240697i
$413$	24.6409			1.21250
$414$	8.08153	−	9.94832i	0.397185	−	0.488933i
$415$	−9.02195			−0.442870
$416$	0.880834	−	3.49630i	0.0431865	−	0.171420i
$417$	−15.2954	−	17.9367i	−0.749020	−	0.878365i
$418$	−3.43575	−	1.98363i	−0.168048	−	0.0970225i
$419$	−2.81453	+	4.87490i	−0.137499	+	0.238155i	−0.926549	−	0.376174i	$-0.877240\pi$
$419$	−2.81453	+	4.87490i	−0.137499	+	0.238155i	0.789051	+	0.614328i	$0.210573\pi$
$420$	−14.5278	−	17.0365i	−0.708882	−	0.831296i
$421$	10.3872	−	5.99704i	0.506240	−	0.292278i	−0.225047	−	0.974348i	$-0.572253\pi$
$421$	10.3872	−	5.99704i	0.506240	−	0.292278i	0.731287	+	0.682070i	$0.238920\pi$
$422$			3.73323i			0.181731i
$423$	14.4618	+	2.31347i	0.703156	+	0.112485i
$424$		−	9.16444i		−	0.445064i
$425$	12.6401	+	21.8933i	0.613134	+	1.06198i
$426$	−3.31299	+	0.611374i	−0.160515	+	0.0296212i
$427$	32.8960	+	18.9925i	1.59195	+	0.919112i
$428$	9.15257	−	15.8527i	0.442406	−	0.766270i
$429$	11.1497	−	5.51422i	0.538314	−	0.266229i
$430$	−19.6880	−	34.1007i	−0.949441	−	1.64448i
$431$			0.0127142i			0.000612420i	1.00000		0.000306210i	$9.74697e-5\pi$
$431$			0.0127142i			0.000612420i	−1.00000		0.000306210i	$0.999903\pi$
$432$	−4.56070	−	2.48999i	−0.219427	−	0.119800i
$433$	30.8717			1.48360			0.741800	−	0.670621i	$-0.233972\pi$
$433$	30.8717			1.48360			0.741800	+	0.670621i	$0.233972\pi$
$434$	15.4089	−	8.89633i	0.739651	−	0.427038i
$435$	−54.7892	−	19.4496i	−2.62694	−	0.932538i
$436$	5.84484	+	3.37452i	0.279917	+	0.161610i
$437$	7.36966	+	4.25487i	0.352539	+	0.203538i
$438$	14.3319	−	2.64479i	0.684806	−	0.126373i
$439$	−8.19780	−	14.1990i	−0.391259	−	0.677681i	0.601357	−	0.798981i	$-0.294627\pi$
$439$	−8.19780	−	14.1990i	−0.391259	−	0.677681i	−0.992616	+	0.121300i	$0.961294\pi$
$440$		−	7.64143i		−	0.364291i
$441$	−12.1993	+	4.66120i	−0.580917	+	0.221962i
$442$	6.73075	+	6.53177i	0.320149	+	0.310685i
$443$	2.02258	+	3.50320i	0.0960955	+	0.166442i	0.910065	−	0.414465i	$-0.136031\pi$
$443$	2.02258	+	3.50320i	0.0960955	+	0.166442i	−0.813970	+	0.580907i	$0.802698\pi$
$444$	6.70418	−	5.71694i	0.318166	−	0.271314i
$445$	−12.0520	+	20.8747i	−0.571320	+	0.989555i
$446$	−1.37650	+	2.38417i	−0.0651793	+	0.112894i
$447$	−10.2680	+	8.75592i	−0.485657	+	0.414141i
$448$	−2.91802	+	1.68472i	−0.137864	+	0.0795956i
$449$		−	15.8943i		−	0.750099i	−0.927005	−	0.375049i	$-0.877626\pi$
$449$		−	15.8943i		−	0.750099i	0.927005	−	0.375049i	$-0.122374\pi$
$450$	10.4061	+	27.2347i	0.490547	+	1.28385i
$451$	16.4189			0.773134
$452$	−2.97526	−	5.15330i	−0.139944	−	0.242391i
$453$	6.71577	+	36.3922i	0.315534	+	1.70986i
$454$	−1.91080	+	3.30960i	−0.0896781	+	0.155327i
$455$	12.7370	+	44.8337i	0.597120	+	2.10184i
$456$	1.15412	−	3.25112i	0.0540464	−	0.152248i
$457$	25.2372	−	14.5707i	1.18055	−	0.681589i	0.224406	−	0.974496i	$-0.427956\pi$
$457$	25.2372	−	14.5707i	1.18055	−	0.681589i	0.956141	+	0.292907i	$0.0946225\pi$
$458$	−10.9742			−0.512790
$459$	11.5412	−	7.03567i	0.538699	−	0.328397i
$460$			16.3908i			0.764226i
$461$	−24.3725	+	14.0714i	−1.13514	+	0.655373i	−0.945222	−	0.326428i	$-0.894155\pi$
$461$	−24.3725	+	14.0714i	−1.13514	+	0.655373i	−0.189917	+	0.981800i	$0.560822\pi$
$462$	−10.9545	−	3.88873i	−0.509648	−	0.180920i
$463$	27.5978	+	15.9336i	1.28258	+	0.740498i	0.977319	−	0.211771i	$-0.0679231\pi$
$463$	27.5978	+	15.9336i	1.28258	+	0.740498i	0.305261	+	0.952269i	$0.401256\pi$
$464$	−4.37469	+	7.57719i	−0.203090	+	0.351762i
$465$	−34.5065	+	6.36778i	−1.60020	+	0.295299i
$466$	−1.95807	+	1.13049i	−0.0907058	+	0.0523690i
$467$	1.94189			0.0898600			0.0449300	−	0.998990i	$-0.485694\pi$
$467$	1.94189			0.0898600			0.0449300	+	0.998990i	$0.485694\pi$
$468$	6.47503	+	8.66453i	0.299308	+	0.400518i
$469$	−19.0874			−0.881376
$470$	−16.2199	+	9.36455i	−0.748167	+	0.431954i
$471$	4.77800	+	5.60310i	0.220159	+	0.258177i
$472$	−3.65653	+	6.33329i	−0.168305	+	0.291513i
$473$	−17.7043	−	10.2216i	−0.814045	−	0.469989i
$474$	7.84450	−	6.68935i	0.360310	−	0.307252i
$475$	−16.7636	+	9.67848i	−0.769167	+	0.444079i
$476$		−	8.76489i		−	0.401738i
$477$	21.3395	+	17.3352i	0.977069	+	0.793722i
$478$	6.30635			0.288446
$479$	9.46110	−	5.46237i	0.432289	−	0.249582i	−0.268033	−	0.963410i	$-0.586373\pi$
$479$	9.46110	−	5.46237i	0.432289	−	0.249582i	0.700321	+	0.713828i	$0.253040\pi$
$480$	6.53459	−	1.20588i	0.298262	−	0.0550408i
$481$	−17.6429	+	5.01225i	−0.804446	+	0.228539i
$482$	9.91557	−	17.1743i	0.451642	−	0.782267i
$483$	23.4973	+	8.34129i	1.06916	+	0.379542i
$484$	3.51637	+	6.09053i	0.159835	+	0.276842i
$485$	−39.5290			−1.79492
$486$	14.4248	−	5.90966i	0.654324	−	0.268068i
$487$			38.3978i			1.73997i	0.493078	+	0.869985i	$0.335872\pi$
$487$			38.3978i			1.73997i	−0.493078	+	0.869985i	$0.664128\pi$
$488$	−9.76304	+	5.63669i	−0.441952	+	0.255161i
$489$	18.0419	+	6.40468i	0.815881	+	0.289629i
$490$	8.35031	−	14.4632i	0.377228	−	0.653379i
$491$	−5.27663	+	9.13938i	−0.238131	+	0.412455i	−0.960178	−	0.279389i	$-0.909868\pi$
$491$	−5.27663	+	9.13938i	−0.238131	+	0.412455i	0.722047	+	0.691844i	$0.243201\pi$
$492$	2.59104	+	14.0406i	0.116813	+	0.633000i
$493$	−11.3798	−	19.7105i	−0.512522	−	0.887714i
$494$	−5.00136	+	5.15372i	−0.225022	+	0.231877i
$495$	17.7932	+	14.4543i	0.799743	+	0.649672i
$496$			5.28060i			0.237106i
$497$	−3.27687	−	5.67571i	−0.146988	−	0.254590i
$498$	−2.64291	−	3.09930i	−0.118432	−	0.138883i
$499$	0.859848	+	0.496434i	0.0384921	+	0.0222234i	0.519123	−	0.854700i	$-0.326259\pi$
$499$	0.859848	+	0.496434i	0.0384921	+	0.0222234i	−0.480630	+	0.876923i	$0.659592\pi$
$500$	−15.6765	−	9.05082i	−0.701073	−	0.404765i
$501$	−12.3935	+	10.5685i	−0.553701	+	0.472164i
$502$	−0.381740	+	0.220397i	−0.0170379	+	0.00983682i
$503$	9.23683			0.411850			0.205925	−	0.978568i	$-0.433980\pi$
$503$	9.23683			0.411850			0.205925	+	0.978568i	$0.433980\pi$
$504$	1.59674	−	9.98142i	0.0711246	−	0.444608i
$505$		−	9.81826i		−	0.436907i
$506$	4.25487	+	7.36966i	0.189152	+	0.327621i
$507$	−4.74864	−	22.0102i	−0.210894	−	0.977509i
$508$	−2.96563	+	5.13662i	−0.131578	+	0.227901i
$509$	8.35176	+	4.82189i	0.370185	+	0.213727i	0.673539	−	0.739151i	$-0.264773\pi$
$509$	8.35176	+	4.82189i	0.370185	+	0.213727i	−0.303354	+	0.952878i	$0.598107\pi$
$510$	−5.78258	+	16.2894i	−0.256057	+	0.721308i
$511$	14.1757	+	24.5530i	0.627095	+	1.08616i
$512$		−	1.00000i		−	0.0441942i
$513$	5.38719	+	8.83709i	0.237850	+	0.390167i
$514$		−	13.5756i		−	0.598795i
$515$	−18.7434	+	10.8215i	−0.825934	+	0.476853i
$516$	5.94712	−	16.7529i	0.261808	−	0.737507i
$517$	−4.86186	+	8.42100i	−0.213825	+	0.370355i
$518$	14.8437	+	8.56999i	0.652193	+	0.376544i
$519$	3.70925	−	0.684499i	0.162818	−	0.0300462i
$520$	−13.4134	−	3.37927i	−0.588216	−	0.148191i
$521$	−18.9584			−0.830581			−0.415291	−	0.909689i	$-0.636320\pi$
$521$	−18.9584			−0.830581			−0.415291	+	0.909689i	$0.636320\pi$
$522$	−9.36856	−	24.5193i	−0.410051	−	1.07318i
$523$	24.4694			1.06997			0.534986	−	0.844861i	$-0.320317\pi$
$523$	24.4694			1.06997			0.534986	+	0.844861i	$0.320317\pi$
$524$	6.88246	+	11.9208i	0.300662	+	0.520762i
$525$	−43.1562	+	36.8011i	−1.88349	+	1.60613i
$526$	19.3803	+	11.1892i	0.845020	+	0.487873i
$527$	−11.8960	−	6.86817i	−0.518199	−	0.299182i
$528$	2.62505	−	2.23850i	0.114241	−	0.0974181i
$529$	2.37332	+	4.11071i	0.103188	+	0.178727i
$530$	−35.1589			−1.52720
$531$	−7.83057	−	20.4941i	−0.339818	−	0.889369i
$532$	6.71125			0.290970
$533$	7.26092	−	28.8208i	0.314505	−	1.24837i
$534$	−10.7016	+	1.97486i	−0.463104	+	0.0854605i
$535$	−60.8181	−	35.1133i	−2.62940	−	1.51808i
$536$	2.83243	−	4.90591i	0.122342	−	0.211903i
$537$	−4.58420	+	12.9136i	−0.197823	+	0.557263i
$538$	26.3722	−	15.2260i	1.13699	−	0.656439i
$539$		−	8.67059i		−	0.373469i
$540$	−9.55270	+	17.4969i	−0.411083	+	0.752946i
$541$		−	6.77020i		−	0.291074i	−0.989353	−	0.145537i	$-0.953509\pi$
$541$		−	6.77020i		−	0.291074i	0.989353	−	0.145537i	$-0.0464909\pi$
$542$	1.01719	+	1.76182i	0.0436919	+	0.0756766i
$543$	0.592154	−	1.66809i	0.0254118	−	0.0715845i
$544$	2.25278	+	1.30064i	0.0965872	+	0.0557646i
$545$	12.9462	−	22.4234i	0.554553	−	0.960514i
$546$	−11.6705	+	17.5092i	−0.499450	+	0.749325i
$547$	−4.23689	−	7.33850i	−0.181156	−	0.313772i	0.761118	−	0.648613i	$-0.224651\pi$
$547$	−4.23689	−	7.33850i	−0.181156	−	0.313772i	−0.942275	+	0.334841i	$0.891317\pi$
$548$		−	3.81984i		−	0.163175i
$549$	5.34234	−	33.3955i	0.228006	−	1.42529i
$550$	−19.3570			−0.825383
$551$	15.0922	−	8.71351i	0.642951	−	0.371208i
$552$	−5.63073	+	4.80156i	−0.239660	+	0.204368i
$553$	17.3685	+	10.0277i	0.738582	+	0.426420i
$554$	−25.0398	−	14.4567i	−1.06384	−	0.614208i
$555$	−21.9327	−	25.7202i	−0.930993	−	1.09176i
$556$	6.80487	+	11.7864i	0.288591	+	0.499854i
$557$			4.77737i			0.202424i	0.994865	+	0.101212i	$0.0322720\pi$
$557$			4.77737i			0.202424i	−0.994865	+	0.101212i	$0.967728\pi$
$558$	−12.2959	−	9.98861i	−0.520528	−	0.422851i
$559$	−25.7719	+	26.5570i	−1.09003	+	1.12324i
$560$	6.46335	+	11.1948i	0.273126	+	0.473068i
$561$	1.62858	+	8.82516i	0.0687588	+	0.372599i
$562$	−10.2555	+	17.7630i	−0.432601	+	0.749287i
$563$	−4.96417	+	8.59819i	−0.209215	+	0.362370i	−0.951467	−	0.307750i	$-0.900424\pi$
$563$	−4.96417	+	8.59819i	−0.209215	+	0.362370i	0.742253	+	0.670120i	$0.233757\pi$
$564$	−7.96848	−	2.82873i	−0.335533	−	0.119111i
$565$	−19.7704	+	11.4144i	−0.831745	+	0.480208i
$566$			1.63998i			0.0689336i
$567$	20.2215	+	22.5986i	0.849224	+	0.949051i
$568$	1.94505			0.0816125
$569$	−14.9307	−	25.8608i	−0.625929	−	1.08414i	−0.988361	−	0.152130i	$-0.951387\pi$
$569$	−14.9307	−	25.8608i	−0.625929	−	1.08414i	0.362432	−	0.932010i	$-0.381947\pi$
$570$	−12.4728	−	4.42770i	−0.522427	−	0.185456i
$571$	−15.0696	+	26.1014i	−0.630645	+	1.09231i	0.356775	+	0.934190i	$0.383876\pi$
$571$	−15.0696	+	26.1014i	−0.630645	+	1.09231i	−0.987420	+	0.158119i	$0.949457\pi$
$572$	−6.90816	+	1.96257i	−0.288845	+	0.0820592i
$573$	6.91720	−	1.27649i	0.288970	−	0.0533262i
$574$	−24.0539	+	13.8875i	−1.00399	+	0.579655i
$575$	41.5205			1.73153
$576$	2.32851	+	1.89157i	0.0970214	+	0.0788153i
$577$			7.87256i			0.327739i	0.986482	+	0.163869i	$0.0523976\pi$
$577$			7.87256i			0.327739i	−0.986482	+	0.163869i	$0.947602\pi$
$578$	8.86230	−	5.11665i	0.368623	−	0.212825i
$579$	21.9326	−	18.7029i	0.911489	−	0.777266i
$580$	29.0695	+	16.7833i	1.20705	+	0.696888i
$581$	3.96186	−	6.86215i	0.164366	−	0.284690i
$582$	−11.5797	−	13.5794i	−0.479994	−	0.562883i
$583$	−15.8082	+	9.12685i	−0.654708	+	0.377996i
$584$	−8.41425			−0.348184
$585$	33.2410	−	24.8411i	1.37435	−	1.02705i
$586$	−12.4220			−0.513150
$587$	18.6643	−	10.7758i	0.770359	−	0.444767i	−0.0626437	−	0.998036i	$-0.519953\pi$
$587$	18.6643	−	10.7758i	0.770359	−	0.444767i	0.833003	+	0.553269i	$0.186620\pi$
$588$	7.41468	−	1.36829i	0.305776	−	0.0564275i
$589$	5.25894	−	9.10875i	0.216691	−	0.375320i
$590$	24.2973	+	14.0281i	1.00031	+	0.577527i
$591$	−34.0261	−	12.0789i	−1.39965	−	0.496861i
$592$	−4.40538	+	2.54345i	−0.181060	+	0.104535i
$593$		−	8.13186i		−	0.333935i	−0.985962	−	0.166968i	$-0.946602\pi$
$593$		−	8.13186i		−	0.333935i	0.985962	−	0.166968i	$-0.0533975\pi$
$594$	0.246899	+	10.3467i	0.0101304	+	0.424532i
$595$	−33.6260			−1.37853
$596$	6.74717	−	3.89548i	0.276375	−	0.159565i
$597$	−8.94453	+	25.1966i	−0.366075	+	1.03123i
$598$	14.8180	−	4.20970i	0.605952	−	0.172148i
$599$	−23.3019	+	40.3601i	−0.952090	+	1.64907i	−0.211199	+	0.977443i	$0.567737\pi$
$599$	−23.3019	+	40.3601i	−0.952090	+	1.64907i	−0.740891	+	0.671625i	$0.765597\pi$
$600$	−3.05469	−	16.5531i	−0.124707	−	0.675779i
$601$	−10.3826	−	17.9832i	−0.423515	−	0.733550i	0.572765	−	0.819719i	$-0.305871\pi$
$601$	−10.3826	−	17.9832i	−0.423515	−	0.733550i	−0.996280	+	0.0861696i	$0.972537\pi$
$602$	34.5829			1.40949
$603$	6.06575	+	15.8752i	0.247016	+	0.646489i
$604$		−	21.3658i		−	0.869363i
$605$	23.3660	−	13.4904i	0.949963	−	0.548461i
$606$	3.37286	−	2.87618i	0.137013	−	0.116837i
$607$	16.3176	−	28.2630i	0.662313	−	1.14716i	−0.317694	−	0.948193i	$-0.602908\pi$
$607$	16.3176	−	28.2630i	0.662313	−	1.14716i	0.980006	−	0.198966i	$-0.0637582\pi$
$608$	−0.995899	+	1.72495i	−0.0403890	+	0.0699559i
$609$	38.8534	−	33.1319i	1.57442	−	1.34257i
$610$	21.6249	+	37.4554i	0.875566	+	1.51652i
$611$	12.6317	+	12.2583i	0.511025	+	0.495917i
$612$	−7.28985	+	2.78537i	−0.294675	+	0.112592i
$613$		−	12.8107i		−	0.517421i	−0.965955	−	0.258711i	$-0.916702\pi$
$613$		−	12.8107i		−	0.517421i	0.965955	−	0.258711i	$-0.0832976\pi$
$614$	12.9390	+	22.4110i	0.522175	+	0.904434i
$615$	53.8661	−	9.94038i	2.17209	−	0.400835i
$616$	5.81211	+	3.35563i	0.234177	+	0.135202i
$617$	−18.6017	−	10.7397i	−0.748874	−	0.432363i	0.0764127	−	0.997076i	$-0.475653\pi$
$617$	−18.6017	−	10.7397i	−0.748874	−	0.432363i	−0.825287	+	0.564714i	$0.808987\pi$
$618$	−9.20825	−	3.26884i	−0.370410	−	0.131492i
$619$	−39.6343	+	22.8829i	−1.59304	+	0.919741i	−0.600256	+	0.799808i	$0.704935\pi$
$619$	−39.6343	+	22.8829i	−1.59304	+	0.919741i	−0.992782	+	0.119933i	$0.961732\pi$
$620$	20.2587			0.813610
$621$	−0.529596	−	22.1937i	−0.0212520	−	0.890602i
$622$			25.3822i			1.01773i
$623$	−10.5849	−	18.3336i	−0.424076	−	0.734522i
$624$	−2.76847	−	5.59782i	−0.110827	−	0.224092i
$625$	−10.4272	+	18.0604i	−0.417086	+	0.722414i
$626$	−8.83342	−	5.09998i	−0.353054	−	0.203836i
$627$	−6.75740	+	1.24700i	−0.269865	+	0.0498004i
$628$	−2.12572	−	3.68185i	−0.0848253	−	0.146922i
$629$		−	13.2325i		−	0.527613i
$630$	−38.2932	−	6.12583i	−1.52564	−	0.244059i
$631$		−	10.7134i		−	0.426495i	−0.976998	−	0.213248i	$-0.931596\pi$
$631$		−	10.7134i		−	0.426495i	0.976998	−	0.213248i	$-0.0684041\pi$
$632$	−5.15470	+	2.97607i	−0.205043	+	0.118382i
$633$	4.19562	+	4.92014i	0.166761	+	0.195558i
$634$	−6.09759	+	10.5613i	−0.242166	+	0.419444i
$635$	19.7064	+	11.3775i	0.782023	+	0.451501i
$636$	−10.2995	−	12.0781i	−0.408402	−	0.478928i
$637$	−15.2199	−	3.83440i	−0.603035	−	0.151924i
$638$	17.4270			0.689942
$639$	−3.67920	+	4.52908i	−0.145547	+	0.179167i
$640$	−3.83645			−0.151649
$641$	19.0700	+	33.0303i	0.753221	+	1.30462i	0.946254	+	0.323425i	$0.104834\pi$
$641$	19.0700	+	33.0303i	0.753221	+	1.30462i	−0.193033	+	0.981192i	$0.561832\pi$
$642$	−5.75372	−	31.1790i	−0.227081	−	1.23054i
$643$	−7.07558	−	4.08509i	−0.279034	−	0.161100i	0.353952	−	0.935264i	$-0.384838\pi$
$643$	−7.07558	−	4.08509i	−0.279034	−	0.161100i	−0.632986	+	0.774163i	$0.718171\pi$
$644$	−12.4669	−	7.19780i	−0.491267	−	0.283633i
$645$	−64.2718	−	22.8158i	−2.53070	−	0.898373i
$646$	−2.59062	−	4.48708i	−0.101927	−	0.176542i
$647$	−0.977276			−0.0384207			−0.0192103	−	0.999815i	$-0.506115\pi$
$647$	−0.977276			−0.0384207			−0.0192103	+	0.999815i	$0.506115\pi$
$648$	−8.80908	+	1.84394i	−0.346053	+	0.0724368i
$649$	14.5661			0.571770
$650$	−8.56024	+	33.9782i	−0.335760	+	1.33274i
$651$	10.3097	−	29.0422i	0.404068	−	1.13825i
$652$	−9.57247	−	5.52667i	−0.374887	−	0.216441i
$653$	−6.98319	+	12.0952i	−0.273273	+	0.473323i	−0.969698	−	0.244307i	$-0.921440\pi$
$653$	−6.98319	+	12.0952i	−0.273273	+	0.473323i	0.696425	+	0.717630i	$0.254773\pi$
$654$	11.4956	−	2.12138i	0.449513	−	0.0829525i
$655$	45.7334	−	26.4042i	1.78695	−	1.03170i
$656$		−	8.24323i		−	0.321844i
$657$	15.9161	−	19.5927i	0.620947	−	0.764384i
$658$		−	16.4492i		−	0.641258i
$659$	9.48438	+	16.4274i	0.369459	+	0.639922i	0.989481	−	0.144663i	$-0.0462096\pi$
$659$	9.48438	+	16.4274i	0.369459	+	0.639922i	−0.620022	+	0.784584i	$0.712876\pi$
$660$	−8.58788	−	10.0709i	−0.334283	−	0.392009i
$661$	15.9467	+	9.20684i	0.620255	+	0.358104i	0.776968	−	0.629540i	$-0.216756\pi$
$661$	15.9467	+	9.20684i	0.620255	+	0.358104i	−0.156713	+	0.987644i	$0.550090\pi$
$662$	−11.2383	+	19.4652i	−0.436787	+	0.756538i
$663$	16.2114	+	1.04402i	0.629601	+	0.0405466i
$664$	1.17582	+	2.03658i	0.0456307	+	0.0790347i
$665$		−	25.7474i		−	0.998440i
$666$	2.41062	−	15.0691i	0.0934098	−	0.583915i
$667$	−37.3808			−1.44739
$668$	8.14388	−	4.70187i	0.315096	−	0.181921i
$669$	0.865333	+	4.68917i	0.0334557	+	0.181294i
$670$	−18.8213	−	10.8665i	−0.727130	−	0.419809i
$671$	19.4460	+	11.2272i	0.750705	+	0.433420i
$672$	−1.95237	+	5.49979i	−0.0753143	+	0.212159i
$673$	13.9695	+	24.1959i	0.538486	+	0.932685i	0.998986	+	0.0450254i	$0.0143369\pi$
$673$	13.9695	+	24.1959i	0.538486	+	0.932685i	−0.460500	+	0.887660i	$0.652330\pi$
$674$			30.7950i			1.18618i
$675$	44.3224	+	24.1985i	1.70597	+	0.931401i
$676$	0.389998	+	12.9941i	0.0149999	+	0.499775i
$677$	1.78613	+	3.09367i	0.0686465	+	0.118899i	0.898306	−	0.439371i	$-0.144799\pi$
$677$	1.78613	+	3.09367i	0.0686465	+	0.118899i	−0.829659	+	0.558270i	$0.811465\pi$
$678$	−9.71276	−	3.44793i	−0.373016	−	0.132417i
$679$	17.3586	−	30.0660i	0.666162	−	1.15383i
$680$	4.98985	−	8.64268i	0.191352	−	0.331431i
$681$	1.20121	+	6.50929i	0.0460306	+	0.249436i
$682$	9.10875	−	5.25894i	0.348792	−	0.201375i
$683$			11.0777i			0.423875i	0.977283	+	0.211938i	$0.0679774\pi$
$683$			11.0777i			0.423875i	−0.977283	+	0.211938i	$0.932023\pi$
$684$	−2.13275	−	5.58182i	−0.0815478	−	0.213426i
$685$	−14.6546			−0.559924
$686$	−4.45921	−	7.72358i	−0.170254	−	0.294888i
$687$	−14.4632	+	12.3334i	−0.551807	+	0.470549i
$688$	−5.13184	+	8.88861i	−0.195650	+	0.338875i
$689$	9.02996	+	31.7850i	0.344014	+	1.21091i
$690$	18.4209	+	21.6020i	0.701273	+	0.822374i
$691$	16.9314	−	9.77532i	0.644099	−	0.371871i	−0.142093	−	0.989853i	$-0.545383\pi$
$691$	16.9314	−	9.77532i	0.644099	−	0.371871i	0.786192	+	0.617983i	$0.212050\pi$
$692$	−2.17769			−0.0827835
$693$	−18.8076	+	7.18619i	−0.714443	+	0.272981i
$694$			29.0471i			1.10261i
$695$	45.2179	−	26.1065i	1.71521	−	0.990277i
$696$	2.75013	+	14.9028i	0.104244	+	0.564888i
$697$	18.5702	+	10.7215i	0.703396	+	0.406106i
$698$	−6.23358	+	10.7969i	−0.235944	+	0.408668i
$699$	−1.31009	+	3.69050i	−0.0495522	+	0.139588i
$700$	28.3583	−	16.3727i	1.07184	−	0.618829i
$701$	46.2105			1.74535			0.872673	−	0.488306i	$-0.162385\pi$
$701$	46.2105			1.74535			0.872673	+	0.488306i	$0.162385\pi$
$702$	18.2713	+	4.14225i	0.689607	+	0.156339i
$703$	10.1321			0.382138
$704$	−1.72495	+	0.995899i	−0.0650114	+	0.0375344i
$705$	−10.8523	+	30.5707i	−0.408720	+	1.15136i
$706$	17.2147	−	29.8167i	0.647882	−	1.12217i
$707$	7.46782	+	4.31155i	0.280856	+	0.162152i
$708$	2.29866	+	12.4563i	0.0863889	+	0.468135i
$709$	−28.1320	+	16.2420i	−1.05652	+	0.609983i	−0.924468	−	0.381260i	$-0.875490\pi$
$709$	−28.1320	+	16.2420i	−1.05652	+	0.609983i	−0.132053	+	0.991243i	$0.542157\pi$
$710$		−	7.46209i		−	0.280047i
$711$	2.82065	−	17.6322i	0.105783	−	0.661259i
$712$	6.28290			0.235462
$713$	−19.5382	+	11.2804i	−0.731712	+	0.422454i
$714$	−9.85048	−	11.5515i	−0.368645	−	0.432305i
$715$	7.52930	+	26.5028i	0.281580	+	0.991149i
$716$	3.95576	−	6.85157i	0.147834	−	0.256055i
$717$	8.31135	−	7.08744i	0.310393	−	0.264685i
$718$	−17.1248	−	29.6610i	−0.639091	−	1.10694i
$719$	30.0876			1.12208			0.561038	−	0.827790i	$-0.310402\pi$
$719$	30.0876			1.12208			0.561038	+	0.827790i	$0.310402\pi$
$720$	7.25690	−	8.93322i	0.270449	−	0.332921i
$721$		−	19.0085i		−	0.707913i
$722$	−13.0187	+	7.51637i	−0.484507	+	0.279730i
$723$	−6.23338	−	33.7782i	−0.231822	−	1.25623i
$724$	−0.510976	+	0.885037i	−0.0189903	+	0.0328921i
$725$	42.5147	−	73.6377i	1.57896	−	2.73483i
$726$	11.4792	+	4.07501i	0.426034	+	0.151238i
$727$	−2.30907	−	3.99942i	−0.0856386	−	0.148330i	0.820025	−	0.572328i	$-0.193960\pi$
$727$	−2.30907	−	3.99942i	−0.0856386	−	0.148330i	−0.905663	+	0.423998i	$0.860626\pi$
$728$	8.46059	−	8.71833i	0.313570	−	0.323123i
$729$	12.3693	−	24.0000i	0.458123	−	0.888889i
$730$			32.2808i			1.19477i
$731$	−13.3494	−	23.1218i	−0.493745	−	0.855191i
$732$	−6.53218	+	18.4010i	−0.241436	+	0.680122i
$733$	38.6651	+	22.3233i	1.42813	+	0.824531i	0.996973	−	0.0777462i	$-0.0247724\pi$
$733$	38.6651	+	22.3233i	1.42813	+	0.824531i	0.431156	+	0.902277i	$0.358106\pi$
$734$	−4.36140	−	2.51806i	−0.160982	−	0.0929432i
$735$	−5.24939	−	28.4460i	−0.193627	−	1.04925i
$736$	3.70000	−	2.13620i	0.136384	−	0.0787413i
$737$	−11.2833			−0.415624
$738$	19.1945	+	15.5926i	0.706558	+	0.573973i
$739$		−	3.94466i		−	0.145107i	−0.997365	−	0.0725534i	$-0.976885\pi$
$739$		−	3.94466i		−	0.145107i	0.997365	−	0.0725534i	$-0.0231148\pi$
$740$	9.75779	+	16.9010i	0.358704	+	0.621293i
$741$	−0.799407	+	12.4131i	−0.0293670	+	0.456005i
$742$	15.4395	−	26.7420i	0.566803	−	0.981731i
$743$	−46.8150	−	27.0287i	−1.71748	−	0.991585i	−0.923466	−	0.383680i	$-0.874657\pi$
$743$	−46.8150	−	27.0287i	−1.71748	−	0.991585i	−0.794010	−	0.607905i	$-0.792010\pi$
$744$	5.93464	+	6.95947i	0.217574	+	0.255146i
$745$	−14.9448	−	25.8852i	−0.547535	−	0.948359i
$746$		−	11.2141i		−	0.410578i
$747$	−6.96635	−	1.11442i	−0.254885	−	0.0407745i
$748$		−	5.18124i		−	0.189445i
$749$	53.4148	−	30.8391i	1.95173	−	1.12683i
$750$	−30.8323	+	5.68976i	−1.12584	+	0.207761i
$751$	−1.96630	+	3.40573i	−0.0717513	+	0.124277i	−0.899669	−	0.436573i	$-0.856192\pi$
$751$	−1.96630	+	3.40573i	−0.0717513	+	0.124277i	0.827918	+	0.560850i	$0.189525\pi$
$752$	4.22784	+	2.44094i	0.154173	+	0.0890120i
$753$	−0.255412	+	0.719490i	−0.00930771	+	0.0262197i
$754$	7.70676	−	30.5905i	0.280664	−	1.11404i
$755$	−81.9689			−2.98315
$756$	−9.11329	−	14.9493i	−0.331447	−	0.543702i
$757$	−0.241542			−0.00877899			−0.00438949	−	0.999990i	$-0.501397\pi$
$757$	−0.241542			−0.00877899			−0.00438949	+	0.999990i	$0.501397\pi$
$758$	2.56312	+	4.43945i	0.0930965	+	0.161248i
$759$	13.8901	+	4.93084i	0.504178	+	0.178978i
$760$	6.61767	+	3.82072i	0.240048	+	0.138592i
$761$	13.6634	+	7.88855i	0.495297	+	0.285960i	0.726769	−	0.686882i	$-0.241021\pi$
$761$	13.6634	+	7.88855i	0.495297	+	0.285960i	−0.231472	+	0.972841i	$0.574354\pi$
$762$	1.86433	+	10.1027i	0.0675375	+	0.365981i
$763$	11.3703	+	19.6939i	0.411631	+	0.712966i
$764$	−4.06108			−0.146925
$765$	10.6859	+	27.9671i	0.386351	+	1.01115i
$766$	18.9420			0.684401
$767$	6.44159	−	25.5686i	0.232592	−	0.923230i
$768$	−1.12386	−	1.31793i	−0.0405537	−	0.0475568i
$769$	−7.04227	−	4.06586i	−0.253951	−	0.146619i	0.367621	−	0.929976i	$-0.380172\pi$
$769$	−7.04227	−	4.06586i	−0.253951	−	0.146619i	−0.621572	+	0.783357i	$0.713506\pi$
$770$	12.8737	−	22.2979i	0.463935	−	0.803559i
$771$	−15.2571	−

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.579434 + 1.63225i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.32246 - 1.91822i) q^{5} +(-0.314323 - 1.70329i) q^{6} +(2.91802 - 1.68472i) q^{7} +1.00000i q^{8} +(-2.32851 - 1.89157i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.579434 + 1.63225i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.32246 - 1.91822i) q^{5} +(-0.314323 - 1.70329i) q^{6} +(2.91802 - 1.68472i) q^{7} +1.00000i q^{8} +(-2.32851 - 1.89157i) q^{9} +3.83645 q^{10} +(1.72495 - 0.995899i) q^{11} +(1.12386 + 1.31793i) q^{12} +(-0.985326 - 3.46830i) q^{13} +(-1.68472 + 2.91802i) q^{14} +(5.05618 - 4.31162i) q^{15} +(-0.500000 - 0.866025i) q^{16} +2.60129 q^{17} +(2.96233 + 0.473890i) q^{18} +1.99180i q^{19} +(-3.32246 + 1.91822i) q^{20} +(1.05909 + 5.73914i) q^{21} +(-0.995899 + 1.72495i) q^{22} +(2.13620 - 3.70000i) q^{23} +(-1.63225 - 0.579434i) q^{24} +(4.85917 + 8.41632i) q^{25} +(2.58747 + 2.51098i) q^{26} +(4.43674 - 2.70469i) q^{27} -3.36944i q^{28} +(-4.37469 - 7.57719i) q^{29} +(-2.22297 + 6.26206i) q^{30} +(-4.57313 - 2.64030i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.626068 + 3.39261i) q^{33} +(-2.25278 + 1.30064i) q^{34} -12.9267 q^{35} +(-2.80240 + 1.07077i) q^{36} -5.08689i q^{37} +(-0.995899 - 1.72495i) q^{38} +(6.23209 + 0.401349i) q^{39} +(1.91822 - 3.32246i) q^{40} +(7.13885 + 4.12162i) q^{41} +(-3.78677 - 4.44070i) q^{42} +(-5.13184 - 8.88861i) q^{43} -1.99180i q^{44} +(4.10794 + 10.7513i) q^{45} +4.27239i q^{46} +(-4.22784 + 2.44094i) q^{47} +(1.70329 - 0.314323i) q^{48} +(2.17657 - 3.76993i) q^{49} +(-8.41632 - 4.85917i) q^{50} +(-1.50727 + 4.24596i) q^{51} +(-3.49630 - 0.880834i) q^{52} -9.16444 q^{53} +(-2.48999 + 4.56070i) q^{54} -7.64143 q^{55} +(1.68472 + 2.91802i) q^{56} +(-3.25112 - 1.15412i) q^{57} +(7.57719 + 4.37469i) q^{58} +(6.33329 + 3.65653i) q^{59} +(-1.20588 - 6.53459i) q^{60} +(5.63669 + 9.76304i) q^{61} +5.28060 q^{62} +(-9.98142 - 1.59674i) q^{63} -1.00000 q^{64} +(-3.37927 + 13.4134i) q^{65} +(-2.23850 - 2.62505i) q^{66} +(-4.90591 - 2.83243i) q^{67} +(1.30064 - 2.25278i) q^{68} +(4.80156 + 5.63073i) q^{69} +(11.1948 - 6.46335i) q^{70} -1.94505i q^{71} +(1.89157 - 2.32851i) q^{72} +8.41425i q^{73} +(2.54345 + 4.40538i) q^{74} +(-16.5531 + 3.05469i) q^{75} +(1.72495 + 0.995899i) q^{76} +(3.35563 - 5.81211i) q^{77} +(-5.59782 + 2.76847i) q^{78} +(2.97607 + 5.15470i) q^{79} +3.83645i q^{80} +(1.84394 + 8.80908i) q^{81} -8.24323 q^{82} +(2.03658 - 1.17582i) q^{83} +(5.49979 + 1.95237i) q^{84} +(-8.64268 - 4.98985i) q^{85} +(8.88861 + 5.13184i) q^{86} +(14.9028 - 2.75013i) q^{87} +(0.995899 + 1.72495i) q^{88} -6.28290i q^{89} +(-8.93322 - 7.25690i) q^{90} +(-8.71833 - 8.46059i) q^{91} +(-2.13620 - 3.70000i) q^{92} +(6.95947 - 5.93464i) q^{93} +(2.44094 - 4.22784i) q^{94} +(3.82072 - 6.61767i) q^{95} +(-1.31793 + 1.12386i) q^{96} +(8.92313 - 5.15177i) q^{97} +4.35315i q^{98} +(-5.90037 - 0.943893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} - 16 q^{9}+O(q^{10}) \) 28 * q + 14 * q^4 - 16 * q^9	\( 28 q + 14 q^{4} - 16 q^{9} + 2 q^{13} + 8 q^{14} - 14 q^{16} + 16 q^{17} - 8 q^{23} + 14 q^{25} + 8 q^{26} + 18 q^{27} - 16 q^{29} - 8 q^{30} - 68 q^{35} - 8 q^{36} - 8 q^{39} - 10 q^{42} - 4 q^{43} + 10 q^{49} + 58 q^{51} - 2 q^{52} - 120 q^{53} - 8 q^{56} + 28 q^{61} + 68 q^{62} - 28 q^{64} - 8 q^{65} - 24 q^{66} + 8 q^{68} - 92 q^{69} + 16 q^{74} + 32 q^{75} - 24 q^{77} - 22 q^{78} + 28 q^{79} + 8 q^{81} - 48 q^{82} + 68 q^{87} - 50 q^{90} + 8 q^{92}+O(q^{100}) \) 28 * q + 14 * q^4 - 16 * q^9 + 2 * q^13 + 8 * q^14 - 14 * q^16 + 16 * q^17 - 8 * q^23 + 14 * q^25 + 8 * q^26 + 18 * q^27 - 16 * q^29 - 8 * q^30 - 68 * q^35 - 8 * q^36 - 8 * q^39 - 10 * q^42 - 4 * q^43 + 10 * q^49 + 58 * q^51 - 2 * q^52 - 120 * q^53 - 8 * q^56 + 28 * q^61 + 68 * q^62 - 28 * q^64 - 8 * q^65 - 24 * q^66 + 8 * q^68 - 92 * q^69 + 16 * q^74 + 32 * q^75 - 24 * q^77 - 22 * q^78 + 28 * q^79 + 8 * q^81 - 48 * q^82 + 68 * q^87 - 50 * q^90 + 8 * q^92

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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