LMFDB - Embedded newform 670.2.h.c.439.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(29,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("670.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.h (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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.6
Character	$\chi$	$=$	670.439
Dual form			670.2.h.c.29.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} -0.433437i q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.23506 + 0.0672889i) q^{5} +(0.216718 + 0.375367i) q^{6} +(0.301725 + 0.174201i) q^{7} +1.00000i q^{8} +2.81213 q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} -0.433437i q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.23506 + 0.0672889i) q^{5} +(0.216718 + 0.375367i) q^{6} +(0.301725 + 0.174201i) q^{7} +1.00000i q^{8} +2.81213 q^{9} +(1.90197 - 1.17580i) q^{10} +(1.33505 - 2.31238i) q^{11} +(-0.375367 - 0.216718i) q^{12} +(-0.235286 + 0.135843i) q^{13} -0.348402 q^{14} +(0.0291655 + 0.968755i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-5.99500 + 3.46121i) q^{17} +(-2.43538 + 1.40607i) q^{18} +(-2.08047 - 3.60348i) q^{19} +(-1.05925 + 1.96926i) q^{20} +(0.0755050 - 0.130778i) q^{21} +2.67010i q^{22} +(2.24402 - 1.29558i) q^{23} +0.433437 q^{24} +(4.99094 - 0.300789i) q^{25} +(0.135843 - 0.235286i) q^{26} -2.51919i q^{27} +(0.301725 - 0.174201i) q^{28} +(2.29831 - 3.98079i) q^{29} +(-0.509635 - 0.824383i) q^{30} +(4.10735 - 7.11415i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.00227 - 0.578661i) q^{33} +(3.46121 - 5.99500i) q^{34} +(-0.686093 - 0.369046i) q^{35} +(1.40607 - 2.43538i) q^{36} +(7.02444 - 4.05556i) q^{37} +(3.60348 + 2.08047i) q^{38} +(0.0588791 + 0.101982i) q^{39} +(-0.0672889 - 2.23506i) q^{40} +(-0.0191495 + 0.0331679i) q^{41} +0.151010i q^{42} +0.925304i q^{43} +(-1.33505 - 2.31238i) q^{44} +(-6.28527 + 0.189225i) q^{45} +(-1.29558 + 2.24402i) q^{46} +(-4.31988 - 2.49409i) q^{47} +(-0.375367 + 0.216718i) q^{48} +(-3.43931 - 5.95706i) q^{49} +(-4.17189 + 2.75596i) q^{50} +(1.50022 + 2.59845i) q^{51} +0.271685i q^{52} -12.8226i q^{53} +(1.25960 + 2.18168i) q^{54} +(-2.82832 + 5.25813i) q^{55} +(-0.174201 + 0.301725i) q^{56} +(-1.56188 + 0.901753i) q^{57} +4.59662i q^{58} +5.66170 q^{59} +(0.853549 + 0.459119i) q^{60} +(1.05220 + 1.82246i) q^{61} +8.21471i q^{62} +(0.848490 + 0.489876i) q^{63} -1.00000 q^{64} +(0.516737 - 0.319448i) q^{65} +1.15732 q^{66} +(-3.00282 - 7.61466i) q^{67} +6.92243i q^{68} +(-0.561553 - 0.972639i) q^{69} +(0.778697 - 0.0234436i) q^{70} +(-7.42454 + 12.8597i) q^{71} +2.81213i q^{72} +(3.59181 - 2.07373i) q^{73} +(-4.05556 + 7.02444i) q^{74} +(-0.130373 - 2.16326i) q^{75} -4.16095 q^{76} +(0.805636 - 0.465134i) q^{77} +(-0.101982 - 0.0588791i) q^{78} +(6.00648 - 10.4035i) q^{79} +(1.17580 + 1.90197i) q^{80} +7.34449 q^{81} -0.0382990i q^{82} +(12.1624 - 7.02197i) q^{83} +(-0.0755050 - 0.130778i) q^{84} +(13.1662 - 8.13940i) q^{85} +(-0.462652 - 0.801337i) q^{86} +(-1.72542 - 0.996172i) q^{87} +(2.31238 + 1.33505i) q^{88} -10.3572 q^{89} +(5.34859 - 3.30651i) q^{90} -0.0946556 q^{91} -2.59117i q^{92} +(-3.08353 - 1.78028i) q^{93} +4.98817 q^{94} +(4.89245 + 7.91399i) q^{95} +(0.216718 - 0.375367i) q^{96} +(-14.6097 + 8.43491i) q^{97} +(5.95706 + 3.43931i) q^{98} +(3.75434 - 6.50272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9}+O(q^{10}) $ 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9	$ 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9} - 10 q^{10} + 24 q^{11} + 24 q^{14} + 28 q^{15} - 26 q^{16} - 24 q^{19} - 8 q^{20} + 4 q^{21} - 12 q^{24} - 28 q^{25} + 4 q^{26} - 20 q^{29} - 10 q^{30} - 30 q^{31} - 16 q^{34} - 14 q^{35} - 24 q^{36} - 8 q^{39} - 20 q^{40} - 10 q^{41} - 24 q^{44} - 16 q^{45} - 8 q^{46} + 14 q^{49} - 8 q^{50} - 44 q^{51} + 42 q^{54} + 16 q^{55} + 12 q^{56} + 80 q^{59} + 14 q^{60} - 20 q^{61} - 52 q^{64} + 10 q^{65} - 40 q^{66} - 4 q^{69} + 48 q^{70} - 74 q^{71} + 34 q^{74} - 16 q^{75} - 48 q^{76} + 32 q^{79} + 8 q^{80} + 4 q^{81} - 4 q^{84} + 20 q^{85} + 12 q^{86} + 84 q^{89} - 30 q^{90} - 16 q^{91} + 136 q^{94} + 2 q^{95} - 6 q^{96} - 96 q^{99}+O(q^{100}) $ 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9 - 10 * q^10 + 24 * q^11 + 24 * q^14 + 28 * q^15 - 26 * q^16 - 24 * q^19 - 8 * q^20 + 4 * q^21 - 12 * q^24 - 28 * q^25 + 4 * q^26 - 20 * q^29 - 10 * q^30 - 30 * q^31 - 16 * q^34 - 14 * q^35 - 24 * q^36 - 8 * q^39 - 20 * q^40 - 10 * q^41 - 24 * q^44 - 16 * q^45 - 8 * q^46 + 14 * q^49 - 8 * q^50 - 44 * q^51 + 42 * q^54 + 16 * q^55 + 12 * q^56 + 80 * q^59 + 14 * q^60 - 20 * q^61 - 52 * q^64 + 10 * q^65 - 40 * q^66 - 4 * q^69 + 48 * q^70 - 74 * q^71 + 34 * q^74 - 16 * q^75 - 48 * q^76 + 32 * q^79 + 8 * q^80 + 4 * q^81 - 4 * q^84 + 20 * q^85 + 12 * q^86 + 84 * q^89 - 30 * q^90 - 16 * q^91 + 136 * q^94 + 2 * q^95 - 6 * q^96 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		−	0.433437i		−	0.250245i	−0.992141	−	0.125122i	$-0.960068\pi$
$3$		−	0.433437i		−	0.250245i	0.992141	−	0.125122i	$-0.0399323\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.23506	+	0.0672889i	−0.999547	+	0.0300925i
$5$	−2.23506	+	0.0672889i	−0.999547	+	0.0300925i
$6$	0.216718	+	0.375367i	0.0884749	+	0.153243i
$7$	0.301725	+	0.174201i	0.114041	+	0.0658417i	0.555936	−	0.831225i	$-0.312360\pi$
$7$	0.301725	+	0.174201i	0.114041	+	0.0658417i	−0.441894	+	0.897067i	$0.645693\pi$
$8$			1.00000i			0.353553i
$9$	2.81213			0.937378
$10$	1.90197	−	1.17580i	0.601456	−	0.371821i
$11$	1.33505	−	2.31238i	0.402533	−	0.697208i	−0.591498	−	0.806307i	$-0.701463\pi$
$11$	1.33505	−	2.31238i	0.402533	−	0.697208i	0.994031	+	0.109098i	$0.0347964\pi$
$12$	−0.375367	−	0.216718i	−0.108359	−	0.0625612i
$13$	−0.235286	+	0.135843i	−0.0652567	+	0.0376760i	−0.532273	−	0.846573i	$-0.678662\pi$
$13$	−0.235286	+	0.135843i	−0.0652567	+	0.0376760i	0.467017	+	0.884249i	$0.345329\pi$
$14$	−0.348402			−0.0931142
$15$	0.0291655	+	0.968755i	0.00753049	+	0.250131i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.99500	+	3.46121i	−1.45400	+	0.839468i	−0.998705	−	0.0508729i	$-0.983800\pi$
$17$	−5.99500	+	3.46121i	−1.45400	+	0.839468i	−0.455295	+	0.890340i	$0.650466\pi$
$18$	−2.43538	+	1.40607i	−0.574024	+	0.331413i
$19$	−2.08047	−	3.60348i	−0.477293	−	0.826696i	0.522368	−	0.852720i	$-0.325049\pi$
$19$	−2.08047	−	3.60348i	−0.477293	−	0.826696i	−0.999661	+	0.0260240i	$0.991715\pi$
$20$	−1.05925	+	1.96926i	−0.236856	+	0.440340i
$21$	0.0755050	−	0.130778i	0.0164765	−	0.0285382i
$22$			2.67010i			0.569268i
$23$	2.24402	−	1.29558i	0.467910	−	0.270148i	−0.247455	−	0.968900i	$-0.579594\pi$
$23$	2.24402	−	1.29558i	0.467910	−	0.270148i	0.715364	+	0.698752i	$0.246261\pi$
$24$	0.433437			0.0884749
$25$	4.99094	−	0.300789i	0.998189	−	0.0601577i
$26$	0.135843	−	0.235286i	0.0266409	−	0.0461434i
$27$		−	2.51919i		−	0.484819i
$28$	0.301725	−	0.174201i	0.0570206	−	0.0329209i
$29$	2.29831	−	3.98079i	0.426786	−	0.739214i	−0.569800	−	0.821784i	$-0.692979\pi$
$29$	2.29831	−	3.98079i	0.426786	−	0.739214i	0.996585	+	0.0825692i	$0.0263126\pi$
$30$	−0.509635	−	0.824383i	−0.0930463	−	0.150511i
$31$	4.10735	−	7.11415i	0.737703	−	1.27774i	−0.215825	−	0.976432i	$-0.569244\pi$
$31$	4.10735	−	7.11415i	0.737703	−	1.27774i	0.953527	−	0.301306i	$-0.0974226\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−1.00227	−	0.578661i	−0.174473	−	0.100732i
$34$	3.46121	−	5.99500i	0.593593	−	1.02813i
$35$	−0.686093	−	0.369046i	−0.115971	−	0.0623801i
$36$	1.40607	−	2.43538i	0.234344	−	0.405896i
$37$	7.02444	−	4.05556i	1.15481	−	0.666730i	0.204756	−	0.978813i	$-0.434360\pi$
$37$	7.02444	−	4.05556i	1.15481	−	0.666730i	0.950055	+	0.312083i	$0.101027\pi$
$38$	3.60348	+	2.08047i	0.584562	+	0.337497i
$39$	0.0588791	+	0.101982i	0.00942821	+	0.0163301i
$40$	−0.0672889	−	2.23506i	−0.0106393	−	0.353393i
$41$	−0.0191495	+	0.0331679i	−0.00299065	+	0.00517995i	−0.867517	−	0.497408i	$-0.834285\pi$
$41$	−0.0191495	+	0.0331679i	−0.00299065	+	0.00517995i	0.864526	+	0.502588i	$0.167619\pi$
$42$			0.151010i			0.0233013i
$43$			0.925304i			0.141108i	0.997508	+	0.0705538i	$0.0224766\pi$
$43$			0.925304i			0.141108i	−0.997508	+	0.0705538i	$0.977523\pi$
$44$	−1.33505	−	2.31238i	−0.201267	−	0.348604i
$45$	−6.28527	+	0.189225i	−0.936953	+	0.0282080i
$46$	−1.29558	+	2.24402i	−0.191023	+	0.330862i
$47$	−4.31988	−	2.49409i	−0.630120	−	0.363800i	0.150679	−	0.988583i	$-0.451854\pi$
$47$	−4.31988	−	2.49409i	−0.630120	−	0.363800i	−0.780799	+	0.624783i	$0.785187\pi$
$48$	−0.375367	+	0.216718i	−0.0541796	+	0.0312806i
$49$	−3.43931	−	5.95706i	−0.491330	−	0.851008i
$50$	−4.17189	+	2.75596i	−0.589994	+	0.389752i
$51$	1.50022	+	2.59845i	0.210072	+	0.363856i
$52$			0.271685i			0.0376760i
$53$		−	12.8226i		−	1.76132i	−0.473746	−	0.880662i	$-0.657099\pi$
$53$		−	12.8226i		−	1.76132i	0.473746	−	0.880662i	$-0.342901\pi$
$54$	1.25960	+	2.18168i	0.171409	+	0.296889i
$55$	−2.82832	+	5.25813i	−0.381370	+	0.709006i
$56$	−0.174201	+	0.301725i	−0.0232786	+	0.0403197i
$57$	−1.56188	+	0.901753i	−0.206876	+	0.119440i
$58$			4.59662i			0.603566i
$59$	5.66170			0.737091			0.368545	−	0.929610i	$-0.379856\pi$
$59$	5.66170			0.737091			0.368545	+	0.929610i	$0.379856\pi$
$60$	0.853549	+	0.459119i	0.110193	+	0.0592721i
$61$	1.05220	+	1.82246i	0.134720	+	0.233342i	0.925490	−	0.378771i	$-0.123653\pi$
$61$	1.05220	+	1.82246i	0.134720	+	0.233342i	−0.790771	+	0.612113i	$0.790320\pi$
$62$			8.21471i			1.04327i
$63$	0.848490	+	0.489876i	0.106900	+	0.0617185i
$64$	−1.00000			−0.125000
$65$	0.516737	−	0.319448i	0.0640934	−	0.0396226i
$66$	1.15732			0.142456
$67$	−3.00282	−	7.61466i	−0.366852	−	0.930279i
$67$	−3.00282	−	7.61466i	−0.366852	−	0.930279i
$68$			6.92243i			0.839468i
$69$	−0.561553	−	0.972639i	−0.0676031	−	0.117092i
$70$	0.778697	−	0.0234436i	0.0930721	−	0.00280204i
$71$	−7.42454	+	12.8597i	−0.881131	+	1.52616i	−0.0310456	+	0.999518i	$0.509884\pi$
$71$	−7.42454	+	12.8597i	−0.881131	+	1.52616i	−0.850085	+	0.526645i	$0.823450\pi$
$72$			2.81213i			0.331413i
$73$	3.59181	−	2.07373i	0.420389	−	0.242712i	−0.274855	−	0.961486i	$-0.588630\pi$
$73$	3.59181	−	2.07373i	0.420389	−	0.242712i	0.695244	+	0.718774i	$0.255296\pi$
$74$	−4.05556	+	7.02444i	−0.471449	+	0.816574i
$75$	−0.130373	−	2.16326i	−0.0150542	−	0.249792i
$76$	−4.16095			−0.477293
$77$	0.805636	−	0.465134i	0.0918108	−	0.0530070i
$78$	−0.101982	−	0.0588791i	−0.0115472	−	0.00666675i
$79$	6.00648	−	10.4035i	0.675782	−	1.17049i	−0.300458	−	0.953795i	$-0.597140\pi$
$79$	6.00648	−	10.4035i	0.675782	−	1.17049i	0.976240	−	0.216693i	$-0.0695271\pi$
$80$	1.17580	+	1.90197i	0.131459	+	0.212647i
$81$	7.34449			0.816054
$82$		−	0.0382990i		−	0.00422942i
$83$	12.1624	−	7.02197i	1.33500	−	0.770761i	0.348936	−	0.937146i	$-0.386543\pi$
$83$	12.1624	−	7.02197i	1.33500	−	0.770761i	0.986061	+	0.166386i	$0.0532096\pi$
$84$	−0.0755050	−	0.130778i	−0.00823827	−	0.0142691i
$85$	13.1662	−	8.13940i	1.42808	−	0.882842i
$86$	−0.462652	−	0.801337i	−0.0498891	−	0.0864104i
$87$	−1.72542	−	0.996172i	−0.184984	−	0.106801i
$88$	2.31238	+	1.33505i	0.246500	+	0.142317i
$89$	−10.3572			−1.09786			−0.548930	−	0.835868i	$-0.684965\pi$
$89$	−10.3572			−1.09786			−0.548930	+	0.835868i	$0.684965\pi$
$90$	5.34859	−	3.30651i	0.563791	−	0.348537i
$91$	−0.0946556			−0.00992260
$92$		−	2.59117i		−	0.270148i
$93$	−3.08353	−	1.78028i	−0.319747	−	0.184606i
$94$	4.98817			0.514491
$95$	4.89245	+	7.91399i	0.501954	+	0.811959i
$96$	0.216718	−	0.375367i	0.0221187	−	0.0383107i
$97$	−14.6097	+	8.43491i	−1.48339	+	0.856435i	−0.999822	−	0.0188719i	$-0.993993\pi$
$97$	−14.6097	+	8.43491i	−1.48339	+	0.856435i	−0.483567	+	0.875307i	$0.660659\pi$
$98$	5.95706	+	3.43931i	0.601754	+	0.347423i
$99$	3.75434	−	6.50272i	0.377326	−	0.653547i
$100$	2.23498	−	4.47268i	0.223498	−	0.447268i
$101$	−8.49634	+	14.7161i	−0.845418	+	1.46431i	0.0398401	+	0.999206i	$0.487315\pi$
$101$	−8.49634	+	14.7161i	−0.845418	+	1.46431i	−0.885258	+	0.465101i	$0.846018\pi$
$102$	−2.59845	−	1.50022i	−0.257285	−	0.148544i
$103$	10.9341	+	6.31283i	1.07737	+	0.622022i	0.930187	−	0.367087i	$-0.119645\pi$
$103$	10.9341	+	6.31283i	1.07737	+	0.622022i	0.147187	+	0.989109i	$0.452978\pi$
$104$	−0.135843	−	0.235286i	−0.0133205	−	0.0230717i
$105$	−0.159958	+	0.297378i	−0.0156103	+	0.0290211i
$106$	6.41131	+	11.1047i	0.622722	+	1.07859i
$107$			10.6840i			1.03286i	0.856328	+	0.516432i	$0.172740\pi$
$107$			10.6840i			1.03286i	−0.856328	+	0.516432i	$0.827260\pi$
$108$	−2.18168	−	1.25960i	−0.209933	−	0.121205i
$109$	11.9703			1.14654			0.573271	−	0.819365i	$-0.305674\pi$
$109$	11.9703			1.14654			0.573271	+	0.819365i	$0.305674\pi$
$110$	−0.179668	−	5.96783i	−0.0171307	−	0.569010i
$111$	−1.75783	−	3.04465i	−0.166846	−	0.288985i
$112$		−	0.348402i		−	0.0329209i
$113$	−13.3130	−	7.68626i	−1.25238	−	0.723063i	−0.280799	−	0.959767i	$-0.590600\pi$
$113$	−13.3130	−	7.68626i	−1.25238	−	0.723063i	−0.971582	+	0.236704i	$0.923933\pi$
$114$	0.901753	−	1.56188i	0.0844569	−	0.146284i
$115$	−4.92832	+	3.04670i	−0.459568	+	0.284106i
$116$	−2.29831	−	3.98079i	−0.213393	−	0.369607i
$117$	−0.661656	+	0.382007i	−0.0611701	+	0.0353166i
$118$	−4.90318	+	2.83085i	−0.451374	+	0.260601i
$119$	−2.41178			−0.221088
$120$	−0.968755	+	0.0291655i	−0.0884348	+	0.00266243i
$121$	1.93527	+	3.35199i	0.175934	+	0.304726i
$122$	−1.82246	−	1.05220i	−0.164998	−	0.0952614i
$123$	0.0143762	+	0.00830009i	0.00129626	+	0.000748394i
$124$	−4.10735	−	7.11415i	−0.368851	−	0.638869i
$125$	−11.1348	+	1.00811i	−0.995927	+	0.0901685i
$126$	−0.979752			−0.0872832
$127$	11.5237	+	6.65321i	1.02256	+	0.590377i	0.914845	−	0.403805i	$-0.132313\pi$
$127$	11.5237	+	6.65321i	1.02256	+	0.590377i	0.107717	+	0.994182i	$0.465646\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	0.401061			0.0353114
$130$	−0.287784	+	0.535019i	−0.0252403	+	0.0469242i
$131$	−16.5542			−1.44635			−0.723173	−	0.690667i	$-0.757317\pi$
$131$	−16.5542			−1.44635			−0.723173	+	0.690667i	$0.757317\pi$
$132$	−1.00227	+	0.578661i	−0.0872364	+	0.0503659i
$133$		−	1.44968i		−	0.125703i
$134$	6.40785	+	5.09308i	0.553554	+	0.439975i
$135$	0.169514	+	5.63053i	0.0145894	+	0.484599i
$136$	−3.46121	−	5.99500i	−0.296797	−	0.514067i
$137$		−	1.87283i		−	0.160007i	−0.996795	−	0.0800035i	$-0.974507\pi$
$137$		−	1.87283i		−	0.160007i	0.996795	−	0.0800035i	$-0.0254932\pi$
$138$	0.972639	+	0.561553i	0.0827965	+	0.0478026i
$139$	−1.38715			−0.117656			−0.0588281	−	0.998268i	$-0.518736\pi$
$139$	−1.38715			−0.117656			−0.0588281	+	0.998268i	$0.518736\pi$
$140$	−0.662649	+	0.409651i	−0.0560041	+	0.0346218i
$141$	−1.08103	+	1.87240i	−0.0910390	+	0.157684i
$142$		−	14.8491i		−	1.24611i
$143$			0.725428i			0.0606633i
$144$	−1.40607	−	2.43538i	−0.117172	−	0.202948i
$145$	−4.86899	+	9.05194i	−0.404348	+	0.751723i
$146$	−2.07373	+	3.59181i	−0.171623	+	0.297260i
$147$	−2.58201	+	1.49072i	−0.212960	+	0.122953i
$148$		−	8.11112i		−	0.666730i
$149$	13.4279			1.10005			0.550027	−	0.835147i	$-0.314617\pi$
$149$	13.4279			1.10005			0.550027	+	0.835147i	$0.314617\pi$
$150$	1.19454	+	1.80825i	0.0975334	+	0.147643i
$151$	−0.616008	−	1.06696i	−0.0501300	−	0.0868277i	0.839872	−	0.542785i	$-0.182630\pi$
$151$	−0.616008	−	1.06696i	−0.0501300	−	0.0868277i	−0.890002	+	0.455957i	$0.849297\pi$
$152$	3.60348	−	2.08047i	0.292281	−	0.168749i
$153$	−16.8587	+	9.73339i	−1.36295	+	0.786898i
$154$	−0.465134	+	0.805636i	−0.0374816	+	0.0649200i
$155$	−8.70146	+	16.1769i	−0.698918	+	1.29936i
$156$	0.117758			0.00942821
$157$	−1.53767	+	0.887772i	−0.122719	+	0.0708519i	−0.560103	−	0.828423i	$-0.689238\pi$
$157$	−1.53767	+	0.887772i	−0.122719	+	0.0708519i	0.437384	+	0.899275i	$0.355905\pi$
$158$			12.0130i			0.955699i
$159$	−5.55779			−0.440762
$160$	−1.96926	−	1.05925i	−0.155684	−	0.0837414i
$161$	0.902767			0.0711480
$162$	−6.36051	+	3.67224i	−0.499729	+	0.288519i
$163$	−12.6118	−	7.28143i	−0.987833	−	0.570326i	−0.0832075	−	0.996532i	$-0.526516\pi$
$163$	−12.6118	−	7.28143i	−0.987833	−	0.570326i	−0.904626	+	0.426206i	$0.859850\pi$
$164$	0.0191495	+	0.0331679i	0.00149532	+	0.00258998i
$165$	2.27906	+	1.22590i	0.177425	+	0.0954359i
$166$	−7.02197	+	12.1624i	−0.545010	+	0.943985i
$167$	10.3311	+	5.96464i	0.799441	+	0.461558i	0.843276	−	0.537481i	$-0.180624\pi$
$167$	10.3311	+	5.96464i	0.799441	+	0.461558i	−0.0438344	+	0.999039i	$0.513957\pi$
$168$	0.130778	+	0.0755050i	0.0100898	+	0.00582534i
$169$	−6.46309	+	11.1944i	−0.497161	+	0.861108i
$170$	−7.33261	+	13.6321i	−0.562385	+	1.04553i
$171$	−5.85057	−	10.1335i	−0.447404	−	0.774926i
$172$	0.801337	+	0.462652i	0.0611014	+	0.0352769i
$173$	9.34337	−	5.39440i	0.710363	−	0.410128i	−0.100832	−	0.994903i	$-0.532151\pi$
$173$	9.34337	−	5.39440i	0.710363	−	0.410128i	0.811196	+	0.584775i	$0.198817\pi$
$174$	1.99234			0.151039
$175$	1.55829	+	0.778671i	0.117796	+	0.0588620i
$176$	−2.67010			−0.201267
$177$		−	2.45399i		−	0.184453i
$178$	8.96960	−	5.17860i	0.672300	−	0.388152i
$179$	9.84443			0.735807			0.367904	−	0.929864i	$-0.380076\pi$
$179$	9.84443			0.735807			0.367904	+	0.929864i	$0.380076\pi$
$180$	−2.97876	+	5.53782i	−0.222024	+	0.412765i
$181$	0.729997	−	1.26439i	0.0542602	−	0.0939815i	−0.837619	−	0.546254i	$-0.816053\pi$
$181$	0.729997	−	1.26439i	0.0542602	−	0.0939815i	0.891880	+	0.452273i	$0.149387\pi$
$182$	0.0819741	−	0.0473278i	0.00607633	−	0.00350817i
$183$	0.789920	−	0.456060i	0.0583925	−	0.0337129i
$184$	1.29558	+	2.24402i	0.0955117	+	0.165431i
$185$	−15.4271	+	9.53707i	−1.13422	+	0.701179i
$186$	3.56055			0.261073
$187$			18.4836i			1.35165i
$188$	−4.31988	+	2.49409i	−0.315060	+	0.181900i
$189$	0.438845	−	0.760102i	0.0319213	−	0.0552893i
$190$	−8.19398	−	4.40750i	−0.594454	−	0.319753i
$191$	5.61441	+	9.72445i	0.406245	+	0.703636i	0.994465	−	0.105064i	$-0.0335047\pi$
$191$	5.61441	+	9.72445i	0.406245	+	0.703636i	−0.588221	+	0.808700i	$0.700171\pi$
$192$			0.433437i			0.0312806i
$193$			6.90019i			0.496686i	0.968672	+	0.248343i	$0.0798861\pi$
$193$			6.90019i			0.496686i	−0.968672	+	0.248343i	$0.920114\pi$
$194$	8.43491	−	14.6097i	0.605591	−	1.04891i
$195$	−0.138460	−	0.223973i	−0.00991535	−	0.0160390i
$196$	−6.87862			−0.491330
$197$	−11.0475	−	6.37825i	−0.787099	−	0.454432i	0.0518415	−	0.998655i	$-0.483491\pi$
$197$	−11.0475	−	6.37825i	−0.787099	−	0.454432i	−0.838940	+	0.544224i	$0.816824\pi$
$198$			7.50869i			0.533619i
$199$	4.17267	+	7.22727i	0.295792	+	0.512328i	0.975169	−	0.221462i	$-0.0710830\pi$
$199$	4.17267	+	7.22727i	0.295792	+	0.512328i	−0.679376	+	0.733790i	$0.737750\pi$
$200$	0.300789	+	4.99094i	0.0212690	+	0.352913i
$201$	−3.30047	+	1.30153i	−0.232797	+	0.0918028i
$202$		−	16.9927i		−	1.19560i
$203$	1.38691	−	0.800735i	0.0973423	−	0.0562006i
$204$	3.00043			0.210072
$205$	0.0405683	−	0.0754206i	0.00283342	−	0.00526760i
$206$	−12.6257			−0.879672
$207$	6.31047	−	3.64335i	0.438608	−	0.253231i
$208$	0.235286	+	0.135843i	0.0163142	+	0.00941899i
$209$	−11.1102			−0.768506
$210$	−0.0101613	−	0.337516i	−0.000701196	−	0.0232908i
$211$	3.22097	+	5.57889i	0.221741	+	0.384067i	0.955337	−	0.295520i	$-0.0954927\pi$
$211$	3.22097	+	5.57889i	0.221741	+	0.384067i	−0.733596	+	0.679586i	$0.762159\pi$
$212$	−11.1047	−	6.41131i	−0.762675	−	0.440331i
$213$	5.57386	+	3.21807i	0.381914	+	0.220498i
$214$	−5.34202	−	9.25265i	−0.365173	−	0.632498i
$215$	−0.0622627	−	2.06811i	−0.00424628	−	0.141044i
$216$	2.51919			0.171409
$217$	2.47858	−	1.43101i	0.168257	−	0.0971432i
$218$	−10.3665	+	5.98513i	−0.702111	+	0.405364i
$219$	−0.898830	−	1.55682i	−0.0607373	−	0.105200i
$220$	3.13951	+	5.07846i	0.211666	+	0.342390i
$221$	0.940360	−	1.62875i	0.0632555	−	0.109562i
$222$	3.04465	+	1.75783i	0.204343	+	0.117978i
$223$		−	13.6697i		−	0.915389i	−0.889109	−	0.457695i	$-0.848675\pi$
$223$		−	13.6697i		−	0.915389i	0.889109	−	0.457695i	$-0.151325\pi$
$224$	0.174201	+	0.301725i	0.0116393	+	0.0201598i
$225$	14.0352	−	0.845858i	0.935680	−	0.0563905i
$226$	15.3725			1.02256
$227$	22.6726	+	13.0900i	1.50483	+	0.868816i	0.999984	+	0.00560747i	$0.00178492\pi$
$227$	22.6726	+	13.0900i	1.50483	+	0.868816i	0.504848	+	0.863208i	$0.331548\pi$
$228$			1.80351i			0.119440i
$229$	−7.20825	−	12.4851i	−0.476335	−	0.825036i	0.523298	−	0.852150i	$-0.324702\pi$
$229$	−7.20825	−	12.4851i	−0.476335	−	0.825036i	−0.999632	+	0.0271141i	$0.991368\pi$
$230$	2.74470	−	5.10268i	0.180980	−	0.336461i
$231$	−0.201606	−	0.349192i	−0.0132647	−	0.0229752i
$232$	3.98079	+	2.29831i	0.261352	+	0.150892i
$233$	−24.3954	−	14.0847i	−1.59820	−	0.922718i	−0.991835	−	0.127528i	$-0.959296\pi$
$233$	−24.3954	−	14.0847i	−1.59820	−	0.922718i	−0.606360	−	0.795190i	$-0.707371\pi$
$234$	0.382007	−	0.661656i	0.0249726	−	0.0432538i
$235$	9.82300	+	5.28374i	0.640782	+	0.344673i
$236$	2.83085	−	4.90318i	0.184273	−	0.319170i
$237$	−4.50927	−	2.60343i	−0.292908	−	0.169111i
$238$	2.08867	−	1.20589i	0.135388	−	0.0781664i
$239$	−2.96502	+	5.13556i	−0.191791	+	0.332192i	−0.945844	−	0.324622i	$-0.894763\pi$
$239$	−2.96502	+	5.13556i	−0.191791	+	0.332192i	0.754053	+	0.656814i	$0.228096\pi$
$240$	0.824383	−	0.509635i	0.0532137	−	0.0328968i
$241$	−9.82586			−0.632939			−0.316470	−	0.948603i	$-0.602498\pi$
$241$	−9.82586			−0.632939			−0.316470	+	0.948603i	$0.602498\pi$
$242$	−3.35199	−	1.93527i	−0.215474	−	0.124404i
$243$		−	10.7409i		−	0.689032i
$244$	2.10439			0.134720
$245$	8.08789	+	13.0829i	0.516716	+	0.835837i
$246$	−0.0166002			−0.00105839
$247$	0.979013	+	0.565234i	0.0622931	+	0.0359650i
$248$	7.11415	+	4.10735i	0.451749	+	0.260817i
$249$	−3.04358	−	5.27163i	−0.192879	−	0.334076i
$250$	9.13896	−	6.44045i	0.577999	−	0.407330i
$251$	3.48670	+	6.03914i	0.220079	+	0.381187i	0.954832	−	0.297147i	$-0.0960353\pi$
$251$	3.48670	+	6.03914i	0.220079	+	0.381187i	−0.734753	+	0.678335i	$0.762702\pi$
$252$	0.848490	−	0.489876i	0.0534498	−	0.0308593i
$253$		−	6.91869i		−	0.434974i
$254$	−13.3064			−0.834919
$255$	−3.52791	−	5.70673i	−0.220927	−	0.357370i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−19.4946	−	11.2552i	−1.21604	−	0.702079i	−0.251969	−	0.967735i	$-0.581078\pi$
$257$	−19.4946	−	11.2552i	−1.21604	−	0.702079i	−0.964068	+	0.265656i	$0.914412\pi$
$258$	−0.347329	+	0.200530i	−0.0216237	+	0.0124845i
$259$	2.82593			0.175595
$260$	−0.0182814	−	0.607231i	−0.00113376	−	0.0376589i
$261$	6.46316	−	11.1945i	0.400059	−	0.692923i
$262$	14.3363	−	8.27709i	0.885702	−	0.511360i
$263$			9.57006i			0.590115i	0.955479	+	0.295058i	$0.0953389\pi$
$263$			9.57006i			0.590115i	−0.955479	+	0.295058i	$0.904661\pi$
$264$	0.578661	−	1.00227i	0.0356141	−	0.0616854i
$265$	0.862820	+	28.6593i	0.0530026	+	1.76053i
$266$	0.724840	+	1.25546i	0.0444428	+	0.0769772i
$267$			4.48919i			0.274734i
$268$	−8.09590	−	1.20682i	−0.494536	−	0.0737181i
$269$	14.5353			0.886235			0.443117	−	0.896464i	$-0.353873\pi$
$269$	14.5353			0.886235			0.443117	+	0.896464i	$0.353873\pi$
$270$	−2.96207	−	4.79143i	−0.180266	−	0.291597i
$271$	4.66875			0.283606			0.141803	−	0.989895i	$-0.454710\pi$
$271$	4.66875			0.283606			0.141803	+	0.989895i	$0.454710\pi$
$272$	5.99500	+	3.46121i	0.363500	+	0.209867i
$273$			0.0410272i			0.00248308i
$274$	0.936417	+	1.62192i	0.0565710	+	0.0979839i
$275$	5.96763	−	11.9425i	0.359862	−	0.720161i
$276$	−1.12311			−0.0676031
$277$			6.03196i			0.362426i	0.983444	+	0.181213i	$0.0580023\pi$
$277$			6.03196i			0.362426i	−0.983444	+	0.181213i	$0.941998\pi$
$278$	1.20130	−	0.693573i	0.0720495	−	0.0415978i
$279$	11.5504	−	20.0059i	0.691506	−	1.19772i
$280$	0.369046	−	0.686093i	0.0220547	−	0.0410019i
$281$	−3.53882	−	6.12941i	−0.211108	−	0.365650i	0.740953	−	0.671556i	$-0.234374\pi$
$281$	−3.53882	−	6.12941i	−0.211108	−	0.365650i	−0.952062	+	0.305906i	$0.901041\pi$
$282$		−	2.16206i		−	0.128749i
$283$			20.8310i			1.23828i	0.785282	+	0.619138i	$0.212518\pi$
$283$			20.8310i			1.23828i	−0.785282	+	0.619138i	$0.787482\pi$
$284$	7.42454	+	12.8597i	0.440565	+	0.763082i
$285$	3.43021	−	2.12057i	0.203188	−	0.125611i
$286$	−0.362714	−	0.628239i	−0.0214477	−	0.0371485i
$287$	−0.0115557	+	0.00667171i	−0.000682114	+	0.000393819i
$288$	2.43538	+	1.40607i	0.143506	+	0.0828533i
$289$	15.4600	−	26.7775i	0.909412	−	1.57515i
$290$	−0.309301	−	10.2737i	−0.0181628	−	0.603293i
$291$	3.65600	+	6.33237i	0.214318	+	0.371210i
$292$		−	4.14746i		−	0.242712i
$293$		−	10.5901i		−	0.618682i	−0.950951	−	0.309341i	$-0.899892\pi$
$293$		−	10.5901i		−	0.618682i	0.950951	−	0.309341i	$-0.100108\pi$
$294$	1.49072	−	2.58201i	0.0869407	−	0.150586i
$295$	−12.6542	+	0.380970i	−0.736757	+	0.0221809i
$296$	4.05556	+	7.02444i	0.235725	+	0.408287i
$297$	−5.82532	−	3.36325i	−0.338020	−	0.195156i
$298$	−11.6289	+	6.71393i	−0.673643	+	0.388928i
$299$	−0.351991	+	0.609666i	−0.0203562	+	0.0352579i
$300$	−1.93862	−	0.968723i	−0.111926	−	0.0559292i
$301$	−0.161189	+	0.279187i	−0.00929076	+	0.0160921i
$302$	1.06696	+	0.616008i	0.0613965	+	0.0354473i
$303$	6.37850	+	3.68263i	0.366435	+	0.211561i
$304$	−2.08047	+	3.60348i	−0.119323	+	0.206674i
$305$	−2.47435	−	4.00249i	−0.141681	−	0.229182i
$306$	9.73339	−	16.8587i	0.556421	−	0.963749i
$307$	15.8419	−	9.14633i	0.904146	−	0.522009i	0.0256029	−	0.999672i	$-0.491849\pi$
$307$	15.8419	−	9.14633i	0.904146	−	0.522009i	0.878543	+	0.477663i	$0.158516\pi$
$308$		−	0.930269i		−	0.0530070i
$309$	2.73621	−	4.73926i	0.155658	−	0.269607i
$310$	−0.552758	−	18.3603i	−0.0313946	−	1.04280i
$311$	13.6948			0.776562			0.388281	−	0.921541i	$-0.373069\pi$
$311$	13.6948			0.776562			0.388281	+	0.921541i	$0.373069\pi$
$312$	−0.101982	+	0.0588791i	−0.00577358	+	0.00333338i
$313$			1.34030i			0.0757585i	0.999282	+	0.0378792i	$0.0120602\pi$
$313$			1.34030i			0.0757585i	−0.999282	+	0.0378792i	$0.987940\pi$
$314$	0.887772	−	1.53767i	0.0500999	−	0.0867755i
$315$	−1.92938	−	1.03781i	−0.108709	−	0.0584737i
$316$	−6.00648	−	10.4035i	−0.337891	−	0.585244i
$317$	8.31975	−	4.80341i	0.467284	−	0.269787i	−0.247818	−	0.968807i	$-0.579714\pi$
$317$	8.31975	−	4.80341i	0.467284	−	0.269787i	0.715102	+	0.699020i	$0.246380\pi$
$318$	4.81319	−	2.77890i	0.269910	−	0.155833i
$319$	−6.13673	−	10.6291i	−0.343591	−	0.595117i
$320$	2.23506	−	0.0672889i	0.124943	−	0.00376156i
$321$	4.63085			0.258469
$322$	−0.781819	+	0.451383i	−0.0435691	+	0.0251546i
$323$	24.9449	+	14.4019i	1.38797	+	0.801344i
$324$	3.67224	−	6.36051i	0.204014	−	0.353362i
$325$	−1.13344	+	0.748754i	−0.0628720	+	0.0415334i
$326$	14.5629			0.806563
$327$		−	5.18835i		−	0.286916i
$328$	−0.0331679	−	0.0191495i	−0.00183139	−	0.00105735i
$329$	−0.868944	−	1.50505i	−0.0479064	−	0.0829763i
$330$	−2.58668	+	0.0778748i	−0.142392	+	0.00428687i
$331$	−4.98195	+	8.62899i	−0.273833	+	0.474292i	−0.969840	−	0.243743i	$-0.921625\pi$
$331$	−4.98195	+	8.62899i	−0.273833	+	0.474292i	0.696007	+	0.718035i	$0.254958\pi$
$332$		−	14.0439i		−	0.770761i
$333$	19.7536	−	11.4048i	1.08249	−	0.624978i
$334$	−11.9293			−0.652741
$335$	7.22384	+	16.8171i	0.394681	+	0.918818i
$336$	−0.151010			−0.00823827
$337$	−9.57683	+	5.52918i	−0.521683	+	0.301194i	−0.737623	−	0.675213i	$-0.764052\pi$
$337$	−9.57683	+	5.52918i	−0.521683	+	0.301194i	0.215940	+	0.976407i	$0.430718\pi$
$338$		−	12.9262i		−	0.703092i
$339$	−3.33151	+	5.77034i	−0.180943	+	0.313402i
$340$	−0.465802	−	15.4720i	−0.0252617	−	0.839087i
$341$	−10.9671	−	18.9955i	−0.593900	−	1.02866i
$342$	10.1335	+	5.85057i	0.547956	+	0.316362i
$343$		−	4.83533i		−	0.261083i
$344$	−0.925304			−0.0498891
$345$	1.32055	+	2.13612i	0.0710960	+	0.115005i
$346$	−5.39440	+	9.34337i	−0.290005	+	0.502303i
$347$	30.8063	+	17.7860i	1.65377	+	0.954804i	0.975503	+	0.219987i	$0.0706015\pi$
$347$	30.8063	+	17.7860i	1.65377	+	0.954804i	0.678266	+	0.734817i	$0.262732\pi$
$348$	−1.72542	+	0.996172i	−0.0924922	+	0.0534004i
$349$	−12.7988			−0.685105			−0.342552	−	0.939499i	$-0.611291\pi$
$349$	−12.7988			−0.685105			−0.342552	+	0.939499i	$0.611291\pi$
$350$	−1.73885	+	0.104795i	−0.0929456	+	0.00560154i
$351$	0.342213	+	0.592731i	0.0182660	+	0.0316376i
$352$	2.31238	−	1.33505i	0.123250	−	0.0711585i
$353$	6.15990	−	3.55642i	0.327858	−	0.189289i	−0.327031	−	0.945013i	$-0.606048\pi$
$353$	6.15990	−	3.55642i	0.327858	−	0.189289i	0.654890	+	0.755724i	$0.272715\pi$
$354$	1.22699	+	2.12522i	0.0652140	+	0.112954i
$355$	15.7289	−	29.2417i	0.834806	−	1.55199i
$356$	−5.17860	+	8.96960i	−0.274465	+	0.475388i
$357$			1.04536i			0.0553261i
$358$	−8.52552	+	4.92221i	−0.450588	+	0.260147i
$359$	2.41395			0.127403			0.0637017	−	0.997969i	$-0.479709\pi$
$359$	2.41395			0.127403			0.0637017	+	0.997969i	$0.479709\pi$
$360$	−0.189225	−	6.28527i	−0.00997305	−	0.331263i
$361$	0.843266	−	1.46058i	0.0443824	−	0.0768726i
$362$			1.45999i			0.0767355i
$363$	1.45287	−	0.838817i	0.0762561	−	0.0440265i
$364$	−0.0473278	+	0.0819741i	−0.00248065	+	0.00429661i
$365$	−7.88834	+	4.87659i	−0.412895	+	0.255252i
$366$	−0.456060	+	0.789920i	−0.0238387	+	0.0412898i
$367$	7.53961	+	4.35299i	0.393564	+	0.227224i	0.683703	−	0.729760i	$-0.260368\pi$
$367$	7.53961	+	4.35299i	0.393564	+	0.227224i	−0.290139	+	0.956985i	$0.593702\pi$
$368$	−2.24402	−	1.29558i	−0.116977	−	0.0675370i
$369$	−0.0538509	+	0.0932725i	−0.00280337	+	0.00485557i
$370$	8.59174	−	15.9729i	0.446663	−	0.830392i
$371$	2.23371	−	3.86890i	0.115969	−	0.200863i
$372$	−3.08353	+	1.78028i	−0.159874	+	0.0923031i
$373$	−20.6308	−	11.9112i	−1.06822	−	0.616740i	−0.140529	−	0.990077i	$-0.544880\pi$
$373$	−20.6308	−	11.9112i	−1.06822	−	0.616740i	−0.927696	+	0.373337i	$0.878214\pi$
$374$	−9.24180	−	16.0073i	−0.477882	−	0.827716i
$375$	0.436954	+	4.82623i	0.0225642	+	0.249225i
$376$	2.49409	−	4.31988i	0.128623	−	0.222781i
$377$			1.24883i			0.0643182i
$378$			0.877690i			0.0451435i
$379$	−8.38403	−	14.5216i	−0.430659	−	0.745923i	0.566271	−	0.824219i	$-0.308385\pi$
$379$	−8.38403	−	14.5216i	−0.430659	−	0.745923i	−0.996930	+	0.0782960i	$0.975052\pi$
$380$	9.29994	−	0.279985i	0.477077	−	0.0143629i
$381$	2.88374	−	4.99479i	0.147739	−	0.255891i
$382$	−9.72445	−	5.61441i	−0.497546	−	0.287258i
$383$	−10.9132	+	6.30075i	−0.557639	+	0.321953i	−0.752197	−	0.658938i	$-0.771006\pi$
$383$	−10.9132	+	6.30075i	−0.557639	+	0.321953i	0.194558	+	0.980891i	$0.437673\pi$
$384$	−0.216718	−	0.375367i	−0.0110594	−	0.0191554i
$385$	−1.76934	+	1.09381i	−0.0901741	+	0.0557458i
$386$	−3.45009	−	5.97574i	−0.175605	−	0.304157i
$387$			2.60208i			0.132271i
$388$			16.8698i			0.856435i
$389$	15.6822	+	27.1624i	0.795121	+	1.37719i	0.922762	+	0.385370i	$0.125926\pi$
$389$	15.6822	+	27.1624i	0.795121	+	1.37719i	−0.127641	+	0.991820i	$0.540741\pi$
$390$	0.231897	+	0.124736i	0.0117425	+	0.00631625i
$391$	−8.96858	+	15.5340i	−0.453561	+	0.785590i
$392$	5.95706	−	3.43931i	0.300877	−	0.173711i
$393$			7.17519i			0.361940i
$394$	12.7565			0.642663
$395$	−12.7248	+	23.6566i	−0.640253	+	1.19029i
$396$	−3.75434	−	6.50272i	−0.188663	−	0.326774i
$397$			8.42010i			0.422593i	0.977422	+	0.211296i	$0.0677685\pi$
$397$			8.42010i			0.422593i	−0.977422	+	0.211296i	$0.932231\pi$
$398$	−7.22727	−	4.17267i	−0.362270	−	0.209157i
$399$	−0.628344			−0.0314566
$400$	−2.75596	−	4.17189i	−0.137798	−	0.208595i
$401$	1.24017			0.0619309			0.0309655	−	0.999520i	$-0.490142\pi$
$401$	1.24017			0.0619309			0.0309655	+	0.999520i	$0.490142\pi$
$402$	2.20753	−	2.77739i	0.110102	−	0.138524i
$403$			2.23181i			0.111175i
$404$	8.49634	+	14.7161i	0.422709	+	0.732153i
$405$	−16.4153	+	0.494202i	−0.815685	+	0.0245571i
$406$	−0.800735	+	1.38691i	−0.0397398	+	0.0688314i
$407$		−	21.6575i		−	1.07352i
$408$	−2.59845	+	1.50022i	−0.128643	+	0.0742718i
$409$	2.41195	−	4.17762i	0.119263	−	0.206570i	−0.800213	−	0.599716i	$-0.795280\pi$
$409$	2.41195	−	4.17762i	0.119263	−	0.206570i	0.919476	+	0.393146i	$0.128613\pi$
$410$	0.00257710	+	0.0856003i	0.000127274	+	0.00422750i
$411$	−0.811755			−0.0400409
$412$	10.9341	−	6.31283i	0.538687	−	0.311011i
$413$	1.70827	+	0.986273i	0.0840587	+	0.0485313i
$414$	−3.64335	+	6.31047i	−0.179061	+	0.310143i
$415$	−26.7111	+	16.5129i	−1.31120	+	0.810585i
$416$	−0.271685			−0.0133205
$417$			0.601240i			0.0294429i
$418$	9.62168	−	5.55508i	0.470612	−	0.271708i
$419$	−16.4910	−	28.5633i	−0.805639	−	1.39541i	−0.915859	−	0.401500i	$-0.868489\pi$
$419$	−16.4910	−	28.5633i	−0.805639	−	1.39541i	0.110220	−	0.993907i	$-0.464844\pi$
$420$	0.177558	+	0.287217i	0.00866393	+	0.0140147i
$421$	0.244428	+	0.423362i	0.0119127	+	0.0206334i	0.871920	−	0.489648i	$-0.162875\pi$
$421$	0.244428	+	0.423362i	0.0119127	+	0.0206334i	−0.860008	+	0.510281i	$0.829541\pi$
$422$	−5.57889	−	3.22097i	−0.271576	−	0.156795i
$423$	−12.1481	−	7.01370i	−0.590660	−	0.341018i
$424$	12.8226			0.622722
$425$	−28.8796	+	19.0780i	−1.40087	+	0.925417i
$426$	−6.43613			−0.311832
$427$			0.733174i			0.0354808i
$428$	9.25265	+	5.34202i	0.447243	+	0.258216i
$429$	0.314427			0.0151807
$430$	1.08797	+	1.75990i	0.0524668	+	0.0848700i
$431$	6.84707	−	11.8595i	0.329812	−	0.571251i	−0.652662	−	0.757649i	$-0.726348\pi$
$431$	6.84707	−	11.8595i	0.329812	−	0.571251i	0.982474	+	0.186398i	$0.0596813\pi$
$432$	−2.18168	+	1.25960i	−0.104966	+	0.0606023i
$433$	12.0786	+	6.97358i	0.580460	+	0.335129i	0.761316	−	0.648381i	$-0.224553\pi$
$433$	12.0786	+	6.97358i	0.580460	+	0.335129i	−0.180856	+	0.983510i	$0.557887\pi$
$434$	−1.43101	+	2.47858i	−0.0686906	+	0.118976i
$435$	3.92344	+	2.11040i	0.188115	+	0.101186i
$436$	5.98513	−	10.3665i	0.286636	−	0.496468i
$437$	−9.33723	−	5.39085i	−0.446660	−	0.257879i
$438$	1.55682	+	0.898830i	0.0743877	+	0.0429478i
$439$	19.5580	+	33.8754i	0.933451	+	1.61679i	0.777372	+	0.629041i	$0.216552\pi$
$439$	19.5580	+	33.8754i	0.933451	+	1.61679i	0.156079	+	0.987745i	$0.450115\pi$
$440$	−5.25813	−	2.82832i	−0.250671	−	0.134835i
$441$	−9.67179	−	16.7520i	−0.460561	−	0.797716i
$442$			1.88072i			0.0894568i
$443$	−17.6750	−	10.2047i	−0.839767	−	0.484839i	0.0174183	−	0.999848i	$-0.494455\pi$
$443$	−17.6750	−	10.2047i	−0.839767	−	0.484839i	−0.857185	+	0.515009i	$0.827789\pi$
$444$	−3.51566			−0.166846
$445$	23.1489	−	0.696924i	1.09736	−	0.0330374i
$446$	6.83484	+	11.8383i	0.323639	+	0.560559i
$447$		−	5.82013i		−	0.275283i
$448$	−0.301725	−	0.174201i	−0.0142551	−	0.00823021i
$449$	−11.4371	+	19.8097i	−0.539750	+	0.934875i	0.459167	+	0.888350i	$0.348148\pi$
$449$	−11.4371	+	19.8097i	−0.539750	+	0.934875i	−0.998917	+	0.0465251i	$0.985185\pi$
$450$	−11.7319	+	7.75013i	−0.553048	+	0.365345i
$451$	0.0511311	+	0.0885617i	0.00240767	+	0.00417021i
$452$	−13.3130	+	7.68626i	−0.626191	+	0.361531i
$453$	−0.462458	+	0.267000i	−0.0217282	+	0.0125448i
$454$	−26.1801			−1.22869
$455$	0.211560	−	0.00636927i	0.00991810	−	0.000298596i
$456$	−0.901753	−	1.56188i	−0.0422285	−	0.0731418i
$457$	7.01661	+	4.05104i	0.328223	+	0.189500i	0.655052	−	0.755584i	$-0.272647\pi$
$457$	7.01661	+	4.05104i	0.328223	+	0.189500i	−0.326829	+	0.945084i	$0.605980\pi$
$458$	12.4851	+	7.20825i	0.583388	+	0.336819i
$459$	8.71946	+	15.1025i	0.406989	+	0.704926i
$460$	0.174357	+	5.79140i	0.00812942	+	0.270025i
$461$	12.4782			0.581169			0.290584	−	0.956849i	$-0.406150\pi$
$461$	12.4782			0.581169			0.290584	+	0.956849i	$0.406150\pi$
$462$	0.349192	+	0.201606i	0.0162459	+	0.00937957i
$463$	5.91194	−	3.41326i	0.274751	−	0.158628i	−0.356294	−	0.934374i	$-0.615960\pi$
$463$	5.91194	−	3.41326i	0.274751	−	0.158628i	0.631045	+	0.775746i	$0.282626\pi$
$464$	−4.59662			−0.213393
$465$	7.01165	+	3.77153i	0.325158	+	0.174901i
$466$	28.1694			1.30492
$467$	7.83064	−	4.52102i	0.362359	−	0.209208i	−0.307756	−	0.951465i	$-0.599578\pi$
$467$	7.83064	−	4.52102i	0.362359	−	0.209208i	0.670115	+	0.742257i	$0.266245\pi$
$468$			0.764015i			0.0353166i
$469$	0.420457	−	2.82062i	0.0194149	−	0.130244i
$470$	−11.1488	+	0.335649i	−0.514258	+	0.0154823i
$471$	0.384793	+	0.666481i	0.0177303	+	0.0307098i
$472$			5.66170i			0.260601i
$473$	2.13965	+	1.23533i	0.0983814	+	0.0568005i
$474$	5.20685			0.239159
$475$	−11.4674	−	17.3590i	−0.526161	−	0.796486i
$476$	−1.20589	+	2.08867i	−0.0552720	+	0.0957339i
$477$		−	36.0589i		−	1.65102i
$478$		−	5.93004i		−	0.271234i
$479$	−13.7909	−	23.8865i	−0.630121	−	1.09140i	−0.987527	−	0.157453i	$-0.949672\pi$
$479$	−13.7909	−	23.8865i	−0.630121	−	1.09140i	0.357405	−	0.933949i	$-0.383661\pi$
$480$	−0.459119	+	0.853549i	−0.0209558	+	0.0389590i
$481$	−1.10184	+	1.90844i	−0.0502394	+	0.0870172i
$482$	8.50944	−	4.91293i	0.387595	−	0.223778i
$483$		−	0.391292i		−	0.0178044i
$484$	3.87054			0.175934
$485$	32.0859	−	19.8356i	1.45695	−	0.900686i
$486$	5.37047	+	9.30193i	0.243610	+	0.421944i
$487$	5.22675	−	3.01766i	0.236847	−	0.136743i	−0.376880	−	0.926262i	$-0.623003\pi$
$487$	5.22675	−	3.01766i	0.236847	−	0.136743i	0.613727	+	0.789519i	$0.289670\pi$
$488$	−1.82246	+	1.05220i	−0.0824988	+	0.0476307i
$489$	−3.15604	+	5.46642i	−0.142721	+	0.247200i
$490$	−13.5458	−	7.28620i	−0.611936	−	0.329157i
$491$	2.44471			0.110328			0.0551642	−	0.998477i	$-0.482432\pi$
$491$	2.44471			0.110328			0.0551642	+	0.998477i	$0.482432\pi$
$492$	0.0143762	−	0.00830009i	0.000648128	−	0.000374197i
$493$			31.8198i			1.43309i
$494$	−1.13047			−0.0508621
$495$	−7.95361	+	14.7866i	−0.357488	+	0.664606i
$496$	−8.21471			−0.368851
$497$	−4.48033	+	2.58672i	−0.200970	+	0.116030i
$498$	5.27163	+	3.04358i	0.236227	+	0.136386i
$499$	7.32097	+	12.6803i	0.327732	+	0.567648i	0.982061	−	0.188561i	$-0.0603824\pi$
$499$	7.32097	+	12.6803i	0.327732	+	0.567648i	−0.654330	+	0.756209i	$0.727049\pi$
$500$	−4.69435	+	10.1471i	−0.209938	+	0.453791i
$501$	2.58529	−	4.47786i	0.115502	−	0.200056i
$502$	−6.03914	−	3.48670i	−0.269540	−	0.155619i
$503$	−20.0303	−	11.5645i	−0.893108	−	0.515636i	−0.0181500	−	0.999835i	$-0.505778\pi$
$503$	−20.0303	−	11.5645i	−0.893108	−	0.515636i	−0.874958	+	0.484199i	$0.839111\pi$
$504$	−0.489876	+	0.848490i	−0.0218208	+	0.0377947i
$505$	17.9996	−	33.4630i	0.800970	−	1.48908i
$506$	3.45934	+	5.99176i	0.153787	+	0.266366i
$507$	4.85207	+	2.80134i	0.215488	+	0.124412i
$508$	11.5237	−	6.65321i	0.511281	−	0.295188i
$509$	22.1039			0.979740			0.489870	−	0.871796i	$-0.337044\pi$
$509$	22.1039			0.979740			0.489870	+	0.871796i	$0.337044\pi$
$510$	5.90863	+	3.17822i	0.261639	+	0.140734i
$511$	1.44498			0.0639222
$512$		−	1.00000i		−	0.0441942i
$513$	−9.07787	+	5.24111i	−0.400798	+	0.231401i
$514$	22.5104			0.992890
$515$	−24.8632	−	13.3738i	−1.09560	−	0.589319i
$516$	0.200530	−	0.347329i	0.00882786	−	0.0152903i
$517$	−11.5345	+	6.65947i	−0.507289	+	0.292883i
$518$	−2.44733	+	1.41296i	−0.107529	+	0.0620821i
$519$	−2.33813	−	4.04976i	−0.102632	−	0.177765i
$520$	0.319448	+	0.516737i	0.0140087	+	0.0226604i
$521$	22.2413			0.974410			0.487205	−	0.873288i	$-0.338016\pi$
$521$	22.2413			0.974410			0.487205	+	0.873288i	$0.338016\pi$
$522$			12.9263i			0.565769i
$523$	−6.66410	+	3.84752i	−0.291401	+	0.168240i	−0.638573	−	0.769561i	$-0.720475\pi$
$523$	−6.66410	+	3.84752i	−0.291401	+	0.168240i	0.347173	+	0.937801i	$0.387142\pi$
$524$	−8.27709	+	14.3363i	−0.361586	+	0.626286i
$525$	0.337505	−	0.675419i	0.0147299	−	0.0294777i
$526$	−4.78503	−	8.28792i	−0.208637	−	0.361370i
$527$			56.8657i			2.47711i
$528$			1.15732i			0.0503659i
$529$	−8.14293	+	14.1040i	−0.354040	+	0.613216i
$530$	−15.0769	−	24.3883i	−0.654897	−	1.05936i
$531$	15.9215			0.690932
$532$	−1.25546	−	0.724840i	−0.0544311	−	0.0314258i
$533$		−	0.0104053i		−	0.000450702i
$534$	−2.24459	−	3.88775i	−0.0971331	−	0.168239i
$535$	−0.718917	−	23.8794i	−0.0310815	−	1.03240i
$536$	7.61466	−	3.00282i	0.328903	−	0.129702i
$537$		−	4.26694i		−	0.184132i
$538$	−12.5880	+	7.26766i	−0.542706	+	0.313331i
$539$	−18.3666			−0.791107
$540$	4.96094	+	2.66846i	0.213485	+	0.114832i
$541$	−21.5924			−0.928330			−0.464165	−	0.885749i	$-0.653646\pi$
$541$	−21.5924			−0.928330			−0.464165	+	0.885749i	$0.653646\pi$
$542$	−4.04325	+	2.33437i	−0.173673	+	0.100270i
$543$	−0.548033	−	0.316407i	−0.0235184	−	0.0135783i
$544$	−6.92243			−0.296797
$545$	−26.7542	+	0.805465i	−1.14602	+	0.0345023i
$546$	−0.0205136	−	0.0355306i	−0.000877901	−	0.00152057i
$547$	−30.0971	−	17.3766i	−1.28686	−	0.742968i	−0.308766	−	0.951138i	$-0.599916\pi$
$547$	−30.0971	−	17.3766i	−1.28686	−	0.742968i	−0.978093	+	0.208170i	$0.933249\pi$
$548$	−1.62192	−	0.936417i	−0.0692851	−	0.0400018i
$549$	2.95892	+	5.12499i	0.126283	+	0.218729i
$550$	0.803137	+	13.3263i	0.0342459	+	0.568237i
$551$	−19.1263			−0.814807
$552$	0.972639	−	0.561553i	0.0413983	−	0.0239013i
$553$	3.62460	−	2.09267i	0.154134	−	0.0889892i
$554$	−3.01598	−	5.22383i	−0.128137	−	0.221939i
$555$	4.13371	+	6.68667i	0.175466	+	0.283834i
$556$	−0.693573	+	1.20130i	−0.0294141	+	0.0509467i
$557$	6.08873	+	3.51533i	0.257988	+	0.148949i	0.623416	−	0.781890i	$-0.285744\pi$
$557$	6.08873	+	3.51533i	0.257988	+	0.148949i	−0.365429	+	0.930839i	$0.619078\pi$
$558$			23.1008i			0.977937i
$559$	−0.125696	−	0.217711i	−0.00531636	−	0.00920821i
$560$	0.0234436	+	0.778697i	0.000990671	+	0.0329059i
$561$	8.01147			0.338245
$562$	6.12941	+	3.53882i	0.258554	+	0.149276i
$563$		−	11.9032i		−	0.501660i	−0.968031	−	0.250830i	$-0.919296\pi$
$563$		−	11.9032i		−	0.501660i	0.968031	−	0.250830i	$-0.0807035\pi$
$564$	1.08103	+	1.87240i	0.0455195	+	0.0788421i
$565$	30.2725	+	16.2834i	1.27357	+	0.685048i
$566$	−10.4155	−	18.0402i	−0.437797	−	0.758286i
$567$	2.21601	+	1.27942i	0.0930638	+	0.0537304i
$568$	−12.8597	−	7.42454i	−0.539580	−	0.311527i
$569$	−19.4265	+	33.6477i	−0.814401	+	1.41058i	0.0953555	+	0.995443i	$0.469601\pi$
$569$	−19.4265	+	33.6477i	−0.814401	+	1.41058i	−0.909757	+	0.415141i	$0.863732\pi$
$570$	−1.91037	+	3.55157i	−0.0800166	+	0.148759i
$571$	12.3692	−	21.4241i	0.517634	−	0.896569i	−0.482156	−	0.876085i	$-0.660146\pi$
$571$	12.3692	−	21.4241i	0.517634	−	0.896569i	0.999790	−	0.0204833i	$-0.00652050\pi$
$572$	0.628239	+	0.362714i	0.0262680	+	0.0151658i
$573$	4.21493	−	2.43349i	0.176081	−	0.101661i
$574$	0.00667171	−	0.0115557i	0.000278472	−	0.000482328i
$575$	10.8101	−	7.14116i	0.450811	−	0.297807i
$576$	−2.81213			−0.117172
$577$	−18.6123	−	10.7458i	−0.774839	−	0.447353i	0.0597593	−	0.998213i	$-0.480967\pi$
$577$	−18.6123	−	10.7458i	−0.774839	−	0.447353i	−0.834598	+	0.550860i	$0.814300\pi$
$578$			30.9200i			1.28610i
$579$	2.99079			0.124293
$580$	5.40471	+	8.74264i	0.224419	+	0.363018i
$581$	4.89293			0.202993
$582$	−6.33237	−	3.65600i	−0.262485	−	0.151546i
$583$	−29.6508	−	17.1189i	−1.22801	−	0.708991i
$584$	2.07373	+	3.59181i	0.0858115	+	0.148630i
$585$	1.45313	−	0.898330i	0.0600797	−	0.0371414i
$586$	5.29507	+	9.17133i	0.218737	+	0.378864i
$587$	−23.8024	+	13.7423i	−0.982429	+	0.567206i	−0.903003	−	0.429635i	$-0.858642\pi$
$587$	−23.8024	+	13.7423i	−0.982429	+	0.567206i	−0.0794265	+	0.996841i	$0.525309\pi$
$588$			2.98144i			0.122953i
$589$	−34.1810			−1.40840
$590$	10.7684	−	6.65704i	0.443328	−	0.274066i
$591$	−2.76457	+	4.78837i	−0.113719	+	0.196967i
$592$	−7.02444	−	4.05556i	−0.288703	−	0.166683i
$593$	34.1545	−	19.7191i	1.40256	−	0.809766i	0.407901	−	0.913026i	$-0.366261\pi$
$593$	34.1545	−	19.7191i	1.40256	−	0.809766i	0.994654	+	0.103261i	$0.0329275\pi$
$594$	6.72650			0.275992
$595$	5.39047	−	0.162286i	0.220988	−	0.00665309i
$596$	6.71393	−	11.6289i	0.275013	−	0.476337i
$597$	3.13256	−	1.80859i	0.128207	−	0.0740205i
$598$		−	0.703982i		−	0.0287880i
$599$	−5.01882	+	8.69285i	−0.205063	+	0.355180i	−0.950153	−	0.311784i	$-0.899073\pi$
$599$	−5.01882	+	8.69285i	−0.205063	+	0.355180i	0.745090	+	0.666964i	$0.232407\pi$
$600$	2.16326	−	0.130373i	0.0883146	−	0.00532245i
$601$	17.4323	+	30.1936i	0.711078	+	1.23162i	0.964453	+	0.264255i	$0.0851262\pi$
$601$	17.4323	+	30.1936i	0.711078	+	1.23162i	−0.253375	+	0.967368i	$0.581540\pi$
$602$		−	0.322377i		−	0.0131391i
$603$	−8.44431	−	21.4134i	−0.343879	−	0.872023i
$604$	−1.23202			−0.0501300
$605$	−4.55099	−	7.36165i	−0.185024	−	0.299294i
$606$	−7.36525			−0.299193
$607$	24.4529	+	14.1179i	0.992514	+	0.573028i	0.906025	−	0.423224i	$-0.139102\pi$
$607$	24.4529	+	14.1179i	0.992514	+	0.573028i	0.0864895	+	0.996253i	$0.472435\pi$
$608$		−	4.16095i		−	0.168749i
$609$	−0.347068	−	0.601139i	−0.0140639	−	0.0243594i
$610$	4.14409	+	2.22909i	0.167789	+	0.0902530i
$611$	1.35521			0.0548260
$612$			19.4668i			0.786898i
$613$	24.6023	−	14.2041i	0.993678	−	0.573700i	0.0873062	−	0.996182i	$-0.472174\pi$
$613$	24.6023	−	14.2041i	0.993678	−	0.573700i	0.906372	+	0.422481i	$0.138841\pi$
$614$	−9.14633	+	15.8419i	−0.369116	+	0.639328i
$615$	−0.0326901	−	0.0175838i	−0.00131819	−	0.000709047i
$616$	0.465134	+	0.805636i	0.0187408	+	0.0324600i
$617$		−	22.2669i		−	0.896431i	−0.893926	−	0.448215i	$-0.852060\pi$
$617$		−	22.2669i		−	0.896431i	0.893926	−	0.448215i	$-0.147940\pi$
$618$			5.47242i			0.220133i
$619$	12.6066	+	21.8354i	0.506704	+	0.877637i	0.999970	+	0.00775835i	$0.00246958\pi$
$619$	12.6066	+	21.8354i	0.506704	+	0.877637i	−0.493266	+	0.869879i	$0.664197\pi$
$620$	9.65887	+	15.6241i	0.387909	+	0.627480i
$621$	−3.26382	−	5.65311i	−0.130973	−	0.226851i
$622$	−11.8601	+	6.84741i	−0.475545	+	0.274556i
$623$	−3.12502	−	1.80423i	−0.125201	−	0.0722850i
$624$	0.0588791	−	0.101982i	0.00235705	−	0.00408253i
$625$	24.8191	−	3.00244i	0.992762	−	0.120098i
$626$	−0.670152	−	1.16074i	−0.0267847	−	0.0463924i
$627$			4.81555i			0.192315i
$628$			1.77554i			0.0708519i
$629$	−28.0743	+	48.6262i	−1.11940	+	1.93885i
$630$	2.18980	−	0.0659264i	0.0872437	−	0.00262657i
$631$	−11.3389	−	19.6395i	−0.451394	−	0.781837i	0.547079	−	0.837081i	$-0.315740\pi$
$631$	−11.3389	−	19.6395i	−0.451394	−	0.781837i	−0.998473	+	0.0552439i	$0.982406\pi$
$632$	10.4035	+	6.00648i	0.413830	+	0.238925i
$633$	2.41809	−	1.39609i	0.0961106	−	0.0554895i
$634$	−4.80341	+	8.31975i	−0.190768	+	0.330420i
$635$	−26.2038	−	14.0949i	−1.03987	−	0.559338i
$636$	−2.77890	+	4.81319i	−0.110190	+	0.190855i
$637$	1.61844	+	0.934409i	0.0641251	+	0.0370226i
$638$	10.6291	+	6.13673i	0.420811	+	0.242955i
$639$	−20.8788	+	36.1631i	−0.825952	+	1.43059i
$640$	−1.90197	+	1.17580i	−0.0751820	+	0.0464776i
$641$	−9.23717	+	15.9992i	−0.364846	+	0.631932i	−0.988751	−	0.149568i	$-0.952212\pi$
$641$	−9.23717	+	15.9992i	−0.364846	+	0.631932i	0.623905	+	0.781500i	$0.285545\pi$
$642$	−4.01043	+	2.31543i	−0.158279	+	0.0913826i
$643$			6.38243i			0.251698i	0.992049	+	0.125849i	$0.0401656\pi$
$643$			6.38243i			0.251698i	−0.992049	+	0.125849i	$0.959834\pi$
$644$	0.451383	−	0.781819i	0.0177870	−	0.0308080i
$645$	−0.896393	+	0.0269869i	−0.0352954	+	0.00106261i
$646$	−28.8038			−1.13327
$647$	33.0367	−	19.0738i	1.29881	−	0.749867i	0.318609	−	0.947886i	$-0.396784\pi$
$647$	33.0367	−	19.0738i	1.29881	−	0.749867i	0.980198	+	0.198020i	$0.0634510\pi$
$648$			7.34449i			0.288519i
$649$	7.55867	−	13.0920i	0.296704	−	0.513906i
$650$	0.607211	−	1.21516i	0.0238168	−	0.0476625i
$651$	−0.620251	−	1.07431i	−0.0243096	−	0.0421054i
$652$	−12.6118	+	7.28143i	−0.493917	+	0.285163i
$653$	−14.2294	+	8.21537i	−0.556841	+	0.321492i	−0.751876	−	0.659304i	$-0.770851\pi$
$653$	−14.2294	+	8.21537i	−0.556841	+	0.321492i	0.195036	+	0.980796i	$0.437518\pi$
$654$	2.59417	+	4.49324i	0.101440	+	0.175700i
$655$	36.9995	−	1.11391i	1.44569	−	0.0435242i
$656$	0.0382990			0.00149532
$657$	10.1006	−	5.83160i	0.394063	−	0.227512i
$658$	1.50505	+	0.868944i	0.0586731	+	0.0338750i
$659$	−21.2319	+	36.7748i	−0.827078	+	1.43254i	0.0732424	+	0.997314i	$0.476665\pi$
$659$	−21.2319	+	36.7748i	−0.827078	+	1.43254i	−0.900321	+	0.435227i	$0.856668\pi$
$660$	2.20119	−	1.36078i	0.0856812	−	0.0529683i
$661$	−36.8824			−1.43456			−0.717280	−	0.696785i	$-0.754613\pi$
$661$	−36.8824			−1.43456			−0.717280	+	0.696785i	$0.754613\pi$
$662$		−	9.96390i		−	0.387258i
$663$	−0.705961	−	0.407587i	−0.0274172	−	0.0158294i
$664$	7.02197	+	12.1624i	0.272505	+	0.471993i
$665$	0.0975473	+	3.24012i	0.00378272	+	0.125646i
$666$	−11.4048	+	19.7536i	−0.441926	+	0.765438i
$667$		−	11.9106i		−	0.461181i
$668$	10.3311	−	5.96464i	0.399721	−	0.230779i
$669$	−5.92494			−0.229071
$670$	−14.6646	−	10.9521i	−0.566543	−	0.423118i
$671$	5.61895			0.216917
$672$	0.130778	−	0.0755050i	0.00504489	−	0.00291267i
$673$			33.3359i			1.28501i	0.766283	+	0.642503i	$0.222104\pi$
$673$			33.3359i			1.28501i	−0.766283	+	0.642503i	$0.777896\pi$
$674$	5.52918	−	9.57683i	0.212976	−	0.368886i
$675$	−0.757744	−	12.5731i	−0.0291656	−	0.483940i
$676$	6.46309	+	11.1944i	0.248581	+	0.430554i
$677$	−8.01130	−	4.62533i	−0.307899	−	0.177766i	0.338087	−	0.941115i	$-0.390220\pi$
$677$	−8.01130	−	4.62533i	−0.307899	−	0.177766i	−0.645986	+	0.763349i	$0.723554\pi$
$678$		−	6.66301i		−	0.255891i
$679$	−5.87747			−0.225557
$680$	8.13940	+	13.1662i	0.312132	+	0.504903i
$681$	5.67370	−	9.82713i	0.217417	−	0.376576i
$682$	18.9955	+	10.9671i	0.727376	+	0.419951i
$683$	40.1995	−	23.2092i	1.53819	−	0.888075i	0.539245	−	0.842149i	$-0.318710\pi$
$683$	40.1995	−	23.2092i	1.53819	−	0.888075i	0.998945	−	0.0459259i	$-0.0146238\pi$
$684$	−11.7011			−0.447404
$685$	0.126021	+	4.18589i	0.00481501	+	0.159935i
$686$	2.41767	+	4.18752i	0.0923069	+	0.159880i
$687$	−5.41148	+	3.12432i	−0.206461	+	0.119200i
$688$	0.801337	−	0.462652i	0.0305507	−	0.0176384i
$689$	1.74186	+	3.01699i	0.0663595	+	0.114938i
$690$	−2.21169	−	1.18965i	−0.0841975	−	0.0452894i
$691$	−21.9409	+	38.0028i	−0.834672	+	1.44569i	0.0596258	+	0.998221i	$0.481009\pi$
$691$	−21.9409	+	38.0028i	−0.834672	+	1.44569i	−0.894297	+	0.447473i	$0.852324\pi$
$692$		−	10.7888i		−	0.410128i
$693$	2.26556	−	1.30802i	0.0860614	−	0.0496876i
$694$	−35.5720			−1.35030
$695$	3.10035	−	0.0933396i	0.117603	−	0.00354057i
$696$	0.996172	−	1.72542i	0.0377598	−	0.0654019i
$697$		−	0.265122i		−	0.0100422i
$698$	11.0841	−	6.39941i	0.419539	−	0.242221i
$699$	−6.10482	+	10.5739i	−0.230905	+	0.399940i
$700$	1.45349	−	0.960182i	0.0549369	−	0.0362915i
$701$	−4.81521	+	8.34019i	−0.181868	+	0.315005i	−0.942517	−	0.334159i	$-0.891548\pi$
$701$	−4.81521	+	8.34019i	−0.181868	+	0.315005i	0.760649	+	0.649164i	$0.224881\pi$
$702$	−0.592731	−	0.342213i	−0.0223712	−	0.0129160i
$703$	−29.2283	−	16.8750i	−1.10237	−	0.636451i
$704$	−1.33505	+	2.31238i	−0.0503167	+	0.0871510i
$705$	2.29017	−	4.25765i	0.0862527	−	0.160352i
$706$	−3.55642	+	6.15990i	−0.133848	+	0.231831i
$707$	−5.12711	+	2.96014i	−0.192825	+	0.111328i
$708$	−2.12522	−	1.22699i	−0.0798705	−	0.0461133i
$709$	−15.1734	−	26.2810i	−0.569847	−	0.987004i	−0.996581	−	0.0826268i	$-0.973669\pi$
$709$	−15.1734	−	26.2810i	−0.569847	−	0.987004i	0.426733	−	0.904377i	$-0.359664\pi$
$710$	0.999178	+	33.1885i	0.0374985	+	1.24554i
$711$	16.8910	−	29.2561i	0.633462	−	1.09719i
$712$		−	10.3572i		−	0.388152i
$713$		−	21.2857i		−	0.797155i
$714$	−0.522678	−	0.905305i	−0.0195607	−	0.0338802i
$715$	−0.0488132	−	1.62137i	−0.00182551	−	0.0606359i
$716$	4.92221	−	8.52552i	0.183952	−	0.318614i
$717$	2.22594	+	1.28515i	0.0831293	+	0.0479947i
$718$	−2.09054	+	1.20697i	−0.0780183	+	0.0450439i
$719$	20.0580	+	34.7415i	0.748037	+	1.29564i	0.948762	+	0.315991i	$0.102337\pi$
$719$	20.0580	+	34.7415i	0.748037	+	1.29564i	−0.200725	+	0.979648i	$0.564330\pi$
$720$	3.30651	+	5.34859i	0.123226	+	0.199330i
$721$	2.19940	+	3.80947i	0.0819100	+	0.141872i
$722$			1.68653i			0.0627662i
$723$			4.25889i			0.158390i
$724$	−0.729997	−	1.26439i	−0.0271301	−	0.0469907i
$725$	10.2734	−	20.5592i	0.381543	−	0.763550i
$726$	−0.838817	+	1.45287i	−0.0311314	+	0.0539212i
$727$	−17.4097	+	10.0515i	−0.645689	+	0.372789i	−0.786803	−	0.617205i	$-0.788265\pi$
$727$	−17.4097	+	10.0515i	−0.645689	+	0.372789i	0.141114	+	0.989993i	$0.454932\pi$
$728$		−	0.0946556i		−	0.00350817i
$729$	17.3779			0.643628
$730$	4.39321	−	8.16742i	0.162600	−	0.302290i
$731$	−3.20268	−	5.54720i	−0.118455	−	0.205170i
$732$		−	0.912121i		−	0.0337129i
$733$	6.49340	+	3.74897i	0.239839	+	0.138471i	0.615103	−	0.788447i	$-0.289114\pi$
$733$	6.49340	+	3.74897i	0.239839	+	0.138471i	−0.375264	+	0.926918i	$0.622448\pi$
$734$	−8.70599			−0.321344
$735$	5.67062	−	3.50559i	0.209164	−	0.129305i
$736$	2.59117			0.0955117
$737$	−21.6169	−	3.22233i	−0.796269	−	0.118696i
$738$		−	0.107702i		−	0.00396456i
$739$	−7.73318	−	13.3943i	−0.284470	−	0.492716i	0.688011	−	0.725700i	$-0.258484\pi$
$739$	−7.73318	−	13.3943i	−0.284470	−	0.492716i	−0.972480	+	0.232985i	$0.925151\pi$
$740$	0.545788	+	18.1288i	0.0200636	+	0.666428i
$741$	0.244993	−	0.424340i	0.00900004	−	0.0155885i
$742$			4.46742i			0.164004i
$743$	25.9314	−	14.9715i	0.951332	−	0.549252i	0.0578375	−	0.998326i	$-0.481579\pi$
$743$	25.9314	−	14.9715i	0.951332	−	0.549252i	0.893494	+	0.449074i	$0.148246\pi$
$744$	1.78028	−	3.08353i	0.0652681	−	0.113048i
$745$	−30.0120	+	0.903546i	−1.09956	+	0.0331034i
$746$	23.8225			0.872202
$747$	34.2023	−	19.7467i	1.25140	−	0.722494i
$748$	16.0073	+	9.24180i	0.585284	+	0.337914i
$749$	−1.86117	+	3.22364i	−0.0680056	+	0.117789i
$750$	−2.79153	−	3.96116i	−0.101932	−	0.144641i
$751$	−36.0877			−1.31686			−0.658429	−	0.752642i	$-0.728779\pi$
$751$	−36.0877			−1.31686			−0.658429	+	0.752642i	$0.728779\pi$
$752$			4.98817i			0.181900i
$753$	2.61759	−	1.51126i	0.0953901	−	0.0550735i
$754$	−0.624417	−	1.08152i	−0.0227399	−	0.0393867i
$755$	1.44861	+	2.34326i	0.0527202	+	0.0852799i
$756$	−0.438845	−	0.760102i	−0.0159606	−	0.0276446i
$757$	26.2503	+	15.1556i	0.954083	+	0.550840i	0.894347	−	0.447374i	$-0.147641\pi$
$757$	26.2503	+	15.1556i	0.954083	+	0.550840i	0.0597361	+	0.998214i	$0.480974\pi$
$758$	14.5216	+	8.38403i	0.527447	+	0.304522i
$759$	−2.99881			−0.108850
$760$	−7.91399	+	4.89245i	−0.287071	+	0.177468i
$761$	31.5003			1.14188			0.570942	−	0.820990i	$-0.306578\pi$
$761$	31.5003			1.14188			0.570942	+	0.820990i	$0.306578\pi$
$762$			5.76749i			0.208934i
$763$	3.61172	+	2.08523i	0.130753	+	0.0754904i
$764$	11.2288			0.406245
$765$	37.0252	−	22.8891i	1.33865	−	0.827556i
$766$	6.30075	−	10.9132i	0.227655	−	0.394310i
$767$	−1.33212	+	0.769100i	−0.0481001	+	0.0277706i
$768$	0.375367	+	0.216718i	0.0135449	+	0.00782015i
$769$	5.27390	−	9.13466i	0.190182	−	0.329404i	−0.755129	−	0.655577i	$-0.772426\pi$
$769$	5.27390	−	9.13466i	0.190182	−	0.329404i	0.945310	+	0.326172i	$0.105759\pi$
$770$	0.985391	−	1.83194i	0.0355110	−	0.0660185i
$771$	−4.87841	+	8.44966i	−0.175692	+	0.304307i
$772$	5.97574	+	3.45009i	0.215072	+	0.124172i
$773$	28.4008	+	16.3972i	1.02151	+	0.589768i	0.914540	−	0.404495i	$-0.132553\pi$
$773$	28.4008	+	16.3972i	1.02151	+	0.589768i	0.106967	+	0.994263i	$0.465886\pi$
$774$	−1.30104	−	2.25347i	−0.0467649	−	0.0809992i
$775$	18.3597	−	36.7418i	0.659501	−	1.31980i
$776$	−8.43491	−	14.6097i	−0.302796	−	0.524457i
$777$		−	1.22486i		−	0.0439416i
$778$	−27.1624	−	15.6822i	−0.973820	−	0.562235i
$779$	0.159360			0.00570966
$780$	−0.263196	+	0.00792382i	−0.00942394	+	0.000283718i
$781$	19.8243	+	34.3367i	0.709369	+	1.22866i
$782$		−	17.9372i		−	0.641432i
$783$	−10.0284	−	5.78988i	−0.358385	−	0.206914i
$784$	−3.43931	+	5.95706i	−0.122832	+	0.212752i
$785$	3.37703	−	2.08769i	0.120531	−	0.0745128i
$786$	−3.58759	−	6.21390i	−0.127965	−	0.221642i
$787$	−27.7897	+	16.0444i	−0.990597	+	0.571921i	−0.905453	−	0.424447i	$-0.860468\pi$
$787$	−27.7897	+	16.0444i	−0.990597	+	0.571921i	−0.0851440	+	0.996369i	$0.527135\pi$
$788$	−11.0475	+	6.37825i	−0.393549	+	0.227216i
$789$	4.14802			0.147673
$790$	−0.808338	−	26.8496i	−0.0287594	−	0.955267i
$791$	−2.67791	−	4.63827i	−0.0952154	−	0.164918i
$792$	6.50272	+	3.75434i	0.231064	+	0.133405i
$793$	−0.495135	−	0.285866i	−0.0175827	−	0.0101514i
$794$	−4.21005	−	7.29202i	−0.149409	−	0.258784i
$795$	12.4220	−	0.373978i	0.440562	−	0.0132636i
$796$	8.34533			0.295792
$797$	−46.4827	−	26.8368i	−1.64650	−	0.950609i	−0.978447	−	0.206498i	$-0.933793\pi$
$797$	−46.4827	−	26.8368i	−1.64650	−	0.950609i	−0.668056	−	0.744111i	$-0.732873\pi$
$798$	0.544162	−	0.314172i	0.0192631	−	0.0111216i
$799$	34.5303			1.22159
$800$	4.47268	+	2.23498i	0.158133	+	0.0790185i
$801$	−29.1258			−1.02911
$802$	−1.07402	+	0.620083i	−0.0379248	+	0.0218959i
$803$		−	11.0742i		−	0.390798i
$804$	−0.523079	+	3.50906i	−0.0184476	+	0.123755i
$805$	−2.01773	+	0.0607462i	−0.0711158	+	0.00214102i
$806$	−1.11591	−	1.93281i	−0.0393062	−	0.0680803i
$807$		−	6.30014i		−	0.221776i
$808$	−14.7161	−	8.49634i	−0.517711	−	0.298900i
$809$	3.97998			0.139929			0.0699643	−	0.997549i	$-0.477711\pi$
$809$	3.97998			0.139929			0.0699643	+	0.997549i	$0.477711\pi$
$810$	13.9690	−	8.63566i	0.490821	−	0.303426i
$811$	12.5330	−	21.7079i	0.440095	−	0.762266i	−0.557601	−	0.830109i	$-0.688278\pi$
$811$	12.5330	−	21.7079i	0.440095	−	0.762266i	0.997696	+	0.0678424i	$0.0216115\pi$
$812$		−	1.60147i		−	0.0562006i
$813$		−	2.02361i		−	0.0709710i
$814$	10.8288	+	18.7560i	0.379548	+	0.657397i
$815$	28.6781	+	15.4258i	1.00455	+	0.540341i
$816$	1.50022	−	2.59845i	0.0525181	−	0.0909640i
$817$	3.33432	−	1.92507i	0.116653	−	0.0673497i
$818$			4.82390i			0.168664i
$819$	−0.266184			−0.00930122
$820$	−0.0450320	−	0.0728435i	−0.00157259	−	0.00254381i
$821$	−13.4788	−	23.3459i	−0.470412	−	0.814778i	0.529015	−	0.848612i	$-0.322561\pi$
$821$	−13.4788	−	23.3459i	−0.470412	−	0.814778i	−0.999427	+	0.0338347i	$0.989228\pi$
$822$	0.703001	−	0.405878i	0.0245200	−	0.0141566i
$823$	−43.8974	+	25.3442i	−1.53017	+	0.883443i	−0.530815	+	0.847488i	$0.678114\pi$
$823$	−43.8974	+	25.3442i	−1.53017	+	0.883443i	−0.999353	+	0.0359558i	$0.988552\pi$
$824$	−6.31283	+	10.9341i	−0.219918	+	0.380909i
$825$	−5.17633	−	2.58659i	−0.180217	−	0.0900535i
$826$	−1.97255			−0.0686337
$827$	9.60912	−	5.54783i	0.334142	−	0.192917i	−0.323537	−	0.946216i	$-0.604872\pi$
$827$	9.60912	−	5.54783i	0.334142	−	0.192917i	0.657679	+	0.753299i	$0.271539\pi$
$828$		−	7.28671i		−	0.253231i
$829$	14.6141			0.507569			0.253785	−	0.967261i	$-0.418325\pi$
$829$	14.6141			0.507569			0.253785	+	0.967261i	$0.418325\pi$
$830$	14.8761	−	27.6561i	0.516357	−	0.959959i
$831$	2.61447			0.0906951
$832$	0.235286	−	0.135843i	0.00815708	−	0.00470949i
$833$	41.2373	+	23.8084i	1.42879	+	0.824911i
$834$	−0.300620	−	0.520689i	−0.0104096	−	0.0180300i
$835$	−23.4918	−	12.6361i	−0.812969	−	0.437291i
$836$	−5.55508	+	9.62168i	−0.192126	+	0.332773i
$837$	−17.9219	−	10.3472i	−0.619471	−	0.357652i
$838$	28.5633	+	16.4910i	0.986702	+	0.569673i
$839$	12.4230	−	21.5172i	0.428889	−	0.742858i	−0.567886	−	0.823107i	$-0.692238\pi$
$839$	12.4230	−	21.5172i	0.428889	−	0.742858i	0.996775	+	0.0802497i	$0.0255718\pi$
$840$	−0.297378	−	0.159958i	−0.0102605	−	0.00551907i
$841$	3.93553	+	6.81654i	0.135708	+	0.235053i
$842$	−0.423362	−	0.244428i	−0.0145900	−	0.00842355i
$843$	−2.65671	+	1.53385i	−0.0915020	+	0.0528287i
$844$	6.44195			0.221741
$845$	13.6921	−	25.4550i	0.471023	−	0.875679i
$846$	14.0274			0.482272
$847$			1.34850i			0.0463351i
$848$	−11.1047	+	6.41131i	−0.381338	+	0.220165i
$849$	9.02893			0.309872
$850$	15.4715	−	30.9618i	0.530668	−	1.06198i
$851$	10.5086	−	18.2015i	0.360231	−	0.623939i
$852$	5.57386	−	3.21807i	0.190957	−	0.110249i
$853$	−2.04880	+	1.18288i	−0.0701497	+	0.0405010i	−0.534665	−	0.845064i	$-0.679562\pi$
$853$	−2.04880	+	1.18288i	−0.0701497	+	0.0405010i	0.464515	+	0.885565i	$0.346229\pi$
$854$	−0.366587	−	0.634947i	−0.0125443	−	0.0217274i
$855$	13.7582	+	22.2552i	0.470521	+	0.761112i
$856$	−10.6840			−0.365173
$857$			41.2911i			1.41048i	0.708971	+	0.705238i	$0.249160\pi$
$857$			41.2911i			1.41048i	−0.708971	+	0.705238i	$0.750840\pi$
$858$	−0.272302	+	0.157213i	−0.00929623	+	0.00536718i
$859$	5.52195	−	9.56429i	0.188406	−	0.326329i	−0.756313	−	0.654210i	$-0.773001\pi$
$859$	5.52195	−	9.56429i	0.188406	−	0.326329i	0.944719	+	0.327881i	$0.106334\pi$
$860$	−1.82216	−	0.980132i	−0.0621353	−	0.0334222i
$861$	0.00289176	+	0.00500868i	9.85511e−5	+	0.000170695i
$862$			13.6941i			0.466425i
$863$		−	38.7296i		−	1.31837i	−0.751980	−	0.659186i	$-0.770901\pi$
$863$		−	38.7296i		−	1.31837i	0.751980	−	0.659186i	$-0.229099\pi$
$864$	1.25960	−	2.18168i	0.0428523	−	0.0742224i
$865$	−20.5200	+	12.6855i	−0.697700	+	0.431319i
$866$	−13.9472			−0.473944
$867$	−11.6063	−	6.70093i	−0.394172	−	0.227575i
$868$		−	2.86202i		−	0.0971432i
$869$	−16.0379	−	27.7785i	−0.544049	−	0.942321i
$870$	−4.45300	+	0.134063i	−0.150971	+	0.00454515i
$871$	1.74092	+	1.38372i	0.0589887	+	0.0468854i
$872$			11.9703i			0.405364i
$873$	−41.0844	+	23.7201i	−1.39050	+	0.802803i
$874$	10.7817			0.364697
$875$	−3.53526	−	1.63552i	−0.119513	−	0.0552906i
$876$	−1.79766			−0.0607373
$877$	−13.2052	+	7.62405i	−0.445909	+	0.257446i	−0.706101	−	0.708111i	$-0.749548\pi$
$877$	−13.2052	+	7.62405i	−0.445909	+	0.257446i	0.260192	+	0.965557i	$0.416214\pi$
$878$	−33.8754	−	19.5580i	−1.14324	−	0.660050i
$879$	−4.59015			−0.154822
$880$	5.96783	−	0.179668i	0.201176	−	0.00605662i
$881$	−17.3972	−	30.1329i	−0.586128	−	1.01520i	−0.994734	−	0.102492i	$-0.967318\pi$
$881$	−17.3972	−	30.1329i	−0.586128	−	1.01520i	0.408606	−	0.912711i	$-0.366015\pi$
$882$	16.7520	+	9.67179i	0.564070	+	0.325666i
$883$	27.4104	+	15.8254i	0.922433	+	0.532567i	0.884410	−	0.466710i	$-0.154561\pi$
$883$	27.4104	+	15.8254i	0.922433	+	0.532567i	0.0380226	+	0.999277i	$0.487894\pi$
$884$	−0.940360	−	1.62875i	−0.0316277	−	0.0547809i
$885$	0.165126	+	5.48480i	0.00555065	+	0.184370i
$886$	20.4094			0.685667
$887$	−13.9331	+	8.04426i	−0.467827	+	0.270100i	−0.715330	−	0.698787i	$-0.753723\pi$
$887$	−13.9331	+	8.04426i	−0.467827	+	0.270100i	0.247503	+	0.968887i	$0.420390\pi$
$888$	3.04465	−	1.75783i	0.102172	−	0.0589889i
$889$	2.31799	+	4.01487i	0.0777428	+	0.134655i
$890$	−19.6991	+	12.1780i	−0.660315	+	0.408208i
$891$	9.80528	−	16.9832i	0.328489	−	0.568960i
$892$	−11.8383	−	6.83484i	−0.396375	−	0.228847i
$893$			20.7555i			0.694557i
$894$	2.91006	+	5.04038i	0.0973271	+	0.168576i
$895$	−22.0028	+	0.662420i	−0.735474	+	0.0221423i
$896$	0.348402			0.0116393
$897$	0.264252	+	0.152566i	0.00882310	+	0.00509402i
$898$		−	22.8742i		−	0.763322i
$899$	−18.8800	−	32.7010i	−0.629682	−	1.09064i
$900$	6.28506	−	12.5778i	0.209502	−	0.419259i
$901$	44.3818	+	76.8716i	1.47857	+	2.56096i
$902$	−0.0885617	−	0.0511311i	−0.00294878	−	0.00170248i
$903$	0.121010	+	0.0698651i	0.00402696	+	0.00232496i
$904$	7.68626	−	13.3130i	0.255641	−	0.442784i
$905$	−1.54650	+	2.87511i	−0.0514075	+	0.0955717i
$906$	0.267000	−	0.462458i	0.00887049	−	0.0153641i
$907$	−2.94809	−	1.70208i	−0.0978896	−	0.0565166i	0.450256	−	0.892899i	$-0.351333\pi$
$907$	−2.94809	−	1.70208i	−0.0978896	−	0.0565166i	−0.548146	+	0.836383i	$0.684666\pi$
$908$	22.6726	−	13.0900i	0.752416	−	0.434408i
$909$	−23.8928	+	41.3836i	−0.792476	+	1.37261i
$910$	−0.180032	+	0.111296i	−0.00596800	+	0.00368943i
$911$	−2.92348			−0.0968592			−0.0484296	−	0.998827i	$-0.515422\pi$
$911$	−2.92348			−0.0968592			−0.0484296	+	0.998827i	$0.515422\pi$
$912$	1.56188	+	0.901753i	0.0517191	+	0.0298600i
$913$		−	37.4988i		−	1.24103i
$914$	−8.10209			−0.267993
$915$	−1.73483	+	1.07247i	−0.0573516	+	0.0354549i
$916$	−14.4165			−0.476335
$917$	−4.99481	−	2.88375i	−0.164943	−	0.0952299i
$918$	−15.1025	−	8.71946i	−0.498458	−	0.287785i
$919$	−13.9128	−	24.0977i	−0.458942	−	0.794911i	0.539964	−	0.841688i	$-0.318438\pi$
$919$	−13.9128	−	24.0977i	−0.458942	−	0.794911i	−0.998905	+	0.0467779i	$0.985105\pi$
$920$	−3.04670	−	4.92832i	−0.100447	−	0.162482i
$921$	−3.96436	−	6.86647i	−0.130630	−	0.226258i
$922$	−10.8065	+	6.23911i	−0.355892	+	0.205474i
$923$		−	4.03427i		−	0.132790i
$924$	−0.403212			−0.0132647
$925$	33.8387	−	22.3539i	1.11261	−	0.734993i
$926$	−3.41326	+	5.91194i	−0.112167	+	0.194278i
$927$	30.7483	+	17.7525i	1.00991	+	0.583069i
$928$	3.98079	−	2.29831i	0.130676	−	0.0754458i
$929$	32.3301			1.06072			0.530358	−	0.847774i	$-0.322057\pi$
$929$	32.3301			1.06072			0.530358	+	0.847774i	$0.322057\pi$
$930$	−7.95804	+	0.239586i	−0.260954	+	0.00785633i
$931$	−14.3108	+	24.7870i	−0.469017	+	0.812361i
$932$	−24.3954	+	14.0847i	−0.799098	+	0.461359i
$933$		−	5.93584i		−	0.194331i
$934$	−4.52102	+	7.83064i	−0.147932	+	0.256226i
$935$	−1.24374	−	41.3119i	−0.0406747	−	1.35104i
$936$	−0.382007	−	0.661656i	−0.0124863	−	0.0216269i
$937$		−	16.8088i		−	0.549119i	−0.961570	−	0.274559i	$-0.911468\pi$
$937$		−	16.8088i		−	0.549119i	0.961570	−	0.274559i	$-0.0885320\pi$
$938$	1.04619	+	2.65296i	0.0341592	+	0.0866222i
$939$	0.580937			0.0189582
$940$	9.48736	−	5.86510i	0.309443	−	0.191299i
$941$	0.280386			0.00914032			0.00457016	−	0.999990i	$-0.498545\pi$
$941$	0.280386			0.00914032			0.00457016	+	0.999990i	$0.498545\pi$
$942$	−0.666481	−	0.384793i	−0.0217151	−	0.0125372i
$943$			0.0992391i			0.00323167i
$944$	−2.83085	−	4.90318i	−0.0921364	−	0.159585i
$945$	−0.929697	+	1.72840i	−0.0302430	+	0.0562248i
$946$	−2.47066			−0.0803280
$947$			3.33974i			0.108527i	0.998527	+	0.0542634i	$0.0172811\pi$
$947$			3.33974i			0.108527i	−0.998527	+	0.0542634i	$0.982719\pi$
$948$	−4.50927	+	2.60343i	−0.146454	+	0.0845554i
$949$	−0.563402	+	0.975840i	−0.0182888	+	0.0316771i
$950$	18.6106	+	9.29964i	0.603807	+	0.301720i
$951$	−2.08197	−	3.60609i	−0.0675127	−	0.116935i
$952$		−	2.41178i		−	0.0781664i
$953$			32.4548i			1.05131i	0.850697	+	0.525657i	$0.176180\pi$
$953$			32.4548i			1.05131i	−0.850697	+	0.525657i	$0.823820\pi$
$954$	18.0295	+	31.2279i	0.583725	+	1.01104i
$955$	−13.2029	−	21.3569i	−0.427235	−	0.691093i
$956$	2.96502	+	5.13556i	0.0958956	+	0.166096i
$957$	−4.60705	+	2.65988i	−0.148925	+	0.0859818i
$958$	23.8865	+	13.7909i	0.771738	+	0.445563i
$959$	0.326249	−	0.565080i	0.0105351	−	0.0182474i
$960$	−0.0291655	−	0.968755i	−0.000941311	−	0.0312664i
$961$	−18.2407	−	31.5938i	−0.588410	−	1.01916i
$962$		−	2.20367i		−	0.0710492i
$963$			30.0449i			0.968184i
$964$	−4.91293	+	8.50944i	−0.158235	+	0.274071i
$965$	−0.464306	−	15.4223i	−0.0149465	−	0.496461i
$966$	0.195646	+	0.338869i	0.00629481	+	0.0109029i
$967$	51.7898	+	29.9009i	1.66545	+	0.961547i	0.970044	+	0.242929i	$0.0781083\pi$
$967$	51.7898	+	29.9009i	1.66545	+	0.961547i	0.695405	+	0.718618i	$0.255225\pi$
$968$	−3.35199	+	1.93527i	−0.107737	+	0.0622020i
$969$	6.24232	−	10.8120i	0.200532	−	0.347332i
$970$	−17.8694	+	33.2210i	−0.573752	+	1.06666i
$971$	25.7055	−	44.5232i	0.824929	−	1.42882i	−0.0770446	−	0.997028i	$-0.524548\pi$
$971$	25.7055	−	44.5232i	0.824929	−	1.42882i	0.901974	−	0.431791i	$-0.142118\pi$
$972$	−9.30193	−	5.37047i	−0.298360	−	0.172258i
$973$	−0.418536	−	0.241642i	−0.0134177	−	0.00774669i
$974$	−3.01766	+	5.22675i	−0.0966922	+	0.167476i
$975$	0.324537	+	0.491275i	0.0103935	+	0.0157334i
$976$	1.05220	−	1.82246i	0.0336800	−	0.0583354i
$977$	−18.0158	+	10.4014i	−0.576378	+	0.332772i	−0.759693	−	0.650282i	$-0.774651\pi$
$977$	−18.0158	+	10.4014i	−0.576378	+	0.332772i	0.183315	+	0.983054i	$0.441317\pi$
$978$		−	6.31208i		−	0.201838i
$979$	−13.8274	+	23.9498i	−0.441926	+	0.765438i
$980$	15.3741	−	0.462854i	0.491107	−	0.0147853i
$981$	33.6620			1.07474
$982$	−2.11718	+	1.22236i	−0.0675621	+	0.0390070i
$983$		−	54.5479i		−	1.73981i	−0.493223	−	0.869903i	$-0.664181\pi$
$983$		−	54.5479i		−	1.73981i	0.493223	−	0.869903i	$-0.335819\pi$
$984$	−0.00830009	+	0.0143762i	−0.000264597	+	0.000458296i
$985$	25.1209	+	13.5124i	0.800417	+	0.430540i
$986$	−15.9099	−	27.5567i	−0.506674	−	0.877585i
$987$	−0.652346	+	0.376632i	−0.0207644	+	0.0119883i
$988$	0.979013	−	0.565234i	0.0311466	−	0.0179825i
$989$	1.19881	+	2.07640i	0.0381199	+	0.0660256i
$990$	−0.505251	−	16.7823i	−0.0160579	−	0.533378i
$991$	−4.30580			−0.136778			−0.0683891	−	0.997659i	$-0.521786\pi$
$991$	−4.30580			−0.136778			−0.0683891	+	0.997659i	$0.521786\pi$
$992$	7.11415	−	4.10735i	0.225874	−	0.130409i
$993$	3.74012	+	2.15936i	0.118689	+	0.0685252i
$994$	2.58672	−	4.48033i	0.0820458	−	0.142108i
$995$	−9.81246	−	15.8726i	−0.311076	−	0.503194i
$996$	−6.08715			−0.192879
$997$		−	25.0958i		−	0.794793i	−0.917647	−	0.397396i	$-0.869914\pi$
$997$		−	25.0958i		−	0.794793i	0.917647	−	0.397396i	$-0.130086\pi$
$998$	−12.6803	−	7.32097i	−0.401388	−	0.231741i
$999$	−10.2167	−	17.6959i	−0.323243	−	0.559873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.h.c.439.6	yes	52
5.4	even	2	inner	670.2.h.c.439.21	yes	52
67.29	even	3	inner	670.2.h.c.29.19	yes	52
335.29	even	6	inner	670.2.h.c.29.8	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.h.c.29.8	✓	52	335.29	even	6	inner
670.2.h.c.29.19	yes	52	67.29	even	3	inner
670.2.h.c.439.6	yes	52	1.1	even	1	trivial
670.2.h.c.439.21	yes	52	5.4	even	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} -0.433437i q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.23506 + 0.0672889i) q^{5} +(0.216718 + 0.375367i) q^{6} +(0.301725 + 0.174201i) q^{7} +1.00000i q^{8} +2.81213 q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} -0.433437i q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.23506 + 0.0672889i) q^{5} +(0.216718 + 0.375367i) q^{6} +(0.301725 + 0.174201i) q^{7} +1.00000i q^{8} +2.81213 q^{9} +(1.90197 - 1.17580i) q^{10} +(1.33505 - 2.31238i) q^{11} +(-0.375367 - 0.216718i) q^{12} +(-0.235286 + 0.135843i) q^{13} -0.348402 q^{14} +(0.0291655 + 0.968755i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-5.99500 + 3.46121i) q^{17} +(-2.43538 + 1.40607i) q^{18} +(-2.08047 - 3.60348i) q^{19} +(-1.05925 + 1.96926i) q^{20} +(0.0755050 - 0.130778i) q^{21} +2.67010i q^{22} +(2.24402 - 1.29558i) q^{23} +0.433437 q^{24} +(4.99094 - 0.300789i) q^{25} +(0.135843 - 0.235286i) q^{26} -2.51919i q^{27} +(0.301725 - 0.174201i) q^{28} +(2.29831 - 3.98079i) q^{29} +(-0.509635 - 0.824383i) q^{30} +(4.10735 - 7.11415i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.00227 - 0.578661i) q^{33} +(3.46121 - 5.99500i) q^{34} +(-0.686093 - 0.369046i) q^{35} +(1.40607 - 2.43538i) q^{36} +(7.02444 - 4.05556i) q^{37} +(3.60348 + 2.08047i) q^{38} +(0.0588791 + 0.101982i) q^{39} +(-0.0672889 - 2.23506i) q^{40} +(-0.0191495 + 0.0331679i) q^{41} +0.151010i q^{42} +0.925304i q^{43} +(-1.33505 - 2.31238i) q^{44} +(-6.28527 + 0.189225i) q^{45} +(-1.29558 + 2.24402i) q^{46} +(-4.31988 - 2.49409i) q^{47} +(-0.375367 + 0.216718i) q^{48} +(-3.43931 - 5.95706i) q^{49} +(-4.17189 + 2.75596i) q^{50} +(1.50022 + 2.59845i) q^{51} +0.271685i q^{52} -12.8226i q^{53} +(1.25960 + 2.18168i) q^{54} +(-2.82832 + 5.25813i) q^{55} +(-0.174201 + 0.301725i) q^{56} +(-1.56188 + 0.901753i) q^{57} +4.59662i q^{58} +5.66170 q^{59} +(0.853549 + 0.459119i) q^{60} +(1.05220 + 1.82246i) q^{61} +8.21471i q^{62} +(0.848490 + 0.489876i) q^{63} -1.00000 q^{64} +(0.516737 - 0.319448i) q^{65} +1.15732 q^{66} +(-3.00282 - 7.61466i) q^{67} +6.92243i q^{68} +(-0.561553 - 0.972639i) q^{69} +(0.778697 - 0.0234436i) q^{70} +(-7.42454 + 12.8597i) q^{71} +2.81213i q^{72} +(3.59181 - 2.07373i) q^{73} +(-4.05556 + 7.02444i) q^{74} +(-0.130373 - 2.16326i) q^{75} -4.16095 q^{76} +(0.805636 - 0.465134i) q^{77} +(-0.101982 - 0.0588791i) q^{78} +(6.00648 - 10.4035i) q^{79} +(1.17580 + 1.90197i) q^{80} +7.34449 q^{81} -0.0382990i q^{82} +(12.1624 - 7.02197i) q^{83} +(-0.0755050 - 0.130778i) q^{84} +(13.1662 - 8.13940i) q^{85} +(-0.462652 - 0.801337i) q^{86} +(-1.72542 - 0.996172i) q^{87} +(2.31238 + 1.33505i) q^{88} -10.3572 q^{89} +(5.34859 - 3.30651i) q^{90} -0.0946556 q^{91} -2.59117i q^{92} +(-3.08353 - 1.78028i) q^{93} +4.98817 q^{94} +(4.89245 + 7.91399i) q^{95} +(0.216718 - 0.375367i) q^{96} +(-14.6097 + 8.43491i) q^{97} +(5.95706 + 3.43931i) q^{98} +(3.75434 - 6.50272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9}+O(q^{10}) \) 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9	\( 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9} - 10 q^{10} + 24 q^{11} + 24 q^{14} + 28 q^{15} - 26 q^{16} - 24 q^{19} - 8 q^{20} + 4 q^{21} - 12 q^{24} - 28 q^{25} + 4 q^{26} - 20 q^{29} - 10 q^{30} - 30 q^{31} - 16 q^{34} - 14 q^{35} - 24 q^{36} - 8 q^{39} - 20 q^{40} - 10 q^{41} - 24 q^{44} - 16 q^{45} - 8 q^{46} + 14 q^{49} - 8 q^{50} - 44 q^{51} + 42 q^{54} + 16 q^{55} + 12 q^{56} + 80 q^{59} + 14 q^{60} - 20 q^{61} - 52 q^{64} + 10 q^{65} - 40 q^{66} - 4 q^{69} + 48 q^{70} - 74 q^{71} + 34 q^{74} - 16 q^{75} - 48 q^{76} + 32 q^{79} + 8 q^{80} + 4 q^{81} - 4 q^{84} + 20 q^{85} + 12 q^{86} + 84 q^{89} - 30 q^{90} - 16 q^{91} + 136 q^{94} + 2 q^{95} - 6 q^{96} - 96 q^{99}+O(q^{100}) \) 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9 - 10 * q^10 + 24 * q^11 + 24 * q^14 + 28 * q^15 - 26 * q^16 - 24 * q^19 - 8 * q^20 + 4 * q^21 - 12 * q^24 - 28 * q^25 + 4 * q^26 - 20 * q^29 - 10 * q^30 - 30 * q^31 - 16 * q^34 - 14 * q^35 - 24 * q^36 - 8 * q^39 - 20 * q^40 - 10 * q^41 - 24 * q^44 - 16 * q^45 - 8 * q^46 + 14 * q^49 - 8 * q^50 - 44 * q^51 + 42 * q^54 + 16 * q^55 + 12 * q^56 + 80 * q^59 + 14 * q^60 - 20 * q^61 - 52 * q^64 + 10 * q^65 - 40 * q^66 - 4 * q^69 + 48 * q^70 - 74 * q^71 + 34 * q^74 - 16 * q^75 - 48 * q^76 + 32 * q^79 + 8 * q^80 + 4 * q^81 - 4 * q^84 + 20 * q^85 + 12 * q^86 + 84 * q^89 - 30 * q^90 - 16 * q^91 + 136 * q^94 + 2 * q^95 - 6 * q^96 - 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more