LMFDB - Embedded newform 930.2.o.e.161.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.4
Character	$\chi$	$=$	930.161
Dual form			930.2.o.e.491.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.474351 - 1.66583i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.66583 + 0.474351i) q^{6} +(1.75266 + 3.03570i) q^{7} +1.00000i q^{8} +(-2.54998 + 1.58038i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.474351 - 1.66583i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.66583 + 0.474351i) q^{6} +(1.75266 + 3.03570i) q^{7} +1.00000i q^{8} +(-2.54998 + 1.58038i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.508798 - 0.881264i) q^{11} +(0.474351 + 1.66583i) q^{12} +(-0.482279 - 0.278444i) q^{13} +(3.03570 - 1.75266i) q^{14} +(0.422115 - 1.67983i) q^{15} +1.00000 q^{16} +(0.748115 + 1.29577i) q^{17} +(1.58038 + 2.54998i) q^{18} +(2.58309 + 4.47405i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(4.22558 - 4.35962i) q^{21} +(-0.881264 - 0.508798i) q^{22} +3.21814 q^{23} +(1.66583 - 0.474351i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.278444 + 0.482279i) q^{26} +(3.84223 + 3.49818i) q^{27} +(-1.75266 - 3.03570i) q^{28} +2.64442 q^{29} +(-1.67983 - 0.422115i) q^{30} +(5.39138 - 1.39033i) q^{31} -1.00000i q^{32} +(-1.70939 - 0.429543i) q^{33} +(1.29577 - 0.748115i) q^{34} +3.50532i q^{35} +(2.54998 - 1.58038i) q^{36} +(2.08724 - 1.20507i) q^{37} +(4.47405 - 2.58309i) q^{38} +(-0.235071 + 0.935475i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(7.86397 + 4.54027i) q^{41} +(-4.35962 - 4.22558i) q^{42} +(-5.69715 + 3.28925i) q^{43} +(-0.508798 + 0.881264i) q^{44} +(-2.99854 + 0.0936563i) q^{45} -3.21814i q^{46} -8.95636i q^{47} +(-0.474351 - 1.66583i) q^{48} +(-2.64364 + 4.57892i) q^{49} +(0.866025 - 0.500000i) q^{50} +(1.80367 - 1.86088i) q^{51} +(0.482279 + 0.278444i) q^{52} +(1.80684 - 3.12954i) q^{53} +(3.49818 - 3.84223i) q^{54} +(0.881264 - 0.508798i) q^{55} +(-3.03570 + 1.75266i) q^{56} +(6.22771 - 6.42526i) q^{57} -2.64442i q^{58} +(-8.22333 + 4.74774i) q^{59} +(-0.422115 + 1.67983i) q^{60} +0.662787i q^{61} +(-1.39033 - 5.39138i) q^{62} +(-9.26680 - 4.97111i) q^{63} -1.00000 q^{64} +(-0.278444 - 0.482279i) q^{65} +(-0.429543 + 1.70939i) q^{66} +(0.768714 - 1.33145i) q^{67} +(-0.748115 - 1.29577i) q^{68} +(-1.52653 - 5.36088i) q^{69} +3.50532 q^{70} +(-9.71728 - 5.61027i) q^{71} +(-1.58038 - 2.54998i) q^{72} +(-5.23937 - 3.02495i) q^{73} +(-1.20507 - 2.08724i) q^{74} +(1.20548 - 1.24372i) q^{75} +(-2.58309 - 4.47405i) q^{76} +3.56700 q^{77} +(0.935475 + 0.235071i) q^{78} +(0.184595 - 0.106576i) q^{79} +(0.866025 + 0.500000i) q^{80} +(4.00481 - 8.05987i) q^{81} +(4.54027 - 7.86397i) q^{82} +(1.71612 - 2.97241i) q^{83} +(-4.22558 + 4.35962i) q^{84} +1.49623i q^{85} +(3.28925 + 5.69715i) q^{86} +(-1.25438 - 4.40515i) q^{87} +(0.881264 + 0.508798i) q^{88} -0.779533 q^{89} +(0.0936563 + 2.99854i) q^{90} -1.95207i q^{91} -3.21814 q^{92} +(-4.87346 - 8.32162i) q^{93} -8.95636 q^{94} +5.16618i q^{95} +(-1.66583 + 0.474351i) q^{96} +13.2793 q^{97} +(4.57892 + 2.64364i) q^{98} +(0.0953043 + 3.05130i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.474351	−	1.66583i	−0.273867	−	0.961768i
$3$	−0.474351	−	1.66583i	−0.273867	−	0.961768i
$4$	−1.00000			−0.500000
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−1.66583	+	0.474351i	−0.680072	+	0.193653i
$7$	1.75266	+	3.03570i	0.662443	+	1.14739i	0.979972	+	0.199137i	$0.0638138\pi$
$7$	1.75266	+	3.03570i	0.662443	+	1.14739i	−0.317528	+	0.948249i	$0.602853\pi$
$8$			1.00000i			0.353553i
$9$	−2.54998	+	1.58038i	−0.849994	+	0.526793i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	0.508798	−	0.881264i	0.153408	−	0.265711i	−0.779070	−	0.626937i	$-0.784308\pi$
$11$	0.508798	−	0.881264i	0.153408	−	0.265711i	0.932478	+	0.361226i	$0.117642\pi$
$12$	0.474351	+	1.66583i	0.136933	+	0.480884i
$13$	−0.482279	−	0.278444i	−0.133760	−	0.0772264i	0.431627	−	0.902052i	$-0.357940\pi$
$13$	−0.482279	−	0.278444i	−0.133760	−	0.0772264i	−0.565387	+	0.824826i	$0.691273\pi$
$14$	3.03570	−	1.75266i	0.811324	−	0.468418i
$15$	0.422115	−	1.67983i	0.108990	−	0.433729i
$16$	1.00000			0.250000
$17$	0.748115	+	1.29577i	0.181445	+	0.314271i	0.942373	−	0.334565i	$-0.108589\pi$
$17$	0.748115	+	1.29577i	0.181445	+	0.314271i	−0.760928	+	0.648836i	$0.775256\pi$
$18$	1.58038	+	2.54998i	0.372499	+	0.601036i
$19$	2.58309	+	4.47405i	0.592602	+	1.02642i	0.993880	+	0.110461i	$0.0352326\pi$
$19$	2.58309	+	4.47405i	0.592602	+	1.02642i	−0.401278	+	0.915956i	$0.631434\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	4.22558	−	4.35962i	0.922097	−	0.951348i
$22$	−0.881264	−	0.508798i	−0.187886	−	0.108476i
$23$	3.21814			0.671029			0.335515	−	0.942035i	$-0.391090\pi$
$23$	3.21814			0.671029			0.335515	+	0.942035i	$0.391090\pi$
$24$	1.66583	−	0.474351i	0.340036	−	0.0968266i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.278444	+	0.482279i	−0.0546073	+	0.0945827i
$27$	3.84223	+	3.49818i	0.739437	+	0.673226i
$28$	−1.75266	−	3.03570i	−0.331222	−	0.573693i
$29$	2.64442			0.491056			0.245528	−	0.969389i	$-0.421039\pi$
$29$	2.64442			0.491056			0.245528	+	0.969389i	$0.421039\pi$
$30$	−1.67983	−	0.422115i	−0.306693	−	0.0770673i
$31$	5.39138	−	1.39033i	0.968320	−	0.249711i
$31$	5.39138	−	1.39033i	0.968320	−	0.249711i
$32$		−	1.00000i		−	0.176777i
$33$	−1.70939	−	0.429543i	−0.297566	−	0.0747738i
$34$	1.29577	−	0.748115i	0.222223	−	0.128301i
$35$			3.50532i			0.592507i
$36$	2.54998	−	1.58038i	0.424997	−	0.263396i
$37$	2.08724	−	1.20507i	0.343140	−	0.198112i	−0.318520	−	0.947916i	$-0.603186\pi$
$37$	2.08724	−	1.20507i	0.343140	−	0.198112i	0.661660	+	0.749804i	$0.269852\pi$
$38$	4.47405	−	2.58309i	0.725786	−	0.419033i
$39$	−0.235071	+	0.935475i	−0.0376414	+	0.149796i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	7.86397	+	4.54027i	1.22815	+	0.709070i	0.966642	−	0.256132i	$-0.0824481\pi$
$41$	7.86397	+	4.54027i	1.22815	+	0.709070i	0.261504	+	0.965202i	$0.415781\pi$
$42$	−4.35962	−	4.22558i	−0.672704	−	0.652021i
$43$	−5.69715	+	3.28925i	−0.868807	+	0.501606i	−0.866952	−	0.498392i	$-0.833924\pi$
$43$	−5.69715	+	3.28925i	−0.868807	+	0.501606i	−0.00185547	+	0.999998i	$0.500591\pi$
$44$	−0.508798	+	0.881264i	−0.0767042	+	0.132856i
$45$	−2.99854	+	0.0936563i	−0.446996	+	0.0139615i
$46$		−	3.21814i		−	0.474489i
$47$		−	8.95636i		−	1.30642i	−0.757177	−	0.653210i	$-0.773422\pi$
$47$		−	8.95636i		−	1.30642i	0.757177	−	0.653210i	$-0.226578\pi$
$48$	−0.474351	−	1.66583i	−0.0684667	−	0.240442i
$49$	−2.64364	+	4.57892i	−0.377663	+	0.654131i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	1.80367	−	1.86088i	0.252564	−	0.260576i
$52$	0.482279	+	0.278444i	0.0668800	+	0.0386132i
$53$	1.80684	−	3.12954i	0.248189	−	0.429876i	−0.714834	−	0.699294i	$-0.753498\pi$
$53$	1.80684	−	3.12954i	0.248189	−	0.429876i	0.963023	+	0.269418i	$0.0868313\pi$
$54$	3.49818	−	3.84223i	0.476042	−	0.522861i
$55$	0.881264	−	0.508798i	0.118830	−	0.0686063i
$56$	−3.03570	+	1.75266i	−0.405662	+	0.234209i
$57$	6.22771	−	6.42526i	0.824880	−	0.851047i
$58$		−	2.64442i		−	0.347229i
$59$	−8.22333	+	4.74774i	−1.07059	+	0.618103i	−0.928342	−	0.371728i	$-0.878765\pi$
$59$	−8.22333	+	4.74774i	−1.07059	+	0.618103i	−0.142245	+	0.989832i	$0.545432\pi$
$60$	−0.422115	+	1.67983i	−0.0544948	+	0.216865i
$61$			0.662787i			0.0848612i	0.999099	+	0.0424306i	$0.0135101\pi$
$61$			0.662787i			0.0848612i	−0.999099	+	0.0424306i	$0.986490\pi$
$62$	−1.39033	−	5.39138i	−0.176572	−	0.684706i
$63$	−9.26680	−	4.97111i	−1.16751	−	0.626301i
$64$	−1.00000			−0.125000
$65$	−0.278444	−	0.482279i	−0.0345367	−	0.0598193i
$66$	−0.429543	+	1.70939i	−0.0528730	+	0.210411i
$67$	0.768714	−	1.33145i	0.0939133	−	0.162663i	−0.815241	−	0.579122i	$-0.803396\pi$
$67$	0.768714	−	1.33145i	0.0939133	−	0.162663i	0.909155	+	0.416459i	$0.136729\pi$
$68$	−0.748115	−	1.29577i	−0.0907223	−	0.157136i
$69$	−1.52653	−	5.36088i	−0.183773	−	0.645374i
$70$	3.50532			0.418966
$71$	−9.71728	−	5.61027i	−1.15323	−	0.665817i	−0.203557	−	0.979063i	$-0.565250\pi$
$71$	−9.71728	−	5.61027i	−1.15323	−	0.665817i	−0.949672	+	0.313246i	$0.898584\pi$
$72$	−1.58038	−	2.54998i	−0.186249	−	0.300518i
$73$	−5.23937	−	3.02495i	−0.613222	−	0.354044i	0.161003	−	0.986954i	$-0.448527\pi$
$73$	−5.23937	−	3.02495i	−0.613222	−	0.354044i	−0.774225	+	0.632910i	$0.781860\pi$
$74$	−1.20507	−	2.08724i	−0.140086	−	0.242637i
$75$	1.20548	−	1.24372i	0.139196	−	0.143612i
$76$	−2.58309	−	4.47405i	−0.296301	−	0.513208i
$77$	3.56700			0.406498
$78$	0.935475	+	0.235071i	0.105922	+	0.0266165i
$79$	0.184595	−	0.106576i	0.0207686	−	0.0119907i	−0.489580	−	0.871959i	$-0.662850\pi$
$79$	0.184595	−	0.106576i	0.0207686	−	0.0119907i	0.510348	+	0.859968i	$0.329516\pi$
$80$	0.866025	+	0.500000i	0.0968246	+	0.0559017i
$81$	4.00481	−	8.05987i	0.444979	−	0.895541i
$82$	4.54027	−	7.86397i	0.501389	−	0.868430i
$83$	1.71612	−	2.97241i	0.188369	−	0.326264i	−0.756338	−	0.654181i	$-0.773013\pi$
$83$	1.71612	−	2.97241i	0.188369	−	0.326264i	0.944707	+	0.327917i	$0.106347\pi$
$84$	−4.22558	+	4.35962i	−0.461049	+	0.475674i
$85$			1.49623i			0.162289i
$86$	3.28925	+	5.69715i	0.354689	+	0.614339i
$87$	−1.25438	−	4.40515i	−0.134484	−	0.472282i
$88$	0.881264	+	0.508798i	0.0939431	+	0.0542381i
$89$	−0.779533			−0.0826303			−0.0413152	−	0.999146i	$-0.513155\pi$
$89$	−0.779533			−0.0826303			−0.0413152	+	0.999146i	$0.513155\pi$
$90$	0.0936563	+	2.99854i	0.00987224	+	0.316074i
$91$		−	1.95207i		−	0.204633i
$92$	−3.21814			−0.335515
$93$	−4.87346	−	8.32162i	−0.505355	−	0.862912i
$94$	−8.95636			−0.923778
$95$			5.16618i			0.530039i
$96$	−1.66583	+	0.474351i	−0.170018	+	0.0484133i
$97$	13.2793			1.34831			0.674155	−	0.738590i	$-0.264508\pi$
$97$	13.2793			1.34831			0.674155	+	0.738590i	$0.264508\pi$
$98$	4.57892	+	2.64364i	0.462540	+	0.267048i
$99$	0.0953043	+	3.05130i	0.00957845	+	0.306667i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$			17.5078i			1.74209i	0.491200	+	0.871047i	$0.336558\pi$
$101$			17.5078i			1.74209i	−0.491200	+	0.871047i	$0.663442\pi$
$102$	−1.86088	−	1.80367i	−0.184255	−	0.178590i
$103$	−0.217920	+	0.377449i	−0.0214723	+	0.0371911i	−0.876562	−	0.481289i	$-0.840169\pi$
$103$	−0.217920	+	0.377449i	−0.0214723	+	0.0371911i	0.855090	+	0.518480i	$0.173502\pi$
$104$	0.278444	−	0.482279i	0.0273037	−	0.0472913i
$105$	5.83927	−	1.66275i	0.569854	−	0.162268i
$106$	−3.12954	−	1.80684i	−0.303968	−	0.175496i
$107$	−15.5778	+	8.99386i	−1.50596	+	0.869469i	−0.505988	+	0.862540i	$0.668872\pi$
$107$	−15.5778	+	8.99386i	−1.50596	+	0.869469i	−0.999976	+	0.00692852i	$0.997795\pi$
$108$	−3.84223	−	3.49818i	−0.369719	−	0.336613i
$109$	7.55577			0.723711			0.361856	−	0.932234i	$-0.382143\pi$
$109$	7.55577			0.723711			0.361856	+	0.932234i	$0.382143\pi$
$110$	−0.508798	−	0.881264i	−0.0485120	−	0.0840252i
$111$	−2.99752	−	2.90536i	−0.284512	−	0.275765i
$112$	1.75266	+	3.03570i	0.165611	+	0.286846i
$113$	4.18028	+	2.41348i	0.393247	+	0.227041i	0.683566	−	0.729889i	$-0.260428\pi$
$113$	4.18028	+	2.41348i	0.393247	+	0.227041i	−0.290319	+	0.956930i	$0.593761\pi$
$114$	−6.42526	−	6.22771i	−0.601781	−	0.583279i
$115$	2.78699	+	1.60907i	0.259888	+	0.150047i
$116$	−2.64442			−0.245528
$117$	1.66985	−	0.0521560i	0.154378	−	0.00482183i
$118$	4.74774	+	8.22333i	0.437065	+	0.757019i
$119$	−2.62238	+	4.54210i	−0.240394	+	0.416374i
$120$	1.67983	+	0.422115i	0.153347	+	0.0385336i
$121$	4.98225	+	8.62951i	0.452932	+	0.784501i
$122$	0.662787			0.0600059
$123$	3.83303	−	15.2537i	0.345613	−	1.37538i
$124$	−5.39138	+	1.39033i	−0.484160	+	0.124855i
$125$			1.00000i			0.0894427i
$126$	−4.97111	+	9.26680i	−0.442861	+	0.825552i
$127$	16.3303	−	9.42828i	1.44908	−	0.836624i	0.450650	−	0.892701i	$-0.351192\pi$
$127$	16.3303	−	9.42828i	1.44908	−	0.836624i	0.998426	+	0.0560764i	$0.0178590\pi$
$128$			1.00000i			0.0883883i
$129$	8.18178	+	7.93022i	0.720366	+	0.698217i
$130$	−0.482279	+	0.278444i	−0.0422987	+	0.0244211i
$131$	−0.711541	+	0.410808i	−0.0621676	+	0.0358925i	−0.530762	−	0.847521i	$-0.678094\pi$
$131$	−0.711541	+	0.410808i	−0.0621676	+	0.0358925i	0.468594	+	0.883414i	$0.344761\pi$
$132$	1.70939	+	0.429543i	0.148783	+	0.0373869i
$133$	−9.05457	+	15.6830i	−0.785131	+	1.35989i
$134$	−1.33145	−	0.768714i	−0.115020	−	0.0664067i
$135$	1.57838	+	4.95063i	0.135845	+	0.426082i
$136$	−1.29577	+	0.748115i	−0.111112	+	0.0641503i
$137$	9.97643	−	17.2797i	0.852344	−	1.47630i	−0.0267437	−	0.999642i	$-0.508514\pi$
$137$	9.97643	−	17.2797i	0.852344	−	1.47630i	0.879087	−	0.476660i	$-0.158153\pi$
$138$	−5.36088	+	1.52653i	−0.456348	+	0.129947i
$139$		−	1.22089i		−	0.103555i	−0.998659	−	0.0517773i	$-0.983511\pi$
$139$		−	1.22089i		−	0.103555i	0.998659	−	0.0517773i	$-0.0164886\pi$
$140$		−	3.50532i		−	0.296254i
$141$	−14.9198	+	4.24846i	−1.25647	+	0.357785i
$142$	−5.61027	+	9.71728i	−0.470804	+	0.815456i
$143$	−0.490765	+	0.283343i	−0.0410398	+	0.0236944i
$144$	−2.54998	+	1.58038i	−0.212498	+	0.131698i
$145$	2.29013	+	1.32221i	0.190185	+	0.109804i
$146$	−3.02495	+	5.23937i	−0.250347	+	0.433614i
$147$	8.88171	+	2.23184i	0.732551	+	0.184079i
$148$	−2.08724	+	1.20507i	−0.171570	+	0.0990560i
$149$	−16.6142	+	9.59220i	−1.36109	+	0.785823i	−0.989768	−	0.142683i	$-0.954427\pi$
$149$	−16.6142	+	9.59220i	−1.36109	+	0.785823i	−0.371317	+	0.928506i	$0.621094\pi$
$150$	−1.24372	−	1.20548i	−0.101549	−	0.0984267i
$151$			23.3009i			1.89620i	0.317971	+	0.948100i	$0.396998\pi$
$151$			23.3009i			1.89620i	−0.317971	+	0.948100i	$0.603002\pi$
$152$	−4.47405	+	2.58309i	−0.362893	+	0.209516i
$153$	−3.95549	−	2.12189i	−0.319783	−	0.171545i
$154$		−	3.56700i		−	0.287437i
$155$	5.36424	+	1.49163i	0.430866	+	0.119810i
$156$	0.235071	−	0.935475i	0.0188207	−	0.0748979i
$157$	10.7418			0.857290			0.428645	−	0.903473i	$-0.358991\pi$
$157$	10.7418			0.857290			0.428645	+	0.903473i	$0.358991\pi$
$158$	−0.106576	−	0.184595i	−0.00847874	−	0.0146856i
$159$	−6.07037	−	1.52539i	−0.481411	−	0.120971i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	5.64031	+	9.76931i	0.444519	+	0.769929i
$162$	−8.05987	−	4.00481i	−0.633243	−	0.314648i
$163$	−3.56174			−0.278977			−0.139488	−	0.990224i	$-0.544546\pi$
$163$	−3.56174			−0.278977			−0.139488	+	0.990224i	$0.544546\pi$
$164$	−7.86397	−	4.54027i	−0.614073	−	0.354535i
$165$	−1.26560	−	1.22669i	−0.0985268	−	0.0954975i
$166$	−2.97241	−	1.71612i	−0.230704	−	0.133197i
$167$	−5.75062	−	9.96036i	−0.444996	−	0.770756i	0.553056	−	0.833144i	$-0.313462\pi$
$167$	−5.75062	−	9.96036i	−0.444996	−	0.770756i	−0.998052	+	0.0623883i	$0.980128\pi$
$168$	4.35962	+	4.22558i	0.336352	+	0.326011i
$169$	−6.34494	−	10.9898i	−0.488072	−	0.845366i
$170$	1.49623			0.114756
$171$	−13.6575	−	7.32648i	−1.04442	−	0.560270i
$172$	5.69715	−	3.28925i	0.434404	−	0.250803i
$173$	2.03876	+	1.17708i	0.155004	+	0.0894917i	0.575496	−	0.817805i	$-0.304809\pi$
$173$	2.03876	+	1.17708i	0.155004	+	0.0894917i	−0.420492	+	0.907296i	$0.638142\pi$
$174$	−4.40515	+	1.25438i	−0.333954	+	0.0950946i
$175$	−1.75266	+	3.03570i	−0.132489	+	0.229477i
$176$	0.508798	−	0.881264i	0.0383521	−	0.0664278i
$177$	11.8097	+	11.4466i	0.887670	+	0.860377i
$178$			0.779533i			0.0584285i
$179$	1.49415	+	2.58794i	0.111678	+	0.193432i	0.916447	−	0.400156i	$-0.131044\pi$
$179$	1.49415	+	2.58794i	0.111678	+	0.193432i	−0.804769	+	0.593588i	$0.797711\pi$
$180$	2.99854	−	0.0936563i	0.223498	−	0.00698073i
$181$	18.9344	+	10.9318i	1.40738	+	0.812552i	0.995135	−	0.0985208i	$-0.0314111\pi$
$181$	18.9344	+	10.9318i	1.40738	+	0.812552i	0.412246	+	0.911073i	$0.364744\pi$
$182$	−1.95207			−0.144697
$183$	1.10409	−	0.314394i	0.0816167	−	0.0232407i
$184$			3.21814i			0.237245i
$185$	2.41014			0.177197
$186$	−8.32162	+	4.87346i	−0.610171	+	0.357340i
$187$	1.52256			0.111340
$188$			8.95636i			0.653210i
$189$	−3.88530	+	17.7950i	−0.282614	+	1.29439i
$190$	5.16618			0.374794
$191$	−8.08961	−	4.67054i	−0.585343	−	0.337948i	0.177911	−	0.984047i	$-0.443066\pi$
$191$	−8.08961	−	4.67054i	−0.585343	−	0.337948i	−0.763254	+	0.646099i	$0.776400\pi$
$192$	0.474351	+	1.66583i	0.0342334	+	0.120221i
$193$	−0.846405	−	1.46602i	−0.0609256	−	0.105526i	0.833954	−	0.551834i	$-0.186072\pi$
$193$	−0.846405	−	1.46602i	−0.0609256	−	0.105526i	−0.894879	+	0.446308i	$0.852739\pi$
$194$		−	13.2793i		−	0.953400i
$195$	−0.671315	+	0.692610i	−0.0480738	+	0.0495988i
$196$	2.64364	−	4.57892i	0.188831	−	0.327065i
$197$	7.92946	−	13.7342i	0.564951	−	0.978524i	−0.432103	−	0.901824i	$-0.642228\pi$
$197$	7.92946	−	13.7342i	0.564951	−	0.978524i	0.997054	−	0.0766996i	$-0.0244383\pi$
$198$	3.05130	−	0.0953043i	0.216847	−	0.00677298i
$199$	−11.7826	−	6.80268i	−0.835246	−	0.482229i	0.0203995	−	0.999792i	$-0.493506\pi$
$199$	−11.7826	−	6.80268i	−0.835246	−	0.482229i	−0.855645	+	0.517562i	$0.826840\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	−2.58261	−	0.648971i	−0.182163	−	0.0457749i
$202$	17.5078			1.23185
$203$	4.63477	+	8.02765i	0.325297	+	0.563431i
$204$	−1.80367	+	1.86088i	−0.126282	+	0.130288i
$205$	4.54027	+	7.86397i	0.317106	+	0.549244i
$206$	0.377449	+	0.217920i	0.0262981	+	0.0151832i
$207$	−8.20621	+	5.08588i	−0.570371	+	0.353493i
$208$	−0.482279	−	0.278444i	−0.0334400	−	0.0193066i
$209$	5.25709			0.363641
$210$	−1.66275	−	5.83927i	−0.114741	−	0.402948i
$211$	−4.46360	−	7.73118i	−0.307287	−	0.532236i	0.670481	−	0.741927i	$-0.266088\pi$
$211$	−4.46360	−	7.73118i	−0.307287	−	0.532236i	−0.977768	+	0.209690i	$0.932754\pi$
$212$	−1.80684	+	3.12954i	−0.124094	+	0.214938i
$213$	−4.73636	+	18.8486i	−0.324530	+	1.29148i
$214$	8.99386	+	15.5778i	0.614807	+	1.06488i
$215$	−6.57850			−0.448650
$216$	−3.49818	+	3.84223i	−0.238021	+	0.261431i
$217$	13.6699	+	13.9298i	0.927972	+	0.945618i
$218$		−	7.55577i		−	0.511741i
$219$	−2.55376	+	10.1628i	−0.172567	+	0.686738i
$220$	−0.881264	+	0.508798i	−0.0594148	+	0.0343032i
$221$		−	0.833232i		−	0.0560493i
$222$	−2.90536	+	2.99752i	−0.194995	+	0.201181i
$223$	6.97582	−	4.02749i	0.467136	−	0.269701i	−0.247904	−	0.968785i	$-0.579742\pi$
$223$	6.97582	−	4.02749i	0.467136	−	0.269701i	0.715040	+	0.699084i	$0.246408\pi$
$224$	3.03570	−	1.75266i	0.202831	−	0.117105i
$225$	−2.64364	−	1.41816i	−0.176243	−	0.0945440i
$226$	2.41348	−	4.18028i	0.160543	−	0.278068i
$227$	−15.0890	−	8.71161i	−1.00149	−	0.578210i	−0.0928007	−	0.995685i	$-0.529582\pi$
$227$	−15.0890	−	8.71161i	−1.00149	−	0.578210i	−0.908689	+	0.417475i	$0.862915\pi$
$228$	−6.22771	+	6.42526i	−0.412440	+	0.425524i
$229$	−12.2125	+	7.05087i	−0.807023	+	0.465935i	−0.845921	−	0.533308i	$-0.820949\pi$
$229$	−12.2125	+	7.05087i	−0.807023	+	0.465935i	0.0388982	+	0.999243i	$0.487615\pi$
$230$	1.60907	−	2.78699i	0.106099	−	0.183769i
$231$	−1.69201	−	5.94202i	−0.111326	−	0.390956i
$232$			2.64442i			0.173615i
$233$		−	2.39244i		−	0.156734i	−0.996925	−	0.0783669i	$-0.975029\pi$
$233$		−	2.39244i		−	0.156734i	0.996925	−	0.0783669i	$-0.0249706\pi$
$234$	−0.0521560	−	1.66985i	−0.00340955	−	0.109161i
$235$	4.47818	−	7.75644i	0.292124	−	0.505974i
$236$	8.22333	−	4.74774i	0.535293	−	0.309052i
$237$	−0.265101	−	0.256950i	−0.0172201	−	0.0166907i
$238$	4.54210	+	2.62238i	0.294421	+	0.169984i
$239$	−5.50979	+	9.54323i	−0.356398	+	0.617300i	−0.987356	−	0.158517i	$-0.949329\pi$
$239$	−5.50979	+	9.54323i	−0.356398	+	0.617300i	0.630958	+	0.775817i	$0.282662\pi$
$240$	0.422115	−	1.67983i	0.0272474	−	0.108432i
$241$	21.5818	−	12.4602i	1.39020	−	0.802634i	0.396866	−	0.917877i	$-0.370098\pi$
$241$	21.5818	−	12.4602i	1.39020	−	0.802634i	0.993337	+	0.115243i	$0.0367646\pi$
$242$	8.62951	−	4.98225i	0.554726	−	0.320271i
$243$	−15.3261	−	2.84813i	−0.983167	−	0.182708i
$244$		−	0.662787i		−	0.0424306i
$245$	−4.57892	+	2.64364i	−0.292536	+	0.168896i
$246$	−15.2537	−	3.83303i	−0.972542	−	0.244385i
$247$		−	2.87698i		−	0.183058i
$248$	1.39033	+	5.39138i	0.0882861	+	0.342353i
$249$	−5.76557	−	1.44880i	−0.365378	−	0.0918140i
$250$	1.00000			0.0632456
$251$	6.60787	+	11.4452i	0.417085	+	0.722413i	0.995645	−	0.0932274i	$-0.0297183\pi$
$251$	6.60787	+	11.4452i	0.417085	+	0.722413i	−0.578560	+	0.815640i	$0.696385\pi$
$252$	9.26680	+	4.97111i	0.583754	+	0.313150i
$253$	1.63739	−	2.83603i	0.102942	−	0.178300i
$254$	−9.42828	−	16.3303i	−0.591583	−	1.02465i
$255$	2.49247	−	0.709739i	0.156084	−	0.0444456i
$256$	1.00000			0.0625000
$257$	−22.1051	−	12.7624i	−1.37888	−	0.796096i	−0.386855	−	0.922141i	$-0.626439\pi$
$257$	−22.1051	−	12.7624i	−1.37888	−	0.796096i	−0.992025	+	0.126044i	$0.959772\pi$
$258$	7.93022	−	8.18178i	0.493714	−	0.509376i
$259$	7.31644	+	4.22415i	0.454622	+	0.262476i
$260$	0.278444	+	0.482279i	0.0172684	+	0.0299097i
$261$	−6.74322	+	4.17918i	−0.417395	+	0.258685i
$262$	0.410808	+	0.711541i	0.0253798	+	0.0439591i
$263$	−17.3755			−1.07142			−0.535709	−	0.844403i	$-0.679956\pi$
$263$	−17.3755			−1.07142			−0.535709	+	0.844403i	$0.679956\pi$
$264$	0.429543	−	1.70939i	0.0264365	−	0.105205i
$265$	3.12954	−	1.80684i	0.192246	−	0.110993i
$266$	15.6830	+	9.05457i	0.961585	+	0.555171i
$267$	0.369773	+	1.29857i	0.0226297	+	0.0794712i
$268$	−0.768714	+	1.33145i	−0.0469567	+	0.0813313i
$269$	5.43030	−	9.40555i	0.331091	−	0.573466i	−0.651635	−	0.758533i	$-0.725917\pi$
$269$	5.43030	−	9.40555i	0.331091	−	0.573466i	0.982726	+	0.185066i	$0.0592499\pi$
$270$	4.95063	−	1.57838i	0.301286	−	0.0960569i
$271$			0.444297i			0.0269891i	0.999909	+	0.0134945i	$0.00429558\pi$
$271$			0.444297i			0.0269891i	−0.999909	+	0.0134945i	$0.995704\pi$
$272$	0.748115	+	1.29577i	0.0453611	+	0.0785678i
$273$	−3.25182	+	0.925967i	−0.196809	+	0.0560421i
$274$	−17.2797	−	9.97643i	−1.04390	−	0.602698i
$275$	1.01760			0.0613634
$276$	1.52653	+	5.36088i	0.0918863	+	0.322687i
$277$			8.03697i			0.482895i	0.970414	+	0.241447i	$0.0776221\pi$
$277$			8.03697i			0.482895i	−0.970414	+	0.241447i	$0.922378\pi$
$278$	−1.22089			−0.0732242
$279$	−11.5507	+	12.0657i	−0.691521	+	0.722357i
$280$	−3.50532			−0.209483
$281$			13.9273i			0.830831i	0.909632	+	0.415415i	$0.136364\pi$
$281$			13.9273i			0.830831i	−0.909632	+	0.415415i	$0.863636\pi$
$282$	4.24846	+	14.9198i	0.252992	+	0.888460i
$283$	−28.1351			−1.67246			−0.836230	−	0.548379i	$-0.815245\pi$
$283$	−28.1351			−1.67246			−0.836230	+	0.548379i	$0.815245\pi$
$284$	9.71728	+	5.61027i	0.576614	+	0.332909i
$285$	8.60599	−	2.45059i	0.509775	−	0.145160i
$286$	0.283343	+	0.490765i	0.0167544	+	0.0290195i
$287$			31.8302i			1.87888i
$288$	1.58038	+	2.54998i	0.0931246	+	0.150259i
$289$	7.38065	−	12.7837i	0.434156	−	0.751980i
$290$	1.32221	−	2.29013i	0.0776428	−	0.134481i
$291$	−6.29906	−	22.1211i	−0.369258	−	1.29676i
$292$	5.23937	+	3.02495i	0.306611	+	0.177022i
$293$	−19.0627	+	11.0058i	−1.11365	+	0.642968i	−0.939773	−	0.341799i	$-0.888964\pi$
$293$	−19.0627	+	11.0058i	−1.11365	+	0.642968i	−0.173880	+	0.984767i	$0.555630\pi$
$294$	2.23184	−	8.88171i	0.130163	−	0.517992i
$295$	−9.49548			−0.552848
$296$	1.20507	+	2.08724i	0.0700431	+	0.121318i
$297$	5.03774	−	1.60615i	0.292319	−	0.0931982i
$298$	9.59220	+	16.6142i	0.555661	+	0.962433i
$299$	−1.55204	−	0.896072i	−0.0897569	−	0.0518212i
$300$	−1.20548	+	1.24372i	−0.0695982	+	0.0718059i
$301$	−19.9703	−	11.5299i	−1.15107	−	0.664571i
$302$	23.3009			1.34082
$303$	29.1651	−	8.30486i	1.67549	−	0.477102i
$304$	2.58309	+	4.47405i	0.148151	+	0.256604i
$305$	−0.331394	+	0.573990i	−0.0189755	+	0.0328666i
$306$	−2.12189	+	3.95549i	−0.121301	+	0.226120i
$307$	−2.89082	−	5.00704i	−0.164988	−	0.285767i	0.771663	−	0.636031i	$-0.219425\pi$
$307$	−2.89082	−	5.00704i	−0.164988	−	0.285767i	−0.936651	+	0.350264i	$0.886092\pi$
$308$	−3.56700			−0.203249
$309$	0.732136	+	0.183975i	0.0416498	+	0.0104660i
$310$	1.49163	−	5.36424i	0.0847188	−	0.304668i
$311$			0.448742i			0.0254458i	0.999919	+	0.0127229i	$0.00404994\pi$
$311$			0.448742i			0.0254458i	−0.999919	+	0.0127229i	$0.995950\pi$
$312$	−0.935475	−	0.235071i	−0.0529608	−	0.0133082i
$313$	15.1343	−	8.73777i	0.855439	−	0.493888i	−0.00704303	−	0.999975i	$-0.502242\pi$
$313$	15.1343	−	8.73777i	0.855439	−	0.493888i	0.862482	+	0.506087i	$0.168909\pi$
$314$		−	10.7418i		−	0.606196i
$315$	−5.53973	−	8.93850i	−0.312128	−	0.503628i
$316$	−0.184595	+	0.106576i	−0.0103843	+	0.00599537i
$317$	1.12178	−	0.647660i	0.0630055	−	0.0363762i	−0.468166	−	0.883640i	$-0.655085\pi$
$317$	1.12178	−	0.647660i	0.0630055	−	0.0363762i	0.531172	+	0.847264i	$0.321752\pi$
$318$	−1.52539	+	6.07037i	−0.0855397	+	0.340409i
$319$	1.34548	−	2.33043i	0.0753322	−	0.130479i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	22.3716	+	21.6838i	1.24866	+	1.21027i
$322$	9.76931	−	5.64031i	0.544422	−	0.314322i
$323$	−3.86490	+	6.69421i	−0.215049	+	0.372476i
$324$	−4.00481	+	8.05987i	−0.222490	+	0.447770i
$325$		−	0.556888i		−	0.0308906i
$326$			3.56174i			0.197266i
$327$	−3.58409	−	12.5866i	−0.198201	−	0.696042i
$328$	−4.54027	+	7.86397i	−0.250694	+	0.434215i
$329$	27.1888	−	15.6975i	1.49897	−	0.865429i
$330$	−1.22669	+	1.26560i	−0.0675269	+	0.0696690i
$331$	−17.5084	−	10.1085i	−0.962351	−	0.555614i	−0.0654553	−	0.997856i	$-0.520850\pi$
$331$	−17.5084	−	10.1085i	−0.962351	−	0.555614i	−0.896896	+	0.442242i	$0.854183\pi$
$332$	−1.71612	+	2.97241i	−0.0941844	+	0.163132i
$333$	−3.41796	+	6.37153i	−0.187303	+	0.349158i
$334$	−9.96036	+	5.75062i	−0.545007	+	0.314660i
$335$	1.33145	−	0.768714i	0.0727449	−	0.0419993i
$336$	4.22558	−	4.35962i	0.230524	−	0.237837i
$337$			11.8084i			0.643243i	0.946868	+	0.321622i	$0.104228\pi$
$337$			11.8084i			0.643243i	−0.946868	+	0.321622i	$0.895772\pi$
$338$	−10.9898	+	6.34494i	−0.597764	+	0.345119i
$339$	2.03753	−	8.10847i	0.110664	−	0.440392i
$340$		−	1.49623i		−	0.0811445i
$341$	1.51788	−	5.45863i	0.0821976	−	0.295601i
$342$	−7.32648	+	13.6575i	−0.396171	+	0.738514i
$343$	6.00365			0.324166
$344$	−3.28925	−	5.69715i	−0.177345	−	0.307170i
$345$	1.35843	−	5.40592i	0.0731352	−	0.291045i
$346$	1.17708	−	2.03876i	0.0632802	−	0.109605i
$347$	2.75581	+	4.77321i	0.147940	+	0.256239i	0.930466	−	0.366379i	$-0.119402\pi$
$347$	2.75581	+	4.77321i	0.147940	+	0.256239i	−0.782526	+	0.622618i	$0.786069\pi$
$348$	1.25438	+	4.40515i	0.0672420	+	0.236141i
$349$	−21.0390			−1.12619			−0.563095	−	0.826392i	$-0.690390\pi$
$349$	−21.0390			−1.12619			−0.563095	+	0.826392i	$0.690390\pi$
$350$	3.03570	+	1.75266i	0.162265	+	0.0936836i
$351$	−0.878978	−	2.75694i	−0.0469164	−	0.147155i
$352$	−0.881264	−	0.508798i	−0.0469715	−	0.0271190i
$353$	−12.9487	−	22.4278i	−0.689189	−	1.19371i	−0.972101	−	0.234564i	$-0.924634\pi$
$353$	−12.9487	−	22.4278i	−0.689189	−	1.19371i	0.282912	−	0.959146i	$-0.408700\pi$
$354$	11.4466	−	11.8097i	0.608379	−	0.627677i
$355$	−5.61027	−	9.71728i	−0.297762	−	0.515740i
$356$	0.779533			0.0413152
$357$	8.81030	+	2.21389i	0.466291	+	0.117172i
$358$	2.58794	−	1.49415i	0.136777	−	0.0789683i
$359$	7.88537	+	4.55262i	0.416174	+	0.240278i	0.693439	−	0.720515i	$-0.256095\pi$
$359$	7.88537	+	4.55262i	0.416174	+	0.240278i	−0.277265	+	0.960793i	$0.589428\pi$
$360$	−0.0936563	−	2.99854i	−0.00493612	−	0.158037i
$361$	−3.84473	+	6.65927i	−0.202354	+	0.350488i
$362$	10.9318	−	18.9344i	0.574561	−	0.995169i
$363$	12.0120	−	12.3930i	0.630464	−	0.650464i
$364$			1.95207i			0.102316i
$365$	−3.02495	−	5.23937i	−0.158333	−	0.274241i
$366$	−0.314394	−	1.10409i	−0.0164336	−	0.0577117i
$367$	−29.0390	−	16.7657i	−1.51582	−	0.875162i	−0.999828	−	0.0185717i	$-0.994088\pi$
$367$	−29.0390	−	16.7657i	−1.51582	−	0.875162i	−0.515997	−	0.856590i	$-0.672579\pi$
$368$	3.21814			0.167757
$369$	−27.2283	+	0.850449i	−1.41745	+	0.0442726i
$370$		−	2.41014i		−	0.125297i
$371$	12.6671			0.657645
$372$	4.87346	+	8.32162i	0.252677	+	0.431456i
$373$	−23.3875			−1.21096			−0.605479	−	0.795862i	$-0.707018\pi$
$373$	−23.3875			−1.21096			−0.605479	+	0.795862i	$0.707018\pi$
$374$		−	1.52256i		−	0.0787296i
$375$	1.66583	−	0.474351i	0.0860231	−	0.0244954i
$376$	8.95636			0.461889
$377$	−1.27535	−	0.736322i	−0.0656837	−	0.0379225i
$378$	17.7950	+	3.88530i	0.915274	+	0.199838i
$379$	−5.80353	−	10.0520i	−0.298107	−	0.516337i	0.677596	−	0.735435i	$-0.263022\pi$
$379$	−5.80353	−	10.0520i	−0.298107	−	0.516337i	−0.975703	+	0.219098i	$0.929689\pi$
$380$		−	5.16618i		−	0.265020i
$381$	−23.4522	−	22.7311i	−1.20149	−	1.16455i
$382$	−4.67054	+	8.08961i	−0.238965	+	0.413900i
$383$	1.14352	−	1.98063i	0.0584311	−	0.101206i	−0.835330	−	0.549749i	$-0.814724\pi$
$383$	1.14352	−	1.98063i	0.0584311	−	0.101206i	0.893761	+	0.448543i	$0.148057\pi$
$384$	1.66583	−	0.474351i	0.0850091	−	0.0242066i
$385$	3.08911	+	1.78350i	0.157436	+	0.0908956i
$386$	−1.46602	+	0.846405i	−0.0746183	+	0.0430809i
$387$	9.32937	−	17.3912i	0.474238	−	0.884043i
$388$	−13.2793			−0.674155
$389$	1.40760	+	2.43804i	0.0713684	+	0.123614i	0.899501	−	0.436918i	$-0.143930\pi$
$389$	1.40760	+	2.43804i	0.0713684	+	0.123614i	−0.828133	+	0.560532i	$0.810597\pi$
$390$	0.692610	+	0.671315i	0.0350717	+	0.0339933i
$391$	2.40754	+	4.16998i	0.121755	+	0.210885i
$392$	−4.57892	−	2.64364i	−0.231270	−	0.133524i
$393$	1.02186	+	0.990439i	0.0515459	+	0.0499610i
$394$	−13.7342	−	7.92946i	−0.691921	−	0.399481i
$395$	0.213152			0.0107248
$396$	−0.0953043	−	3.05130i	−0.00478922	−	0.153334i
$397$	−2.67976	−	4.64148i	−0.134493	−	0.232949i	0.790910	−	0.611932i	$-0.209607\pi$
$397$	−2.67976	−	4.64148i	−0.134493	−	0.232949i	−0.925404	+	0.378983i	$0.876274\pi$
$398$	−6.80268	+	11.7826i	−0.340988	+	0.590608i
$399$	30.4202	+	7.64414i	1.52292	+	0.382685i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	11.7824			0.588384			0.294192	−	0.955746i	$-0.404950\pi$
$401$	11.7824			0.588384			0.294192	+	0.955746i	$0.404950\pi$
$402$	−0.648971	+	2.58261i	−0.0323677	+	0.128809i
$403$	−2.98728	−	0.830669i	−0.148807	−	0.0413786i
$404$		−	17.5078i		−	0.871047i
$405$	7.49820	−	4.97764i	0.372589	−	0.247341i
$406$	8.02765	−	4.63477i	0.398406	−	0.230020i
$407$		−	2.45255i		−	0.121568i
$408$	1.86088	+	1.80367i	0.0921275	+	0.0892949i
$409$	−0.573155	+	0.330911i	−0.0283407	+	0.0163625i	−0.514103	−	0.857728i	$-0.671875\pi$
$409$	−0.573155	+	0.330911i	−0.0283407	+	0.0163625i	0.485763	+	0.874091i	$0.338542\pi$
$410$	7.86397	−	4.54027i	0.388374	−	0.224228i
$411$	−33.5173	−	8.42240i	−1.65329	−	0.415446i
$412$	0.217920	−	0.377449i	0.0107362	−	0.0185956i
$413$	−28.8254	−	16.6424i	−1.41841	−	0.818917i
$414$	5.08588	+	8.20621i	0.249957	+	0.403313i
$415$	2.97241	−	1.71612i	0.145910	−	0.0842411i
$416$	−0.278444	+	0.482279i	−0.0136518	+	0.0236457i
$417$	−2.03380	+	0.579131i	−0.0995955	+	0.0283602i
$418$		−	5.25709i		−	0.257133i
$419$			4.45152i			0.217471i	0.994071	+	0.108736i	$0.0346802\pi$
$419$			4.45152i			0.217471i	−0.994071	+	0.108736i	$0.965320\pi$
$420$	−5.83927	+	1.66275i	−0.284927	+	0.0811341i
$421$	5.24985	−	9.09301i	0.255862	−	0.443166i	−0.709267	−	0.704940i	$-0.750974\pi$
$421$	5.24985	−	9.09301i	0.255862	−	0.443166i	0.965129	+	0.261774i	$0.0843073\pi$
$422$	−7.73118	+	4.46360i	−0.376348	+	0.217285i
$423$	14.1544	+	22.8386i	0.688212	+	1.11045i
$424$	3.12954	+	1.80684i	0.151984	+	0.0877480i
$425$	−0.748115	+	1.29577i	−0.0362889	+	0.0628542i
$426$	18.8486	+	4.73636i	0.913217	+	0.229477i
$427$	−2.01202	+	1.16164i	−0.0973685	+	0.0562157i
$428$	15.5778	−	8.99386i	0.752982	−	0.434734i
$429$	0.704797	+	0.683127i	0.0340279	+	0.0329817i
$430$			6.57850i			0.317244i
$431$	10.1716	−	5.87257i	0.489948	−	0.282872i	−0.234605	−	0.972091i	$-0.575380\pi$
$431$	10.1716	−	5.87257i	0.489948	−	0.282872i	0.724553	+	0.689219i	$0.242046\pi$
$432$	3.84223	+	3.49818i	0.184859	+	0.168306i
$433$		−	0.986441i		−	0.0474053i	−0.999719	−	0.0237027i	$-0.992455\pi$
$433$		−	0.986441i		−	0.0474053i	0.999719	−	0.0237027i	$-0.00754550\pi$
$434$	13.9298	−	13.6699i	0.668653	−	0.656175i
$435$	1.11625	−	4.44217i	0.0535200	−	0.212986i
$436$	−7.55577			−0.361856
$437$	8.31276	+	14.3981i	0.397653	+	0.688756i
$438$	10.1628	+	2.55376i	0.485597	+	0.122023i
$439$	−0.755941	+	1.30933i	−0.0360791	+	0.0624909i	−0.883501	−	0.468429i	$-0.844820\pi$
$439$	−0.755941	+	1.30933i	−0.0360791	+	0.0624909i	0.847422	+	0.530920i	$0.178153\pi$
$440$	0.508798	+	0.881264i	0.0242560	+	0.0420126i
$441$	−0.495187	−	15.8541i	−0.0235803	−	0.754957i
$442$	−0.833232			−0.0396328
$443$	32.6594	+	18.8559i	1.55169	+	0.895871i	0.998004	+	0.0631476i	$0.0201139\pi$
$443$	32.6594	+	18.8559i	1.55169	+	0.895871i	0.553690	+	0.832723i	$0.313219\pi$
$444$	2.99752	+	2.90536i	0.142256	+	0.137882i
$445$	−0.675095	−	0.389767i	−0.0320026	−	0.0184767i
$446$	−4.02749	−	6.97582i	−0.190707	−	0.330315i
$447$	23.8599	+	23.1263i	1.12854	+	1.09384i
$448$	−1.75266	−	3.03570i	−0.0828054	−	0.143423i
$449$	19.1329			0.902938			0.451469	−	0.892287i	$-0.350900\pi$
$449$	19.1329			0.902938			0.451469	+	0.892287i	$0.350900\pi$
$450$	−1.41816	+	2.64364i	−0.0668527	+	0.124622i
$451$	8.00235	−	4.62016i	0.376816	−	0.217555i
$452$	−4.18028	−	2.41348i	−0.196624	−	0.113521i
$453$	38.8154	−	11.0528i	1.82370	−	0.519307i
$454$	−8.71161	+	15.0890i	−0.408856	+	0.708160i
$455$	0.976035	−	1.69054i	0.0457572	−	0.0792538i
$456$	6.42526	+	6.22771i	0.300891	+	0.291639i
$457$			33.8765i			1.58468i	0.610082	+	0.792338i	$0.291136\pi$
$457$			33.8765i			1.58468i	−0.610082	+	0.792338i	$0.708864\pi$
$458$	7.05087	+	12.2125i	0.329466	+	0.570651i
$459$	−1.65842	+	7.59570i	−0.0774086	+	0.354537i
$460$	−2.78699	−	1.60907i	−0.129944	−	0.0750233i
$461$	−20.2187			−0.941678			−0.470839	−	0.882219i	$-0.656049\pi$
$461$	−20.2187			−0.941678			−0.470839	+	0.882219i	$0.656049\pi$
$462$	−5.94202	+	1.69201i	−0.276448	+	0.0787195i
$463$			4.75152i			0.220822i	0.993886	+	0.110411i	$0.0352167\pi$
$463$			4.75152i			0.220822i	−0.993886	+	0.110411i	$0.964783\pi$
$464$	2.64442			0.122764
$465$	−0.0597329	−	9.64347i	−0.00277005	−	0.447205i
$466$	−2.39244			−0.110828
$467$			4.46882i			0.206792i	0.994640	+	0.103396i	$0.0329709\pi$
$467$			4.46882i			0.206792i	−0.994640	+	0.103396i	$0.967029\pi$
$468$	−1.66985	+	0.0521560i	−0.0771888	+	0.00241091i
$469$	5.38918			0.248849
$470$	−7.75644	−	4.47818i	−0.357778	−	0.206563i
$471$	−5.09539	−	17.8940i	−0.234783	−	0.824514i
$472$	−4.74774	−	8.22333i	−0.218533	−	0.378509i
$473$			6.69426i			0.307802i
$474$	−0.256950	+	0.265101i	−0.0118021	+	0.0121765i
$475$	−2.58309	+	4.47405i	−0.118520	+	0.205283i
$476$	2.62238	−	4.54210i	0.120197	−	0.208187i
$477$	0.338445	+	10.8358i	0.0154963	+	0.496136i
$478$	9.54323	+	5.50979i	0.436497	+	0.252012i
$479$	−7.32007	+	4.22624i	−0.334463	+	0.193102i	−0.657821	−	0.753175i	$-0.728522\pi$
$479$	−7.32007	+	4.22624i	−0.334463	+	0.193102i	0.323358	+	0.946277i	$0.395188\pi$
$480$	−1.67983	−	0.422115i	−0.0766733	−	0.0192668i
$481$	−1.34217			−0.0611979
$482$	−12.4602	−	21.5818i	−0.567548	−	0.983022i
$483$	13.5985	−	14.0299i	0.618754	−	0.638382i
$484$	−4.98225	−	8.62951i	−0.226466	−	0.392250i
$485$	11.5002	+	6.63966i	0.522198	+	0.301491i
$486$	−2.84813	+	15.3261i	−0.129194	+	0.695204i
$487$	−29.2380	−	16.8806i	−1.32490	−	0.764931i	−0.340394	−	0.940283i	$-0.610560\pi$
$487$	−29.2380	−	16.8806i	−1.32490	−	0.764931i	−0.984506	+	0.175352i	$0.943894\pi$
$488$	−0.662787			−0.0300030
$489$	1.68952	+	5.93325i	0.0764025	+	0.268311i
$490$	2.64364	+	4.57892i	0.119427	+	0.206854i
$491$	3.86335	−	6.69152i	0.174351	−	0.301984i	−0.765586	−	0.643334i	$-0.777551\pi$
$491$	3.86335	−	6.69152i	0.174351	−	0.301984i	0.939936	+	0.341350i	$0.110884\pi$
$492$	−3.83303	+	15.2537i	−0.172806	+	0.687691i
$493$	1.97833	+	3.42657i	0.0890995	+	0.154325i
$494$	−2.87698			−0.129442
$495$	−1.44311	+	2.69016i	−0.0648632	+	0.120914i
$496$	5.39138	−	1.39033i	0.242080	−	0.0624277i
$497$		−	39.3316i		−	1.76426i
$498$	−1.44880	+	5.76557i	−0.0649223	+	0.258362i
$499$	28.3347	−	16.3590i	1.26843	−	0.732330i	0.293742	−	0.955885i	$-0.405099\pi$
$499$	28.3347	−	16.3590i	1.26843	−	0.732330i	0.974691	+	0.223554i	$0.0717660\pi$
$500$		−	1.00000i		−	0.0447214i
$501$	−13.8645	+	14.3043i	−0.619418	+	0.639067i
$502$	11.4452	−	6.60787i	0.510823	−	0.294924i
$503$	25.7137	−	14.8458i	1.14652	−	0.661942i	0.198482	−	0.980105i	$-0.436399\pi$
$503$	25.7137	−	14.8458i	1.14652	−	0.661942i	0.948036	+	0.318162i	$0.103066\pi$
$504$	4.97111	−	9.26680i	0.221431	−	0.412776i
$505$	−8.75391	+	15.1622i	−0.389544	+	0.674710i
$506$	−2.83603	−	1.63739i	−0.126077	−	0.0727906i
$507$	−15.2973	+	15.7826i	−0.679379	+	0.700930i
$508$	−16.3303	+	9.42828i	−0.724538	+	0.418312i
$509$	−13.1355	+	22.7513i	−0.582219	+	1.00843i	0.412997	+	0.910733i	$0.364482\pi$
$509$	−13.1355	+	22.7513i	−0.582219	+	1.00843i	−0.995216	+	0.0977008i	$0.968851\pi$
$510$	−0.709739	−	2.49247i	−0.0314278	−	0.110368i
$511$		−	21.2069i		−	0.938137i
$512$		−	1.00000i		−	0.0441942i
$513$	−5.72620	+	26.2264i	−0.252818	+	1.15793i
$514$	−12.7624	+	22.1051i	−0.562925	+	0.975015i
$515$	−0.377449	+	0.217920i	−0.0166324	+	0.00960271i
$516$	−8.18178	−	7.93022i	−0.360183	−	0.349109i
$517$	−7.89292	−	4.55698i	−0.347130	−	0.200416i
$518$	4.22415	−	7.31644i	0.185598	−	0.321466i
$519$	0.993726	−	3.95458i	0.0436197	−	0.173587i
$520$	0.482279	−	0.278444i	0.0211493	−	0.0122106i
$521$	33.3101	−	19.2316i	1.45934	−	0.842552i	0.460364	−	0.887730i	$-0.347719\pi$
$521$	33.3101	−	19.2316i	1.45934	−	0.842552i	0.998979	+	0.0451783i	$0.0143856\pi$
$522$	4.17918	+	6.74322i	0.182918	+	0.295143i
$523$		−	7.33956i		−	0.320937i	−0.987041	−	0.160468i	$-0.948700\pi$
$523$		−	7.33956i		−	0.320937i	0.987041	−	0.160468i	$-0.0513004\pi$
$524$	0.711541	−	0.410808i	0.0310838	−	0.0179462i
$525$	5.88833	+	1.47965i	0.256988	+	0.0645771i
$526$			17.3755i			0.757607i
$527$	5.83493	+	5.94588i	0.254173	+	0.259007i
$528$	−1.70939	−	0.429543i	−0.0743915	−	0.0186934i
$529$	−12.6436			−0.549720
$530$	−1.80684	−	3.12954i	−0.0784842	−	0.135939i
$531$	13.4661	−	25.1026i	0.584380	−	1.08936i
$532$	9.05457	−	15.6830i	0.392565	−	0.679943i
$533$	−2.52842	−	4.37935i	−0.109518	−	0.189691i
$534$	1.29857	−	0.369773i	0.0561946	−	0.0160016i
$535$	−17.9877			−0.777677
$536$	1.33145	+	0.768714i	0.0575099	+	0.0332034i
$537$	3.60232	−	3.71659i	0.155452	−	0.160383i
$538$	−9.40555	−	5.43030i	−0.405502	−	0.234117i
$539$	2.69016	+	4.65949i	0.115873	+	0.200698i
$540$	−1.57838	−	4.95063i	−0.0679225	−	0.213041i
$541$	−13.7846	−	23.8755i	−0.592644	−	1.02649i	−0.993875	−	0.110513i	$-0.964751\pi$
$541$	−13.7846	−	23.8755i	−0.592644	−	1.02649i	0.401231	−	0.915977i	$-0.368583\pi$
$542$	0.444297			0.0190842
$543$	9.22892	−	36.7270i	0.396051	−	1.57610i
$544$	1.29577	−	0.748115i	0.0555558	−	0.0320752i
$545$	6.54349	+	3.77788i	0.280292	+	0.161827i
$546$	0.925967	+	3.25182i	0.0396277	+	0.139165i
$547$	17.8437	−	30.9062i	0.762941	−	1.32145i	−0.178387	−	0.983960i	$-0.557088\pi$
$547$	17.8437	−	30.9062i	0.762941	−	1.32145i	0.941328	−	0.337493i	$-0.109579\pi$
$548$	−9.97643	+	17.2797i	−0.426172	+	0.738151i
$549$	−1.04745	−	1.69009i	−0.0447042	−	0.0721315i
$550$		−	1.01760i		−	0.0433905i
$551$	6.83078	+	11.8313i	0.291001	+	0.504028i
$552$	5.36088	−	1.52653i	0.228174	−	0.0649734i
$553$	0.647065	+	0.373583i	0.0275160	+	0.0158864i
$554$	8.03697			0.341458
$555$	−1.14325	−	4.01488i	−0.0485283	−	0.170422i
$556$			1.22089i			0.0517773i
$557$	−7.54761			−0.319803			−0.159901	−	0.987133i	$-0.551118\pi$
$557$	−7.54761			−0.319803			−0.159901	+	0.987133i	$0.551118\pi$
$558$	12.0657	+	11.5507i	0.510783	+	0.488979i
$559$	3.66349			0.154949
$560$			3.50532i			0.148127i
$561$	−0.722228	−	2.53632i	−0.0304925	−	0.107084i
$562$	13.9273			0.587486
$563$	−14.7599	−	8.52162i	−0.622054	−	0.359143i	0.155614	−	0.987818i	$-0.450264\pi$
$563$	−14.7599	−	8.52162i	−0.622054	−	0.359143i	−0.777668	+	0.628675i	$0.783598\pi$
$564$	14.9198	−	4.24846i	0.628236	−	0.178892i
$565$	2.41348	+	4.18028i	0.101536	+	0.175866i
$566$			28.1351i			1.18261i
$567$	31.4864	−	1.96881i	1.32230	−	0.0826824i
$568$	5.61027	−	9.71728i	0.235402	−	0.407728i
$569$	−16.3440	+	28.3087i	−0.685178	+	1.18676i	0.288203	+	0.957569i	$0.406942\pi$
$569$	−16.3440	+	28.3087i	−0.685178	+	1.18676i	−0.973381	+	0.229194i	$0.926391\pi$
$570$	−2.45059	−	8.60599i	−0.102644	−	0.360465i
$571$	−36.0942	−	20.8390i	−1.51049	−	0.872084i	−0.999925	−	0.0122468i	$-0.996102\pi$
$571$	−36.0942	−	20.8390i	−1.51049	−	0.872084i	−0.510569	−	0.859837i	$-0.670565\pi$
$572$	0.490765	−	0.283343i	0.0205199	−	0.0118472i
$573$	−3.94301	+	15.6914i	−0.164721	+	0.655517i
$574$	31.8302			1.32857
$575$	1.60907	+	2.78699i	0.0671029	+	0.116226i
$576$	2.54998	−	1.58038i	0.106249	−	0.0658491i
$577$	−18.9525	−	32.8266i	−0.789002	−	1.36659i	−0.926579	−	0.376100i	$-0.877265\pi$
$577$	−18.9525	−	32.8266i	−0.789002	−	1.36659i	0.137577	−	0.990491i	$-0.456069\pi$
$578$	−12.7837	−	7.38065i	−0.531730	−	0.306994i
$579$	−2.04064	+	2.10537i	−0.0848061	+	0.0874963i
$580$	−2.29013	−	1.32221i	−0.0950926	−	0.0549018i
$581$	12.0311			0.499135
$582$	−22.1211	+	6.29906i	−0.916949	+	0.261105i
$583$	−1.83864	−	3.18461i	−0.0761485	−	0.131893i
$584$	3.02495	−	5.23937i	0.125173	−	0.216807i
$585$	1.47221	+	0.789756i	0.0608684	+	0.0326524i
$586$	11.0058	+	19.0627i	0.454647	+	0.787471i
$587$	26.0324			1.07447			0.537237	−	0.843431i	$-0.319468\pi$
$587$	26.0324			1.07447			0.537237	+	0.843431i	$0.319468\pi$
$588$	−8.88171	−	2.23184i	−0.366276	−	0.0920394i
$589$	20.1468	+	20.5299i	0.830136	+	0.845921i
$590$			9.49548i			0.390923i
$591$	−26.6403	−	6.69429i	−1.09583	−	0.275366i
$592$	2.08724	−	1.20507i	0.0857850	−	0.0495280i
$593$		−	16.4572i		−	0.675817i	−0.941179	−	0.337908i	$-0.890281\pi$
$593$		−	16.4572i		−	0.675817i	0.941179	−	0.337908i	$-0.109719\pi$
$594$	−1.60615	−	5.03774i	−0.0659011	−	0.206701i
$595$	−4.54210	+	2.62238i	−0.186208	+	0.107507i
$596$	16.6142	−	9.59220i	0.680543	−	0.392912i
$597$	−5.74303	+	22.8547i	−0.235047	+	0.935379i
$598$	−0.896072	+	1.55204i	−0.0366431	+	0.0634677i
$599$	−17.7128	−	10.2265i	−0.723724	−	0.417842i	0.0923976	−	0.995722i	$-0.470547\pi$
$599$	−17.7128	−	10.2265i	−0.723724	−	0.417842i	−0.816122	+	0.577880i	$0.803880\pi$
$600$	1.24372	+	1.20548i	0.0507745	+	0.0492133i
$601$	−10.8743	+	6.27830i	−0.443573	+	0.256097i	−0.705112	−	0.709096i	$-0.749103\pi$
$601$	−10.8743	+	6.27830i	−0.443573	+	0.256097i	0.261539	+	0.965193i	$0.415770\pi$
$602$	−11.5299	+	19.9703i	−0.469923	+	0.813930i
$603$	0.143990	+	4.61003i	0.00586372	+	0.187735i
$604$		−	23.3009i		−	0.948100i
$605$			9.96450i			0.405114i
$606$	−8.30486	−	29.1651i	−0.337362	−	1.18475i
$607$	−8.27295	+	14.3292i	−0.335789	+	0.581603i	−0.983636	−	0.180167i	$-0.942336\pi$
$607$	−8.27295	+	14.3292i	−0.335789	+	0.581603i	0.647847	+	0.761770i	$0.275669\pi$
$608$	4.47405	−	2.58309i	0.181447	−	0.104758i
$609$	11.1742	−	11.5287i	0.452802	−	0.467165i
$610$	0.573990	+	0.331394i	0.0232402	+	0.0134177i
$611$	−2.49384	+	4.31946i	−0.100890	+	0.174747i
$612$	3.95549	+	2.12189i	0.159891	+	0.0857725i
$613$	28.1131	−	16.2311i	1.13548	−	0.655568i	0.190171	−	0.981751i	$-0.439096\pi$
$613$	28.1131	−	16.2311i	1.13548	−	0.655568i	0.945307	+	0.326183i	$0.105763\pi$
$614$	−5.00704	+	2.89082i	−0.202068	+	0.116664i
$615$	10.9464	−	11.2936i	0.441400	−	0.455402i
$616$			3.56700i			0.143719i
$617$	−0.546152	+	0.315321i	−0.0219873	+	0.0126943i	−0.510953	−	0.859608i	$-0.670708\pi$
$617$	−0.546152	+	0.315321i	−0.0219873	+	0.0126943i	0.488966	+	0.872303i	$0.337374\pi$
$618$	0.183975	−	0.732136i	0.00740055	−	0.0294508i
$619$		−	45.8973i		−	1.84477i	−0.386274	−	0.922384i	$-0.626238\pi$
$619$		−	45.8973i		−	1.84477i	0.386274	−	0.922384i	$-0.373762\pi$
$620$	−5.36424	−	1.49163i	−0.215433	−	0.0599052i
$621$	12.3648	+	11.2577i	0.496184	+	0.451754i
$622$	0.448742			0.0179929
$623$	−1.36626	−	2.36643i	−0.0547379	−	0.0948089i
$624$	−0.235071	+	0.935475i	−0.00941035	+	0.0374490i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−8.73777	−	15.1343i	−0.349232	−	0.604887i
$627$	−2.49371	−	8.75742i	−0.0995891	−	0.349738i
$628$	−10.7418			−0.428645
$629$	3.12299	+	1.80306i	0.124522	+	0.0718927i
$630$	−8.93850	+	5.53973i	−0.356119	+	0.220708i
$631$	16.2083	+	9.35789i	0.645244	+	0.372532i	0.786632	−	0.617423i	$-0.211823\pi$
$631$	16.2083	+	9.35789i	0.645244	+	0.372532i	−0.141388	+	0.989954i	$0.545156\pi$
$632$	0.106576	+	0.184595i	0.00423937	+	0.00734280i
$633$	−10.7615	+	11.1029i	−0.427732	+	0.441300i
$634$	−0.647660	−	1.12178i	−0.0257219	−	0.0445516i
$635$	18.8566			0.748300
$636$	6.07037	+	1.52539i	0.240706	+	0.0604857i
$637$	2.54994	−	1.47221i	0.101032	−	0.0583311i
$638$	−2.33043	−	1.34548i	−0.0922627	−	0.0532679i
$639$	33.6452	−	1.05088i	1.33098	−	0.0415720i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	3.71167	−	6.42881i	0.146602	−	0.253923i	−0.783367	−	0.621559i	$-0.786500\pi$
$641$	3.71167	−	6.42881i	0.146602	−	0.253923i	0.929970	+	0.367636i	$0.119833\pi$
$642$	21.6838	−	22.3716i	0.855789	−	0.882936i
$643$			17.2741i			0.681222i	0.940204	+	0.340611i	$0.110634\pi$
$643$			17.2741i			0.681222i	−0.940204	+	0.340611i	$0.889366\pi$
$644$	−5.64031	−	9.76931i	−0.222259	−	0.384965i
$645$	3.12052	+	10.9587i	0.122870	+	0.431497i
$646$	6.69421	+	3.86490i	0.263380	+	0.152062i
$647$	−8.93872			−0.351418			−0.175709	−	0.984442i	$-0.556222\pi$
$647$	−8.93872			−0.351418			−0.175709	+	0.984442i	$0.556222\pi$
$648$	8.05987	+	4.00481i	0.316622	+	0.157324i
$649$			9.66257i			0.379289i
$650$	−0.556888			−0.0218429
$651$	16.7204	−	29.3793i	0.655324	−	1.15147i
$652$	3.56174			0.139488
$653$		−	22.3040i		−	0.872823i	−0.899747	−	0.436411i	$-0.856249\pi$
$653$		−	22.3040i		−	0.872823i	0.899747	−	0.436411i	$-0.143751\pi$
$654$	−12.5866	+	3.58409i	−0.492176	+	0.140149i
$655$	−0.821617			−0.0321032
$656$	7.86397	+	4.54027i	0.307037	+	0.177268i
$657$	18.1409	−	0.566612i	0.707743	−	0.0221056i
$658$	−15.6975	−	27.1888i	−0.611951	−	1.05993i
$659$			23.8067i			0.927377i	0.885998	+	0.463688i	$0.153474\pi$
$659$			23.8067i			0.927377i	−0.885998	+	0.463688i	$0.846526\pi$
$660$	1.26560	+	1.22669i	0.0492634	+	0.0477488i
$661$	−20.5693	+	35.6271i	−0.800054	+	1.38573i	0.119527	+	0.992831i	$0.461862\pi$
$661$	−20.5693	+	35.6271i	−0.800054	+	1.38573i	−0.919580	+	0.392902i	$0.871471\pi$
$662$	−10.1085	+	17.5084i	−0.392878	+	0.680485i
$663$	−1.38802	+	0.395245i	−0.0539064	+	0.0153500i
$664$	2.97241	+	1.71612i	0.115352	+	0.0665984i
$665$	−15.6830	+	9.05457i	−0.608160	+	0.351121i
$666$	6.37153	+	3.41796i	0.246892	+	0.132443i
$667$	8.51012			0.329513
$668$	5.75062	+	9.96036i	0.222498	+	0.385378i
$669$	−10.0181	−	9.71009i	−0.387323	−	0.375414i
$670$	−0.768714	−	1.33145i	−0.0296980	−	0.0514384i
$671$	0.584090	+	0.337225i	0.0225486	+	0.0130184i
$672$	−4.35962	−	4.22558i	−0.168176	−	0.163005i
$673$	−40.8232	−	23.5693i	−1.57362	−	0.908529i	−0.995720	−	0.0924207i	$-0.970540\pi$
$673$	−40.8232	−	23.5693i	−1.57362	−	0.908529i	−0.577899	−	0.816109i	$-0.696127\pi$
$674$	11.8084			0.454842
$675$	−1.10840	+	5.07656i	−0.0426624	+	0.195397i
$676$	6.34494	+	10.9898i	0.244036	+	0.422683i
$677$	9.59632	−	16.6213i	0.368816	−	0.638809i	−0.620564	−	0.784155i	$-0.713096\pi$
$677$	9.59632	−	16.6213i	0.368816	−	0.638809i	0.989381	+	0.145347i	$0.0464298\pi$
$678$	−8.10847	−	2.03753i	−0.311404	−	0.0782511i
$679$	23.2741	+	40.3120i	0.893179	+	1.54703i
$680$	−1.49623			−0.0573778
$681$	−7.35460	+	29.2680i	−0.281829	+	1.12155i
$682$	−5.45863	−	1.51788i	−0.209022	−	0.0581225i
$683$		−	28.8541i		−	1.10407i	−0.833821	−	0.552035i	$-0.813852\pi$
$683$		−	28.8541i		−	1.10407i	0.833821	−	0.552035i	$-0.186148\pi$
$684$	13.6575	+	7.32648i	0.522208	+	0.280135i
$685$	17.2797	−	9.97643i	0.660223	−	0.381180i
$686$		−	6.00365i		−	0.229220i
$687$	17.5386	+	16.9993i	0.669138	+	0.648564i
$688$	−5.69715	+	3.28925i	−0.217202	+	0.125402i
$689$	−1.74280	+	1.00621i	−0.0663955	+	0.0383335i
$690$	−5.40592	−	1.35843i	−0.205800	−	0.0517144i
$691$	20.3713	−	35.2841i	0.774959	−	1.34227i	−0.159858	−	0.987140i	$-0.551104\pi$
$691$	20.3713	−	35.2841i	0.774959	−	1.34227i	0.934817	−	0.355129i	$-0.115563\pi$
$692$	−2.03876	−	1.17708i	−0.0775021	−	0.0447459i
$693$	−9.09579	+	5.63721i	−0.345520	+	0.214140i
$694$	4.77321	−	2.75581i	0.181188	−	0.104609i
$695$	0.610446	−	1.05732i	0.0231555	−	0.0401065i
$696$	4.40515	−	1.25438i	0.166977	−	0.0475473i
$697$			13.5866i			0.514628i
$698$			21.0390i			0.796337i
$699$	−3.98539	+	1.13486i	−0.150741	+	0.0429242i
$700$	1.75266	−	3.03570i	0.0662443	−	0.114739i
$701$	−6.09463	+	3.51874i	−0.230191	+	0.132901i	−0.610660	−	0.791893i	$-0.709096\pi$
$701$	−6.09463	+	3.51874i	−0.230191	+	0.132901i	0.380469	+	0.924794i	$0.375763\pi$
$702$	−2.75694	+	0.878978i	−0.104054	+	0.0331749i
$703$	10.7831	+	6.22560i	0.406691	+	0.234803i
$704$	−0.508798	+	0.881264i	−0.0191761	+	0.0332139i
$705$	−15.0451	−	3.78061i	−0.566633	−	0.142386i
$706$	−22.4278	+	12.9487i	−0.844081	+	0.487330i
$707$	−53.1485	+	30.6853i	−1.99885	+	1.15404i
$708$	−11.8097	−	11.4466i	−0.443835	−	0.430189i
$709$		−	22.0251i		−	0.827169i	−0.910466	−	0.413585i	$-0.864277\pi$
$709$		−	22.0251i		−	0.827169i	0.910466	−	0.413585i	$-0.135723\pi$
$710$	−9.71728	+	5.61027i	−0.364683	+	0.210550i
$711$	−0.302284	+	0.563497i	−0.0113365	+	0.0211328i
$712$		−	0.779533i		−	0.0292142i
$713$	17.3502	−	4.47428i	0.649771	−	0.167563i
$714$	2.21389	−	8.81030i	0.0828529	−	0.329717i
$715$	−0.566687			−0.0211929
$716$	−1.49415	−	2.58794i	−0.0558390	−	0.0967160i
$717$	18.5110	+	4.65153i	0.691305	+	0.173714i
$718$	4.55262	−	7.88537i	0.169902	−	0.294279i
$719$	−18.1976	−	31.5191i	−0.678656	−	1.17547i	−0.975386	−	0.220505i	$-0.929230\pi$
$719$	−18.1976	−	31.5191i	−0.678656	−	1.17547i	0.296730	−	0.954961i	$-0.404104\pi$
$720$	−2.99854	+	0.0936563i	−0.111749	+	0.00349037i
$721$	−1.52776			−0.0568968
$722$	6.65927	+	3.84473i	0.247832	+	0.143086i
$723$	−30.9940	−	30.0410i	−1.15268	−	1.11724i
$724$	−18.9344	−	10.9318i	−0.703690	−	0.406276i
$725$	1.32221	+	2.29013i	0.0491056	+	0.0850534i
$726$	−12.3930	−	12.0120i	−0.459947	−	0.445806i
$727$	3.84543	+	6.66048i	0.142619	+	0.247024i	0.928482	−	0.371377i	$-0.121114\pi$
$727$	3.84543	+	6.66048i	0.142619	+	0.247024i	−0.785863	+	0.618401i	$0.787781\pi$
$728$	1.95207			0.0723485
$729$	2.52543	+	26.8816i	0.0935346	+	0.995616i
$730$	−5.23937	+	3.02495i	−0.193918	+	0.111959i
$731$	−8.52425	−	4.92148i	−0.315281	−	0.182027i
$732$	−1.10409	+	0.314394i	−0.0408084	+	0.0116203i
$733$	2.30501	−	3.99239i	0.0851374	−	0.147462i	−0.820312	−	0.571916i	$-0.806200\pi$
$733$	2.30501	−	3.99239i	0.0851374	−	0.147462i	0.905450	+	0.424454i	$0.139534\pi$
$734$	−16.7657	+	29.0390i	−0.618833	+	1.07185i
$735$	6.57587	+	6.37368i	0.242555	+	0.235097i
$736$		−	3.21814i		−	0.118622i
$737$	−0.782240	−	1.35488i	−0.0288142	−	0.0499076i
$738$	0.850449	+	27.2283i	0.0313055	+	1.00229i
$739$	2.74609	+	1.58546i	0.101017	+	0.0583220i	0.549657	−	0.835390i	$-0.314758\pi$
$739$	2.74609	+	1.58546i	0.101017	+	0.0583220i	−0.448641	+	0.893712i	$0.648092\pi$
$740$	−2.41014			−0.0885984
$741$	−4.79257	+	1.36470i	−0.176059	+	0.0501336i
$742$		−	12.6671i		−	0.465025i
$743$	−30.5226			−1.11977			−0.559883	−	0.828571i	$-0.689154\pi$
$743$	−30.5226			−1.11977			−0.559883	+	0.828571i	$0.689154\pi$
$744$	8.32162	−	4.87346i	0.305085	−	0.178670i
$745$	−19.1844			−0.702862
$746$			23.3875i			0.856276i
$747$	0.321451	+	10.2917i	0.0117613	+	0.376554i
$748$	−1.52256			−0.0556702
$749$	−54.6052	−	31.5264i	−1.99523	−	1.15195i
$750$	−0.474351	−	1.66583i	−0.0173209	−	0.0608275i
$751$	19.5846	+	33.9216i	0.714654	+	1.23782i	0.963093	+	0.269169i	$0.0867490\pi$
$751$	19.5846	+	33.9216i	0.714654	+	1.23782i	−0.248439	+	0.968647i	$0.579918\pi$
$752$		−	8.95636i		−	0.326605i
$753$	15.9313	−	16.4366i	0.580567	−	0.598984i
$754$	−0.736322	+	1.27535i	−0.0268153	+	0.0464454i
$755$	−11.6505	+	20.1792i	−0.424003	+	0.734395i
$756$	3.88530	−	17.7950i	0.141307	−	0.647197i
$757$	37.5703	+	21.6912i	1.36552	+	0.788382i	0.990352	−	0.138576i	$-0.0442526\pi$
$757$	37.5703	+	21.6912i	1.36552	+	0.788382i	0.375165	+	0.926958i	$0.377586\pi$
$758$	−10.0520	+	5.80353i	−0.365105	+	0.210794i
$759$	−5.50105	−	1.38233i	−0.199675	−	0.0501754i
$760$	−5.16618			−0.187397
$761$	20.1815	+	34.9553i	0.731577	+	1.26713i	0.956209	+	0.292685i	$0.0945488\pi$
$761$	20.1815	+	34.9553i	0.731577	+	1.26713i	−0.224632	+	0.974444i	$0.572118\pi$
$762$	−22.7311	+	23.4522i	−0.823462	+	0.849583i
$763$	13.2427	+	22.9370i	0.479418	+	0.830376i
$764$	8.08961	+	4.67054i	0.292672	+	0.168974i
$765$	−2.36461	−	3.81536i	−0.0854926	−	0.137945i
$766$	−1.98063	−	1.14352i	−0.0715632	−	0.0413170i
$767$	5.28792			0.190936
$768$	−0.474351	−	1.66583i	−0.0171167	−	0.0601105i
$769$	7.20267	+	12.4754i	0.259735	+	0.449874i	0.966171	−	0.257903i	$-0.0830315\pi$
$769$	7.20267	+	12.4754i	0.259735	+	0.449874i	−0.706436	+	0.707777i	$0.749698\pi$
$770$	1.78350	−	3.08911i	0.0642729	−	0.111324i
$771$	−10.7744	+	42.8772i	−0.388030	+	1.54419i
$772$	0.846405	+	1.46602i	0.0304628	+	0.0527631i
$773$	0.596764			0.0214641			0.0107321	−	0.999942i	$-0.496584\pi$
$773$	0.596764			0.0214641			0.0107321	+	0.999942i	$0.496584\pi$
$774$	−17.3912	−	9.32937i	−0.625113	−	0.335337i
$775$	3.89975	+	3.97391i	0.140083	+	0.142747i
$776$			13.2793i			0.476700i
$777$	3.56615	−	14.1917i	0.127935	−	0.509124i
$778$	2.43804	−	1.40760i	0.0874080	−	0.0504650i
$779$			46.9117i			1.68079i
$780$	0.671315	−	0.692610i	0.0240369	−	0.0247994i
$781$	−9.88827	+	5.70899i	−0.353830	+	0.204284i
$782$	4.16998	−	2.40754i	0.149118	−	0.0860935i
$783$	10.1605	+	9.25066i	0.363105	+	0.330592i
$784$	−2.64364	+	4.57892i	−0.0944156	+	0.163533i
$785$	9.30268	+	5.37091i	0.332027	+	0.191696i
$786$	0.990439	−	1.02186i	0.0353278	−	0.0364484i
$787$	−44.6959	+	25.8052i	−1.59324	+	0.919856i	−0.600490	+	0.799632i	$0.705028\pi$
$787$	−44.6959	+	25.8052i	−1.59324	+	0.919856i	−0.992747	+	0.120224i	$0.961639\pi$
$788$	−7.92946	+	13.7342i	−0.282475	+	0.489262i
$789$	8.24208	+	28.9446i	0.293426	+	1.03045i
$790$		−	0.213152i		−	0.00758361i
$791$			16.9201i			0.601608i
$792$	−3.05130	+	0.0953043i	−0.108423	+	0.00338649i
$793$	0.184549	−	0.319648i	0.00655353	−	0.0113510i
$794$	−4.64148	+	2.67976i	−0.164720	+	0.0951011i
$795$	−4.49440	−	4.35621i	−0.159400	−	0.154499i
$796$	11.7826	+	6.80268i	0.417623	+	0.241115i
$797$	23.5456	−	40.7822i	0.834028	−	1.44458i	−0.0607919	−	0.998150i	$-0.519363\pi$
$797$	23.5456	−	40.7822i	0.834028	−	1.44458i	0.894820	−	0.446428i	$-0.147304\pi$
$798$	7.64414	−	30.4202i	0.270600	−	1.07686i
$799$	11.6054	−	6.70039i	0.410570	−	0.237043i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	1.98779	−	1.23196i	0.0702353	−	0.0435290i
$802$		−	11.7824i		−	0.416050i
$803$	−5.33157	+	3.07818i	−0.188147	+	0.108627i
$804$	2.58261	+	0.648971i	0.0910817	+	0.0228874i
$805$			11.2806i			0.397590i
$806$	−0.830669	+	2.98728i	−0.0292591	+	0.105222i
$807$	−18.2439	−	4.58442i	−0.642216	−	0.161379i
$808$	−17.5078			−0.615923
$809$	−4.47657	−	7.75365i	−0.157388	−	0.272604i	0.776538	−	0.630070i	$-0.216974\pi$
$809$	−4.47657	−	7.75365i	−0.157388	−	0.272604i	−0.933926	+	0.357467i	$0.883641\pi$
$810$	−4.97764	−	7.49820i	−0.174897	−	0.263460i
$811$	19.0738	−	33.0368i	0.669772	−	1.16008i	−0.308195	−	0.951323i	$-0.599725\pi$
$811$	19.0738	−	33.0368i	0.669772	−	1.16008i	0.977968	−	0.208756i	$-0.0669416\pi$
$812$	−4.63477	−	8.02765i	−0.162648	−	0.281715i
$813$	0.740123	−	0.210753i	0.0259572	−	0.00739142i
$814$	−2.45255			−0.0859617
$815$	−3.08456	−	1.78087i	−0.108047	−	0.0623811i
$816$	1.80367	−	1.86088i	0.0631411	−	0.0651440i
$817$	−29.4325	−	16.9929i	−1.02971	−	0.594506i
$818$	0.330911	+	0.573155i	0.0115700	+	0.0200399i
$819$	3.08501	+	4.97774i	0.107799	+	0.173936i
$820$	−4.54027	−	7.86397i	−0.158553	−	0.274622i
$821$	1.33931			0.0467422			0.0233711	−	0.999727i	$-0.492560\pi$
$821$	1.33931			0.0467422			0.0233711	+	0.999727i	$0.492560\pi$
$822$	−8.42240	+	33.5173i	−0.293765	+	1.16905i
$823$	−21.0797	+	12.1704i	−0.734792	+	0.424233i	−0.820173	−	0.572116i	$-0.806123\pi$
$823$	−21.0797	+	12.1704i	−0.734792	+	0.424233i	0.0853804	+	0.996348i	$0.472789\pi$
$824$	−0.377449	−	0.217920i	−0.0131491	−	0.00759161i
$825$	−0.482698	−	1.69514i	−0.0168054	−	0.0590173i
$826$	−16.6424	+	28.8254i	−0.579062	+	1.00296i
$827$	−17.0711	+	29.5680i	−0.593621	+	1.02818i	0.400119	+	0.916463i	$0.368969\pi$
$827$	−17.0711	+	29.5680i	−0.593621	+	1.02818i	−0.993740	+	0.111718i	$0.964365\pi$
$828$	8.20621	−	5.08588i	0.285185	−	0.176747i
$829$			32.3395i			1.12320i	0.827409	+	0.561599i	$0.189814\pi$
$829$			32.3395i			1.12320i	−0.827409	+	0.561599i	$0.810186\pi$
$830$	−1.71612	−	2.97241i	−0.0595674	−	0.103174i
$831$	13.3882	−	3.81235i	0.464432	−	0.132249i
$832$	0.482279	+	0.278444i	0.0167200	+	0.00965330i
$833$	−7.91098			−0.274099
$834$	0.579131	+	2.03380i	0.0200537	+	0.0704247i
$835$		−	11.5012i		−	0.398017i
$836$	−5.25709			−0.181820
$837$	25.5785	+	13.5181i	0.884124	+	0.467253i
$838$	4.45152			0.153775
$839$			23.2464i			0.802555i	0.915956	+	0.401278i	$0.131434\pi$
$839$			23.2464i			0.802555i	−0.915956	+	0.401278i	$0.868566\pi$
$840$	1.66275	+	5.83927i	0.0573705	+	0.201474i
$841$	−22.0070			−0.758864
$842$	−9.09301	−	5.24985i	−0.313366	−	0.180922i
$843$	23.2005	−	6.60642i	0.799066	−	0.227537i
$844$	4.46360	+	7.73118i	0.153643	+	0.266118i
$845$		−	12.6899i		−	0.436545i
$846$	22.8386	−	14.1544i	0.785206	−	0.486639i
$847$	−17.4644	+	30.2492i	−0.600083	+	1.03937i
$848$	1.80684	−	3.12954i	0.0620472	−	0.107469i
$849$	13.3459	+	46.8684i	0.458031	+	1.60852i
$850$	1.29577	+	0.748115i	0.0444447	+	0.0256601i
$851$	6.71703	−	3.87808i	0.230257	−	0.132939i
$852$	4.73636	−	18.8486i	0.162265	−	0.645742i
$853$	27.9332			0.956415			0.478207	−	0.878247i	$-0.341287\pi$
$853$	27.9332			0.956415			0.478207	+	0.878247i	$0.341287\pi$
$854$	1.16164	+	2.01202i	0.0397505	+	0.0688499i
$855$	−8.16452	−	13.1737i	−0.279221	−	0.450530i
$856$	−8.99386	−	15.5778i	−0.307404	−	0.532439i
$857$	−30.8970	−	17.8384i	−1.05542	−	0.609348i	−0.131259	−	0.991348i	$-0.541902\pi$
$857$	−30.8970	−	17.8384i	−1.05542	−	0.609348i	−0.924162	+	0.382000i	$0.875235\pi$
$858$	0.683127	−	0.704797i	0.0233216	−	0.0240614i
$859$	−27.9755	−	16.1517i	−0.954512	−	0.551088i	−0.0600327	−	0.998196i	$-0.519120\pi$
$859$	−27.9755	−	16.1517i	−0.954512	−	0.551088i	−0.894480	+	0.447108i	$0.852454\pi$
$860$	6.57850			0.224325
$861$	53.0237	−	15.0987i	1.80704	−	0.514562i
$862$	−5.87257	−	10.1716i	−0.200020	−	0.346446i
$863$	−10.9154	+	18.9061i	−0.371565	+	0.643570i	−0.989807	−	0.142418i	$-0.954512\pi$
$863$	−10.9154	+	18.9061i	−0.371565	+	0.643570i	0.618241	+	0.785988i	$0.287845\pi$
$864$	3.49818	−	3.84223i	0.119011	−	0.130715i
$865$	1.17708	+	2.03876i	0.0400219	+	0.0693200i
$866$	−0.986441			−0.0335206
$867$	−24.7964	−	6.23096i	−0.842131	−	0.211615i
$868$	−13.6699	−	13.9298i	−0.463986	−	0.472809i
$869$		−	0.216903i		−	0.00735792i
$870$	−4.44217	−	1.11625i	−0.150604	−	0.0378444i
$871$	−0.741469	+	0.428087i	−0.0251237	+	0.0145052i
$872$			7.55577i			0.255871i
$873$	−33.8620	+	20.9863i	−1.14606	+	0.710280i
$874$	14.3981	−	8.31276i	0.487024	−	0.281183i
$875$	−3.03570	+	1.75266i	−0.102625	+	0.0592507i
$876$	2.55376	−	10.1628i	0.0862834	−	0.343369i
$877$	−14.0024	+	24.2529i	−0.472829	+	0.818963i	−0.999516	−	0.0310954i	$-0.990100\pi$
$877$	−14.0024	+	24.2529i	−0.472829	+	0.818963i	0.526688	+	0.850059i	$0.323434\pi$
$878$	1.30933	+	0.755941i	0.0441877	+	0.0255118i
$879$	27.3762	+	26.5345i	0.923378	+	0.894987i
$880$	0.881264	−	0.508798i	0.0297074	−	0.0171516i
$881$	−6.16441	+	10.6771i	−0.207684	+	0.359720i	−0.950985	−	0.309238i	$-0.899926\pi$
$881$	−6.16441	+	10.6771i	−0.207684	+	0.359720i	0.743300	+	0.668958i	$0.233259\pi$
$882$	−15.8541	+	0.495187i	−0.533835	+	0.0166738i
$883$			26.1480i			0.879951i	0.898010	+	0.439976i	$0.145013\pi$
$883$			26.1480i			0.879951i	−0.898010	+	0.439976i	$0.854987\pi$
$884$			0.833232i			0.0280246i
$885$	4.50419	+	15.8179i	0.151407	+	0.531712i
$886$	18.8559	−	32.6594i	0.633476	−	1.09721i
$887$	7.69703	−	4.44388i	0.258441	−	0.149211i	−0.365182	−	0.930936i	$-0.618993\pi$
$887$	7.69703	−	4.44388i	0.258441	−	0.149211i	0.623623	+	0.781725i	$0.285660\pi$
$888$	2.90536	−	2.99752i	0.0974975	−	0.100590i
$889$	57.2428	+	33.0491i	1.91986	+	1.10843i
$890$	−0.389767	+	0.675095i	−0.0130650	+	0.0226292i
$891$	−5.06523	−	7.63014i	−0.169692	−	0.255619i
$892$	−6.97582	+	4.02749i	−0.233568	+	0.134850i
$893$	40.0712	−	23.1351i	1.34093	−	0.774187i
$894$	23.1263	−	23.8599i	0.773460	−	0.797995i
$895$			2.98830i			0.0998878i
$896$	−3.03570	+	1.75266i	−0.101416	+	0.0585523i
$897$	−0.756491	+	3.01049i	−0.0252585	+	0.100517i
$898$		−	19.1329i		−	0.638474i
$899$	14.2571	−	3.67662i	0.475500	−	0.122622i
$900$	2.64364	+	1.41816i	0.0881213	+	0.0472720i
$901$	5.40691			0.180130
$902$	−4.62016	−	8.00235i	−0.153834	−	0.266449i
$903$	−9.73387	+	38.7364i	−0.323923	+	1.28907i
$904$	−2.41348	+	4.18028i	−0.0802713	+	0.139034i
$905$	10.9318	+	18.9344i	0.363384	+	0.629400i
$906$	−11.0528	−	38.8154i	−0.367205	−	1.28955i
$907$	−22.6580			−0.752347			−0.376174	−	0.926549i	$-0.622760\pi$
$907$	−22.6580			−0.752347			−0.376174	+	0.926549i	$0.622760\pi$
$908$	15.0890	+	8.71161i	0.500745	+	0.289105i
$909$	−27.6690	−	44.6446i	−0.917722	−	1.48077i
$910$	−1.69054	−	0.976035i	−0.0560409	−	0.0323552i
$911$	−20.8726	−	36.1524i	−0.691539	−	1.19778i	−0.971333	−	0.237721i	$-0.923600\pi$
$911$	−20.8726	−	36.1524i	−0.691539	−	1.19778i	0.279794	−	0.960060i	$-0.409734\pi$
$912$	6.22771	−	6.42526i	0.206220	−	0.212762i
$913$	−1.74632	−	3.02471i	−0.0577947	−	0.100103i
$914$	33.8765			1.12054
$915$	1.11337	+	0.279772i	0.0368068	+	0.00924899i
$916$	12.2125	−	7.05087i	0.403511	−	0.232967i
$917$	−2.49418	−	1.44001i	−0.0823650	−	0.0475535i
$918$	7.59570	+	1.65842i	0.250695	+	0.0547361i
$919$	27.6822	−	47.9471i	0.913153	−	1.58163i	0.103570	−	0.994622i	$-0.466973\pi$
$919$	27.6822	−	47.9471i	0.913153	−	1.58163i	0.809583	−	0.587005i	$-0.199693\pi$
$920$	−1.60907	+	2.78699i	−0.0530495	+	0.0918845i
$921$	−6.96962	+	7.19070i	−0.229657	+	0.236942i
$922$			20.2187i			0.665867i
$923$	3.12429	+	5.41143i	0.102837	+	0.178119i
$924$	1.69201	+	5.94202i	0.0556631	+	0.195478i
$925$	2.08724	+	1.20507i	0.0686280	+	0.0396224i
$926$	4.75152			0.156145
$927$	−0.0408192	−	1.30688i	−0.00134068	−	0.0429237i
$928$		−	2.64442i		−	0.0868073i
$929$	−13.1951			−0.432917			−0.216459	−	0.976292i	$-0.569451\pi$
$929$	−13.1951			−0.432917			−0.216459	+	0.976292i	$0.569451\pi$
$930$	−9.64347	+	0.0597329i	−0.316222	+	0.00195872i
$931$	−27.3150			−0.895214
$932$			2.39244i			0.0783669i
$933$	0.747528	−	0.212861i	0.0244730	−	0.00696877i
$934$	4.46882			0.146224
$935$	1.31857	+	0.761279i	0.0431220	+	0.0248965i
$936$	0.0521560	+	1.66985i	0.00170477	+	0.0545807i
$937$	−12.0937	−	20.9469i	−0.395083	−	0.684304i	0.598029	−	0.801475i	$-0.295951\pi$
$937$	−12.0937	−	20.9469i	−0.395083	−	0.684304i	−0.993112	+	0.117171i	$0.962618\pi$
$938$		−	5.38918i		−	0.175963i
$939$	−21.7346	−	21.0663i	−0.709282	−	0.687474i
$940$	−4.47818	+	7.75644i	−0.146062	+	0.252987i
$941$	−23.1741	+	40.1388i	−0.755455	+	1.30849i	0.189693	+	0.981843i	$0.439251\pi$
$941$	−23.1741	+	40.1388i	−0.755455	+	1.30849i	−0.945148	+	0.326643i	$0.894083\pi$
$942$	−17.8940	+	5.09539i	−0.583019	+	0.166017i
$943$	25.3074	+	14.6112i	0.824122	+	0.475807i
$944$	−8.22333	+	4.74774i	−0.267647	+	0.154526i
$945$	−12.2623	+	13.4682i	−0.398891	+	0.438122i
$946$	6.69426			0.217649
$947$	12.4511	+	21.5659i	0.404605	+	0.700796i	0.994275	−	0.106848i	$-0.0340757\pi$
$947$	12.4511	+	21.5659i	0.404605	+	0.700796i	−0.589670	+	0.807644i	$0.700742\pi$
$948$	0.265101	+	0.256950i	0.00861007	+	0.00834534i
$949$	1.68456	+	2.91774i	0.0546831	+	0.0947139i
$950$	4.47405	+	2.58309i	0.145157	+	0.0838066i
$951$	−1.61101	−	1.56148i	−0.0522406	−	0.0506344i
$952$	−4.54210	−	2.62238i	−0.147210	−	0.0849919i
$953$	54.5547			1.76720			0.883600	−	0.468243i	$-0.155113\pi$
$953$	54.5547			1.76720			0.883600	+	0.468243i	$0.155113\pi$
$954$	10.8358	−	0.338445i	0.350821	−	0.0109575i
$955$	−4.67054	−	8.08961i	−0.151135	−	0.261773i
$956$	5.50979	−	9.54323i	0.178199	−	0.308650i
$957$	−4.52033	−	1.13589i	−0.146122	−	0.0367181i
$958$	4.22624	+	7.32007i	0.136544	+	0.236501i
$959$	69.9412			2.25852
$960$	−0.422115	+	1.67983i	−0.0136237	+	0.0542162i
$961$	27.1340	−	14.9916i	0.875289	−	0.483600i
$962$			1.34217i			0.0432735i
$963$	25.5095	−	47.5530i	0.822031	−	1.53237i
$964$	−21.5818	+	12.4602i	−0.695101	+	0.401317i
$965$		−	1.69281i		−	0.0544935i
$966$	−14.0299	−	13.5985i	−0.451404	−	0.437525i
$967$	−35.0773	+	20.2519i	−1.12801	+	0.651257i	−0.943434	−	0.331561i	$-0.892425\pi$
$967$	−35.0773	+	20.2519i	−1.12801	+	0.651257i	−0.184576	+	0.982818i	$0.559091\pi$
$968$	−8.62951	+	4.98225i	−0.277363	+	0.160136i
$969$	12.9847	+	3.26286i	0.417130	+	0.104818i
$970$	6.63966	−	11.5002i	0.213187	−	0.369250i
$971$	−47.5688	−	27.4639i	−1.52656	−	0.881358i	−0.999503	−	0.0315255i	$-0.989963\pi$
$971$	−47.5688	−	27.4639i	−1.52656	−	0.881358i	−0.527053	−	0.849832i	$-0.676703\pi$
$972$	15.3261	+	2.84813i	0.491584	+	0.0913538i
$973$	3.70626	−	2.13981i	0.118817	−	0.0685991i
$974$	−16.8806	+	29.2380i	−0.540888	+	0.936846i
$975$	−0.927680	+	0.264160i	−0.0297095	+	0.00845990i
$976$			0.662787i			0.0212153i
$977$		−	9.01668i		−	0.288469i	−0.989544	−	0.144235i	$-0.953928\pi$
$977$		−	9.01668i		−	0.288469i	0.989544	−	0.144235i	$-0.0460720\pi$
$978$	5.93325	−	1.68952i	0.189724	−	0.0540247i
$979$	−0.396625	+	0.686975i	−0.0126762	+	0.0219558i
$980$	4.57892	−	2.64364i	0.146268	−	0.0844479i
$981$	−19.2671	+	11.9410i	−0.615150	+	0.381246i
$982$	−6.69152	−	3.86335i	−0.213535	−	0.123284i
$983$	10.0029	−	17.3255i	0.319042	−	0.552596i	−0.661247	−	0.750168i	$-0.729972\pi$
$983$	10.0029	−	17.3255i	0.319042	−	0.552596i	0.980288	+	0.197572i	$0.0633057\pi$
$984$	15.2537	+	3.83303i	0.486271	+	0.122192i
$985$	13.7342	−	7.92946i	0.437609	−	0.252654i
$986$	3.42657	−	1.97833i	0.109124	−	0.0630029i
$987$	−39.0463	−	37.8458i	−1.24286	−	1.20465i
$988$			2.87698i			0.0915291i
$989$	−18.3342	+	10.5853i	−0.582995	+	0.336592i
$990$	2.69016	+	1.44311i	0.0854988	+	0.0458652i
$991$			53.7889i			1.70866i	0.519730	+	0.854330i	$0.326032\pi$
$991$			53.7889i			1.70866i	−0.519730	+	0.854330i	$0.673968\pi$
$992$	−1.39033	−	5.39138i	−0.0441430	−	0.171176i
$993$	−8.53390	+	33.9611i	−0.270815	+	1.07772i
$994$	−39.3316			−1.24752
$995$	−6.80268	−	11.7826i	−0.215660	−	0.373533i
$996$	5.76557	+	1.44880i	0.182689	+	0.0459070i
$997$	5.51236	−	9.54769i	0.174578	−	0.302378i	−0.765437	−	0.643511i	$-0.777477\pi$
$997$	5.51236	−	9.54769i	0.174578	−	0.302378i	0.940015	+	0.341133i	$0.110810\pi$
$998$	−16.3590	−	28.3347i	−0.517836	−	0.896918i
$999$	12.2352	+	2.67140i	0.387104	+	0.0845193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.e.161.4	✓	40
3.2	odd	2	inner	930.2.o.e.161.16	yes	40
31.26	odd	6	inner	930.2.o.e.491.6	yes	40
93.26	even	6	inner	930.2.o.e.491.14	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.e.161.4	✓	40	1.1	even	1	trivial
930.2.o.e.161.16	yes	40	3.2	odd	2	inner
930.2.o.e.491.6	yes	40	31.26	odd	6	inner
930.2.o.e.491.14	yes	40	93.26	even	6	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.474351 - 1.66583i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.66583 + 0.474351i) q^{6} +(1.75266 + 3.03570i) q^{7} +1.00000i q^{8} +(-2.54998 + 1.58038i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.474351 - 1.66583i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.66583 + 0.474351i) q^{6} +(1.75266 + 3.03570i) q^{7} +1.00000i q^{8} +(-2.54998 + 1.58038i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.508798 - 0.881264i) q^{11} +(0.474351 + 1.66583i) q^{12} +(-0.482279 - 0.278444i) q^{13} +(3.03570 - 1.75266i) q^{14} +(0.422115 - 1.67983i) q^{15} +1.00000 q^{16} +(0.748115 + 1.29577i) q^{17} +(1.58038 + 2.54998i) q^{18} +(2.58309 + 4.47405i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(4.22558 - 4.35962i) q^{21} +(-0.881264 - 0.508798i) q^{22} +3.21814 q^{23} +(1.66583 - 0.474351i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.278444 + 0.482279i) q^{26} +(3.84223 + 3.49818i) q^{27} +(-1.75266 - 3.03570i) q^{28} +2.64442 q^{29} +(-1.67983 - 0.422115i) q^{30} +(5.39138 - 1.39033i) q^{31} -1.00000i q^{32} +(-1.70939 - 0.429543i) q^{33} +(1.29577 - 0.748115i) q^{34} +3.50532i q^{35} +(2.54998 - 1.58038i) q^{36} +(2.08724 - 1.20507i) q^{37} +(4.47405 - 2.58309i) q^{38} +(-0.235071 + 0.935475i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(7.86397 + 4.54027i) q^{41} +(-4.35962 - 4.22558i) q^{42} +(-5.69715 + 3.28925i) q^{43} +(-0.508798 + 0.881264i) q^{44} +(-2.99854 + 0.0936563i) q^{45} -3.21814i q^{46} -8.95636i q^{47} +(-0.474351 - 1.66583i) q^{48} +(-2.64364 + 4.57892i) q^{49} +(0.866025 - 0.500000i) q^{50} +(1.80367 - 1.86088i) q^{51} +(0.482279 + 0.278444i) q^{52} +(1.80684 - 3.12954i) q^{53} +(3.49818 - 3.84223i) q^{54} +(0.881264 - 0.508798i) q^{55} +(-3.03570 + 1.75266i) q^{56} +(6.22771 - 6.42526i) q^{57} -2.64442i q^{58} +(-8.22333 + 4.74774i) q^{59} +(-0.422115 + 1.67983i) q^{60} +0.662787i q^{61} +(-1.39033 - 5.39138i) q^{62} +(-9.26680 - 4.97111i) q^{63} -1.00000 q^{64} +(-0.278444 - 0.482279i) q^{65} +(-0.429543 + 1.70939i) q^{66} +(0.768714 - 1.33145i) q^{67} +(-0.748115 - 1.29577i) q^{68} +(-1.52653 - 5.36088i) q^{69} +3.50532 q^{70} +(-9.71728 - 5.61027i) q^{71} +(-1.58038 - 2.54998i) q^{72} +(-5.23937 - 3.02495i) q^{73} +(-1.20507 - 2.08724i) q^{74} +(1.20548 - 1.24372i) q^{75} +(-2.58309 - 4.47405i) q^{76} +3.56700 q^{77} +(0.935475 + 0.235071i) q^{78} +(0.184595 - 0.106576i) q^{79} +(0.866025 + 0.500000i) q^{80} +(4.00481 - 8.05987i) q^{81} +(4.54027 - 7.86397i) q^{82} +(1.71612 - 2.97241i) q^{83} +(-4.22558 + 4.35962i) q^{84} +1.49623i q^{85} +(3.28925 + 5.69715i) q^{86} +(-1.25438 - 4.40515i) q^{87} +(0.881264 + 0.508798i) q^{88} -0.779533 q^{89} +(0.0936563 + 2.99854i) q^{90} -1.95207i q^{91} -3.21814 q^{92} +(-4.87346 - 8.32162i) q^{93} -8.95636 q^{94} +5.16618i q^{95} +(-1.66583 + 0.474351i) q^{96} +13.2793 q^{97} +(4.57892 + 2.64364i) q^{98} +(0.0953043 + 3.05130i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

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