LMFDB - Embedded newform 570.2.bf.a.89.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(29,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 17]))

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

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

chi := DirichletCharacter("570.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bf (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			89.7
Character	$\chi$	$=$	570.89
Dual form			570.2.bf.a.269.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 - 0.766044i) q^{2} +(-0.977291 + 1.43000i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.23454 - 0.0827774i) q^{5} +(1.72363 - 0.170539i) q^{6} +(-1.14096 - 0.658735i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-1.08981 - 2.79505i) q^{9} +O(q^{10})$	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.977291 + 1.43000i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.23454 - 0.0827774i) q^{5} +(1.72363 - 0.170539i) q^{6} +(-1.14096 - 0.658735i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-1.08981 - 2.79505i) q^{9} +(-1.49974 - 1.65855i) q^{10} +(2.83265 - 1.63543i) q^{11} +(-1.23857 - 1.21076i) q^{12} +(0.592390 - 0.215612i) q^{13} +(0.228776 + 1.29746i) q^{14} +(-2.06542 + 3.27629i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.12210 - 2.61976i) q^{17} +(-1.44062 + 2.63147i) q^{18} +(-4.29744 - 0.729393i) q^{19} +(-0.306503 + 2.21496i) q^{20} +(2.05704 - 0.987803i) q^{21} +(-3.07360 - 1.11870i) q^{22} +(0.00940327 - 0.0533286i) q^{23} +(-0.131358 + 1.72706i) q^{24} +(4.98630 - 0.369938i) q^{25} +(-0.545950 - 0.315204i) q^{26} +(5.06199 + 1.17316i) q^{27} +(0.846854 - 1.00924i) q^{28} +(6.16648 + 5.17430i) q^{29} +(3.83741 - 0.523753i) q^{30} +(1.01542 + 0.586251i) q^{31} +(0.342020 + 0.939693i) q^{32} +(-0.429654 + 5.64898i) q^{33} +(-4.01370 - 0.707724i) q^{34} +(-2.60405 - 1.37752i) q^{35} +(2.94183 - 0.587894i) q^{36} +3.17220 q^{37} +(2.20359 + 3.76087i) q^{38} +(-0.270611 + 1.05783i) q^{39} +(1.89378 - 1.18895i) q^{40} +(4.99046 + 1.81638i) q^{41} +(-2.07894 - 0.940841i) q^{42} +(5.75075 - 1.01401i) q^{43} +(1.11870 + 3.07360i) q^{44} +(-2.66658 - 6.15543i) q^{45} +(-0.0468964 + 0.0270756i) q^{46} +(-2.96369 - 2.48683i) q^{47} +(1.40744 - 1.00951i) q^{48} +(-2.63214 - 4.55899i) q^{49} +(-3.48852 - 3.58193i) q^{50} +(0.695051 + 7.02488i) q^{51} +(0.109469 + 0.620831i) q^{52} +(5.06479 + 0.893059i) q^{53} +(-2.35509 - 4.63180i) q^{54} +(6.19428 - 3.88891i) q^{55} -1.31747 q^{56} +(5.24288 - 5.43251i) q^{57} -8.04977i q^{58} +(4.27319 - 3.58563i) q^{59} +(-2.86786 - 2.60296i) q^{60} +(0.166865 - 0.946339i) q^{61} +(-0.203603 - 1.15469i) q^{62} +(-0.597772 + 3.90695i) q^{63} +(0.500000 - 0.866025i) q^{64} +(1.30587 - 0.530830i) q^{65} +(4.60355 - 3.30196i) q^{66} +(-1.52596 - 1.28043i) q^{67} +(2.03781 + 3.52959i) q^{68} +(0.0670702 + 0.0655642i) q^{69} +(0.618609 + 2.88027i) q^{70} +(-0.158531 - 0.899077i) q^{71} +(-2.34133 - 1.87568i) q^{72} +(3.00215 - 8.24833i) q^{73} +(-2.03905 - 2.43005i) q^{74} +(-4.34405 + 7.49195i) q^{75} +(1.46455 - 4.10549i) q^{76} -4.30926 q^{77} +(0.984294 - 0.472663i) q^{78} +(-4.62822 + 12.7159i) q^{79} +(-2.12809 - 0.686471i) q^{80} +(-6.62465 + 6.09213i) q^{81} +(-1.81638 - 4.99046i) q^{82} +(-3.82053 + 6.61736i) q^{83} +(0.615594 + 2.19732i) q^{84} +(6.75959 - 6.11238i) q^{85} +(-4.47329 - 3.75354i) q^{86} +(-13.4257 + 3.76129i) q^{87} +(1.63543 - 2.83265i) q^{88} +(-13.5101 + 4.91727i) q^{89} +(-3.00129 + 5.99935i) q^{90} +(-0.817927 - 0.144223i) q^{91} +(0.0508856 + 0.0185208i) q^{92} +(-1.83070 + 0.879109i) q^{93} +3.86882i q^{94} +(-9.66316 - 1.27412i) q^{95} +(-1.67801 - 0.429264i) q^{96} +(11.3663 - 9.53743i) q^{97} +(-1.80049 + 4.94680i) q^{98} +(-7.65815 - 6.13510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) $ 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$3$	−0.977291	+	1.43000i	−0.564239	+	0.825612i
$3$	−0.977291	+	1.43000i	−0.564239	+	0.825612i
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	2.23454	−	0.0827774i	0.999315	−	0.0370192i
$5$	2.23454	−	0.0827774i	0.999315	−	0.0370192i
$6$	1.72363	−	0.170539i	0.703671	−	0.0696222i
$7$	−1.14096	−	0.658735i	−0.431244	−	0.248979i	0.268633	−	0.963243i	$-0.413428\pi$
$7$	−1.14096	−	0.658735i	−0.431244	−	0.248979i	−0.699876	+	0.714264i	$0.746762\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−1.08981	−	2.79505i	−0.363269	−	0.931684i
$10$	−1.49974	−	1.65855i	−0.474260	−	0.524478i
$11$	2.83265	−	1.63543i	0.854076	−	0.493101i	−0.00794814	−	0.999968i	$-0.502530\pi$
$11$	2.83265	−	1.63543i	0.854076	−	0.493101i	0.862024	+	0.506867i	$0.169197\pi$
$12$	−1.23857	−	1.21076i	−0.357545	−	0.349516i
$13$	0.592390	−	0.215612i	0.164299	−	0.0598001i	−0.258561	−	0.965995i	$-0.583248\pi$
$13$	0.592390	−	0.215612i	0.164299	−	0.0598001i	0.422860	+	0.906195i	$0.361026\pi$
$14$	0.228776	+	1.29746i	0.0611431	+	0.346760i
$15$	−2.06542	+	3.27629i	−0.533289	+	0.845933i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	3.12210	−	2.61976i	0.757221	−	0.635384i	−0.180181	−	0.983634i	$-0.557668\pi$
$17$	3.12210	−	2.61976i	0.757221	−	0.635384i	0.937402	+	0.348249i	$0.113224\pi$
$18$	−1.44062	+	2.63147i	−0.339558	+	0.620242i
$19$	−4.29744	−	0.729393i	−0.985900	−	0.167334i
$19$	−4.29744	−	0.729393i	−0.985900	−	0.167334i
$20$	−0.306503	+	2.21496i	−0.0685362	+	0.495281i
$21$	2.05704	−	0.987803i	0.448884	−	0.215556i
$22$	−3.07360	−	1.11870i	−0.655295	−	0.238508i
$23$	0.00940327	−	0.0533286i	0.00196072	−	0.0111198i	−0.983812	−	0.179205i	$-0.942647\pi$
$23$	0.00940327	−	0.0533286i	0.00196072	−	0.0111198i	0.985772	+	0.168086i	$0.0537585\pi$
$24$	−0.131358	+	1.72706i	−0.0268133	+	0.352535i
$25$	4.98630	−	0.369938i	0.997259	−	0.0739876i
$26$	−0.545950	−	0.315204i	−0.107070	−	0.0618166i
$27$	5.06199	+	1.17316i	0.974180	+	0.225774i
$28$	0.846854	−	1.00924i	0.160040	−	0.190729i
$29$	6.16648	+	5.17430i	1.14509	+	0.960842i	0.999593	−	0.0285166i	$-0.00907836\pi$
$29$	6.16648	+	5.17430i	1.14509	+	0.960842i	0.145494	+	0.989359i	$0.453523\pi$
$30$	3.83741	−	0.523753i	0.700611	−	0.0956238i
$31$	1.01542	+	0.586251i	0.182374	+	0.105294i	0.588408	−	0.808564i	$-0.299755\pi$
$31$	1.01542	+	0.586251i	0.182374	+	0.105294i	−0.406034	+	0.913858i	$0.633088\pi$
$32$	0.342020	+	0.939693i	0.0604612	+	0.166116i
$33$	−0.429654	+	5.64898i	−0.0747931	+	0.983362i
$34$	−4.01370	−	0.707724i	−0.688344	−	0.121374i
$35$	−2.60405	−	1.37752i	−0.440165	−	0.232844i
$36$	2.94183	−	0.587894i	0.490305	−	0.0979823i
$37$	3.17220			0.521506			0.260753	−	0.965405i	$-0.416029\pi$
$37$	3.17220			0.521506			0.260753	+	0.965405i	$0.416029\pi$
$38$	2.20359	+	3.76087i	0.357470	+	0.610094i
$39$	−0.270611	+	1.05783i	−0.0433325	+	0.169389i
$40$	1.89378	−	1.18895i	0.299432	−	0.187990i
$41$	4.99046	+	1.81638i	0.779380	+	0.283671i	0.700914	−	0.713246i	$-0.252776\pi$
$41$	4.99046	+	1.81638i	0.779380	+	0.283671i	0.0784657	+	0.996917i	$0.474998\pi$
$42$	−2.07894	−	0.940841i	−0.320788	−	0.145175i
$43$	5.75075	−	1.01401i	0.876982	−	0.154636i	0.283006	−	0.959118i	$-0.408668\pi$
$43$	5.75075	−	1.01401i	0.876982	−	0.154636i	0.593976	+	0.804483i	$0.297557\pi$
$44$	1.11870	+	3.07360i	0.168650	+	0.463363i
$45$	−2.66658	−	6.15543i	−0.397510	−	0.917598i
$46$	−0.0468964	+	0.0270756i	−0.00691450	+	0.00399209i
$47$	−2.96369	−	2.48683i	−0.432299	−	0.362742i	0.400520	−	0.916288i	$-0.368830\pi$
$47$	−2.96369	−	2.48683i	−0.432299	−	0.362742i	−0.832818	+	0.553547i	$0.813274\pi$
$48$	1.40744	−	1.00951i	0.203147	−	0.145710i
$49$	−2.63214	−	4.55899i	−0.376019	−	0.651285i
$50$	−3.48852	−	3.58193i	−0.493351	−	0.506562i
$51$	0.695051	+	7.02488i	0.0973267	+	0.983679i
$52$	0.109469	+	0.620831i	0.0151807	+	0.0860938i
$53$	5.06479	+	0.893059i	0.695702	+	0.122671i	0.510306	−	0.859993i	$-0.329532\pi$
$53$	5.06479	+	0.893059i	0.695702	+	0.122671i	0.185396	+	0.982664i	$0.440643\pi$
$54$	−2.35509	−	4.63180i	−0.320488	−	0.630308i
$55$	6.19428	−	3.88891i	0.835236	−	0.524380i
$56$	−1.31747			−0.176054
$57$	5.24288	−	5.43251i	0.694436	−	0.719554i
$58$		−	8.04977i		−	1.05699i
$59$	4.27319	−	3.58563i	0.556322	−	0.466810i	−0.320753	−	0.947163i	$-0.603936\pi$
$59$	4.27319	−	3.58563i	0.556322	−	0.466810i	0.877075	+	0.480353i	$0.159491\pi$
$60$	−2.86786	−	2.60296i	−0.370239	−	0.336041i
$61$	0.166865	−	0.946339i	0.0213649	−	0.121166i	−0.972260	−	0.233902i	$-0.924850\pi$
$61$	0.166865	−	0.946339i	0.0213649	−	0.121166i	0.993625	+	0.112736i	$0.0359615\pi$
$62$	−0.203603	−	1.15469i	−0.0258576	−	0.146646i
$63$	−0.597772	+	3.90695i	−0.0753122	+	0.492229i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	1.30587	−	0.530830i	0.161973	−	0.0658414i
$66$	4.60355	−	3.30196i	0.566658	−	0.406443i
$67$	−1.52596	−	1.28043i	−0.186426	−	0.156430i	0.544798	−	0.838567i	$-0.316606\pi$
$67$	−1.52596	−	1.28043i	−0.186426	−	0.156430i	−0.731224	+	0.682137i	$0.761051\pi$
$68$	2.03781	+	3.52959i	0.247121	+	0.428025i
$69$	0.0670702	+	0.0655642i	0.00807431	+	0.00789301i
$70$	0.618609	+	2.88027i	0.0739379	+	0.344258i
$71$	−0.158531	−	0.899077i	−0.0188142	−	0.106701i	0.973954	−	0.226744i	$-0.0728079\pi$
$71$	−0.158531	−	0.899077i	−0.0188142	−	0.106701i	−0.992769	+	0.120043i	$0.961697\pi$
$72$	−2.34133	−	1.87568i	−0.275928	−	0.221051i
$73$	3.00215	−	8.24833i	0.351375	−	0.965394i	−0.630554	−	0.776145i	$-0.717172\pi$
$73$	3.00215	−	8.24833i	0.351375	−	0.965394i	0.981929	−	0.189249i	$-0.0606053\pi$
$74$	−2.03905	−	2.43005i	−0.237035	−	0.282487i
$75$	−4.34405	+	7.49195i	−0.501608	+	0.865095i
$76$	1.46455	−	4.10549i	0.167996	−	0.470932i
$77$	−4.30926			−0.491086
$78$	0.984294	−	0.472663i	0.111449	−	0.0535185i
$79$	−4.62822	+	12.7159i	−0.520716	+	1.43065i	0.349010	+	0.937119i	$0.386518\pi$
$79$	−4.62822	+	12.7159i	−0.520716	+	1.43065i	−0.869726	+	0.493535i	$0.835704\pi$
$80$	−2.12809	−	0.686471i	−0.237927	−	0.0767498i
$81$	−6.62465	+	6.09213i	−0.736072	+	0.676904i
$82$	−1.81638	−	4.99046i	−0.200586	−	0.551105i
$83$	−3.82053	+	6.61736i	−0.419358	+	0.726349i	−0.995875	−	0.0907359i	$-0.971078\pi$
$83$	−3.82053	+	6.61736i	−0.419358	+	0.726349i	0.576517	+	0.817085i	$0.304411\pi$
$84$	0.615594	+	2.19732i	0.0671668	+	0.239748i
$85$	6.75959	−	6.11238i	0.733181	−	0.662980i
$86$	−4.47329	−	3.75354i	−0.482368	−	0.404754i
$87$	−13.4257	+	3.76129i	−1.43939	+	0.403253i
$88$	1.63543	−	2.83265i	0.174338	−	0.301961i
$89$	−13.5101	+	4.91727i	−1.43207	+	0.521230i	−0.937523	−	0.347923i	$-0.886887\pi$
$89$	−13.5101	+	4.91727i	−1.43207	+	0.521230i	−0.494543	+	0.869153i	$0.664665\pi$
$90$	−3.00129	+	5.99935i	−0.316364	+	0.632387i
$91$	−0.817927	−	0.144223i	−0.0857420	−	0.0151186i
$92$	0.0508856	+	0.0185208i	0.00530519	+	0.00193093i
$93$	−1.83070	+	0.879109i	−0.189834	+	0.0911593i
$94$			3.86882i			0.399039i
$95$	−9.66316	−	1.27412i	−0.991419	−	0.130722i
$96$	−1.67801	−	0.429264i	−0.171262	−	0.0438115i
$97$	11.3663	−	9.53743i	1.15407	−	0.968380i	0.154263	−	0.988030i	$-0.450700\pi$
$97$	11.3663	−	9.53743i	1.15407	−	0.968380i	0.999807	+	0.0196500i	$0.00625521\pi$
$98$	−1.80049	+	4.94680i	−0.181877	+	0.499702i
$99$	−7.65815	−	6.13510i	−0.769673	−	0.616601i
$100$	−0.501543	+	4.97478i	−0.0501543	+	0.497478i
$101$	2.22197	+	6.10481i	0.221094	+	0.607451i	0.999801	−	0.0199365i	$-0.00634640\pi$
$101$	2.22197	+	6.10481i	0.221094	+	0.607451i	−0.778707	+	0.627388i	$0.784124\pi$
$102$	4.93460	−	5.04794i	0.488598	−	0.499821i
$103$	2.04733	+	3.54608i	0.201729	+	0.349406i	0.949086	−	0.315018i	$-0.102010\pi$
$103$	2.04733	+	3.54608i	0.201729	+	0.349406i	−0.747356	+	0.664423i	$0.768677\pi$
$104$	0.405219	−	0.482921i	0.0397350	−	0.0473543i
$105$	4.51477	−	2.37756i	0.440597	−	0.232026i
$106$	−2.57146	−	4.45390i	−0.249762	−	0.432601i
$107$	7.18638	+	4.14906i	0.694734	+	0.401105i	0.805383	−	0.592755i	$-0.201960\pi$
$107$	7.18638	+	4.14906i	0.694734	+	0.401105i	−0.110649	+	0.993860i	$0.535293\pi$
$108$	−2.03434	+	4.78137i	−0.195754	+	0.460087i
$109$	−13.8778	+	2.44702i	−1.32925	+	0.234382i	−0.792764	−	0.609528i	$-0.791359\pi$
$109$	−13.8778	+	2.44702i	−1.32925	+	0.234382i	−0.536484	+	0.843911i	$0.680248\pi$
$110$	−6.96068	−	2.24535i	−0.663675	−	0.214086i
$111$	−3.10016	+	4.53625i	−0.294254	+	0.430562i
$112$	0.846854	+	1.00924i	0.0800202	+	0.0953643i
$113$		−	11.2911i		−	1.06218i	−0.847316	−	0.531089i	$-0.821783\pi$
$113$		−	11.2911i		−	1.06218i	0.847316	−	0.531089i	$-0.178217\pi$
$114$	−7.53161	−	0.524327i	−0.705399	−	0.0491077i
$115$	0.0165975	−	0.119943i	0.00154773	−	0.0111847i
$116$	−6.16648	+	5.17430i	−0.572544	+	0.480421i
$117$	−1.24824	−	1.42079i	−0.115400	−	0.131352i
$118$	−5.49351	−	0.968654i	−0.505719	−	0.0891718i
$119$	−5.28793	+	0.932405i	−0.484744	+	0.0854734i
$120$	−0.150562	+	3.87006i	−0.0137444	+	0.353286i
$121$	−0.150733	+	0.261077i	−0.0137030	+	0.0237342i
$122$	−0.832197	+	0.480469i	−0.0753435	+	0.0434996i
$123$	−7.47456	+	5.36124i	−0.673958	+	0.483407i
$124$	−0.753669	+	0.898188i	−0.0676815	+	0.0806597i
$125$	11.1114	−	1.23939i	0.993837	−	0.110855i
$126$	3.37714	−	2.05342i	0.300859	−	0.182933i
$127$	−17.3913	+	6.32990i	−1.54322	+	0.561688i	−0.966816	−	0.255474i	$-0.917769\pi$
$127$	−17.3913	+	6.32990i	−1.54322	+	0.561688i	−0.576409	+	0.817162i	$0.695546\pi$
$128$	−0.984808	+	0.173648i	−0.0870455	+	0.0153485i
$129$	−4.17012	+	9.21457i	−0.367158	+	0.811298i
$130$	−1.24604	−	0.659143i	−0.109285	−	0.0578106i
$131$	−7.48641	−	8.92196i	−0.654091	−	0.779515i	0.332434	−	0.943126i	$-0.392130\pi$
$131$	−7.48641	−	8.92196i	−0.654091	−	0.779515i	−0.986525	+	0.163612i	$0.947686\pi$
$132$	−5.48855	−	1.40406i	−0.477717	−	0.122208i
$133$	4.42274	+	3.66309i	0.383500	+	0.317630i
$134$			1.99200i			0.172082i
$135$	11.4083	+	2.20244i	0.981870	+	0.189556i
$136$	1.39394	−	3.82983i	0.119530	−	0.328405i
$137$	−2.91356	+	16.5236i	−0.248923	+	1.41171i	0.562281	+	0.826946i	$0.309924\pi$
$137$	−2.91356	+	16.5236i	−0.248923	+	1.41171i	−0.811204	+	0.584764i	$0.801187\pi$
$138$	0.00711320	−	0.0935227i	0.000605516	−	0.00796118i
$139$	4.15155	−	1.51104i	0.352130	−	0.128165i	−0.159898	−	0.987134i	$-0.551117\pi$
$139$	4.15155	−	1.51104i	0.352130	−	0.128165i	0.512028	+	0.858969i	$0.328894\pi$
$140$	1.80878	−	2.32529i	0.152870	−	0.196522i
$141$	6.45256	−	1.80772i	0.543403	−	0.152238i
$142$	−0.586831	+	0.699357i	−0.0492457	+	0.0586888i
$143$	1.32541	−	1.57957i	0.110837	−	0.132090i
$144$	0.0681183	+	2.99923i	0.00567653	+	0.249936i
$145$	14.2075	+	11.0517i	1.17987	+	0.917794i
$146$	−8.24833	+	3.00215i	−0.682637	+	0.248459i
$147$	9.09172	+	0.691504i	0.749873	+	0.0570343i
$148$	−0.550847	+	3.12401i	−0.0452793	+	0.256792i
$149$	5.37465	−	14.7667i	0.440309	−	1.20974i	−0.498981	−	0.866613i	$-0.666292\pi$
$149$	5.37465	−	14.7667i	0.440309	−	1.20974i	0.939290	−	0.343125i	$-0.111485\pi$
$150$	8.53146	−	1.48800i	0.696591	−	0.121494i
$151$		−	7.40959i		−	0.602984i	−0.953469	−	0.301492i	$-0.902515\pi$
$151$		−	7.40959i		−	0.602984i	0.953469	−	0.301492i	$-0.0974846\pi$
$152$	−4.08639	+	1.51705i	−0.331450	+	0.123049i
$153$	−10.7248	−	5.87142i	−0.867052	−	0.474676i
$154$	2.76994	+	3.30109i	0.223208	+	0.266009i
$155$	2.31751	+	1.22594i	0.186147	+	0.0984702i
$156$	−0.994773	−	0.450191i	−0.0796456	−	0.0360442i
$157$	15.9632	−	2.81474i	1.27400	−	0.224641i	0.504570	−	0.863371i	$-0.331651\pi$
$157$	15.9632	−	2.81474i	1.27400	−	0.224641i	0.769431	+	0.638730i	$0.220540\pi$
$158$	12.7159	−	4.62822i	1.01163	−	0.368201i
$159$	−6.22685	+	6.36988i	−0.493821	+	0.505164i
$160$	0.842041	+	2.07146i	0.0665692	+	0.163764i
$161$	−0.0458582	+	0.0546517i	−0.00361413	+	0.00430716i
$162$	8.92508	+	1.15883i	0.701221	+	0.0910459i
$163$	−20.4834	+	11.8261i	−1.60438	+	0.926289i	−0.613783	+	0.789475i	$0.710353\pi$
$163$	−20.4834	+	11.8261i	−1.60438	+	0.926289i	−0.990597	+	0.136815i	$0.956314\pi$
$164$	−2.65537	+	4.59924i	−0.207350	+	0.359140i
$165$	−0.492468	+	12.6584i	−0.0383386	+	0.985456i
$166$	7.52498	−	1.32686i	0.584052	−	0.102984i
$167$	11.4396	+	2.01710i	0.885220	+	0.156088i	0.597732	−	0.801696i	$-0.296069\pi$
$167$	11.4396	+	2.01710i	0.885220	+	0.156088i	0.287488	+	0.957784i	$0.407180\pi$
$168$	1.28755	−	1.88398i	0.0993368	−	0.145353i
$169$	−9.65414	+	8.10079i	−0.742626	+	0.623137i
$170$	−9.02734	−	1.24919i	−0.692365	−	0.0958085i
$171$	2.64468	+	12.8065i	0.202244	+	0.979335i
$172$			5.83947i			0.445255i
$173$	−16.6982	−	19.9001i	−1.26954	−	1.51298i	−0.755392	−	0.655273i	$-0.772553\pi$
$173$	−16.6982	−	19.9001i	−1.26954	−	1.51298i	−0.514146	−	0.857703i	$-0.671891\pi$
$174$	11.5112	+	7.86697i	0.872661	+	0.596393i
$175$	−5.93287	−	2.86256i	−0.448483	−	0.216390i
$176$	−3.22117	+	0.567979i	−0.242805	+	0.0428130i
$177$	0.951310	+	9.61488i	0.0715048	+	0.722698i
$178$	12.4510	+	7.18857i	0.933239	+	0.538806i
$179$	2.64887	+	4.58797i	0.197986	+	0.342921i	0.947875	−	0.318642i	$-0.103227\pi$
$179$	2.64887	+	4.58797i	0.197986	+	0.342921i	−0.749890	+	0.661563i	$0.769893\pi$
$180$	6.52497	−	1.55719i	0.486342	−	0.116066i
$181$	2.09597	−	2.49788i	0.155793	−	0.185666i	−0.682502	−	0.730883i	$-0.739108\pi$
$181$	2.09597	−	2.49788i	0.155793	−	0.185666i	0.838295	+	0.545217i	$0.183553\pi$
$182$	0.415272	+	0.719273i	0.0307820	+	0.0533161i
$183$	1.19019	+	1.16347i	0.0879814	+	0.0860059i
$184$	−0.0185208	−	0.0508856i	−0.00136537	−	0.00375133i
$185$	7.08839	−	0.262586i	0.521149	−	0.0193057i
$186$	1.85018	+	0.837314i	0.135662	+	0.0613948i
$187$	4.55940	−	12.5268i	0.333416	−	0.916053i
$188$	2.96369	−	2.48683i	0.216149	−	0.181371i
$189$	−5.00274	−	4.67304i	−0.363896	−	0.339913i
$190$	5.23532	+	8.22140i	0.379810	+	0.596443i
$191$		−	23.4487i		−	1.69669i	−0.529443	−	0.848346i	$-0.677599\pi$
$191$		−	23.4487i		−	1.69669i	0.529443	−	0.848346i	$-0.322401\pi$
$192$	0.749772	+	1.56136i	0.0541101	+	0.112681i
$193$	−16.4500	−	5.98730i	−1.18409	−	0.430975i	−0.326448	−	0.945215i	$-0.605852\pi$
$193$	−16.4500	−	5.98730i	−1.18409	−	0.430975i	−0.857647	+	0.514240i	$0.828074\pi$
$194$	−14.6122	−	2.57652i	−1.04909	−	0.184984i
$195$	−0.517126	+	2.38617i	−0.0370322	+	0.170877i
$196$	4.94680	−	1.80049i	0.353343	−	0.128606i
$197$	−3.37708	+	5.84927i	−0.240607	+	0.416743i	−0.960887	−	0.276940i	$-0.910680\pi$
$197$	−3.37708	+	5.84927i	−0.240607	+	0.416743i	0.720280	+	0.693683i	$0.244013\pi$
$198$	0.222806	+	9.81005i	0.0158341	+	0.697170i
$199$	−2.03109	−	1.70429i	−0.143980	−	0.120814i	0.567953	−	0.823061i	$-0.307736\pi$
$199$	−2.03109	−	1.70429i	−0.143980	−	0.120814i	−0.711933	+	0.702247i	$0.752180\pi$
$200$	4.13329	−	2.81352i	0.292268	−	0.198946i
$201$	3.32232	−	0.930769i	0.234339	−	0.0656514i
$202$	3.24830	−	5.62622i	0.228550	−	0.395860i
$203$	−3.62724	−	9.96576i	−0.254582	−	0.699459i
$204$	−7.03885	−	0.535365i	−0.492818	−	0.0374830i
$205$	11.3017	+	3.64567i	0.789347	+	0.254625i
$206$	1.40046	−	3.84772i	0.0975744	−	0.268084i
$207$	−0.159304	+	0.0318352i	−0.0110724	+	0.00221270i
$208$	−0.630409			−0.0437110
$209$	−13.3660	+	4.96205i	−0.924546	+	0.343232i
$210$	−4.72335	−	1.93025i	−0.325942	−	0.133200i
$211$	−9.74000	−	11.6077i	−0.670529	−	0.799105i	0.318327	−	0.947981i	$-0.396879\pi$
$211$	−9.74000	−	11.6077i	−0.670529	−	0.799105i	−0.988856	+	0.148876i	$0.952435\pi$
$212$	−1.75898	+	4.83277i	−0.120807	+	0.331916i
$213$	1.44061	+	0.651959i	0.0987091	+	0.0446715i
$214$	−1.44095	−	8.17205i	−0.0985015	−	0.558630i
$215$	12.7663	−	2.74188i	0.870656	−	0.186995i
$216$	4.97039	−	1.51501i	0.338192	−	0.103083i
$217$	−0.772368	−	1.33778i	−0.0524318	−	0.0908145i
$218$	10.7950	+	9.05806i	0.731128	+	0.613489i
$219$	8.86115	+	12.3541i	0.598781	+	0.834812i
$220$	2.75420	+	6.77547i	0.185688	+	0.456802i
$221$	1.28465	−	2.22508i	0.0864150	−	0.149675i
$222$	5.46771	−	0.540984i	0.366969	−	0.0363084i
$223$	1.19464	+	6.77514i	0.0799990	+	0.453697i	0.998324	+	0.0578700i	$0.0184309\pi$
$223$	1.19464	+	6.77514i	0.0799990	+	0.453697i	−0.918325	+	0.395827i	$0.870458\pi$
$224$	0.228776	−	1.29746i	0.0152858	−	0.0866899i
$225$	−6.46809	−	13.5338i	−0.431206	−	0.902253i
$226$	−8.64949	+	7.25778i	−0.575355	+	0.482780i
$227$			8.29036i			0.550250i	0.961408	+	0.275125i	$0.0887193\pi$
$227$			8.29036i			0.550250i	−0.961408	+	0.275125i	$0.911281\pi$
$228$	4.43957	+	6.10658i	0.294017	+	0.404418i
$229$	−22.7873			−1.50583			−0.752913	−	0.658120i	$-0.771352\pi$
$229$	−22.7873			−1.50583			−0.752913	+	0.658120i	$0.771352\pi$
$230$	−0.102550	+	0.0643834i	−0.00676197	+	0.00424532i
$231$	4.21140	−	6.16225i	0.277090	−	0.405446i
$232$	7.92748	+	1.39783i	0.520465	+	0.0917719i
$233$	−2.79926	−	15.8754i	−0.183386	−	1.04003i	−0.928012	−	0.372550i	$-0.878483\pi$
$233$	−2.79926	−	15.8754i	−0.183386	−	1.04003i	0.744627	−	0.667481i	$-0.232628\pi$
$234$	−0.286033	+	1.86947i	−0.0186986	+	0.122211i
$235$	−6.82832	−	5.31158i	−0.445431	−	0.346490i
$236$	2.78913	+	4.83091i	0.181557	+	0.314466i
$237$	−13.6607	−	19.0455i	−0.887357	−	1.23714i
$238$	4.11328	+	3.45145i	0.266624	+	0.223724i
$239$	16.3377	−	9.43255i	1.05680	−	0.610141i	0.132251	−	0.991216i	$-0.457779\pi$
$239$	16.3377	−	9.43255i	1.05680	−	0.610141i	0.924544	+	0.381075i	$0.124446\pi$
$240$	3.06141	−	2.37229i	0.197613	−	0.153130i
$241$	1.23767	+	3.40046i	0.0797251	+	0.219043i	0.973151	−	0.230168i	$-0.0739275\pi$
$241$	1.23767	+	3.40046i	0.0797251	+	0.219043i	−0.893426	+	0.449211i	$0.851705\pi$
$242$	0.296885	−	0.0523489i	0.0190845	−	0.00336511i
$243$	−2.23755	−	15.4270i	−0.143539	−	0.989645i
$244$	0.902986	+	0.328660i	0.0578078	+	0.0210403i
$245$	−6.25898	−	9.96935i	−0.399872	−	0.636918i
$246$	8.91150	+	2.27971i	0.568177	+	0.145349i
$247$	−2.70303	+	0.494496i	−0.171990	+	0.0314640i
$248$	1.17250			0.0744539
$249$	−5.72906	−	11.9304i	−0.363064	−	0.756061i
$250$	−8.09172	−	7.71518i	−0.511765	−	0.487951i
$251$	13.9249	+	2.45534i	0.878933	+	0.154980i	0.594866	−	0.803825i	$-0.297205\pi$
$251$	13.9249	+	2.45534i	0.878933	+	0.154980i	0.284067	+	0.958804i	$0.408316\pi$
$252$	−3.74379	−	1.26712i	−0.235837	−	0.0798213i
$253$	−0.0605791	−	0.166440i	−0.00380857	−	0.0104640i
$254$	16.0279	+	9.25370i	1.00568	+	0.580628i
$255$	2.13462	+	15.6398i	0.133675	+	0.979402i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−19.9040	+	23.7206i	−1.24157	+	1.47965i	−0.422086	+	0.906556i	$0.638702\pi$
$257$	−19.9040	+	23.7206i	−1.24157	+	1.47965i	−0.819489	+	0.573095i	$0.805742\pi$
$258$	9.73927	−	2.72852i	0.606340	−	0.169870i
$259$	−3.61936	−	2.08964i	−0.224896	−	0.129844i
$260$	0.296004	+	1.37821i	0.0183574	+	0.0854728i
$261$	7.74216	−	22.8746i	0.479227	−	1.41590i
$262$	−2.02244	+	11.4698i	−0.124947	+	0.708609i
$263$	−16.5949	−	6.04005i	−1.02329	−	0.372446i	−0.224765	−	0.974413i	$-0.572162\pi$
$263$	−16.5949	−	6.04005i	−1.02329	−	0.372446i	−0.798521	+	0.601967i	$0.794384\pi$
$264$	2.45240	+	5.10699i	0.150935	+	0.314313i
$265$	11.3914	+	1.57632i	0.699767	+	0.0968327i
$266$	−0.0367974	−	5.74260i	−0.00225619	−	0.352102i
$267$	6.17158	−	24.1250i	0.377695	−	1.47643i
$268$	1.52596	−	1.28043i	0.0932128	−	0.0782148i
$269$	29.3992	+	10.7004i	1.79250	+	0.652417i	0.999040	+	0.0437959i	$0.0139451\pi$
$269$	29.3992	+	10.7004i	1.79250	+	0.652417i	0.793461	+	0.608621i	$0.208277\pi$
$270$	−5.64595	−	10.1550i	−0.343601	−	0.618011i
$271$	0.724087	+	4.10650i	0.0439851	+	0.249452i	0.998870	−	0.0475238i	$-0.0151330\pi$
$271$	0.724087	+	4.10650i	0.0439851	+	0.249452i	−0.954885	+	0.296976i	$0.904022\pi$
$272$	−3.82983	+	1.39394i	−0.232217	+	0.0845202i
$273$	1.00559	−	1.02869i	0.0608611	−	0.0622591i
$274$	14.5306	−	8.38927i	0.877828	−	0.506814i
$275$	13.5194	−	9.20265i	0.815252	−	0.554940i
$276$	−0.0762148	+	0.0546662i	−0.00458759	+	0.00329052i
$277$	−9.19741	+	5.31013i	−0.552619	+	0.319055i	−0.750178	−	0.661236i	$-0.770032\pi$
$277$	−9.19741	+	5.31013i	−0.552619	+	0.319055i	0.197559	+	0.980291i	$0.436699\pi$
$278$	−3.82609	−	2.20900i	−0.229474	−	0.132487i
$279$	0.531995	−	3.47704i	0.0318497	−	0.208165i
$280$	−2.94394	+	0.109057i	−0.175934	+	0.00651739i
$281$	−4.86020	+	27.5636i	−0.289935	+	1.64430i	0.397169	+	0.917746i	$0.369993\pi$
$281$	−4.86020	+	27.5636i	−0.289935	+	1.64430i	−0.687104	+	0.726559i	$0.741118\pi$
$282$	−5.53242	−	3.78096i	−0.329451	−	0.225153i
$283$	−12.2842	−	14.6397i	−0.730220	−	0.870242i	0.265361	−	0.964149i	$-0.414509\pi$
$283$	−12.2842	−	14.6397i	−0.730220	−	0.870242i	−0.995581	+	0.0939069i	$0.970064\pi$
$284$	0.912946			0.0541734
$285$	11.2657	−	12.5731i	0.667323	−	0.744768i
$286$	−2.06198			−0.121927
$287$	−4.49742	−	5.35982i	−0.265474	−	0.316380i
$288$	2.25376	−	1.98005i	0.132804	−	0.116675i
$289$	−0.0676089	+	0.383429i	−0.00397699	+	0.0225547i
$290$	−0.666339	−	17.9875i	−0.0391288	−	1.05626i
$291$	2.53039	+	25.5746i	0.148334	+	1.49921i
$292$	7.60170	+	4.38885i	0.444856	+	0.256838i
$293$	10.7733	−	6.21996i	0.629382	−	0.363374i	−0.151131	−	0.988514i	$-0.548292\pi$
$293$	10.7733	−	6.21996i	0.629382	−	0.363374i	0.780513	+	0.625140i	$0.214958\pi$
$294$	−5.31433	−	7.40916i	−0.309938	−	0.432111i
$295$	9.25179	−	8.36595i	0.538660	−	0.487084i
$296$	2.74721	−	1.58610i	0.159678	−	0.0921902i
$297$	16.2574	−	4.95539i	0.943353	−	0.287541i
$298$	−14.7667	+	5.37465i	−0.855414	+	0.311345i
$299$	−0.00592790	−	0.0336188i	−0.000342819	−	0.00194423i
$300$	−6.62379	−	5.57902i	−0.382425	−	0.322105i
$301$	−7.22936	−	2.63127i	−0.416694	−	0.151664i
$302$	−5.67607	+	4.76279i	−0.326621	+	0.274068i
$303$	−10.9014	−	2.78875i	−0.626269	−	0.160210i
$304$	3.78880	+	2.15522i	0.217303	+	0.123610i
$305$	0.294531	−	2.12844i	0.0168648	−	0.121874i
$306$	2.39603	+	11.9898i	0.136972	+	0.685410i
$307$	−14.8749	−	5.41403i	−0.848956	−	0.308995i	−0.119342	−	0.992853i	$-0.538078\pi$
$307$	−14.8749	−	5.41403i	−0.848956	−	0.308995i	−0.729615	+	0.683858i	$0.760301\pi$
$308$	0.748296	−	4.24380i	0.0426381	−	0.241813i
$309$	−7.07174	−	0.537866i	−0.402297	−	0.0305981i
$310$	−0.550539	−	2.56334i	−0.0312685	−	0.145588i
$311$	20.2113	+	11.6690i	1.14608	+	0.661687i	0.947928	−	0.318485i	$-0.103174\pi$
$311$	20.2113	+	11.6690i	1.14608	+	0.661687i	0.198148	+	0.980172i	$0.436507\pi$
$312$	0.294561	+	1.05142i	0.0166762	+	0.0595248i
$313$	19.2354	−	22.9239i	1.08725	−	1.29573i	0.134856	−	0.990865i	$-0.456943\pi$
$313$	19.2354	−	22.9239i	1.08725	−	1.29573i	0.952394	−	0.304870i	$-0.0986129\pi$
$314$	−12.4171	−	10.4192i	−0.700740	−	0.587991i
$315$	−1.01234	+	8.77969i	−0.0570386	+	0.494680i
$316$	−11.7191	−	6.76601i	−0.659249	−	0.380618i
$317$	5.66010	+	15.5510i	0.317903	+	0.873431i	0.990998	+	0.133875i	$0.0427422\pi$
$317$	5.66010	+	15.5510i	0.317903	+	0.873431i	−0.673095	+	0.739556i	$0.735036\pi$
$318$	8.88215	+	0.675564i	0.498086	+	0.0378837i
$319$	25.9297	+	4.57210i	1.45178	+	0.255989i
$320$	1.04558	−	1.97655i	0.0584497	−	0.110493i
$321$	−12.9563	+	6.22170i	−0.723153	+	0.347261i
$322$	0.0713427			0.00397578
$323$	−15.3279	+	8.98100i	−0.852866	+	0.499716i
$324$	−4.84922	−	7.58189i	−0.269401	−	0.421216i
$325$	2.87407	−	1.29425i	0.159425	−	0.0717923i
$326$	22.2257	+	8.08951i	1.23097	+	0.448036i
$327$	10.0634	−	22.2367i	0.556505	−	1.22969i
$328$	5.23006	−	0.922201i	0.288782	−	0.0509200i
$329$	1.74330	+	4.78967i	0.0961111	+	0.264063i
$330$	10.0135	−	7.75942i	0.551223	−	0.427142i
$331$	0.513552	−	0.296500i	0.0282274	−	0.0162971i	−0.485820	−	0.874059i	$-0.661479\pi$
$331$	0.513552	−	0.296500i	0.0282274	−	0.0162971i	0.514047	+	0.857762i	$0.328146\pi$
$332$	−5.85339	−	4.91158i	−0.321247	−	0.269558i
$333$	−3.45708	−	8.86647i	−0.189447	−	0.485879i
$334$	−5.80802	−	10.0598i	−0.317801	−	0.550447i
$335$	−3.51580	−	2.73486i	−0.192089	−	0.149421i
$336$	−2.27084	+	0.224680i	−0.123884	+	0.0122573i
$337$	1.33738	+	7.58464i	0.0728516	+	0.413162i	0.999323	+	0.0367962i	$0.0117152\pi$
$337$	1.33738	+	7.58464i	0.0728516	+	0.413162i	−0.926471	+	0.376366i	$0.877174\pi$
$338$	12.4111	+	2.18842i	0.675076	+	0.119034i
$339$	16.1463	+	11.0347i	0.876946	+	0.599322i
$340$	4.84573	+	7.71830i	0.262796	+	0.418584i
$341$	3.83509			0.207682
$342$	8.11036	−	10.2578i	0.438558	−	0.554677i
$343$			16.1578i			0.872440i
$344$	4.47329	−	3.75354i	0.241184	−	0.202377i
$345$	0.155298	+	0.140954i	0.00836097	+	0.00758869i
$346$	−4.51098	+	25.5831i	−0.242512	+	1.37535i
$347$	6.36972	+	36.1245i	0.341945	+	1.93926i	0.343193	+	0.939265i	$0.388492\pi$
$347$	6.36972	+	36.1245i	0.341945	+	1.93926i	−0.00124829	+	0.999999i	$0.500397\pi$
$348$	−1.37280	−	13.8749i	−0.0735898	−	0.743771i
$349$	8.87535	−	15.3725i	0.475086	−	0.822874i	−0.524506	−	0.851406i	$-0.675750\pi$
$349$	8.87535	−	15.3725i	0.475086	−	0.822874i	0.999593	+	0.0285327i	$0.00908348\pi$
$350$	1.62072	+	6.38486i	0.0866314	+	0.341285i
$351$	3.25162	−	0.396461i	0.173559	−	0.0211615i
$352$	2.50563	+	2.10247i	0.133550	+	0.112062i
$353$	4.23405	+	7.33360i	0.225356	+	0.390328i	0.956426	−	0.291974i	$-0.0943122\pi$
$353$	4.23405	+	7.33360i	0.225356	+	0.390328i	−0.731070	+	0.682302i	$0.760979\pi$
$354$	6.75393	−	6.90907i	0.358967	−	0.367213i
$355$	−0.428667	−	1.99590i	−0.0227513	−	0.105931i
$356$	−2.49656	−	14.1587i	−0.132318	−	0.750410i
$357$	3.83451	−	8.47298i	0.202944	−	0.448438i
$358$	1.81193	−	4.97824i	0.0957636	−	0.263108i
$359$	−0.861523	−	1.02672i	−0.0454695	−	0.0541884i	0.742830	−	0.669480i	$-0.233483\pi$
$359$	−0.861523	−	1.02672i	−0.0454695	−	0.0541884i	−0.788300	+	0.615291i	$0.789038\pi$
$360$	−5.38704	−	3.99747i	−0.283922	−	0.210685i
$361$	17.9360	+	6.26905i	0.943998	+	0.329950i
$362$	−3.26076			−0.171382
$363$	−0.226030	−	0.470696i	−0.0118635	−	0.0247051i
$364$	0.284063	−	0.780457i	0.0148890	−	0.0409071i
$365$	6.02563	−	18.6797i	0.315396	−	0.977740i
$366$	0.126227	−	1.65960i	0.00659798	−	0.0867487i
$367$	11.2419	+	30.8868i	0.586821	+	1.61228i	0.776279	+	0.630390i	$0.217105\pi$
$367$	11.2419	+	30.8868i	0.586821	+	1.61228i	−0.189457	+	0.981889i	$0.560673\pi$
$368$	−0.0270756	+	0.0468964i	−0.00141142	+	0.00244464i
$369$	−0.361759	−	15.9281i	−0.0188324	−	0.829185i
$370$	−4.75748	−	5.26124i	−0.247330	−	0.273519i
$371$	−5.19045	−	4.35530i	−0.269475	−	0.226116i
$372$	−0.547856	−	1.95554i	−0.0284050	−	0.101390i
$373$	−12.9116	+	22.3635i	−0.668537	+	1.15794i	0.309777	+	0.950809i	$0.399746\pi$
$373$	−12.9116	+	22.3635i	−0.668537	+	1.15794i	−0.978313	+	0.207130i	$0.933588\pi$
$374$	−12.5268	+	4.55940i	−0.647747	+	0.235761i
$375$	−9.08677	+	17.1006i	−0.469239	+	0.883071i
$376$	−3.81005	−	0.671814i	−0.196488	−	0.0346462i
$377$	4.76861	+	1.73563i	0.245596	+	0.0893896i
$378$	−0.364054	+	6.83609i	−0.0187249	+	0.351611i
$379$			20.5880i			1.05754i	0.848766	+	0.528768i	$0.177346\pi$
$379$			20.5880i			1.05754i	−0.848766	+	0.528768i	$0.822654\pi$
$380$	2.93276	−	9.29510i	0.150447	−	0.476829i
$381$	7.94455	−	31.0557i	0.407012	−	1.59103i
$382$	−17.9628	+	15.0726i	−0.919055	+	0.771179i
$383$	3.33320	−	9.15789i	0.170319	−	0.467946i	−0.824939	−	0.565222i	$-0.808791\pi$
$383$	3.33320	−	9.15789i	0.170319	−	0.467946i	0.995257	+	0.0972755i	$0.0310128\pi$
$384$	0.714126	−	1.57798i	0.0364426	−	0.0805260i
$385$	−9.62920	+	0.356710i	−0.490750	+	0.0181796i
$386$	5.98730	+	16.4500i	0.304746	+	0.837282i
$387$	−9.10143	−	14.9686i	−0.462652	−	0.760896i
$388$	7.41881	+	12.8498i	0.376633	+	0.652347i
$389$	−0.902396	+	1.07543i	−0.0457533	+	0.0545267i	−0.788436	−	0.615117i	$-0.789109\pi$
$389$	−0.902396	+	1.07543i	−0.0457533	+	0.0545267i	0.742682	+	0.669644i	$0.233553\pi$
$390$	2.16031	−	1.13766i	0.109392	−	0.0576076i
$391$	−0.110350	−	0.191132i	−0.00558064	−	0.00966595i
$392$	−4.55899	−	2.63214i	−0.230264	−	0.132943i
$393$	20.0748	−	1.98623i	1.01264	−	0.100192i
$394$	6.65155	−	1.17285i	0.335100	−	0.0590872i
$395$	−9.28933	+	28.7973i	−0.467397	+	1.44895i
$396$	7.37172	−	6.47646i	0.370443	−	0.325454i
$397$	−6.70500	−	7.99071i	−0.336514	−	0.401042i	0.571077	−	0.820896i	$-0.306526\pi$
$397$	−6.70500	−	7.99071i	−0.336514	−	0.401042i	−0.907592	+	0.419854i	$0.862081\pi$
$398$			2.65140i			0.132903i
$399$	−9.56052	+	2.74463i	−0.478625	+	0.137403i
$400$	−4.81211	−	1.35779i	−0.240606	−	0.0678893i
$401$	6.84360	−	5.74246i	0.341753	−	0.286765i	−0.455715	−	0.890126i	$-0.650617\pi$
$401$	6.84360	−	5.74246i	0.341753	−	0.286765i	0.797468	+	0.603361i	$0.206172\pi$
$402$	−2.84856	−	1.94676i	−0.142073	−	0.0970956i
$403$	0.727925	+	0.128353i	0.0362605	+	0.00639371i
$404$	−6.39790	+	1.12812i	−0.318308	+	0.0561262i
$405$	−14.2987	+	14.1615i	−0.710509	+	0.703688i
$406$	−5.30267	+	9.18450i	−0.263167	+	0.455819i
$407$	8.98573	−	5.18791i	0.445406	−	0.257155i
$408$	4.11437	+	5.73619i	0.203692	+	0.283984i
$409$	−6.69145	+	7.97456i	−0.330871	+	0.394316i	−0.905674	−	0.423975i	$-0.860634\pi$
$409$	−6.69145	+	7.97456i	−0.330871	+	0.394316i	0.574803	+	0.818292i	$0.305079\pi$
$410$	−4.47186	−	11.0010i	−0.220850	−	0.543301i
$411$	−20.7814	−	20.3148i	−1.02507	−	1.00206i
$412$	−3.84772	+	1.40046i	−0.189564	+	0.0689955i
$413$	−7.23754	+	1.27617i	−0.356136	+	0.0627964i
$414$	0.126786	+	0.101571i	0.00623118	+	0.00499193i
$415$	−7.98935	+	15.1030i	−0.392182	+	0.741376i
$416$	0.405219	+	0.482921i	0.0198675	+	0.0236771i
$417$	−1.89648	+	7.41345i	−0.0928712	+	0.363038i
$418$	12.3927	+	7.04941i	0.606145	+	0.344798i
$419$		−	32.7258i		−	1.59876i	−0.600825	−	0.799381i	$-0.705161\pi$
$419$		−	32.7258i		−	1.59876i	0.600825	−	0.799381i	$-0.294839\pi$
$420$	1.55745	+	4.85904i	0.0759960	+	0.237097i
$421$	11.0652	−	30.4013i	0.539283	−	1.48167i	−0.308447	−	0.951242i	$-0.599809\pi$
$421$	11.0652	−	30.4013i	0.539283	−	1.48167i	0.847730	−	0.530428i	$-0.177969\pi$
$422$	−2.63125	+	14.9225i	−0.128087	+	0.726418i
$423$	−3.72098	+	10.9938i	−0.180920	+	0.534538i
$424$	4.83277	−	1.75898i	0.234700	−	0.0854238i
$425$	14.5986	−	14.2179i	0.708135	−	0.689668i
$426$	−0.426578	−	1.52264i	−0.0206678	−	0.0737723i
$427$	−0.813774	+	0.969818i	−0.0393813	+	0.0469328i
$428$	−5.33393	+	6.35673i	−0.257825	+	0.307264i
$429$	0.963468	+	3.43904i	0.0465167	+	0.166038i
$430$	−10.3064	−	8.01713i	−0.497021	−	0.386620i
$431$	−24.1273	+	8.78162i	−1.16217	+	0.422996i	−0.849873	−	0.526988i	$-0.823321\pi$
$431$	−24.1273	+	8.78162i	−1.16217	+	0.422996i	−0.312299	+	0.949984i	$0.601099\pi$
$432$	−4.35547	−	2.83371i	−0.209553	−	0.136337i
$433$	−5.21716	+	29.5880i	−0.250721	+	1.42191i	0.556101	+	0.831114i	$0.312297\pi$
$433$	−5.21716	+	29.5880i	−0.250721	+	1.42191i	−0.806822	+	0.590794i	$0.798814\pi$
$434$	−0.528331	+	1.45158i	−0.0253607	+	0.0696779i
$435$	−29.6888	+	9.51608i	−1.42347	+	0.456261i
$436$		−	14.0918i		−	0.674877i
$437$	−0.0793075	+	0.222318i	−0.00379379	+	0.0106349i
$438$	3.76794	−	14.7291i	0.180039	−	0.703783i
$439$	9.40233	+	11.2053i	0.448749	+	0.534798i	0.942234	−	0.334957i	$-0.108722\pi$
$439$	9.40233	+	11.2053i	0.448749	+	0.534798i	−0.493485	+	0.869754i	$0.664277\pi$
$440$	3.41995	−	6.46503i	0.163040	−	0.308208i
$441$	−9.87411	+	12.3254i	−0.470196	+	0.586923i
$442$	−2.53027	+	0.446155i	−0.120353	+	0.0212214i
$443$	1.19514	−	0.434997i	0.0567830	−	0.0206673i	−0.313472	−	0.949597i	$-0.601492\pi$
$443$	1.19514	−	0.434997i	0.0567830	−	0.0206673i	0.370256	+	0.928930i	$0.379270\pi$
$444$	−3.92900	−	3.84077i	−0.186462	−	0.182275i
$445$	−29.7817	+	12.1061i	−1.41179	+	0.573886i
$446$	4.42216	−	5.27012i	0.209395	−	0.249548i
$447$	15.8638	+	22.1171i	0.750334	+	1.04611i
$448$	−1.14096	+	0.658735i	−0.0539054	+	0.0311223i
$449$	−9.75714	+	16.8999i	−0.460468	+	0.797553i	−0.998984	−	0.0450615i	$-0.985652\pi$
$449$	−9.75714	+	16.8999i	−0.460468	+	0.797553i	0.538517	+	0.842615i	$0.318985\pi$
$450$	−6.20988	+	13.6542i	−0.292737	+	0.643665i
$451$	17.1068	−	3.01639i	0.805528	−	0.142036i
$452$	11.1196	+	1.96068i	0.523020	+	0.0922226i
$453$	10.5957	+	7.24132i	0.497830	+	0.340227i
$454$	6.35078	−	5.32894i	0.298057	−	0.250100i
$455$	−1.83963	−	0.254565i	−0.0862430	−	0.0119342i
$456$	1.82421	−	7.32614i	0.0854265	−	0.343078i
$457$			24.4506i			1.14375i	0.820340	+	0.571877i	$0.193784\pi$
$457$			24.4506i			1.14375i	−0.820340	+	0.571877i	$0.806216\pi$
$458$	14.6474	+	17.4561i	0.684427	+	0.815668i
$459$	18.8774	−	9.59846i	0.881123	−	0.448018i
$460$	0.115239	+	0.0371733i	0.00537303	+	0.00173321i
$461$	−28.5853	+	5.04036i	−1.33135	+	0.234753i	−0.793645	−	0.608381i	$-0.791819\pi$
$461$	−28.5853	+	5.04036i	−1.33135	+	0.234753i	−0.537704	+	0.843134i	$0.680708\pi$
$462$	−7.42760	+	0.734897i	−0.345563	+	0.0341905i
$463$	14.9402	+	8.62574i	0.694331	+	0.400872i	0.805233	−	0.592959i	$-0.202040\pi$
$463$	14.9402	+	8.62574i	0.694331	+	0.400872i	−0.110901	+	0.993831i	$0.535374\pi$
$464$	−4.02489	−	6.97131i	−0.186851	−	0.323635i
$465$	−4.01798	+	2.11594i	−0.186329	+	0.0981243i
$466$	−10.3619	+	12.3489i	−0.480007	+	0.572050i
$467$	−6.75997	−	11.7086i	−0.312814	−	0.541810i	0.666156	−	0.745812i	$-0.267938\pi$
$467$	−6.75997	−	11.7086i	−0.312814	−	0.541810i	−0.978970	+	0.204002i	$0.934605\pi$
$468$	1.61596	−	0.982558i	0.0746976	−	0.0454188i
$469$	0.897598	+	2.46613i	0.0414472	+	0.113875i
$470$	0.320251	+	8.64502i	0.0147721	+	0.398765i
$471$	−11.5756	+	25.5782i	−0.533375	+	1.17858i
$472$	1.90788	−	5.24185i	0.0878171	−	0.241276i
$473$	14.6315	−	12.2773i	0.672758	−	0.564511i
$474$	−5.80880	+	22.7069i	−0.266807	+	1.04296i
$475$	−21.6981	−	2.04719i	−0.995579	−	0.0939313i
$476$		−	5.36951i		−	0.246111i
$477$	−3.02349	−	15.1296i	−0.138436	−	0.692738i
$478$	−17.7274	−	6.45225i	−0.810832	−	0.295119i
$479$	6.76192	+	1.19231i	0.308960	+	0.0544780i	0.325979	−	0.945377i	$-0.394306\pi$
$479$	6.76192	+	1.19231i	0.308960	+	0.0544780i	−0.0170184	+	0.999855i	$0.505417\pi$
$480$	−3.78512	−	0.820303i	−0.172766	−	0.0374415i
$481$	1.87918	−	0.683966i	0.0856832	−	0.0311861i
$482$	1.80935	−	3.13388i	0.0824135	−	0.142744i
$483$	−0.0333352	−	0.118988i	−0.00151680	−	0.00541414i
$484$	−0.230936	−	0.193778i	−0.0104971	−	0.00880810i
$485$	24.6089	−	22.2526i	1.11743	−	1.01044i
$486$	−10.3795	+	11.6304i	−0.470825	+	0.527564i
$487$	−10.3484	+	17.9239i	−0.468929	+	0.812208i	−0.999369	−	0.0355139i	$-0.988693\pi$
$487$	−10.3484	+	17.9239i	−0.468929	+	0.812208i	0.530441	+	0.847722i	$0.322027\pi$
$488$	−0.328660	−	0.902986i	−0.0148777	−	0.0408763i
$489$	3.10690	−	40.8487i	0.140499	−	1.84724i
$490$	−3.61377	+	11.2028i	−0.163253	+	0.506092i
$491$	−2.75264	+	7.56282i	−0.124225	+	0.341305i	−0.986180	−	0.165680i	$-0.947018\pi$
$491$	−2.75264	+	7.56282i	−0.124225	+	0.341305i	0.861955	+	0.506986i	$0.169240\pi$
$492$	−3.98184	−	8.29197i	−0.179515	−	0.373831i
$493$	32.8078			1.47759
$494$	2.11628	+	1.75278i	0.0952159	+	0.0788615i
$495$	−17.6203	−	13.0752i	−0.791972	−	0.587686i
$496$	−0.753669	−	0.898188i	−0.0338407	−	0.0403298i
$497$	−0.411375	+	1.13024i	−0.0184527	+	0.0506984i
$498$	−5.45668	+	12.0575i	−0.244520	+	0.540307i
$499$	−2.73791	−	15.5275i	−0.122566	−	0.695105i	−0.982724	−	0.185077i	$-0.940746\pi$
$499$	−2.73791	−	15.5275i	−0.122566	−	0.695105i	0.860158	−	0.510027i	$-0.170365\pi$
$500$	−0.708917	+	11.1578i	−0.0317037	+	0.498994i
$501$	−14.0642	+	14.3873i	−0.628344	+	0.642777i
$502$	−7.06986	−	12.2454i	−0.315544	−	0.546537i
$503$	20.9842	+	17.6078i	0.935638	+	0.785093i	0.976821	−	0.214058i	$-0.0686682\pi$
$503$	20.9842	+	17.6078i	0.935638	+	0.785093i	−0.0411830	+	0.999152i	$0.513113\pi$
$504$	1.43579	+	3.68240i	0.0639551	+	0.164027i
$505$	5.47041	+	13.4575i	0.243430	+	0.598850i
$506$	−0.0885607	+	0.153392i	−0.00393700	+	0.00681909i
$507$	−2.14923	−	21.7223i	−0.0954507	−	0.964719i
$508$	−3.21377	−	18.2262i	−0.142588	−	0.808658i
$509$	−3.92282	+	22.2474i	−0.173876	+	0.986100i	0.765557	+	0.643368i	$0.222463\pi$
$509$	−3.92282	+	22.2474i	−0.173876	+	0.986100i	−0.939433	+	0.342732i	$0.888648\pi$
$510$	10.6087	−	11.6883i	0.469760	−	0.517566i
$511$	−8.85881	+	7.43342i	−0.391891	+	0.328835i
$512$		−	1.00000i		−	0.0441942i
$513$	−20.8979	−	8.73374i	−0.922664	−	0.385604i
$514$	30.9651			1.36581
$515$	4.86837	+	7.75437i	0.214526	+	0.341698i
$516$	−8.35045	−	5.70686i	−0.367608	−	0.251230i
$517$	−12.4621	−	2.19741i	−0.548084	−	0.0966420i
$518$	0.725724	+	4.11579i	0.0318865	+	0.180837i
$519$	44.7761	−	4.43021i	1.96545	−	0.194465i
$520$	0.865501	−	1.11265i	0.0379547	−	0.0487928i
$521$	−7.82946	−	13.5610i	−0.343015	−	0.594120i	0.641976	−	0.766725i	$-0.278115\pi$
$521$	−7.82946	−	13.5610i	−0.343015	−	0.594120i	−0.984991	+	0.172605i	$0.944782\pi$
$522$	−22.4995	+	8.77269i	−0.984778	+	0.383970i
$523$	−9.46665	−	7.94346i	−0.413948	−	0.347343i	0.411908	−	0.911226i	$-0.364863\pi$
$523$	−9.46665	−	7.94346i	−0.413948	−	0.347343i	−0.825855	+	0.563882i	$0.809307\pi$
$524$	10.0864	−	5.82339i	0.440627	−	0.254396i
$525$	9.89161	−	5.68646i	0.431705	−	0.248177i
$526$	6.04005	+	16.5949i	0.263359	+	0.723573i
$527$	4.70607	−	0.829807i	0.205000	−	0.0361469i
$528$	2.33581	−	5.16136i	0.101653	−	0.224619i
$529$	21.6102	+	7.86546i	0.939573	+	0.341977i
$530$	−6.11470	−	9.73954i	−0.265606	−	0.423059i
$531$	−14.6790	−	8.03615i	−0.637014	−	0.348739i
$532$	−4.37544	+	3.71946i	−0.189699	+	0.161259i
$533$	3.34794			0.145015
$534$	−22.4479	+	10.7796i	−0.971414	+	0.466478i
$535$	16.4017	+	8.67635i	0.709106	+	0.375111i
$536$	−1.96174	−	0.345907i	−0.0847341	−	0.0149409i
$537$	−9.14952	−	0.695899i	−0.394831	−	0.0300303i
$538$	−10.7004	−	29.3992i	−0.461329	−	1.26749i
$539$	−14.9118	−	8.60935i	−0.642298	−	0.370831i
$540$	−4.15001	+	10.8525i	−0.178588	+	0.467019i
$541$	−14.3906	−	12.0751i	−0.618700	−	0.519151i	0.278695	−	0.960380i	$-0.410098\pi$
$541$	−14.3906	−	12.0751i	−0.618700	−	0.519151i	−0.897394	+	0.441229i	$0.854543\pi$
$542$	2.68033	−	3.19429i	0.115130	−	0.137207i
$543$	1.52360	+	5.43840i	0.0653840	+	0.233384i
$544$	3.52959	+	2.03781i	0.151330	+	0.0873703i
$545$	−30.8078	+	6.61672i	−1.31966	+	0.283429i
$546$	−1.43440	−	0.109099i	−0.0613868	−	0.00466899i
$547$	3.01408	−	17.0937i	0.128873	−	0.730873i	−0.850060	−	0.526687i	$-0.823434\pi$
$547$	3.01408	−	17.0937i	0.128873	−	0.730873i	0.978932	−	0.204186i	$-0.0654548\pi$
$548$	−15.7667	−	5.73860i	−0.673519	−	0.245141i
$549$	−2.82692	+	0.564929i	−0.120650	+	0.0241106i
$550$	−15.7398	−	4.44113i	−0.671145	−	0.189370i
$551$	−22.7260	−	26.7340i	−0.968160	−	1.13891i
$552$	0.0908666	+	0.0232452i	0.00386754	+	0.000989380i
$553$	13.6571	−	11.4596i	0.580757	−	0.487313i
$554$	9.97978	+	3.63234i	0.424000	+	0.154323i
$555$	−6.55192	+	10.3930i	−0.278113	+	0.441160i
$556$	0.767176	+	4.35087i	0.0325355	+	0.184518i
$557$	−37.5151	+	13.6544i	−1.58956	+	0.578554i	−0.977256	−	0.212065i	$-0.931981\pi$
$557$	−37.5151	+	13.6544i	−1.58956	+	0.578554i	−0.612309	+	0.790619i	$0.709759\pi$
$558$	−3.00553	+	1.82747i	−0.127234	+	0.0773628i
$559$	3.18806	−	1.84063i	0.134840	−	0.0778502i
$560$	1.97587	+	2.18508i	0.0834956	+	0.0923367i
$561$	13.4575	+	18.7623i	0.568178	+	0.792145i
$562$	24.2390	−	13.9944i	1.02246	−	0.590318i
$563$	−38.8083	−	22.4060i	−1.63558	−	0.944300i	−0.982330	−	0.187155i	$-0.940073\pi$
$563$	−38.8083	−	22.4060i	−1.63558	−	0.944300i	−0.653246	−	0.757146i	$-0.726593\pi$
$564$	0.659785	+	6.66844i	0.0277820	+	0.280792i
$565$	−0.934648	−	25.2304i	−0.0393209	−	1.06145i
$566$	−3.31856	+	18.8205i	−0.139489	+	0.791084i
$567$	11.5716	−	2.58701i	0.485961	−	0.108644i
$568$	−0.586831	−	0.699357i	−0.0246229	−	0.0293444i
$569$	−16.2168			−0.679845			−0.339923	−	0.940453i	$-0.610401\pi$
$569$	−16.2168			−0.679845			−0.339923	+	0.940453i	$0.610401\pi$
$570$	−16.8730	−	0.548180i	−0.706734	−	0.0229607i
$571$	15.4916			0.648303			0.324152	−	0.946005i	$-0.394921\pi$
$571$	15.4916			0.648303			0.324152	+	0.946005i	$0.394921\pi$
$572$	1.32541	+	1.57957i	0.0554184	+	0.0660450i
$573$	33.5317	+	22.9162i	1.40081	+	0.957339i
$574$	−1.21497	+	6.89045i	−0.0507120	+	0.287602i
$575$	0.0271592	−	0.269391i	0.00113262	−	0.0112344i
$576$	−2.96549	−	0.453727i	−0.123562	−	0.0189053i
$577$	−1.23629	−	0.713774i	−0.0514675	−	0.0297148i	0.474045	−	0.880500i	$-0.342793\pi$
$577$	−1.23629	−	0.713774i	−0.0514675	−	0.0297148i	−0.525513	+	0.850786i	$0.676127\pi$
$578$	0.337182	−	0.194672i	0.0140249	−	0.00809729i
$579$	24.6383	−	17.6721i	1.02393	−	0.734429i
$580$	−13.3509	+	12.0726i	−0.554366	+	0.501287i
$581$	8.71817	−	5.03344i	0.361691	−	0.208822i
$582$	17.9648	−	18.3774i	0.744665	−	0.761770i
$583$	15.8073	−	5.75339i	0.654672	−	0.238281i
$584$	−1.52423	−	8.64434i	−0.0630731	−	0.357705i
$585$	−2.90684	−	3.07147i	−0.120183	−	0.126990i
$586$	−11.6897	−	4.25470i	−0.482897	−	0.175760i
$587$	9.69157	−	8.13219i	0.400014	−	0.335651i	−0.420485	−	0.907299i	$-0.638140\pi$
$587$	9.69157	−	8.13219i	0.400014	−	0.335651i	0.820499	+	0.571648i	$0.193696\pi$
$588$	−2.25976	+	8.83352i	−0.0931909	+	0.364288i
$589$	−3.93608	−	3.26001i	−0.162183	−	0.134327i
$590$	−12.3556	−	1.70975i	−0.508673	−	0.0703894i
$591$	−5.06408	−	10.5457i	−0.208308	−	0.433791i
$592$	−2.98089	−	1.08496i	−0.122514	−	0.0445914i
$593$	−6.64678	+	37.6957i	−0.272950	+	1.54798i	0.472448	+	0.881359i	$0.343371\pi$
$593$	−6.64678	+	37.6957i	−0.272950	+	1.54798i	−0.745398	+	0.666620i	$0.767740\pi$
$594$	−14.2461	−	9.26866i	−0.584526	−	0.380298i
$595$	−11.7389	+	2.52121i	−0.481248	+	0.103360i
$596$	13.6091	+	7.85722i	0.557450	+	0.321844i
$597$	4.42210	−	1.23888i	0.180984	−	0.0507039i
$598$	−0.0219431	+	0.0261508i	−0.000897321	+	0.00106939i
$599$	−0.596444	−	0.500476i	−0.0243700	−	0.0204489i	0.630521	−	0.776172i	$-0.282841\pi$
$599$	−0.596444	−	0.500476i	−0.0243700	−	0.0204489i	−0.654891	+	0.755723i	$0.727286\pi$
$600$	−0.0160837	+	8.66024i	−0.000656612	+	0.353553i
$601$	−18.2021	−	10.5090i	−0.742479	−	0.428670i	0.0804911	−	0.996755i	$-0.474351\pi$
$601$	−18.2021	−	10.5090i	−0.742479	−	0.428670i	−0.822970	+	0.568085i	$0.807684\pi$
$602$	2.63127	+	7.22936i	0.107243	+	0.294647i
$603$	−1.91588	+	5.66056i	−0.0780205	+	0.230516i
$604$	7.29702	+	1.28666i	0.296912	+	0.0523535i
$605$	−0.315206	+	0.595862i	−0.0128150	+	0.0242252i
$606$	4.87097	+	10.1435i	0.197870	+	0.412053i
$607$	35.7122			1.44951			0.724757	−	0.689004i	$-0.241952\pi$
$607$	35.7122			1.44951			0.724757	+	0.689004i	$0.241952\pi$
$608$	−0.784405	−	4.28774i	−0.0318118	−	0.173891i
$609$	17.7959	+	4.55249i	0.721127	+	0.184476i
$610$	−1.81980	+	1.14251i	−0.0736816	+	0.0462590i
$611$	−2.29185	−	0.834166i	−0.0927184	−	0.0337467i
$612$	7.64457	−	9.54235i	0.309013	−	0.385727i
$613$	−42.7399	+	7.53619i	−1.72625	+	0.304384i	−0.946737	−	0.322007i	$-0.895643\pi$
$613$	−42.7399	+	7.53619i	−1.72625	+	0.304384i	−0.779509	+	0.626391i	$0.784532\pi$
$614$	5.41403	+	14.8749i	0.218492	+	0.600303i
$615$	−16.2584	+	12.5986i	−0.655601	+	0.508025i
$616$	−3.73193	+	2.15463i	−0.150364	+	0.0868126i
$617$	−13.6494	−	11.4532i	−0.549506	−	0.461090i	0.325268	−	0.945622i	$-0.394546\pi$
$617$	−13.6494	−	11.4532i	−0.549506	−	0.461090i	−0.874774	+	0.484532i	$0.838990\pi$
$618$	4.13359	+	5.76300i	0.166278	+	0.231822i
$619$	6.33105	+	10.9657i	0.254466	+	0.440749i	0.964750	−	0.263166i	$-0.0847668\pi$
$619$	6.33105	+	10.9657i	0.254466	+	0.440749i	−0.710284	+	0.703915i	$0.751434\pi$
$620$	−1.60975	+	2.06942i	−0.0646491	+	0.0831099i
$621$	0.110162	−	0.258917i	0.00442065	−	0.0103900i
$622$	−4.05259	−	22.9834i	−0.162494	−	0.921551i
$623$	18.6537	+	3.28915i	0.747344	+	0.131777i
$624$	0.616092	−	0.901485i	0.0246634	−	0.0360883i
$625$	24.7263	−	3.68924i	0.989052	−	0.147570i
$626$	−29.9250			−1.19604
$627$	5.96674	−	23.9628i	0.238289	−	0.956981i
$628$			16.2094i			0.646827i
$629$	9.90394	−	8.31039i	0.394896	−	0.331357i
$630$	7.37635	−	4.86798i	0.293881	−	0.193945i
$631$	−3.74024	+	21.2119i	−0.148896	+	0.844434i	0.815259	+	0.579096i	$0.196595\pi$
$631$	−3.74024	+	21.2119i	−0.148896	+	0.844434i	−0.964156	+	0.265338i	$0.914517\pi$
$632$	2.34981	+	13.3264i	0.0934704	+	0.530097i
$633$	26.1178	−	2.58413i	1.03809	−	0.102710i
$634$	8.27451	−	14.3319i	0.328623	−	0.569192i
$635$	−38.3374	+	15.5840i	−1.52137	+	0.618432i
$636$	−5.19182	−	7.23836i	−0.205869	−	0.287020i
$637$	−2.54223	−	2.13318i	−0.100727	−	0.0845197i
$638$	−13.1648	−	22.8022i	−0.521201	−	0.902747i
$639$	−2.34020	+	1.42292i	−0.0925768	+	0.0562900i
$640$	−2.18621	+	0.469543i	−0.0864177	+	0.0185603i
$641$	1.27777	+	7.24662i	0.0504690	+	0.286224i	0.999588	−	0.0286928i	$-0.00913445\pi$
$641$	1.27777	+	7.24662i	0.0504690	+	0.286224i	−0.949119	+	0.314917i	$0.898023\pi$
$642$	13.0943	+	5.92591i	0.516790	+	0.233877i
$643$	0.842520	−	2.31480i	0.0332257	−	0.0912870i	−0.921971	−	0.387260i	$-0.873422\pi$
$643$	0.842520	−	2.31480i	0.0332257	−	0.0912870i	0.955196	+	0.295973i	$0.0956438\pi$
$644$	−0.0458582	−	0.0546517i	−0.00180707	−	0.00215358i
$645$	−8.55552	+	20.9355i	−0.336873	+	0.824333i
$646$	16.7324	+	5.96896i	0.658328	+	0.234846i
$647$	10.5697			0.415537			0.207768	−	0.978178i	$-0.433380\pi$
$647$	10.5697			0.415537			0.207768	+	0.978178i	$0.433380\pi$
$648$	−2.69104	+	8.58826i	−0.105714	+	0.337379i
$649$	6.24040	−	17.1454i	0.244957	−	0.673014i
$650$	−2.83887	−	1.36973i	−0.111350	−	0.0537254i
$651$	2.66786	+	0.202913i	0.104562	+	0.00795280i
$652$	−8.08951	−	22.2257i	−0.316810	−	0.870427i
$653$	1.57775	−	2.73274i	0.0617422	−	0.106941i	−0.833502	−	0.552516i	$-0.813668\pi$
$653$	1.57775	−	2.73274i	0.0617422	−	0.106941i	0.895244	+	0.445576i	$0.147001\pi$
$654$	−23.5029	+	6.58447i	−0.919035	+	0.257473i
$655$	−17.4672	−	19.3167i	−0.682499	−	0.754767i
$656$	−4.06826	−	3.41368i	−0.158839	−	0.133282i
$657$	−26.3263	+	0.597921i	−1.02709	+	0.0233271i
$658$	2.54853	−	4.41418i	0.0993520	−	0.172083i
$659$	−40.3334	+	14.6802i	−1.57117	+	0.571858i	−0.973260	−	0.229706i	$-0.926223\pi$
$659$	−40.3334	+	14.6802i	−1.57117	+	0.571858i	−0.597908	+	0.801565i	$0.704001\pi$
$660$	−12.3806	−	2.68310i	−0.481914	−	0.104439i
$661$	−14.2238	−	2.50804i	−0.553241	−	0.0975514i	−0.109963	−	0.993936i	$-0.535073\pi$
$661$	−14.2238	−	2.50804i	−0.553241	−	0.0975514i	−0.443278	+	0.896384i	$0.646184\pi$
$662$	−0.557237	−	0.202818i	−0.0216576	−	0.00788273i
$663$	1.92639	+	4.01161i	0.0748149	+	0.155798i
$664$			7.64106i			0.296531i
$665$	10.1860	+	7.81919i	0.394996	+	0.303215i
$666$	−4.56994	+	8.34753i	−0.177081	+	0.323460i
$667$	0.333923	−	0.280195i	0.0129296	−	0.0108492i
$668$	−3.97292	+	10.9155i	−0.153717	+	0.422333i
$669$	−10.8560	−	4.91294i	−0.419716	−	0.189945i
$670$	0.164892	+	4.45119i	0.00637035	+	0.171964i
$671$	−1.07500	−	2.95354i	−0.0415000	−	0.114020i
$672$	1.63178	+	1.59514i	0.0629473	+	0.0615339i
$673$	−7.53961	−	13.0590i	−0.290631	−	0.503387i	0.683328	−	0.730111i	$-0.260532\pi$
$673$	−7.53961	−	13.0590i	−0.290631	−	0.503387i	−0.973959	+	0.226724i	$0.927198\pi$
$674$	4.95053	−	5.89981i	0.190687	−	0.227252i
$675$	25.6746	+	3.97708i	0.988214	+	0.153078i
$676$	−6.30129	−	10.9142i	−0.242357	−	0.419775i
$677$	27.0191	+	15.5995i	1.03843	+	0.599537i	0.919388	−	0.393352i	$-0.128685\pi$
$677$	27.0191	+	15.5995i	1.03843	+	0.599537i	0.119041	+	0.992889i	$0.462018\pi$
$678$	−1.92557	−	19.4617i	−0.0739512	−	0.747423i
$679$	−19.2511	+	3.39450i	−0.738791	+	0.130269i
$680$	2.79779	−	8.67327i	0.107290	−	0.332605i
$681$	−11.8552	−	8.10209i	−0.454293	−	0.310473i
$682$	−2.46515	−	2.93785i	−0.0943954	−	0.112496i
$683$		−	24.3802i		−	0.932881i	−0.884553	−	0.466440i	$-0.845536\pi$
$683$		−	24.3802i		−	0.932881i	0.884553	−	0.466440i	$-0.154464\pi$
$684$	−13.0712	+	0.380684i	−0.499788	+	0.0145558i
$685$	−5.14268	+	37.1638i	−0.196492	+	1.41996i
$686$	12.3776	−	10.3860i	0.472579	−	0.396541i
$687$	22.2698	−	32.5858i	0.849645	−	1.24323i
$688$	−5.75075	−	1.01401i	−0.219245	−	0.0386589i
$689$	3.19289	−	0.562992i	0.121639	−	0.0214483i
$690$	0.00815314	−	0.209568i	0.000310385	−	0.00797814i
$691$	−21.0762	+	36.5050i	−0.801776	+	1.38872i	0.116670	+	0.993171i	$0.462778\pi$
$691$	−21.0762	+	36.5050i	−0.801776	+	1.38872i	−0.918446	+	0.395546i	$0.870555\pi$
$692$	22.4974	−	12.9889i	0.855222	−	0.493763i
$693$	4.69626	+	12.0446i	0.178396	+	0.457537i
$694$	23.5786	−	28.0999i	0.895031	−	1.06666i
$695$	9.15171	−	3.72013i	0.347144	−	0.141113i
$696$	−9.74635	+	9.97022i	−0.369434	+	0.377920i
$697$	20.3392	−	7.40287i	0.770403	−	0.280404i
$698$	−17.4810	+	3.08238i	−0.661666	+	0.116670i
$699$	25.4375	+	11.5119i	0.962135	+	0.435421i
$700$	3.84931	−	5.34566i	0.145490	−	0.202047i
$701$	18.0947	+	21.5644i	0.683427	+	0.814476i	0.990544	−	0.137196i	$-0.0438089\pi$
$701$	18.0947	+	21.5644i	0.683427	+	0.814476i	−0.307117	+	0.951672i	$0.599364\pi$
$702$	−2.39381	−	2.23604i	−0.0903484	−	0.0843940i
$703$	−13.6323	−	2.31378i	−0.514153	−	0.0872659i
$704$		−	3.27086i		−	0.123275i
$705$	14.2688	−	4.57355i	0.537395	−	0.172250i
$706$	2.89626	−	7.95742i	0.109002	−	0.299481i
$707$	1.48627	−	8.42905i	0.0558969	−	0.317007i
$708$	−9.63400	−	0.732748i	−0.362068	−	0.0275384i
$709$	−9.49114	+	3.45449i	−0.356447	+	0.129736i	−0.514036	−	0.857769i	$-0.671850\pi$
$709$	−9.49114	+	3.45449i	−0.356447	+	0.129736i	0.157589	+	0.987505i	$0.449628\pi$
$710$	−1.25340	+	1.61132i	−0.0470394	+	0.0604716i
$711$	40.5856	−	0.921778i	1.52208	−	0.0345694i
$712$	−9.24144	+	11.0135i	−0.346338	+	0.412749i
$713$	0.0408122	−	0.0486380i	0.00152843	−	0.00182151i
$714$	−8.95545	+	2.50892i	−0.335149	+	0.0938941i
$715$	2.83093	−	3.63931i	0.105871	−	0.136103i
$716$	−4.97824	+	1.81193i	−0.186046	+	0.0677151i
$717$	−2.47808	+	32.5812i	−0.0925456	+	1.21677i
$718$	−0.232739	+	1.31993i	−0.00868575	+	0.0492594i
$719$	10.7327	−	29.4878i	0.400262	−	1.09971i	−0.561894	−	0.827209i	$-0.689927\pi$
$719$	10.7327	−	29.4878i	0.400262	−	1.09971i	0.962156	−	0.272501i	$-0.0878508\pi$
$720$	0.400481	+	6.69624i	0.0149250	+	0.249554i
$721$		−	5.39460i		−	0.200905i
$722$	−6.72665	−	17.7694i	−0.250340	−	0.661309i
$723$	−6.07222	−	1.55337i	−0.225828	−	0.0577706i
$724$	2.09597	+	2.49788i	0.0778963	+	0.0928332i
$725$	32.6621	+	23.5193i	1.21304	+	0.873487i
$726$	−0.215284	+	0.475707i	−0.00798995	+	0.0176551i
$727$	35.6502	−	6.28609i	1.32219	−	0.233138i	0.532389	−	0.846500i	$-0.321294\pi$
$727$	35.6502	−	6.28609i	1.32219	−	0.233138i	0.789802	+	0.613362i	$0.210183\pi$
$728$	−0.780457	+	0.284063i	−0.0289257	+	0.0105281i
$729$	24.2474	+	11.8770i	0.898052	+	0.439889i
$730$	−18.1827	+	7.39118i	−0.672971	+	0.273560i
$731$	15.2980	−	18.2314i	0.565816	−	0.674314i
$732$	−1.35246	+	0.970075i	−0.0499885	+	0.0358550i
$733$	21.0150	−	12.1330i	0.776206	−	0.448143i	−0.0588778	−	0.998265i	$-0.518752\pi$
$733$	21.0150	−	12.1330i	0.776206	−	0.448143i	0.835084	+	0.550122i	$0.185419\pi$
$734$	16.4345	−	28.4654i	0.606610	−	1.05068i
$735$	20.3730	+	0.792601i	0.751470	+	0.0292355i
$736$	0.0533286	−	0.00940327i	0.00196572	−	0.000346609i
$737$	−6.41656	−	1.13141i	−0.236357	−	0.0416761i
$738$	−11.9691	+	10.5155i	−0.440589	+	0.387082i
$739$	−0.951635	+	0.798517i	−0.0350065	+	0.0293739i	−0.660123	−	0.751157i	$-0.729496\pi$
$739$	−0.951635	+	0.798517i	−0.0350065	+	0.0293739i	0.625117	+	0.780531i	$0.285051\pi$
$740$	−0.972289	+	7.02630i	−0.0357421	+	0.258292i
$741$	1.93451	−	4.34860i	0.0710661	−	0.159750i
$742$			6.77565i			0.248742i
$743$	27.2474	+	32.4722i	0.999609	+	1.19129i	0.981502	+	0.191452i	$0.0613196\pi$
$743$	27.2474	+	32.4722i	0.999609	+	1.19129i	0.0181073	+	0.999836i	$0.494236\pi$
$744$	−1.14587	+	1.67668i	−0.0420098	+	0.0614700i
$745$	10.7875	−	33.4417i	0.395223	−	1.22521i
$746$	25.4309	−	4.48415i	0.931090	−	0.164176i
$747$	22.6595	+	3.46696i	0.829068	+	0.126849i
$748$	11.5448	+	6.66539i	0.422119	+	0.243711i
$749$	−5.46627	−	9.46785i	−0.199733	−	0.345948i
$750$	18.9407	−	4.03119i	0.691616	−	0.147198i
$751$	15.2865	−	18.2178i	0.557813	−	0.664775i	−0.411269	−	0.911514i	$-0.634914\pi$
$751$	15.2865	−	18.2178i	0.557813	−	0.664775i	0.969082	+	0.246739i	$0.0793589\pi$
$752$	1.93441	+	3.35050i	0.0705407	+	0.122180i
$753$	−17.1198	+	17.5131i	−0.623881	+	0.638212i
$754$	−1.73563	−	4.76861i	−0.0632080	−	0.173662i
$755$	−0.613346	−	16.5570i	−0.0223220	−	0.602571i
$756$	5.47076	−	4.11527i	0.198970	−	0.149671i
$757$	−14.8974	+	40.9304i	−0.541457	+	1.48764i	0.303513	+	0.952827i	$0.401840\pi$
$757$	−14.8974	+	40.9304i	−0.541457	+	1.48764i	−0.844970	+	0.534813i	$0.820382\pi$
$758$	15.7714	−	13.2337i	0.572841	−	0.480671i
$759$	0.297212	+	0.0760317i	0.0107881	+	0.00275978i
$760$	−9.00560	+	3.72815i	−0.326668	+	0.135234i
$761$			11.9464i			0.433055i	0.976277	+	0.216528i	$0.0694731\pi$
$761$			11.9464i			0.433055i	−0.976277	+	0.216528i	$0.930527\pi$
$762$	−28.8967	+	13.8763i	−1.04682	+	0.502686i
$763$	17.4460	+	6.34981i	0.631586	+	0.229878i
$764$	23.0925	+	4.07183i	0.835457	+	0.147314i
$765$	−24.4511	−	12.2321i	−0.884030	−	0.442253i
$766$	−9.15789	+	3.33320i	−0.330888	+	0.120433i
$767$	1.75829	−	3.04545i	0.0634882	−	0.109965i
$768$	−1.66784	+	0.467254i	−0.0601828	+	0.0168606i
$769$	13.1537	+	11.0373i	0.474335	+	0.398014i	0.848373	−	0.529399i	$-0.177583\pi$
$769$	13.1537	+	11.0373i	0.474335	+	0.398014i	−0.374038	+	0.927413i	$0.622027\pi$
$770$	6.46279	+	7.14711i	0.232903	+	0.257564i
$771$	−14.4686	−	51.6446i	−0.521072	−	1.85994i
$772$	8.75285	−	15.1604i	0.315022	−	0.545634i
$773$	1.55329	+	4.26763i	0.0558680	+	0.153496i	0.964487	−	0.264129i	$-0.0850846\pi$
$773$	1.55329	+	4.26763i	0.0558680	+	0.153496i	−0.908619	+	0.417626i	$0.862862\pi$
$774$	−5.61632	+	16.5937i	−0.201874	+	0.596449i
$775$	5.28004	+	2.54758i	0.189665	+	0.0915117i
$776$	5.07476	−	13.9428i	0.182173	−	0.500517i
$777$	6.52536	−	3.13351i	0.234096	−	0.112414i
$778$	1.40388			0.0503315
$779$	−20.1214	−	11.4458i	−0.720923	−	0.410088i
$780$	−2.26012	−	0.923624i	−0.0809253	−	0.0330710i
$781$	−1.91944	−	2.28750i	−0.0686830	−	0.0818532i
$782$	−0.0754838	+	0.207390i	−0.00269930	+	0.00741625i
$783$	25.1444	+	33.4265i	0.898588	+	1.19456i
$784$	0.914131	+	5.18429i	0.0326475	+	0.185153i
$785$	35.4373	−	7.61102i	1.26481	−	0.271649i
$786$	−14.4254	−	14.1015i	−0.514536	−	0.502983i
$787$	−26.5576	−	45.9991i	−0.946675	−	1.63969i	−0.752361	−	0.658751i	$-0.771085\pi$
$787$	−26.5576	−	45.9991i	−0.946675	−	1.63969i	−0.194314	−	0.980939i	$-0.562248\pi$
$788$	−5.17399	−	4.34149i	−0.184316	−	0.154659i
$789$	24.8553	−	17.8279i	0.884873	−	0.634688i
$790$	28.0311	−	11.3945i	0.997301	−	0.405399i
$791$	−7.43785	+	12.8827i	−0.264459	+	0.458057i
$792$	−9.69971	−	1.48408i	−0.344664	−	0.0527344i
$793$	−0.105193	−	0.596580i	−0.00373552	−	0.0211852i
$794$	−1.81135	+	10.2727i	−0.0642823	+	0.364563i
$795$	−13.3868	+	14.7492i	−0.474782	+	0.523099i
$796$	2.03109	−	1.70429i	0.0719901	−	0.0604069i
$797$			14.3302i			0.507602i	0.967256	+	0.253801i	$0.0816808\pi$
$797$			14.3302i			0.507602i	−0.967256	+	0.253801i	$0.918319\pi$
$798$	8.24789	+	5.55957i	0.291972	+	0.196807i
$799$	−15.7678			−0.557826
$800$	2.05304	+	4.55906i	0.0725860	+	0.161187i
$801$	28.4674	+	32.4025i	1.00585	+	1.14489i
$802$	−8.79796	−	1.55132i	−0.310667	−	0.0547789i
$803$	−4.98554	−	28.2744i	−0.175936	−	0.997783i
$804$	0.339713	+	3.43348i	0.0119808	+	0.121089i
$805$	−0.0979479	+	0.125917i	−0.00345221	+	0.00443800i
$806$	−0.369577	−	0.640127i	−0.0130178	−	0.0225475i
$807$	−44.0332	+	31.5835i	−1.55004	+	1.11179i
$808$	4.97669	+	4.17593i	0.175079	+	0.146909i
$809$	3.22566	−	1.86234i	0.113408	−	0.0654763i	−0.442223	−	0.896905i	$-0.645810\pi$
$809$	3.22566	−	1.86234i	0.113408	−	0.0654763i	0.555631	+	0.831429i	$0.312477\pi$
$810$	20.0393	+	1.85064i	0.704111	+	0.0650249i
$811$	6.88080	+	18.9049i	0.241618	+	0.663839i	0.999929	+	0.0119462i	$0.00380267\pi$
$811$	6.88080	+	18.9049i	0.241618	+	0.663839i	−0.758311	+	0.651893i	$0.773975\pi$
$812$	10.4442	−	1.84160i	0.366520	−	0.0646274i
$813$	−6.57994	−	2.97780i	−0.230769	−	0.104436i
$814$	−9.75009	−	3.54874i	−0.341740	−	0.124383i
$815$	−44.7918	+	28.1213i	−1.56899	+	0.985047i
$816$	1.74951	−	6.83894i	0.0612452	−	0.239411i
$817$	−25.4531	+	0.163098i	−0.890492	+	0.00570608i
$818$	10.4100			0.363979
$819$	0.488272	+	2.44332i	0.0170616	+	0.0853767i
$820$	−5.55281	+	10.4970i	−0.193912	+	0.366570i
$821$	−8.46967	−	1.49343i	−0.295593	−	0.0521211i	0.0238848	−	0.999715i	$-0.492397\pi$
$821$	−8.46967	−	1.49343i	−0.295593	−	0.0521211i	−0.319478	+	0.947594i	$0.603508\pi$
$822$	−2.20400	+	28.9776i	−0.0768732	+	1.01071i
$823$	8.34661	+	22.9321i	0.290945	+	0.799364i	0.995929	+	0.0901408i	$0.0287317\pi$
$823$	8.34661	+	22.9321i	0.290945	+	0.799364i	−0.704984	+	0.709223i	$0.749046\pi$
$824$	3.54608	+	2.04733i	0.123534	+	0.0713221i
$825$	−0.0526074	+	28.3264i	−0.00183155	+	0.986200i
$826$	5.62981	+	4.72397i	0.195886	+	0.164368i
$827$	11.0417	−	13.1590i	0.383957	−	0.457583i	−0.539102	−	0.842241i	$-0.681236\pi$
$827$	11.0417	−	13.1590i	0.383957	−	0.457583i	0.923059	+	0.384658i	$0.125681\pi$
$828$	−0.00368869	−	0.162412i	−0.000128191	−	0.00564421i
$829$	14.9589	+	8.63655i	0.519545	+	0.299960i	0.736749	−	0.676167i	$-0.236360\pi$
$829$	14.9589	+	8.63655i	0.519545	+	0.299960i	−0.217203	+	0.976126i	$0.569693\pi$
$830$	16.7050	−	3.58781i	0.579839	−	0.124535i
$831$	1.39506	−	18.3418i	0.0483939	−	0.636272i
$832$	0.109469	−	0.620831i	0.00379516	−	0.0215234i
$833$	−20.1612	−	7.33809i	−0.698546	−	0.254250i
$834$	6.89807	−	3.31249i	0.238861	−	0.114702i
$835$	25.7291	+	3.56035i	0.890391	+	0.123211i
$836$	−2.56568	−	14.0246i	−0.0887359	−	0.485051i
$837$	4.45226	+	4.15883i	0.153893	+	0.143750i
$838$	−25.0694	+	21.0358i	−0.866009	+	0.726668i
$839$	−7.46609	−	2.71743i	−0.257758	−	0.0938162i	0.209909	−	0.977721i	$-0.432683\pi$
$839$	−7.46609	−	2.71743i	−0.257758	−	0.0938162i	−0.467667	+	0.883905i	$0.654905\pi$
$840$	2.72113	−	4.31641i	0.0938879	−	0.148930i
$841$	6.21641	+	35.2550i	0.214359	+	1.21569i
$842$	−30.4013	+	11.0652i	−1.04770	+	0.381331i
$843$	−34.6661	−	33.8877i	−1.19396	−	1.16715i
$844$	13.1227	−	7.57637i	0.451701	−	0.260790i
$845$	−20.9020	+	18.9006i	−0.719049	+	0.650202i
$846$	10.8136	−	4.21627i	0.371778	−	0.144958i
$847$	0.343961	−	0.198586i	0.0118186	−	0.00682349i
$848$	−4.45390	−	2.57146i	−0.152948	−	0.0883043i
$849$	32.9401	−	3.25914i	1.13050	−	0.111853i
$850$	−20.2753	−	2.04410i	−0.695437	−	0.0701120i
$851$	0.0298291	−	0.169169i	0.00102253	−	0.00579904i
$852$	−0.892214	+	1.30551i	−0.0305667	+	0.0447262i
$853$	−27.5955	−	32.8871i	−0.944852	−	1.12603i	−0.991885	−	0.127138i	$-0.959421\pi$
$853$	−27.5955	−	32.8871i	−0.944852	−	1.12603i	0.0470326	−	0.998893i	$-0.485024\pi$
$854$	1.26601			0.0433219
$855$	6.96972	+	28.3976i	0.238359	+	0.971177i
$856$	8.29812			0.283624
$857$	−4.41877	−	5.26609i	−0.150942	−	0.179886i	0.685275	−	0.728285i	$-0.259682\pi$
$857$	−4.41877	−	5.26609i	−0.150942	−	0.179886i	−0.836217	+	0.548399i	$0.815238\pi$
$858$	2.01515	−	2.94863i	0.0687962	−	0.100665i
$859$	4.94388	−	28.0382i	0.168683	−	0.956649i	−0.776502	−	0.630115i	$-0.783008\pi$
$859$	4.94388	−	28.0382i	0.168683	−	0.956649i	0.945185	−	0.326535i	$-0.105881\pi$
$860$	0.483376	+	13.0485i	0.0164830	+	0.444950i
$861$	12.0598	−	1.19322i	0.410998	−	0.0406648i
$862$	22.2358	+	12.8379i	0.757356	+	0.437260i
$863$	−13.6811	+	7.89878i	−0.465709	+	0.268877i	−0.714442	−	0.699695i	$-0.753319\pi$
$863$	−13.6811	+	7.89878i	−0.465709	+	0.268877i	0.248733	+	0.968572i	$0.419986\pi$
$864$	0.628896	+	5.15795i	0.0213955	+	0.175477i
$865$	−38.9599	−	43.0852i	−1.32468	−	1.46494i
$866$	26.0193	−	15.0222i	0.884170	−	0.510476i
$867$	−0.482230	−	0.471402i	−0.0163774	−	0.0160097i
$868$	1.45158	−	0.528331i	0.0492697	−	0.0179327i
$869$	7.68590	+	43.5889i	0.260726	+	1.47865i
$870$	26.3734	+	16.6262i	0.894141	+	0.563679i
$871$	−1.18004	−	0.429500i	−0.0399841	−	0.0145530i
$872$	−10.7950	+	9.05806i	−0.365564	+	0.306745i
$873$	−39.0447	−	21.3754i	−1.32146	−	0.723447i
$874$	0.221283	−	0.0821500i	0.00748502	−	0.00277877i
$875$	−13.4942	−	5.90539i	−0.456186	−	0.199639i
$876$	−13.7051	+	6.58127i	−0.463053	+	0.222360i
$877$	8.93354	+	3.25154i	0.301664	+	0.109797i	0.488418	−	0.872610i	$-0.337574\pi$
$877$	8.93354	+	3.25154i	0.301664	+	0.109797i	−0.186753	+	0.982407i	$0.559797\pi$
$878$	2.54003	−	14.4052i	0.0857217	−	0.486152i
$879$	−1.63408	+	21.4845i	−0.0551162	+	0.724654i
$880$	−7.15080	+	1.53581i	−0.241053	+	0.0517721i
$881$	15.4747	+	8.93433i	0.521356	+	0.301005i	0.737489	−	0.675359i	$-0.236011\pi$
$881$	15.4747	+	8.93433i	0.521356	+	0.301005i	−0.216133	+	0.976364i	$0.569344\pi$
$882$	15.7887	−	0.358593i	0.531635	−	0.0120745i
$883$	20.1297	−	23.9896i	0.677417	−	0.807314i	−0.312356	−	0.949965i	$-0.601118\pi$
$883$	20.1297	−	23.9896i	0.677417	−	0.807314i	0.989773	+	0.142651i	$0.0455626\pi$
$884$	1.96820	+	1.65152i	0.0661978	+	0.0555465i
$885$	2.92163	+	21.4060i	0.0982095	+	0.719556i
$886$	−1.10145	−	0.635923i	−0.0370040	−	0.0213643i
$887$	−10.4904	−	28.8223i	−0.352235	−	0.967757i	−0.981651	−	0.190688i	$-0.938928\pi$
$887$	−10.4904	−	28.8223i	−0.352235	−	0.967757i	0.629416	−	0.777069i	$-0.283294\pi$
$888$	−0.416694	+	5.47859i	−0.0139833	+	0.183849i
$889$	24.0125	+	4.23405i	0.805354	+	0.142006i
$890$	28.4172	+	15.0325i	0.952546	+	0.503889i
$891$	−8.80203	+	28.0910i	−0.294879	+	0.941085i
$892$	−6.87966			−0.230348
$893$	10.9224	+	12.8487i	0.365504	+	0.429965i
$894$	6.74563	−	26.3690i	0.225608	−	0.881913i
$895$	6.29877	+	10.0327i	0.210545	+	0.335357i
$896$	1.23802	+	0.450602i	0.0413593	+	0.0150535i
$897$	0.0538682	+	0.0243784i	0.00179861	+	0.000813972i
$898$	19.2178	−	3.38862i	0.641306	−	0.113080i
$899$	3.22811	+	8.86917i	0.107664	+	0.295803i
$900$	14.4514	−	4.01971i	0.481712	−	0.133990i
$901$	18.1524	−	10.4803i	0.604744	−	0.349149i
$902$	−13.3067	−	11.1657i	−0.443066	−	0.371776i
$903$	10.8279	−	7.76648i	0.360330	−	0.258452i
$904$	−5.64555	−	9.77838i	−0.187768	−	0.325224i
$905$	4.47676	−	5.75511i	0.148813	−	0.191306i
$906$	−1.26362	−	12.7714i	−0.0419811	−	0.424302i
$907$	−10.2562	−	58.1657i	−0.340551	−	1.93136i	−0.363431	−	0.931621i	$-0.618395\pi$
$907$	−10.2562	−	58.1657i	−0.340551	−	1.93136i	0.0228803	−	0.999738i	$-0.492716\pi$
$908$	−8.16441	−	1.43961i	−0.270945	−	0.0477750i
$909$	14.6417	−	12.8636i	0.485636	−	0.426658i
$910$	0.987480	+	1.57287i	0.0327347	+	0.0521400i
$911$	−13.2559			−0.439188			−0.219594	−	0.975591i	$-0.570473\pi$
$911$	−13.2559			−0.439188			−0.219594	+	0.975591i	$0.570473\pi$
$912$	−6.78473	+	3.31172i	−0.224665	+	0.109662i
$913$			24.9929i			0.827143i
$914$	18.7303	−	15.7166i	0.619543	−	0.519858i
$915$	2.75583	+	2.50128i	0.0911050	+	0.0826899i
$916$	3.95697	−	22.4411i	0.130742	−	0.741474i
$917$	2.66451	+	15.1112i	0.0879899	+	0.499015i
$918$	−19.4870	−	8.29118i	−0.643168	−	0.273650i
$919$	16.9437	−	29.3474i	0.558922	−	0.968082i	−0.438665	−	0.898651i	$-0.644548\pi$
$919$	16.9437	−	29.3474i	0.558922	−	0.968082i	0.997587	−	0.0694309i	$-0.0221183\pi$
$920$	−0.0455976	−	0.112172i	−0.00150331	−	0.00369822i
$921$	22.2792	−	15.9801i	0.734124	−	0.526561i
$922$	22.2354	+	18.6577i	0.732284	+	0.614459i
$923$	−0.287765	−	0.498423i	−0.00947189	−	0.0164058i
$924$	5.33733	+	5.21749i	0.175585	+	0.171643i
$925$	15.8175	−	1.17352i	0.520077	−	0.0385850i
$926$	−2.99569	−	16.9894i	−0.0984445	−	0.558306i
$927$	7.68029	−	9.58694i	0.252254	−	0.314876i
$928$	−2.75318	+	7.56431i	−0.0903777	+	0.248311i
$929$	−3.66441	−	4.36708i	−0.120226	−	0.143279i	0.702575	−	0.711610i	$-0.252034\pi$
$929$	−3.66441	−	4.36708i	−0.120226	−	0.143279i	−0.822800	+	0.568331i	$0.807589\pi$
$930$	4.20361	+	1.71785i	0.137842	+	0.0563307i
$931$	7.98614	+	21.5119i	0.261735	+	0.705023i
$932$	16.1203			0.528038
$933$	−36.4389	+	17.4982i	−1.19296	+	0.572864i
$934$	−4.62409	+	12.7046i	−0.151305	+	0.415707i
$935$	9.15119	−	28.3691i	0.299276	−	0.927768i
$936$	−1.79140	−	0.606318i	−0.0585537	−	0.0198181i
$937$	−2.94289	−	8.08551i	−0.0961399	−	0.264142i	0.882295	−	0.470696i	$-0.155997\pi$
$937$	−2.94289	−	8.08551i	−0.0961399	−	0.264142i	−0.978435	+	0.206554i	$0.933775\pi$
$938$	1.31220	−	2.27280i	0.0428448	−	0.0742094i
$939$	13.9826	+	49.9100i	0.456304	+	1.62875i
$940$	6.41662	−	5.80224i	0.209287	−	0.189248i
$941$	15.1564	+	12.7177i	0.494083	+	0.414585i	0.855487	−	0.517824i	$-0.173258\pi$
$941$	15.1564	+	12.7177i	0.494083	+	0.414585i	−0.361404	+	0.932409i	$0.617702\pi$
$942$	27.0347	−	7.57392i	0.880837	−	0.246772i
$943$	0.143792	−	0.249055i	0.00468250	−	0.00811033i
$944$	−5.24185	+	1.90788i	−0.170608	+	0.0620961i
$945$	−11.5656	−	10.0280i	−0.376230	−	0.326209i
$946$	−18.8099	−	3.31670i	−0.611563	−	0.107835i
$947$	51.2213	+	18.6430i	1.66447	+	0.605817i	0.991056	−	0.133448i	$-0.0426050\pi$
$947$	51.2213	+	18.6430i	1.66447	+	0.605817i	0.673414	+	0.739266i	$0.264827\pi$
$948$	21.1283	−	10.1459i	0.686216	−	0.329524i
$949$		−	5.53353i		−	0.179626i
$950$	12.3791	+	17.9376i	0.401630	+	0.581974i
$951$	−27.7695	−	7.10390i	−0.900488	−	0.230360i
$952$	−4.11328	+	3.45145i	−0.133312	+	0.111862i
$953$	2.69864	−	7.41444i	0.0874174	−	0.240177i	−0.888279	−	0.459304i	$-0.848099\pi$
$953$	2.69864	−	7.41444i	0.0874174	−	0.240177i	0.975696	+	0.219127i	$0.0703209\pi$
$954$	−9.64650	+	12.0413i	−0.312317	+	0.389850i
$955$	−1.94102	−	52.3970i	−0.0628101	−	1.69553i
$956$	6.45225	+	17.7274i	0.208681	+	0.573345i
$957$	−31.8790	+	32.6112i	−1.03050	+	1.05417i
$958$	−3.43312	−	5.94633i	−0.110919	−	0.192117i
$959$	14.2090	−	16.9336i	0.458832	−	0.546814i
$960$	1.80464	+	3.42685i	0.0582444	+	0.110601i
$961$	−14.8126	−	25.6562i	−0.477826	−	0.827620i
$962$	−1.73186	−	0.999891i	−0.0558375	−	0.0322378i
$963$	3.76508	−	24.6080i	0.121328	−	0.792981i
$964$	−3.56372	+	0.628380i	−0.114780	+	0.0202387i
$965$	−37.2537	−	12.0171i	−1.19924	−	0.386846i
$966$	−0.0697226	+	0.102020i	−0.00224329	+	0.00328245i
$967$	−6.61765	−	7.88660i	−0.212809	−	0.253616i	0.649071	−	0.760728i	$-0.275158\pi$
$967$	−6.61765	−	7.88660i	−0.212809	−	0.253616i	−0.861880	+	0.507112i	$0.830713\pi$
$968$			0.301465i			0.00968946i
$969$	2.13696	−	30.6959i	0.0686489	−	0.986096i
$970$	−32.8647	−	4.54778i	−1.05522	−	0.146020i
$971$	−19.9838	+	16.7684i	−0.641309	+	0.538122i	−0.904420	−	0.426643i	$-0.859696\pi$
$971$	−19.9838	+	16.7684i	−0.641309	+	0.538122i	0.263111	+	0.964766i	$0.415252\pi$
$972$	15.5812	+	0.475317i	0.499768	+	0.0152458i
$973$	−5.73215	−	1.01073i	−0.183764	−	0.0324026i
$974$	20.3823	−	3.59395i	0.653090	−	0.115157i
$975$	−0.958015	+	5.37479i	−0.0306811	+	0.172131i
$976$	−0.480469	+	0.832197i	−0.0153794	+	0.0266380i
$977$	−11.3486	+	6.55214i	−0.363075	+	0.209622i	−0.670429	−	0.741974i	$-0.733890\pi$
$977$	−11.3486	+	6.55214i	−0.363075	+	0.209622i	0.307354	+	0.951595i	$0.400557\pi$
$978$	−33.2890	+	23.8770i	−1.06447	+	0.763503i
$979$	−30.2275	+	36.0237i	−0.966075	+	1.15132i
$980$	10.9048	−	4.43273i	0.348339	−	0.141598i
$981$	21.9636	+	36.1223i	0.701245	+	1.15330i
$982$	7.56282	−	2.75264i	0.241339	−	0.0878403i
$983$	−34.9912	+	6.16990i	−1.11605	+	0.196789i	−0.701105	−	0.713058i	$-0.747309\pi$
$983$	−34.9912	+	6.16990i	−1.11605	+	0.196789i	−0.414943	+	0.909848i	$0.636198\pi$
$984$	−3.79254	+	8.38025i	−0.120902	+	0.267153i
$985$	−7.06201	+	13.3500i	−0.225014	+	0.425365i
$986$	−21.0884	−	25.1322i	−0.671593	−	0.800373i
$987$	−8.55294	−	2.18798i	−0.272243	−	0.0696442i
$988$	−0.0176075	−	2.74783i	−0.000560169	−	0.0874201i
$989$		−	0.316215i		−	0.0100550i
$990$	1.30992	+	21.9025i	0.0416319	+	0.696106i
$991$	−12.3305	+	33.8777i	−0.391690	+	1.07616i	0.574540	+	0.818477i	$0.305181\pi$
$991$	−12.3305	+	33.8777i	−0.391690	+	1.07616i	−0.966230	+	0.257683i	$0.917041\pi$
$992$	−0.203603	+	1.15469i	−0.00646439	+	0.0366614i
$993$	−0.0778952	+	1.02415i	−0.00247193	+	0.0325003i
$994$	1.13024	−	0.411375i	0.0358491	−	0.0130480i
$995$	−4.67962	−	3.64016i	−0.148354	−	0.115401i
$996$	12.7440	−	3.57032i	0.403810	−	0.113130i
$997$	30.1751	−	35.9613i	0.955656	−	1.13891i	−0.0345652	−	0.999402i	$-0.511005\pi$
$997$	30.1751	−	35.9613i	0.955656	−	1.13891i	0.990221	−	0.139504i	$-0.0445509\pi$
$998$	−10.1348	+	12.0782i	−0.320812	+	0.382329i
$999$	16.0576	+	3.72148i	0.508041	+	0.117742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bf.a.89.7	✓	240
3.2	odd	2	inner	570.2.bf.a.89.31	yes	240
5.4	even	2	inner	570.2.bf.a.89.34	yes	240
15.14	odd	2	inner	570.2.bf.a.89.10	yes	240
19.3	odd	18	inner	570.2.bf.a.269.10	yes	240
57.41	even	18	inner	570.2.bf.a.269.34	yes	240
95.79	odd	18	inner	570.2.bf.a.269.31	yes	240
285.269	even	18	inner	570.2.bf.a.269.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.89.7	✓	240	1.1	even	1	trivial
570.2.bf.a.89.10	yes	240	15.14	odd	2	inner
570.2.bf.a.89.31	yes	240	3.2	odd	2	inner
570.2.bf.a.89.34	yes	240	5.4	even	2	inner
570.2.bf.a.269.7	yes	240	285.269	even	18	inner
570.2.bf.a.269.10	yes	240	19.3	odd	18	inner
570.2.bf.a.269.31	yes	240	95.79	odd	18	inner
570.2.bf.a.269.34	yes	240	57.41	even	18	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.977291 + 1.43000i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.23454 - 0.0827774i) q^{5} +(1.72363 - 0.170539i) q^{6} +(-1.14096 - 0.658735i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-1.08981 - 2.79505i) q^{9} +O(q^{10})\)	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.977291 + 1.43000i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(2.23454 - 0.0827774i) q^{5} +(1.72363 - 0.170539i) q^{6} +(-1.14096 - 0.658735i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-1.08981 - 2.79505i) q^{9} +(-1.49974 - 1.65855i) q^{10} +(2.83265 - 1.63543i) q^{11} +(-1.23857 - 1.21076i) q^{12} +(0.592390 - 0.215612i) q^{13} +(0.228776 + 1.29746i) q^{14} +(-2.06542 + 3.27629i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.12210 - 2.61976i) q^{17} +(-1.44062 + 2.63147i) q^{18} +(-4.29744 - 0.729393i) q^{19} +(-0.306503 + 2.21496i) q^{20} +(2.05704 - 0.987803i) q^{21} +(-3.07360 - 1.11870i) q^{22} +(0.00940327 - 0.0533286i) q^{23} +(-0.131358 + 1.72706i) q^{24} +(4.98630 - 0.369938i) q^{25} +(-0.545950 - 0.315204i) q^{26} +(5.06199 + 1.17316i) q^{27} +(0.846854 - 1.00924i) q^{28} +(6.16648 + 5.17430i) q^{29} +(3.83741 - 0.523753i) q^{30} +(1.01542 + 0.586251i) q^{31} +(0.342020 + 0.939693i) q^{32} +(-0.429654 + 5.64898i) q^{33} +(-4.01370 - 0.707724i) q^{34} +(-2.60405 - 1.37752i) q^{35} +(2.94183 - 0.587894i) q^{36} +3.17220 q^{37} +(2.20359 + 3.76087i) q^{38} +(-0.270611 + 1.05783i) q^{39} +(1.89378 - 1.18895i) q^{40} +(4.99046 + 1.81638i) q^{41} +(-2.07894 - 0.940841i) q^{42} +(5.75075 - 1.01401i) q^{43} +(1.11870 + 3.07360i) q^{44} +(-2.66658 - 6.15543i) q^{45} +(-0.0468964 + 0.0270756i) q^{46} +(-2.96369 - 2.48683i) q^{47} +(1.40744 - 1.00951i) q^{48} +(-2.63214 - 4.55899i) q^{49} +(-3.48852 - 3.58193i) q^{50} +(0.695051 + 7.02488i) q^{51} +(0.109469 + 0.620831i) q^{52} +(5.06479 + 0.893059i) q^{53} +(-2.35509 - 4.63180i) q^{54} +(6.19428 - 3.88891i) q^{55} -1.31747 q^{56} +(5.24288 - 5.43251i) q^{57} -8.04977i q^{58} +(4.27319 - 3.58563i) q^{59} +(-2.86786 - 2.60296i) q^{60} +(0.166865 - 0.946339i) q^{61} +(-0.203603 - 1.15469i) q^{62} +(-0.597772 + 3.90695i) q^{63} +(0.500000 - 0.866025i) q^{64} +(1.30587 - 0.530830i) q^{65} +(4.60355 - 3.30196i) q^{66} +(-1.52596 - 1.28043i) q^{67} +(2.03781 + 3.52959i) q^{68} +(0.0670702 + 0.0655642i) q^{69} +(0.618609 + 2.88027i) q^{70} +(-0.158531 - 0.899077i) q^{71} +(-2.34133 - 1.87568i) q^{72} +(3.00215 - 8.24833i) q^{73} +(-2.03905 - 2.43005i) q^{74} +(-4.34405 + 7.49195i) q^{75} +(1.46455 - 4.10549i) q^{76} -4.30926 q^{77} +(0.984294 - 0.472663i) q^{78} +(-4.62822 + 12.7159i) q^{79} +(-2.12809 - 0.686471i) q^{80} +(-6.62465 + 6.09213i) q^{81} +(-1.81638 - 4.99046i) q^{82} +(-3.82053 + 6.61736i) q^{83} +(0.615594 + 2.19732i) q^{84} +(6.75959 - 6.11238i) q^{85} +(-4.47329 - 3.75354i) q^{86} +(-13.4257 + 3.76129i) q^{87} +(1.63543 - 2.83265i) q^{88} +(-13.5101 + 4.91727i) q^{89} +(-3.00129 + 5.99935i) q^{90} +(-0.817927 - 0.144223i) q^{91} +(0.0508856 + 0.0185208i) q^{92} +(-1.83070 + 0.879109i) q^{93} +3.86882i q^{94} +(-9.66316 - 1.27412i) q^{95} +(-1.67801 - 0.429264i) q^{96} +(11.3663 - 9.53743i) q^{97} +(-1.80049 + 4.94680i) q^{98} +(-7.65815 - 6.13510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) \) 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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