LMFDB - Embedded newform 670.2.h.c.439.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("670.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.1
Character	$\chi$	$=$	670.439
Dual form			670.2.h.c.29.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} -2.72838i q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.87831 + 1.21324i) q^{5} +(1.36419 + 2.36285i) q^{6} +(2.29856 + 1.32708i) q^{7} +1.00000i q^{8} -4.44406 q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} -2.72838i q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.87831 + 1.21324i) q^{5} +(1.36419 + 2.36285i) q^{6} +(2.29856 + 1.32708i) q^{7} +1.00000i q^{8} -4.44406 q^{9} +(1.02005 - 1.98985i) q^{10} +(-0.0662493 + 0.114747i) q^{11} +(-2.36285 - 1.36419i) q^{12} +(4.47362 - 2.58285i) q^{13} -2.65415 q^{14} +(3.31017 + 5.12475i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.65943 - 2.69013i) q^{17} +(3.84867 - 2.22203i) q^{18} +(-3.42344 - 5.92958i) q^{19} +(0.111537 + 2.23328i) q^{20} +(3.62077 - 6.27136i) q^{21} -0.132499i q^{22} +(-0.726796 + 0.419616i) q^{23} +2.72838 q^{24} +(2.05611 - 4.55767i) q^{25} +(-2.58285 + 4.47362i) q^{26} +3.93995i q^{27} +(2.29856 - 1.32708i) q^{28} +(-2.17978 + 3.77548i) q^{29} +(-5.42907 - 2.78308i) q^{30} +(0.496435 - 0.859850i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.313074 + 0.180753i) q^{33} +(-2.69013 + 4.65943i) q^{34} +(-5.92748 + 0.296037i) q^{35} +(-2.22203 + 3.84867i) q^{36} +(-7.66951 + 4.42800i) q^{37} +(5.92958 + 3.42344i) q^{38} +(-7.04699 - 12.2057i) q^{39} +(-1.21324 - 1.87831i) q^{40} +(2.54910 - 4.41518i) q^{41} +7.24154i q^{42} -10.3300i q^{43} +(0.0662493 + 0.114747i) q^{44} +(8.34733 - 5.39170i) q^{45} +(0.419616 - 0.726796i) q^{46} +(-1.22545 - 0.707512i) q^{47} +(-2.36285 + 1.36419i) q^{48} +(0.0222652 + 0.0385645i) q^{49} +(0.498190 + 4.97512i) q^{50} +(-7.33969 - 12.7127i) q^{51} -5.16569i q^{52} +8.07078i q^{53} +(-1.96997 - 3.41209i) q^{54} +(-0.0147786 - 0.295907i) q^{55} +(-1.32708 + 2.29856i) q^{56} +(-16.1781 + 9.34045i) q^{57} -4.35955i q^{58} -6.21973 q^{59} +(6.09325 - 0.304316i) q^{60} +(-0.678768 - 1.17566i) q^{61} +0.992870i q^{62} +(-10.2150 - 5.89761i) q^{63} -1.00000 q^{64} +(-5.26926 + 10.2790i) q^{65} -0.361507 q^{66} +(5.92211 - 5.65054i) q^{67} -5.38025i q^{68} +(1.14487 + 1.98298i) q^{69} +(4.98533 - 3.22012i) q^{70} +(0.571995 - 0.990725i) q^{71} -4.44406i q^{72} +(9.51495 - 5.49346i) q^{73} +(4.42800 - 7.66951i) q^{74} +(-12.4351 - 5.60986i) q^{75} -6.84688 q^{76} +(-0.304557 + 0.175836i) q^{77} +(12.2057 + 7.04699i) q^{78} +(-2.22428 + 3.85256i) q^{79} +(1.98985 + 1.02005i) q^{80} -2.58251 q^{81} +5.09821i q^{82} +(3.96390 - 2.28856i) q^{83} +(-3.62077 - 6.27136i) q^{84} +(-5.48811 + 10.7059i) q^{85} +(5.16498 + 8.94600i) q^{86} +(10.3010 + 5.94726i) q^{87} +(-0.114747 - 0.0662493i) q^{88} +17.0429 q^{89} +(-4.53315 + 8.84301i) q^{90} +13.7105 q^{91} +0.839232i q^{92} +(-2.34600 - 1.35446i) q^{93} +1.41502 q^{94} +(13.6243 + 6.98415i) q^{95} +(1.36419 - 2.36285i) q^{96} +(6.39828 - 3.69405i) q^{97} +(-0.0385645 - 0.0222652i) q^{98} +(0.294416 - 0.509943i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9}+O(q^{10}) $ 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9	$ 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9} - 10 q^{10} + 24 q^{11} + 24 q^{14} + 28 q^{15} - 26 q^{16} - 24 q^{19} - 8 q^{20} + 4 q^{21} - 12 q^{24} - 28 q^{25} + 4 q^{26} - 20 q^{29} - 10 q^{30} - 30 q^{31} - 16 q^{34} - 14 q^{35} - 24 q^{36} - 8 q^{39} - 20 q^{40} - 10 q^{41} - 24 q^{44} - 16 q^{45} - 8 q^{46} + 14 q^{49} - 8 q^{50} - 44 q^{51} + 42 q^{54} + 16 q^{55} + 12 q^{56} + 80 q^{59} + 14 q^{60} - 20 q^{61} - 52 q^{64} + 10 q^{65} - 40 q^{66} - 4 q^{69} + 48 q^{70} - 74 q^{71} + 34 q^{74} - 16 q^{75} - 48 q^{76} + 32 q^{79} + 8 q^{80} + 4 q^{81} - 4 q^{84} + 20 q^{85} + 12 q^{86} + 84 q^{89} - 30 q^{90} - 16 q^{91} + 136 q^{94} + 2 q^{95} - 6 q^{96} - 96 q^{99}+O(q^{100}) $ 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9 - 10 * q^10 + 24 * q^11 + 24 * q^14 + 28 * q^15 - 26 * q^16 - 24 * q^19 - 8 * q^20 + 4 * q^21 - 12 * q^24 - 28 * q^25 + 4 * q^26 - 20 * q^29 - 10 * q^30 - 30 * q^31 - 16 * q^34 - 14 * q^35 - 24 * q^36 - 8 * q^39 - 20 * q^40 - 10 * q^41 - 24 * q^44 - 16 * q^45 - 8 * q^46 + 14 * q^49 - 8 * q^50 - 44 * q^51 + 42 * q^54 + 16 * q^55 + 12 * q^56 + 80 * q^59 + 14 * q^60 - 20 * q^61 - 52 * q^64 + 10 * q^65 - 40 * q^66 - 4 * q^69 + 48 * q^70 - 74 * q^71 + 34 * q^74 - 16 * q^75 - 48 * q^76 + 32 * q^79 + 8 * q^80 + 4 * q^81 - 4 * q^84 + 20 * q^85 + 12 * q^86 + 84 * q^89 - 30 * q^90 - 16 * q^91 + 136 * q^94 + 2 * q^95 - 6 * q^96 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		−	2.72838i		−	1.57523i	−0.616167	−	0.787616i	$-0.711315\pi$
$3$		−	2.72838i		−	1.57523i	0.616167	−	0.787616i	$-0.288685\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.87831	+	1.21324i	−0.840007	+	0.542576i
$5$	−1.87831	+	1.21324i	−0.840007	+	0.542576i
$6$	1.36419	+	2.36285i	0.556928	+	0.964628i
$7$	2.29856	+	1.32708i	0.868776	+	0.501588i	0.866941	−	0.498410i	$-0.166083\pi$
$7$	2.29856	+	1.32708i	0.868776	+	0.501588i	0.00183447	+	0.999998i	$0.499416\pi$
$8$			1.00000i			0.353553i
$9$	−4.44406			−1.48135
$10$	1.02005	−	1.98985i	0.322567	−	0.629246i
$11$	−0.0662493	+	0.114747i	−0.0199749	+	0.0345976i	−0.875840	−	0.482601i	$-0.839692\pi$
$11$	−0.0662493	+	0.114747i	−0.0199749	+	0.0345976i	0.855865	+	0.517199i	$0.173025\pi$
$12$	−2.36285	−	1.36419i	−0.682095	−	0.393808i
$13$	4.47362	−	2.58285i	1.24076	−	0.716353i	0.271511	−	0.962435i	$-0.412477\pi$
$13$	4.47362	−	2.58285i	1.24076	−	0.716353i	0.969249	+	0.246083i	$0.0791434\pi$
$14$	−2.65415			−0.709352
$15$	3.31017	+	5.12475i	0.854682	+	1.32320i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.65943	−	2.69013i	1.13008	−	0.652451i	0.186124	−	0.982526i	$-0.440407\pi$
$17$	4.65943	−	2.69013i	1.13008	−	0.652451i	0.943955	+	0.330075i	$0.107074\pi$
$18$	3.84867	−	2.22203i	0.907140	−	0.523738i
$19$	−3.42344	−	5.92958i	−0.785391	−	1.36034i	−0.928765	−	0.370669i	$-0.879128\pi$
$19$	−3.42344	−	5.92958i	−0.785391	−	1.36034i	0.143374	−	0.989669i	$-0.454205\pi$
$20$	0.111537	+	2.23328i	0.0249405	+	0.499378i
$21$	3.62077	−	6.27136i	0.790117	−	1.36852i
$22$		−	0.132499i		−	0.0282488i
$23$	−0.726796	+	0.419616i	−0.151548	+	0.0874960i	−0.573856	−	0.818956i	$-0.694553\pi$
$23$	−0.726796	+	0.419616i	−0.151548	+	0.0874960i	0.422309	+	0.906452i	$0.361220\pi$
$24$	2.72838			0.556928
$25$	2.05611	−	4.55767i	0.411223	−	0.911535i
$26$	−2.58285	+	4.47362i	−0.506538	+	0.877350i
$27$			3.93995i			0.758243i
$28$	2.29856	−	1.32708i	0.434388	−	0.250794i
$29$	−2.17978	+	3.77548i	−0.404774	+	0.701090i	−0.994295	−	0.106663i	$-0.965983\pi$
$29$	−2.17978	+	3.77548i	−0.404774	+	0.701090i	0.589521	+	0.807753i	$0.299317\pi$
$30$	−5.42907	−	2.78308i	−0.991208	−	0.508118i
$31$	0.496435	−	0.859850i	0.0891623	−	0.154434i	−0.817995	−	0.575225i	$-0.804914\pi$
$31$	0.496435	−	0.859850i	0.0891623	−	0.154434i	0.907157	+	0.420792i	$0.138248\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	0.313074	+	0.180753i	0.0544992	+	0.0314651i
$34$	−2.69013	+	4.65943i	−0.461353	+	0.799086i
$35$	−5.92748	+	0.296037i	−1.00193	+	0.0500395i
$36$	−2.22203	+	3.84867i	−0.370338	+	0.641445i
$37$	−7.66951	+	4.42800i	−1.26086	+	0.727958i	−0.973241	−	0.229787i	$-0.926197\pi$
$37$	−7.66951	+	4.42800i	−1.26086	+	0.727958i	−0.287619	+	0.957745i	$0.592864\pi$
$38$	5.92958	+	3.42344i	0.961904	+	0.555356i
$39$	−7.04699	−	12.2057i	−1.12842	−	1.95448i
$40$	−1.21324	−	1.87831i	−0.191830	−	0.296987i
$41$	2.54910	−	4.41518i	0.398103	−	0.689535i	−0.595389	−	0.803438i	$-0.703002\pi$
$41$	2.54910	−	4.41518i	0.398103	−	0.689535i	0.993492	+	0.113903i	$0.0363353\pi$
$42$			7.24154i			1.11739i
$43$		−	10.3300i		−	1.57530i	−0.616121	−	0.787651i	$-0.711297\pi$
$43$		−	10.3300i		−	1.57530i	0.616121	−	0.787651i	$-0.288703\pi$
$44$	0.0662493	+	0.114747i	0.00998746	+	0.0172988i
$45$	8.34733	−	5.39170i	1.24435	−	0.803747i
$46$	0.419616	−	0.726796i	0.0618690	−	0.107160i
$47$	−1.22545	−	0.707512i	−0.178750	−	0.103201i	0.407955	−	0.913002i	$-0.366242\pi$
$47$	−1.22545	−	0.707512i	−0.178750	−	0.103201i	−0.586705	+	0.809801i	$0.699575\pi$
$48$	−2.36285	+	1.36419i	−0.341048	+	0.196904i
$49$	0.0222652	+	0.0385645i	0.00318075	+	0.00550922i
$50$	0.498190	+	4.97512i	0.0704546	+	0.703588i
$51$	−7.33969	−	12.7127i	−1.02776	−	1.78014i
$52$		−	5.16569i		−	0.716353i
$53$			8.07078i			1.10861i	0.832314	+	0.554304i	$0.187015\pi$
$53$			8.07078i			1.10861i	−0.832314	+	0.554304i	$0.812985\pi$
$54$	−1.96997	−	3.41209i	−0.268079	−	0.464327i
$55$	−0.0147786	−	0.295907i	−0.00199274	−	0.0399001i
$56$	−1.32708	+	2.29856i	−0.177338	+	0.307159i
$57$	−16.1781	+	9.34045i	−2.14285	+	1.23717i
$58$		−	4.35955i		−	0.572437i
$59$	−6.21973			−0.809740			−0.404870	−	0.914374i	$-0.632683\pi$
$59$	−6.21973			−0.809740			−0.404870	+	0.914374i	$0.632683\pi$
$60$	6.09325	−	0.304316i	0.786635	−	0.0392871i
$61$	−0.678768	−	1.17566i	−0.0869074	−	0.150528i	0.819295	−	0.573372i	$-0.194365\pi$
$61$	−0.678768	−	1.17566i	−0.0869074	−	0.150528i	−0.906202	+	0.422844i	$0.861032\pi$
$62$			0.992870i			0.126095i
$63$	−10.2150	−	5.89761i	−1.28696	−	0.743029i
$64$	−1.00000			−0.125000
$65$	−5.26926	+	10.2790i	−0.653571	+	1.27495i
$66$	−0.361507			−0.0444984
$67$	5.92211	−	5.65054i	0.723501	−	0.690323i
$67$	5.92211	−	5.65054i	0.723501	−	0.690323i
$68$		−	5.38025i		−	0.652451i
$69$	1.14487	+	1.98298i	0.137826	+	0.238722i
$70$	4.98533	−	3.22012i	0.595861	−	0.384877i
$71$	0.571995	−	0.990725i	0.0678833	−	0.117577i	−0.830086	−	0.557635i	$-0.811709\pi$
$71$	0.571995	−	0.990725i	0.0678833	−	0.117577i	0.897969	+	0.440058i	$0.145042\pi$
$72$		−	4.44406i		−	0.523738i
$73$	9.51495	−	5.49346i	1.11364	−	0.642961i	0.173871	−	0.984769i	$-0.444373\pi$
$73$	9.51495	−	5.49346i	1.11364	−	0.642961i	0.939770	+	0.341808i	$0.111039\pi$
$74$	4.42800	−	7.66951i	0.514744	−	0.891563i
$75$	−12.4351	−	5.60986i	−1.43588	−	0.647771i
$76$	−6.84688			−0.785391
$77$	−0.304557	+	0.175836i	−0.0347074	+	0.0200384i
$78$	12.2057	+	7.04699i	1.38203	+	0.797914i
$79$	−2.22428	+	3.85256i	−0.250251	+	0.433447i	−0.963595	−	0.267367i	$-0.913846\pi$
$79$	−2.22428	+	3.85256i	−0.250251	+	0.433447i	0.713344	+	0.700814i	$0.247180\pi$
$80$	1.98985	+	1.02005i	0.222472	+	0.114045i
$81$	−2.58251			−0.286945
$82$			5.09821i			0.563003i
$83$	3.96390	−	2.28856i	0.435095	−	0.251202i	−0.266420	−	0.963857i	$-0.585841\pi$
$83$	3.96390	−	2.28856i	0.435095	−	0.251202i	0.701515	+	0.712655i	$0.252507\pi$
$84$	−3.62077	−	6.27136i	−0.395058	−	0.684261i
$85$	−5.48811	+	10.7059i	−0.595270	+	1.16122i
$86$	5.16498	+	8.94600i	0.556954	+	0.964672i
$87$	10.3010	+	5.94726i	1.10438	+	0.637613i
$88$	−0.114747	−	0.0662493i	−0.0122321	−	0.00706220i
$89$	17.0429			1.80655			0.903274	−	0.429065i	$-0.141157\pi$
$89$	17.0429			1.80655			0.903274	+	0.429065i	$0.141157\pi$
$90$	−4.53315	+	8.84301i	−0.477836	+	0.932135i
$91$	13.7105			1.43726
$92$			0.839232i			0.0874960i
$93$	−2.34600	−	1.35446i	−0.243269	−	0.140451i
$94$	1.41502			0.145949
$95$	13.6243	+	6.98415i	1.39782	+	0.716559i
$96$	1.36419	−	2.36285i	0.139232	−	0.241157i
$97$	6.39828	−	3.69405i	0.649647	−	0.375074i	−0.138674	−	0.990338i	$-0.544284\pi$
$97$	6.39828	−	3.69405i	0.649647	−	0.375074i	0.788321	+	0.615264i	$0.210951\pi$
$98$	−0.0385645	−	0.0222652i	−0.00389561	−	0.00224913i
$99$	0.294416	−	0.509943i	0.0295899	−	0.0512512i
$100$	−2.91900	−	4.05948i	−0.291900	−	0.405948i
$101$	2.86752	−	4.96670i	0.285329	−	0.494205i	−0.687360	−	0.726317i	$-0.741230\pi$
$101$	2.86752	−	4.96670i	0.285329	−	0.494205i	0.972689	+	0.232112i	$0.0745637\pi$
$102$	12.7127	+	7.33969i	1.25875	+	0.726737i
$103$	2.79130	+	1.61156i	0.275035	+	0.158792i	0.631174	−	0.775642i	$-0.282574\pi$
$103$	2.79130	+	1.61156i	0.275035	+	0.158792i	−0.356139	+	0.934433i	$0.615907\pi$
$104$	2.58285	+	4.47362i	0.253269	+	0.438675i
$105$	0.807703	+	16.1724i	0.0788237	+	1.57827i
$106$	−4.03539	−	6.98950i	−0.391952	−	0.678881i
$107$		−	15.2234i		−	1.47170i	−0.677143	−	0.735851i	$-0.736782\pi$
$107$		−	15.2234i		−	1.47170i	0.677143	−	0.735851i	$-0.263218\pi$
$108$	3.41209	+	1.96997i	0.328329	+	0.189561i
$109$	7.85365			0.752243			0.376122	−	0.926570i	$-0.377257\pi$
$109$	7.85365			0.752243			0.376122	+	0.926570i	$0.377257\pi$
$110$	0.160752	+	0.248874i	0.0153271	+	0.0237292i
$111$	12.0813	+	20.9254i	1.14670	+	1.98615i
$112$		−	2.65415i		−	0.250794i
$113$	−13.3780	−	7.72377i	−1.25849	−	0.726591i	−0.285712	−	0.958316i	$-0.592230\pi$
$113$	−13.3780	−	7.72377i	−1.25849	−	0.726591i	−0.972782	+	0.231724i	$0.925563\pi$
$114$	9.34045	−	16.1781i	0.874813	−	1.51522i
$115$	0.856057	−	1.66995i	0.0798277	−	0.155723i
$116$	2.17978	+	3.77548i	0.202387	+	0.350545i
$117$	−19.8810	+	11.4783i	−1.83800	+	1.06117i
$118$	5.38644	−	3.10986i	0.495862	−	0.286286i
$119$	14.2800			1.30905
$120$	−5.12475	+	3.31017i	−0.467824	+	0.302176i
$121$	5.49122	+	9.51108i	0.499202	+	0.864643i
$122$	1.17566	+	0.678768i	0.106439	+	0.0614528i
$123$	−12.0463	−	6.95493i	−1.08618	−	0.627105i
$124$	−0.496435	−	0.859850i	−0.0445812	−	0.0772168i
$125$	1.66751	+	11.0553i	0.149147	+	0.988815i
$126$	11.7952			1.05080
$127$	14.8267	+	8.56019i	1.31565	+	0.759594i	0.983026	−	0.183464i	$-0.0587311\pi$
$127$	14.8267	+	8.56019i	1.31565	+	0.759594i	0.332629	+	0.943058i	$0.392064\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−28.1840			−2.48147
$130$	−0.576168	−	11.5365i	−0.0505333	−	1.01181i
$131$	−7.39435			−0.646048			−0.323024	−	0.946391i	$-0.604699\pi$
$131$	−7.39435			−0.646048			−0.323024	+	0.946391i	$0.604699\pi$
$132$	0.313074	−	0.180753i	0.0272496	−	0.0157326i
$133$		−	18.1727i		−	1.57577i
$134$	−2.30343	+	7.85457i	−0.198986	+	0.678531i
$135$	−4.78009	−	7.40045i	−0.411404	−	0.636929i
$136$	2.69013	+	4.65943i	0.230676	+	0.399543i
$137$			11.1386i			0.951635i	0.879544	+	0.475818i	$0.157848\pi$
$137$			11.1386i			0.951635i	−0.879544	+	0.475818i	$0.842152\pi$
$138$	−1.98298	−	1.14487i	−0.168802	−	0.0974580i
$139$	−15.1397			−1.28413			−0.642064	−	0.766651i	$-0.721922\pi$
$139$	−15.1397			−1.28413			−0.642064	+	0.766651i	$0.721922\pi$
$140$	−2.70736	+	5.28137i	−0.228814	+	0.446357i
$141$	−1.93036	+	3.34349i	−0.162566	+	0.281572i
$142$			1.14399i			0.0960015i
$143$			0.684447i			0.0572364i
$144$	2.22203	+	3.84867i	0.185169	+	0.320722i
$145$	−0.486253	−	9.73612i	−0.0403811	−	0.808541i
$146$	−5.49346	+	9.51495i	−0.454642	+	0.787463i
$147$	0.105219	−	0.0607480i	0.00867829	−	0.00501041i
$148$			8.85599i			0.727958i
$149$	−14.4694			−1.18538			−0.592690	−	0.805431i	$-0.701934\pi$
$149$	−14.4694			−1.18538			−0.592690	+	0.805431i	$0.701934\pi$
$150$	13.5740	−	1.35925i	1.10831	−	0.110982i
$151$	−4.24257	−	7.34835i	−0.345256	−	0.598001i	0.640144	−	0.768255i	$-0.278875\pi$
$151$	−4.24257	−	7.34835i	−0.345256	−	0.598001i	−0.985400	+	0.170254i	$0.945541\pi$
$152$	5.92958	−	3.42344i	0.480952	−	0.277678i
$153$	−20.7068	+	11.9551i	−1.67405	+	0.966511i
$154$	0.175836	−	0.304557i	0.0141693	−	0.0245419i
$155$	0.110742	+	2.21736i	0.00889502	+	0.178103i
$156$	−14.0940			−1.12842
$157$	10.4310	−	6.02232i	0.832482	−	0.480633i	−0.0222200	−	0.999753i	$-0.507073\pi$
$157$	10.4310	−	6.02232i	0.832482	−	0.480633i	0.854702	+	0.519120i	$0.173740\pi$
$158$		−	4.44855i		−	0.353908i
$159$	22.0202			1.74631
$160$	−2.23328	+	0.111537i	−0.176557	+	0.00881781i
$161$	−2.22745			−0.175548
$162$	2.23652	−	1.29125i	0.175718	−	0.101451i
$163$	15.5738	+	8.99155i	1.21984	+	0.704273i	0.964883	−	0.262680i	$-0.0846065\pi$
$163$	15.5738	+	8.99155i	1.21984	+	0.704273i	0.254954	+	0.966953i	$0.417940\pi$
$164$	−2.54910	−	4.41518i	−0.199052	−	0.344767i
$165$	−0.807347	+	0.0403215i	−0.0628519	+	0.00313903i
$166$	−2.28856	+	3.96390i	−0.177627	+	0.307658i
$167$	−2.01612	−	1.16400i	−0.156012	−	0.0900734i	0.419962	−	0.907542i	$-0.362043\pi$
$167$	−2.01612	−	1.16400i	−0.156012	−	0.0900734i	−0.575973	+	0.817468i	$0.695377\pi$
$168$	6.27136	+	3.62077i	0.483846	+	0.279348i
$169$	6.84220	−	11.8510i	0.526323	−	0.911618i
$170$	−0.600099	−	12.0156i	−0.0460255	−	0.921557i
$171$	15.2140	+	26.3514i	1.16344	+	2.01514i
$172$	−8.94600	−	5.16498i	−0.682126	−	0.393826i
$173$	−13.9553	+	8.05707i	−1.06100	+	0.612568i	−0.925708	−	0.378238i	$-0.876530\pi$
$173$	−13.9553	+	8.05707i	−1.06100	+	0.612568i	−0.135291	+	0.990806i	$0.543197\pi$
$174$	−11.8945			−0.901721
$175$	10.7745	−	7.74748i	0.814475	−	0.585655i
$176$	0.132499			0.00998746
$177$			16.9698i			1.27553i
$178$	−14.7596	+	8.52147i	−1.10628	+	0.638711i
$179$	7.06802			0.528289			0.264144	−	0.964483i	$-0.414910\pi$
$179$	7.06802			0.528289			0.264144	+	0.964483i	$0.414910\pi$
$180$	−0.495679	−	9.92485i	−0.0369457	−	0.739755i
$181$	−10.0752	+	17.4508i	−0.748885	+	1.29711i	0.199473	+	0.979903i	$0.436077\pi$
$181$	−10.0752	+	17.4508i	−0.748885	+	1.29711i	−0.948358	+	0.317203i	$0.897256\pi$
$182$	−11.8737	+	6.85527i	−0.880136	+	0.508147i
$183$	−3.20765	+	1.85194i	−0.237116	+	0.136899i
$184$	−0.419616	−	0.726796i	−0.0309345	−	0.0535801i
$185$	9.03354	−	17.6221i	0.664159	−	1.29560i
$186$	2.70893			0.198628
$187$			0.712876i			0.0521307i
$188$	−1.22545	+	0.707512i	−0.0893749	+	0.0516006i
$189$	−5.22861	+	9.05622i	−0.380325	+	0.658743i
$190$	−15.2910	+	0.763684i	−1.10933	+	0.0554034i
$191$	7.35999	+	12.7479i	0.532550	+	0.922404i	0.999278	+	0.0380030i	$0.0120996\pi$
$191$	7.35999	+	12.7479i	0.532550	+	0.922404i	−0.466727	+	0.884401i	$0.654567\pi$
$192$			2.72838i			0.196904i
$193$			24.1291i			1.73685i	0.495822	+	0.868424i	$0.334867\pi$
$193$			24.1291i			1.73685i	−0.495822	+	0.868424i	$0.665133\pi$
$194$	−3.69405	+	6.39828i	−0.265217	+	0.459370i
$195$	28.0449	+	14.3765i	2.00834	+	1.02953i
$196$	0.0445305			0.00318075
$197$	−16.3232	−	9.42419i	−1.16298	−	0.671446i	−0.210962	−	0.977494i	$-0.567660\pi$
$197$	−16.3232	−	9.42419i	−1.16298	−	0.671446i	−0.952016	+	0.306048i	$0.900993\pi$
$198$			0.588832i			0.0418465i
$199$	−7.86850	−	13.6286i	−0.557783	−	0.966109i	−0.997681	−	0.0680610i	$-0.978319\pi$
$199$	−7.86850	−	13.6286i	−0.557783	−	0.966109i	0.439898	−	0.898048i	$-0.355015\pi$
$200$	4.55767	+	2.05611i	0.322276	+	0.145389i
$201$	−15.4168	−	16.1578i	−1.08742	−	1.13968i
$202$			5.73505i			0.403516i
$203$	−10.0207	+	5.78546i	−0.703316	+	0.406060i
$204$	−14.6794			−1.02776
$205$	0.568641	+	11.3857i	0.0397156	+	0.795215i
$206$	−3.22312			−0.224565
$207$	3.22993	−	1.86480i	0.224495	−	0.129612i
$208$	−4.47362	−	2.58285i	−0.310190	−	0.179088i
$209$	0.907203			0.0627525
$210$	−8.78570	−	13.6019i	−0.606271	−	0.938619i
$211$	−2.91518	−	5.04924i	−0.200689	−	0.347604i	0.748061	−	0.663629i	$-0.230985\pi$
$211$	−2.91518	−	5.04924i	−0.200689	−	0.347604i	−0.948751	+	0.316026i	$0.897651\pi$
$212$	6.98950	+	4.03539i	0.480041	+	0.277152i
$213$	−2.70307	−	1.56062i	−0.185212	−	0.106932i
$214$	7.61170	+	13.1839i	0.520325	+	0.901230i
$215$	12.5327	+	19.4029i	0.854721	+	1.32327i
$216$	−3.93995			−0.268079
$217$	2.28217	−	1.31761i	0.154924	−	0.0894455i
$218$	−6.80146	+	3.92682i	−0.460653	+	0.265958i
$219$	−14.9882	−	25.9604i	−1.01281	−	1.75424i
$220$	−0.263652	−	0.135155i	−0.0177754	−	0.00911215i
$221$	13.8964	−	24.0692i	0.934771	−	1.61907i
$222$	−20.9254	−	12.0813i	−1.40442	−	0.810841i
$223$			24.2806i			1.62595i	0.582299	+	0.812975i	$0.302153\pi$
$223$			24.2806i			1.62595i	−0.582299	+	0.812975i	$0.697847\pi$
$224$	1.32708	+	2.29856i	0.0886690	+	0.153579i
$225$	−9.13750	+	20.2546i	−0.609166	+	1.35031i
$226$	15.4475			1.02756
$227$	13.4384	+	7.75866i	0.891937	+	0.514960i	0.874576	−	0.484889i	$-0.161140\pi$
$227$	13.4384	+	7.75866i	0.891937	+	0.514960i	0.0173616	+	0.999849i	$0.494473\pi$
$228$			18.6809i			1.23717i
$229$	9.14135	+	15.8333i	0.604078	+	1.04629i	0.992197	+	0.124684i	$0.0397916\pi$
$229$	9.14135	+	15.8333i	0.604078	+	1.04629i	−0.388119	+	0.921609i	$0.626875\pi$
$230$	0.0936058	+	1.87424i	0.00617218	+	0.123584i
$231$	0.479747	+	0.830946i	0.0315650	+	0.0546723i
$232$	−3.77548	−	2.17978i	−0.247873	−	0.143109i
$233$	−2.29363	−	1.32423i	−0.150261	−	0.0867532i	0.422984	−	0.906137i	$-0.360983\pi$
$233$	−2.29363	−	1.32423i	−0.150261	−	0.0867532i	−0.573245	+	0.819384i	$0.694316\pi$
$234$	11.4783	−	19.8810i	0.750362	−	1.29966i
$235$	3.16015	−	0.157828i	0.206146	−	0.0102956i
$236$	−3.10986	+	5.38644i	−0.202435	+	0.350628i
$237$	10.5113	+	6.06867i	0.682779	+	0.394203i
$238$	−12.3669	+	7.14001i	−0.801624	+	0.462818i
$239$	11.4394	−	19.8136i	0.739952	−	1.28163i	−0.212565	−	0.977147i	$-0.568182\pi$
$239$	11.4394	−	19.8136i	0.739952	−	1.28163i	0.952516	−	0.304487i	$-0.0984850\pi$
$240$	2.78308	−	5.42907i	0.179647	−	0.350445i
$241$	4.78141			0.307998			0.153999	−	0.988071i	$-0.450785\pi$
$241$	4.78141			0.307998			0.153999	+	0.988071i	$0.450785\pi$
$242$	−9.51108	−	5.49122i	−0.611395	−	0.352989i
$243$			18.8659i			1.21025i
$244$	−1.35754			−0.0869074
$245$	−0.0886090	−	0.0454232i	−0.00566102	−	0.00290198i
$246$	13.9099			0.886860
$247$	−30.6304	−	17.6845i	−1.94896	−	1.12523i
$248$	0.859850	+	0.496435i	0.0546006	+	0.0315236i
$249$	−6.24406	−	10.8150i	−0.395701	−	0.685375i
$250$	−6.97175	−	8.74041i	−0.440932	−	0.552792i
$251$	3.47633	+	6.02118i	0.219424	+	0.380054i	0.954632	−	0.297788i	$-0.0962489\pi$
$251$	3.47633	+	6.02118i	0.219424	+	0.380054i	−0.735208	+	0.677842i	$0.762916\pi$
$252$	−10.2150	+	5.89761i	−0.643482	+	0.371514i
$253$		−	0.111197i		−	0.00699090i
$254$	−17.1204			−1.07423
$255$	29.2097	+	14.9737i	1.82919	+	0.937687i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.9346	+	8.62252i	0.931597	+	0.537858i	0.887316	−	0.461161i	$-0.152567\pi$
$257$	14.9346	+	8.62252i	0.931597	+	0.537858i	0.0442806	+	0.999019i	$0.485900\pi$
$258$	24.4081	−	14.0920i	1.51958	−	0.877331i
$259$	−23.5052			−1.46054
$260$	6.26721	+	9.70279i	0.388676	+	0.601741i
$261$	9.68706	−	16.7785i	0.599614	−	1.03856i
$262$	6.40370	−	3.69718i	0.395622	−	0.228412i
$263$			16.6825i			1.02869i	0.857585	+	0.514343i	$0.171964\pi$
$263$			16.6825i			1.02869i	−0.857585	+	0.514343i	$0.828036\pi$
$264$	−0.180753	+	0.313074i	−0.0111246	+	0.0192684i
$265$	−9.79177	−	15.1595i	−0.601504	−	0.931238i
$266$	9.08634	+	15.7380i	0.557119	+	0.964959i
$267$		−	46.4996i		−	2.84573i
$268$	−1.93245	−	7.95397i	−0.118043	−	0.485866i
$269$	−12.2389			−0.746221			−0.373111	−	0.927787i	$-0.621709\pi$
$269$	−12.2389			−0.746221			−0.373111	+	0.927787i	$0.621709\pi$
$270$	7.83990	+	4.01893i	0.477121	+	0.244585i
$271$	−2.58233			−0.156865			−0.0784326	−	0.996919i	$-0.524992\pi$
$271$	−2.58233			−0.156865			−0.0784326	+	0.996919i	$0.524992\pi$
$272$	−4.65943	−	2.69013i	−0.282520	−	0.163113i
$273$		−	37.4076i		−	2.26401i
$274$	−5.56930	−	9.64632i	−0.336454	−	0.582755i
$275$	0.386764	+	0.537876i	0.0233228	+	0.0324352i
$276$	2.28974			0.137826
$277$		−	6.48668i		−	0.389747i	−0.980828	−	0.194873i	$-0.937570\pi$
$277$		−	6.48668i		−	0.389747i	0.980828	−	0.194873i	$-0.0624296\pi$
$278$	13.1113	−	7.56983i	0.786365	−	0.454008i
$279$	−2.20619	+	3.82123i	−0.132081	+	0.228771i
$280$	−0.296037	−	5.92748i	−0.0176916	−	0.354235i
$281$	6.87879	+	11.9144i	0.410354	+	0.710754i	0.994928	−	0.100586i	$-0.0320717\pi$
$281$	6.87879	+	11.9144i	0.410354	+	0.710754i	−0.584574	+	0.811340i	$0.698738\pi$
$282$		−	3.86073i		−	0.229903i
$283$			11.6421i			0.692052i	0.938225	+	0.346026i	$0.112469\pi$
$283$			11.6421i			0.692052i	−0.938225	+	0.346026i	$0.887531\pi$
$284$	−0.571995	−	0.990725i	−0.0339417	−	0.0587887i
$285$	19.0554	−	37.1722i	1.12875	−	2.20189i
$286$	−0.342224	−	0.592749i	−0.0202361	−	0.0350500i
$287$	11.7186	−	6.76571i	0.691725	−	0.399367i
$288$	−3.84867	−	2.22203i	−0.226785	−	0.130934i
$289$	5.97355	−	10.3465i	0.351386	−	0.608618i
$290$	5.28917	+	8.18860i	0.310591	+	0.480851i
$291$	−10.0788	−	17.4569i	−0.590828	−	1.02334i
$292$		−	10.9869i		−	0.642961i
$293$		−	0.149053i		−	0.00870775i	−0.999991	−	0.00435387i	$-0.998614\pi$
$293$		−	0.149053i		−	0.00870775i	0.999991	−	0.00435387i	$-0.00138589\pi$
$294$	−0.0607480	+	0.105219i	−0.00354290	+	0.00613648i
$295$	11.6826	−	7.54600i	0.680187	−	0.439345i
$296$	−4.42800	−	7.66951i	−0.257372	−	0.445781i
$297$	−0.452098	−	0.261019i	−0.0262334	−	0.0151458i
$298$	12.5309	−	7.23470i	0.725894	−	0.419095i
$299$	−2.16761	+	3.75441i	−0.125356	+	0.217123i
$300$	−11.0758	+	7.96415i	−0.639463	+	0.459811i
$301$	13.7086	−	23.7441i	0.790153	−	1.36858i
$302$	7.34835	+	4.24257i	0.422850	+	0.244133i
$303$	−13.5510	−	7.82369i	−0.778487	−	0.449460i
$304$	−3.42344	+	5.92958i	−0.196348	+	0.340084i
$305$	2.70129	+	1.38475i	0.154676	+	0.0792907i
$306$	11.9551	−	20.7068i	0.683427	−	1.18373i
$307$	27.3714	−	15.8029i	1.56217	−	0.901920i	0.565133	−	0.825000i	$-0.308825\pi$
$307$	27.3714	−	15.8029i	1.56217	−	0.901920i	0.997037	−	0.0769198i	$-0.0245085\pi$
$308$			0.351672i			0.0200384i
$309$	4.39694	−	7.61573i	0.250133	−	0.433244i
$310$	−1.20459	−	1.86492i	−0.0684159	−	0.105920i
$311$	−10.8838			−0.617166			−0.308583	−	0.951197i	$-0.599855\pi$
$311$	−10.8838			−0.617166			−0.308583	+	0.951197i	$0.599855\pi$
$312$	12.2057	−	7.04699i	0.691014	−	0.398957i
$313$			17.7209i			1.00164i	0.865550	+	0.500822i	$0.166969\pi$
$313$			17.7209i			1.00164i	−0.865550	+	0.500822i	$0.833031\pi$
$314$	−6.02232	+	10.4310i	−0.339859	+	0.588653i
$315$	26.3421	−	1.31561i	1.48421	−	0.0741261i
$316$	2.22428	+	3.85256i	0.125125	+	0.216723i
$317$	5.65656	−	3.26582i	0.317704	−	0.183426i	−0.332665	−	0.943045i	$-0.607948\pi$
$317$	5.65656	−	3.26582i	0.317704	−	0.183426i	0.650369	+	0.759619i	$0.274614\pi$
$318$	−19.0700	+	11.0101i	−1.06939	+	0.617415i
$319$	−0.288817	−	0.500246i	−0.0161707	−	0.0280084i
$320$	1.87831	−	1.21324i	0.105001	−	0.0678220i
$321$	−41.5353			−2.31827
$322$	1.92903	−	1.11373i	0.107501	−	0.0620655i
$323$	−31.9026	−	18.4190i	−1.77511	−	1.02486i
$324$	−1.29125	+	2.23652i	−0.0717364	+	0.124251i
$325$	−2.57349	−	25.6999i	−0.142752	−	1.42558i
$326$	−17.9831			−0.995992
$327$		−	21.4277i		−	1.18496i
$328$	4.41518	+	2.54910i	0.243787	+	0.140751i
$329$	−1.87785	−	3.25253i	−0.103529	−	0.179318i
$330$	0.679022	−	0.438593i	0.0373790	−	0.0241438i
$331$	−14.4137	+	24.9652i	−0.792246	+	1.37221i	0.132327	+	0.991206i	$0.457755\pi$
$331$	−14.4137	+	24.9652i	−0.792246	+	1.37221i	−0.924573	+	0.381004i	$0.875578\pi$
$332$		−	4.57712i		−	0.251202i
$333$	34.0838	−	19.6783i	1.86778	−	1.07836i
$334$	2.32801			0.127383
$335$	−4.26814	+	17.7984i	−0.233193	+	0.972430i
$336$	−7.24154			−0.395058
$337$	−11.4188	+	6.59265i	−0.622022	+	0.359124i	−0.777656	−	0.628690i	$-0.783591\pi$
$337$	−11.4188	+	6.59265i	−0.622022	+	0.359124i	0.155634	+	0.987815i	$0.450258\pi$
$338$			13.6844i			0.744333i
$339$	−21.0734	+	36.5002i	−1.14455	+	1.98242i
$340$	6.52752	+	10.1058i	0.354004	+	0.548064i
$341$	0.0657769	+	0.113929i	0.00356202	+	0.00616960i
$342$	−26.3514	−	15.2140i	−1.42492	−	0.822678i
$343$		−	18.4609i		−	0.996794i
$344$	10.3300			0.556954
$345$	−4.55625	−	2.33565i	−0.245300	−	0.125747i
$346$	8.05707	−	13.9553i	0.433151	−	0.750240i
$347$	29.4580	+	17.0076i	1.58139	+	0.913015i	0.994657	+	0.103233i	$0.0329188\pi$
$347$	29.4580	+	17.0076i	1.58139	+	0.913015i	0.586731	+	0.809782i	$0.300415\pi$
$348$	10.3010	−	5.94726i	0.552189	−	0.318807i
$349$	23.7423			1.27089			0.635447	−	0.772144i	$-0.280816\pi$
$349$	23.7423			1.27089			0.635447	+	0.772144i	$0.280816\pi$
$350$	−5.45724	+	12.0968i	−0.291702	+	0.646599i
$351$	10.1763	+	17.6258i	0.543170	+	0.940797i
$352$	−0.114747	+	0.0662493i	−0.00611605	+	0.00353110i
$353$	−10.4553	+	6.03636i	−0.556478	+	0.321283i	−0.751731	−	0.659470i	$-0.770781\pi$
$353$	−10.4553	+	6.03636i	−0.556478	+	0.321283i	0.195252	+	0.980753i	$0.437447\pi$
$354$	−8.48489	−	14.6963i	−0.450967	−	0.781098i
$355$	0.127598	+	2.55486i	0.00677218	+	0.135598i
$356$	8.52147	−	14.7596i	0.451637	−	0.782258i
$357$		−	38.9613i		−	2.06205i
$358$	−6.12108	+	3.53401i	−0.323509	+	0.186778i
$359$	25.2033			1.33018			0.665091	−	0.746762i	$-0.268393\pi$
$359$	25.2033			1.33018			0.665091	+	0.746762i	$0.268393\pi$
$360$	5.39170	+	8.34733i	0.284167	+	0.439943i
$361$	−13.9399	+	24.1446i	−0.733679	+	1.27077i
$362$		−	20.1504i		−	1.05908i
$363$	25.9498	−	14.9821i	1.36201	−	0.786359i
$364$	6.85527	−	11.8737i	0.359314	−	0.622350i
$365$	−11.2072	+	21.8623i	−0.586611	+	1.14433i
$366$	1.85194	−	3.20765i	0.0968024	−	0.167667i
$367$	−12.7038	−	7.33454i	−0.663133	−	0.382860i	0.130337	−	0.991470i	$-0.458394\pi$
$367$	−12.7038	−	7.33454i	−0.663133	−	0.382860i	−0.793470	+	0.608610i	$0.791727\pi$
$368$	0.726796	+	0.419616i	0.0378869	+	0.0218740i
$369$	−11.3284	+	19.6213i	−0.589731	+	1.02144i
$370$	0.987774	+	19.7780i	0.0513519	+	1.02821i
$371$	−10.7106	+	18.5512i	−0.556064	+	0.963131i
$372$	−2.34600	+	1.35446i	−0.121634	+	0.0702256i
$373$	4.21207	+	2.43184i	0.218093	+	0.125916i	0.605067	−	0.796175i	$-0.293146\pi$
$373$	4.21207	+	2.43184i	0.218093	+	0.125916i	−0.386974	+	0.922091i	$0.626480\pi$
$374$	−0.356438	−	0.617369i	−0.0184310	−	0.0319234i
$375$	30.1630	−	4.54960i	1.55761	−	0.234941i
$376$	0.707512	−	1.22545i	0.0364872	−	0.0631976i
$377$			22.5201i			1.15985i
$378$		−	10.4572i		−	0.537861i
$379$	5.58708	+	9.67711i	0.286989	+	0.497080i	0.973090	−	0.230427i	$-0.0740124\pi$
$379$	5.58708	+	9.67711i	0.286989	+	0.497080i	−0.686101	+	0.727507i	$0.740679\pi$
$380$	12.8606	−	8.30689i	0.659734	−	0.426134i
$381$	23.3554	−	40.4528i	1.19654	−	2.07246i
$382$	−12.7479	−	7.35999i	−0.652238	−	0.376570i
$383$	21.9890	−	12.6954i	1.12359	−	0.648702i	0.181272	−	0.983433i	$-0.441979\pi$
$383$	21.9890	−	12.6954i	1.12359	−	0.648702i	0.942314	+	0.334731i	$0.108645\pi$
$384$	−1.36419	−	2.36285i	−0.0696160	−	0.120579i
$385$	0.358722	−	0.699774i	0.0182822	−	0.0356638i
$386$	−12.0645	−	20.8964i	−0.614068	−	1.06360i
$387$			45.9069i			2.33358i
$388$		−	7.38810i		−	0.375074i
$389$	16.5559	+	28.6756i	0.839417	+	1.45391i	0.890383	+	0.455212i	$0.150437\pi$
$389$	16.5559	+	28.6756i	0.839417	+	1.45391i	−0.0509663	+	0.998700i	$0.516230\pi$
$390$	−31.4759	+	1.57201i	−1.59384	+	0.0796016i
$391$	−2.25764	+	3.91035i	−0.114174	+	0.197755i
$392$	−0.0385645	+	0.0222652i	−0.00194780	+	0.00112456i
$393$			20.1746i			1.01767i
$394$	18.8484			0.949568
$395$	−0.496180	−	9.93489i	−0.0249655	−	0.499878i
$396$	−0.294416	−	0.509943i	−0.0147950	−	0.0256256i
$397$		−	4.41967i		−	0.221817i	−0.993831	−	0.110908i	$-0.964624\pi$
$397$		−	4.41967i		−	0.221817i	0.993831	−	0.110908i	$-0.0353760\pi$
$398$	13.6286	+	7.86850i	0.683142	+	0.394412i
$399$	−49.5820			−2.48220
$400$	−4.97512	+	0.498190i	−0.248756	+	0.0249095i
$401$	−23.1137			−1.15424			−0.577121	−	0.816658i	$-0.695824\pi$
$401$	−23.1137			−1.15424			−0.577121	+	0.816658i	$0.695824\pi$
$402$	21.4302	+	6.28464i	1.06884	+	0.313449i
$403$		−	5.12886i		−	0.255487i
$404$	−2.86752	−	4.96670i	−0.142665	−	0.247102i
$405$	4.85076	−	3.13319i	0.241036	−	0.155690i
$406$	5.78546	−	10.0207i	0.287128	−	0.497320i
$407$		−	1.17341i		−	0.0581636i
$408$	12.7127	−	7.33969i	0.629373	−	0.363369i
$409$	−9.09718	+	15.7568i	−0.449827	+	0.779123i	−0.998374	−	0.0569966i	$-0.981848\pi$
$409$	−9.09718	+	15.7568i	−0.449827	+	0.779123i	0.548548	+	0.836119i	$0.315181\pi$
$410$	−6.18533	−	9.57603i	−0.305472	−	0.472926i
$411$	30.3904			1.49905
$412$	2.79130	−	1.61156i	0.137518	−	0.0793958i
$413$	−14.2964	−	8.25406i	−0.703482	−	0.406156i
$414$	−1.86480	+	3.22993i	−0.0916499	+	0.158742i
$415$	−4.66888	+	9.10778i	−0.229186	+	0.447083i
$416$	5.16569			0.253269
$417$			41.3067i			2.02280i
$418$	−0.785661	+	0.453601i	−0.0384279	+	0.0221864i
$419$	−0.751300	−	1.30129i	−0.0367034	−	0.0635721i	0.847090	−	0.531449i	$-0.178352\pi$
$419$	−0.751300	−	1.30129i	−0.0367034	−	0.0635721i	−0.883794	+	0.467877i	$0.845019\pi$
$420$	14.4096	+	7.38672i	0.703115	+	0.360435i
$421$	−7.74439	−	13.4137i	−0.377439	−	0.653743i	0.613250	−	0.789889i	$-0.289862\pi$
$421$	−7.74439	−	13.4137i	−0.377439	−	0.653743i	−0.990689	+	0.136146i	$0.956528\pi$
$422$	5.04924	+	2.91518i	0.245793	+	0.141909i
$423$	5.44596	+	3.14423i	0.264792	+	0.152878i
$424$	−8.07078			−0.391952
$425$	−2.68038	−	26.7674i	−0.130018	−	1.29841i
$426$	3.12124			0.151225
$427$		−	3.60311i		−	0.174367i
$428$	−13.1839	−	7.61170i	−0.637266	−	0.367926i
$429$	1.86743			0.0901605
$430$	−20.5551	−	10.5370i	−0.991253	−	0.508141i
$431$	−10.5779	+	18.3215i	−0.509521	+	0.882517i	0.490418	+	0.871487i	$0.336844\pi$
$431$	−10.5779	+	18.3215i	−0.509521	+	0.882517i	−0.999939	+	0.0110295i	$0.996489\pi$
$432$	3.41209	−	1.96997i	0.164164	−	0.0947804i
$433$	−13.3976	−	7.73509i	−0.643846	−	0.371725i	0.142248	−	0.989831i	$-0.454567\pi$
$433$	−13.3976	−	7.73509i	−0.643846	−	0.371725i	−0.786095	+	0.618106i	$0.787900\pi$
$434$	−1.31761	+	2.28217i	−0.0632475	+	0.109548i
$435$	−26.5638	+	1.32668i	−1.27364	+	0.0636096i
$436$	3.92682	−	6.80146i	0.188061	−	0.325731i
$437$	4.97629	+	2.87306i	0.238048	+	0.137437i
$438$	25.9604	+	14.9882i	1.24044	+	0.716166i
$439$	−16.3569	−	28.3311i	−0.780674	−	1.35217i	−0.931549	−	0.363615i	$-0.881542\pi$
$439$	−16.3569	−	28.3311i	−0.780674	−	1.35217i	0.150875	−	0.988553i	$-0.451791\pi$
$440$	0.295907	−	0.0147786i	0.0141068	−	0.000704540i
$441$	−0.0989481	−	0.171383i	−0.00471181	−	0.00816110i
$442$			27.7927i			1.32197i
$443$	−31.1253	−	17.9702i	−1.47881	−	0.853791i	−0.479097	−	0.877762i	$-0.659036\pi$
$443$	−31.1253	−	17.9702i	−1.47881	−	0.853791i	−0.999713	+	0.0239713i	$0.992369\pi$
$444$	24.1625			1.14670
$445$	−32.0120	+	20.6771i	−1.51751	+	0.980189i
$446$	−12.1403	−	21.0276i	−0.574860	−	0.995687i
$447$			39.4780i			1.86725i
$448$	−2.29856	−	1.32708i	−0.108597	−	0.0626985i
$449$	16.7654	−	29.0386i	0.791209	−	1.37041i	−0.134010	−	0.990980i	$-0.542785\pi$
$449$	16.7654	−	29.0386i	0.791209	−	1.37041i	0.925219	−	0.379434i	$-0.123881\pi$
$450$	−2.21398	−	22.1097i	−0.104368	−	1.04226i
$451$	0.337753	+	0.585005i	0.0159042	+	0.0275468i
$452$	−13.3780	+	7.72377i	−0.629247	+	0.363296i
$453$	−20.0491	+	11.5754i	−0.941989	+	0.543858i
$454$	−15.5173			−0.728264
$455$	−25.7527	+	16.6341i	−1.20730	+	0.779820i
$456$	−9.34045	−	16.1781i	−0.437407	−	0.757611i
$457$	27.9757	+	16.1518i	1.30865	+	0.755547i	0.981870	−	0.189555i	$-0.0607045\pi$
$457$	27.9757	+	16.1518i	1.30865	+	0.755547i	0.326776	+	0.945102i	$0.394038\pi$
$458$	−15.8333	−	9.14135i	−0.739841	−	0.427147i
$459$	10.5990	+	18.3579i	0.494717	+	0.856874i
$460$	−1.01819	−	1.57634i	−0.0474732	−	0.0734972i
$461$	10.7247			0.499499			0.249750	−	0.968310i	$-0.419652\pi$
$461$	10.7247			0.499499			0.249750	+	0.968310i	$0.419652\pi$
$462$	−0.830946	−	0.479747i	−0.0386591	−	0.0223199i
$463$	−6.78332	+	3.91635i	−0.315248	+	0.182008i	−0.649272	−	0.760556i	$-0.724926\pi$
$463$	−6.78332	+	3.91635i	−0.315248	+	0.182008i	0.334025	+	0.942564i	$0.391593\pi$
$464$	4.35955			0.202387
$465$	6.04980	−	0.302147i	0.280553	−	0.0140117i
$466$	2.64846			0.122688
$467$	9.12562	−	5.26868i	0.422283	−	0.243805i	−0.273770	−	0.961795i	$-0.588271\pi$
$467$	9.12562	−	5.26868i	0.422283	−	0.243805i	0.696054	+	0.717990i	$0.254938\pi$
$468$			22.9567i			1.06117i
$469$	21.1111	−	5.12902i	0.974818	−	0.236836i
$470$	−2.65786	+	1.71676i	−0.122598	+	0.0791882i
$471$	−16.4312	−	28.4596i	−0.757109	−	1.31135i
$472$		−	6.21973i		−	0.286286i
$473$	1.18533	+	0.684352i	0.0545017	+	0.0314665i
$474$	−12.1373			−0.557487
$475$	−34.0641	+	3.41105i	−1.56297	+	0.156510i
$476$	7.14001	−	12.3669i	0.327262	−	0.566834i
$477$		−	35.8671i		−	1.64224i
$478$			22.8788i			1.04645i
$479$	2.10835	+	3.65178i	0.0963331	+	0.166854i	0.910164	−	0.414248i	$-0.135955\pi$
$479$	2.10835	+	3.65178i	0.0963331	+	0.166854i	−0.813831	+	0.581102i	$0.802622\pi$
$480$	0.304316	+	6.09325i	0.0138901	+	0.278118i
$481$	−22.8737	+	39.6184i	−1.04295	+	1.80644i
$482$	−4.14082	+	2.39070i	−0.188609	+	0.108894i
$483$			6.07733i			0.276528i
$484$	10.9824			0.499202
$485$	−7.53621	+	14.7012i	−0.342202	+	0.667547i
$486$	−9.43295	−	16.3384i	−0.427887	−	0.741123i
$487$	25.7970	−	14.8939i	1.16897	−	0.674907i	0.215536	−	0.976496i	$-0.430850\pi$
$487$	25.7970	−	14.8939i	1.16897	−	0.674907i	0.953438	+	0.301588i	$0.0975169\pi$
$488$	1.17566	−	0.678768i	0.0532197	−	0.0307264i
$489$	24.5324	−	42.4913i	1.10939	−	1.92152i
$490$	0.0994492	−	0.00496681i	0.00449266	−	0.000224378i
$491$	13.9494			0.629529			0.314764	−	0.949170i	$-0.398075\pi$
$491$	13.9494			0.629529			0.314764	+	0.949170i	$0.398075\pi$
$492$	−12.0463	+	6.95493i	−0.543088	+	0.313552i
$493$			23.4555i			1.05638i
$494$	35.3689			1.59132
$495$	0.0656768	+	1.31503i	0.00295195	+	0.0591062i
$496$	−0.992870			−0.0445812
$497$	2.62954	−	1.51816i	0.117951	−	0.0680989i
$498$	10.8150	+	6.24406i	0.484633	+	0.279803i
$499$	−11.4768	−	19.8785i	−0.513774	−	0.889883i	−0.999872	−	0.0159789i	$-0.994914\pi$
$499$	−11.4768	−	19.8785i	−0.513774	−	0.889883i	0.486098	−	0.873904i	$-0.338420\pi$
$500$	10.4079	+	4.08354i	0.465456	+	0.182621i
$501$	−3.17585	+	5.50073i	−0.141886	+	0.245754i
$502$	−6.02118	−	3.47633i	−0.268738	−	0.155156i
$503$	−14.7342	−	8.50677i	−0.656964	−	0.379298i	0.134155	−	0.990960i	$-0.457168\pi$
$503$	−14.7342	−	8.50677i	−0.656964	−	0.379298i	−0.791119	+	0.611662i	$0.790501\pi$
$504$	5.89761	−	10.2150i	0.262700	−	0.455010i
$505$	0.639672	+	12.8080i	0.0284650	+	0.569948i
$506$	0.0555985	+	0.0962995i	0.00247166	+	0.00428104i
$507$	−32.3341	−	18.6681i	−1.43601	−	0.829080i
$508$	14.8267	−	8.56019i	0.657827	−	0.379797i
$509$	−16.8240			−0.745710			−0.372855	−	0.927890i	$-0.621621\pi$
$509$	−16.8240			−0.745710			−0.372855	+	0.927890i	$0.621621\pi$
$510$	−32.7832	+	1.63730i	−1.45167	+	0.0725008i
$511$	29.1610			1.29000
$512$		−	1.00000i		−	0.0441942i
$513$	23.3622	−	13.4882i	1.03147	−	0.595517i
$514$	−17.2450			−0.760646
$515$	−7.19814	+	0.359498i	−0.317188	+	0.0158414i
$516$	−14.0920	+	24.4081i	−0.620367	+	1.07451i
$517$	0.162370	−	0.0937444i	0.00714103	−	0.00412287i
$518$	20.3561	−	11.7526i	0.894394	−	0.516379i
$519$	21.9828	+	38.0753i	0.964936	+	1.67132i
$520$	−10.2790	−	5.26926i	−0.450762	−	0.231072i
$521$	−19.1242			−0.837845			−0.418922	−	0.908022i	$-0.637592\pi$
$521$	−19.1242			−0.837845			−0.418922	+	0.908022i	$0.637592\pi$
$522$			19.3741i			0.847982i
$523$	−20.5972	+	11.8918i	−0.900651	+	0.519991i	−0.877411	−	0.479739i	$-0.840731\pi$
$523$	−20.5972	+	11.8918i	−0.900651	+	0.519991i	−0.0232393	+	0.999730i	$0.507398\pi$
$524$	−3.69718	+	6.40370i	−0.161512	+	0.279747i
$525$	−21.1381	−	29.3969i	−0.922542	−	1.28299i
$526$	−8.34124	−	14.4475i	−0.363695	−	0.629939i
$527$		−	5.34189i		−	0.232696i
$528$		−	0.361507i		−	0.0157326i
$529$	−11.1478	+	19.3086i	−0.484689	+	0.839506i
$530$	16.0596	+	8.23259i	0.697587	+	0.357601i
$531$	27.6409			1.19951
$532$	−15.7380	−	9.08634i	−0.682329	−	0.393943i
$533$		−	26.3358i		−	1.14073i
$534$	23.2498	+	40.2698i	1.00612	+	1.74265i
$535$	18.4696	+	28.5943i	0.798510	+	1.23624i
$536$	5.65054	+	5.92211i	0.244066	+	0.255796i
$537$		−	19.2842i		−	0.832177i
$538$	10.5992	−	6.11947i	0.456965	−	0.263829i
$539$	−0.00590023			−0.000254141
$540$	−8.79902	+	0.439451i	−0.378650	+	0.0189110i
$541$	−30.1142			−1.29471			−0.647354	−	0.762189i	$-0.724125\pi$
$541$	−30.1142			−1.29471			−0.647354	+	0.762189i	$0.724125\pi$
$542$	2.23636	−	1.29116i	0.0960599	−	0.0554602i
$543$	47.6124	+	27.4890i	2.04324	+	1.17967i
$544$	5.38025			0.230676
$545$	−14.7516	+	9.52833i	−0.631889	+	0.408149i
$546$	18.7038	+	32.3959i	0.800448	+	1.38642i
$547$	5.11859	+	2.95522i	0.218855	+	0.126356i	0.605420	−	0.795906i	$-0.293005\pi$
$547$	5.11859	+	2.95522i	0.218855	+	0.126356i	−0.386565	+	0.922262i	$0.626338\pi$
$548$	9.64632	+	5.56930i	0.412070	+	0.237909i
$549$	3.01649	+	5.22471i	0.128741	+	0.222985i
$550$	−0.603886	−	0.272432i	−0.0257498	−	0.0116166i
$551$	29.8494			1.27163
$552$	−1.98298	+	1.14487i	−0.0844011	+	0.0487290i
$553$	−10.2253	+	5.90357i	−0.434823	+	0.251045i
$554$	3.24334	+	5.61763i	0.137796	+	0.238670i
$555$	−48.0798	−	24.6469i	−2.04087	−	1.04620i
$556$	−7.56983	+	13.1113i	−0.321032	+	0.556044i
$557$	−29.5828	−	17.0796i	−1.25346	−	0.723687i	−0.281668	−	0.959512i	$-0.590888\pi$
$557$	−29.5828	−	17.0796i	−1.25346	−	0.723687i	−0.971796	+	0.235825i	$0.924221\pi$
$558$		−	4.41237i		−	0.186791i
$559$	−26.6807	−	46.2123i	−1.12847	−	1.95457i
$560$	3.22012	+	4.98533i	0.136075	+	0.210669i
$561$	1.94500			0.0821178
$562$	−11.9144	−	6.87879i	−0.502579	−	0.290164i
$563$		−	30.5540i		−	1.28770i	−0.765153	−	0.643848i	$-0.777337\pi$
$563$		−	30.5540i		−	1.28770i	0.765153	−	0.643848i	$-0.222663\pi$
$564$	1.93036	+	3.34349i	0.0812829	+	0.140786i
$565$	34.4988	−	1.72298i	1.45137	−	0.0724863i
$566$	−5.82106	−	10.0824i	−0.244677	−	0.423793i
$567$	−5.93606	−	3.42719i	−0.249291	−	0.143928i
$568$	0.990725	+	0.571995i	0.0415699	+	0.0240004i
$569$	−2.82647	+	4.89559i	−0.118492	+	0.205234i	−0.919170	−	0.393861i	$-0.871139\pi$
$569$	−2.82647	+	4.89559i	−0.118492	+	0.205234i	0.800678	+	0.599094i	$0.204473\pi$
$570$	2.08362	+	41.7198i	0.0872732	+	1.74745i
$571$	−3.68259	+	6.37844i	−0.154112	+	0.266929i	−0.932735	−	0.360562i	$-0.882585\pi$
$571$	−3.68259	+	6.37844i	−0.154112	+	0.266929i	0.778624	+	0.627491i	$0.215918\pi$
$572$	0.592749	+	0.342224i	0.0247841	+	0.0143091i
$573$	34.7811	−	20.0809i	1.45300	−	0.838890i
$574$	−6.76571	+	11.7186i	−0.282395	+	0.489123i
$575$	0.418097	+	4.17528i	0.0174358	+	0.174121i
$576$	4.44406			0.185169
$577$	−13.2113	−	7.62755i	−0.549993	−	0.317539i	0.199126	−	0.979974i	$-0.436190\pi$
$577$	−13.2113	−	7.62755i	−0.549993	−	0.317539i	−0.749119	+	0.662435i	$0.769523\pi$
$578$			11.9471i			0.496934i
$579$	65.8333			2.73594
$580$	−8.67486	−	4.44695i	−0.360204	−	0.184650i
$581$	12.1484			0.504000
$582$	17.4569	+	10.0788i	0.723614	+	0.417778i
$583$	−0.926100	−	0.534684i	−0.0383551	−	0.0221443i
$584$	5.49346	+	9.51495i	0.227321	+	0.393731i
$585$	23.4169	−	45.6803i	0.968169	−	1.88865i
$586$	0.0745263	+	0.129083i	0.00307865	+	0.00533238i
$587$	−12.5710	+	7.25785i	−0.518859	+	0.299564i	−0.736468	−	0.676473i	$-0.763508\pi$
$587$	−12.5710	+	7.25785i	−0.518859	+	0.299564i	0.217609	+	0.976036i	$0.430174\pi$
$588$		−	0.121496i		−	0.00501041i
$589$	−6.79806			−0.280109
$590$	−6.34442	+	12.3763i	−0.261196	+	0.509525i
$591$	−25.7128	+	44.5358i	−1.05768	+	1.83196i
$592$	7.66951	+	4.42800i	0.315215	+	0.181990i
$593$	19.6855	−	11.3654i	0.808385	−	0.466722i	−0.0380094	−	0.999277i	$-0.512102\pi$
$593$	19.6855	−	11.3654i	0.808385	−	0.466722i	0.846395	+	0.532556i	$0.178768\pi$
$594$	0.522037			0.0214195
$595$	−26.8223	+	17.3250i	−1.09961	+	0.710257i
$596$	−7.23470	+	12.5309i	−0.296345	+	0.513284i
$597$	−37.1841	+	21.4683i	−1.52184	+	0.878637i
$598$		−	4.33522i		−	0.177280i
$599$	−0.598535	+	1.03669i	−0.0244555	+	0.0423581i	−0.877994	−	0.478671i	$-0.841119\pi$
$599$	−0.598535	+	1.03669i	−0.0244555	+	0.0423581i	0.853539	+	0.521030i	$0.174452\pi$
$600$	5.60986	−	12.4351i	0.229022	−	0.507660i
$601$	16.7674	+	29.0420i	0.683956	+	1.18465i	0.973764	+	0.227562i	$0.0730755\pi$
$601$	16.7674	+	29.0420i	0.683956	+	1.18465i	−0.289807	+	0.957085i	$0.593591\pi$
$602$			27.4173i			1.11744i
$603$	−26.3182	+	25.1113i	−1.07176	+	1.02261i
$604$	−8.48515			−0.345256
$605$	−21.8534	−	11.2026i	−0.888468	−	0.455451i
$606$	15.6474			0.635632
$607$	3.48090	+	2.00970i	0.141285	+	0.0815712i	0.568977	−	0.822354i	$-0.307340\pi$
$607$	3.48090	+	2.00970i	0.141285	+	0.0815712i	−0.427691	+	0.903925i	$0.640673\pi$
$608$		−	6.84688i		−	0.277678i
$609$	15.7849	+	27.3403i	0.639638	+	1.10789i
$610$	−3.03177	+	0.151416i	−0.122753	+	0.00613066i
$611$	−7.30958			−0.295714
$612$			23.9102i			0.966511i
$613$	10.4455	−	6.03068i	0.421888	−	0.243577i	−0.273997	−	0.961731i	$-0.588346\pi$
$613$	10.4455	−	6.03068i	0.421888	−	0.243577i	0.695885	+	0.718154i	$0.255012\pi$
$614$	−15.8029	+	27.3714i	−0.637753	+	1.10462i
$615$	31.0647	−	1.55147i	1.25265	−	0.0625613i
$616$	−0.175836	−	0.304557i	−0.00708463	−	0.0122709i
$617$			39.2468i			1.58002i	0.613096	+	0.790009i	$0.289924\pi$
$617$			39.2468i			1.58002i	−0.613096	+	0.790009i	$0.710076\pi$
$618$			8.79389i			0.353742i
$619$	12.7356	+	22.0587i	0.511887	+	0.886615i	0.999905	+	0.0137812i	$0.00438682\pi$
$619$	12.7356	+	22.0587i	0.511887	+	0.886615i	−0.488018	+	0.872834i	$0.662280\pi$
$620$	1.97566	+	1.01277i	0.0793445	+	0.0406740i
$621$	−1.65326	−	2.86354i	−0.0663432	−	0.114910i
$622$	9.42569	−	5.44192i	0.377936	−	0.218201i
$623$	39.1743	+	22.6173i	1.56948	+	0.906142i
$624$	−7.04699	+	12.2057i	−0.282105	+	0.488621i
$625$	−16.5448	−	18.7422i	−0.661791	−	0.749688i
$626$	−8.86045	−	15.3468i	−0.354135	−	0.613380i
$627$		−	2.47519i		−	0.0988497i
$628$		−	12.0446i		−	0.480633i
$629$	−23.8237	+	41.2639i	−0.949914	+	1.64530i
$630$	−22.1551	+	14.3104i	−0.882680	+	0.570140i
$631$	−10.8615	−	18.8127i	−0.432391	−	0.748923i	0.564688	−	0.825305i	$-0.308997\pi$
$631$	−10.8615	−	18.8127i	−0.432391	−	0.748923i	−0.997079	+	0.0763814i	$0.975663\pi$
$632$	−3.85256	−	2.22428i	−0.153247	−	0.0884770i
$633$	−13.7762	+	7.95372i	−0.547557	+	0.316132i
$634$	−3.26582	+	5.65656i	−0.129702	+	0.224651i
$635$	−38.2347	+	1.90956i	−1.51730	+	0.0757787i
$636$	11.0101	−	19.0700i	0.436578	−	0.756176i
$637$	0.199213	+	0.115015i	0.00789309	+	0.00455708i
$638$	0.500246	+	0.288817i	0.0198049	+	0.0114344i
$639$	−2.54198	+	4.40284i	−0.100559	+	0.174174i
$640$	−1.02005	+	1.98985i	−0.0403209	+	0.0786557i
$641$	12.5073	−	21.6633i	0.494008	−	0.855648i	−0.505968	−	0.862552i	$-0.668865\pi$
$641$	12.5073	−	21.6633i	0.494008	−	0.855648i	0.999976	+	0.00690476i	$0.00219787\pi$
$642$	35.9706	−	20.7676i	1.41965	−	0.819633i
$643$		−	26.7577i		−	1.05522i	−0.849487	−	0.527610i	$-0.823088\pi$
$643$		−	26.7577i		−	1.05522i	0.849487	−	0.527610i	$-0.176912\pi$
$644$	−1.11373	+	1.92903i	−0.0438869	+	0.0760144i
$645$	52.9384	−	34.1939i	2.08445	−	1.34638i
$646$	36.8380			1.44937
$647$	−34.9453	+	20.1757i	−1.37384	+	0.793188i	−0.991409	−	0.130795i	$-0.958247\pi$
$647$	−34.9453	+	20.1757i	−1.37384	+	0.793188i	−0.382433	+	0.923983i	$0.624914\pi$
$648$		−	2.58251i		−	0.101451i
$649$	0.412053	−	0.713696i	0.0161745	−	0.0280150i
$650$	15.0787	+	20.9701i	0.591435	+	0.822513i
$651$	−3.59495	−	6.22664i	−0.140897	−	0.244041i
$652$	15.5738	−	8.99155i	0.609918	−	0.352136i
$653$	−30.4290	+	17.5682i	−1.19078	+	0.687497i	−0.958484	−	0.285148i	$-0.907957\pi$
$653$	−30.4290	+	17.5682i	−1.19078	+	0.687497i	−0.232297	+	0.972645i	$0.574624\pi$
$654$	10.7139	+	18.5570i	0.418946	+	0.725635i
$655$	13.8889	−	8.97110i	0.542684	−	0.350530i
$656$	−5.09821			−0.199052
$657$	−42.2850	+	24.4133i	−1.64969	+	0.952452i
$658$	3.25253	+	1.87785i	0.126797	+	0.0732061i
$659$	12.4780	−	21.6126i	0.486075	−	0.841907i	−0.513796	−	0.857912i	$-0.671761\pi$
$659$	12.4780	−	21.6126i	0.486075	−	0.841907i	0.999872	+	0.0160047i	$0.00509468\pi$
$660$	−0.368754	+	0.719344i	−0.0143537	+	0.0280004i
$661$	36.3549			1.41404			0.707021	−	0.707193i	$-0.250039\pi$
$661$	36.3549			1.41404			0.707021	+	0.707193i	$0.250039\pi$
$662$		−	28.8273i		−	1.12040i
$663$	−65.6700	−	37.9146i	−2.55041	−	1.47248i
$664$	2.28856	+	3.96390i	0.0888133	+	0.153829i
$665$	22.0478	+	34.1340i	0.854975	+	1.32366i
$666$	−19.6783	+	34.0838i	−0.762518	+	1.32072i
$667$		−	3.65868i		−	0.141665i
$668$	−2.01612	+	1.16400i	−0.0780058	+	0.0450367i
$669$	66.2467			2.56125
$670$	−5.20288	−	17.5479i	−0.201005	−	0.677936i
$671$	0.179872			0.00694387
$672$	6.27136	−	3.62077i	0.241923	−	0.139674i
$673$			1.66920i			0.0643430i	0.999482	+	0.0321715i	$0.0102423\pi$
$673$			1.66920i			0.0643430i	−0.999482	+	0.0321715i	$0.989758\pi$
$674$	6.59265	−	11.4188i	0.253939	−	0.439836i
$675$	17.9570	+	8.10098i	0.691165	+	0.311807i
$676$	−6.84220	−	11.8510i	−0.263161	−	0.455809i
$677$	−17.7915	−	10.2719i	−0.683781	−	0.394781i	0.117497	−	0.993073i	$-0.462513\pi$
$677$	−17.7915	−	10.2719i	−0.683781	−	0.394781i	−0.801278	+	0.598292i	$0.795846\pi$
$678$		−	42.1468i		−	1.61864i
$679$	19.6091			0.752530
$680$	−10.7059	−	5.48811i	−0.410552	−	0.210460i
$681$	21.1686	−	36.6650i	0.811181	−	1.40501i
$682$	−0.113929	−	0.0657769i	−0.00436257	−	0.00251873i
$683$	29.1705	−	16.8416i	1.11618	−	0.644425i	0.175754	−	0.984434i	$-0.443764\pi$
$683$	29.1705	−	16.8416i	1.11618	−	0.644425i	0.940422	+	0.340009i	$0.110430\pi$
$684$	30.4280			1.16344
$685$	−13.5138	−	20.9218i	−0.516334	−	0.799380i
$686$	9.23044	+	15.9876i	0.352420	+	0.610409i
$687$	43.1992	−	24.9411i	1.64815	−	0.951562i
$688$	−8.94600	+	5.16498i	−0.341063	+	0.196913i
$689$	20.8456	+	36.1056i	0.794154	+	1.37552i
$690$	5.11365	−	0.255392i	0.194673	−	0.00972261i
$691$	−10.2405	+	17.7371i	−0.389569	+	0.674753i	−0.992392	−	0.123122i	$-0.960709\pi$
$691$	−10.2405	+	17.7371i	−0.389569	+	0.674753i	0.602823	+	0.797875i	$0.294043\pi$
$692$			16.1141i			0.612568i
$693$	1.35347	−	0.781425i	0.0514140	−	0.0296839i
$694$	−34.0152			−1.29120
$695$	28.4370	−	18.3680i	1.07868	−	0.696737i
$696$	−5.94726	+	10.3010i	−0.225430	+	0.390457i
$697$		−	27.4296i		−	1.03897i
$698$	−20.5614	+	11.8711i	−0.778261	+	0.449329i
$699$	−3.61301	+	6.25791i	−0.136656	+	0.236696i
$700$	−1.32227	−	13.2047i	−0.0499772	−	0.499092i
$701$	−12.7457	+	22.0763i	−0.481400	+	0.833809i	−0.999772	−	0.0213458i	$-0.993205\pi$
$701$	−12.7457	+	22.0763i	−0.481400	+	0.833809i	0.518372	+	0.855155i	$0.326538\pi$
$702$	−17.6258	−	10.1763i	−0.665244	−	0.384079i
$703$	52.5123	+	30.3180i	1.98054	+	1.14346i
$704$	0.0662493	−	0.114747i	0.00249687	−	0.00432470i
$705$	−0.430615	−	8.62210i	−0.0162179	−	0.324727i
$706$	6.03636	−	10.4553i	0.227181	−	0.393490i
$707$	13.1824	−	7.61085i	0.495774	−	0.286235i
$708$	14.6963	+	8.48489i	0.552320	+	0.318882i
$709$	−5.35140	−	9.26889i	−0.200976	−	0.348101i	0.747867	−	0.663848i	$-0.231078\pi$
$709$	−5.35140	−	9.26889i	−0.200976	−	0.348101i	−0.948843	+	0.315748i	$0.897745\pi$
$710$	−1.38793	−	2.14877i	−0.0520881	−	0.0806419i
$711$	9.88482	−	17.1210i	0.370710	−	0.642088i
$712$			17.0429i			0.638711i
$713$			0.833248i			0.0312054i
$714$	19.4807	+	33.7415i	0.729045	+	1.26274i
$715$	−0.830397	−	1.28561i	−0.0310551	−	0.0480789i
$716$	3.53401	−	6.12108i	0.132072	−	0.228756i
$717$	−54.0590	−	31.2110i	−2.01887	−	1.16560i
$718$	−21.8267	+	12.6017i	−0.814567	+	0.470290i
$719$	−3.57700	−	6.19555i	−0.133400	−	0.231055i	0.791585	−	0.611059i	$-0.209256\pi$
$719$	−3.57700	−	6.19555i	−0.133400	−	0.231055i	−0.924985	+	0.380004i	$0.875923\pi$
$720$	−8.84301	−	4.53315i	−0.329560	−	0.168941i
$721$	4.27732	+	7.40854i	0.159296	+	0.275908i
$722$		−	27.8798i		−	1.03758i
$723$		−	13.0455i		−	0.485167i
$724$	10.0752	+	17.4508i	0.374442	+	0.648553i
$725$	12.7256	+	17.6975i	0.472615	+	0.657270i
$726$	−14.9821	+	25.9498i	−0.556039	+	0.963089i
$727$	6.17499	−	3.56513i	0.229018	−	0.132224i	−0.381101	−	0.924533i	$-0.624455\pi$
$727$	6.17499	−	3.56513i	0.229018	−	0.132224i	0.610119	+	0.792310i	$0.291122\pi$
$728$			13.7105i			0.508147i
$729$	43.7258			1.61948
$730$	−1.22545	−	24.5369i	−0.0453560	−	0.908152i
$731$	−27.7889	−	48.1317i	−1.02781	−	1.78022i
$732$			3.70388i			0.136899i
$733$	8.78499	+	5.07201i	0.324481	+	0.187339i	0.653388	−	0.757023i	$-0.273347\pi$
$733$	8.78499	+	5.07201i	0.324481	+	0.187339i	−0.328907	+	0.944362i	$0.606680\pi$
$734$	14.6691			0.541446
$735$	−0.123932	+	0.241759i	−0.00457129	+	0.00891741i
$736$	−0.839232			−0.0309345
$737$	0.256047	+	1.05389i	0.00943162	+	0.0388205i
$738$		−	22.6567i		−	0.834006i
$739$	−0.0229563	−	0.0397615i	−0.000844461	−	0.00146265i	0.865603	−	0.500731i	$-0.166935\pi$
$739$	−0.0229563	−	0.0397615i	−0.000844461	−	0.00146265i	−0.866447	+	0.499268i	$0.833602\pi$
$740$	−10.7444	−	16.6343i	−0.394972	−	0.611490i
$741$	−48.2499	+	83.5713i	−1.77251	+	3.07007i
$742$		−	21.4211i		−	0.786393i
$743$	21.8841	−	12.6348i	0.802850	−	0.463526i	−0.0416167	−	0.999134i	$-0.513251\pi$
$743$	21.8841	−	12.6348i	0.802850	−	0.463526i	0.844467	+	0.535608i	$0.179918\pi$
$744$	1.35446	−	2.34600i	0.0496570	−	0.0860085i
$745$	27.1781	−	17.5548i	0.995727	−	0.643158i
$746$	−4.86368			−0.178072
$747$	−17.6158	+	10.1705i	−0.644529	+	0.372119i
$748$	0.617369	+	0.356438i	0.0225732	+	0.0130327i
$749$	20.2026	−	34.9920i	0.738188	−	1.27858i
$750$	−23.8472	+	19.0216i	−0.870775	+	0.694570i
$751$	13.4889			0.492215			0.246108	−	0.969243i	$-0.420848\pi$
$751$	13.4889			0.492215			0.246108	+	0.969243i	$0.420848\pi$
$752$			1.41502i			0.0516006i
$753$	16.4281	−	9.48475i	0.598672	−	0.345644i
$754$	−11.2601	−	19.5030i	−0.410067	−	0.710257i
$755$	16.8842	+	8.65526i	0.614478	+	0.314997i
$756$	5.22861	+	9.05622i	0.190163	+	0.329371i
$757$	33.2858	+	19.2176i	1.20979	+	0.698474i	0.962714	−	0.270521i	$-0.0871959\pi$
$757$	33.2858	+	19.2176i	1.20979	+	0.698474i	0.247079	+	0.968995i	$0.420529\pi$
$758$	−9.67711	−	5.58708i	−0.351488	−	0.202932i
$759$	−0.303388			−0.0110123
$760$	−6.98415	+	13.6243i	−0.253342	+	0.494204i
$761$	42.5057			1.54083			0.770415	−	0.637542i	$-0.220049\pi$
$761$	42.5057			1.54083			0.770415	+	0.637542i	$0.220049\pi$
$762$			46.7109i			1.69216i
$763$	18.0521	+	10.4224i	0.653531	+	0.377316i
$764$	14.7200			0.532550
$765$	24.3895	−	47.5776i	0.881805	−	1.72017i
$766$	−12.6954	+	21.9890i	−0.458702	+	0.794495i
$767$	−27.8247	+	16.0646i	−1.00469	+	0.580059i
$768$	2.36285	+	1.36419i	0.0852619	+	0.0492260i
$769$	−26.5858	+	46.0480i	−0.958709	+	1.66053i	−0.233065	+	0.972461i	$0.574875\pi$
$769$	−26.5858	+	46.0480i	−0.958709	+	1.66053i	−0.725644	+	0.688071i	$0.758458\pi$
$770$	0.0392245	+	0.785383i	0.00141355	+	0.0283032i
$771$	23.5255	−	40.7474i	0.847250	−	1.46748i
$772$	20.8964	+	12.0645i	0.752077	+	0.434212i
$773$	−20.2240	−	11.6763i	−0.727407	−	0.419969i	0.0900659	−	0.995936i	$-0.471292\pi$
$773$	−20.2240	−	11.6763i	−0.727407	−	0.419969i	−0.817473	+	0.575967i	$0.804626\pi$
$774$	−22.9535	−	39.7566i	−0.825045	−	1.42902i
$775$	−2.89819	−	4.03054i	−0.104106	−	0.144781i
$776$	3.69405	+	6.39828i	0.132609	+	0.229685i
$777$			64.1310i			2.30069i
$778$	−28.6756	−	16.5559i	−1.02807	−	0.593557i
$779$	−34.9068			−1.25067
$780$	26.4729	−	17.0993i	0.947882	−	0.612254i
$781$	0.0757886	+	0.131270i	0.00271193	+	0.00469720i
$782$		−	4.51528i		−	0.161466i
$783$	−14.8752	−	8.58820i	−0.531596	−	0.306917i
$784$	0.0222652	−	0.0385645i	0.000795187	−	0.00137730i
$785$	−12.2861	+	23.9670i	−0.438510	+	0.855420i
$786$	−10.0873	−	17.4717i	−0.359802	−	0.623196i
$787$	28.4906	−	16.4491i	1.01558	−	0.586346i	0.102761	−	0.994706i	$-0.467232\pi$
$787$	28.4906	−	16.4491i	1.01558	−	0.586346i	0.912821	+	0.408360i	$0.133899\pi$
$788$	−16.3232	+	9.42419i	−0.581489	+	0.335723i
$789$	45.5162			1.62042
$790$	5.39715	+	8.35577i	0.192022	+	0.297285i
$791$	−20.5001	−	35.5072i	−0.728899	−	1.26249i
$792$	0.509943	+	0.294416i	0.0181200	+	0.0104616i
$793$	−6.07311	−	3.50631i	−0.215662	−	0.124513i
$794$	2.20984	+	3.82755i	0.0784241	+	0.135835i
$795$	−41.3608	+	26.7157i	−1.46692	+	0.947507i
$796$	−15.7370			−0.557783
$797$	22.8009	+	13.1641i	0.807651	+	0.466297i	0.846139	−	0.532962i	$-0.178921\pi$
$797$	22.8009	+	13.1641i	0.807651	+	0.466297i	−0.0384885	+	0.999259i	$0.512254\pi$
$798$	42.9393	−	24.7910i	1.52003	−	0.877592i
$799$	−7.61319			−0.269335
$800$	4.05948	−	2.91900i	0.143524	−	0.103202i
$801$	−75.7398			−2.67614
$802$	20.0170	−	11.5568i	0.706826	−	0.408086i
$803$			1.45575i			0.0513723i
$804$	−21.7015	+	5.27246i	−0.765351	+	0.185946i
$805$	4.18385	−	2.70242i	0.147461	−	0.0952479i
$806$	2.56443	+	4.44172i	0.0903282	+	0.156453i
$807$			33.3925i			1.17547i
$808$	4.96670	+	2.86752i	0.174728	+	0.100879i
$809$	−26.7450			−0.940303			−0.470152	−	0.882586i	$-0.655801\pi$
$809$	−26.7450			−0.940303			−0.470152	+	0.882586i	$0.655801\pi$
$810$	−2.63428	+	5.13881i	−0.0925593	+	0.180559i
$811$	15.2967	−	26.4946i	0.537138	−	0.930351i	−0.461918	−	0.886923i	$-0.652839\pi$
$811$	15.2967	−	26.4946i	0.537138	−	0.930351i	0.999057	−	0.0434284i	$-0.0138281\pi$
$812$			11.5709i			0.406060i
$813$			7.04557i			0.247099i
$814$	0.586703	+	1.01620i	0.0205639	+	0.0356178i
$815$	−40.1614	+	2.00579i	−1.40679	+	0.0702597i
$816$	−7.33969	+	12.7127i	−0.256940	+	0.445034i
$817$	−61.2522	+	35.3640i	−2.14294	+	1.23723i
$818$		−	18.1944i		−	0.636151i
$819$	−60.9305			−2.12908
$820$	10.1447	+	5.20042i	0.354267	+	0.181606i
$821$	−12.6173	−	21.8538i	−0.440348	−	0.762704i	0.557368	−	0.830266i	$-0.311811\pi$
$821$	−12.6173	−	21.8538i	−0.440348	−	0.762704i	−0.997715	+	0.0675615i	$0.978478\pi$
$822$	−26.3188	+	15.1952i	−0.917974	+	0.529993i
$823$	−16.2051	+	9.35604i	−0.564875	+	0.326131i	−0.755100	−	0.655610i	$-0.772412\pi$
$823$	−16.2051	+	9.35604i	−0.564875	+	0.326131i	0.190225	+	0.981741i	$0.439078\pi$
$824$	−1.61156	+	2.79130i	−0.0561413	+	0.0972396i
$825$	1.46753	−	1.05524i	0.0510929	−	0.0367387i
$826$	16.5081			0.574391
$827$	35.8050	−	20.6720i	1.24506	−	0.718837i	0.274941	−	0.961461i	$-0.411342\pi$
$827$	35.8050	−	20.6720i	1.24506	−	0.718837i	0.970120	+	0.242625i	$0.0780083\pi$
$828$		−	3.72960i		−	0.129612i
$829$	−5.47644			−0.190205			−0.0951023	−	0.995467i	$-0.530318\pi$
$829$	−5.47644			−0.190205			−0.0951023	+	0.995467i	$0.530318\pi$
$830$	−0.510520	−	10.2220i	−0.0177204	−	0.354811i
$831$	−17.6981			−0.613941
$832$	−4.47362	+	2.58285i	−0.155095	+	0.0895441i
$833$	0.207487	+	0.119793i	0.00718899	+	0.00415057i
$834$	−20.6534	−	35.7727i	−0.715168	−	1.23871i
$835$	5.19911	−	0.259660i	0.179923	−	0.00898591i
$836$	0.453601	−	0.785661i	0.0156881	−	0.0271726i
$837$	3.38776	+	1.95593i	0.117098	+	0.0676067i
$838$	1.30129	+	0.751300i	0.0449523	+	0.0259532i
$839$	18.4302	−	31.9221i	0.636282	−	1.10207i	−0.349960	−	0.936765i	$-0.613805\pi$
$839$	18.4302	−	31.9221i	0.636282	−	1.10207i	0.986242	−	0.165309i	$-0.0528620\pi$
$840$	−16.1724	+	0.807703i	−0.558001	+	0.0278684i
$841$	4.99715	+	8.65531i	0.172315	+	0.298459i
$842$	13.4137	+	7.74439i	0.462266	+	0.266889i
$843$	32.5071	−	18.7680i	1.11960	−	0.646403i
$844$	−5.83036			−0.200689
$845$	1.52632	+	30.5611i	0.0525071	+	1.05134i
$846$	−6.28845			−0.216202
$847$			29.1491i			1.00157i
$848$	6.98950	−	4.03539i	0.240021	−	0.138576i
$849$	31.7641			1.09014
$850$	15.7050	+	21.8410i	0.538676	+	0.749142i
$851$	3.71612	−	6.43650i	0.127387	−	0.220640i
$852$	−2.70307	+	1.56062i	−0.0926058	+	0.0534660i
$853$	−10.1295	+	5.84827i	−0.346827	+	0.200241i	−0.663287	−	0.748365i	$-0.730839\pi$
$853$	−10.1295	+	5.84827i	−0.346827	+	0.200241i	0.316460	+	0.948606i	$0.397506\pi$
$854$	1.80156	+	3.12038i	0.0616479	+	0.106777i
$855$	−60.5471	−	31.0380i	−2.07067	−	1.06148i
$856$	15.2234			0.520325
$857$		−	51.4948i		−	1.75903i	−0.475871	−	0.879515i	$-0.657867\pi$
$857$		−	51.4948i		−	1.75903i	0.475871	−	0.879515i	$-0.342133\pi$
$858$	−1.61724	+	0.933716i	−0.0552118	+	0.0318766i
$859$	−19.9237	+	34.5088i	−0.679786	+	1.17742i	0.295259	+	0.955417i	$0.404594\pi$
$859$	−19.9237	+	34.5088i	−0.679786	+	1.17742i	−0.975045	+	0.222007i	$0.928739\pi$
$860$	23.0697	−	1.15218i	0.786671	−	0.0392889i
$861$	−18.4594	−	31.9727i	−0.629096	−	1.08963i
$862$		−	21.1559i		−	0.720572i
$863$		−	9.84653i		−	0.335180i	−0.985857	−	0.167590i	$-0.946402\pi$
$863$		−	9.84653i		−	0.335180i	0.985857	−	0.167590i	$-0.0535984\pi$
$864$	−1.96997	+	3.41209i	−0.0670198	+	0.116082i
$865$	16.4372	−	32.0647i	0.558882	−	1.09023i
$866$	15.4702			0.525698
$867$	−28.2292	−	16.2981i	−0.958713	−	0.553513i
$868$		−	2.63523i		−	0.0894455i
$869$	−0.294714	−	0.510459i	−0.00999748	−	0.0173161i
$870$	22.3416	−	14.4309i	0.757452	−	0.489252i
$871$	11.8988	−	40.5743i	0.403176	−	1.37481i
$872$			7.85365i			0.265958i
$873$	−28.4343	+	16.4166i	−0.962357	+	0.555617i
$874$	−5.74612			−0.194366
$875$	−10.8383	+	27.6242i	−0.366403	+	0.933869i
$876$	−29.9765			−1.01281
$877$	45.3744	−	26.1969i	1.53218	−	0.884607i	0.532924	−	0.846163i	$-0.321093\pi$
$877$	45.3744	−	26.1969i	1.53218	−	0.884607i	0.999261	−	0.0384444i	$-0.0122402\pi$
$878$	28.3311	+	16.3569i	0.956127	+	0.552020i
$879$	−0.406672			−0.0137167
$880$	−0.248874	+	0.160752i	−0.00838953	+	0.00541895i
$881$	13.7570	+	23.8278i	0.463485	+	0.802779i	0.999132	−	0.0416627i	$-0.0132655\pi$
$881$	13.7570	+	23.8278i	0.463485	+	0.802779i	−0.535647	+	0.844442i	$0.679932\pi$
$882$	0.171383	+	0.0989481i	0.00577077	+	0.00333175i
$883$	−28.9367	−	16.7066i	−0.973796	−	0.562222i	−0.0734048	−	0.997302i	$-0.523387\pi$
$883$	−28.9367	−	16.7066i	−0.973796	−	0.562222i	−0.900391	+	0.435081i	$0.856720\pi$
$884$	−13.8964	−	24.0692i	−0.467385	−	0.809535i
$885$	−20.5884	−	31.8746i	−0.692070	−	1.07145i
$886$	35.9404			1.20744
$887$	26.8165	−	15.4825i	0.900411	−	0.519852i	0.0230772	−	0.999734i	$-0.492654\pi$
$887$	26.8165	−	15.4825i	0.900411	−	0.519852i	0.877333	+	0.479881i	$0.159320\pi$
$888$	−20.9254	+	12.0813i	−0.702209	+	0.405420i
$889$	22.7200	+	39.3523i	0.762006	+	1.31983i
$890$	17.3846	−	33.9129i	0.582733	−	1.13676i
$891$	0.171089	−	0.296336i	0.00573171	−	0.00992762i
$892$	21.0276	+	12.1403i	0.704057	+	0.406488i
$893$			9.68851i			0.324214i
$894$	−19.7390	−	34.1890i	−0.660171	−	1.14345i
$895$	−13.2759	+	8.57518i	−0.443766	+	0.286637i
$896$	2.65415			0.0886690
$897$	10.2435	+	5.91406i	0.342019	+	0.197465i
$898$			33.5308i			1.11894i
$899$	2.16423	+	3.74856i	0.0721812	+	0.125022i
$900$	12.9722	+	18.0406i	0.432408	+	0.601353i
$901$	21.7114	+	37.6053i	0.723313	+	1.25281i
$902$	−0.585005	−	0.337753i	−0.0194785	−	0.0112459i
$903$	−64.7828	−	37.4024i	−2.15584	−	1.24467i
$904$	7.72377	−	13.3780i	0.256889	−	0.444945i
$905$	−2.24753	−	45.0017i	−0.0747103	−	1.49591i
$906$	11.5754	−	20.0491i	0.384565	−	0.666087i
$907$	−1.32218	−	0.763360i	−0.0439022	−	0.0253470i	0.477888	−	0.878421i	$-0.341402\pi$
$907$	−1.32218	−	0.763360i	−0.0439022	−	0.0253470i	−0.521790	+	0.853074i	$0.674736\pi$
$908$	13.4384	−	7.75866i	0.445969	−	0.257480i
$909$	−12.7434	+	22.0723i	−0.422673	+	0.732092i
$910$	13.9854	−	27.2819i	0.463612	−	0.904387i
$911$	−22.7769			−0.754632			−0.377316	−	0.926085i	$-0.623153\pi$
$911$	−22.7769			−0.754632			−0.377316	+	0.926085i	$0.623153\pi$
$912$	16.1781	+	9.34045i	0.535712	+	0.309293i
$913$			0.606462i			0.0200710i
$914$	−32.3035			−1.06850
$915$	3.77813	−	7.37016i	0.124901	−	0.243650i
$916$	18.2827			0.604078
$917$	−16.9964	−	9.81287i	−0.561270	−	0.324050i
$918$	−18.3579	−	10.5990i	−0.605902	−	0.349817i
$919$	−3.91138	−	6.77472i	−0.129025	−	0.223477i	0.794274	−	0.607559i	$-0.207851\pi$
$919$	−3.91138	−	6.77472i	−0.129025	−	0.223477i	−0.923299	+	0.384082i	$0.874518\pi$
$920$	1.66995	+	0.856057i	0.0550565	+	0.0282234i
$921$	−43.1163	−	74.6797i	−1.42073	−	2.46078i
$922$	−9.28786	+	5.36235i	−0.305879	+	0.176600i
$923$		−	5.90950i		−	0.194514i
$924$	0.959494			0.0315650
$925$	4.41196	+	44.0596i	0.145064	+	1.44867i
$926$	3.91635	−	6.78332i	0.128699	−	0.222914i
$927$	−12.4047	−	7.16186i	−0.407424	−	0.235226i
$928$	−3.77548	+	2.17978i	−0.123936	+	0.0715547i
$929$	−3.81192			−0.125065			−0.0625325	−	0.998043i	$-0.519918\pi$
$929$	−3.81192			−0.125065			−0.0625325	+	0.998043i	$0.519918\pi$
$930$	−5.08821	+	3.28657i	−0.166849	+	0.107771i
$931$	0.152447	−	0.264047i	0.00499626	−	0.00865378i
$932$	−2.29363	+	1.32423i	−0.0751305	+	0.0433766i
$933$			29.6953i			0.972180i
$934$	−5.26868	+	9.12562i	−0.172396	+	0.298599i
$935$	−0.864887	−	1.33900i	−0.0282848	−	0.0437901i
$936$	−11.4783	−	19.8810i	−0.375181	−	0.649832i
$937$			33.3383i			1.08911i	0.838724	+	0.544557i	$0.183302\pi$
$937$			33.3383i			1.08911i	−0.838724	+	0.544557i	$0.816698\pi$
$938$	−15.7182	+	14.9974i	−0.513217	+	0.489682i
$939$	48.3494			1.57782
$940$	1.44339	−	2.81569i	0.0470783	−	0.0918376i
$941$	2.16839			0.0706874			0.0353437	−	0.999375i	$-0.488747\pi$
$941$	2.16839			0.0706874			0.0353437	+	0.999375i	$0.488747\pi$
$942$	28.4596	+	16.4312i	0.927265	+	0.535357i
$943$			4.27858i			0.139330i
$944$	3.10986	+	5.38644i	0.101217	+	0.175314i
$945$	−1.16637	−	23.3539i	−0.0379421	−	0.759704i
$946$	−1.36870			−0.0445004
$947$			16.7010i			0.542711i	0.962479	+	0.271356i	$0.0874719\pi$
$947$			16.7010i			0.542711i	−0.962479	+	0.271356i	$0.912528\pi$
$948$	10.5113	−	6.06867i	0.341390	−	0.197101i
$949$	28.3775	−	49.1513i	0.921173	−	1.59552i
$950$	27.7948	−	19.9861i	0.901783	−	0.648434i
$951$	−8.91039	−	15.4332i	−0.288939	−	0.500457i
$952$			14.2800i			0.462818i
$953$		−	40.3854i		−	1.30821i	−0.756403	−	0.654106i	$-0.773045\pi$
$953$		−	40.3854i		−	1.30821i	0.756403	−	0.654106i	$-0.226955\pi$
$954$	17.9335	+	31.0618i	0.580619	+	1.00566i
$955$	−29.2906	−	15.0151i	−0.947820	−	0.485877i
$956$	−11.4394	−	19.8136i	−0.369976	−	0.640817i
$957$	−1.36486	+	0.788004i	−0.0441197	+	0.0254725i
$958$	−3.65178	−	2.10835i	−0.117983	−	0.0681178i
$959$	−14.7818	+	25.6028i	−0.477329	+	0.826758i
$960$	−3.31017	−	5.12475i	−0.106835	−	0.165401i
$961$	15.0071	+	25.9931i	0.484100	+	0.838486i
$962$		−	45.7473i		−	1.47495i
$963$			67.6537i			2.18011i
$964$	2.39070	−	4.14082i	0.0769994	−	0.133367i
$965$	−29.2743	−	45.3219i	−0.942372	−	1.45896i
$966$	−3.03867	−	5.26312i	−0.0977675	−	0.169338i
$967$	−18.5783	−	10.7262i	−0.597437	−	0.344930i	0.170596	−	0.985341i	$-0.445431\pi$
$967$	−18.5783	−	10.7262i	−0.597437	−	0.344930i	−0.768033	+	0.640411i	$0.778764\pi$
$968$	−9.51108	+	5.49122i	−0.305698	+	0.176495i
$969$	−50.2540	+	87.0425i	−1.61439	+	2.79621i
$970$	−0.824049	−	16.4997i	−0.0264586	−	0.529774i
$971$	11.5327	−	19.9752i	0.370102	−	0.641036i	−0.619479	−	0.785013i	$-0.712656\pi$
$971$	11.5327	−	19.9752i	0.370102	−	0.641036i	0.989581	+	0.143978i	$0.0459894\pi$
$972$	16.3384	+	9.43295i	0.524053	+	0.302562i
$973$	−34.7995	−	20.0915i	−1.11562	−	0.644103i
$974$	−14.8939	+	25.7970i	−0.477232	+	0.826589i
$975$	−70.1192	+	7.02147i	−2.24561	+	0.224867i
$976$	−0.678768	+	1.17566i	−0.0217268	+	0.0376320i
$977$	1.87580	−	1.08299i	0.0600122	−	0.0346480i	−0.469694	−	0.882829i	$-0.655636\pi$
$977$	1.87580	−	1.08299i	0.0600122	−	0.0346480i	0.529706	+	0.848181i	$0.322302\pi$
$978$			49.0648i			1.56892i
$979$	−1.12908	+	1.95563i	−0.0360856	+	0.0625022i
$980$	−0.0836421	+	0.0540260i	−0.00267185	+	0.00172580i
$981$	−34.9021			−1.11434
$982$	−12.0806	+	6.97471i	−0.385506	+	0.222572i
$983$			20.3247i			0.648257i	0.946013	+	0.324128i	$0.105071\pi$
$983$			20.3247i			0.648257i	−0.946013	+	0.324128i	$0.894929\pi$
$984$	6.95493	−	12.0463i	0.221715	−	0.384022i
$985$	42.0938	−	2.10230i	1.34122	−	0.0669848i
$986$	−11.7277	−	20.3131i	−0.373488	−	0.646899i
$987$	−8.87413	+	5.12348i	−0.282467	+	0.163082i
$988$	−30.6304	+	17.6845i	−0.974482	+	0.562617i
$989$	4.33461	+	7.50777i	0.137833	+	0.238733i
$990$	−0.714392	−	1.10601i	−0.0227049	−	0.0351513i
$991$	−8.53903			−0.271251			−0.135626	−	0.990760i	$-0.543304\pi$
$991$	−8.53903			−0.271251			−0.135626	+	0.990760i	$0.543304\pi$
$992$	0.859850	−	0.496435i	0.0273003	−	0.0157618i
$993$	68.1145	+	39.3259i	2.16155	+	1.24797i
$994$	−1.51816	+	2.62954i	−0.0481532	+	0.0834038i
$995$	31.3143	+	16.0525i	0.992729	+	0.508898i
$996$	−12.4881			−0.395701
$997$			38.4082i			1.21640i	0.793783	+	0.608201i	$0.208108\pi$
$997$			38.4082i			1.21640i	−0.793783	+	0.608201i	$0.791892\pi$
$998$	19.8785	+	11.4768i	0.629242	+	0.363293i
$999$	−17.4461	−	30.2175i	−0.551969	−	0.956038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.h.c.439.1	yes	52
5.4	even	2	inner	670.2.h.c.439.26	yes	52
67.29	even	3	inner	670.2.h.c.29.14	yes	52
335.29	even	6	inner	670.2.h.c.29.13	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.h.c.29.13	✓	52	335.29	even	6	inner
670.2.h.c.29.14	yes	52	67.29	even	3	inner
670.2.h.c.439.1	yes	52	1.1	even	1	trivial
670.2.h.c.439.26	yes	52	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} -2.72838i q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.87831 + 1.21324i) q^{5} +(1.36419 + 2.36285i) q^{6} +(2.29856 + 1.32708i) q^{7} +1.00000i q^{8} -4.44406 q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} -2.72838i q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.87831 + 1.21324i) q^{5} +(1.36419 + 2.36285i) q^{6} +(2.29856 + 1.32708i) q^{7} +1.00000i q^{8} -4.44406 q^{9} +(1.02005 - 1.98985i) q^{10} +(-0.0662493 + 0.114747i) q^{11} +(-2.36285 - 1.36419i) q^{12} +(4.47362 - 2.58285i) q^{13} -2.65415 q^{14} +(3.31017 + 5.12475i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.65943 - 2.69013i) q^{17} +(3.84867 - 2.22203i) q^{18} +(-3.42344 - 5.92958i) q^{19} +(0.111537 + 2.23328i) q^{20} +(3.62077 - 6.27136i) q^{21} -0.132499i q^{22} +(-0.726796 + 0.419616i) q^{23} +2.72838 q^{24} +(2.05611 - 4.55767i) q^{25} +(-2.58285 + 4.47362i) q^{26} +3.93995i q^{27} +(2.29856 - 1.32708i) q^{28} +(-2.17978 + 3.77548i) q^{29} +(-5.42907 - 2.78308i) q^{30} +(0.496435 - 0.859850i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.313074 + 0.180753i) q^{33} +(-2.69013 + 4.65943i) q^{34} +(-5.92748 + 0.296037i) q^{35} +(-2.22203 + 3.84867i) q^{36} +(-7.66951 + 4.42800i) q^{37} +(5.92958 + 3.42344i) q^{38} +(-7.04699 - 12.2057i) q^{39} +(-1.21324 - 1.87831i) q^{40} +(2.54910 - 4.41518i) q^{41} +7.24154i q^{42} -10.3300i q^{43} +(0.0662493 + 0.114747i) q^{44} +(8.34733 - 5.39170i) q^{45} +(0.419616 - 0.726796i) q^{46} +(-1.22545 - 0.707512i) q^{47} +(-2.36285 + 1.36419i) q^{48} +(0.0222652 + 0.0385645i) q^{49} +(0.498190 + 4.97512i) q^{50} +(-7.33969 - 12.7127i) q^{51} -5.16569i q^{52} +8.07078i q^{53} +(-1.96997 - 3.41209i) q^{54} +(-0.0147786 - 0.295907i) q^{55} +(-1.32708 + 2.29856i) q^{56} +(-16.1781 + 9.34045i) q^{57} -4.35955i q^{58} -6.21973 q^{59} +(6.09325 - 0.304316i) q^{60} +(-0.678768 - 1.17566i) q^{61} +0.992870i q^{62} +(-10.2150 - 5.89761i) q^{63} -1.00000 q^{64} +(-5.26926 + 10.2790i) q^{65} -0.361507 q^{66} +(5.92211 - 5.65054i) q^{67} -5.38025i q^{68} +(1.14487 + 1.98298i) q^{69} +(4.98533 - 3.22012i) q^{70} +(0.571995 - 0.990725i) q^{71} -4.44406i q^{72} +(9.51495 - 5.49346i) q^{73} +(4.42800 - 7.66951i) q^{74} +(-12.4351 - 5.60986i) q^{75} -6.84688 q^{76} +(-0.304557 + 0.175836i) q^{77} +(12.2057 + 7.04699i) q^{78} +(-2.22428 + 3.85256i) q^{79} +(1.98985 + 1.02005i) q^{80} -2.58251 q^{81} +5.09821i q^{82} +(3.96390 - 2.28856i) q^{83} +(-3.62077 - 6.27136i) q^{84} +(-5.48811 + 10.7059i) q^{85} +(5.16498 + 8.94600i) q^{86} +(10.3010 + 5.94726i) q^{87} +(-0.114747 - 0.0662493i) q^{88} +17.0429 q^{89} +(-4.53315 + 8.84301i) q^{90} +13.7105 q^{91} +0.839232i q^{92} +(-2.34600 - 1.35446i) q^{93} +1.41502 q^{94} +(13.6243 + 6.98415i) q^{95} +(1.36419 - 2.36285i) q^{96} +(6.39828 - 3.69405i) q^{97} +(-0.0385645 - 0.0222652i) q^{98} +(0.294416 - 0.509943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9}+O(q^{10}) \) 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9	\( 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9} - 10 q^{10} + 24 q^{11} + 24 q^{14} + 28 q^{15} - 26 q^{16} - 24 q^{19} - 8 q^{20} + 4 q^{21} - 12 q^{24} - 28 q^{25} + 4 q^{26} - 20 q^{29} - 10 q^{30} - 30 q^{31} - 16 q^{34} - 14 q^{35} - 24 q^{36} - 8 q^{39} - 20 q^{40} - 10 q^{41} - 24 q^{44} - 16 q^{45} - 8 q^{46} + 14 q^{49} - 8 q^{50} - 44 q^{51} + 42 q^{54} + 16 q^{55} + 12 q^{56} + 80 q^{59} + 14 q^{60} - 20 q^{61} - 52 q^{64} + 10 q^{65} - 40 q^{66} - 4 q^{69} + 48 q^{70} - 74 q^{71} + 34 q^{74} - 16 q^{75} - 48 q^{76} + 32 q^{79} + 8 q^{80} + 4 q^{81} - 4 q^{84} + 20 q^{85} + 12 q^{86} + 84 q^{89} - 30 q^{90} - 16 q^{91} + 136 q^{94} + 2 q^{95} - 6 q^{96} - 96 q^{99}+O(q^{100}) \) 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9 - 10 * q^10 + 24 * q^11 + 24 * q^14 + 28 * q^15 - 26 * q^16 - 24 * q^19 - 8 * q^20 + 4 * q^21 - 12 * q^24 - 28 * q^25 + 4 * q^26 - 20 * q^29 - 10 * q^30 - 30 * q^31 - 16 * q^34 - 14 * q^35 - 24 * q^36 - 8 * q^39 - 20 * q^40 - 10 * q^41 - 24 * q^44 - 16 * q^45 - 8 * q^46 + 14 * q^49 - 8 * q^50 - 44 * q^51 + 42 * q^54 + 16 * q^55 + 12 * q^56 + 80 * q^59 + 14 * q^60 - 20 * q^61 - 52 * q^64 + 10 * q^65 - 40 * q^66 - 4 * q^69 + 48 * q^70 - 74 * q^71 + 34 * q^74 - 16 * q^75 - 48 * q^76 + 32 * q^79 + 8 * q^80 + 4 * q^81 - 4 * q^84 + 20 * q^85 + 12 * q^86 + 84 * q^89 - 30 * q^90 - 16 * q^91 + 136 * q^94 + 2 * q^95 - 6 * q^96 - 96 * q^99

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