LMFDB - Embedded newform 731.2.d.c.560.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(560,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("731.560");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.d (of order $2$, degree $1$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 29 x^{18} + 358 x^{16} + 2458 x^{14} + 10298 x^{12} + 27188 x^{10} + 45053 x^{8} + 44980 x^{6} + \cdots + 36 $ x^20 + 29x^18 + 358x^16 + 2458x^14 + 10298x^12 + 27188x^10 + 45053x^8 + 44980x^6 + 24400x^4 + 5448*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			560.17
Root			$-0.799077i$ of defining polynomial
Character	$\chi$	$=$	731.560
Dual form			731.2.d.c.560.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.52220 q^{2} -3.34912i q^{3} +4.36148 q^{4} -0.720920i q^{5} -8.44715i q^{6} +2.87134i q^{7} +5.95611 q^{8} -8.21664 q^{9} +O(q^{10})$	\(q+2.52220 q^{2} -3.34912i q^{3} +4.36148 q^{4} -0.720920i q^{5} -8.44715i q^{6} +2.87134i q^{7} +5.95611 q^{8} -8.21664 q^{9} -1.81830i q^{10} -3.81272i q^{11} -14.6071i q^{12} -0.101117 q^{13} +7.24209i q^{14} -2.41445 q^{15} +6.29952 q^{16} +(-0.659346 + 4.07004i) q^{17} -20.7240 q^{18} +4.87091 q^{19} -3.14427i q^{20} +9.61648 q^{21} -9.61642i q^{22} -6.75238i q^{23} -19.9477i q^{24} +4.48027 q^{25} -0.255036 q^{26} +17.4712i q^{27} +12.5233i q^{28} +7.17495i q^{29} -6.08972 q^{30} +2.16604i q^{31} +3.97642 q^{32} -12.7693 q^{33} +(-1.66300 + 10.2655i) q^{34} +2.07001 q^{35} -35.8367 q^{36} +6.52416i q^{37} +12.2854 q^{38} +0.338653i q^{39} -4.29387i q^{40} -1.97428i q^{41} +24.2547 q^{42} +1.00000 q^{43} -16.6291i q^{44} +5.92354i q^{45} -17.0308i q^{46} -6.84315 q^{47} -21.0979i q^{48} -1.24461 q^{49} +11.3001 q^{50} +(13.6311 + 2.20823i) q^{51} -0.441018 q^{52} +4.32468 q^{53} +44.0657i q^{54} -2.74866 q^{55} +17.1020i q^{56} -16.3133i q^{57} +18.0966i q^{58} -7.28346 q^{59} -10.5306 q^{60} +0.685045i q^{61} +5.46317i q^{62} -23.5928i q^{63} -2.56973 q^{64} +0.0728970i q^{65} -32.2066 q^{66} +14.0355 q^{67} +(-2.87572 + 17.7514i) q^{68} -22.6146 q^{69} +5.22097 q^{70} +6.17146i q^{71} -48.9392 q^{72} +0.879246i q^{73} +16.4552i q^{74} -15.0050i q^{75} +21.2444 q^{76} +10.9476 q^{77} +0.854148i q^{78} -9.32626i q^{79} -4.54145i q^{80} +33.8632 q^{81} -4.97952i q^{82} -4.59754 q^{83} +41.9421 q^{84} +(2.93418 + 0.475336i) q^{85} +2.52220 q^{86} +24.0298 q^{87} -22.7090i q^{88} -17.1032 q^{89} +14.9403i q^{90} -0.290341i q^{91} -29.4503i q^{92} +7.25432 q^{93} -17.2598 q^{94} -3.51154i q^{95} -13.3175i q^{96} -12.2951i q^{97} -3.13914 q^{98} +31.3277i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 42 q^{4} + 18 q^{8} - 18 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 42 * q^4 + 18 * q^8 - 18 * q^9	$ 20 q + 2 q^{2} + 42 q^{4} + 18 q^{8} - 18 q^{9} - 4 q^{13} + 26 q^{15} + 6 q^{16} + 16 q^{17} - 22 q^{18} - 4 q^{19} + 20 q^{21} - 2 q^{25} + 22 q^{26} - 72 q^{30} + 38 q^{32} - 12 q^{33} + 12 q^{34} - 30 q^{35} - 104 q^{36} - 22 q^{38} + 26 q^{42} + 20 q^{43} - 34 q^{47} + 22 q^{49} + 42 q^{50} + 52 q^{51} - 110 q^{52} + 14 q^{53} + 12 q^{55} + 20 q^{59} + 42 q^{60} - 22 q^{64} + 50 q^{66} - 12 q^{67} + 50 q^{68} - 82 q^{69} - 30 q^{70} - 50 q^{72} + 2 q^{76} + 78 q^{77} + 44 q^{81} + 20 q^{83} + 62 q^{84} + 76 q^{85} + 2 q^{86} + 12 q^{87} - 46 q^{89} + 58 q^{93} - 18 q^{94} - 62 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 + 42 * q^4 + 18 * q^8 - 18 * q^9 - 4 * q^13 + 26 * q^15 + 6 * q^16 + 16 * q^17 - 22 * q^18 - 4 * q^19 + 20 * q^21 - 2 * q^25 + 22 * q^26 - 72 * q^30 + 38 * q^32 - 12 * q^33 + 12 * q^34 - 30 * q^35 - 104 * q^36 - 22 * q^38 + 26 * q^42 + 20 * q^43 - 34 * q^47 + 22 * q^49 + 42 * q^50 + 52 * q^51 - 110 * q^52 + 14 * q^53 + 12 * q^55 + 20 * q^59 + 42 * q^60 - 22 * q^64 + 50 * q^66 - 12 * q^67 + 50 * q^68 - 82 * q^69 - 30 * q^70 - 50 * q^72 + 2 * q^76 + 78 * q^77 + 44 * q^81 + 20 * q^83 + 62 * q^84 + 76 * q^85 + 2 * q^86 + 12 * q^87 - 46 * q^89 + 58 * q^93 - 18 * q^94 - 62 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$-1$	$1$

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 $

$2$	2.52220			1.78346			0.891731	−	0.452565i	$-0.149491\pi$
$2$	2.52220			1.78346			0.891731	+	0.452565i	$0.149491\pi$
$3$		−	3.34912i		−	1.93362i	−0.255500	−	0.966809i	$-0.582240\pi$
$3$		−	3.34912i		−	1.93362i	0.255500	−	0.966809i	$-0.417760\pi$
$4$	4.36148			2.18074
$5$		−	0.720920i		−	0.322405i	−0.986921	−	0.161203i	$-0.948463\pi$
$5$		−	0.720920i		−	0.322405i	0.986921	−	0.161203i	$-0.0515372\pi$
$6$		−	8.44715i		−	3.44854i
$7$			2.87134i			1.08527i	0.839970	+	0.542633i	$0.182572\pi$
$7$			2.87134i			1.08527i	−0.839970	+	0.542633i	$0.817428\pi$
$8$	5.95611			2.10580
$9$	−8.21664			−2.73888
$10$		−	1.81830i		−	0.574997i
$11$		−	3.81272i		−	1.14958i	−0.818302	−	0.574789i	$-0.805084\pi$
$11$		−	3.81272i		−	1.14958i	0.818302	−	0.574789i	$-0.194916\pi$
$12$		−	14.6071i		−	4.21671i
$13$	−0.101117			−0.0280447			−0.0140224	−	0.999902i	$-0.504464\pi$
$13$	−0.101117			−0.0280447			−0.0140224	+	0.999902i	$0.504464\pi$
$14$			7.24209i			1.93553i
$15$	−2.41445			−0.623408
$16$	6.29952			1.57488
$17$	−0.659346	+	4.07004i	−0.159915	+	0.987131i
$17$	−0.659346	+	4.07004i	−0.159915	+	0.987131i
$18$	−20.7240			−4.88469
$19$	4.87091			1.11746			0.558732	−	0.829348i	$-0.311288\pi$
$19$	4.87091			1.11746			0.558732	+	0.829348i	$0.311288\pi$
$20$		−	3.14427i		−	0.703081i
$21$	9.61648			2.09849
$22$		−	9.61642i		−	2.05023i
$23$		−	6.75238i		−	1.40797i	−0.710215	−	0.703984i	$-0.751402\pi$
$23$		−	6.75238i		−	1.40797i	0.710215	−	0.703984i	$-0.248598\pi$
$24$		−	19.9477i		−	4.07182i
$25$	4.48027			0.896055
$26$	−0.255036			−0.0500167
$27$			17.4712i			3.36233i
$28$			12.5233i			2.36668i
$29$			7.17495i			1.33236i	0.745793	+	0.666178i	$0.232071\pi$
$29$			7.17495i			1.33236i	−0.745793	+	0.666178i	$0.767929\pi$
$30$	−6.08972			−1.11183
$31$			2.16604i			0.389031i	0.980899	+	0.194516i	$0.0623135\pi$
$31$			2.16604i			0.389031i	−0.980899	+	0.194516i	$0.937686\pi$
$32$	3.97642			0.702938
$33$	−12.7693			−2.22284
$34$	−1.66300	+	10.2655i	−0.285202	+	1.76051i
$35$	2.07001			0.349895
$36$	−35.8367			−5.97278
$37$			6.52416i			1.07257i	0.844038	+	0.536283i	$0.180172\pi$
$37$			6.52416i			1.07257i	−0.844038	+	0.536283i	$0.819828\pi$
$38$	12.2854			1.99296
$39$			0.338653i			0.0542278i
$40$		−	4.29387i		−	0.678921i
$41$		−	1.97428i		−	0.308331i	−0.988045	−	0.154165i	$-0.950731\pi$
$41$		−	1.97428i		−	0.308331i	0.988045	−	0.154165i	$-0.0492689\pi$
$42$	24.2547			3.74258
$43$	1.00000			0.152499
$43$	1.00000			0.152499
$44$		−	16.6291i		−	2.50693i
$45$			5.92354i			0.883029i
$46$		−	17.0308i		−	2.51106i
$47$	−6.84315			−0.998176			−0.499088	−	0.866551i	$-0.666332\pi$
$47$	−6.84315			−0.998176			−0.499088	+	0.866551i	$0.666332\pi$
$48$		−	21.0979i		−	3.04522i
$49$	−1.24461			−0.177801
$50$	11.3001			1.59808
$51$	13.6311	+	2.20823i	1.90873	+	0.309214i
$52$	−0.441018			−0.0611582
$53$	4.32468			0.594041			0.297021	−	0.954871i	$-0.404007\pi$
$53$	4.32468			0.594041			0.297021	+	0.954871i	$0.404007\pi$
$54$			44.0657i			5.99659i
$55$	−2.74866			−0.370630
$56$			17.1020i			2.28535i
$57$		−	16.3133i		−	2.16075i
$58$			18.0966i			2.37621i
$59$	−7.28346			−0.948226			−0.474113	−	0.880464i	$-0.657231\pi$
$59$	−7.28346			−0.948226			−0.474113	+	0.880464i	$0.657231\pi$
$60$	−10.5306			−1.35949
$61$			0.685045i			0.0877110i	0.999038	+	0.0438555i	$0.0139641\pi$
$61$			0.685045i			0.0877110i	−0.999038	+	0.0438555i	$0.986036\pi$
$62$			5.46317i			0.693823i
$63$		−	23.5928i		−	2.97241i
$64$	−2.56973			−0.321217
$65$			0.0728970i			0.00904176i
$66$	−32.2066			−3.96436
$67$	14.0355			1.71471			0.857354	−	0.514727i	$-0.172107\pi$
$67$	14.0355			1.71471			0.857354	+	0.514727i	$0.172107\pi$
$68$	−2.87572	+	17.7514i	−0.348733	+	2.15267i
$69$	−22.6146			−2.72247
$70$	5.22097			0.624025
$71$			6.17146i			0.732417i	0.930533	+	0.366209i	$0.119344\pi$
$71$			6.17146i			0.732417i	−0.930533	+	0.366209i	$0.880656\pi$
$72$	−48.9392			−5.76754
$73$			0.879246i			0.102908i	0.998675	+	0.0514540i	$0.0163856\pi$
$73$			0.879246i			0.102908i	−0.998675	+	0.0514540i	$0.983614\pi$
$74$			16.4552i			1.91288i
$75$		−	15.0050i		−	1.73263i
$76$	21.2444			2.43690
$77$	10.9476			1.24760
$78$			0.854148i			0.0967133i
$79$		−	9.32626i		−	1.04929i	−0.851322	−	0.524643i	$-0.824199\pi$
$79$		−	9.32626i		−	1.04929i	0.851322	−	0.524643i	$-0.175801\pi$
$80$		−	4.54145i		−	0.507749i
$81$	33.8632			3.76258
$82$		−	4.97952i		−	0.549897i
$83$	−4.59754			−0.504645			−0.252323	−	0.967643i	$-0.581194\pi$
$83$	−4.59754			−0.504645			−0.252323	+	0.967643i	$0.581194\pi$
$84$	41.9421			4.57625
$85$	2.93418	+	0.475336i	0.318256	+	0.0515574i
$86$	2.52220			0.271975
$87$	24.0298			2.57627
$88$		−	22.7090i		−	2.42078i
$89$	−17.1032			−1.81294			−0.906469	−	0.422273i	$-0.861232\pi$
$89$	−17.1032			−1.81294			−0.906469	+	0.422273i	$0.861232\pi$
$90$			14.9403i			1.57485i
$91$		−	0.290341i		−	0.0304360i
$92$		−	29.4503i		−	3.07041i
$93$	7.25432			0.752238
$94$	−17.2598			−1.78021
$95$		−	3.51154i		−	0.360276i
$96$		−	13.3175i		−	1.35921i
$97$		−	12.2951i		−	1.24838i	−0.781274	−	0.624188i	$-0.785430\pi$
$97$		−	12.2951i		−	1.24838i	0.781274	−	0.624188i	$-0.214570\pi$
$98$	−3.13914			−0.317101
$99$			31.3277i			3.14855i
$100$	19.5406			1.95406
$101$	−8.32265			−0.828135			−0.414067	−	0.910246i	$-0.635892\pi$
$101$	−8.32265			−0.828135			−0.414067	+	0.910246i	$0.635892\pi$
$102$	34.3803	+	5.56960i	3.40416	+	0.551472i
$103$	1.06757			0.105190			0.0525952	−	0.998616i	$-0.483251\pi$
$103$	1.06757			0.105190			0.0525952	+	0.998616i	$0.483251\pi$
$104$	−0.602262			−0.0590567
$105$		−	6.93271i		−	0.676563i
$106$	10.9077			1.05945
$107$		−	14.7975i		−	1.43053i	−0.698854	−	0.715265i	$-0.746306\pi$
$107$		−	14.7975i		−	1.43053i	0.698854	−	0.715265i	$-0.253694\pi$
$108$			76.2001i			7.33236i
$109$			13.9444i			1.33563i	0.744326	+	0.667816i	$0.232771\pi$
$109$			13.9444i			1.33563i	−0.744326	+	0.667816i	$0.767229\pi$
$110$	−6.93267			−0.661004
$111$	21.8502			2.07393
$112$			18.0881i			1.70916i
$113$			9.32359i			0.877090i	0.898709	+	0.438545i	$0.144506\pi$
$113$			9.32359i			0.877090i	−0.898709	+	0.438545i	$0.855494\pi$
$114$		−	41.1453i		−	3.85361i
$115$	−4.86792			−0.453936
$116$			31.2934i			2.90552i
$117$	0.830840			0.0768111
$118$	−18.3703			−1.69112
$119$	−11.6865	−	1.89321i	−1.07130	−	0.173550i
$120$	−14.3807			−1.31277
$121$	−3.53682			−0.321529
$122$			1.72782i			0.156429i
$123$	−6.61211			−0.596194
$124$			9.44711i			0.848376i
$125$		−	6.83452i		−	0.611298i
$126$		−	59.5056i		−	5.30118i
$127$	−2.07715			−0.184317			−0.0921585	−	0.995744i	$-0.529377\pi$
$127$	−2.07715			−0.184317			−0.0921585	+	0.995744i	$0.529377\pi$
$128$	−14.4342			−1.27582
$129$		−	3.34912i		−	0.294874i
$130$			0.183861i			0.0161256i
$131$			15.5648i			1.35991i	0.733256	+	0.679953i	$0.238000\pi$
$131$			15.5648i			1.35991i	−0.733256	+	0.679953i	$0.762000\pi$
$132$	−55.6929			−4.84744
$133$			13.9861i			1.21275i
$134$	35.4003			3.05812
$135$	12.5953			1.08403
$136$	−3.92714	+	24.2416i	−0.336749	+	2.07870i
$137$	−18.9797			−1.62154			−0.810772	−	0.585362i	$-0.800952\pi$
$137$	−18.9797			−1.62154			−0.810772	+	0.585362i	$0.800952\pi$
$138$	−57.0384			−4.85543
$139$		−	12.9612i		−	1.09935i	−0.835378	−	0.549676i	$-0.814751\pi$
$139$		−	12.9612i		−	1.09935i	0.835378	−	0.549676i	$-0.185249\pi$
$140$	9.02829			0.763030
$141$			22.9186i			1.93009i
$142$			15.5656i			1.30624i
$143$			0.385530i			0.0322396i
$144$	−51.7609			−4.31341
$145$	5.17257			0.429558
$146$			2.21763i			0.183533i
$147$			4.16834i			0.343799i
$148$			28.4550i			2.33898i
$149$	13.3720			1.09548			0.547738	−	0.836650i	$-0.315489\pi$
$149$	13.3720			1.09548			0.547738	+	0.836650i	$0.315489\pi$
$150$		−	37.8456i		−	3.09008i
$151$	11.3063			0.920096			0.460048	−	0.887894i	$-0.347832\pi$
$151$	11.3063			0.920096			0.460048	+	0.887894i	$0.347832\pi$
$152$	29.0117			2.35316
$153$	5.41761	−	33.4421i	0.437988	−	2.70363i
$154$	27.6120			2.22504
$155$	1.56154			0.125426
$156$			1.47703i			0.118257i
$157$	−1.08706			−0.0867565			−0.0433783	−	0.999059i	$-0.513812\pi$
$157$	−1.08706			−0.0867565			−0.0433783	+	0.999059i	$0.513812\pi$
$158$		−	23.5227i		−	1.87136i
$159$		−	14.4839i		−	1.14865i
$160$		−	2.86668i		−	0.226631i
$161$	19.3884			1.52802
$162$	85.4097			6.71042
$163$			3.31951i			0.260004i	0.991514	+	0.130002i	$0.0414984\pi$
$163$			3.31951i			0.260004i	−0.991514	+	0.130002i	$0.958502\pi$
$164$		−	8.61078i		−	0.672389i
$165$			9.20562i			0.716656i
$166$	−11.5959			−0.900016
$167$		−	0.953509i		−	0.0737847i	−0.999319	−	0.0368924i	$-0.988254\pi$
$167$		−	0.953509i		−	0.0737847i	0.999319	−	0.0368924i	$-0.0117459\pi$
$168$	57.2768			4.41900
$169$	−12.9898			−0.999213
$170$	7.40057	+	1.19889i	0.567598	+	0.0919506i
$171$	−40.0225			−3.06060
$172$	4.36148			0.332559
$173$		−	0.179939i		−	0.0136805i	−0.999977	−	0.00684026i	$-0.997823\pi$
$173$		−	0.179939i		−	0.0136805i	0.999977	−	0.00684026i	$-0.00217734\pi$
$174$	60.6079			4.59468
$175$			12.8644i			0.972457i
$176$		−	24.0183i		−	1.81045i
$177$			24.3932i			1.83351i
$178$	−43.1377			−3.23331
$179$	−10.4780			−0.783163			−0.391581	−	0.920143i	$-0.628072\pi$
$179$	−10.4780			−0.783163			−0.391581	+	0.920143i	$0.628072\pi$
$180$			25.8354i			1.92565i
$181$		−	4.20480i		−	0.312540i	−0.987714	−	0.156270i	$-0.950053\pi$
$181$		−	4.20480i		−	0.312540i	0.987714	−	0.156270i	$-0.0499471\pi$
$182$		−	0.732296i		−	0.0542814i
$183$	2.29430			0.169600
$184$		−	40.2179i		−	2.96490i
$185$	4.70340			0.345801
$186$	18.2968			1.34159
$187$	15.5179	+	2.51390i	1.13478	+	0.183835i
$188$	−29.8462			−2.17676
$189$	−50.1657			−3.64902
$190$		−	8.85679i		−	0.642539i
$191$	−21.9917			−1.59127			−0.795633	−	0.605778i	$-0.792862\pi$
$191$	−21.9917			−1.59127			−0.795633	+	0.605778i	$0.792862\pi$
$192$			8.60636i			0.621111i
$193$			5.55047i			0.399532i	0.979844	+	0.199766i	$0.0640182\pi$
$193$			5.55047i			0.399532i	−0.979844	+	0.199766i	$0.935982\pi$
$194$		−	31.0106i		−	2.22643i
$195$	0.244141			0.0174833
$196$	−5.42832			−0.387737
$197$		−	12.7143i		−	0.905859i	−0.891546	−	0.452930i	$-0.850379\pi$
$197$		−	12.7143i		−	0.905859i	0.891546	−	0.452930i	$-0.149621\pi$
$198$			79.0147i			5.61533i
$199$			20.7995i			1.47444i	0.675653	+	0.737220i	$0.263862\pi$
$199$			20.7995i			1.47444i	−0.675653	+	0.737220i	$0.736138\pi$
$200$	26.6850			1.88691
$201$		−	47.0066i		−	3.31559i
$202$	−20.9914			−1.47695
$203$	−20.6018			−1.44596
$204$	59.4517	+	9.63115i	4.16245	+	0.674316i
$205$	−1.42330			−0.0994074
$206$	2.69261			0.187603
$207$			55.4819i			3.85626i
$208$	−0.636987			−0.0441671
$209$		−	18.5714i		−	1.28461i
$210$		−	17.4857i		−	1.20663i
$211$		−	12.2620i		−	0.844149i	−0.906561	−	0.422074i	$-0.861302\pi$
$211$		−	12.2620i		−	0.844149i	0.906561	−	0.422074i	$-0.138698\pi$
$212$	18.8620			1.29545
$213$	20.6690			1.41622
$214$		−	37.3222i		−	2.55130i
$215$		−	0.720920i		−	0.0491663i
$216$			104.060i			7.08040i
$217$	−6.21943			−0.422202
$218$			35.1705i			2.38205i
$219$	2.94471			0.198985
$220$	−11.9882			−0.808246
$221$	0.0666709	−	0.411550i	0.00448477	−	0.0276838i
$222$	55.1106			3.69878
$223$	8.56343			0.573450			0.286725	−	0.958013i	$-0.407433\pi$
$223$	8.56343			0.573450			0.286725	+	0.958013i	$0.407433\pi$
$224$			11.4177i			0.762874i
$225$	−36.8128			−2.45419
$226$			23.5159i			1.56426i
$227$			7.50886i			0.498381i	0.968455	+	0.249190i	$0.0801645\pi$
$227$			7.50886i			0.498381i	−0.968455	+	0.249190i	$0.919836\pi$
$228$		−	71.1501i		−	4.71203i
$229$	−19.8169			−1.30954			−0.654770	−	0.755828i	$-0.727235\pi$
$229$	−19.8169			−1.30954			−0.654770	+	0.755828i	$0.727235\pi$
$230$	−12.2779			−0.809578
$231$		−	36.6649i		−	2.41238i
$232$			42.7348i			2.80568i
$233$		−	5.23807i		−	0.343157i	−0.985170	−	0.171579i	$-0.945113\pi$
$233$		−	5.23807i		−	0.343157i	0.985170	−	0.171579i	$-0.0548867\pi$
$234$	2.09554			0.136990
$235$			4.93336i			0.321817i
$236$	−31.7666			−2.06783
$237$	−31.2348			−2.02892
$238$	−29.4756	−	4.77504i	−1.91062	−	0.309520i
$239$	28.6065			1.85040			0.925200	−	0.379480i	$-0.123897\pi$
$239$	28.6065			1.85040			0.925200	+	0.379480i	$0.123897\pi$
$240$	−15.2099			−0.981794
$241$		−	26.9100i		−	1.73343i	−0.498805	−	0.866714i	$-0.666228\pi$
$241$		−	26.9100i		−	1.73343i	0.498805	−	0.866714i	$-0.333772\pi$
$242$	−8.92055			−0.573435
$243$		−	60.9986i		−	3.91306i
$244$			2.98781i			0.191275i
$245$			0.897262i			0.0573239i
$246$	−16.6771			−1.06329
$247$	−0.492531			−0.0313390
$248$			12.9011i			0.819223i
$249$			15.3977i			0.975791i
$250$		−	17.2380i		−	1.09023i
$251$	−8.81852			−0.556620			−0.278310	−	0.960491i	$-0.589774\pi$
$251$	−8.81852			−0.556620			−0.278310	+	0.960491i	$0.589774\pi$
$252$		−	102.899i		−	6.48205i
$253$	−25.7449			−1.61857
$254$	−5.23898			−0.328723
$255$	1.59196	−	9.82692i	0.0996923	−	0.615386i
$256$	−31.2665			−1.95415
$257$	1.67385			0.104412			0.0522058	−	0.998636i	$-0.483375\pi$
$257$	1.67385			0.104412			0.0522058	+	0.998636i	$0.483375\pi$
$258$		−	8.44715i		−	0.525897i
$259$	−18.7331			−1.16402
$260$			0.317939i			0.0197177i
$261$		−	58.9540i		−	3.64916i
$262$			39.2576i			2.42534i
$263$	−0.751432			−0.0463353			−0.0231676	−	0.999732i	$-0.507375\pi$
$263$	−0.751432			−0.0463353			−0.0231676	+	0.999732i	$0.507375\pi$
$264$	−76.0551			−4.68087
$265$		−	3.11775i		−	0.191522i
$266$			35.2756i			2.16289i
$267$			57.2808i			3.50553i
$268$	61.2154			3.73933
$269$		−	7.69156i		−	0.468963i	−0.972121	−	0.234481i	$-0.924661\pi$
$269$		−	7.69156i		−	0.468963i	0.972121	−	0.234481i	$-0.0753391\pi$
$270$	31.7679			1.93333
$271$	28.1190			1.70811			0.854053	−	0.520186i	$-0.174137\pi$
$271$	28.1190			1.70811			0.854053	+	0.520186i	$0.174137\pi$
$272$	−4.15356	+	25.6393i	−0.251847	+	1.55461i
$273$	−0.972387			−0.0588516
$274$	−47.8705			−2.89196
$275$		−	17.0820i		−	1.03008i
$276$	−98.6329			−5.93700
$277$		−	14.4716i		−	0.869512i	−0.900548	−	0.434756i	$-0.856835\pi$
$277$		−	14.4716i		−	0.869512i	0.900548	−	0.434756i	$-0.143165\pi$
$278$		−	32.6906i		−	1.96065i
$279$		−	17.7975i		−	1.06551i
$280$	12.3292			0.736810
$281$	9.19959			0.548802			0.274401	−	0.961615i	$-0.411520\pi$
$281$	9.19959			0.548802			0.274401	+	0.961615i	$0.411520\pi$
$282$			57.8051i			3.44224i
$283$			15.2108i			0.904191i	0.891970	+	0.452095i	$0.149323\pi$
$283$			15.2108i			0.904191i	−0.891970	+	0.452095i	$0.850677\pi$
$284$			26.9167i			1.59721i
$285$	−11.7606			−0.696637
$286$			0.972381i			0.0574981i
$287$	5.66884			0.334621
$288$	−32.6728			−1.92526
$289$	−16.1305	−	5.36714i	−0.948854	−	0.315714i
$290$	13.0462			0.766101
$291$	−41.1778			−2.41388
$292$			3.83481i			0.224415i
$293$	−21.9846			−1.28436			−0.642178	−	0.766555i	$-0.721969\pi$
$293$	−21.9846			−1.28436			−0.642178	+	0.766555i	$0.721969\pi$
$294$			10.5134i			0.613153i
$295$			5.25079i			0.305713i
$296$			38.8586i			2.25861i
$297$	66.6126			3.86526
$298$	33.7268			1.95374
$299$			0.682779i			0.0394861i
$300$		−	65.4439i		−	3.77841i
$301$			2.87134i			0.165501i
$302$	28.5168			1.64096
$303$			27.8736i			1.60130i
$304$	30.6844			1.75987
$305$	0.493862			0.0282785
$306$	13.6643	−	84.3475i	0.781134	−	4.82183i
$307$	−32.5116			−1.85554			−0.927768	−	0.373158i	$-0.878275\pi$
$307$	−32.5116			−1.85554			−0.927768	+	0.373158i	$0.878275\pi$
$308$	47.7478			2.72068
$309$		−	3.57541i		−	0.203398i
$310$	3.93850			0.223692
$311$			32.0521i			1.81751i	0.417330	+	0.908755i	$0.362966\pi$
$311$			32.0521i			1.81751i	−0.417330	+	0.908755i	$0.637034\pi$
$312$			2.01705i			0.114193i
$313$			0.339820i			0.0192078i	0.999954	+	0.00960388i	$0.00305706\pi$
$313$			0.339820i			0.0192078i	−0.999954	+	0.00960388i	$0.996943\pi$
$314$	−2.74177			−0.154727
$315$	−17.0085			−0.958320
$316$		−	40.6763i		−	2.28822i
$317$		−	1.81786i		−	0.102101i	−0.998696	−	0.0510507i	$-0.983743\pi$
$317$		−	1.81786i		−	0.102101i	0.998696	−	0.0510507i	$-0.0162570\pi$
$318$		−	36.5313i		−	2.04857i
$319$	27.3561			1.53165
$320$			1.85257i			0.103562i
$321$	−49.5587			−2.76610
$322$	48.9014			2.72517
$323$	−3.21162	+	19.8248i	−0.178699	+	1.10308i
$324$	147.694			8.20520
$325$	−0.453031			−0.0251296
$326$			8.37246i			0.463707i
$327$	46.7016			2.58260
$328$		−	11.7590i		−	0.649284i
$329$		−	19.6490i		−	1.08329i
$330$			23.2184i			1.27813i
$331$	23.1545			1.27269			0.636343	−	0.771407i	$-0.280446\pi$
$331$	23.1545			1.27269			0.636343	+	0.771407i	$0.280446\pi$
$332$	−20.0521			−1.10050
$333$		−	53.6067i		−	2.93763i
$334$		−	2.40494i		−	0.131592i
$335$		−	10.1185i		−	0.552830i
$336$	60.5793			3.30487
$337$			7.81840i			0.425896i	0.977064	+	0.212948i	$0.0683064\pi$
$337$			7.81840i			0.425896i	−0.977064	+	0.212948i	$0.931694\pi$
$338$	−32.7628			−1.78206
$339$	31.2259			1.69596
$340$	12.7973	+	2.07316i	0.694033	+	0.112433i
$341$	8.25848			0.447222
$342$	−100.945			−5.45846
$343$			16.5257i			0.892304i
$344$	5.95611			0.321132
$345$			16.3033i			0.877739i
$346$		−	0.453842i		−	0.0243987i
$347$			5.02856i			0.269947i	0.990849	+	0.134974i	$0.0430950\pi$
$347$			5.02856i			0.269947i	−0.990849	+	0.134974i	$0.956905\pi$
$348$	104.805			5.61816
$349$	−13.5130			−0.723332			−0.361666	−	0.932308i	$-0.617792\pi$
$349$	−13.5130			−0.723332			−0.361666	+	0.932308i	$0.617792\pi$
$350$			32.4466i			1.73434i
$351$		−	1.76663i		−	0.0942956i
$352$		−	15.1610i		−	0.808082i
$353$	−8.60686			−0.458097			−0.229048	−	0.973415i	$-0.573561\pi$
$353$	−8.60686			−0.458097			−0.229048	+	0.973415i	$0.573561\pi$
$354$			61.5245i			3.26999i
$355$	4.44912			0.236135
$356$	−74.5953			−3.95354
$357$	−6.34059	+	39.1395i	−0.335580	+	2.07148i
$358$	−26.4276			−1.39674
$359$	14.2150			0.750242			0.375121	−	0.926976i	$-0.377601\pi$
$359$	14.2150			0.750242			0.375121	+	0.926976i	$0.377601\pi$
$360$			35.2812i			1.85948i
$361$	4.72580			0.248726
$362$		−	10.6053i		−	0.557404i
$363$			11.8452i			0.621714i
$364$		−	1.26631i		−	0.0663729i
$365$	0.633866			0.0331781
$366$	5.78668			0.302474
$367$		−	23.4070i		−	1.22183i	−0.791695	−	0.610917i	$-0.790801\pi$
$367$		−	23.4070i		−	1.22183i	0.791695	−	0.610917i	$-0.209199\pi$
$368$		−	42.5368i		−	2.21738i
$369$			16.2220i			0.844481i
$370$	11.8629			0.616722
$371$			12.4176i			0.644692i
$372$	31.6396			1.64043
$373$	13.8221			0.715683			0.357842	−	0.933782i	$-0.383513\pi$
$373$	13.8221			0.715683			0.357842	+	0.933782i	$0.383513\pi$
$374$	39.1393	+	6.34055i	2.02384	+	0.327862i
$375$	−22.8896			−1.18202
$376$	−40.7585			−2.10196
$377$		−	0.725508i		−	0.0373656i
$378$	−126.528			−6.50789
$379$		−	1.69826i		−	0.0872340i	−0.999048	−	0.0436170i	$-0.986112\pi$
$379$		−	1.69826i		−	0.0872340i	0.999048	−	0.0436170i	$-0.0138881\pi$
$380$		−	15.3155i		−	0.785668i
$381$			6.95663i			0.356399i
$382$	−55.4675			−2.83796
$383$	8.94512			0.457074			0.228537	−	0.973535i	$-0.426606\pi$
$383$	8.94512			0.457074			0.228537	+	0.973535i	$0.426606\pi$
$384$			48.3420i			2.46694i
$385$		−	7.89235i		−	0.402232i
$386$			13.9994i			0.712550i
$387$	−8.21664			−0.417675
$388$		−	53.6247i		−	2.72238i
$389$	33.0925			1.67786			0.838928	−	0.544242i	$-0.183183\pi$
$389$	33.0925			1.67786			0.838928	+	0.544242i	$0.183183\pi$
$390$	0.615772			0.0311808
$391$	27.4825	+	4.45216i	1.38985	+	0.225155i
$392$	−7.41301			−0.374414
$393$	52.1286			2.62954
$394$		−	32.0681i		−	1.61557i
$395$	−6.72348			−0.338295
$396$			136.635i			6.86617i
$397$		−	1.85863i		−	0.0932819i	−0.998912	−	0.0466409i	$-0.985148\pi$
$397$		−	1.85863i		−	0.0932819i	0.998912	−	0.0466409i	$-0.0148517\pi$
$398$			52.4605i			2.62961i
$399$	46.8411			2.34499
$400$	28.2236			1.41118
$401$		−	8.33181i		−	0.416071i	−0.978121	−	0.208035i	$-0.933293\pi$
$401$		−	8.33181i		−	0.416071i	0.978121	−	0.208035i	$-0.0667069\pi$
$402$		−	118.560i		−	5.91323i
$403$		−	0.219022i		−	0.0109103i
$404$	−36.2990			−1.80594
$405$		−	24.4127i		−	1.21307i
$406$	−51.9617			−2.57881
$407$	24.8748			1.23300
$408$	81.1882	+	13.1525i	4.01942	+	0.651144i
$409$	31.0158			1.53363			0.766816	−	0.641866i	$-0.221840\pi$
$409$	31.0158			1.53363			0.766816	+	0.641866i	$0.221840\pi$
$410$	−3.58984			−0.177289
$411$			63.5653i			3.13545i
$412$	4.65616			0.229393
$413$		−	20.9133i		−	1.02908i
$414$			139.936i			6.87749i
$415$			3.31446i			0.162700i
$416$	−0.402082			−0.0197137
$417$	−43.4086			−2.12573
$418$		−	46.8408i		−	2.29106i
$419$			24.8631i			1.21464i	0.794456	+	0.607321i	$0.207756\pi$
$419$			24.8631i			1.21464i	−0.794456	+	0.607321i	$0.792244\pi$
$420$		−	30.2369i		−	1.47541i
$421$	9.77818			0.476559			0.238280	−	0.971197i	$-0.423417\pi$
$421$	9.77818			0.476559			0.238280	+	0.971197i	$0.423417\pi$
$422$		−	30.9271i		−	1.50551i
$423$	56.2277			2.73388
$424$	25.7583			1.25093
$425$	−2.95405	+	18.2349i	−0.143293	+	0.884523i
$426$	52.1312			2.52577
$427$	−1.96700			−0.0951897
$428$		−	64.5390i		−	3.11961i
$429$	1.29119			0.0623391
$430$		−	1.81830i		−	0.0876863i
$431$		−	28.2071i		−	1.35869i	−0.733819	−	0.679345i	$-0.762264\pi$
$431$		−	28.2071i		−	1.35869i	0.733819	−	0.679345i	$-0.237736\pi$
$432$			110.060i			5.29527i
$433$	−29.0135			−1.39430			−0.697151	−	0.716924i	$-0.745549\pi$
$433$	−29.0135			−1.39430			−0.697151	+	0.716924i	$0.745549\pi$
$434$	−15.6866			−0.752982
$435$		−	17.3236i		−	0.830602i
$436$			60.8182i			2.91266i
$437$		−	32.8903i		−	1.57335i
$438$	7.42713			0.354882
$439$			8.07879i			0.385580i	0.981240	+	0.192790i	$0.0617536\pi$
$439$			8.07879i			0.385580i	−0.981240	+	0.192790i	$0.938246\pi$
$440$	−16.3713			−0.780473
$441$	10.2265			0.486975
$442$	0.168157	−	1.03801i	0.00799842	−	0.0493731i
$443$	9.21851			0.437985			0.218992	−	0.975727i	$-0.429723\pi$
$443$	9.21851			0.437985			0.218992	+	0.975727i	$0.429723\pi$
$444$	95.2993			4.52270
$445$			12.3300i			0.584500i
$446$	21.5987			1.02273
$447$		−	44.7845i		−	2.11823i
$448$		−	7.37859i		−	0.348605i
$449$			12.2641i			0.578777i	0.957212	+	0.289389i	$0.0934519\pi$
$449$			12.2641i			0.578777i	−0.957212	+	0.289389i	$0.906548\pi$
$450$	−92.8491			−4.37695
$451$	−7.52738			−0.354450
$452$			40.6646i			1.91270i
$453$		−	37.8663i		−	1.77911i
$454$			18.9388i			0.888843i
$455$	−0.209312			−0.00981271
$456$		−	97.1638i		−	4.55011i
$457$	−28.4826			−1.33236			−0.666180	−	0.745791i	$-0.732072\pi$
$457$	−28.4826			−1.33236			−0.666180	+	0.745791i	$0.732072\pi$
$458$	−49.9822			−2.33552
$459$	−71.1084	−	11.5195i	−3.31906	−	0.537686i
$460$	−21.2313			−0.989916
$461$	20.0642			0.934485			0.467243	−	0.884129i	$-0.345247\pi$
$461$	20.0642			0.934485			0.467243	+	0.884129i	$0.345247\pi$
$462$		−	92.4762i		−	4.30238i
$463$	13.6164			0.632809			0.316404	−	0.948624i	$-0.397524\pi$
$463$	13.6164			0.632809			0.316404	+	0.948624i	$0.397524\pi$
$464$			45.1988i			2.09830i
$465$		−	5.22978i		−	0.242525i
$466$		−	13.2114i		−	0.612008i
$467$	18.9530			0.877039			0.438520	−	0.898722i	$-0.355503\pi$
$467$	18.9530			0.877039			0.438520	+	0.898722i	$0.355503\pi$
$468$	3.62369			0.167505
$469$			40.3007i			1.86091i
$470$			12.4429i			0.573948i
$471$			3.64069i			0.167754i
$472$	−43.3811			−1.99678
$473$		−	3.81272i		−	0.175309i
$474$	−78.7803			−3.61850
$475$	21.8230			1.00131
$476$	−50.9704	−	8.25718i	−2.33622	−	0.378467i
$477$	−35.5344			−1.62701
$478$	72.1512			3.30012
$479$			13.3107i			0.608180i	0.952643	+	0.304090i	$0.0983523\pi$
$479$			13.3107i			0.608180i	−0.952643	+	0.304090i	$0.901648\pi$
$480$	−9.60086			−0.438217
$481$		−	0.659702i		−	0.0300798i
$482$		−	67.8724i		−	3.09150i
$483$		−	64.9342i		−	2.95461i
$484$	−15.4257			−0.701170
$485$	−8.86376			−0.402483
$486$		−	153.851i		−	6.97880i
$487$		−	13.1125i		−	0.594185i	−0.954849	−	0.297093i	$-0.903983\pi$
$487$		−	13.1125i		−	0.594185i	0.954849	−	0.297093i	$-0.0960170\pi$
$488$			4.08020i			0.184702i
$489$	11.1175			0.502749
$490$			2.26307i			0.102235i
$491$	−2.74947			−0.124082			−0.0620409	−	0.998074i	$-0.519761\pi$
$491$	−2.74947			−0.124082			−0.0620409	+	0.998074i	$0.519761\pi$
$492$	−28.8386			−1.30014
$493$	−29.2024	−	4.73078i	−1.31521	−	0.213064i
$494$	−1.24226			−0.0558919
$495$	22.5848			1.01511
$496$			13.6450i			0.612678i
$497$	−17.7204			−0.794867
$498$			38.8361i			1.74029i
$499$		−	36.5260i		−	1.63513i	−0.575837	−	0.817564i	$-0.695324\pi$
$499$		−	36.5260i		−	1.63513i	0.575837	−	0.817564i	$-0.304676\pi$
$500$		−	29.8086i		−	1.33308i
$501$	−3.19342			−0.142671
$502$	−22.2421			−0.992711
$503$		−	15.5555i		−	0.693584i	−0.937942	−	0.346792i	$-0.887271\pi$
$503$		−	15.5555i		−	0.693584i	0.937942	−	0.346792i	$-0.112729\pi$
$504$		−	140.521i		−	6.25931i
$505$			5.99996i			0.266995i
$506$	−64.9338			−2.88666
$507$			43.5044i			1.93210i
$508$	−9.05943			−0.401947
$509$	3.08212			0.136613			0.0683064	−	0.997664i	$-0.478240\pi$
$509$	3.08212			0.136613			0.0683064	+	0.997664i	$0.478240\pi$
$510$	4.01523	−	24.7854i	0.177797	−	1.09752i
$511$	−2.52462			−0.111682
$512$	−49.9917			−2.20934
$513$			85.1006i			3.75728i
$514$	4.22177			0.186214
$515$		−	0.769629i		−	0.0339139i
$516$		−	14.6071i		−	0.643043i
$517$			26.0910i			1.14748i
$518$	−47.2486			−2.07598
$519$	−0.602639			−0.0264529
$520$			0.434183i			0.0190402i
$521$		−	37.6253i		−	1.64839i	−0.566303	−	0.824197i	$-0.691627\pi$
$521$		−	37.6253i		−	1.64839i	0.566303	−	0.824197i	$-0.308373\pi$
$522$		−	148.694i		−	6.50814i
$523$	−10.8705			−0.475334			−0.237667	−	0.971347i	$-0.576383\pi$
$523$	−10.8705			−0.475334			−0.237667	+	0.971347i	$0.576383\pi$
$524$			67.8856i			2.96560i
$525$	43.0845			1.88036
$526$	−1.89526			−0.0826372
$527$	−8.81586	−	1.42817i	−0.384025	−	0.0622119i
$528$	−80.4403			−3.50071
$529$	−22.5947			−0.982376
$530$		−	7.86358i		−	0.341572i
$531$	59.8455			2.59708
$532$			60.9999i			2.64468i
$533$			0.199633i			0.00864706i
$534$			144.473i			6.25198i
$535$	−10.6678			−0.461210
$536$	83.5969			3.61083
$537$			35.0921i			1.51434i
$538$		−	19.3996i		−	0.836377i
$539$			4.74534i			0.204396i
$540$	54.9341			2.36399
$541$			13.2387i			0.569178i	0.958650	+	0.284589i	$0.0918571\pi$
$541$			13.2387i			0.569178i	−0.958650	+	0.284589i	$0.908143\pi$
$542$	70.9216			3.04634
$543$	−14.0824			−0.604334
$544$	−2.62184	+	16.1842i	−0.112410	+	0.693892i
$545$	10.0528			0.430615
$546$	−2.45255			−0.104960
$547$			12.7546i			0.545348i	0.962107	+	0.272674i	$0.0879080\pi$
$547$			12.7546i			0.545348i	−0.962107	+	0.272674i	$0.912092\pi$
$548$	−82.7794			−3.53616
$549$		−	5.62876i		−	0.240230i
$550$		−	43.0842i		−	1.83712i
$551$			34.9486i			1.48886i
$552$	−134.695			−5.73299
$553$	26.7789			1.13875
$554$		−	36.5001i		−	1.55074i
$555$		−	15.7523i		−	0.668646i
$556$		−	56.5298i		−	2.39740i
$557$	15.4129			0.653067			0.326534	−	0.945186i	$-0.394119\pi$
$557$	15.4129			0.653067			0.326534	+	0.945186i	$0.394119\pi$
$558$		−	44.8889i		−	1.90030i
$559$	−0.101117			−0.00427678
$560$	13.0401			0.551043
$561$	8.41937	−	51.9715i	0.355466	−	2.19424i
$562$	23.2032			0.978767
$563$	−24.8074			−1.04551			−0.522755	−	0.852483i	$-0.675096\pi$
$563$	−24.8074			−1.04551			−0.522755	+	0.852483i	$0.675096\pi$
$564$			99.9587i			4.20902i
$565$	6.72156			0.282778
$566$			38.3647i			1.61259i
$567$			97.2329i			4.08340i
$568$			36.7579i			1.54233i
$569$	41.2649			1.72992			0.864958	−	0.501844i	$-0.167345\pi$
$569$	41.2649			1.72992			0.864958	+	0.501844i	$0.167345\pi$
$570$	−29.6625			−1.24243
$571$		−	15.5340i		−	0.650079i	−0.945700	−	0.325039i	$-0.894622\pi$
$571$		−	15.5340i		−	0.650079i	0.945700	−	0.325039i	$-0.105378\pi$
$572$			1.68148i			0.0703061i
$573$			73.6531i			3.07690i
$574$	14.2979			0.596784
$575$		−	30.2525i		−	1.26162i
$576$	21.1146			0.879774
$577$	−6.56703			−0.273389			−0.136695	−	0.990613i	$-0.543648\pi$
$577$	−6.56703			−0.273389			−0.136695	+	0.990613i	$0.543648\pi$
$578$	−40.6844	−	13.5370i	−1.69225	−	0.563064i
$579$	18.5892			0.772542
$580$	22.5600			0.936754
$581$		−	13.2011i		−	0.547674i
$582$	−103.858			−4.30507
$583$		−	16.4888i		−	0.682896i
$584$			5.23688i			0.216704i
$585$		−	0.598969i		−	0.0247643i
$586$	−55.4496			−2.29060
$587$	4.41271			0.182132			0.0910661	−	0.995845i	$-0.470973\pi$
$587$	4.41271			0.182132			0.0910661	+	0.995845i	$0.470973\pi$
$588$			18.1801i			0.749736i
$589$			10.5506i			0.434729i
$590$			13.2435i			0.545227i
$591$	−42.5819			−1.75159
$592$			41.0991i			1.68916i
$593$	−8.82880			−0.362556			−0.181278	−	0.983432i	$-0.558023\pi$
$593$	−8.82880			−0.362556			−0.181278	+	0.983432i	$0.558023\pi$
$594$	168.010			6.89354
$595$	−1.36485	+	8.42502i	−0.0559534	+	0.345392i
$596$	58.3216			2.38895
$597$	69.6603			2.85100
$598$			1.72210i			0.0704220i
$599$	34.6290			1.41490			0.707452	−	0.706761i	$-0.249845\pi$
$599$	34.6290			1.41490			0.707452	+	0.706761i	$0.249845\pi$
$600$		−	89.3714i		−	3.64857i
$601$		−	21.9325i		−	0.894644i	−0.894373	−	0.447322i	$-0.852378\pi$
$601$		−	21.9325i		−	0.894644i	0.894373	−	0.447322i	$-0.147622\pi$
$602$			7.24209i			0.295166i
$603$	−115.325			−4.69638
$604$	49.3123			2.00649
$605$			2.54976i			0.103663i
$606$			70.3027i			2.85585i
$607$		−	7.64001i		−	0.310098i	−0.987907	−	0.155049i	$-0.950446\pi$
$607$		−	7.64001i		−	0.310098i	0.987907	−	0.155049i	$-0.0495536\pi$
$608$	19.3688			0.785508
$609$			68.9978i			2.79593i
$610$	1.24562			0.0504336
$611$	0.691957			0.0279936
$612$	23.6288	−	145.857i	0.955136	−	5.89591i
$613$	22.1264			0.893676			0.446838	−	0.894615i	$-0.352550\pi$
$613$	22.1264			0.893676			0.446838	+	0.894615i	$0.352550\pi$
$614$	−82.0007			−3.30928
$615$			4.76680i			0.192216i
$616$	65.2052			2.62719
$617$		−	15.1512i		−	0.609965i	−0.952358	−	0.304983i	$-0.901349\pi$
$617$		−	15.1512i		−	0.609965i	0.952358	−	0.304983i	$-0.0986506\pi$
$618$		−	9.01789i		−	0.362753i
$619$			5.39840i			0.216980i	0.994098	+	0.108490i	$0.0346015\pi$
$619$			5.39840i			0.216980i	−0.994098	+	0.108490i	$0.965398\pi$
$620$	6.81061			0.273521
$621$	117.972			4.73405
$622$			80.8418i			3.24146i
$623$		−	49.1092i		−	1.96752i
$624$			2.13335i			0.0854023i
$625$	17.4742			0.698969
$626$			0.857093i			0.0342563i
$627$	−62.1980			−2.48395
$628$	−4.74117			−0.189193
$629$	−26.5536	−	4.30168i	−1.05876	−	0.171519i
$630$	−42.8988			−1.70913
$631$	−27.9969			−1.11454			−0.557269	−	0.830332i	$-0.688151\pi$
$631$	−27.9969			−1.11454			−0.557269	+	0.830332i	$0.688151\pi$
$632$		−	55.5482i		−	2.20959i
$633$	−41.0669			−1.63226
$634$		−	4.58501i		−	0.182094i
$635$			1.49746i			0.0594248i
$636$		−	63.1712i		−	2.50490i
$637$	0.125851			0.00498638
$638$	68.9974			2.73163
$639$		−	50.7086i		−	2.00600i
$640$			10.4059i			0.411330i
$641$		−	19.8781i		−	0.785138i	−0.919722	−	0.392569i	$-0.871586\pi$
$641$		−	19.8781i		−	0.785138i	0.919722	−	0.392569i	$-0.128414\pi$
$642$	−124.997			−4.93323
$643$			29.8673i			1.17785i	0.808188	+	0.588925i	$0.200449\pi$
$643$			29.8673i			1.17785i	−0.808188	+	0.588925i	$0.799551\pi$
$644$	84.5620			3.33221
$645$	−2.41445			−0.0950689
$646$	−8.10033	+	50.0021i	−0.318703	+	1.96731i
$647$	−4.90933			−0.193006			−0.0965029	−	0.995333i	$-0.530766\pi$
$647$	−4.90933			−0.193006			−0.0965029	+	0.995333i	$0.530766\pi$
$648$	201.693			7.92325
$649$			27.7698i			1.09006i
$650$	−1.14263			−0.0448177
$651$			20.8296i			0.816378i
$652$			14.4780i			0.567001i
$653$		−	33.0674i		−	1.29403i	−0.762479	−	0.647013i	$-0.776018\pi$
$653$		−	33.0674i		−	1.29403i	0.762479	−	0.647013i	$-0.223982\pi$
$654$	117.791			4.60597
$655$	11.2210			0.438440
$656$		−	12.4370i		−	0.485584i
$657$		−	7.22445i		−	0.281853i
$658$		−	49.5587i		−	1.93200i
$659$	−10.5877			−0.412439			−0.206220	−	0.978506i	$-0.566116\pi$
$659$	−10.5877			−0.412439			−0.206220	+	0.978506i	$0.566116\pi$
$660$			40.1501i			1.56284i
$661$	29.3246			1.14059			0.570297	−	0.821438i	$-0.306828\pi$
$661$	29.3246			1.14059			0.570297	+	0.821438i	$0.306828\pi$
$662$	58.4001			2.26979
$663$	−1.37833	−	0.223289i	−0.0535299	−	0.00867183i
$664$	−27.3834			−1.06268
$665$	10.0828			0.390995
$666$		−	135.207i		−	5.23915i
$667$	48.4480			1.87592
$668$		−	4.15870i		−	0.160905i
$669$		−	28.6800i		−	1.10883i
$670$		−	25.5207i		−	0.985952i
$671$	2.61188			0.100831
$672$	38.2392			1.47511
$673$			22.6774i			0.874150i	0.899425	+	0.437075i	$0.143985\pi$
$673$			22.6774i			0.874150i	−0.899425	+	0.437075i	$0.856015\pi$
$674$			19.7196i			0.759569i
$675$			78.2756i			3.01283i
$676$	−56.6546			−2.17902
$677$			19.4162i			0.746226i	0.927786	+	0.373113i	$0.121710\pi$
$677$			19.4162i			0.746226i	−0.927786	+	0.373113i	$0.878290\pi$
$678$	78.7578			3.02467
$679$	35.3034			1.35482
$680$	17.4763	+	2.83115i	0.670184	+	0.108570i
$681$	25.1481			0.963678
$682$	20.8295			0.797603
$683$		−	48.3208i		−	1.84895i	−0.381248	−	0.924473i	$-0.624506\pi$
$683$		−	48.3208i		−	1.84895i	0.381248	−	0.924473i	$-0.375494\pi$
$684$	−174.557			−6.67437
$685$			13.6828i			0.522794i
$686$			41.6811i			1.59139i
$687$			66.3694i			2.53215i
$688$	6.29952			0.240167
$689$	−0.437298			−0.0166597
$690$			41.1201i			1.56542i
$691$			33.3663i			1.26931i	0.772794	+	0.634657i	$0.218858\pi$
$691$			33.3663i			1.26931i	−0.772794	+	0.634657i	$0.781142\pi$
$692$		−	0.784800i		−	0.0298336i
$693$	−89.9526			−3.41702
$694$			12.6830i			0.481441i
$695$	−9.34396			−0.354437
$696$	143.124			5.42511
$697$	8.03541	+	1.30173i	0.304363	+	0.0493067i
$698$	−34.0823			−1.29004
$699$	−17.5429			−0.663535
$700$			56.1078i			2.12068i
$701$	−27.4742			−1.03769			−0.518843	−	0.854869i	$-0.673637\pi$
$701$	−27.4742			−1.03769			−0.518843	+	0.854869i	$0.673637\pi$
$702$		−	4.45578i		−	0.168173i
$703$			31.7786i			1.19855i
$704$			9.79767i			0.369264i
$705$	16.5224			0.622271
$706$	−21.7082			−0.816999
$707$		−	23.8972i		−	0.898746i
$708$			106.390i			3.99840i
$709$			11.0377i			0.414530i	0.978285	+	0.207265i	$0.0664563\pi$
$709$			11.0377i			0.414530i	−0.978285	+	0.207265i	$0.933544\pi$
$710$	11.2216			0.421138
$711$			76.6305i			2.87387i
$712$	−101.869			−3.81769
$713$	14.6259			0.547744
$714$	−15.9922	+	98.7176i	−0.598494	+	3.69441i
$715$	0.277936			0.0103942
$716$	−45.6996			−1.70787
$717$		−	95.8067i		−	3.57797i
$718$	35.8531			1.33803
$719$		−	36.6075i		−	1.36523i	−0.730779	−	0.682614i	$-0.760843\pi$
$719$		−	36.6075i		−	1.36523i	0.730779	−	0.682614i	$-0.239157\pi$
$720$			37.3154i			1.39066i
$721$			3.06535i			0.114159i
$722$	11.9194			0.443594
$723$	−90.1251			−3.35179
$724$		−	18.3391i		−	0.681569i
$725$			32.1458i			1.19386i
$726$			29.8760i			1.10880i
$727$	18.4933			0.685880			0.342940	−	0.939357i	$-0.388577\pi$
$727$	18.4933			0.685880			0.342940	+	0.939357i	$0.388577\pi$
$728$		−	1.72930i		−	0.0640921i
$729$	−102.702			−3.80379
$730$	1.59873			0.0591718
$731$	−0.659346	+	4.07004i	−0.0243868	+	0.150536i
$732$	10.0065			0.369852
$733$	−47.4106			−1.75115			−0.875575	−	0.483083i	$-0.839517\pi$
$733$	−47.4106			−1.75115			−0.875575	+	0.483083i	$0.839517\pi$
$734$		−	59.0369i		−	2.17909i
$735$	3.00504			0.110843
$736$		−	26.8503i		−	0.989715i
$737$		−	53.5134i		−	1.97119i
$738$			40.9150i			1.50610i
$739$	−8.01244			−0.294742			−0.147371	−	0.989081i	$-0.547081\pi$
$739$	−8.01244			−0.294742			−0.147371	+	0.989081i	$0.547081\pi$
$740$	20.5138			0.754101
$741$			1.64955i			0.0605976i
$742$			31.3198i			1.14978i
$743$		−	2.56815i		−	0.0942163i	−0.998890	−	0.0471081i	$-0.984999\pi$
$743$		−	2.56815i		−	0.0942163i	0.998890	−	0.0471081i	$-0.0150005\pi$
$744$	43.2075			1.58406
$745$		−	9.64013i		−	0.353187i
$746$	34.8622			1.27639
$747$	37.7763			1.38216
$748$	67.6811	+	10.9643i	2.47467	+	0.400895i
$749$	42.4887			1.55250
$750$	−57.7322			−2.10808
$751$			25.7795i			0.940707i	0.882478	+	0.470353i	$0.155873\pi$
$751$			25.7795i			0.940707i	−0.882478	+	0.470353i	$0.844127\pi$
$752$	−43.1086			−1.57201
$753$			29.5343i			1.07629i
$754$		−	1.82987i		−	0.0666401i
$755$		−	8.15096i		−	0.296644i
$756$	−218.797			−7.95755
$757$	13.1611			0.478347			0.239173	−	0.970977i	$-0.423124\pi$
$757$	13.1611			0.478347			0.239173	+	0.970977i	$0.423124\pi$
$758$		−	4.28336i		−	0.155579i
$759$			86.2230i			3.12970i
$760$		−	20.9151i		−	0.758670i
$761$	0.0705362			0.00255693			0.00127847	−	0.999999i	$-0.499593\pi$
$761$	0.0705362			0.00255693			0.00127847	+	0.999999i	$0.499593\pi$
$762$			17.5460i			0.635624i
$763$	−40.0392			−1.44952
$764$	−95.9165			−3.47014
$765$	−24.1091	−	3.90566i	−0.871665	−	0.141209i
$766$	22.5614			0.815175
$767$	0.736480			0.0265927
$768$			104.715i			3.77859i
$769$	−14.5207			−0.523630			−0.261815	−	0.965118i	$-0.584321\pi$
$769$	−14.5207			−0.523630			−0.261815	+	0.965118i	$0.584321\pi$
$770$		−	19.9061i		−	0.717365i
$771$		−	5.60592i		−	0.201892i
$772$			24.2083i			0.871274i
$773$	19.0866			0.686498			0.343249	−	0.939244i	$-0.388473\pi$
$773$	19.0866			0.686498			0.343249	+	0.939244i	$0.388473\pi$
$774$	−20.7240			−0.744908
$775$			9.70443i			0.348594i
$776$		−	73.2308i		−	2.62883i
$777$			62.7395i			2.25077i
$778$	83.4658			2.99239
$779$		−	9.61655i		−	0.344549i
$780$	1.06482			0.0381265
$781$	23.5300			0.841970
$782$	69.3163	+	11.2292i	2.47874	+	0.401556i
$783$	−125.355			−4.47982
$784$	−7.84043			−0.280015
$785$			0.783680i			0.0279707i
$786$	131.478			4.68968
$787$		−	2.49646i		−	0.0889892i	−0.999010	−	0.0444946i	$-0.985832\pi$
$787$		−	2.49646i		−	0.0889892i	0.999010	−	0.0444946i	$-0.0141677\pi$
$788$		−	55.4533i		−	1.97544i
$789$			2.51664i			0.0895947i
$790$	−16.9579			−0.603337
$791$	−26.7712			−0.951875
$792$			186.591i			6.63023i
$793$		−	0.0692695i		−	0.00245983i
$794$		−	4.68782i		−	0.166365i
$795$	−10.4417			−0.370330
$796$			90.7167i			3.21537i
$797$	−41.7732			−1.47968			−0.739841	−	0.672781i	$-0.765100\pi$
$797$	−41.7732			−1.47968			−0.739841	+	0.672781i	$0.765100\pi$
$798$	118.142			4.18220
$799$	4.51200	−	27.8519i	0.159623	−	0.985330i
$800$	17.8154			0.629871
$801$	140.531			4.96542
$802$		−	21.0145i		−	0.742046i
$803$	3.35232			0.118301
$804$		−	205.018i		−	7.23043i
$805$		−	13.9775i		−	0.492641i
$806$		−	0.552418i		−	0.0194581i
$807$	−25.7600			−0.906794
$808$	−49.5706			−1.74389
$809$			28.9274i			1.01703i	0.861052	+	0.508516i	$0.169806\pi$
$809$			28.9274i			1.01703i	−0.861052	+	0.508516i	$0.830194\pi$
$810$		−	61.5735i		−	2.16347i
$811$		−	34.4765i		−	1.21063i	−0.795985	−	0.605317i	$-0.793046\pi$
$811$		−	34.4765i		−	1.21063i	0.795985	−	0.605317i	$-0.206954\pi$
$812$	−89.8540			−3.15326
$813$		−	94.1739i		−	3.30282i
$814$	62.7391			2.19900
$815$	2.39310			0.0838266
$816$	85.8693	+	13.9108i	3.00603	+	0.486976i
$817$	4.87091			0.170412
$818$	78.2280			2.73518
$819$			2.38562i			0.0833605i
$820$	−6.20768			−0.216782
$821$		−	10.1289i		−	0.353501i	−0.984256	−	0.176750i	$-0.943441\pi$
$821$		−	10.1289i		−	0.353501i	0.984256	−	0.176750i	$-0.0565585\pi$
$822$			160.324i			5.59195i
$823$			22.0196i			0.767554i	0.923426	+	0.383777i	$0.125377\pi$
$823$			22.0196i			0.767554i	−0.923426	+	0.383777i	$0.874623\pi$
$824$	6.35854			0.221510
$825$	−57.2098			−1.99179
$826$		−	52.7475i		−	1.83532i
$827$		−	29.9244i		−	1.04057i	−0.853991	−	0.520287i	$-0.825825\pi$
$827$		−	29.9244i		−	1.04057i	0.853991	−	0.520287i	$-0.174175\pi$
$828$			241.983i			8.40949i
$829$	6.94740			0.241293			0.120647	−	0.992696i	$-0.461503\pi$
$829$	6.94740			0.241293			0.120647	+	0.992696i	$0.461503\pi$
$830$			8.35971i			0.290170i
$831$	−48.4671			−1.68130
$832$	0.259843			0.00900844
$833$	0.820627	−	5.06561i	0.0284330	−	0.175513i
$834$	−109.485			−3.79115
$835$	−0.687403			−0.0237886
$836$		−	80.9988i		−	2.80140i
$837$	−37.8432			−1.30805
$838$			62.7097i			2.16627i
$839$		−	17.9342i		−	0.619156i	−0.950874	−	0.309578i	$-0.899812\pi$
$839$		−	17.9342i		−	0.619156i	0.950874	−	0.309578i	$-0.100188\pi$
$840$		−	41.2920i		−	1.42471i
$841$	−22.4800			−0.775171
$842$	24.6625			0.849926
$843$		−	30.8106i		−	1.06117i
$844$		−	53.4803i		−	1.84087i
$845$			9.36458i			0.322151i
$846$	141.817			4.87578
$847$		−	10.1554i		−	0.348944i
$848$	27.2434			0.935544
$849$	50.9430			1.74836
$850$	−7.45070	+	45.9921i	−0.255557	+	1.57751i
$851$	44.0536			1.51014
$852$	90.1473			3.08839
$853$		−	2.11182i		−	0.0723074i	−0.999346	−	0.0361537i	$-0.988489\pi$
$853$		−	2.11182i		−	0.0723074i	0.999346	−	0.0361537i	$-0.0115106\pi$
$854$	−4.96116			−0.169767
$855$			28.8530i			0.986753i
$856$		−	88.1356i		−	3.01241i
$857$			2.78752i			0.0952197i	0.998866	+	0.0476099i	$0.0151604\pi$
$857$			2.78752i			0.0952197i	−0.998866	+	0.0476099i	$0.984840\pi$
$858$	3.25663			0.111179
$859$	37.6640			1.28508			0.642539	−	0.766253i	$-0.277881\pi$
$859$	37.6640			1.28508			0.642539	+	0.766253i	$0.277881\pi$
$860$		−	3.14427i		−	0.107219i
$861$		−	18.9856i		−	0.647029i
$862$		−	71.1440i		−	2.42317i
$863$	58.1271			1.97867			0.989334	−	0.145665i	$-0.0465321\pi$
$863$	58.1271			1.97867			0.989334	+	0.145665i	$0.0465321\pi$
$864$			69.4727i			2.36351i
$865$	−0.129722			−0.00441067
$866$	−73.1779			−2.48668
$867$	−17.9752	+	54.0231i	−0.610470	+	1.83472i
$868$	−27.1259			−0.920713
$869$	−35.5584			−1.20624
$870$		−	43.6934i		−	1.48135i
$871$	−1.41922			−0.0480885
$872$			83.0544i			2.81258i
$873$			101.024i			3.41915i
$874$		−	82.9557i		−	2.80602i
$875$	19.6242			0.663420
$876$	12.8433			0.433934
$877$			52.8544i			1.78477i	0.451278	+	0.892384i	$0.350968\pi$
$877$			52.8544i			1.78477i	−0.451278	+	0.892384i	$0.649032\pi$
$878$			20.3763i			0.687667i
$879$			73.6293i			2.48346i
$880$	−17.3153			−0.583697
$881$		−	24.8218i		−	0.836268i	−0.908385	−	0.418134i	$-0.862684\pi$
$881$		−	24.8218i		−	0.836268i	0.908385	−	0.418134i	$-0.137316\pi$
$882$	25.7932			0.868502
$883$	46.0566			1.54993			0.774964	−	0.632005i	$-0.217768\pi$
$883$	46.0566			1.54993			0.774964	+	0.632005i	$0.217768\pi$
$884$	0.290784	−	1.79496i	0.00978011	−	0.0603712i
$885$	17.5855			0.591132
$886$	23.2509			0.781130
$887$		−	36.4203i		−	1.22287i	−0.791293	−	0.611437i	$-0.790592\pi$
$887$		−	36.4203i		−	1.22287i	0.791293	−	0.611437i	$-0.209408\pi$
$888$	130.142			4.36729
$889$		−	5.96420i		−	0.200033i
$890$			31.0988i			1.04243i
$891$		−	129.111i		−	4.32538i
$892$	37.3492			1.25054
$893$	−33.3324			−1.11543
$894$		−	112.955i		−	3.77779i
$895$			7.55380i			0.252496i
$896$		−	41.4456i		−	1.38460i
$897$	2.28671			0.0763511
$898$			30.9324i			1.03223i
$899$	−15.5412			−0.518328
$900$	−160.558			−5.35194
$901$	−2.85146	+	17.6017i	−0.0949960	+	0.586396i
$902$	−18.9855			−0.632149
$903$	9.61648			0.320017
$904$			55.5323i			1.84698i
$905$	−3.03132			−0.100765
$906$		−	95.5063i		−	3.17298i
$907$			41.3058i			1.37154i	0.727821	+	0.685768i	$0.240533\pi$
$907$			41.3058i			1.37154i	−0.727821	+	0.685768i	$0.759467\pi$
$908$			32.7497i			1.08684i
$909$	68.3842			2.26816
$910$	−0.527927			−0.0175006
$911$			31.6662i			1.04915i	0.851365	+	0.524574i	$0.175776\pi$
$911$			31.6662i			1.04915i	−0.851365	+	0.524574i	$0.824224\pi$
$912$		−	102.766i		−	3.40292i
$913$			17.5291i			0.580129i
$914$	−71.8387			−2.37621
$915$		−	1.65401i		−	0.0546798i
$916$	−86.4311			−2.85577
$917$	−44.6920			−1.47586
$918$	−179.349	−	29.0546i	−5.91942	−	0.958944i
$919$	−22.0368			−0.726927			−0.363464	−	0.931608i	$-0.618406\pi$
$919$	−22.0368			−0.726927			−0.363464	+	0.931608i	$0.618406\pi$
$920$	−28.9939			−0.955900
$921$			108.885i			3.58790i
$922$	50.6060			1.66662
$923$		−	0.624038i		−	0.0205404i
$924$		−	159.913i		−	5.26076i
$925$			29.2300i			0.961078i
$926$	34.3433			1.12859
$927$	−8.77180			−0.288104
$928$			28.5306i			0.936563i
$929$			26.2521i			0.861304i	0.902518	+	0.430652i	$0.141716\pi$
$929$			26.2521i			0.861304i	−0.902518	+	0.430652i	$0.858284\pi$
$930$		−	13.1905i		−	0.432535i
$931$	−6.06237			−0.198686
$932$		−	22.8457i		−	0.748336i
$933$	107.347			3.51437
$934$	47.8031			1.56417
$935$	1.81232	−	11.1872i	0.0592692	−	0.365860i
$936$	4.94857			0.161749
$937$	−0.709524			−0.0231792			−0.0115896	−	0.999933i	$-0.503689\pi$
$937$	−0.709524			−0.0231792			−0.0115896	+	0.999933i	$0.503689\pi$
$938$			101.646i			3.31887i
$939$	1.13810			0.0371405
$940$			21.5167i			0.701798i
$941$			49.7038i			1.62030i	0.586224	+	0.810149i	$0.300614\pi$
$941$			49.7038i			1.62030i	−0.586224	+	0.810149i	$0.699386\pi$
$942$			9.18253i			0.299183i
$943$	−13.3311			−0.434120
$944$	−45.8823			−1.49334
$945$			36.1654i			1.17646i
$946$		−	9.61642i		−	0.312657i
$947$		−	29.2420i		−	0.950237i	−0.879922	−	0.475119i	$-0.842405\pi$
$947$		−	29.2420i		−	0.950237i	0.879922	−	0.475119i	$-0.157595\pi$
$948$	−136.230			−4.42454
$949$		−	0.0889065i		−	0.00288603i
$950$	55.0420			1.78580
$951$	−6.08825			−0.197425
$952$	−69.6060	−	11.2762i	−2.25594	−	0.365462i
$953$	18.8616			0.610987			0.305494	−	0.952194i	$-0.401179\pi$
$953$	18.8616			0.610987			0.305494	+	0.952194i	$0.401179\pi$
$954$	−89.6247			−2.90171
$955$			15.8543i			0.513033i
$956$	124.766			4.03524
$957$		−	91.6189i		−	2.96162i
$958$			33.5721i			1.08467i
$959$		−	54.4972i		−	1.75981i
$960$	6.20449			0.200249
$961$	26.3083			0.848655
$962$		−	1.66390i		−	0.0536462i
$963$			121.586i			3.91805i
$964$		−	117.367i		−	3.78015i
$965$	4.00144			0.128811
$966$		−	163.777i		−	5.26943i
$967$	−31.8557			−1.02441			−0.512205	−	0.858863i	$-0.671171\pi$
$967$	−31.8557			−1.02441			−0.512205	+	0.858863i	$0.671171\pi$
$968$	−21.0657			−0.677076
$969$	66.3959	+	10.7561i	2.13294	+	0.345536i
$970$	−22.3562			−0.717813
$971$	55.8883			1.79354			0.896771	−	0.442495i	$-0.145907\pi$
$971$	55.8883			1.79354			0.896771	+	0.442495i	$0.145907\pi$
$972$		−	266.044i		−	8.53337i
$973$	37.2159			1.19309
$974$		−	33.0724i		−	1.05971i
$975$			1.51726i			0.0485911i
$976$			4.31545i			0.138134i
$977$	−17.6258			−0.563901			−0.281950	−	0.959429i	$-0.590981\pi$
$977$	−17.6258			−0.563901			−0.281950	+	0.959429i	$0.590981\pi$
$978$	28.0404			0.896633
$979$			65.2097i			2.08411i
$980$			3.91339i			0.125009i
$981$		−	114.576i		−	3.65814i
$982$	−6.93470			−0.221295
$983$		−	23.6606i		−	0.754656i	−0.926080	−	0.377328i	$-0.876843\pi$
$983$		−	23.6606i		−	0.754656i	0.926080	−	0.377328i	$-0.123157\pi$
$984$	−39.3825			−1.25547
$985$	−9.16602			−0.292054
$986$	−73.6542	−	11.9320i	−2.34563	−	0.379991i
$987$	−65.8070			−2.09466
$988$	−2.14816			−0.0683421
$989$		−	6.75238i		−	0.214713i
$990$	56.9632			1.81041
$991$		−	2.27096i		−	0.0721394i	−0.999349	−	0.0360697i	$-0.988516\pi$
$991$		−	2.27096i		−	0.0721394i	0.999349	−	0.0360697i	$-0.0114838\pi$
$992$			8.61306i			0.273465i
$993$		−	77.5472i		−	2.46089i
$994$	−44.6942			−1.41762
$995$	14.9948			0.475367
$996$			67.1568i			2.12795i
$997$		−	40.9774i		−	1.29777i	−0.760887	−	0.648884i	$-0.775236\pi$
$997$		−	40.9774i		−	1.29777i	0.760887	−	0.648884i	$-0.224764\pi$
$998$		−	92.1258i		−	2.91619i
$999$	−113.985			−3.60632

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.d.c.560.17	✓	20
17.16	even	2	inner	731.2.d.c.560.18	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.d.c.560.17	✓	20	1.1	even	1	trivial
731.2.d.c.560.18	yes	20	17.16	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.52220 q^{2} -3.34912i q^{3} +4.36148 q^{4} -0.720920i q^{5} -8.44715i q^{6} +2.87134i q^{7} +5.95611 q^{8} -8.21664 q^{9} +O(q^{10})\)	\(q+2.52220 q^{2} -3.34912i q^{3} +4.36148 q^{4} -0.720920i q^{5} -8.44715i q^{6} +2.87134i q^{7} +5.95611 q^{8} -8.21664 q^{9} -1.81830i q^{10} -3.81272i q^{11} -14.6071i q^{12} -0.101117 q^{13} +7.24209i q^{14} -2.41445 q^{15} +6.29952 q^{16} +(-0.659346 + 4.07004i) q^{17} -20.7240 q^{18} +4.87091 q^{19} -3.14427i q^{20} +9.61648 q^{21} -9.61642i q^{22} -6.75238i q^{23} -19.9477i q^{24} +4.48027 q^{25} -0.255036 q^{26} +17.4712i q^{27} +12.5233i q^{28} +7.17495i q^{29} -6.08972 q^{30} +2.16604i q^{31} +3.97642 q^{32} -12.7693 q^{33} +(-1.66300 + 10.2655i) q^{34} +2.07001 q^{35} -35.8367 q^{36} +6.52416i q^{37} +12.2854 q^{38} +0.338653i q^{39} -4.29387i q^{40} -1.97428i q^{41} +24.2547 q^{42} +1.00000 q^{43} -16.6291i q^{44} +5.92354i q^{45} -17.0308i q^{46} -6.84315 q^{47} -21.0979i q^{48} -1.24461 q^{49} +11.3001 q^{50} +(13.6311 + 2.20823i) q^{51} -0.441018 q^{52} +4.32468 q^{53} +44.0657i q^{54} -2.74866 q^{55} +17.1020i q^{56} -16.3133i q^{57} +18.0966i q^{58} -7.28346 q^{59} -10.5306 q^{60} +0.685045i q^{61} +5.46317i q^{62} -23.5928i q^{63} -2.56973 q^{64} +0.0728970i q^{65} -32.2066 q^{66} +14.0355 q^{67} +(-2.87572 + 17.7514i) q^{68} -22.6146 q^{69} +5.22097 q^{70} +6.17146i q^{71} -48.9392 q^{72} +0.879246i q^{73} +16.4552i q^{74} -15.0050i q^{75} +21.2444 q^{76} +10.9476 q^{77} +0.854148i q^{78} -9.32626i q^{79} -4.54145i q^{80} +33.8632 q^{81} -4.97952i q^{82} -4.59754 q^{83} +41.9421 q^{84} +(2.93418 + 0.475336i) q^{85} +2.52220 q^{86} +24.0298 q^{87} -22.7090i q^{88} -17.1032 q^{89} +14.9403i q^{90} -0.290341i q^{91} -29.4503i q^{92} +7.25432 q^{93} -17.2598 q^{94} -3.51154i q^{95} -13.3175i q^{96} -12.2951i q^{97} -3.13914 q^{98} +31.3277i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 42 q^{4} + 18 q^{8} - 18 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 42 * q^4 + 18 * q^8 - 18 * q^9	\( 20 q + 2 q^{2} + 42 q^{4} + 18 q^{8} - 18 q^{9} - 4 q^{13} + 26 q^{15} + 6 q^{16} + 16 q^{17} - 22 q^{18} - 4 q^{19} + 20 q^{21} - 2 q^{25} + 22 q^{26} - 72 q^{30} + 38 q^{32} - 12 q^{33} + 12 q^{34} - 30 q^{35} - 104 q^{36} - 22 q^{38} + 26 q^{42} + 20 q^{43} - 34 q^{47} + 22 q^{49} + 42 q^{50} + 52 q^{51} - 110 q^{52} + 14 q^{53} + 12 q^{55} + 20 q^{59} + 42 q^{60} - 22 q^{64} + 50 q^{66} - 12 q^{67} + 50 q^{68} - 82 q^{69} - 30 q^{70} - 50 q^{72} + 2 q^{76} + 78 q^{77} + 44 q^{81} + 20 q^{83} + 62 q^{84} + 76 q^{85} + 2 q^{86} + 12 q^{87} - 46 q^{89} + 58 q^{93} - 18 q^{94} - 62 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 42 * q^4 + 18 * q^8 - 18 * q^9 - 4 * q^13 + 26 * q^15 + 6 * q^16 + 16 * q^17 - 22 * q^18 - 4 * q^19 + 20 * q^21 - 2 * q^25 + 22 * q^26 - 72 * q^30 + 38 * q^32 - 12 * q^33 + 12 * q^34 - 30 * q^35 - 104 * q^36 - 22 * q^38 + 26 * q^42 + 20 * q^43 - 34 * q^47 + 22 * q^49 + 42 * q^50 + 52 * q^51 - 110 * q^52 + 14 * q^53 + 12 * q^55 + 20 * q^59 + 42 * q^60 - 22 * q^64 + 50 * q^66 - 12 * q^67 + 50 * q^68 - 82 * q^69 - 30 * q^70 - 50 * q^72 + 2 * q^76 + 78 * q^77 + 44 * q^81 + 20 * q^83 + 62 * q^84 + 76 * q^85 + 2 * q^86 + 12 * q^87 - 46 * q^89 + 58 * q^93 - 18 * q^94 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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