LMFDB - Embedded newform 731.2.d.c.560.1

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			560.1
Root			$-1.20836i$ of defining polynomial
Character	$\chi$	$=$	731.560
Dual form			731.2.d.c.560.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35369 q^{2} -1.62169i q^{3} +3.53987 q^{4} -0.259122i q^{5} +3.81697i q^{6} -1.04097i q^{7} -3.62439 q^{8} +0.370107 q^{9} +O(q^{10})$	\(q-2.35369 q^{2} -1.62169i q^{3} +3.53987 q^{4} -0.259122i q^{5} +3.81697i q^{6} -1.04097i q^{7} -3.62439 q^{8} +0.370107 q^{9} +0.609893i q^{10} -3.29289i q^{11} -5.74059i q^{12} -0.845057 q^{13} +2.45011i q^{14} -0.420216 q^{15} +1.45095 q^{16} +(-3.66913 + 1.88082i) q^{17} -0.871119 q^{18} +2.70123 q^{19} -0.917258i q^{20} -1.68813 q^{21} +7.75045i q^{22} -3.45542i q^{23} +5.87765i q^{24} +4.93286 q^{25} +1.98901 q^{26} -5.46528i q^{27} -3.68488i q^{28} -6.17840i q^{29} +0.989060 q^{30} -4.24082i q^{31} +3.83368 q^{32} -5.34006 q^{33} +(8.63601 - 4.42686i) q^{34} -0.269737 q^{35} +1.31013 q^{36} +7.67893i q^{37} -6.35786 q^{38} +1.37042i q^{39} +0.939157i q^{40} +3.87669i q^{41} +3.97333 q^{42} +1.00000 q^{43} -11.6564i q^{44} -0.0959028i q^{45} +8.13300i q^{46} -3.53679 q^{47} -2.35300i q^{48} +5.91639 q^{49} -11.6104 q^{50} +(3.05011 + 5.95021i) q^{51} -2.99140 q^{52} -12.0025 q^{53} +12.8636i q^{54} -0.853259 q^{55} +3.77286i q^{56} -4.38056i q^{57} +14.5421i q^{58} -1.58575 q^{59} -1.48751 q^{60} -4.40881i q^{61} +9.98158i q^{62} -0.385269i q^{63} -11.9252 q^{64} +0.218973i q^{65} +12.5689 q^{66} -9.54045 q^{67} +(-12.9883 + 6.65785i) q^{68} -5.60364 q^{69} +0.634878 q^{70} -13.8561i q^{71} -1.34141 q^{72} -3.06103i q^{73} -18.0739i q^{74} -7.99958i q^{75} +9.56200 q^{76} -3.42778 q^{77} -3.22556i q^{78} -0.391325i q^{79} -0.375973i q^{80} -7.75270 q^{81} -9.12454i q^{82} -1.93729 q^{83} -5.97576 q^{84} +(0.487360 + 0.950752i) q^{85} -2.35369 q^{86} -10.0195 q^{87} +11.9347i q^{88} -8.91762 q^{89} +0.225726i q^{90} +0.879675i q^{91} -12.2318i q^{92} -6.87731 q^{93} +8.32452 q^{94} -0.699946i q^{95} -6.21706i q^{96} +1.22584i q^{97} -13.9254 q^{98} -1.21872i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.35369			−1.66431			−0.832156	−	0.554541i	$-0.812894\pi$
$2$	−2.35369			−1.66431			−0.832156	+	0.554541i	$0.812894\pi$
$3$		−	1.62169i		−	0.936286i	−0.883653	−	0.468143i	$-0.844923\pi$
$3$		−	1.62169i		−	0.936286i	0.883653	−	0.468143i	$-0.155077\pi$
$4$	3.53987			1.76994
$5$		−	0.259122i		−	0.115883i	−0.998320	−	0.0579414i	$-0.981546\pi$
$5$		−	0.259122i		−	0.115883i	0.998320	−	0.0579414i	$-0.0184536\pi$
$6$			3.81697i			1.55827i
$7$		−	1.04097i		−	0.393448i	−0.980459	−	0.196724i	$-0.936970\pi$
$7$		−	1.04097i		−	0.393448i	0.980459	−	0.196724i	$-0.0630303\pi$
$8$	−3.62439			−1.28141
$9$	0.370107			0.123369
$10$			0.609893i			0.192865i
$11$		−	3.29289i		−	0.992844i	−0.868081	−	0.496422i	$-0.834647\pi$
$11$		−	3.29289i		−	0.992844i	0.868081	−	0.496422i	$-0.165353\pi$
$12$		−	5.74059i		−	1.65717i
$13$	−0.845057			−0.234377			−0.117188	−	0.993110i	$-0.537388\pi$
$13$	−0.845057			−0.234377			−0.117188	+	0.993110i	$0.537388\pi$
$14$			2.45011i			0.654820i
$15$	−0.420216			−0.108499
$16$	1.45095			0.362738
$17$	−3.66913	+	1.88082i	−0.889895	+	0.456165i
$17$	−3.66913	+	1.88082i	−0.889895	+	0.456165i
$18$	−0.871119			−0.205325
$19$	2.70123			0.619704			0.309852	−	0.950785i	$-0.399721\pi$
$19$	2.70123			0.619704			0.309852	+	0.950785i	$0.399721\pi$
$20$		−	0.917258i		−	0.205105i
$21$	−1.68813			−0.368380
$22$			7.75045i			1.65240i
$23$		−	3.45542i		−	0.720505i	−0.932855	−	0.360253i	$-0.882690\pi$
$23$		−	3.45542i		−	0.720505i	0.932855	−	0.360253i	$-0.117310\pi$
$24$			5.87765i			1.19977i
$25$	4.93286			0.986571
$26$	1.98901			0.390076
$27$		−	5.46528i		−	1.05179i
$28$		−	3.68488i		−	0.696378i
$29$		−	6.17840i		−	1.14730i	−0.819100	−	0.573650i	$-0.805527\pi$
$29$		−	6.17840i		−	1.14730i	0.819100	−	0.573650i	$-0.194473\pi$
$30$	0.989060			0.180577
$31$		−	4.24082i		−	0.761673i	−0.924642	−	0.380837i	$-0.875636\pi$
$31$		−	4.24082i		−	0.761673i	0.924642	−	0.380837i	$-0.124364\pi$
$32$	3.83368			0.677705
$33$	−5.34006			−0.929585
$34$	8.63601	−	4.42686i	1.48106	−	0.759201i
$35$	−0.269737			−0.0455938
$36$	1.31013			0.218355
$37$			7.67893i			1.26241i	0.775616	+	0.631205i	$0.217439\pi$
$37$			7.67893i			1.26241i	−0.775616	+	0.631205i	$0.782561\pi$
$38$	−6.35786			−1.03138
$39$			1.37042i			0.219444i
$40$			0.939157i			0.148494i
$41$			3.87669i			0.605437i	0.953080	+	0.302719i	$0.0978943\pi$
$41$			3.87669i			0.605437i	−0.953080	+	0.302719i	$0.902106\pi$
$42$	3.97333			0.613099
$43$	1.00000			0.152499
$43$	1.00000			0.152499
$44$		−	11.6564i		−	1.75727i
$45$		−	0.0959028i		−	0.0142964i
$46$			8.13300i			1.19915i
$47$	−3.53679			−0.515894			−0.257947	−	0.966159i	$-0.583046\pi$
$47$	−3.53679			−0.515894			−0.257947	+	0.966159i	$0.583046\pi$
$48$		−	2.35300i		−	0.339626i
$49$	5.91639			0.845199
$50$	−11.6104			−1.64196
$51$	3.05011	+	5.95021i	0.427101	+	0.833196i
$52$	−2.99140			−0.414832
$53$	−12.0025			−1.64868			−0.824338	−	0.566098i	$-0.808452\pi$
$53$	−12.0025			−1.64868			−0.824338	+	0.566098i	$0.808452\pi$
$54$			12.8636i			1.75051i
$55$	−0.853259			−0.115053
$56$			3.77286i			0.504170i
$57$		−	4.38056i		−	0.580220i
$58$			14.5421i			1.90947i
$59$	−1.58575			−0.206447			−0.103223	−	0.994658i	$-0.532916\pi$
$59$	−1.58575			−0.206447			−0.103223	+	0.994658i	$0.532916\pi$
$60$	−1.48751			−0.192037
$61$		−	4.40881i		−	0.564490i	−0.959342	−	0.282245i	$-0.908921\pi$
$61$		−	4.40881i		−	0.564490i	0.959342	−	0.282245i	$-0.0910792\pi$
$62$			9.98158i			1.26766i
$63$		−	0.385269i		−	0.0485393i
$64$	−11.9252			−1.49065
$65$			0.218973i			0.0271602i
$66$	12.5689			1.54712
$67$	−9.54045			−1.16555			−0.582776	−	0.812633i	$-0.698033\pi$
$67$	−9.54045			−1.16555			−0.582776	+	0.812633i	$0.698033\pi$
$68$	−12.9883	+	6.65785i	−1.57506	+	0.807383i
$69$	−5.60364			−0.674599
$70$	0.634878			0.0758824
$71$		−	13.8561i		−	1.64442i	−0.569187	−	0.822208i	$-0.692742\pi$
$71$		−	13.8561i		−	1.64442i	0.569187	−	0.822208i	$-0.307258\pi$
$72$	−1.34141			−0.158087
$73$		−	3.06103i		−	0.358266i	−0.983825	−	0.179133i	$-0.942671\pi$
$73$		−	3.06103i		−	0.358266i	0.983825	−	0.179133i	$-0.0573293\pi$
$74$		−	18.0739i		−	2.10104i
$75$		−	7.99958i		−	0.923712i
$76$	9.56200			1.09684
$77$	−3.42778			−0.390632
$78$		−	3.22556i		−	0.365223i
$79$		−	0.391325i		−	0.0440275i	−0.999758	−	0.0220137i	$-0.992992\pi$
$79$		−	0.391325i		−	0.0440275i	0.999758	−	0.0220137i	$-0.00700776\pi$
$80$		−	0.375973i		−	0.0420350i
$81$	−7.75270			−0.861411
$82$		−	9.12454i		−	1.00764i
$83$	−1.93729			−0.212645			−0.106323	−	0.994332i	$-0.533908\pi$
$83$	−1.93729			−0.212645			−0.106323	+	0.994332i	$0.533908\pi$
$84$	−5.97576			−0.652008
$85$	0.487360	+	0.950752i	0.0528616	+	0.103124i
$86$	−2.35369			−0.253805
$87$	−10.0195			−1.07420
$88$			11.9347i			1.27224i
$89$	−8.91762			−0.945266			−0.472633	−	0.881259i	$-0.656696\pi$
$89$	−8.91762			−0.945266			−0.472633	+	0.881259i	$0.656696\pi$
$90$			0.225726i			0.0237936i
$91$			0.879675i			0.0922150i
$92$		−	12.2318i		−	1.27525i
$93$	−6.87731			−0.713144
$94$	8.32452			0.858608
$95$		−	0.699946i		−	0.0718130i
$96$		−	6.21706i		−	0.634526i
$97$			1.22584i			0.124465i	0.998062	+	0.0622326i	$0.0198221\pi$
$97$			1.22584i			0.124465i	−0.998062	+	0.0622326i	$0.980178\pi$
$98$	−13.9254			−1.40667
$99$		−	1.21872i		−	0.122486i
$100$	17.4617			1.74617
$101$	−15.7867			−1.57083			−0.785417	−	0.618967i	$-0.787551\pi$
$101$	−15.7867			−1.57083			−0.785417	+	0.618967i	$0.787551\pi$
$102$	−7.17902	−	14.0050i	−0.710829	−	1.38670i
$103$	−7.16183			−0.705676			−0.352838	−	0.935684i	$-0.614783\pi$
$103$	−7.16183			−0.705676			−0.352838	+	0.935684i	$0.614783\pi$
$104$	3.06281			0.300334
$105$			0.437431i			0.0426889i
$106$	28.2503			2.74391
$107$			13.5585i			1.31075i	0.755302	+	0.655377i	$0.227490\pi$
$107$			13.5585i			1.31075i	−0.755302	+	0.655377i	$0.772510\pi$
$108$		−	19.3464i		−	1.86161i
$109$			9.46650i			0.906726i	0.891326	+	0.453363i	$0.149776\pi$
$109$			9.46650i			0.906726i	−0.891326	+	0.453363i	$0.850224\pi$
$110$	2.00831			0.191485
$111$	12.4529			1.18198
$112$		−	1.51039i		−	0.142718i
$113$		−	14.6798i		−	1.38096i	−0.723350	−	0.690481i	$-0.757399\pi$
$113$		−	14.6798i		−	1.38096i	0.723350	−	0.690481i	$-0.242601\pi$
$114$			10.3105i			0.965667i
$115$	−0.895375			−0.0834941
$116$		−	21.8708i		−	2.03065i
$117$	−0.312762			−0.0289148
$118$	3.73236			0.343592
$119$	1.95786	+	3.81944i	0.179477	+	0.350127i
$120$	1.52303			0.139033
$121$	0.156875			0.0142614
$122$			10.3770i			0.939488i
$123$	6.28681			0.566862
$124$		−	15.0119i		−	1.34811i
$125$		−	2.57382i		−	0.230209i
$126$			0.906805i			0.0807846i
$127$	−2.22201			−0.197171			−0.0985856	−	0.995129i	$-0.531432\pi$
$127$	−2.22201			−0.197171			−0.0985856	+	0.995129i	$0.531432\pi$
$128$	20.4009			1.80320
$129$		−	1.62169i		−	0.142782i
$130$		−	0.515395i		−	0.0452031i
$131$			17.8287i			1.55770i	0.627212	+	0.778848i	$0.284196\pi$
$131$			17.8287i			1.55770i	−0.627212	+	0.778848i	$0.715804\pi$
$132$	−18.9031			−1.64531
$133$		−	2.81188i		−	0.243821i
$134$	22.4553			1.93984
$135$	−1.41617			−0.121885
$136$	13.2984	−	6.81681i	1.14032	−	0.584536i
$137$	−2.51769			−0.215101			−0.107550	−	0.994200i	$-0.534301\pi$
$137$	−2.51769			−0.215101			−0.107550	+	0.994200i	$0.534301\pi$
$138$	13.1892			1.12274
$139$		−	5.34642i		−	0.453478i	−0.973956	−	0.226739i	$-0.927194\pi$
$139$		−	5.34642i		−	0.453478i	0.973956	−	0.226739i	$-0.0728064\pi$
$140$	−0.954834			−0.0806982
$141$			5.73559i			0.483024i
$142$			32.6130i			2.73682i
$143$			2.78268i			0.232699i
$144$	0.537007			0.0447506
$145$	−1.60096			−0.132952
$146$			7.20472i			0.596267i
$147$		−	9.59458i		−	0.791347i
$148$			27.1824i			2.23438i
$149$	19.7200			1.61553			0.807764	−	0.589506i	$-0.200677\pi$
$149$	19.7200			1.61553			0.807764	+	0.589506i	$0.200677\pi$
$150$			18.8286i			1.53735i
$151$	18.1178			1.47441			0.737203	−	0.675671i	$-0.236146\pi$
$151$	18.1178			1.47441			0.737203	+	0.675671i	$0.236146\pi$
$152$	−9.79029			−0.794097
$153$	−1.35797	+	0.696104i	−0.109786	+	0.0562767i
$154$	8.06795			0.650134
$155$	−1.09889			−0.0882648
$156$			4.85113i			0.388401i
$157$	5.14859			0.410902			0.205451	−	0.978667i	$-0.434134\pi$
$157$	5.14859			0.410902			0.205451	+	0.978667i	$0.434134\pi$
$158$			0.921059i			0.0732755i
$159$			19.4645i			1.54363i
$160$		−	0.993390i		−	0.0785344i
$161$	−3.59697			−0.283481
$162$	18.2475			1.43366
$163$		−	3.27390i		−	0.256432i	−0.991746	−	0.128216i	$-0.959075\pi$
$163$		−	3.27390i		−	0.256432i	0.991746	−	0.128216i	$-0.0409251\pi$
$164$			13.7230i			1.07159i
$165$			1.38373i			0.107723i
$166$	4.55979			0.353908
$167$		−	20.0169i		−	1.54896i	−0.632600	−	0.774479i	$-0.718012\pi$
$167$		−	20.0169i		−	1.54896i	0.632600	−	0.774479i	$-0.281988\pi$
$168$	6.11843			0.472047
$169$	−12.2859			−0.945068
$170$	−1.14710	−	2.23778i	−0.0879783	−	0.171630i
$171$	0.999744			0.0764523
$172$	3.53987			0.269913
$173$		−	9.73449i		−	0.740100i	−0.929012	−	0.370050i	$-0.879341\pi$
$173$		−	9.73449i		−	0.740100i	0.929012	−	0.370050i	$-0.120659\pi$
$174$	23.5828			1.78781
$175$		−	5.13493i		−	0.388164i
$176$		−	4.77782i		−	0.360142i
$177$			2.57160i			0.193293i
$178$	20.9893			1.57322
$179$	5.24754			0.392220			0.196110	−	0.980582i	$-0.437169\pi$
$179$	5.24754			0.392220			0.196110	+	0.980582i	$0.437169\pi$
$180$		−	0.339484i		−	0.0253036i
$181$		−	0.895490i		−	0.0665612i	−0.999446	−	0.0332806i	$-0.989404\pi$
$181$		−	0.895490i		−	0.0665612i	0.999446	−	0.0332806i	$-0.0105955\pi$
$182$		−	2.07049i		−	0.153475i
$183$	−7.14974			−0.528524
$184$			12.5238i			0.923266i
$185$	1.98978			0.146291
$186$	16.1871			1.18689
$187$	6.19332	+	12.0820i	0.452900	+	0.883527i
$188$	−12.5198			−0.913099
$189$	−5.68917			−0.413826
$190$			1.64746i			0.119519i
$191$	16.2261			1.17408			0.587039	−	0.809559i	$-0.300294\pi$
$191$	16.2261			1.17408			0.587039	+	0.809559i	$0.300294\pi$
$192$			19.3390i			1.39568i
$193$		−	8.85438i		−	0.637352i	−0.947864	−	0.318676i	$-0.896762\pi$
$193$		−	8.85438i		−	0.637352i	0.947864	−	0.318676i	$-0.103238\pi$
$194$		−	2.88525i		−	0.207149i
$195$	0.355107			0.0254297
$196$	20.9433			1.49595
$197$			19.8759i			1.41610i	0.706164	+	0.708048i	$0.250424\pi$
$197$			19.8759i			1.41610i	−0.706164	+	0.708048i	$0.749576\pi$
$198$			2.86850i			0.203855i
$199$		−	22.4486i		−	1.59134i	−0.605732	−	0.795669i	$-0.707120\pi$
$199$		−	22.4486i		−	1.59134i	0.605732	−	0.795669i	$-0.292880\pi$
$200$	−17.8786			−1.26421
$201$			15.4717i			1.09129i
$202$	37.1570			2.61436
$203$	−6.43150			−0.451403
$204$	10.7970	+	21.0630i	0.755941	+	1.47470i
$205$	1.00453			0.0701598
$206$	16.8568			1.17447
$207$		−	1.27888i		−	0.0888881i
$208$	−1.22614			−0.0850173
$209$		−	8.89484i		−	0.615269i
$210$		−	1.02958i		−	0.0710476i
$211$			12.0191i			0.827431i	0.910406	+	0.413716i	$0.135769\pi$
$211$			12.0191i			0.827431i	−0.910406	+	0.413716i	$0.864231\pi$
$212$	−42.4875			−2.91805
$213$	−22.4704			−1.53964
$214$		−	31.9127i		−	2.18150i
$215$		−	0.259122i		−	0.0176720i
$216$			19.8083i			1.34778i
$217$	−4.41454			−0.299679
$218$		−	22.2812i		−	1.50908i
$219$	−4.96405			−0.335440
$220$	−3.02043			−0.203637
$221$	3.10063	−	1.58940i	0.208571	−	0.106914i
$222$	−29.3103			−1.96718
$223$	19.2685			1.29031			0.645157	−	0.764050i	$-0.276792\pi$
$223$	19.2685			1.29031			0.645157	+	0.764050i	$0.276792\pi$
$224$		−	3.99073i		−	0.266642i
$225$	1.82569			0.121712
$226$			34.5518i			2.29835i
$227$			12.4934i			0.829215i	0.910000	+	0.414607i	$0.136081\pi$
$227$			12.4934i			0.829215i	−0.910000	+	0.414607i	$0.863919\pi$
$228$		−	15.5066i		−	1.02695i
$229$	0.712178			0.0470620			0.0235310	−	0.999723i	$-0.492509\pi$
$229$	0.712178			0.0470620			0.0235310	+	0.999723i	$0.492509\pi$
$230$	2.10744			0.138960
$231$			5.55882i			0.365743i
$232$			22.3929i			1.47017i
$233$			9.70558i			0.635834i	0.948119	+	0.317917i	$0.102983\pi$
$233$			9.70558i			0.635834i	−0.948119	+	0.317917i	$0.897017\pi$
$234$	0.736146			0.0481233
$235$			0.916459i			0.0597832i
$236$	−5.61334			−0.365397
$237$	−0.634609			−0.0412223
$238$	−4.60821	−	8.98979i	−0.298706	−	0.582721i
$239$	4.95754			0.320676			0.160338	−	0.987062i	$-0.448742\pi$
$239$	4.95754			0.320676			0.160338	+	0.987062i	$0.448742\pi$
$240$	−0.609713			−0.0393568
$241$			19.0264i			1.22560i	0.790240	+	0.612798i	$0.209956\pi$
$241$			19.0264i			1.22560i	−0.790240	+	0.612798i	$0.790044\pi$
$242$	−0.369236			−0.0237354
$243$		−	3.82334i		−	0.245268i
$244$		−	15.6066i		−	0.999112i
$245$		−	1.53307i		−	0.0979440i
$246$	−14.7972			−0.943436
$247$	−2.28269			−0.145244
$248$			15.3704i			0.976019i
$249$			3.14169i			0.199097i
$250$			6.05798i			0.383140i
$251$	14.7787			0.932823			0.466411	−	0.884568i	$-0.345547\pi$
$251$	14.7787			0.932823			0.466411	+	0.884568i	$0.345547\pi$
$252$		−	1.36380i		−	0.0859115i
$253$	−11.3783			−0.715349
$254$	5.22992			0.328154
$255$	1.54183	−	0.790349i	0.0965531	−	0.0494936i
$256$	−24.1671			−1.51044
$257$	3.83939			0.239494			0.119747	−	0.992804i	$-0.461792\pi$
$257$	3.83939			0.239494			0.119747	+	0.992804i	$0.461792\pi$
$258$			3.81697i			0.237634i
$259$	7.99350			0.496692
$260$			0.775135i			0.0480719i
$261$		−	2.28667i		−	0.141541i
$262$		−	41.9632i		−	2.59249i
$263$	0.931650			0.0574480			0.0287240	−	0.999587i	$-0.490856\pi$
$263$	0.931650			0.0574480			0.0287240	+	0.999587i	$0.490856\pi$
$264$	19.3544			1.19118
$265$			3.11012i			0.191053i
$266$			6.61831i			0.405795i
$267$			14.4617i			0.885039i
$268$	−33.7720			−2.06295
$269$		−	25.3532i		−	1.54581i	−0.634521	−	0.772906i	$-0.718803\pi$
$269$		−	25.3532i		−	1.54581i	0.634521	−	0.772906i	$-0.281197\pi$
$270$	3.33324			0.202854
$271$	−8.92469			−0.542136			−0.271068	−	0.962560i	$-0.587377\pi$
$271$	−8.92469			−0.542136			−0.271068	+	0.962560i	$0.587377\pi$
$272$	−5.32373	+	2.72897i	−0.322799	+	0.165468i
$273$	1.42656			0.0863396
$274$	5.92587			0.357995
$275$		−	16.2434i		−	0.979511i
$276$	−19.8362			−1.19400
$277$		−	7.01787i		−	0.421663i	−0.977522	−	0.210832i	$-0.932383\pi$
$277$		−	7.01787i		−	0.421663i	0.977522	−	0.210832i	$-0.0676172\pi$
$278$			12.5838i			0.754728i
$279$		−	1.56956i		−	0.0939669i
$280$	0.977630			0.0584246
$281$	9.31281			0.555556			0.277778	−	0.960645i	$-0.410402\pi$
$281$	9.31281			0.555556			0.277778	+	0.960645i	$0.410402\pi$
$282$		−	13.4998i		−	0.803903i
$283$			5.32326i			0.316435i	0.987404	+	0.158217i	$0.0505747\pi$
$283$			5.32326i			0.316435i	−0.987404	+	0.158217i	$0.949425\pi$
$284$		−	49.0488i		−	2.91051i
$285$	−1.13510			−0.0672375
$286$		−	6.54958i		−	0.387285i
$287$	4.03550			0.238208
$288$	1.41887			0.0836079
$289$	9.92506	−	13.8019i	0.583827	−	0.811878i
$290$	3.76816			0.221274
$291$	1.98794			0.116535
$292$		−	10.8357i		−	0.634108i
$293$	15.1787			0.886752			0.443376	−	0.896336i	$-0.353781\pi$
$293$	15.1787			0.886752			0.443376	+	0.896336i	$0.353781\pi$
$294$			22.5827i			1.31705i
$295$			0.410901i			0.0239236i
$296$		−	27.8314i		−	1.61767i
$297$	−17.9966			−1.04427
$298$	−46.4149			−2.68874
$299$			2.92003i			0.168870i
$300$		−	28.3175i		−	1.63491i
$301$		−	1.04097i		−	0.0600002i
$302$	−42.6438			−2.45387
$303$			25.6012i			1.47075i
$304$	3.91935			0.224790
$305$	−1.14242			−0.0654147
$306$	3.19625	−	1.63841i	0.182717	−	0.0936619i
$307$	6.72272			0.383686			0.191843	−	0.981426i	$-0.438554\pi$
$307$	6.72272			0.383686			0.191843	+	0.981426i	$0.438554\pi$
$308$	−12.1339			−0.691394
$309$			11.6143i			0.660715i
$310$	2.58644			0.146900
$311$		−	7.76879i		−	0.440528i	−0.975440	−	0.220264i	$-0.929308\pi$
$311$		−	7.76879i		−	0.440528i	0.975440	−	0.220264i	$-0.0706919\pi$
$312$		−	4.96695i		−	0.281198i
$313$		−	28.2545i		−	1.59704i	−0.601969	−	0.798519i	$-0.705617\pi$
$313$		−	28.2545i		−	1.59704i	0.601969	−	0.798519i	$-0.294383\pi$
$314$	−12.1182			−0.683869
$315$	−0.0998315			−0.00562487
$316$		−	1.38524i		−	0.0779259i
$317$		−	1.57334i		−	0.0883674i	−0.999023	−	0.0441837i	$-0.985931\pi$
$317$		−	1.57334i		−	0.0883674i	0.999023	−	0.0441837i	$-0.0140687\pi$
$318$		−	45.8134i		−	2.56909i
$319$	−20.3448			−1.13909
$320$			3.09008i			0.172741i
$321$	21.9878			1.22724
$322$	8.46617			0.471801
$323$	−9.91116	+	5.08051i	−0.551472	+	0.282687i
$324$	−27.4436			−1.52464
$325$	−4.16855			−0.231229
$326$			7.70577i			0.426783i
$327$	15.3518			0.848955
$328$		−	14.0506i		−	0.775816i
$329$			3.68167i			0.202977i
$330$		−	3.25687i		−	0.179285i
$331$	8.47786			0.465985			0.232993	−	0.972479i	$-0.425148\pi$
$331$	8.47786			0.465985			0.232993	+	0.972479i	$0.425148\pi$
$332$	−6.85776			−0.376369
$333$			2.84203i			0.155742i
$334$			47.1137i			2.57795i
$335$			2.47214i			0.135067i
$336$	−2.44939			−0.133625
$337$		−	6.92504i		−	0.377231i	−0.982051	−	0.188616i	$-0.939600\pi$
$337$		−	6.92504i		−	0.377231i	0.982051	−	0.188616i	$-0.0604000\pi$
$338$	28.9172			1.57289
$339$	−23.8062			−1.29298
$340$	1.72519	+	3.36554i	0.0935617	+	0.182522i
$341$	−13.9645			−0.756222
$342$	−2.35309			−0.127241
$343$		−	13.4455i		−	0.725990i
$344$	−3.62439			−0.195414
$345$			1.45202i			0.0781744i
$346$			22.9120i			1.23176i
$347$		−	26.8573i		−	1.44178i	−0.693052	−	0.720888i	$-0.743734\pi$
$347$		−	26.8573i		−	1.44178i	0.693052	−	0.720888i	$-0.256266\pi$
$348$	−35.4677			−1.90127
$349$	−11.3764			−0.608965			−0.304482	−	0.952518i	$-0.598483\pi$
$349$	−11.3764			−0.608965			−0.304482	+	0.952518i	$0.598483\pi$
$350$			12.0861i			0.646027i
$351$			4.61848i			0.246516i
$352$		−	12.6239i		−	0.672856i
$353$	23.8404			1.26890			0.634449	−	0.772965i	$-0.281227\pi$
$353$	23.8404			1.26890			0.634449	+	0.772965i	$0.281227\pi$
$354$		−	6.05275i		−	0.321700i
$355$	−3.59042			−0.190559
$356$	−31.5672			−1.67306
$357$	6.19396	−	3.17506i	0.327819	−	0.168042i
$358$	−12.3511			−0.652776
$359$	9.55790			0.504447			0.252223	−	0.967669i	$-0.418838\pi$
$359$	9.55790			0.504447			0.252223	+	0.967669i	$0.418838\pi$
$360$			0.347589i			0.0183195i
$361$	−11.7034			−0.615967
$362$			2.10771i			0.110779i
$363$		−	0.254403i		−	0.0133527i
$364$			3.11394i			0.163215i
$365$	−0.793179			−0.0415169
$366$	16.8283			0.879630
$367$			17.1395i			0.894675i	0.894365	+	0.447337i	$0.147628\pi$
$367$			17.1395i			0.894675i	−0.894365	+	0.447337i	$0.852372\pi$
$368$		−	5.01365i		−	0.261354i
$369$			1.43479i			0.0746923i
$370$	−4.68333			−0.243475
$371$			12.4942i			0.648668i
$372$	−24.3448			−1.26222
$373$	−14.6150			−0.756736			−0.378368	−	0.925655i	$-0.623515\pi$
$373$	−14.6150			−0.756736			−0.378368	+	0.925655i	$0.623515\pi$
$374$	−14.5772	−	28.4374i	−0.753768	−	1.47046i
$375$	−4.17395			−0.215542
$376$	12.8187			0.661073
$377$			5.22110i			0.268901i
$378$	13.3906			0.688736
$379$		−	10.1182i		−	0.519737i	−0.965644	−	0.259868i	$-0.916321\pi$
$379$		−	10.1182i		−	0.519737i	0.965644	−	0.259868i	$-0.0836792\pi$
$380$		−	2.47772i		−	0.127104i
$381$			3.60341i			0.184609i
$382$	−38.1912			−1.95403
$383$	18.9943			0.970563			0.485281	−	0.874358i	$-0.338717\pi$
$383$	18.9943			0.970563			0.485281	+	0.874358i	$0.338717\pi$
$384$		−	33.0841i		−	1.68831i
$385$			0.888213i			0.0452675i
$386$			20.8405i			1.06075i
$387$	0.370107			0.0188136
$388$			4.33932i			0.220295i
$389$	−2.49679			−0.126592			−0.0632962	−	0.997995i	$-0.520161\pi$
$389$	−2.49679			−0.126592			−0.0632962	+	0.997995i	$0.520161\pi$
$390$	−0.835813			−0.0423230
$391$	6.49901	+	12.6784i	0.328669	+	0.641174i
$392$	−21.4433			−1.08305
$393$	28.9126			1.45845
$394$		−	46.7817i		−	2.35683i
$395$	−0.101401			−0.00510203
$396$		−	4.31412i		−	0.216793i
$397$		−	13.1663i		−	0.660797i	−0.943841	−	0.330399i	$-0.892817\pi$
$397$		−	13.1663i		−	0.660797i	0.943841	−	0.330399i	$-0.107183\pi$
$398$			52.8371i			2.64848i
$399$	−4.56002			−0.228286
$400$	7.15733			0.357867
$401$			36.7207i			1.83374i	0.399180	+	0.916872i	$0.369295\pi$
$401$			36.7207i			1.83374i	−0.399180	+	0.916872i	$0.630705\pi$
$402$		−	36.4156i		−	1.81625i
$403$			3.58373i			0.178518i
$404$	−55.8829			−2.78028
$405$			2.00889i			0.0998227i
$406$	15.1378			0.751276
$407$	25.2859			1.25337
$408$	−11.0548	−	21.5659i	−0.547293	−	1.06767i
$409$	−3.68618			−0.182270			−0.0911349	−	0.995839i	$-0.529049\pi$
$409$	−3.68618			−0.182270			−0.0911349	+	0.995839i	$0.529049\pi$
$410$	−2.36437			−0.116768
$411$			4.08293i			0.201396i
$412$	−25.3520			−1.24900
$413$			1.65071i			0.0812260i
$414$			3.01008i			0.147938i
$415$			0.501994i			0.0246419i
$416$	−3.23968			−0.158838
$417$	−8.67026			−0.424585
$418$			20.9357i			1.02400i
$419$			29.6116i			1.44662i	0.690522	+	0.723312i	$0.257381\pi$
$419$			29.6116i			1.44662i	−0.690522	+	0.723312i	$0.742619\pi$
$420$			1.54845i			0.0755565i
$421$	5.93062			0.289041			0.144520	−	0.989502i	$-0.453836\pi$
$421$	5.93062			0.289041			0.144520	+	0.989502i	$0.453836\pi$
$422$		−	28.2894i		−	1.37710i
$423$	−1.30899			−0.0636453
$424$	43.5018			2.11264
$425$	−18.0993	+	9.27779i	−0.877945	+	0.450039i
$426$	52.8883			2.56245
$427$	−4.58942			−0.222098
$428$			47.9955i			2.31995i
$429$	4.51266			0.217873
$430$			0.609893i			0.0294117i
$431$		−	5.35594i		−	0.257987i	−0.991645	−	0.128993i	$-0.958825\pi$
$431$		−	5.35594i		−	0.257987i	0.991645	−	0.128993i	$-0.0411746\pi$
$432$		−	7.92986i		−	0.381525i
$433$	−2.61826			−0.125826			−0.0629128	−	0.998019i	$-0.520039\pi$
$433$	−2.61826			−0.125826			−0.0629128	+	0.998019i	$0.520039\pi$
$434$	10.3905			0.498759
$435$			2.59626i			0.124481i
$436$			33.5102i			1.60485i
$437$		−	9.33388i		−	0.446500i
$438$	11.6839			0.558276
$439$		−	22.6635i		−	1.08167i	−0.841129	−	0.540835i	$-0.818108\pi$
$439$		−	22.6635i		−	1.08167i	0.841129	−	0.540835i	$-0.181892\pi$
$440$	3.09254			0.147431
$441$	2.18970			0.104271
$442$	−7.29793	+	3.74095i	−0.347127	+	0.177939i
$443$	26.1934			1.24449			0.622244	−	0.782823i	$-0.286221\pi$
$443$	26.1934			1.24449			0.622244	+	0.782823i	$0.286221\pi$
$444$	44.0816			2.09202
$445$			2.31075i			0.109540i
$446$	−45.3521			−2.14748
$447$		−	31.9799i		−	1.51260i
$448$			12.4137i			0.586494i
$449$			24.4881i			1.15567i	0.816155	+	0.577834i	$0.196102\pi$
$449$			24.4881i			1.15567i	−0.816155	+	0.577834i	$0.803898\pi$
$450$	−4.29710			−0.202567
$451$	12.7655			0.601105
$452$		−	51.9647i		−	2.44422i
$453$		−	29.3815i		−	1.38047i
$454$		−	29.4056i		−	1.38007i
$455$	0.227943			0.0106861
$456$			15.8769i			0.743502i
$457$	8.31026			0.388738			0.194369	−	0.980929i	$-0.437734\pi$
$457$	8.31026			0.388738			0.194369	+	0.980929i	$0.437734\pi$
$458$	−1.67625			−0.0783259
$459$	10.2792	+	20.0528i	0.479792	+	0.935987i
$460$	−3.16951			−0.147779
$461$	34.9406			1.62735			0.813673	−	0.581322i	$-0.197464\pi$
$461$	34.9406			1.62735			0.813673	+	0.581322i	$0.197464\pi$
$462$		−	13.0838i		−	0.608711i
$463$	35.4429			1.64717			0.823586	−	0.567192i	$-0.191970\pi$
$463$	35.4429			1.64717			0.823586	+	0.567192i	$0.191970\pi$
$464$		−	8.96456i		−	0.416169i
$465$			1.78206i			0.0826411i
$466$		−	22.8440i		−	1.05823i
$467$	−21.7653			−1.00718			−0.503589	−	0.863943i	$-0.667987\pi$
$467$	−21.7653			−1.00718			−0.503589	+	0.863943i	$0.667987\pi$
$468$	−1.10714			−0.0511774
$469$			9.93128i			0.458584i
$470$		−	2.15706i		−	0.0994979i
$471$		−	8.34943i		−	0.384722i
$472$	5.74736			0.264544
$473$		−	3.29289i		−	0.151407i
$474$	1.49368			0.0686068
$475$	13.3248			0.611382
$476$	6.93059	+	13.5203i	0.317663	+	0.619703i
$477$	−4.44223			−0.203396
$478$	−11.6685			−0.533706
$479$			10.2151i			0.466738i	0.972388	+	0.233369i	$0.0749750\pi$
$479$			10.2151i			0.466738i	−0.972388	+	0.233369i	$0.925025\pi$
$480$	−1.61097			−0.0735306
$481$		−	6.48914i		−	0.295879i
$482$		−	44.7822i		−	2.03977i
$483$			5.83319i			0.265419i
$484$	0.555317			0.0252417
$485$	0.317642			0.0144234
$486$			8.99898i			0.408202i
$487$		−	4.37990i		−	0.198472i	−0.995064	−	0.0992362i	$-0.968360\pi$
$487$		−	4.37990i		−	0.198472i	0.995064	−	0.0992362i	$-0.0316399\pi$
$488$			15.9792i			0.723346i
$489$	−5.30927			−0.240094
$490$			3.60837i			0.163009i
$491$	16.3128			0.736186			0.368093	−	0.929789i	$-0.380011\pi$
$491$	16.3128			0.736186			0.368093	+	0.929789i	$0.380011\pi$
$492$	22.2545			1.00331
$493$	11.6204	+	22.6694i	0.523358	+	1.02098i
$494$	5.37276			0.241732
$495$	−0.315797			−0.0141940
$496$		−	6.15322i		−	0.276288i
$497$	−14.4237			−0.646992
$498$		−	7.39458i		−	0.331359i
$499$		−	41.5349i		−	1.85936i	−0.368371	−	0.929679i	$-0.620085\pi$
$499$		−	41.5349i		−	1.85936i	0.368371	−	0.929679i	$-0.379915\pi$
$500$		−	9.11099i		−	0.407456i
$501$	−32.4614			−1.45027
$502$	−34.7845			−1.55251
$503$			23.6867i			1.05614i	0.849202	+	0.528068i	$0.177083\pi$
$503$			23.6867i			1.05614i	−0.849202	+	0.528068i	$0.822917\pi$
$504$			1.39636i			0.0621990i
$505$			4.09067i			0.182033i
$506$	26.7811			1.19056
$507$			19.9239i			0.884853i
$508$	−7.86562			−0.348980
$509$	−9.50711			−0.421395			−0.210698	−	0.977551i	$-0.567574\pi$
$509$	−9.50711			−0.421395			−0.210698	+	0.977551i	$0.567574\pi$
$510$	−3.62899	+	1.86024i	−0.160694	+	0.0823728i
$511$	−3.18642			−0.140959
$512$	16.0801			0.710646
$513$		−	14.7630i		−	0.651801i
$514$	−9.03674			−0.398593
$515$			1.85579i			0.0817757i
$516$		−	5.74059i		−	0.252715i
$517$			11.6463i			0.512202i
$518$	−18.8143			−0.826651
$519$	−15.7864			−0.692945
$520$		−	0.793642i		−	0.0348035i
$521$		−	19.1259i		−	0.837919i	−0.908005	−	0.418960i	$-0.862395\pi$
$521$		−	19.1259i		−	0.837919i	0.908005	−	0.418960i	$-0.137605\pi$
$522$			5.38212i			0.235569i
$523$	−25.3569			−1.10878			−0.554391	−	0.832256i	$-0.687049\pi$
$523$	−25.3569			−1.10878			−0.554391	+	0.832256i	$0.687049\pi$
$524$			63.1112i			2.75702i
$525$	−8.32729			−0.363433
$526$	−2.19282			−0.0956115
$527$	7.97620	+	15.5601i	0.347449	+	0.677809i
$528$	−7.74817			−0.337196
$529$	11.0601			0.480872
$530$		−	7.32027i		−	0.317972i
$531$	−0.586896			−0.0254691
$532$		−	9.95371i		−	0.431548i
$533$		−	3.27603i		−	0.141900i
$534$		−	34.0383i		−	1.47298i
$535$	3.51331			0.151894
$536$	34.5783			1.49355
$537$		−	8.50991i		−	0.367230i
$538$			59.6736i			2.57271i
$539$		−	19.4820i		−	0.839150i
$540$	−5.01307			−0.215728
$541$			15.5443i			0.668303i	0.942519	+	0.334152i	$0.108450\pi$
$541$			15.5443i			0.668303i	−0.942519	+	0.334152i	$0.891550\pi$
$542$	21.0060			0.902284
$543$	−1.45221			−0.0623203
$544$	−14.0663	+	7.21045i	−0.603087	+	0.309145i
$545$	2.45298			0.105074
$546$	−3.35770			−0.143696
$547$			37.8925i			1.62017i	0.586315	+	0.810083i	$0.300578\pi$
$547$			37.8925i			1.62017i	−0.586315	+	0.810083i	$0.699422\pi$
$548$	−8.91231			−0.380715
$549$		−	1.63173i		−	0.0696407i
$550$			38.2319i			1.63021i
$551$		−	16.6893i		−	0.710987i
$552$	20.3098			0.864440
$553$	−0.407356			−0.0173225
$554$			16.5179i			0.701779i
$555$		−	3.22681i		−	0.136971i
$556$		−	18.9256i		−	0.802626i
$557$	−28.8818			−1.22376			−0.611881	−	0.790950i	$-0.709587\pi$
$557$	−28.8818			−1.22376			−0.611881	+	0.790950i	$0.709587\pi$
$558$			3.69426i			0.156390i
$559$	−0.845057			−0.0357421
$560$	−0.391375			−0.0165386
$561$	19.5934	−	10.0437i	0.827234	−	0.424044i
$562$	−21.9195			−0.924618
$563$	3.24306			0.136679			0.0683393	−	0.997662i	$-0.478230\pi$
$563$	3.24306			0.136679			0.0683393	+	0.997662i	$0.478230\pi$
$564$			20.3033i			0.854921i
$565$	−3.80386			−0.160030
$566$		−	12.5293i		−	0.526646i
$567$			8.07029i			0.338920i
$568$			50.2198i			2.10718i
$569$	3.16621			0.132734			0.0663671	−	0.997795i	$-0.478859\pi$
$569$	3.16621			0.132734			0.0663671	+	0.997795i	$0.478859\pi$
$570$	2.67168			0.111904
$571$			7.07166i			0.295940i	0.988992	+	0.147970i	$0.0472739\pi$
$571$			7.07166i			0.295940i	−0.988992	+	0.147970i	$0.952726\pi$
$572$			9.85034i			0.411863i
$573$		−	26.3137i		−	1.09927i
$574$	−9.49833			−0.396453
$575$		−	17.0451i		−	0.710830i
$576$	−4.41361			−0.183900
$577$	−26.0282			−1.08357			−0.541784	−	0.840518i	$-0.682251\pi$
$577$	−26.0282			−1.08357			−0.541784	+	0.840518i	$0.682251\pi$
$578$	−23.3606	+	32.4855i	−0.971671	+	1.35122i
$579$	−14.3591			−0.596744
$580$	−5.66719			−0.235317
$581$			2.01665i			0.0836648i
$582$	−4.67900			−0.193951
$583$			39.5230i			1.63688i
$584$			11.0944i			0.459088i
$585$			0.0810434i			0.00335073i
$586$	−35.7261			−1.47583
$587$	42.1295			1.73887			0.869436	−	0.494045i	$-0.164482\pi$
$587$	42.1295			1.73887			0.869436	+	0.494045i	$0.164482\pi$
$588$		−	33.9636i		−	1.40063i
$589$		−	11.4554i		−	0.472012i
$590$		−	0.967136i		−	0.0398163i
$591$	32.2326			1.32587
$592$			11.1418i			0.457923i
$593$	4.09200			0.168038			0.0840192	−	0.996464i	$-0.473224\pi$
$593$	4.09200			0.168038			0.0840192	+	0.996464i	$0.473224\pi$
$594$	42.3584			1.73799
$595$	0.989700	−	0.507325i	0.0405737	−	0.0207983i
$596$	69.8064			2.85938
$597$	−36.4047			−1.48995
$598$		−	6.87285i		−	0.281052i
$599$	−40.3423			−1.64834			−0.824171	−	0.566340i	$-0.808359\pi$
$599$	−40.3423			−1.64834			−0.824171	+	0.566340i	$0.808359\pi$
$600$			28.9936i			1.18366i
$601$			28.6124i			1.16713i	0.812068	+	0.583563i	$0.198342\pi$
$601$			28.6124i			1.16713i	−0.812068	+	0.583563i	$0.801658\pi$
$602$			2.45011i			0.0998592i
$603$	−3.53099			−0.143793
$604$	64.1347			2.60960
$605$		−	0.0406497i		−	0.00165265i
$606$		−	60.2573i		−	2.44779i
$607$		−	6.40795i		−	0.260091i	−0.991508	−	0.130045i	$-0.958488\pi$
$607$		−	6.40795i		−	0.260091i	0.991508	−	0.130045i	$-0.0415123\pi$
$608$	10.3556			0.419977
$609$			10.4299i			0.422642i
$610$	2.68890			0.108871
$611$	2.98879			0.120913
$612$	−4.80705	+	2.46412i	−0.194313	+	0.0996061i
$613$	26.2346			1.05961			0.529803	−	0.848121i	$-0.322266\pi$
$613$	26.2346			1.05961			0.529803	+	0.848121i	$0.322266\pi$
$614$	−15.8232			−0.638573
$615$		−	1.62905i		−	0.0656896i
$616$	12.4236			0.500562
$617$		−	3.29175i		−	0.132521i	−0.997802	−	0.0662605i	$-0.978893\pi$
$617$		−	3.29175i		−	0.132521i	0.997802	−	0.0662605i	$-0.0211068\pi$
$618$		−	27.3365i		−	1.09964i
$619$			36.8609i			1.48157i	0.671744	+	0.740783i	$0.265545\pi$
$619$			36.8609i			1.48157i	−0.671744	+	0.740783i	$0.734455\pi$
$620$	−3.88992			−0.156223
$621$	−18.8849			−0.757823
$622$			18.2854i			0.733176i
$623$			9.28293i			0.371913i
$624$			1.98842i			0.0796005i
$625$	23.9973			0.959894
$626$			66.5024i			2.65797i
$627$	−14.4247			−0.576068
$628$	18.2253			0.727270
$629$	−14.4427	−	28.1750i	−0.575867	−	1.12341i
$630$	0.234973			0.00936154
$631$	26.1213			1.03987			0.519937	−	0.854205i	$-0.325955\pi$
$631$	26.1213			1.03987			0.519937	+	0.854205i	$0.325955\pi$
$632$			1.41831i			0.0564175i
$633$	19.4914			0.774712
$634$			3.70315i			0.147071i
$635$			0.575770i			0.0228487i
$636$			68.9017i			2.73213i
$637$	−4.99969			−0.198095
$638$	47.8854			1.89580
$639$		−	5.12824i		−	0.202870i
$640$		−	5.28632i		−	0.208960i
$641$			22.0937i			0.872647i	0.899790	+	0.436324i	$0.143720\pi$
$641$			22.0937i			0.872647i	−0.899790	+	0.436324i	$0.856280\pi$
$642$	−51.7526			−2.04251
$643$		−	24.0805i		−	0.949643i	−0.880082	−	0.474822i	$-0.842513\pi$
$643$		−	24.0805i		−	0.949643i	0.880082	−	0.474822i	$-0.157487\pi$
$644$	−12.7328			−0.501744
$645$	−0.420216			−0.0165460
$646$	23.3278	−	11.9580i	0.917821	−	0.470480i
$647$	43.9029			1.72600			0.863000	−	0.505203i	$-0.168582\pi$
$647$	43.9029			1.72600			0.863000	+	0.505203i	$0.168582\pi$
$648$	28.0988			1.10382
$649$			5.22169i			0.204969i
$650$	9.81148			0.384838
$651$			7.15904i			0.280585i
$652$		−	11.5892i		−	0.453868i
$653$		−	39.4913i		−	1.54542i	−0.634762	−	0.772708i	$-0.718902\pi$
$653$		−	39.4913i		−	1.54542i	0.634762	−	0.772708i	$-0.281098\pi$
$654$	−36.1334			−1.41293
$655$	4.61979			0.180510
$656$			5.62489i			0.219615i
$657$		−	1.13291i		−	0.0441990i
$658$		−	8.66553i		−	0.337818i
$659$	38.1714			1.48695			0.743473	−	0.668766i	$-0.233177\pi$
$659$	38.1714			1.48695			0.743473	+	0.668766i	$0.233177\pi$
$660$			4.89821i			0.190663i
$661$	4.62200			0.179775			0.0898876	−	0.995952i	$-0.471349\pi$
$661$	4.62200			0.179775			0.0898876	+	0.995952i	$0.471349\pi$
$662$	−19.9543			−0.775545
$663$	−2.57752	−	5.02827i	−0.100102	−	0.195282i
$664$	7.02149			0.272487
$665$	−0.728620			−0.0282547
$666$		−	6.68927i		−	0.259204i
$667$	−21.3490			−0.826636
$668$		−	70.8574i		−	2.74156i
$669$		−	31.2476i		−	1.20810i
$670$		−	5.81866i		−	0.224794i
$671$	−14.5177			−0.560451
$672$	−6.47174			−0.249653
$673$		−	29.0896i		−	1.12132i	−0.828046	−	0.560660i	$-0.810547\pi$
$673$		−	29.0896i		−	1.12132i	0.828046	−	0.560660i	$-0.189453\pi$
$674$			16.2994i			0.627831i
$675$		−	26.9595i		−	1.03767i
$676$	−43.4904			−1.67271
$677$		−	23.3889i		−	0.898907i	−0.893304	−	0.449454i	$-0.851619\pi$
$677$		−	23.3889i		−	0.898907i	0.893304	−	0.449454i	$-0.148381\pi$
$678$	56.0325			2.15192
$679$	1.27606			0.0489706
$680$	−1.76638	−	3.44589i	−0.0677377	−	0.132144i
$681$	20.2604			0.776382
$682$	32.8683			1.25859
$683$			17.0258i			0.651475i	0.945460	+	0.325738i	$0.105613\pi$
$683$			17.0258i			0.651475i	−0.945460	+	0.325738i	$0.894387\pi$
$684$	3.53896			0.135316
$685$			0.652389i			0.0249265i
$686$			31.6466i			1.20827i
$687$		−	1.15493i		−	0.0440635i
$688$	1.45095			0.0553170
$689$	10.1428			0.386411
$690$		−	3.41762i		−	0.130107i
$691$		−	6.68095i		−	0.254155i	−0.991893	−	0.127078i	$-0.959440\pi$
$691$		−	6.68095i		−	0.254155i	0.991893	−	0.127078i	$-0.0405597\pi$
$692$		−	34.4588i		−	1.30993i
$693$	−1.26865			−0.0481920
$694$			63.2139i			2.39957i
$695$	−1.38537			−0.0525502
$696$	36.3145			1.37650
$697$	−7.29134	−	14.2241i	−0.276179	−	0.538776i
$698$	26.7766			1.01351
$699$	15.7395			0.595322
$700$		−	18.1770i		−	0.687026i
$701$	30.2450			1.14234			0.571169	−	0.820833i	$-0.306490\pi$
$701$	30.2450			1.14234			0.571169	+	0.820833i	$0.306490\pi$
$702$		−	10.8705i		−	0.410280i
$703$			20.7425i			0.782320i
$704$			39.2684i			1.47998i
$705$	1.48622			0.0559741
$706$	−56.1130			−2.11184
$707$			16.4334i			0.618041i
$708$			9.10312i			0.342116i
$709$			20.6787i			0.776606i	0.921532	+	0.388303i	$0.126939\pi$
$709$			20.6787i			0.776606i	−0.921532	+	0.388303i	$0.873061\pi$
$710$	8.45074			0.317150
$711$		−	0.144832i		−	0.00543163i
$712$	32.3209			1.21128
$713$	−14.6538			−0.548789
$714$	−14.5787	+	7.47311i	−0.545594	+	0.279674i
$715$	0.721053			0.0269659
$716$	18.5756			0.694204
$717$		−	8.03961i		−	0.300245i
$718$	−22.4964			−0.839557
$719$			9.18016i			0.342362i	0.985240	+	0.171181i	$0.0547583\pi$
$719$			9.18016i			0.342362i	−0.985240	+	0.171181i	$0.945242\pi$
$720$		−	0.139150i		−	0.00518582i
$721$			7.45522i			0.277647i
$722$	27.5462			1.02516
$723$	30.8550			1.14751
$724$		−	3.16992i		−	0.117809i
$725$		−	30.4772i		−	1.13189i
$726$			0.598787i			0.0222231i
$727$	32.6007			1.20909			0.604546	−	0.796570i	$-0.293355\pi$
$727$	32.6007			1.20909			0.604546	+	0.796570i	$0.293355\pi$
$728$		−	3.18828i		−	0.118166i
$729$	−29.4584			−1.09105
$730$	1.86690			0.0690971
$731$	−3.66913	+	1.88082i	−0.135708	+	0.0695645i
$732$	−25.3092			−0.935454
$733$	11.1503			0.411845			0.205923	−	0.978568i	$-0.433980\pi$
$733$	11.1503			0.411845			0.205923	+	0.978568i	$0.433980\pi$
$734$		−	40.3411i		−	1.48902i
$735$	−2.48616			−0.0917035
$736$		−	13.2470i		−	0.488290i
$737$			31.4157i			1.15721i
$738$		−	3.37706i		−	0.124311i
$739$	−17.3835			−0.639463			−0.319731	−	0.947508i	$-0.603593\pi$
$739$	−17.3835			−0.639463			−0.319731	+	0.947508i	$0.603593\pi$
$740$	7.04356			0.258926
$741$			3.70183i			0.135990i
$742$		−	29.4076i		−	1.07959i
$743$			28.0271i			1.02822i	0.857726	+	0.514108i	$0.171877\pi$
$743$			28.0271i			1.02822i	−0.857726	+	0.514108i	$0.828123\pi$
$744$	24.9260			0.913832
$745$		−	5.10989i		−	0.187212i
$746$	34.3992			1.25944
$747$	−0.717005			−0.0262339
$748$	21.9236	+	42.7689i	0.801605	+	1.56379i
$749$	14.1140			0.515714
$750$	9.82419			0.358729
$751$		−	48.3216i		−	1.76328i	−0.471922	−	0.881641i	$-0.656439\pi$
$751$		−	48.3216i		−	1.76328i	0.471922	−	0.881641i	$-0.343561\pi$
$752$	−5.13171			−0.187134
$753$		−	23.9665i		−	0.873388i
$754$		−	12.2889i		−	0.447535i
$755$		−	4.69472i		−	0.170858i
$756$	−20.1389			−0.732446
$757$	9.78269			0.355558			0.177779	−	0.984070i	$-0.443109\pi$
$757$	9.78269			0.355558			0.177779	+	0.984070i	$0.443109\pi$
$758$			23.8151i			0.865004i
$759$			18.4522i			0.669771i
$760$			2.53688i			0.0920222i
$761$	17.2134			0.623985			0.311993	−	0.950085i	$-0.399004\pi$
$761$	17.2134			0.623985			0.311993	+	0.950085i	$0.399004\pi$
$762$		−	8.48133i		−	0.307246i
$763$	9.85430			0.356750
$764$	57.4382			2.07804
$765$	0.180376	+	0.351880i	0.00652149	+	0.0127223i
$766$	−44.7067			−1.61532
$767$	1.34005			0.0483863
$768$			39.1917i			1.41421i
$769$	−43.0928			−1.55397			−0.776983	−	0.629522i	$-0.783251\pi$
$769$	−43.0928			−1.55397			−0.776983	+	0.629522i	$0.783251\pi$
$770$		−	2.09058i		−	0.0753393i
$771$		−	6.22631i		−	0.224235i
$772$		−	31.3434i		−	1.12807i
$773$	−23.3206			−0.838783			−0.419391	−	0.907806i	$-0.637756\pi$
$773$	−23.3206			−0.838783			−0.419391	+	0.907806i	$0.637756\pi$
$774$	−0.871119			−0.0313117
$775$		−	20.9193i		−	0.751445i
$776$		−	4.44292i		−	0.159491i
$777$		−	12.9630i		−	0.465046i
$778$	5.87668			0.210689
$779$			10.4718i			0.375192i
$780$	1.25703			0.0450090
$781$	−45.6266			−1.63265
$782$	−15.2967	−	29.8411i	−0.547008	−	1.06711i
$783$	−33.7667			−1.20672
$784$	8.58439			0.306585
$785$		−	1.33411i		−	0.0476164i
$786$	−68.0515			−2.42732
$787$			2.48861i			0.0887093i	0.999016	+	0.0443547i	$0.0141232\pi$
$787$			2.48861i			0.0887093i	−0.999016	+	0.0443547i	$0.985877\pi$
$788$			70.3580i			2.50640i
$789$		−	1.51085i		−	0.0537878i
$790$	0.238666			0.00849137
$791$	−15.2812			−0.543337
$792$			4.41712i			0.156956i
$793$			3.72570i			0.132303i
$794$			30.9894i			1.09977i
$795$	5.04366			0.178880
$796$		−	79.4651i		−	2.81657i
$797$	−21.3988			−0.757984			−0.378992	−	0.925400i	$-0.623729\pi$
$797$	−21.3988			−0.757984			−0.378992	+	0.925400i	$0.623729\pi$
$798$	10.7329			0.379940
$799$	12.9769	−	6.65205i	0.459091	−	0.235333i
$800$	18.9110			0.668605
$801$	−3.30048			−0.116617
$802$		−	86.4293i		−	3.05192i
$803$	−10.0796			−0.355702
$804$			54.7678i			1.93151i
$805$			0.932054i			0.0328506i
$806$		−	8.43501i		−	0.297111i
$807$	−41.1151			−1.44732
$808$	57.2171			2.01289
$809$		−	30.3424i		−	1.06678i	−0.845869	−	0.533391i	$-0.820918\pi$
$809$		−	30.3424i		−	1.06678i	0.845869	−	0.533391i	$-0.179082\pi$
$810$		−	4.72832i		−	0.166136i
$811$			17.0404i			0.598369i	0.954195	+	0.299185i	$0.0967146\pi$
$811$			17.0404i			0.598369i	−0.954195	+	0.299185i	$0.903285\pi$
$812$	−22.7667			−0.798954
$813$			14.4731i			0.507594i
$814$	−59.5152			−2.08601
$815$	−0.848340			−0.0297160
$816$	4.42556	+	8.63346i	0.154926	+	0.302232i
$817$	2.70123			0.0945040
$818$	8.67614			0.303354
$819$			0.325574i			0.0113765i
$820$	3.55592			0.124178
$821$			20.0652i			0.700279i	0.936698	+	0.350139i	$0.113866\pi$
$821$			20.0652i			0.700279i	−0.936698	+	0.350139i	$0.886134\pi$
$822$		−	9.60996i		−	0.335186i
$823$		−	38.6640i		−	1.34774i	−0.738849	−	0.673871i	$-0.764630\pi$
$823$		−	38.6640i		−	1.34774i	0.738849	−	0.673871i	$-0.235370\pi$
$824$	25.9572			0.904264
$825$	−26.3418			−0.917102
$826$		−	3.88526i		−	0.135185i
$827$		−	20.9300i		−	0.727807i	−0.931437	−	0.363903i	$-0.881444\pi$
$827$		−	20.9300i		−	0.727807i	0.931437	−	0.363903i	$-0.118556\pi$
$828$		−	4.52706i		−	0.157326i
$829$	−22.6962			−0.788271			−0.394135	−	0.919052i	$-0.628956\pi$
$829$	−22.6962			−0.788271			−0.394135	+	0.919052i	$0.628956\pi$
$830$		−	1.18154i		−	0.0410119i
$831$	−11.3808			−0.394797
$832$	10.0775			0.349374
$833$	−21.7080	+	11.1276i	−0.752138	+	0.385550i
$834$	20.4071			0.706641
$835$	−5.18683			−0.179497
$836$		−	31.4866i		−	1.08899i
$837$	−23.1773			−0.801124
$838$		−	69.6967i		−	2.40763i
$839$			33.1427i			1.14421i	0.820180	+	0.572106i	$0.193873\pi$
$839$			33.1427i			1.14421i	−0.820180	+	0.572106i	$0.806127\pi$
$840$		−	1.58542i		−	0.0547021i
$841$	−9.17265			−0.316298
$842$	−13.9589			−0.481054
$843$		−	15.1025i		−	0.520159i
$844$			42.5462i			1.46450i
$845$			3.18354i			0.109517i
$846$	3.08096			0.105926
$847$		−	0.163301i		−	0.00561110i
$848$	−17.4151			−0.598037
$849$	8.63270			0.296273
$850$	42.6002	−	21.8371i	1.46117	−	0.749006i
$851$	26.5340			0.909572
$852$	−79.5422			−2.72507
$853$			56.2439i			1.92575i	0.269940	+	0.962877i	$0.412996\pi$
$853$			56.2439i			1.92575i	−0.269940	+	0.962877i	$0.587004\pi$
$854$	10.8021			0.369640
$855$		−	0.259055i		−	0.00885950i
$856$		−	49.1414i		−	1.67962i
$857$		−	42.6246i		−	1.45603i	−0.685561	−	0.728015i	$-0.740443\pi$
$857$		−	42.6246i		−	1.45603i	0.685561	−	0.728015i	$-0.259557\pi$
$858$	−10.6214			−0.362609
$859$	−21.6376			−0.738267			−0.369133	−	0.929376i	$-0.620345\pi$
$859$	−21.6376			−0.738267			−0.369133	+	0.929376i	$0.620345\pi$
$860$		−	0.917258i		−	0.0312782i
$861$		−	6.54435i		−	0.223031i
$862$			12.6062i			0.429370i
$863$	16.0391			0.545979			0.272989	−	0.962017i	$-0.411988\pi$
$863$	16.0391			0.545979			0.272989	+	0.962017i	$0.411988\pi$
$864$		−	20.9522i		−	0.712807i
$865$	−2.52242			−0.0857648
$866$	6.16259			0.209413
$867$	−22.3825	−	16.0954i	−0.760150	−	0.546629i
$868$	−15.6269			−0.530412
$869$	−1.28859			−0.0437124
$870$		−	6.11081i		−	0.207176i
$871$	8.06223			0.273178
$872$		−	34.3103i		−	1.16189i
$873$			0.453692i			0.0153552i
$874$			21.9691i			0.743115i
$875$	−2.67926			−0.0905754
$876$	−17.5721			−0.593707
$877$			16.6650i			0.562738i	0.959600	+	0.281369i	$0.0907885\pi$
$877$			16.6650i			0.562738i	−0.959600	+	0.281369i	$0.909211\pi$
$878$			53.3429i			1.80024i
$879$		−	24.6153i		−	0.830253i
$880$	−1.23804			−0.0417342
$881$		−	37.1847i		−	1.25278i	−0.779508	−	0.626392i	$-0.784531\pi$
$881$		−	37.1847i		−	1.25278i	0.779508	−	0.626392i	$-0.215469\pi$
$882$	−5.15388			−0.173540
$883$	−6.71985			−0.226141			−0.113070	−	0.993587i	$-0.536069\pi$
$883$	−6.71985			−0.226141			−0.113070	+	0.993587i	$0.536069\pi$
$884$	10.9758	−	5.62626i	0.369157	−	0.189232i
$885$	0.666356			0.0223993
$886$	−61.6513			−2.07122
$887$			22.2120i			0.745805i	0.927871	+	0.372902i	$0.121637\pi$
$887$			22.2120i			0.745805i	−0.927871	+	0.372902i	$0.878363\pi$
$888$	−45.1341			−1.51460
$889$			2.31303i			0.0775766i
$890$		−	5.43880i		−	0.182309i
$891$			25.5288i			0.855246i
$892$	68.2080			2.28377
$893$	−9.55367			−0.319701
$894$			75.2708i			2.51743i
$895$		−	1.35975i		−	0.0454515i
$896$		−	21.2367i		−	0.709467i
$897$	4.73540			0.158110
$898$		−	57.6376i		−	1.92339i
$899$	−26.2015			−0.873868
$900$	6.46269			0.215423
$901$	44.0389	−	22.5746i	1.46715	−	0.752068i
$902$	−30.0461			−1.00043
$903$	−1.68813			−0.0561774
$904$			53.2054i			1.76959i
$905$	−0.232041			−0.00771330
$906$			69.1552i			2.29753i
$907$			46.9571i			1.55918i	0.626288	+	0.779592i	$0.284573\pi$
$907$			46.9571i			1.55918i	−0.626288	+	0.779592i	$0.715427\pi$
$908$			44.2250i			1.46766i
$909$	−5.84277			−0.193792
$910$	−0.536508			−0.0177851
$911$		−	20.9430i		−	0.693874i	−0.937888	−	0.346937i	$-0.887222\pi$
$911$		−	20.9430i		−	0.693874i	0.937888	−	0.346937i	$-0.112778\pi$
$912$		−	6.35598i		−	0.210468i
$913$			6.37929i			0.211124i
$914$	−19.5598			−0.646981
$915$			1.85265i			0.0612469i
$916$	2.52102			0.0832968
$917$	18.5590			0.612873
$918$	−24.1941	−	47.1983i	−0.798523	−	1.55777i
$919$	18.5799			0.612895			0.306447	−	0.951888i	$-0.400860\pi$
$919$	18.5799			0.612895			0.306447	+	0.951888i	$0.400860\pi$
$920$	3.24518			0.106991
$921$		−	10.9022i		−	0.359239i
$922$	−82.2395			−2.70841
$923$			11.7092i			0.385413i
$924$			19.6775i			0.647343i
$925$			37.8791i			1.24546i
$926$	−83.4217			−2.74141
$927$	−2.65065			−0.0870586
$928$		−	23.6860i		−	0.777532i
$929$			40.3930i			1.32525i	0.748950	+	0.662626i	$0.230558\pi$
$929$			40.3930i			1.32525i	−0.748950	+	0.662626i	$0.769442\pi$
$930$		−	4.19442i		−	0.137541i
$931$	15.9815			0.523773
$932$			34.3565i			1.12538i
$933$	−12.5986			−0.412460
$934$	51.2288			1.67626
$935$	3.13072	−	1.60482i	0.102386	−	0.0524834i
$936$	1.13357			0.0370519
$937$	8.78452			0.286978			0.143489	−	0.989652i	$-0.454168\pi$
$937$	8.78452			0.286978			0.143489	+	0.989652i	$0.454168\pi$
$938$		−	23.3752i		−	0.763227i
$939$	−45.8202			−1.49528
$940$			3.24415i			0.105812i
$941$		−	32.0584i		−	1.04507i	−0.852617	−	0.522536i	$-0.824986\pi$
$941$		−	32.0584i		−	1.04507i	0.852617	−	0.522536i	$-0.175014\pi$
$942$			19.6520i			0.640297i
$943$	13.3956			0.436221
$944$	−2.30084			−0.0748860
$945$			1.47419i			0.0479553i
$946$			7.75045i			0.251989i
$947$			42.1025i			1.36815i	0.729413	+	0.684073i	$0.239793\pi$
$947$			42.1025i			1.36815i	−0.729413	+	0.684073i	$0.760207\pi$
$948$	−2.24644			−0.0729609
$949$			2.58674i			0.0839693i
$950$	−31.3624			−1.01753
$951$	−2.55147			−0.0827371
$952$	−7.09606	−	13.8431i	−0.229985	−	0.448658i
$953$	34.4869			1.11714			0.558571	−	0.829457i	$-0.311350\pi$
$953$	34.4869			1.11714			0.558571	+	0.829457i	$0.311350\pi$
$954$	10.4556			0.338514
$955$		−	4.20453i		−	0.136055i
$956$	17.5490			0.567577
$957$			32.9930i			1.06651i
$958$		−	24.0431i		−	0.776798i
$959$			2.62083i			0.0846310i
$960$	5.01117			0.161735
$961$	13.0155			0.419854
$962$			15.2734i			0.492436i
$963$			5.01812i			0.161707i
$964$			67.3509i			2.16923i
$965$	−2.29436			−0.0738581
$966$		−	13.7295i		−	0.441741i
$967$	14.1460			0.454905			0.227453	−	0.973789i	$-0.426960\pi$
$967$	14.1460			0.454905			0.227453	+	0.973789i	$0.426960\pi$
$968$	−0.568576			−0.0182747
$969$	8.23903	+	16.0729i	0.264676	+	0.516335i
$970$	−0.747631			−0.0240050
$971$	−27.7901			−0.891827			−0.445914	−	0.895076i	$-0.647121\pi$
$971$	−27.7901			−0.891827			−0.445914	+	0.895076i	$0.647121\pi$
$972$		−	13.5341i		−	0.434108i
$973$	−5.56544			−0.178420
$974$			10.3090i			0.330320i
$975$			6.76011i			0.216497i
$976$		−	6.39697i		−	0.204762i
$977$	19.8969			0.636557			0.318279	−	0.947997i	$-0.396895\pi$
$977$	19.8969			0.636557			0.318279	+	0.947997i	$0.396895\pi$
$978$	12.4964			0.399591
$979$			29.3647i			0.938501i
$980$		−	5.42686i		−	0.173355i
$981$			3.50362i			0.111862i
$982$	−38.3953			−1.22524
$983$			59.2583i			1.89005i	0.327004	+	0.945023i	$0.393961\pi$
$983$			59.2583i			1.89005i	−0.327004	+	0.945023i	$0.606039\pi$
$984$	−22.7858			−0.726386
$985$	5.15027			0.164101
$986$	−27.3509	−	53.3568i	−0.871032	−	1.69923i
$987$	5.97055			0.190045
$988$	−8.08044			−0.257073
$989$		−	3.45542i		−	0.109876i
$990$	0.743290			0.0236233
$991$		−	38.4950i		−	1.22283i	−0.791308	−	0.611417i	$-0.790600\pi$
$991$		−	38.4950i		−	1.22283i	0.791308	−	0.611417i	$-0.209400\pi$
$992$		−	16.2579i		−	0.516190i
$993$		−	13.7485i		−	0.436295i
$994$	33.9490			1.07680
$995$	−5.81691			−0.184409
$996$			11.1212i			0.352388i
$997$		−	42.6805i		−	1.35171i	−0.737036	−	0.675853i	$-0.763775\pi$
$997$		−	42.6805i		−	1.35171i	0.737036	−	0.675853i	$-0.236225\pi$
$998$			97.7604i			3.09455i
$999$	41.9676			1.32779

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.d.c.560.1	✓	20
17.16	even	2	inner	731.2.d.c.560.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.d.c.560.1	✓	20	1.1	even	1	trivial
731.2.d.c.560.2	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)

\(f(q)\)	\(=\)	\(q-2.35369 q^{2} -1.62169i q^{3} +3.53987 q^{4} -0.259122i q^{5} +3.81697i q^{6} -1.04097i q^{7} -3.62439 q^{8} +0.370107 q^{9} +O(q^{10})\)	\(q-2.35369 q^{2} -1.62169i q^{3} +3.53987 q^{4} -0.259122i q^{5} +3.81697i q^{6} -1.04097i q^{7} -3.62439 q^{8} +0.370107 q^{9} +0.609893i q^{10} -3.29289i q^{11} -5.74059i q^{12} -0.845057 q^{13} +2.45011i q^{14} -0.420216 q^{15} +1.45095 q^{16} +(-3.66913 + 1.88082i) q^{17} -0.871119 q^{18} +2.70123 q^{19} -0.917258i q^{20} -1.68813 q^{21} +7.75045i q^{22} -3.45542i q^{23} +5.87765i q^{24} +4.93286 q^{25} +1.98901 q^{26} -5.46528i q^{27} -3.68488i q^{28} -6.17840i q^{29} +0.989060 q^{30} -4.24082i q^{31} +3.83368 q^{32} -5.34006 q^{33} +(8.63601 - 4.42686i) q^{34} -0.269737 q^{35} +1.31013 q^{36} +7.67893i q^{37} -6.35786 q^{38} +1.37042i q^{39} +0.939157i q^{40} +3.87669i q^{41} +3.97333 q^{42} +1.00000 q^{43} -11.6564i q^{44} -0.0959028i q^{45} +8.13300i q^{46} -3.53679 q^{47} -2.35300i q^{48} +5.91639 q^{49} -11.6104 q^{50} +(3.05011 + 5.95021i) q^{51} -2.99140 q^{52} -12.0025 q^{53} +12.8636i q^{54} -0.853259 q^{55} +3.77286i q^{56} -4.38056i q^{57} +14.5421i q^{58} -1.58575 q^{59} -1.48751 q^{60} -4.40881i q^{61} +9.98158i q^{62} -0.385269i q^{63} -11.9252 q^{64} +0.218973i q^{65} +12.5689 q^{66} -9.54045 q^{67} +(-12.9883 + 6.65785i) q^{68} -5.60364 q^{69} +0.634878 q^{70} -13.8561i q^{71} -1.34141 q^{72} -3.06103i q^{73} -18.0739i q^{74} -7.99958i q^{75} +9.56200 q^{76} -3.42778 q^{77} -3.22556i q^{78} -0.391325i q^{79} -0.375973i q^{80} -7.75270 q^{81} -9.12454i q^{82} -1.93729 q^{83} -5.97576 q^{84} +(0.487360 + 0.950752i) q^{85} -2.35369 q^{86} -10.0195 q^{87} +11.9347i q^{88} -8.91762 q^{89} +0.225726i q^{90} +0.879675i q^{91} -12.2318i q^{92} -6.87731 q^{93} +8.32452 q^{94} -0.699946i q^{95} -6.21706i q^{96} +1.22584i q^{97} -13.9254 q^{98} -1.21872i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 42 q^{4} + 18 q^{8} - 18 q^{9}+O(q^{10}) \) 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

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Database

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