LMFDB - Embedded newform 494.2.d.c.77.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [494,2,Mod(77,494)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("494.77"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(494, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 494 = 2 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	494.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.94460985985$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 36x^{12} + 492x^{10} + 3171x^{8} + 9678x^{6} + 11765x^{4} + 1893x^{2} + 4 $ x^14 + 36x^12 + 492x^10 + 3171x^8 + 9678x^6 + 11765x^4 + 1893x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			77.10
Root			$-0.431028i$ of defining polynomial
Character	$\chi$	$=$	494.77
Dual form			494.2.d.c.77.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -0.431028 q^{3} -1.00000 q^{4} +0.638027i q^{5} -0.431028i q^{6} -2.88689i q^{7} -1.00000i q^{8} -2.81422 q^{9} -0.638027 q^{10} +4.60137i q^{11} +0.431028 q^{12} +(-3.23697 + 1.58809i) q^{13} +2.88689 q^{14} -0.275008i q^{15} +1.00000 q^{16} -6.56224 q^{17} -2.81422i q^{18} +1.00000i q^{19} -0.638027i q^{20} +1.24433i q^{21} -4.60137 q^{22} -8.91550 q^{23} +0.431028i q^{24} +4.59292 q^{25} +(-1.58809 - 3.23697i) q^{26} +2.50609 q^{27} +2.88689i q^{28} +0.265542 q^{29} +0.275008 q^{30} -2.61805i q^{31} +1.00000i q^{32} -1.98332i q^{33} -6.56224i q^{34} +1.84191 q^{35} +2.81422 q^{36} -5.69657i q^{37} -1.00000 q^{38} +(1.39522 - 0.684513i) q^{39} +0.638027 q^{40} +0.820197i q^{41} -1.24433 q^{42} -0.882033 q^{43} -4.60137i q^{44} -1.79555i q^{45} -8.91550i q^{46} +1.44894i q^{47} -0.431028 q^{48} -1.33411 q^{49} +4.59292i q^{50} +2.82851 q^{51} +(3.23697 - 1.58809i) q^{52} -8.64940 q^{53} +2.50609i q^{54} -2.93580 q^{55} -2.88689 q^{56} -0.431028i q^{57} +0.265542i q^{58} +8.55699i q^{59} +0.275008i q^{60} +6.21427 q^{61} +2.61805 q^{62} +8.12432i q^{63} -1.00000 q^{64} +(-1.01325 - 2.06527i) q^{65} +1.98332 q^{66} +10.0382i q^{67} +6.56224 q^{68} +3.84283 q^{69} +1.84191i q^{70} +3.88072i q^{71} +2.81422i q^{72} -8.05237i q^{73} +5.69657 q^{74} -1.97968 q^{75} -1.00000i q^{76} +13.2836 q^{77} +(0.684513 + 1.39522i) q^{78} -9.12448 q^{79} +0.638027i q^{80} +7.36245 q^{81} -0.820197 q^{82} +8.35868i q^{83} -1.24433i q^{84} -4.18689i q^{85} -0.882033i q^{86} -0.114456 q^{87} +4.60137 q^{88} -15.1114i q^{89} +1.79555 q^{90} +(4.58465 + 9.34476i) q^{91} +8.91550 q^{92} +1.12845i q^{93} -1.44894 q^{94} -0.638027 q^{95} -0.431028i q^{96} +2.31791i q^{97} -1.33411i q^{98} -12.9492i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 4 q^{3} - 14 q^{4} + 30 q^{9} - 4 q^{10} - 4 q^{12} - 2 q^{13} + 2 q^{14} + 14 q^{16} - 32 q^{17} + 10 q^{22} - 6 q^{23} - 14 q^{25} + 10 q^{26} + 10 q^{27} - 14 q^{29} - 26 q^{30} + 2 q^{35} - 30 q^{36}+ \cdots - 4 q^{95}+O(q^{100}) $ 14 * q + 4 * q^3 - 14 * q^4 + 30 * q^9 - 4 * q^10 - 4 * q^12 - 2 * q^13 + 2 * q^14 + 14 * q^16 - 32 * q^17 + 10 * q^22 - 6 * q^23 - 14 * q^25 + 10 * q^26 + 10 * q^27 - 14 * q^29 - 26 * q^30 + 2 * q^35 - 30 * q^36 - 14 * q^38 + 36 * q^39 + 4 * q^40 - 6 * q^42 - 46 * q^43 + 4 * q^48 - 28 * q^49 + 32 * q^51 + 2 * q^52 + 42 * q^53 + 16 * q^55 - 2 * q^56 - 12 * q^61 - 22 * q^62 - 14 * q^64 + 2 * q^65 + 12 * q^66 + 32 * q^68 - 96 * q^69 - 6 * q^74 - 10 * q^75 + 52 * q^77 + 22 * q^78 - 8 * q^79 + 102 * q^81 - 30 * q^82 - 32 * q^87 - 10 * q^88 + 76 * q^90 + 22 * q^91 + 6 * q^92 - 2 * q^94 - 4 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/494\mathbb{Z}\right)^\times$.

$n$	$287$	$457$
$\chi(n)$	$1$	$-1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.431028			−0.248854			−0.124427	−	0.992229i	$-0.539709\pi$
$3$	−0.431028			−0.248854			−0.124427	+	0.992229i	$0.539709\pi$
$4$	−1.00000			−0.500000
$5$			0.638027i			0.285334i	0.989771	+	0.142667i	$0.0455679\pi$
$5$			0.638027i			0.285334i	−0.989771	+	0.142667i	$0.954432\pi$
$6$		−	0.431028i		−	0.175966i
$7$		−	2.88689i		−	1.09114i	−0.838065	−	0.545570i	$-0.816313\pi$
$7$		−	2.88689i		−	1.09114i	0.838065	−	0.545570i	$-0.183687\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.81422			−0.938072
$10$	−0.638027			−0.201762
$11$			4.60137i			1.38736i	0.720281	+	0.693682i	$0.244013\pi$
$11$			4.60137i			1.38736i	−0.720281	+	0.693682i	$0.755987\pi$
$12$	0.431028			0.124427
$13$	−3.23697	+	1.58809i	−0.897773	+	0.440458i
$13$	−3.23697	+	1.58809i	−0.897773	+	0.440458i
$14$	2.88689			0.771553
$15$		−	0.275008i		−	0.0710066i
$16$	1.00000			0.250000
$17$	−6.56224			−1.59158			−0.795789	−	0.605574i	$-0.792943\pi$
$17$	−6.56224			−1.59158			−0.795789	+	0.605574i	$0.792943\pi$
$18$		−	2.81422i		−	0.663317i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$		−	0.638027i		−	0.142667i
$21$			1.24433i			0.271535i
$22$	−4.60137			−0.981015
$23$	−8.91550			−1.85901			−0.929505	−	0.368810i	$-0.879765\pi$
$23$	−8.91550			−1.85901			−0.929505	+	0.368810i	$0.879765\pi$
$24$			0.431028i			0.0879832i
$25$	4.59292			0.918584
$26$	−1.58809	−	3.23697i	−0.311451	−	0.634822i
$27$	2.50609			0.482297
$28$			2.88689i			0.545570i
$29$	0.265542			0.0493099			0.0246549	−	0.999696i	$-0.492151\pi$
$29$	0.265542			0.0493099			0.0246549	+	0.999696i	$0.492151\pi$
$30$	0.275008			0.0502093
$31$		−	2.61805i		−	0.470216i	−0.971969	−	0.235108i	$-0.924456\pi$
$31$		−	2.61805i		−	0.470216i	0.971969	−	0.235108i	$-0.0755443\pi$
$32$			1.00000i			0.176777i
$33$		−	1.98332i		−	0.345251i
$34$		−	6.56224i		−	1.12542i
$35$	1.84191			0.311340
$36$	2.81422			0.469036
$37$		−	5.69657i		−	0.936510i	−0.883593	−	0.468255i	$-0.844883\pi$
$37$		−	5.69657i		−	0.936510i	0.883593	−	0.468255i	$-0.155117\pi$
$38$	−1.00000			−0.162221
$39$	1.39522	−	0.684513i	0.223414	−	0.109610i
$40$	0.638027			0.100881
$41$			0.820197i			0.128093i	0.997947	+	0.0640466i	$0.0204006\pi$
$41$			0.820197i			0.128093i	−0.997947	+	0.0640466i	$0.979599\pi$
$42$	−1.24433			−0.192004
$43$	−0.882033			−0.134509			−0.0672544	−	0.997736i	$-0.521424\pi$
$43$	−0.882033			−0.134509			−0.0672544	+	0.997736i	$0.521424\pi$
$44$		−	4.60137i		−	0.693682i
$45$		−	1.79555i		−	0.267664i
$46$		−	8.91550i		−	1.31452i
$47$			1.44894i			0.211349i	0.994401	+	0.105675i	$0.0337002\pi$
$47$			1.44894i			0.211349i	−0.994401	+	0.105675i	$0.966300\pi$
$48$	−0.431028			−0.0622135
$49$	−1.33411			−0.190587
$50$			4.59292i			0.649537i
$51$	2.82851			0.396070
$52$	3.23697	−	1.58809i	0.448887	−	0.220229i
$53$	−8.64940			−1.18809			−0.594043	−	0.804433i	$-0.702469\pi$
$53$	−8.64940			−1.18809			−0.594043	+	0.804433i	$0.702469\pi$
$54$			2.50609i			0.341035i
$55$	−2.93580			−0.395863
$56$	−2.88689			−0.385776
$57$		−	0.431028i		−	0.0570910i
$58$			0.265542i			0.0348673i
$59$			8.55699i			1.11402i	0.830504	+	0.557012i	$0.188052\pi$
$59$			8.55699i			1.11402i	−0.830504	+	0.557012i	$0.811948\pi$
$60$			0.275008i			0.0355033i
$61$	6.21427			0.795655			0.397828	−	0.917460i	$-0.369764\pi$
$61$	6.21427			0.795655			0.397828	+	0.917460i	$0.369764\pi$
$62$	2.61805			0.332493
$63$			8.12432i			1.02357i
$64$	−1.00000			−0.125000
$65$	−1.01325	−	2.06527i	−0.125678	−	0.256166i
$66$	1.98332			0.244129
$67$			10.0382i			1.22637i	0.789941	+	0.613183i	$0.210111\pi$
$67$			10.0382i			1.22637i	−0.789941	+	0.613183i	$0.789889\pi$
$68$	6.56224			0.795789
$69$	3.84283			0.462622
$70$			1.84191i			0.220151i
$71$			3.88072i			0.460556i	0.973125	+	0.230278i	$0.0739636\pi$
$71$			3.88072i			0.460556i	−0.973125	+	0.230278i	$0.926036\pi$
$72$			2.81422i			0.331658i
$73$		−	8.05237i		−	0.942459i	−0.882011	−	0.471229i	$-0.843810\pi$
$73$		−	8.05237i		−	0.942459i	0.882011	−	0.471229i	$-0.156190\pi$
$74$	5.69657			0.662213
$75$	−1.97968			−0.228593
$76$		−	1.00000i		−	0.114708i
$77$	13.2836			1.51381
$78$	0.684513	+	1.39522i	0.0775058	+	0.157978i
$79$	−9.12448			−1.02658			−0.513292	−	0.858214i	$-0.671574\pi$
$79$	−9.12448			−1.02658			−0.513292	+	0.858214i	$0.671574\pi$
$80$			0.638027i			0.0713336i
$81$	7.36245			0.818050
$82$	−0.820197			−0.0905756
$83$			8.35868i			0.917484i	0.888569	+	0.458742i	$0.151700\pi$
$83$			8.35868i			0.917484i	−0.888569	+	0.458742i	$0.848300\pi$
$84$		−	1.24433i		−	0.135767i
$85$		−	4.18689i		−	0.454132i
$86$		−	0.882033i		−	0.0951121i
$87$	−0.114456			−0.0122710
$88$	4.60137			0.490507
$89$		−	15.1114i		−	1.60181i	−0.598793	−	0.800904i	$-0.704353\pi$
$89$		−	15.1114i		−	1.60181i	0.598793	−	0.800904i	$-0.295647\pi$
$90$	1.79555			0.189267
$91$	4.58465	+	9.34476i	0.480601	+	0.979597i
$92$	8.91550			0.929505
$93$			1.12845i			0.117015i
$94$	−1.44894			−0.149447
$95$	−0.638027			−0.0654602
$96$		−	0.431028i		−	0.0439916i
$97$			2.31791i			0.235349i	0.993052	+	0.117674i	$0.0375439\pi$
$97$			2.31791i			0.235349i	−0.993052	+	0.117674i	$0.962456\pi$
$98$		−	1.33411i		−	0.134765i
$99$		−	12.9492i		−	1.30145i
$100$	−4.59292			−0.459292
$101$	2.24285			0.223172			0.111586	−	0.993755i	$-0.464407\pi$
$101$	2.24285			0.223172			0.111586	+	0.993755i	$0.464407\pi$
$102$			2.82851i			0.280064i
$103$	−2.15291			−0.212132			−0.106066	−	0.994359i	$-0.533826\pi$
$103$	−2.15291			−0.212132			−0.106066	+	0.994359i	$0.533826\pi$
$104$	1.58809	+	3.23697i	0.155725	+	0.317411i
$105$	−0.793915			−0.0774782
$106$		−	8.64940i		−	0.840104i
$107$	11.0137			1.06474			0.532369	−	0.846512i	$-0.321302\pi$
$107$	11.0137			1.06474			0.532369	+	0.846512i	$0.321302\pi$
$108$	−2.50609			−0.241148
$109$			13.2324i			1.26743i	0.773566	+	0.633715i	$0.218471\pi$
$109$			13.2324i			1.26743i	−0.773566	+	0.633715i	$0.781529\pi$
$110$		−	2.93580i		−	0.279917i
$111$			2.45538i			0.233054i
$112$		−	2.88689i		−	0.272785i
$113$	4.63583			0.436102			0.218051	−	0.975937i	$-0.430030\pi$
$113$	4.63583			0.436102			0.218051	+	0.975937i	$0.430030\pi$
$114$	0.431028			0.0403695
$115$		−	5.68833i		−	0.530440i
$116$	−0.265542			−0.0246549
$117$	9.10952	−	4.46924i	0.842176	−	0.413181i
$118$	−8.55699			−0.787734
$119$			18.9444i			1.73663i
$120$	−0.275008			−0.0251046
$121$	−10.1726			−0.924779
$122$			6.21427i			0.562613i
$123$		−	0.353528i		−	0.0318765i
$124$			2.61805i			0.235108i
$125$			6.12055i			0.547438i
$126$	−8.12432			−0.723772
$127$	−10.8022			−0.958540			−0.479270	−	0.877668i	$-0.659098\pi$
$127$	−10.8022			−0.958540			−0.479270	+	0.877668i	$0.659098\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	0.380181			0.0334731
$130$	2.06527	−	1.01325i	0.181136	−	0.0888677i
$131$	17.5634			1.53452			0.767260	−	0.641336i	$-0.221620\pi$
$131$	17.5634			1.53452			0.767260	+	0.641336i	$0.221620\pi$
$132$			1.98332i			0.172626i
$133$	2.88689			0.250325
$134$	−10.0382			−0.867172
$135$			1.59895i			0.137616i
$136$			6.56224i			0.562708i
$137$			21.4219i			1.83019i	0.403236	+	0.915096i	$0.367885\pi$
$137$			21.4219i			1.83019i	−0.403236	+	0.915096i	$0.632115\pi$
$138$			3.84283i			0.327123i
$139$	−9.72043			−0.824476			−0.412238	−	0.911076i	$-0.635253\pi$
$139$	−9.72043			−0.824476			−0.412238	+	0.911076i	$0.635253\pi$
$140$	−1.84191			−0.155670
$141$		−	0.624533i		−	0.0525952i
$142$	−3.88072			−0.325662
$143$	−7.30740	−	14.8945i	−0.611076	−	1.24554i
$144$	−2.81422			−0.234518
$145$			0.169423i			0.0140698i
$146$	8.05237			0.666419
$147$	0.575038			0.0474284
$148$			5.69657i			0.468255i
$149$		−	21.4534i		−	1.75753i	−0.477255	−	0.878765i	$-0.658368\pi$
$149$		−	21.4534i		−	1.75753i	0.477255	−	0.878765i	$-0.341632\pi$
$150$		−	1.97968i		−	0.161640i
$151$			4.67100i			0.380121i	0.981772	+	0.190060i	$0.0608684\pi$
$151$			4.67100i			0.380121i	−0.981772	+	0.190060i	$0.939132\pi$
$152$	1.00000			0.0811107
$153$	18.4676			1.49301
$154$			13.2836i			1.07042i
$155$	1.67039			0.134169
$156$	−1.39522	+	0.684513i	−0.111707	+	0.0548049i
$157$	12.8145			1.02271			0.511356	−	0.859369i	$-0.329143\pi$
$157$	12.8145			1.02271			0.511356	+	0.859369i	$0.329143\pi$
$158$		−	9.12448i		−	0.725905i
$159$	3.72813			0.295660
$160$	−0.638027			−0.0504405
$161$			25.7380i			2.02844i
$162$			7.36245i			0.578449i
$163$			0.682086i			0.0534251i	0.999643	+	0.0267126i	$0.00850388\pi$
$163$			0.682086i			0.0534251i	−0.999643	+	0.0267126i	$0.991496\pi$
$164$		−	0.820197i		−	0.0640466i
$165$	1.26541			0.0985121
$166$	−8.35868			−0.648759
$167$			9.17257i			0.709795i	0.934905	+	0.354897i	$0.115484\pi$
$167$			9.17257i			0.709795i	−0.934905	+	0.354897i	$0.884516\pi$
$168$	1.24433			0.0960020
$169$	7.95592	−	10.2812i	0.611994	−	0.790863i
$170$	4.18689			0.321120
$171$		−	2.81422i		−	0.215208i
$172$	0.882033			0.0672544
$173$	−23.2870			−1.77048			−0.885240	−	0.465135i	$-0.846006\pi$
$173$	−23.2870			−1.77048			−0.885240	+	0.465135i	$0.846006\pi$
$174$		−	0.114456i		−	0.00867688i
$175$		−	13.2592i		−	1.00230i
$176$			4.60137i			0.346841i
$177$		−	3.68830i		−	0.277230i
$178$	15.1114			1.13265
$179$	−15.3521			−1.14747			−0.573735	−	0.819041i	$-0.694506\pi$
$179$	−15.3521			−1.14747			−0.573735	+	0.819041i	$0.694506\pi$
$180$			1.79555i			0.133832i
$181$	−0.346337			−0.0257430			−0.0128715	−	0.999917i	$-0.504097\pi$
$181$	−0.346337			−0.0257430			−0.0128715	+	0.999917i	$0.504097\pi$
$182$	−9.34476	+	4.58465i	−0.692679	+	0.339837i
$183$	−2.67852			−0.198002
$184$			8.91550i			0.657259i
$185$	3.63457			0.267219
$186$	−1.12845			−0.0827421
$187$		−	30.1953i		−	2.20810i
$188$		−	1.44894i		−	0.105675i
$189$		−	7.23479i		−	0.526254i
$190$		−	0.638027i		−	0.0462874i
$191$	−1.64856			−0.119286			−0.0596429	−	0.998220i	$-0.518996\pi$
$191$	−1.64856			−0.119286			−0.0596429	+	0.998220i	$0.518996\pi$
$192$	0.431028			0.0311068
$193$		−	11.2563i		−	0.810245i	−0.914262	−	0.405123i	$-0.867229\pi$
$193$		−	11.2563i		−	0.810245i	0.914262	−	0.405123i	$-0.132771\pi$
$194$	−2.31791			−0.166417
$195$	0.436738	+	0.890190i	0.0312754	+	0.0637479i
$196$	1.33411			0.0952936
$197$		−	17.3398i		−	1.23541i	−0.786410	−	0.617705i	$-0.788063\pi$
$197$		−	17.3398i		−	1.23541i	0.786410	−	0.617705i	$-0.211937\pi$
$198$	12.9492			0.920262
$199$	−12.5635			−0.890600			−0.445300	−	0.895382i	$-0.646903\pi$
$199$	−12.5635			−0.890600			−0.445300	+	0.895382i	$0.646903\pi$
$200$		−	4.59292i		−	0.324769i
$201$		−	4.32676i		−	0.305186i
$202$			2.24285i			0.157807i
$203$		−	0.766589i		−	0.0538040i
$204$	−2.82851			−0.198035
$205$	−0.523308			−0.0365494
$206$		−	2.15291i		−	0.150000i
$207$	25.0901			1.74388
$208$	−3.23697	+	1.58809i	−0.224443	+	0.110114i
$209$	−4.60137			−0.318283
$210$		−	0.793915i		−	0.0547854i
$211$	−12.3579			−0.850751			−0.425376	−	0.905017i	$-0.639858\pi$
$211$	−12.3579			−0.850751			−0.425376	+	0.905017i	$0.639858\pi$
$212$	8.64940			0.594043
$213$		−	1.67270i		−	0.114611i
$214$			11.0137i			0.752883i
$215$		−	0.562761i		−	0.0383800i
$216$		−	2.50609i		−	0.170518i
$217$	−7.55801			−0.513071
$218$	−13.2324			−0.896209
$219$			3.47080i			0.234535i
$220$	2.93580			0.197931
$221$	21.2418	−	10.4215i	1.42888	−	0.701023i
$222$	−2.45538			−0.164794
$223$		−	9.63105i		−	0.644943i	−0.946579	−	0.322471i	$-0.895486\pi$
$223$		−	9.63105i		−	0.644943i	0.946579	−	0.322471i	$-0.104514\pi$
$224$	2.88689			0.192888
$225$	−12.9255			−0.861698
$226$			4.63583i			0.308371i
$227$		−	3.55891i		−	0.236213i	−0.993001	−	0.118107i	$-0.962318\pi$
$227$		−	3.55891i		−	0.236213i	0.993001	−	0.118107i	$-0.0376825\pi$
$228$			0.431028i			0.0285455i
$229$			1.35007i			0.0892149i	0.999005	+	0.0446075i	$0.0142037\pi$
$229$			1.35007i			0.0892149i	−0.999005	+	0.0446075i	$0.985796\pi$
$230$	5.68833			0.375077
$231$	−5.72561			−0.376717
$232$		−	0.265542i		−	0.0174337i
$233$	3.00177			0.196652			0.0983262	−	0.995154i	$-0.468651\pi$
$233$	3.00177			0.196652			0.0983262	+	0.995154i	$0.468651\pi$
$234$	4.46924	+	9.10952i	0.292163	+	0.595508i
$235$	−0.924462			−0.0603053
$236$		−	8.55699i		−	0.557012i
$237$	3.93291			0.255470
$238$	−18.9444			−1.22799
$239$			28.7946i			1.86257i	0.364291	+	0.931285i	$0.381311\pi$
$239$			28.7946i			1.86257i	−0.364291	+	0.931285i	$0.618689\pi$
$240$		−	0.275008i		−	0.0177517i
$241$		−	6.96565i		−	0.448697i	−0.974509	−	0.224348i	$-0.927975\pi$
$241$		−	6.96565i		−	0.448697i	0.974509	−	0.224348i	$-0.0720254\pi$
$242$		−	10.1726i		−	0.653918i
$243$	−10.6917			−0.685872
$244$	−6.21427			−0.397828
$245$		−	0.851199i		−	0.0543811i
$246$	0.353528			0.0225401
$247$	−1.58809	−	3.23697i	−0.101048	−	0.205963i
$248$	−2.61805			−0.166246
$249$		−	3.60282i		−	0.228320i
$250$	−6.12055			−0.387097
$251$	3.51444			0.221830			0.110915	−	0.993830i	$-0.464622\pi$
$251$	3.51444			0.221830			0.110915	+	0.993830i	$0.464622\pi$
$252$		−	8.12432i		−	0.511784i
$253$		−	41.0235i		−	2.57912i
$254$		−	10.8022i		−	0.677790i
$255$			1.80467i			0.113013i
$256$	1.00000			0.0625000
$257$	−20.8301			−1.29935			−0.649673	−	0.760213i	$-0.725094\pi$
$257$	−20.8301			−1.29935			−0.649673	+	0.760213i	$0.725094\pi$
$258$			0.380181i			0.0236690i
$259$	−16.4453			−1.02186
$260$	1.01325	+	2.06527i	0.0628389	+	0.128083i
$261$	−0.747292			−0.0462562
$262$			17.5634i			1.08507i
$263$	9.99847			0.616532			0.308266	−	0.951300i	$-0.400251\pi$
$263$	9.99847			0.616532			0.308266	+	0.951300i	$0.400251\pi$
$264$	−1.98332			−0.122065
$265$		−	5.51855i		−	0.339002i
$266$			2.88689i			0.177006i
$267$			6.51344i			0.398616i
$268$		−	10.0382i		−	0.613183i
$269$	8.68190			0.529345			0.264672	−	0.964338i	$-0.414736\pi$
$269$	8.68190			0.529345			0.264672	+	0.964338i	$0.414736\pi$
$270$	−1.59895			−0.0973092
$271$		−	9.21067i		−	0.559509i	−0.960072	−	0.279754i	$-0.909747\pi$
$271$		−	9.21067i		−	0.559509i	0.960072	−	0.279754i	$-0.0902530\pi$
$272$	−6.56224			−0.397894
$273$	−1.97611	−	4.02785i	−0.119600	−	0.243777i
$274$	−21.4219			−1.29414
$275$			21.1337i			1.27441i
$276$	−3.84283			−0.231311
$277$	−14.0245			−0.842651			−0.421325	−	0.906910i	$-0.638435\pi$
$277$	−14.0245			−0.842651			−0.421325	+	0.906910i	$0.638435\pi$
$278$		−	9.72043i		−	0.582992i
$279$			7.36775i			0.441096i
$280$		−	1.84191i		−	0.110075i
$281$			28.3975i			1.69405i	0.531551	+	0.847026i	$0.321609\pi$
$281$			28.3975i			1.69405i	−0.531551	+	0.847026i	$0.678391\pi$
$282$	0.624533			0.0371904
$283$	−1.01213			−0.0601648			−0.0300824	−	0.999547i	$-0.509577\pi$
$283$	−1.01213			−0.0601648			−0.0300824	+	0.999547i	$0.509577\pi$
$284$		−	3.88072i		−	0.230278i
$285$	0.275008			0.0162900
$286$	14.8945	−	7.30740i	0.880729	−	0.432096i
$287$	2.36781			0.139768
$288$		−	2.81422i		−	0.165829i
$289$	26.0630			1.53312
$290$	−0.169423			−0.00994885
$291$		−	0.999086i		−	0.0585674i
$292$			8.05237i			0.471229i
$293$		−	31.9167i		−	1.86459i	−0.361695	−	0.932296i	$-0.617802\pi$
$293$		−	31.9167i		−	1.86459i	0.361695	−	0.932296i	$-0.382198\pi$
$294$			0.575038i			0.0335369i
$295$	−5.45959			−0.317870
$296$	−5.69657			−0.331106
$297$			11.5314i			0.669121i
$298$	21.4534			1.24276
$299$	28.8592	−	14.1586i	1.66897	−	0.818816i
$300$	1.97968			0.114297
$301$			2.54633i			0.146768i
$302$	−4.67100			−0.268786
$303$	−0.966732			−0.0555373
$304$			1.00000i			0.0573539i
$305$			3.96487i			0.227028i
$306$			18.4676i			1.05572i
$307$			25.0291i			1.42849i	0.699897	+	0.714244i	$0.253229\pi$
$307$			25.0291i			1.42849i	−0.699897	+	0.714244i	$0.746771\pi$
$308$	−13.2836			−0.756904
$309$	0.927962			0.0527899
$310$			1.67039i			0.0948716i
$311$	11.8393			0.671348			0.335674	−	0.941978i	$-0.391036\pi$
$311$	11.8393			0.671348			0.335674	+	0.941978i	$0.391036\pi$
$312$	−0.684513	−	1.39522i	−0.0387529	−	0.0789889i
$313$	−27.5763			−1.55870			−0.779352	−	0.626586i	$-0.784452\pi$
$313$	−27.5763			−1.55870			−0.779352	+	0.626586i	$0.784452\pi$
$314$			12.8145i			0.723166i
$315$	−5.18354			−0.292059
$316$	9.12448			0.513292
$317$		−	6.30277i		−	0.353999i	−0.984211	−	0.176999i	$-0.943361\pi$
$317$		−	6.30277i		−	0.353999i	0.984211	−	0.176999i	$-0.0566390\pi$
$318$			3.72813i			0.209063i
$319$			1.22185i			0.0684107i
$320$		−	0.638027i		−	0.0356668i
$321$	−4.74723			−0.264964
$322$	−25.7380			−1.43432
$323$		−	6.56224i		−	0.365133i
$324$	−7.36245			−0.409025
$325$	−14.8671	+	7.29399i	−0.824680	+	0.404598i
$326$	−0.682086			−0.0377773
$327$		−	5.70352i		−	0.315405i
$328$	0.820197			0.0452878
$329$	4.18292			0.230612
$330$			1.26541i			0.0696585i
$331$		−	25.0818i		−	1.37862i	−0.724465	−	0.689311i	$-0.757913\pi$
$331$		−	25.0818i		−	1.37862i	0.724465	−	0.689311i	$-0.242087\pi$
$332$		−	8.35868i		−	0.458742i
$333$			16.0314i			0.878514i
$334$	−9.17257			−0.501901
$335$	−6.40467			−0.349925
$336$			1.24433i			0.0678837i
$337$	−14.5105			−0.790435			−0.395218	−	0.918588i	$-0.629331\pi$
$337$	−14.5105			−0.790435			−0.395218	+	0.918588i	$0.629331\pi$
$338$	10.2812	+	7.95592i	0.559224	+	0.432745i
$339$	−1.99817			−0.108526
$340$			4.18689i			0.227066i
$341$	12.0466			0.652360
$342$	2.81422			0.152175
$343$		−	16.3568i		−	0.883183i
$344$			0.882033i			0.0475561i
$345$			2.45183i			0.132002i
$346$		−	23.2870i		−	1.25192i
$347$	−30.6848			−1.64725			−0.823624	−	0.567137i	$-0.808051\pi$
$347$	−30.6848			−1.64725			−0.823624	+	0.567137i	$0.808051\pi$
$348$	0.114456			0.00613548
$349$			27.8794i			1.49235i	0.665751	+	0.746174i	$0.268111\pi$
$349$			27.8794i			1.49235i	−0.665751	+	0.746174i	$0.731889\pi$
$350$	13.2592			0.708736
$351$	−8.11213	+	3.97990i	−0.432993	+	0.212432i
$352$	−4.60137			−0.245254
$353$		−	19.4245i		−	1.03386i	−0.856027	−	0.516931i	$-0.827075\pi$
$353$		−	19.4245i		−	1.03386i	0.856027	−	0.516931i	$-0.172925\pi$
$354$	3.68830			0.196031
$355$	−2.47600			−0.131413
$356$			15.1114i			0.800904i
$357$		−	8.16558i		−	0.432168i
$358$		−	15.3521i		−	0.811384i
$359$		−	9.30740i		−	0.491226i	−0.969368	−	0.245613i	$-0.921011\pi$
$359$		−	9.30740i		−	0.491226i	0.969368	−	0.245613i	$-0.0789892\pi$
$360$	−1.79555			−0.0946336
$361$	−1.00000			−0.0526316
$362$		−	0.346337i		−	0.0182030i
$363$	4.38466			0.230135
$364$	−4.58465	−	9.34476i	−0.240301	−	0.489798i
$365$	5.13763			0.268916
$366$		−	2.67852i		−	0.140009i
$367$	33.7248			1.76042			0.880211	−	0.474582i	$-0.157401\pi$
$367$	33.7248			1.76042			0.880211	+	0.474582i	$0.157401\pi$
$368$	−8.91550			−0.464752
$369$		−	2.30821i		−	0.120161i
$370$			3.63457i			0.188952i
$371$			24.9698i			1.29637i
$372$		−	1.12845i		−	0.0585075i
$373$	−34.8087			−1.80233			−0.901163	−	0.433481i	$-0.857285\pi$
$373$	−34.8087			−1.80233			−0.901163	+	0.433481i	$0.857285\pi$
$374$	30.1953			1.56136
$375$		−	2.63813i		−	0.136232i
$376$	1.44894			0.0747233
$377$	−0.859550	+	0.421705i	−0.0442691	+	0.0217189i
$378$	7.23479			0.372117
$379$			20.9251i			1.07485i	0.843311	+	0.537426i	$0.180603\pi$
$379$			20.9251i			1.07485i	−0.843311	+	0.537426i	$0.819397\pi$
$380$	0.638027			0.0327301
$381$	4.65605			0.238536
$382$		−	1.64856i		−	0.0843478i
$383$			31.2027i			1.59438i	0.603727	+	0.797191i	$0.293682\pi$
$383$			31.2027i			1.59438i	−0.603727	+	0.797191i	$0.706318\pi$
$384$			0.431028i			0.0219958i
$385$			8.47531i			0.431942i
$386$	11.2563			0.572930
$387$	2.48223			0.126179
$388$		−	2.31791i		−	0.117674i
$389$	2.75731			0.139801			0.0699007	−	0.997554i	$-0.477732\pi$
$389$	2.75731			0.139801			0.0699007	+	0.997554i	$0.477732\pi$
$390$	−0.890190	+	0.436738i	−0.0450765	+	0.0221151i
$391$	58.5057			2.95876
$392$			1.33411i			0.0673827i
$393$	−7.57031			−0.381872
$394$	17.3398			0.873566
$395$		−	5.82167i		−	0.292920i
$396$			12.9492i			0.650724i
$397$		−	6.80518i		−	0.341542i	−0.985311	−	0.170771i	$-0.945374\pi$
$397$		−	6.80518i		−	0.341542i	0.985311	−	0.170771i	$-0.0546258\pi$
$398$		−	12.5635i		−	0.629749i
$399$	−1.24433			−0.0622943
$400$	4.59292			0.229646
$401$			15.1868i			0.758392i	0.925316	+	0.379196i	$0.123799\pi$
$401$			15.1868i			0.758392i	−0.925316	+	0.379196i	$0.876201\pi$
$402$	4.32676			0.215799
$403$	4.15771	+	8.47454i	0.207110	+	0.422147i
$404$	−2.24285			−0.111586
$405$			4.69745i			0.233418i
$406$	0.766589			0.0380452
$407$	26.2120			1.29928
$408$		−	2.82851i		−	0.140032i
$409$			39.2965i			1.94309i	0.236863	+	0.971543i	$0.423881\pi$
$409$			39.2965i			1.94309i	−0.236863	+	0.971543i	$0.576119\pi$
$410$		−	0.523308i		−	0.0258443i
$411$		−	9.23341i		−	0.455451i
$412$	2.15291			0.106066
$413$	24.7030			1.21556
$414$			25.0901i			1.23311i
$415$	−5.33307			−0.261790
$416$	−1.58809	−	3.23697i	−0.0778627	−	0.158705i
$417$	4.18977			0.205174
$418$		−	4.60137i		−	0.225060i
$419$	12.6390			0.617454			0.308727	−	0.951151i	$-0.400097\pi$
$419$	12.6390			0.617454			0.308727	+	0.951151i	$0.400097\pi$
$420$	0.793915			0.0387391
$421$		−	15.3280i		−	0.747043i	−0.927621	−	0.373522i	$-0.878150\pi$
$421$		−	15.3280i		−	0.747043i	0.927621	−	0.373522i	$-0.121850\pi$
$422$		−	12.3579i		−	0.601572i
$423$		−	4.07763i		−	0.198261i
$424$			8.64940i			0.420052i
$425$	−30.1399			−1.46200
$426$	1.67270			0.0810424
$427$		−	17.9399i		−	0.868171i
$428$	−11.0137			−0.532369
$429$	3.14969	+	6.41993i	0.152069	+	0.309957i
$430$	0.562761			0.0271388
$431$			9.76456i			0.470343i	0.971954	+	0.235171i	$0.0755651\pi$
$431$			9.76456i			0.470343i	−0.971954	+	0.235171i	$0.924435\pi$
$432$	2.50609			0.120574
$433$	4.85897			0.233507			0.116754	−	0.993161i	$-0.462751\pi$
$433$	4.85897			0.233507			0.116754	+	0.993161i	$0.462751\pi$
$434$		−	7.55801i		−	0.362796i
$435$		−	0.0730260i		−	0.00350133i
$436$		−	13.2324i		−	0.633715i
$437$		−	8.91550i		−	0.426486i
$438$	−3.47080			−0.165841
$439$	−34.9555			−1.66833			−0.834167	−	0.551512i	$-0.814051\pi$
$439$	−34.9555			−1.66833			−0.834167	+	0.551512i	$0.814051\pi$
$440$			2.93580i			0.139959i
$441$	3.75447			0.178784
$442$	10.4215	+	21.2418i	0.495698	+	1.01037i
$443$	−37.2490			−1.76976			−0.884878	−	0.465823i	$-0.845758\pi$
$443$	−37.2490			−1.76976			−0.884878	+	0.465823i	$0.845758\pi$
$444$		−	2.45538i		−	0.116527i
$445$	9.64150			0.457051
$446$	9.63105			0.456043
$447$			9.24701i			0.437368i
$448$			2.88689i			0.136393i
$449$			21.2015i			1.00056i	0.865863	+	0.500281i	$0.166770\pi$
$449$			21.2015i			1.00056i	−0.865863	+	0.500281i	$0.833230\pi$
$450$		−	12.9255i		−	0.609312i
$451$	−3.77402			−0.177712
$452$	−4.63583			−0.218051
$453$		−	2.01333i		−	0.0945946i
$454$	3.55891			0.167028
$455$	−5.96221	+	2.92513i	−0.279513	+	0.137132i
$456$	−0.431028			−0.0201847
$457$		−	13.5355i		−	0.633162i	−0.948565	−	0.316581i	$-0.897465\pi$
$457$		−	13.5355i		−	0.633162i	0.948565	−	0.316581i	$-0.102535\pi$
$458$	−1.35007			−0.0630845
$459$	−16.4456			−0.767613
$460$			5.68833i			0.265220i
$461$		−	1.67381i		−	0.0779570i	−0.999240	−	0.0389785i	$-0.987590\pi$
$461$		−	1.67381i		−	0.0779570i	0.999240	−	0.0389785i	$-0.0124104\pi$
$462$		−	5.72561i		−	0.266379i
$463$			32.6931i			1.51938i	0.650288	+	0.759688i	$0.274648\pi$
$463$			32.6931i			1.51938i	−0.650288	+	0.759688i	$0.725352\pi$
$464$	0.265542			0.0123275
$465$	−0.719983			−0.0333884
$466$			3.00177i			0.139054i
$467$	1.81373			0.0839293			0.0419646	−	0.999119i	$-0.486638\pi$
$467$	1.81373			0.0839293			0.0419646	+	0.999119i	$0.486638\pi$
$468$	−9.10952	+	4.46924i	−0.421088	+	0.206591i
$469$	28.9793			1.33814
$470$		−	0.924462i		−	0.0426423i
$471$	−5.52342			−0.254506
$472$	8.55699			0.393867
$473$		−	4.05856i		−	0.186613i
$474$			3.93291i			0.180644i
$475$			4.59292i			0.210738i
$476$		−	18.9444i		−	0.868317i
$477$	24.3413			1.11451
$478$	−28.7946			−1.31704
$479$		−	14.8087i		−	0.676627i	−0.941033	−	0.338314i	$-0.890144\pi$
$479$		−	14.8087i		−	0.676627i	0.941033	−	0.338314i	$-0.109856\pi$
$480$	0.275008			0.0125523
$481$	9.04669	+	18.4396i	0.412493	+	0.840774i
$482$	6.96565			0.317277
$483$		−	11.0938i		−	0.504786i
$484$	10.1726			0.462390
$485$	−1.47889			−0.0671531
$486$		−	10.6917i		−	0.484985i
$487$		−	0.510775i		−	0.0231454i	−0.999933	−	0.0115727i	$-0.996316\pi$
$487$		−	0.510775i		−	0.0231454i	0.999933	−	0.0115727i	$-0.00368379\pi$
$488$		−	6.21427i		−	0.281307i
$489$		−	0.293998i		−	0.0132951i
$490$	0.851199			0.0384532
$491$	−5.42068			−0.244632			−0.122316	−	0.992491i	$-0.539032\pi$
$491$	−5.42068			−0.244632			−0.122316	+	0.992491i	$0.539032\pi$
$492$			0.353528i			0.0159383i
$493$	−1.74255			−0.0784805
$494$	3.23697	−	1.58809i	0.145638	−	0.0714517i
$495$	8.26197			0.371348
$496$		−	2.61805i		−	0.117554i
$497$	11.2032			0.502531
$498$	3.60282			0.161446
$499$			33.5451i			1.50168i	0.660483	+	0.750841i	$0.270352\pi$
$499$			33.5451i			1.50168i	−0.660483	+	0.750841i	$0.729648\pi$
$500$		−	6.12055i		−	0.273719i
$501$		−	3.95363i		−	0.176635i
$502$			3.51444i			0.156857i
$503$	14.5305			0.647883			0.323941	−	0.946077i	$-0.394992\pi$
$503$	14.5305			0.647883			0.323941	+	0.946077i	$0.394992\pi$
$504$	8.12432			0.361886
$505$			1.43100i			0.0636788i
$506$	41.0235			1.82372
$507$	−3.42922	+	4.43149i	−0.152297	+	0.196809i
$508$	10.8022			0.479270
$509$		−	23.3050i		−	1.03298i	−0.856294	−	0.516488i	$-0.827239\pi$
$509$		−	23.3050i		−	1.03298i	0.856294	−	0.516488i	$-0.172761\pi$
$510$	−1.80467			−0.0799119
$511$	−23.2463			−1.02835
$512$			1.00000i			0.0441942i
$513$			2.50609i			0.110647i
$514$		−	20.8301i		−	0.918777i
$515$		−	1.37361i		−	0.0605286i
$516$	−0.380181			−0.0167365
$517$	−6.66710			−0.293219
$518$		−	16.4453i		−	0.722567i
$519$	10.0374			0.440591
$520$	−2.06527	+	1.01325i	−0.0905682	+	0.0444338i
$521$	−9.97738			−0.437117			−0.218559	−	0.975824i	$-0.570135\pi$
$521$	−9.97738			−0.437117			−0.218559	+	0.975824i	$0.570135\pi$
$522$		−	0.747292i		−	0.0327081i
$523$	31.7209			1.38706			0.693530	−	0.720428i	$-0.256055\pi$
$523$	31.7209			1.38706			0.693530	+	0.720428i	$0.256055\pi$
$524$	−17.5634			−0.767260
$525$			5.71510i			0.249427i
$526$			9.99847i			0.435954i
$527$			17.1803i			0.748384i
$528$		−	1.98332i		−	0.0863128i
$529$	56.4861			2.45592
$530$	5.51855			0.239711
$531$		−	24.0812i		−	1.04504i
$532$	−2.88689			−0.125162
$533$	−1.30255	−	2.65495i	−0.0564197	−	0.114999i
$534$	−6.51344			−0.281864
$535$			7.02706i			0.303806i
$536$	10.0382			0.433586
$537$	6.61718			0.285553
$538$			8.68190i			0.374303i
$539$		−	6.13873i		−	0.264414i
$540$		−	1.59895i		−	0.0688080i
$541$		−	5.53445i		−	0.237945i	−0.992898	−	0.118972i	$-0.962040\pi$
$541$		−	5.53445i		−	0.237945i	0.992898	−	0.118972i	$-0.0379600\pi$
$542$	9.21067			0.395632
$543$	0.149281			0.00640625
$544$		−	6.56224i		−	0.281354i
$545$	−8.44261			−0.361642
$546$	4.02785	−	1.97611i	0.172376	−	0.0845697i
$547$	−8.75795			−0.374463			−0.187231	−	0.982316i	$-0.559951\pi$
$547$	−8.75795			−0.374463			−0.187231	+	0.982316i	$0.559951\pi$
$548$		−	21.4219i		−	0.915096i
$549$	−17.4883			−0.746382
$550$	−21.1337			−0.901145
$551$			0.265542i			0.0113125i
$552$		−	3.84283i		−	0.163562i
$553$			26.3413i			1.12015i
$554$		−	14.0245i		−	0.595844i
$555$	−1.56660			−0.0664985
$556$	9.72043			0.412238
$557$		−	9.54096i		−	0.404263i	−0.979358	−	0.202132i	$-0.935213\pi$
$557$		−	9.54096i		−	0.404263i	0.979358	−	0.202132i	$-0.0647869\pi$
$558$	−7.36775			−0.311902
$559$	2.85511	−	1.40075i	0.120758	−	0.0592455i
$560$	1.84191			0.0778350
$561$			13.0150i			0.549494i
$562$	−28.3975			−1.19788
$563$	17.5768			0.740775			0.370387	−	0.928877i	$-0.379225\pi$
$563$	17.5768			0.740775			0.370387	+	0.928877i	$0.379225\pi$
$564$			0.624533i			0.0262976i
$565$			2.95778i			0.124435i
$566$		−	1.01213i		−	0.0425429i
$567$		−	21.2546i		−	0.892607i
$568$	3.88072			0.162831
$569$	13.4946			0.565725			0.282863	−	0.959160i	$-0.408716\pi$
$569$	13.4946			0.565725			0.282863	+	0.959160i	$0.408716\pi$
$570$			0.275008i			0.0115188i
$571$	26.9508			1.12786			0.563928	−	0.825824i	$-0.309290\pi$
$571$	26.9508			1.12786			0.563928	+	0.825824i	$0.309290\pi$
$572$	7.30740	+	14.8945i	0.305538	+	0.622769i
$573$	0.710576			0.0296847
$574$			2.36781i			0.0988306i
$575$	−40.9482			−1.70766
$576$	2.81422			0.117259
$577$		−	24.6662i		−	1.02687i	−0.858129	−	0.513434i	$-0.828373\pi$
$577$		−	24.6662i		−	1.02687i	0.858129	−	0.513434i	$-0.171627\pi$
$578$			26.0630i			1.08408i
$579$			4.85177i			0.201633i
$580$		−	0.169423i		−	0.00703490i
$581$	24.1306			1.00110
$582$	0.999086			0.0414134
$583$		−	39.7990i		−	1.64831i
$584$	−8.05237			−0.333210
$585$	2.85150	+	5.81212i	0.117895	+	0.240302i
$586$	31.9167			1.31847
$587$		−	21.8785i		−	0.903023i	−0.892265	−	0.451512i	$-0.850885\pi$
$587$		−	21.8785i		−	0.903023i	0.892265	−	0.451512i	$-0.149115\pi$
$588$	−0.575038			−0.0237142
$589$	2.61805			0.107875
$590$		−	5.45959i		−	0.224768i
$591$			7.47393i			0.307437i
$592$		−	5.69657i		−	0.234128i
$593$			32.5713i			1.33754i	0.743469	+	0.668771i	$0.233179\pi$
$593$			32.5713i			1.33754i	−0.743469	+	0.668771i	$0.766821\pi$
$594$	−11.5314			−0.473140
$595$	−12.0871			−0.495522
$596$			21.4534i			0.878765i
$597$	5.41520			0.221629
$598$	14.1586	+	28.8592i	0.578990	+	1.18014i
$599$	−28.4380			−1.16194			−0.580972	−	0.813924i	$-0.697327\pi$
$599$	−28.4380			−1.16194			−0.580972	+	0.813924i	$0.697327\pi$
$600$			1.97968i			0.0808200i
$601$	−11.7155			−0.477885			−0.238943	−	0.971034i	$-0.576801\pi$
$601$	−11.7155			−0.477885			−0.238943	+	0.971034i	$0.576801\pi$
$602$	−2.54633			−0.103781
$603$		−	28.2498i		−	1.15042i
$604$		−	4.67100i		−	0.190060i
$605$		−	6.49038i		−	0.263871i
$606$		−	0.966732i		−	0.0392708i
$607$	47.3729			1.92281			0.961404	−	0.275142i	$-0.0887250\pi$
$607$	47.3729			1.92281			0.961404	+	0.275142i	$0.0887250\pi$
$608$	−1.00000			−0.0405554
$609$			0.330421i			0.0133893i
$610$	−3.96487			−0.160533
$611$	−2.30105	−	4.69017i	−0.0930905	−	0.189744i
$612$	−18.4676			−0.746507
$613$			25.2516i			1.01990i	0.860204	+	0.509951i	$0.170336\pi$
$613$			25.2516i			1.01990i	−0.860204	+	0.509951i	$0.829664\pi$
$614$	−25.0291			−1.01009
$615$	0.225560			0.00909547
$616$		−	13.2836i		−	0.535212i
$617$			14.4484i			0.581670i	0.956773	+	0.290835i	$0.0939331\pi$
$617$			14.4484i			0.581670i	−0.956773	+	0.290835i	$0.906067\pi$
$618$			0.927962i			0.0373281i
$619$		−	2.56785i		−	0.103211i	−0.998668	−	0.0516053i	$-0.983566\pi$
$619$		−	2.56785i		−	0.103211i	0.998668	−	0.0516053i	$-0.0164338\pi$
$620$	−1.67039			−0.0670844
$621$	−22.3430			−0.896595
$622$			11.8393i			0.474714i
$623$	−43.6250			−1.74780
$624$	1.39522	−	0.684513i	0.0558536	−	0.0274024i
$625$	19.0595			0.762381
$626$		−	27.5763i		−	1.10217i
$627$	1.98332			0.0792060
$628$	−12.8145			−0.511356
$629$			37.3823i			1.49053i
$630$		−	5.18354i		−	0.206517i
$631$			2.86547i			0.114073i	0.998372	+	0.0570364i	$0.0181651\pi$
$631$			2.86547i			0.114073i	−0.998372	+	0.0570364i	$0.981835\pi$
$632$			9.12448i			0.362952i
$633$	5.32659			0.211713
$634$	6.30277			0.250315
$635$		−	6.89210i		−	0.273504i
$636$	−3.72813			−0.147830
$637$	4.31847	−	2.11869i	0.171104	−	0.0839456i
$638$	−1.22185			−0.0483737
$639$		−	10.9212i		−	0.432035i
$640$	0.638027			0.0252202
$641$	−43.0464			−1.70023			−0.850115	−	0.526597i	$-0.823468\pi$
$641$	−43.0464			−1.70023			−0.850115	+	0.526597i	$0.823468\pi$
$642$		−	4.74723i		−	0.187358i
$643$		−	24.8973i		−	0.981855i	−0.871201	−	0.490927i	$-0.836658\pi$
$643$		−	24.8973i		−	0.981855i	0.871201	−	0.490927i	$-0.163342\pi$
$644$		−	25.7380i		−	1.01422i
$645$			0.242566i			0.00955102i
$646$	6.56224			0.258188
$647$	30.8434			1.21258			0.606290	−	0.795244i	$-0.292657\pi$
$647$	30.8434			1.21258			0.606290	+	0.795244i	$0.292657\pi$
$648$		−	7.36245i		−	0.289224i
$649$	−39.3738			−1.54556
$650$	−7.29399	−	14.8671i	−0.286094	−	0.583137i
$651$	3.25771			0.127680
$652$		−	0.682086i		−	0.0267126i
$653$	17.9116			0.700936			0.350468	−	0.936575i	$-0.386023\pi$
$653$	17.9116			0.700936			0.350468	+	0.936575i	$0.386023\pi$
$654$	5.70352			0.223025
$655$			11.2059i			0.437852i
$656$			0.820197i			0.0320233i
$657$			22.6611i			0.884094i
$658$			4.18292i			0.163067i
$659$	−45.0518			−1.75497			−0.877485	−	0.479605i	$-0.840780\pi$
$659$	−45.0518			−1.75497			−0.877485	+	0.479605i	$0.840780\pi$
$660$	−1.26541			−0.0492560
$661$			22.1057i			0.859811i	0.902874	+	0.429905i	$0.141453\pi$
$661$			22.1057i			0.859811i	−0.902874	+	0.429905i	$0.858547\pi$
$662$	25.0818			0.974833
$663$	−9.15579	+	4.49194i	−0.355581	+	0.174452i
$664$	8.35868			0.324380
$665$			1.84191i			0.0714263i
$666$	−16.0314			−0.621203
$667$	−2.36744			−0.0916675
$668$		−	9.17257i		−	0.354897i
$669$			4.15125i			0.160497i
$670$		−	6.40467i		−	0.247434i
$671$			28.5941i			1.10386i
$672$	−1.24433			−0.0480010
$673$	−46.4541			−1.79067			−0.895337	−	0.445390i	$-0.853065\pi$
$673$	−46.4541			−1.79067			−0.895337	+	0.445390i	$0.853065\pi$
$674$		−	14.5105i		−	0.558922i
$675$	11.5103			0.443030
$676$	−7.95592	+	10.2812i	−0.305997	+	0.395431i
$677$	−19.6630			−0.755709			−0.377855	−	0.925865i	$-0.623338\pi$
$677$	−19.6630			−0.755709			−0.377855	+	0.925865i	$0.623338\pi$
$678$		−	1.99817i		−	0.0767393i
$679$	6.69155			0.256798
$680$	−4.18689			−0.160560
$681$			1.53399i			0.0587827i
$682$			12.0466i			0.461288i
$683$			1.20504i			0.0461095i	0.999734	+	0.0230547i	$0.00733920\pi$
$683$			1.20504i			0.0461095i	−0.999734	+	0.0230547i	$0.992661\pi$
$684$			2.81422i			0.107604i
$685$	−13.6677			−0.522217
$686$	16.3568			0.624505
$687$		−	0.581916i		−	0.0222015i
$688$	−0.882033			−0.0336272
$689$	27.9978	−	13.7361i	1.06663	−	0.523302i
$690$	−2.45183			−0.0933395
$691$			24.1867i			0.920106i	0.887891	+	0.460053i	$0.152170\pi$
$691$			24.1867i			0.920106i	−0.887891	+	0.460053i	$0.847830\pi$
$692$	23.2870			0.885240
$693$	−37.3830			−1.42006
$694$		−	30.6848i		−	1.16478i
$695$		−	6.20190i		−	0.235251i
$696$			0.114456i			0.00433844i
$697$		−	5.38233i		−	0.203870i
$698$	−27.8794			−1.05525
$699$	−1.29385			−0.0489378
$700$			13.2592i			0.501152i
$701$	−1.39426			−0.0526605			−0.0263303	−	0.999653i	$-0.508382\pi$
$701$	−1.39426			−0.0526605			−0.0263303	+	0.999653i	$0.508382\pi$
$702$	−3.97990	−	8.11213i	−0.150212	−	0.306172i
$703$	5.69657			0.214850
$704$		−	4.60137i		−	0.173421i
$705$	0.398469			0.0150072
$706$	19.4245			0.731050
$707$		−	6.47486i		−	0.243512i
$708$			3.68830i			0.138615i
$709$		−	15.0569i		−	0.565474i	−0.959198	−	0.282737i	$-0.908758\pi$
$709$		−	15.0569i		−	0.565474i	0.959198	−	0.282737i	$-0.0912423\pi$
$710$		−	2.47600i		−	0.0929227i
$711$	25.6783			0.963010
$712$	−15.1114			−0.566325
$713$			23.3412i			0.874135i
$714$	8.16558			0.305589
$715$	9.50308	−	4.66232i	0.355395	−	0.174361i
$716$	15.3521			0.573735
$717$		−	12.4113i		−	0.463508i
$718$	9.30740			0.347349
$719$	−47.0705			−1.75543			−0.877716	−	0.479181i	$-0.840934\pi$
$719$	−47.0705			−1.75543			−0.877716	+	0.479181i	$0.840934\pi$
$720$		−	1.79555i		−	0.0669161i
$721$			6.21519i			0.231466i
$722$		−	1.00000i		−	0.0372161i
$723$			3.00239i			0.111660i
$724$	0.346337			0.0128715
$725$	1.21961			0.0452953
$726$			4.38466i			0.162730i
$727$	1.88605			0.0699499			0.0349750	−	0.999388i	$-0.488865\pi$
$727$	1.88605			0.0699499			0.0349750	+	0.999388i	$0.488865\pi$
$728$	9.34476	−	4.58465i	0.346340	−	0.169918i
$729$	−17.4789			−0.647368
$730$			5.13763i			0.190152i
$731$	5.78812			0.214081
$732$	2.67852			0.0990010
$733$		−	7.17673i		−	0.265079i	−0.991178	−	0.132539i	$-0.957687\pi$
$733$		−	7.17673i		−	0.265079i	0.991178	−	0.132539i	$-0.0423131\pi$
$734$			33.7248i			1.24481i
$735$			0.366890i			0.0135330i
$736$		−	8.91550i		−	0.328630i
$737$	−46.1896			−1.70142
$738$	2.30821			0.0849664
$739$		−	32.5256i		−	1.19647i	−0.801320	−	0.598237i	$-0.795868\pi$
$739$		−	32.5256i		−	1.19647i	0.801320	−	0.598237i	$-0.204132\pi$
$740$	−3.63457			−0.133609
$741$	0.684513	+	1.39522i	0.0251462	+	0.0512548i
$742$	−24.9698			−0.916671
$743$		−	43.6215i		−	1.60032i	−0.599788	−	0.800159i	$-0.704748\pi$
$743$		−	43.6215i		−	1.60032i	0.599788	−	0.800159i	$-0.295252\pi$
$744$	1.12845			0.0413711
$745$	13.6878			0.501484
$746$		−	34.8087i		−	1.27444i
$747$		−	23.5231i		−	0.860666i
$748$			30.1953i			1.10405i
$749$		−	31.7954i		−	1.16178i
$750$	2.63813			0.0963307
$751$	−29.7930			−1.08716			−0.543582	−	0.839356i	$-0.682932\pi$
$751$	−29.7930			−1.08716			−0.543582	+	0.839356i	$0.682932\pi$
$752$			1.44894i			0.0528374i
$753$	−1.51482			−0.0552032
$754$	−0.421705	−	0.859550i	−0.0153576	−	0.0313030i
$755$	−2.98023			−0.108462
$756$			7.23479i			0.263127i
$757$	−20.8435			−0.757570			−0.378785	−	0.925485i	$-0.623658\pi$
$757$	−20.8435			−0.757570			−0.378785	+	0.925485i	$0.623658\pi$
$758$	−20.9251			−0.760035
$759$			17.6823i			0.641825i
$760$			0.638027i			0.0231437i
$761$			21.5917i			0.782699i	0.920242	+	0.391349i	$0.127992\pi$
$761$			21.5917i			0.782699i	−0.920242	+	0.391349i	$0.872008\pi$
$762$			4.65605i			0.168671i
$763$	38.2003			1.38294
$764$	1.64856			0.0596429
$765$			11.7828i			0.426008i
$766$	−31.2027			−1.12740
$767$	−13.5893	−	27.6987i	−0.490681	−	1.00014i
$768$	−0.431028			−0.0155534
$769$		−	22.0124i		−	0.793788i	−0.917864	−	0.396894i	$-0.870088\pi$
$769$		−	22.0124i		−	0.793788i	0.917864	−	0.396894i	$-0.129912\pi$
$770$	−8.47531			−0.305429
$771$	8.97836			0.323348
$772$			11.2563i			0.405123i
$773$		−	21.5838i		−	0.776314i	−0.921593	−	0.388157i	$-0.873112\pi$
$773$		−	21.5838i		−	0.776314i	0.921593	−	0.388157i	$-0.126888\pi$
$774$			2.48223i			0.0892220i
$775$		−	12.0245i		−	0.431933i
$776$	2.31791			0.0832083
$777$	7.08840			0.254295
$778$			2.75731i			0.0988545i
$779$	−0.820197			−0.0293866
$780$	−0.436738	−	0.890190i	−0.0156377	−	0.0318739i
$781$	−17.8566			−0.638959
$782$			58.5057i			2.09216i
$783$	0.665471			0.0237820
$784$	−1.33411			−0.0476468
$785$			8.17602i			0.291815i
$786$		−	7.57031i		−	0.270024i
$787$			46.8382i			1.66960i	0.550551	+	0.834801i	$0.314417\pi$
$787$			46.8382i			1.66960i	−0.550551	+	0.834801i	$0.685583\pi$
$788$			17.3398i			0.617705i
$789$	−4.30962			−0.153427
$790$	5.82167			0.207126
$791$		−	13.3831i		−	0.475848i
$792$	−12.9492			−0.460131
$793$	−20.1154	+	9.86884i	−0.714318	+	0.350453i
$794$	6.80518			0.241507
$795$			2.37865i			0.0843620i
$796$	12.5635			0.445300
$797$	26.6794			0.945034			0.472517	−	0.881322i	$-0.343346\pi$
$797$	26.6794			0.945034			0.472517	+	0.881322i	$0.343346\pi$
$798$		−	1.24433i		−	0.0440487i
$799$		−	9.50829i		−	0.336379i
$800$			4.59292i			0.162384i
$801$			42.5268i			1.50261i
$802$	−15.1868			−0.536264
$803$	37.0519			1.30753
$804$			4.32676i			0.152593i
$805$	−16.4216			−0.578784
$806$	−8.47454	+	4.15771i	−0.298503	+	0.146449i
$807$	−3.74214			−0.131730
$808$		−	2.24285i		−	0.0789033i
$809$	−26.6389			−0.936574			−0.468287	−	0.883577i	$-0.655129\pi$
$809$	−26.6389			−0.936574			−0.468287	+	0.883577i	$0.655129\pi$
$810$	−4.69745			−0.165051
$811$		−	23.8647i		−	0.838004i	−0.907985	−	0.419002i	$-0.862380\pi$
$811$		−	23.8647i		−	0.838004i	0.907985	−	0.419002i	$-0.137620\pi$
$812$			0.766589i			0.0269020i
$813$			3.97006i			0.139236i
$814$			26.2120i			0.918730i
$815$	−0.435190			−0.0152440
$816$	2.82851			0.0990176
$817$		−	0.882033i		−	0.0308584i
$818$	−39.2965			−1.37397
$819$	−12.9022	−	26.2982i	−0.450839	−	0.918932i
$820$	0.523308			0.0182747
$821$		−	54.0858i		−	1.88761i	−0.330505	−	0.943804i	$-0.607219\pi$
$821$		−	54.0858i		−	1.88761i	0.330505	−	0.943804i	$-0.392781\pi$
$822$	9.23341			0.322052
$823$	22.0038			0.767004			0.383502	−	0.923540i	$-0.374718\pi$
$823$	22.0038			0.767004			0.383502	+	0.923540i	$0.374718\pi$
$824$			2.15291i			0.0750000i
$825$		−	9.10922i		−	0.317142i
$826$			24.7030i			0.859529i
$827$			37.8098i			1.31477i	0.753553	+	0.657387i	$0.228338\pi$
$827$			37.8098i			1.31477i	−0.753553	+	0.657387i	$0.771662\pi$
$828$	−25.0901			−0.871942
$829$	18.1992			0.632085			0.316042	−	0.948745i	$-0.397646\pi$
$829$	18.1992			0.632085			0.316042	+	0.948745i	$0.397646\pi$
$830$		−	5.33307i		−	0.185113i
$831$	6.04495			0.209697
$832$	3.23697	−	1.58809i	0.112222	−	0.0550572i
$833$	8.75475			0.303334
$834$			4.18977i			0.145080i
$835$	−5.85235			−0.202529
$836$	4.60137			0.159142
$837$		−	6.56106i		−	0.226784i
$838$			12.6390i			0.436606i
$839$		−	16.1631i		−	0.558011i	−0.960290	−	0.279005i	$-0.909995\pi$
$839$		−	16.1631i		−	0.558011i	0.960290	−	0.279005i	$-0.0900048\pi$
$840$			0.793915i			0.0273927i
$841$	−28.9295			−0.997569
$842$	15.3280			0.528239
$843$		−	12.2401i		−	0.421572i
$844$	12.3579			0.425376
$845$	6.55970	+	5.07609i	0.225660	+	0.174623i
$846$	4.07763			0.140192
$847$			29.3671i			1.00906i
$848$	−8.64940			−0.297021
$849$	0.436256			0.0149723
$850$		−	30.1399i		−	1.03379i
$851$			50.7878i			1.74098i
$852$			1.67270i			0.0573056i
$853$			38.6925i			1.32481i	0.749148	+	0.662403i	$0.230463\pi$
$853$			38.6925i			1.32481i	−0.749148	+	0.662403i	$0.769537\pi$
$854$	17.9399			0.613890
$855$	1.79555			0.0614064
$856$		−	11.0137i		−	0.376442i
$857$	32.1909			1.09962			0.549811	−	0.835289i	$-0.314700\pi$
$857$	32.1909			1.09962			0.549811	+	0.835289i	$0.314700\pi$
$858$	−6.41993	+	3.14969i	−0.219173	+	0.107529i
$859$	35.8795			1.22419			0.612096	−	0.790783i	$-0.290327\pi$
$859$	35.8795			1.22419			0.612096	+	0.790783i	$0.290327\pi$
$860$			0.562761i			0.0191900i
$861$	−1.02059			−0.0347817
$862$	−9.76456			−0.332582
$863$		−	19.9851i		−	0.680300i	−0.940371	−	0.340150i	$-0.889522\pi$
$863$		−	19.9851i		−	0.680300i	0.940371	−	0.340150i	$-0.110478\pi$
$864$			2.50609i			0.0852589i
$865$		−	14.8578i		−	0.505179i
$866$			4.85897i			0.165114i
$867$	−11.2339			−0.381523
$868$	7.55801			0.256536
$869$		−	41.9851i		−	1.42425i
$870$	0.0730260			0.00247581
$871$	−15.9417	−	32.4935i	−0.540163	−	1.10100i
$872$	13.2324			0.448104
$873$		−	6.52311i		−	0.220774i
$874$	8.91550			0.301571
$875$	17.6693			0.597332
$876$		−	3.47080i		−	0.117267i
$877$		−	36.1665i		−	1.22125i	−0.791918	−	0.610627i	$-0.790917\pi$
$877$		−	36.1665i		−	1.22125i	0.791918	−	0.610627i	$-0.209083\pi$
$878$		−	34.9555i		−	1.17969i
$879$			13.7570i			0.464011i
$880$	−2.93580			−0.0989657
$881$	21.5906			0.727407			0.363703	−	0.931515i	$-0.381512\pi$
$881$	21.5906			0.727407			0.363703	+	0.931515i	$0.381512\pi$
$882$			3.75447i			0.126420i
$883$	−14.6780			−0.493955			−0.246977	−	0.969021i	$-0.579437\pi$
$883$	−14.6780			−0.493955			−0.246977	+	0.969021i	$0.579437\pi$
$884$	−21.2418	+	10.4215i	−0.714438	+	0.350511i
$885$	2.35324			0.0791031
$886$		−	37.2490i		−	1.25141i
$887$	1.82719			0.0613510			0.0306755	−	0.999529i	$-0.490234\pi$
$887$	1.82719			0.0613510			0.0306755	+	0.999529i	$0.490234\pi$
$888$	2.45538			0.0823972
$889$			31.1847i			1.04590i
$890$			9.64150i			0.323184i
$891$			33.8773i			1.13493i
$892$			9.63105i			0.322471i
$893$	−1.44894			−0.0484869
$894$	−9.24701			−0.309266
$895$		−	9.79506i		−	0.327413i
$896$	−2.88689			−0.0964441
$897$	−12.4391	+	6.10277i	−0.415330	+	0.203766i
$898$	−21.2015			−0.707505
$899$		−	0.695201i		−	0.0231863i
$900$	12.9255			0.430849
$901$	56.7594			1.89093
$902$		−	3.77402i		−	0.125661i
$903$		−	1.09754i		−	0.0365238i
$904$		−	4.63583i		−	0.154185i
$905$		−	0.220972i		−	0.00734536i
$906$	2.01333			0.0668885
$907$	16.6533			0.552963			0.276481	−	0.961019i	$-0.410832\pi$
$907$	16.6533			0.552963			0.276481	+	0.961019i	$0.410832\pi$
$908$			3.55891i			0.118107i
$909$	−6.31187			−0.209352
$910$	−2.92513	−	5.96221i	−0.0969671	−	0.197645i
$911$	−8.19602			−0.271546			−0.135773	−	0.990740i	$-0.543352\pi$
$911$	−8.19602			−0.271546			−0.135773	+	0.990740i	$0.543352\pi$
$912$		−	0.431028i		−	0.0142728i
$913$	−38.4613			−1.27288
$914$	13.5355			0.447713
$915$		−	1.70897i		−	0.0564968i
$916$		−	1.35007i		−	0.0446075i
$917$		−	50.7035i		−	1.67438i
$918$		−	16.4456i		−	0.542784i
$919$	29.1620			0.961965			0.480983	−	0.876730i	$-0.340280\pi$
$919$	29.1620			0.961965			0.480983	+	0.876730i	$0.340280\pi$
$920$	−5.68833			−0.187539
$921$		−	10.7883i		−	0.355485i
$922$	1.67381			0.0551239
$923$	−6.16294	−	12.5617i	−0.202856	−	0.413475i
$924$	5.72561			0.188359
$925$		−	26.1639i		−	0.860264i
$926$	−32.6931			−1.07436
$927$	6.05874			0.198995
$928$			0.265542i			0.00871684i
$929$		−	31.6120i		−	1.03716i	−0.855030	−	0.518578i	$-0.826462\pi$
$929$		−	31.6120i		−	1.03716i	0.855030	−	0.518578i	$-0.173538\pi$
$930$		−	0.719983i		−	0.0236092i
$931$		−	1.33411i		−	0.0437237i
$932$	−3.00177			−0.0983262
$933$	−5.10309			−0.167068
$934$			1.81373i			0.0593470i
$935$	19.2654			0.630046
$936$	−4.46924	−	9.10952i	−0.146082	−	0.297754i
$937$	12.9749			0.423872			0.211936	−	0.977284i	$-0.432023\pi$
$937$	12.9749			0.423872			0.211936	+	0.977284i	$0.432023\pi$
$938$			28.9793i			0.946206i
$939$	11.8861			0.387890
$940$	0.924462			0.0301526
$941$			10.8460i			0.353569i	0.984250	+	0.176785i	$0.0565696\pi$
$941$			10.8460i			0.353569i	−0.984250	+	0.176785i	$0.943430\pi$
$942$		−	5.52342i		−	0.179963i
$943$		−	7.31246i		−	0.238127i
$944$			8.55699i			0.278506i
$945$	4.61599			0.150158
$946$	4.05856			0.131955
$947$			57.7947i			1.87807i	0.343816	+	0.939037i	$0.388280\pi$
$947$			57.7947i			1.87807i	−0.343816	+	0.939037i	$0.611720\pi$
$948$	−3.93291			−0.127735
$949$	12.7879	+	26.0653i	0.415114	+	0.846114i
$950$	−4.59292			−0.149014
$951$			2.71667i			0.0880940i
$952$	18.9444			0.613993
$953$	−3.47179			−0.112462			−0.0562312	−	0.998418i	$-0.517908\pi$
$953$	−3.47179			−0.112462			−0.0562312	+	0.998418i	$0.517908\pi$
$954$			24.3413i			0.788077i
$955$		−	1.05183i		−	0.0340363i
$956$		−	28.7946i		−	0.931285i
$957$		−	0.526653i		−	0.0170243i
$958$	14.8087			0.478448
$959$	61.8424			1.99700
$960$			0.275008i			0.00887583i
$961$	24.1458			0.778897
$962$	−18.4396	+	9.04669i	−0.594517	+	0.291677i
$963$	−30.9950			−0.998801
$964$			6.96565i			0.224348i
$965$	7.18182			0.231191
$966$	11.0938			0.356937
$967$		−	30.3475i		−	0.975910i	−0.872869	−	0.487955i	$-0.837743\pi$
$967$		−	30.3475i		−	0.975910i	0.872869	−	0.487955i	$-0.162257\pi$
$968$			10.1726i			0.326959i
$969$			2.82851i			0.0908648i
$970$		−	1.47889i		−	0.0474844i
$971$	−11.1055			−0.356392			−0.178196	−	0.983995i	$-0.557026\pi$
$971$	−11.1055			−0.356392			−0.178196	+	0.983995i	$0.557026\pi$
$972$	10.6917			0.342936
$973$			28.0618i			0.899619i
$974$	0.510775			0.0163663
$975$	6.40815	−	3.14391i	0.205225	−	0.100686i
$976$	6.21427			0.198914
$977$			46.1906i			1.47777i	0.673833	+	0.738884i	$0.264647\pi$
$977$			46.1906i			1.47777i	−0.673833	+	0.738884i	$0.735353\pi$
$978$	0.293998			0.00940103
$979$	69.5332			2.22229
$980$			0.851199i			0.0271905i
$981$		−	37.2387i		−	1.18894i
$982$		−	5.42068i		−	0.172981i
$983$		−	26.9821i		−	0.860595i	−0.902687	−	0.430298i	$-0.858409\pi$
$983$		−	26.9821i		−	0.860595i	0.902687	−	0.430298i	$-0.141591\pi$
$984$	−0.353528			−0.0112700
$985$	11.0633			0.352505
$986$		−	1.74255i		−	0.0554941i
$987$	−1.80296			−0.0573887
$988$	1.58809	+	3.23697i	0.0505240	+	0.102982i
$989$	7.86377			0.250053
$990$			8.26197i			0.262582i
$991$	4.48629			0.142512			0.0712558	−	0.997458i	$-0.477299\pi$
$991$	4.48629			0.142512			0.0712558	+	0.997458i	$0.477299\pi$
$992$	2.61805			0.0831232
$993$			10.8110i			0.343076i
$994$			11.2032i			0.355343i
$995$		−	8.01583i		−	0.254119i
$996$			3.60282i			0.114160i
$997$	49.3812			1.56392			0.781960	−	0.623329i	$-0.214220\pi$
$997$	49.3812			1.56392			0.781960	+	0.623329i	$0.214220\pi$
$998$	−33.5451			−1.06185
$999$		−	14.2761i		−	0.451676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	494.2.d.c.77.10	yes	14
13.5	odd	4		6422.2.a.bf.1.3		7
13.8	odd	4		6422.2.a.be.1.3		7
13.12	even	2	inner	494.2.d.c.77.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.d.c.77.3	✓	14	13.12	even	2	inner
494.2.d.c.77.10	yes	14	1.1	even	1	trivial
6422.2.a.be.1.3		7	13.8	odd	4
6422.2.a.bf.1.3		7	13.5	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 494 = 2 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	494.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -0.431028 q^{3} -1.00000 q^{4} +0.638027i q^{5} -0.431028i q^{6} -2.88689i q^{7} -1.00000i q^{8} -2.81422 q^{9} -0.638027 q^{10} +4.60137i q^{11} +0.431028 q^{12} +(-3.23697 + 1.58809i) q^{13} +2.88689 q^{14} -0.275008i q^{15} +1.00000 q^{16} -6.56224 q^{17} -2.81422i q^{18} +1.00000i q^{19} -0.638027i q^{20} +1.24433i q^{21} -4.60137 q^{22} -8.91550 q^{23} +0.431028i q^{24} +4.59292 q^{25} +(-1.58809 - 3.23697i) q^{26} +2.50609 q^{27} +2.88689i q^{28} +0.265542 q^{29} +0.275008 q^{30} -2.61805i q^{31} +1.00000i q^{32} -1.98332i q^{33} -6.56224i q^{34} +1.84191 q^{35} +2.81422 q^{36} -5.69657i q^{37} -1.00000 q^{38} +(1.39522 - 0.684513i) q^{39} +0.638027 q^{40} +0.820197i q^{41} -1.24433 q^{42} -0.882033 q^{43} -4.60137i q^{44} -1.79555i q^{45} -8.91550i q^{46} +1.44894i q^{47} -0.431028 q^{48} -1.33411 q^{49} +4.59292i q^{50} +2.82851 q^{51} +(3.23697 - 1.58809i) q^{52} -8.64940 q^{53} +2.50609i q^{54} -2.93580 q^{55} -2.88689 q^{56} -0.431028i q^{57} +0.265542i q^{58} +8.55699i q^{59} +0.275008i q^{60} +6.21427 q^{61} +2.61805 q^{62} +8.12432i q^{63} -1.00000 q^{64} +(-1.01325 - 2.06527i) q^{65} +1.98332 q^{66} +10.0382i q^{67} +6.56224 q^{68} +3.84283 q^{69} +1.84191i q^{70} +3.88072i q^{71} +2.81422i q^{72} -8.05237i q^{73} +5.69657 q^{74} -1.97968 q^{75} -1.00000i q^{76} +13.2836 q^{77} +(0.684513 + 1.39522i) q^{78} -9.12448 q^{79} +0.638027i q^{80} +7.36245 q^{81} -0.820197 q^{82} +8.35868i q^{83} -1.24433i q^{84} -4.18689i q^{85} -0.882033i q^{86} -0.114456 q^{87} +4.60137 q^{88} -15.1114i q^{89} +1.79555 q^{90} +(4.58465 + 9.34476i) q^{91} +8.91550 q^{92} +1.12845i q^{93} -1.44894 q^{94} -0.638027 q^{95} -0.431028i q^{96} +2.31791i q^{97} -1.33411i q^{98} -12.9492i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 4 q^{3} - 14 q^{4} + 30 q^{9} - 4 q^{10} - 4 q^{12} - 2 q^{13} + 2 q^{14} + 14 q^{16} - 32 q^{17} + 10 q^{22} - 6 q^{23} - 14 q^{25} + 10 q^{26} + 10 q^{27} - 14 q^{29} - 26 q^{30} + 2 q^{35} - 30 q^{36}+ \cdots - 4 q^{95}+O(q^{100}) \) 14 * q + 4 * q^3 - 14 * q^4 + 30 * q^9 - 4 * q^10 - 4 * q^12 - 2 * q^13 + 2 * q^14 + 14 * q^16 - 32 * q^17 + 10 * q^22 - 6 * q^23 - 14 * q^25 + 10 * q^26 + 10 * q^27 - 14 * q^29 - 26 * q^30 + 2 * q^35 - 30 * q^36 - 14 * q^38 + 36 * q^39 + 4 * q^40 - 6 * q^42 - 46 * q^43 + 4 * q^48 - 28 * q^49 + 32 * q^51 + 2 * q^52 + 42 * q^53 + 16 * q^55 - 2 * q^56 - 12 * q^61 - 22 * q^62 - 14 * q^64 + 2 * q^65 + 12 * q^66 + 32 * q^68 - 96 * q^69 - 6 * q^74 - 10 * q^75 + 52 * q^77 + 22 * q^78 - 8 * q^79 + 102 * q^81 - 30 * q^82 - 32 * q^87 - 10 * q^88 + 76 * q^90 + 22 * q^91 + 6 * q^92 - 2 * q^94 - 4 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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