LMFDB - Embedded newform 354.2.c.b.353.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(353,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.353");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.c (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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.41542366334681088.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - x^{8} - 2x^{7} + 2x^{6} + 14x^{5} + 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 $ x^10 - x^9 - x^8 - 2x^7 + 2x^6 + 14x^5 + 6x^4 - 18x^3 - 27x^2 - 81*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			353.7
Root			$-0.869925 - 1.49774i$ of defining polynomial
Character	$\chi$	$=$	354.353
Dual form			354.2.c.b.353.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.869925 - 1.49774i) q^{3} +1.00000 q^{4} -1.66014i q^{5} +(0.869925 - 1.49774i) q^{6} -3.57946 q^{7} +1.00000 q^{8} +(-1.48646 - 2.60585i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.869925 - 1.49774i) q^{3} +1.00000 q^{4} -1.66014i q^{5} +(0.869925 - 1.49774i) q^{6} -3.57946 q^{7} +1.00000 q^{8} +(-1.48646 - 2.60585i) q^{9} -1.66014i q^{10} +4.82340 q^{11} +(0.869925 - 1.49774i) q^{12} -0.418899i q^{13} -3.57946 q^{14} +(-2.48646 - 1.44420i) q^{15} +1.00000 q^{16} +0.742751i q^{17} +(-1.48646 - 2.60585i) q^{18} +1.24394 q^{19} -1.66014i q^{20} +(-3.11386 + 5.36111i) q^{21} +4.82340 q^{22} -1.25480 q^{23} +(0.869925 - 1.49774i) q^{24} +2.24394 q^{25} -0.418899i q^{26} +(-5.19599 - 0.0405586i) q^{27} -3.57946 q^{28} +4.78075i q^{29} +(-2.48646 - 1.44420i) q^{30} +10.4469i q^{31} +1.00000 q^{32} +(4.19599 - 7.22420i) q^{33} +0.742751i q^{34} +5.94240i q^{35} +(-1.48646 - 2.60585i) q^{36} +6.02199i q^{37} +1.24394 q^{38} +(-0.627402 - 0.364411i) q^{39} -1.66014i q^{40} -9.24875i q^{41} +(-3.11386 + 5.36111i) q^{42} -3.58258i q^{43} +4.82340 q^{44} +(-4.32607 + 2.46773i) q^{45} -1.25480 q^{46} +8.39199 q^{47} +(0.869925 - 1.49774i) q^{48} +5.81253 q^{49} +2.24394 q^{50} +(1.11245 + 0.646138i) q^{51} -0.418899i q^{52} -9.66765i q^{53} +(-5.19599 - 0.0405586i) q^{54} -8.00751i q^{55} -3.57946 q^{56} +(1.08213 - 1.86310i) q^{57} +4.78075i q^{58} +(-5.47701 + 5.38539i) q^{59} +(-2.48646 - 1.44420i) q^{60} +9.08804i q^{61} +10.4469i q^{62} +(5.32072 + 9.32752i) q^{63} +1.00000 q^{64} -0.695430 q^{65} +(4.19599 - 7.22420i) q^{66} +13.0941i q^{67} +0.742751i q^{68} +(-1.09159 + 1.87937i) q^{69} +5.94240i q^{70} +4.01996i q^{71} +(-1.48646 - 2.60585i) q^{72} -10.6897i q^{73} +6.02199i q^{74} +(1.95206 - 3.36084i) q^{75} +1.24394 q^{76} -17.2652 q^{77} +(-0.627402 - 0.364411i) q^{78} +3.55772 q^{79} -1.66014i q^{80} +(-4.58087 + 7.74697i) q^{81} -9.24875i q^{82} +2.87316 q^{83} +(-3.11386 + 5.36111i) q^{84} +1.23307 q^{85} -3.58258i q^{86} +(7.16033 + 4.15890i) q^{87} +4.82340 q^{88} -16.0885 q^{89} +(-4.32607 + 2.46773i) q^{90} +1.49943i q^{91} -1.25480 q^{92} +(15.6468 + 9.08804i) q^{93} +8.39199 q^{94} -2.06511i q^{95} +(0.869925 - 1.49774i) q^{96} -11.5275i q^{97} +5.81253 q^{98} +(-7.16979 - 12.5690i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - q^{3} + 10 q^{4} - q^{6} - 2 q^{7} + 10 q^{8} + 3 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - q^3 + 10 * q^4 - q^6 - 2 * q^7 + 10 * q^8 + 3 * q^9	$ 10 q + 10 q^{2} - q^{3} + 10 q^{4} - q^{6} - 2 q^{7} + 10 q^{8} + 3 q^{9} - 4 q^{11} - q^{12} - 2 q^{14} - 7 q^{15} + 10 q^{16} + 3 q^{18} - 6 q^{19} - 3 q^{21} - 4 q^{22} + 8 q^{23} - q^{24} + 4 q^{25} - 10 q^{27} - 2 q^{28} - 7 q^{30} + 10 q^{32} + 3 q^{36} - 6 q^{38} + 4 q^{39} - 3 q^{42} - 4 q^{44} - 11 q^{45} + 8 q^{46} - q^{48} + 8 q^{49} + 4 q^{50} + 2 q^{51} - 10 q^{54} - 2 q^{56} - 3 q^{57} - 20 q^{59} - 7 q^{60} - 19 q^{63} + 10 q^{64} - 16 q^{65} - 14 q^{69} + 3 q^{72} - 4 q^{75} - 6 q^{76} - 48 q^{77} + 4 q^{78} + 6 q^{79} + 7 q^{81} - 12 q^{83} - 3 q^{84} - 4 q^{85} - 15 q^{87} - 4 q^{88} + 16 q^{89} - 11 q^{90} + 8 q^{92} + 52 q^{93} - q^{96} + 8 q^{98} - 2 q^{99}+O(q^{100}) $ 10 * q + 10 * q^2 - q^3 + 10 * q^4 - q^6 - 2 * q^7 + 10 * q^8 + 3 * q^9 - 4 * q^11 - q^12 - 2 * q^14 - 7 * q^15 + 10 * q^16 + 3 * q^18 - 6 * q^19 - 3 * q^21 - 4 * q^22 + 8 * q^23 - q^24 + 4 * q^25 - 10 * q^27 - 2 * q^28 - 7 * q^30 + 10 * q^32 + 3 * q^36 - 6 * q^38 + 4 * q^39 - 3 * q^42 - 4 * q^44 - 11 * q^45 + 8 * q^46 - q^48 + 8 * q^49 + 4 * q^50 + 2 * q^51 - 10 * q^54 - 2 * q^56 - 3 * q^57 - 20 * q^59 - 7 * q^60 - 19 * q^63 + 10 * q^64 - 16 * q^65 - 14 * q^69 + 3 * q^72 - 4 * q^75 - 6 * q^76 - 48 * q^77 + 4 * q^78 + 6 * q^79 + 7 * q^81 - 12 * q^83 - 3 * q^84 - 4 * q^85 - 15 * q^87 - 4 * q^88 + 16 * q^89 - 11 * q^90 + 8 * q^92 + 52 * q^93 - q^96 + 8 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.869925	−	1.49774i	0.502252	−	0.864722i
$3$	0.869925	−	1.49774i	0.502252	−	0.864722i
$4$	1.00000			0.500000
$5$		−	1.66014i		−	0.742437i	−0.928546	−	0.371218i	$-0.878940\pi$
$5$		−	1.66014i		−	0.742437i	0.928546	−	0.371218i	$-0.121060\pi$
$6$	0.869925	−	1.49774i	0.355146	−	0.611450i
$7$	−3.57946			−1.35291			−0.676454	−	0.736485i	$-0.736484\pi$
$7$	−3.57946			−1.35291			−0.676454	+	0.736485i	$0.736484\pi$
$8$	1.00000			0.353553
$9$	−1.48646	−	2.60585i	−0.495487	−	0.868616i
$10$		−	1.66014i		−	0.524982i
$11$	4.82340			1.45431			0.727154	−	0.686474i	$-0.240842\pi$
$11$	4.82340			1.45431			0.727154	+	0.686474i	$0.240842\pi$
$12$	0.869925	−	1.49774i	0.251126	−	0.432361i
$13$		−	0.418899i		−	0.116182i	−0.998311	−	0.0580908i	$-0.981499\pi$
$13$		−	0.418899i		−	0.116182i	0.998311	−	0.0580908i	$-0.0185013\pi$
$14$	−3.57946			−0.956651
$15$	−2.48646	−	1.44420i	−0.642001	−	0.372890i
$16$	1.00000			0.250000
$17$			0.742751i			0.180143i	0.995935	+	0.0900717i	$0.0287096\pi$
$17$			0.742751i			0.180143i	−0.995935	+	0.0900717i	$0.971290\pi$
$18$	−1.48646	−	2.60585i	−0.350362	−	0.614204i
$19$	1.24394			0.285379			0.142689	−	0.989768i	$-0.454425\pi$
$19$	1.24394			0.285379			0.142689	+	0.989768i	$0.454425\pi$
$20$		−	1.66014i		−	0.371218i
$21$	−3.11386	+	5.36111i	−0.679500	+	1.16989i
$22$	4.82340			1.02835
$23$	−1.25480			−0.261645			−0.130822	−	0.991406i	$-0.541762\pi$
$23$	−1.25480			−0.261645			−0.130822	+	0.991406i	$0.541762\pi$
$24$	0.869925	−	1.49774i	0.177573	−	0.305725i
$25$	2.24394			0.448787
$26$		−	0.418899i		−	0.0821528i
$27$	−5.19599	−	0.0405586i	−0.999970	−	0.00780551i
$28$	−3.57946			−0.676454
$29$			4.78075i			0.887763i	0.896085	+	0.443882i	$0.146399\pi$
$29$			4.78075i			0.887763i	−0.896085	+	0.443882i	$0.853601\pi$
$30$	−2.48646	−	1.44420i	−0.453963	−	0.263673i
$31$			10.4469i			1.87632i	0.346198	+	0.938161i	$0.387472\pi$
$31$			10.4469i			1.87632i	−0.346198	+	0.938161i	$0.612528\pi$
$32$	1.00000			0.176777
$33$	4.19599	−	7.22420i	0.730429	−	1.25757i
$34$			0.742751i			0.127381i
$35$			5.94240i			1.00445i
$36$	−1.48646	−	2.60585i	−0.247743	−	0.434308i
$37$			6.02199i			0.990010i	0.868890	+	0.495005i	$0.164834\pi$
$37$			6.02199i			0.990010i	−0.868890	+	0.495005i	$0.835166\pi$
$38$	1.24394			0.201793
$39$	−0.627402	−	0.364411i	−0.100465	−	0.0583524i
$40$		−	1.66014i		−	0.262491i
$41$		−	9.24875i		−	1.44441i	−0.691678	−	0.722206i	$-0.743128\pi$
$41$		−	9.24875i		−	1.44441i	0.691678	−	0.722206i	$-0.256872\pi$
$42$	−3.11386	+	5.36111i	−0.480479	+	0.827237i
$43$		−	3.58258i		−	0.546338i	−0.961966	−	0.273169i	$-0.911928\pi$
$43$		−	3.58258i		−	0.546338i	0.961966	−	0.273169i	$-0.0880719\pi$
$44$	4.82340			0.727154
$45$	−4.32607	+	2.46773i	−0.644892	+	0.367868i
$46$	−1.25480			−0.185011
$47$	8.39199			1.22410			0.612049	−	0.790820i	$-0.290346\pi$
$47$	8.39199			1.22410			0.612049	+	0.790820i	$0.290346\pi$
$48$	0.869925	−	1.49774i	0.125563	−	0.216180i
$49$	5.81253			0.830361
$50$	2.24394			0.317341
$51$	1.11245	+	0.646138i	0.155774	+	0.0904774i
$52$		−	0.418899i		−	0.0580908i
$53$		−	9.66765i		−	1.32795i	−0.747753	−	0.663977i	$-0.768867\pi$
$53$		−	9.66765i		−	1.32795i	0.747753	−	0.663977i	$-0.231133\pi$
$54$	−5.19599	−	0.0405586i	−0.707085	−	0.00551933i
$55$		−	8.00751i		−	1.07973i
$56$	−3.57946			−0.478325
$57$	1.08213	−	1.86310i	0.143332	−	0.246773i
$58$			4.78075i			0.627744i
$59$	−5.47701	+	5.38539i	−0.713046	+	0.701118i
$59$	−5.47701	+	5.38539i	−0.713046	+	0.701118i
$60$	−2.48646	−	1.44420i	−0.321001	−	0.186445i
$61$			9.08804i			1.16360i	0.813330	+	0.581802i	$0.197652\pi$
$61$			9.08804i			1.16360i	−0.813330	+	0.581802i	$0.802348\pi$
$62$			10.4469i			1.32676i
$63$	5.32072	+	9.32752i	0.670348	+	1.17516i
$64$	1.00000			0.125000
$65$	−0.695430			−0.0862575
$66$	4.19599	−	7.22420i	0.516491	−	0.889238i
$67$			13.0941i			1.59970i	0.600203	+	0.799848i	$0.295087\pi$
$67$			13.0941i			1.59970i	−0.600203	+	0.799848i	$0.704913\pi$
$68$			0.742751i			0.0900717i
$69$	−1.09159	+	1.87937i	−0.131411	+	0.226250i
$70$			5.94240i			0.710253i
$71$			4.01996i			0.477082i	0.971132	+	0.238541i	$0.0766691\pi$
$71$			4.01996i			0.477082i	−0.971132	+	0.238541i	$0.923331\pi$
$72$	−1.48646	−	2.60585i	−0.175181	−	0.307102i
$73$		−	10.6897i		−	1.25113i	−0.780172	−	0.625565i	$-0.784869\pi$
$73$		−	10.6897i		−	1.25113i	0.780172	−	0.625565i	$-0.215131\pi$
$74$			6.02199i			0.700043i
$75$	1.95206	−	3.36084i	0.225404	−	0.388076i
$76$	1.24394			0.142689
$77$	−17.2652			−1.96755
$78$	−0.627402	−	0.364411i	−0.0710393	−	0.0412614i
$79$	3.55772			0.400275			0.200138	−	0.979768i	$-0.435861\pi$
$79$	3.55772			0.400275			0.200138	+	0.979768i	$0.435861\pi$
$80$		−	1.66014i		−	0.185609i
$81$	−4.58087	+	7.74697i	−0.508986	+	0.860775i
$82$		−	9.24875i		−	1.02135i
$83$	2.87316			0.315370			0.157685	−	0.987489i	$-0.449597\pi$
$83$	2.87316			0.315370			0.157685	+	0.987489i	$0.449597\pi$
$84$	−3.11386	+	5.36111i	−0.339750	+	0.584945i
$85$	1.23307			0.133745
$86$		−	3.58258i		−	0.386320i
$87$	7.16033	+	4.15890i	0.767668	+	0.445881i
$88$	4.82340			0.514176
$89$	−16.0885			−1.70538			−0.852691	−	0.522415i	$-0.825031\pi$
$89$	−16.0885			−1.70538			−0.852691	+	0.522415i	$0.825031\pi$
$90$	−4.32607	+	2.46773i	−0.456008	+	0.260122i
$91$			1.49943i			0.157183i
$92$	−1.25480			−0.130822
$93$	15.6468	+	9.08804i	1.62250	+	0.942386i
$94$	8.39199			0.865567
$95$		−	2.06511i		−	0.211876i
$96$	0.869925	−	1.49774i	0.0887864	−	0.152863i
$97$		−	11.5275i		−	1.17044i	−0.810876	−	0.585218i	$-0.801009\pi$
$97$		−	11.5275i		−	1.17044i	0.810876	−	0.585218i	$-0.198991\pi$
$98$	5.81253			0.587154
$99$	−7.16979	−	12.5690i	−0.720591	−	1.26324i
$100$	2.24394			0.224394
$101$	−11.2652			−1.12092			−0.560462	−	0.828180i	$-0.689376\pi$
$101$	−11.2652			−1.12092			−0.560462	+	0.828180i	$0.689376\pi$
$102$	1.11245	+	0.646138i	0.110149	+	0.0639771i
$103$			1.60162i			0.157812i	0.996882	+	0.0789059i	$0.0251427\pi$
$103$			1.60162i			0.157812i	−0.996882	+	0.0789059i	$0.974857\pi$
$104$		−	0.418899i		−	0.0410764i
$105$	8.90018	+	5.16945i	0.868569	+	0.504486i
$106$		−	9.66765i		−	0.939005i
$107$		−	0.0585239i		−	0.00565772i	−0.999996	−	0.00282886i	$-0.999100\pi$
$107$		−	0.0585239i		−	0.00565772i	0.999996	−	0.00282886i	$-0.000900456\pi$
$108$	−5.19599	−	0.0405586i	−0.499985	−	0.00390275i
$109$			5.56810i			0.533327i	0.963790	+	0.266664i	$0.0859212\pi$
$109$			5.56810i			0.533327i	−0.963790	+	0.266664i	$0.914079\pi$
$110$		−	8.00751i		−	0.763486i
$111$	9.01939	+	5.23868i	0.856083	+	0.497234i
$112$	−3.57946			−0.338227
$113$	3.43798			0.323418			0.161709	−	0.986839i	$-0.448299\pi$
$113$	3.43798			0.323418			0.161709	+	0.986839i	$0.448299\pi$
$114$	1.08213	−	1.86310i	0.101351	−	0.174495i
$115$			2.08315i			0.194255i
$116$			4.78075i			0.443882i
$117$	−1.09159	+	0.622676i	−0.100917	+	0.0575664i
$118$	−5.47701	+	5.38539i	−0.504199	+	0.495765i
$119$		−	2.65865i		−	0.243718i
$120$	−2.48646	−	1.44420i	−0.226982	−	0.131837i
$121$	12.2652			1.11501
$122$			9.08804i			0.822793i
$123$	−13.8522	−	8.04572i	−1.24901	−	0.725458i
$124$			10.4469i			0.938161i
$125$		−	12.0259i		−	1.07563i
$126$	5.32072	+	9.32752i	0.474008	+	0.830962i
$127$	−22.0994			−1.96101			−0.980503	−	0.196505i	$-0.937041\pi$
$127$	−22.0994			−1.96101			−0.980503	+	0.196505i	$0.937041\pi$
$128$	1.00000			0.0883883
$129$	−5.36578	−	3.11658i	−0.472431	−	0.274399i
$130$	−0.695430			−0.0609933
$131$	−13.6966			−1.19667			−0.598337	−	0.801245i	$-0.704172\pi$
$131$	−13.6966			−1.19667			−0.598337	+	0.801245i	$0.704172\pi$
$132$	4.19599	−	7.22420i	0.365214	−	0.628786i
$133$	−4.45262			−0.386091
$134$			13.0941i			1.13116i
$135$	−0.0673329	+	8.62608i	−0.00579510	+	0.742414i
$136$			0.742751i			0.0636903i
$137$		−	7.16560i		−	0.612199i	−0.952000	−	0.306099i	$-0.900976\pi$
$137$		−	7.16560i		−	0.612199i	0.952000	−	0.306099i	$-0.0990240\pi$
$138$	−1.09159	+	1.87937i	−0.0929219	+	0.159983i
$139$	5.20504			0.441486			0.220743	−	0.975332i	$-0.429152\pi$
$139$	5.20504			0.441486			0.220743	+	0.975332i	$0.429152\pi$
$140$			5.94240i			0.502225i
$141$	7.30040	−	12.5690i	0.614805	−	1.05850i
$142$			4.01996i			0.337348i
$143$		−	2.02051i		−	0.168964i
$144$	−1.48646	−	2.60585i	−0.123872	−	0.217154i
$145$	7.93672			0.659108
$146$		−	10.6897i		−	0.884682i
$147$	5.05647	−	8.70567i	0.417050	−	0.718031i
$148$			6.02199i			0.495005i
$149$	8.82075			0.722624			0.361312	−	0.932445i	$-0.382329\pi$
$149$	8.82075			0.722624			0.361312	+	0.932445i	$0.382329\pi$
$150$	1.95206	−	3.36084i	0.159385	−	0.274411i
$151$			0.872794i			0.0710270i	0.999369	+	0.0355135i	$0.0113067\pi$
$151$			0.872794i			0.0710270i	−0.999369	+	0.0355135i	$0.988693\pi$
$152$	1.24394			0.100897
$153$	1.93549	−	1.10407i	0.156475	−	0.0892587i
$154$	−17.2652			−1.39127
$155$	17.3434			1.39305
$156$	−0.627402	−	0.364411i	−0.0502324	−	0.0291762i
$157$		−	23.3287i		−	1.86183i	−0.365231	−	0.930917i	$-0.619010\pi$
$157$		−	23.3287i		−	1.86183i	0.365231	−	0.930917i	$-0.380990\pi$
$158$	3.55772			0.283037
$159$	−14.4796	−	8.41013i	−1.14831	−	0.666967i
$160$		−	1.66014i		−	0.131246i
$161$	4.49152			0.353981
$162$	−4.58087	+	7.74697i	−0.359907	+	0.608660i
$163$	4.74255			0.371465			0.185732	−	0.982600i	$-0.440534\pi$
$163$	4.74255			0.371465			0.185732	+	0.982600i	$0.440534\pi$
$164$		−	9.24875i		−	0.722206i
$165$	−11.9932	−	6.96594i	−0.933668	−	0.542297i
$166$	2.87316			0.223001
$167$			7.18517i			0.556005i	0.960580	+	0.278003i	$0.0896724\pi$
$167$			7.18517i			0.556005i	−0.960580	+	0.278003i	$0.910328\pi$
$168$	−3.11386	+	5.36111i	−0.240240	+	0.413618i
$169$	12.8245			0.986502
$170$	1.23307			0.0945721
$171$	−1.84906	−	3.24151i	−0.141401	−	0.247884i
$172$		−	3.58258i		−	0.273169i
$173$	−4.12797			−0.313843			−0.156922	−	0.987611i	$-0.550157\pi$
$173$	−4.12797			−0.313843			−0.156922	+	0.987611i	$0.550157\pi$
$174$	7.16033	+	4.15890i	0.542823	+	0.315285i
$175$	−8.03208			−0.607168
$176$	4.82340			0.363577
$177$	3.30133	+	12.8880i	0.248143	+	0.968723i
$178$	−16.0885			−1.20589
$179$	12.7736			0.954746			0.477373	−	0.878701i	$-0.341589\pi$
$179$	12.7736			0.954746			0.477373	+	0.878701i	$0.341589\pi$
$180$	−4.32607	+	2.46773i	−0.322446	+	0.183934i
$181$	−6.91511			−0.513996			−0.256998	−	0.966412i	$-0.582733\pi$
$181$	−6.91511			−0.513996			−0.256998	+	0.966412i	$0.582733\pi$
$182$			1.49943i			0.111145i
$183$	13.6115	+	7.90592i	1.00619	+	0.584422i
$184$	−1.25480			−0.0925054
$185$	9.99735			0.735020
$186$	15.6468	+	9.08804i	1.14728	+	0.666368i
$187$			3.58258i			0.261984i
$188$	8.39199			0.612049
$189$	18.5988	+	0.145178i	1.35287	+	0.0105601i
$190$		−	2.06511i		−	0.149819i
$191$	3.69921			0.267665			0.133833	−	0.991004i	$-0.457272\pi$
$191$	3.69921			0.267665			0.133833	+	0.991004i	$0.457272\pi$
$192$	0.869925	−	1.49774i	0.0627814	−	0.108090i
$193$	−11.9714			−0.861724			−0.430862	−	0.902418i	$-0.641790\pi$
$193$	−11.9714			−0.861724			−0.430862	+	0.902418i	$0.641790\pi$
$194$		−	11.5275i		−	0.827623i
$195$	−0.604972	+	1.04157i	−0.0433230	+	0.0745887i
$196$	5.81253			0.415181
$197$		−	12.7702i		−	0.909841i	−0.890532	−	0.454920i	$-0.849668\pi$
$197$		−	12.7702i		−	0.909841i	0.890532	−	0.454920i	$-0.150332\pi$
$198$	−7.16979	−	12.5690i	−0.509534	−	0.893242i
$199$	7.63327			0.541108			0.270554	−	0.962705i	$-0.412793\pi$
$199$	7.63327			0.541108			0.270554	+	0.962705i	$0.412793\pi$
$200$	2.24394			0.158670
$201$	19.6115	+	11.3909i	1.38329	+	0.803450i
$202$	−11.2652			−0.792613
$203$		−	17.1125i		−	1.20106i
$204$	1.11245	+	0.646138i	0.0778870	+	0.0452387i
$205$	−15.3542			−1.07239
$206$			1.60162i			0.111590i
$207$	1.86522	+	3.26983i	0.129641	+	0.227269i
$208$		−	0.418899i		−	0.0290454i
$209$	6.00000			0.415029
$210$	8.90018	+	5.16945i	0.614171	+	0.356726i
$211$			18.3522i			1.26342i	0.775204	+	0.631710i	$0.217647\pi$
$211$			18.3522i			1.26342i	−0.775204	+	0.631710i	$0.782353\pi$
$212$		−	9.66765i		−	0.663977i
$213$	6.02086	+	3.49707i	0.412543	+	0.239615i
$214$		−	0.0585239i		−	0.00400061i
$215$	−5.94758			−0.405622
$216$	−5.19599	−	0.0405586i	−0.353543	−	0.00275966i
$217$		−	37.3943i		−	2.53849i
$218$			5.56810i			0.377119i
$219$	−16.0103	−	9.29920i	−1.08188	−	0.628382i
$220$		−	8.00751i		−	0.539866i
$221$	0.311137			0.0209294
$222$	9.01939	+	5.23868i	0.605342	+	0.351597i
$223$	−11.9108			−0.797607			−0.398804	−	0.917036i	$-0.630574\pi$
$223$	−11.9108			−0.797607			−0.398804	+	0.917036i	$0.630574\pi$
$224$	−3.57946			−0.239163
$225$	−3.33552	−	5.84736i	−0.222368	−	0.389824i
$226$	3.43798			0.228691
$227$	−8.70313			−0.577647			−0.288823	−	0.957382i	$-0.593264\pi$
$227$	−8.70313			−0.577647			−0.288823	+	0.957382i	$0.593264\pi$
$228$	1.08213	−	1.86310i	0.0716659	−	0.123387i
$229$		−	17.0329i		−	1.12557i	−0.826604	−	0.562783i	$-0.809730\pi$
$229$		−	17.0329i		−	1.12557i	0.826604	−	0.562783i	$-0.190270\pi$
$230$			2.08315i			0.137359i
$231$	−15.0194	+	25.8587i	−0.988203	+	1.70138i
$232$			4.78075i			0.313872i
$233$	−9.87973			−0.647243			−0.323621	−	0.946187i	$-0.604900\pi$
$233$	−9.87973			−0.647243			−0.323621	+	0.946187i	$0.604900\pi$
$234$	−1.09159	+	0.622676i	−0.0713592	+	0.0407056i
$235$		−	13.9319i		−	0.908815i
$236$	−5.47701	+	5.38539i	−0.356523	+	0.350559i
$237$	3.09495	−	5.32855i	0.201039	−	0.346127i
$238$		−	2.65865i		−	0.172334i
$239$		−	6.14770i		−	0.397662i	−0.980034	−	0.198831i	$-0.936286\pi$
$239$		−	6.14770i		−	0.397662i	0.980034	−	0.198831i	$-0.0637145\pi$
$240$	−2.48646	−	1.44420i	−0.160500	−	0.0932225i
$241$	16.4096			1.05703			0.528516	−	0.848923i	$-0.322749\pi$
$241$	16.4096			1.05703			0.528516	+	0.848923i	$0.322749\pi$
$242$	12.2652			0.788434
$243$	7.61795	+	13.6003i	0.488692	+	0.872457i
$244$			9.08804i			0.581802i
$245$		−	9.64961i		−	0.616491i
$246$	−13.8522	−	8.04572i	−0.883187	−	0.512977i
$247$		−	0.521083i		−	0.0331557i
$248$			10.4469i			0.663380i
$249$	2.49944	−	4.30325i	0.158395	−	0.272708i
$250$		−	12.0259i		−	0.760588i
$251$		−	5.45388i		−	0.344246i	−0.985075	−	0.172123i	$-0.944937\pi$
$251$		−	5.45388i		−	0.344246i	0.985075	−	0.172123i	$-0.0550626\pi$
$252$	5.32072	+	9.32752i	0.335174	+	0.587579i
$253$	−6.05242			−0.380512
$254$	−22.0994			−1.38664
$255$	1.07268	−	1.84682i	0.0671737	−	0.115652i
$256$	1.00000			0.0625000
$257$			20.1335i			1.25589i	0.778256	+	0.627947i	$0.216105\pi$
$257$			20.1335i			1.25589i	−0.778256	+	0.627947i	$0.783895\pi$
$258$	−5.36578	−	3.11658i	−0.334059	−	0.194030i
$259$		−	21.5555i		−	1.33939i
$260$	−0.695430			−0.0431288
$261$	12.4579	−	7.10640i	0.771125	−	0.439875i
$262$	−13.6966			−0.846176
$263$			28.6271i			1.76522i	0.470102	+	0.882612i	$0.344217\pi$
$263$			28.6271i			1.76522i	−0.470102	+	0.882612i	$0.655783\pi$
$264$	4.19599	−	7.22420i	0.258246	−	0.444619i
$265$	−16.0496			−0.985922
$266$	−4.45262			−0.273008
$267$	−13.9958	+	24.0965i	−0.856531	+	1.47468i
$268$			13.0941i			0.799848i
$269$	−5.51883			−0.336489			−0.168244	−	0.985745i	$-0.553810\pi$
$269$	−5.51883			−0.336489			−0.168244	+	0.985745i	$0.553810\pi$
$270$	−0.0673329	+	8.62608i	−0.00409775	+	0.524966i
$271$	−30.9726			−1.88145			−0.940725	−	0.339170i	$-0.889854\pi$
$271$	−30.9726			−1.88145			−0.940725	+	0.339170i	$0.889854\pi$
$272$			0.742751i			0.0450359i
$273$	2.24576	+	1.30439i	0.135920	+	0.0789454i
$274$		−	7.16560i		−	0.432890i
$275$	10.8234			0.652675
$276$	−1.09159	+	1.87937i	−0.0657057	+	0.113125i
$277$	19.9781			1.20037			0.600185	−	0.799861i	$-0.295094\pi$
$277$	19.9781			1.20037			0.600185	+	0.799861i	$0.295094\pi$
$278$	5.20504			0.312177
$279$	27.2231	−	15.5289i	1.62980	−	0.929693i
$280$			5.94240i			0.355126i
$281$			23.4938i			1.40152i	0.713395	+	0.700762i	$0.247156\pi$
$281$			23.4938i			1.40152i	−0.713395	+	0.700762i	$0.752844\pi$
$282$	7.30040	−	12.5690i	0.434733	−	0.748475i
$283$		−	13.7557i		−	0.817692i	−0.912603	−	0.408846i	$-0.865931\pi$
$283$		−	13.7557i		−	0.817692i	0.912603	−	0.408846i	$-0.134069\pi$
$284$			4.01996i			0.238541i
$285$	−3.09300	−	1.79649i	−0.183213	−	0.106415i
$286$		−	2.02051i		−	0.119476i
$287$			33.1055i			1.95416i
$288$	−1.48646	−	2.60585i	−0.0875905	−	0.153551i
$289$	16.4483			0.967548
$290$	7.93672			0.466060
$291$	−17.2652	−	10.0280i	−1.01210	−	0.587853i
$292$		−	10.6897i		−	0.625565i
$293$		−	19.3118i		−	1.12821i	−0.825704	−	0.564103i	$-0.809222\pi$
$293$		−	19.3118i		−	1.12821i	0.825704	−	0.564103i	$-0.190778\pi$
$294$	5.05647	−	8.70567i	0.294899	−	0.507725i
$295$	8.94049	+	9.09259i	0.520536	+	0.529391i
$296$			6.02199i			0.350021i
$297$	−25.0623	−	0.195630i	−1.45426	−	0.0113516i
$298$	8.82075			0.510972
$299$			0.525636i			0.0303983i
$300$	1.95206	−	3.36084i	0.112702	−	0.194038i
$301$			12.8237i			0.739146i
$302$			0.872794i			0.0502237i
$303$	−9.79984	+	16.8723i	−0.562986	+	0.969287i
$304$	1.24394			0.0713447
$305$	15.0874			0.863903
$306$	1.93549	−	1.10407i	0.110645	−	0.0631154i
$307$	−26.6117			−1.51881			−0.759404	−	0.650619i	$-0.774509\pi$
$307$	−26.6117			−1.51881			−0.759404	+	0.650619i	$0.774509\pi$
$308$	−17.2652			−0.983773
$309$	2.39881	+	1.39329i	0.136463	+	0.0792613i
$310$	17.3434			0.985036
$311$		−	13.4625i		−	0.763389i	−0.924288	−	0.381695i	$-0.875341\pi$
$311$		−	13.4625i		−	0.763389i	0.924288	−	0.381695i	$-0.124659\pi$
$312$	−0.627402	−	0.364411i	−0.0355196	−	0.0206307i
$313$			4.24421i			0.239897i	0.992780	+	0.119949i	$0.0382730\pi$
$313$			4.24421i			0.239897i	−0.992780	+	0.119949i	$0.961727\pi$
$314$		−	23.3287i		−	1.31652i
$315$	15.4850	−	8.83314i	0.872480	−	0.497691i
$316$	3.55772			0.200138
$317$		−	5.48243i		−	0.307924i	−0.988077	−	0.153962i	$-0.950797\pi$
$317$		−	5.48243i		−	0.307924i	0.988077	−	0.153962i	$-0.0492033\pi$
$318$	−14.4796	−	8.41013i	−0.811978	−	0.471617i
$319$			23.0595i			1.29108i
$320$		−	1.66014i		−	0.0928046i
$321$	−0.0876537	−	0.0509114i	−0.00489235	−	0.00284160i
$322$	4.49152			0.250303
$323$			0.923935i			0.0514091i
$324$	−4.58087	+	7.74697i	−0.254493	+	0.430387i
$325$		−	0.939982i		−	0.0521408i
$326$	4.74255			0.262665
$327$	8.33957	+	4.84383i	0.461179	+	0.267864i
$328$		−	9.24875i		−	0.510677i
$329$	−30.0388			−1.65609
$330$	−11.9932	−	6.96594i	−0.660203	−	0.383462i
$331$	32.1662			1.76802			0.884008	−	0.467472i	$-0.154835\pi$
$331$	32.1662			1.76802			0.884008	+	0.467472i	$0.154835\pi$
$332$	2.87316			0.157685
$333$	15.6924	−	8.95145i	0.859938	−	0.490537i
$334$			7.18517i			0.393155i
$335$	21.7380			1.18767
$336$	−3.11386	+	5.36111i	−0.169875	+	0.292472i
$337$			17.9638i			0.978550i	0.872129	+	0.489275i	$0.162739\pi$
$337$			17.9638i			0.978550i	−0.872129	+	0.489275i	$0.837261\pi$
$338$	12.8245			0.697562
$339$	2.99078	−	5.14920i	0.162437	−	0.279666i
$340$	1.23307			0.0668726
$341$			50.3896i			2.72875i
$342$	−1.84906	−	3.24151i	−0.0999858	−	0.175281i
$343$	4.25050			0.229506
$344$		−	3.58258i		−	0.193160i
$345$	3.12002	+	1.81218i	0.167976	+	0.0975647i
$346$	−4.12797			−0.221921
$347$	−30.2193			−1.62226			−0.811129	−	0.584868i	$-0.801146\pi$
$347$	−30.2193			−1.62226			−0.811129	+	0.584868i	$0.801146\pi$
$348$	7.16033	+	4.15890i	0.383834	+	0.222940i
$349$			27.1281i			1.45214i	0.687623	+	0.726068i	$0.258654\pi$
$349$			27.1281i			1.45214i	−0.687623	+	0.726068i	$0.741346\pi$
$350$	−8.03208			−0.429333
$351$	−0.0169899	+	2.17660i	−0.000906856	+	0.116178i
$352$	4.82340			0.257088
$353$	15.5292			0.826534			0.413267	−	0.910610i	$-0.364388\pi$
$353$	15.5292			0.826534			0.413267	+	0.910610i	$0.364388\pi$
$354$	3.30133	+	12.8880i	0.175464	+	0.684991i
$355$	6.67370			0.354203
$356$	−16.0885			−0.852691
$357$	−3.98196	−	2.31282i	−0.210748	−	0.122408i
$358$	12.7736			0.675107
$359$		−	9.70378i		−	0.512146i	−0.966657	−	0.256073i	$-0.917571\pi$
$359$		−	9.70378i		−	0.512146i	0.966657	−	0.256073i	$-0.0824287\pi$
$360$	−4.32607	+	2.46773i	−0.228004	+	0.130061i
$361$	−17.4526			−0.918559
$362$	−6.91511			−0.363450
$363$	10.6698	−	18.3700i	0.560017	−	0.964176i
$364$			1.49943i			0.0785915i
$365$	−17.7463			−0.928885
$366$	13.6115	+	7.90592i	0.711487	+	0.413249i
$367$			21.1320i			1.10308i	0.834147	+	0.551541i	$0.185960\pi$
$367$			21.1320i			1.10308i	−0.834147	+	0.551541i	$0.814040\pi$
$368$	−1.25480			−0.0654112
$369$	−24.1008	+	13.7479i	−1.25464	+	0.715687i
$370$	9.99735			0.519737
$371$			34.6050i			1.79660i
$372$	15.6468	+	9.08804i	0.811248	+	0.471193i
$373$	−26.4779			−1.37097			−0.685486	−	0.728085i	$-0.740410\pi$
$373$	−26.4779			−1.37097			−0.685486	+	0.728085i	$0.740410\pi$
$374$			3.58258i			0.185251i
$375$	−18.0118	−	10.4617i	−0.930123	−	0.540239i
$376$	8.39199			0.432784
$377$	2.00265			0.103142
$378$	18.5988	+	0.145178i	0.956622	+	0.00746714i
$379$	2.78409			0.143009			0.0715047	−	0.997440i	$-0.477220\pi$
$379$	2.78409			0.143009			0.0715047	+	0.997440i	$0.477220\pi$
$380$		−	2.06511i		−	0.105938i
$381$	−19.2248	+	33.0992i	−0.984918	+	1.69572i
$382$	3.69921			0.189268
$383$		−	35.3588i		−	1.80675i	−0.428853	−	0.903374i	$-0.641082\pi$
$383$		−	35.3588i		−	1.80675i	0.428853	−	0.903374i	$-0.358918\pi$
$384$	0.869925	−	1.49774i	0.0443932	−	0.0764313i
$385$			28.6626i			1.46078i
$386$	−11.9714			−0.609331
$387$	−9.33565	+	5.32536i	−0.474558	+	0.270703i
$388$		−	11.5275i		−	0.585218i
$389$		−	12.5625i		−	0.636943i	−0.947932	−	0.318472i	$-0.896830\pi$
$389$		−	12.5625i		−	0.636943i	0.947932	−	0.318472i	$-0.103170\pi$
$390$	−0.604972	+	1.04157i	−0.0306340	+	0.0527422i
$391$		−	0.932006i		−	0.0471336i
$392$	5.81253			0.293577
$393$	−11.9150	+	20.5139i	−0.601031	+	1.03479i
$394$		−	12.7702i		−	0.643354i
$395$		−	5.90632i		−	0.297179i
$396$	−7.16979	−	12.5690i	−0.360295	−	0.631618i
$397$			32.5653i			1.63440i	0.576351	+	0.817202i	$0.304476\pi$
$397$			32.5653i			1.63440i	−0.576351	+	0.817202i	$0.695524\pi$
$398$	7.63327			0.382621
$399$	−3.87345	+	6.66888i	−0.193915	+	0.333861i
$400$	2.24394			0.112197
$401$	25.7353			1.28516			0.642581	−	0.766218i	$-0.277864\pi$
$401$	25.7353			1.28516			0.642581	+	0.766218i	$0.277864\pi$
$402$	19.6115	+	11.3909i	0.978135	+	0.568125i
$403$	4.37620			0.217994
$404$	−11.2652			−0.560462
$405$	12.8611	+	7.60489i	0.639071	+	0.377890i
$406$		−	17.1125i		−	0.849280i
$407$			29.0465i			1.43978i
$408$	1.11245	+	0.646138i	0.0550744	+	0.0319886i
$409$		−	2.79568i		−	0.138237i	−0.997608	−	0.0691186i	$-0.977981\pi$
$409$		−	2.79568i		−	0.138237i	0.997608	−	0.0691186i	$-0.0220187\pi$
$410$	−15.3542			−0.758291
$411$	−10.7322	−	6.23354i	−0.529381	−	0.307478i
$412$			1.60162i			0.0789059i
$413$	19.6047	−	19.2768i	0.964685	−	0.948548i
$414$	1.86522	+	3.26983i	0.0916704	+	0.160703i
$415$		−	4.76985i		−	0.234143i
$416$		−	0.418899i		−	0.0205382i
$417$	4.52799	−	7.79580i	0.221737	−	0.381762i
$418$	6.00000			0.293470
$419$	26.4494			1.29214			0.646070	−	0.763278i	$-0.276411\pi$
$419$	26.4494			1.29214			0.646070	+	0.763278i	$0.276411\pi$
$420$	8.90018	+	5.16945i	0.434284	+	0.252243i
$421$			11.9509i			0.582452i	0.956654	+	0.291226i	$0.0940631\pi$
$421$			11.9509i			0.582452i	−0.956654	+	0.291226i	$0.905937\pi$
$422$			18.3522i			0.893374i
$423$	−12.4744	−	21.8682i	−0.606524	−	1.06327i
$424$		−	9.66765i		−	0.469503i
$425$			1.66669i			0.0808461i
$426$	6.02086	+	3.49707i	0.291712	+	0.169433i
$427$		−	32.5303i		−	1.57425i
$428$		−	0.0585239i		−	0.00282886i
$429$	−3.02621	−	1.75770i	−0.146107	−	0.0848624i
$430$	−5.94758			−0.286818
$431$	−11.5375			−0.555742			−0.277871	−	0.960618i	$-0.589629\pi$
$431$	−11.5375			−0.555742			−0.277871	+	0.960618i	$0.589629\pi$
$432$	−5.19599	−	0.0405586i	−0.249992	−	0.00195138i
$433$	−36.2956			−1.74425			−0.872127	−	0.489279i	$-0.837260\pi$
$433$	−36.2956			−1.74425			−0.872127	+	0.489279i	$0.837260\pi$
$434$		−	37.3943i		−	1.79499i
$435$	6.90435	−	11.8872i	0.331038	−	0.569945i
$436$			5.56810i			0.266664i
$437$	−1.56090			−0.0746678
$438$	−16.0103	−	9.29920i	−0.765004	−	0.444333i
$439$	11.5445			0.550988			0.275494	−	0.961303i	$-0.411159\pi$
$439$	11.5445			0.550988			0.275494	+	0.961303i	$0.411159\pi$
$440$		−	8.00751i		−	0.381743i
$441$	−8.64009	−	15.1466i	−0.411433	−	0.721265i
$442$	0.311137			0.0147993
$443$	−12.3499			−0.586762			−0.293381	−	0.955996i	$-0.594780\pi$
$443$	−12.3499			−0.586762			−0.293381	+	0.955996i	$0.594780\pi$
$444$	9.01939	+	5.23868i	0.428041	+	0.248617i
$445$			26.7092i			1.26614i
$446$	−11.9108			−0.563993
$447$	7.67339	−	13.2112i	0.362939	−	0.624868i
$448$	−3.57946			−0.169114
$449$			28.4979i			1.34490i	0.740143	+	0.672450i	$0.234758\pi$
$449$			28.4979i			1.34490i	−0.740143	+	0.672450i	$0.765242\pi$
$450$	−3.33552	−	5.84736i	−0.157238	−	0.275647i
$451$		−	44.6104i		−	2.10062i
$452$	3.43798			0.161709
$453$	1.30722	+	0.759266i	0.0614186	+	0.0356734i
$454$	−8.70313			−0.408458
$455$	2.48926			0.116699
$456$	1.08213	−	1.86310i	0.0506755	−	0.0872475i
$457$			22.4605i			1.05066i	0.850900	+	0.525328i	$0.176057\pi$
$457$			22.4605i			1.05066i	−0.850900	+	0.525328i	$0.823943\pi$
$458$		−	17.0329i		−	0.795896i
$459$	0.0301249	−	3.85933i	0.00140611	−	0.180138i
$460$			2.08315i			0.0971274i
$461$			6.76019i			0.314854i	0.987531	+	0.157427i	$0.0503198\pi$
$461$			6.76019i			0.314854i	−0.987531	+	0.157427i	$0.949680\pi$
$462$	−15.0194	+	25.8587i	−0.698765	+	1.20306i
$463$		−	32.1740i		−	1.49525i	−0.664119	−	0.747627i	$-0.731193\pi$
$463$		−	32.1740i		−	1.49525i	0.664119	−	0.747627i	$-0.268807\pi$
$464$			4.78075i			0.221941i
$465$	15.0874	−	25.9759i	0.699662	−	1.20460i
$466$	−9.87973			−0.457670
$467$	29.7721			1.37769			0.688844	−	0.724909i	$-0.258118\pi$
$467$	29.7721			1.37769			0.688844	+	0.724909i	$0.258118\pi$
$468$	−1.09159	+	0.622676i	−0.0504586	+	0.0287832i
$469$		−	46.8697i		−	2.16424i
$470$		−	13.9319i		−	0.642629i
$471$	−34.9404	−	20.2942i	−1.60997	−	0.935109i
$472$	−5.47701	+	5.38539i	−0.252100	+	0.247883i
$473$		−	17.2802i		−	0.794545i
$474$	3.09495	−	5.32855i	0.142156	−	0.244749i
$475$	2.79132			0.128074
$476$		−	2.65865i		−	0.121859i
$477$	−25.1924	+	14.3706i	−1.15348	+	0.657983i
$478$		−	6.14770i		−	0.281189i
$479$			11.4600i			0.523623i	0.965119	+	0.261811i	$0.0843199\pi$
$479$			11.4600i			0.523623i	−0.965119	+	0.261811i	$0.915680\pi$
$480$	−2.48646	−	1.44420i	−0.113491	−	0.0659183i
$481$	2.52261			0.115021
$482$	16.4096			0.747435
$483$	3.90729	−	6.72714i	0.177788	−	0.306095i
$484$	12.2652			0.557507
$485$	−19.1372			−0.868975
$486$	7.61795	+	13.6003i	0.345557	+	0.616920i
$487$	8.42054			0.381571			0.190786	−	0.981632i	$-0.438896\pi$
$487$	8.42054			0.381571			0.190786	+	0.981632i	$0.438896\pi$
$488$			9.08804i			0.411396i
$489$	4.12566	−	7.10311i	0.186569	−	0.321214i
$490$		−	9.64961i		−	0.435925i
$491$			7.10664i			0.320718i	0.987059	+	0.160359i	$0.0512652\pi$
$491$			7.10664i			0.320718i	−0.987059	+	0.160359i	$0.948735\pi$
$492$	−13.8522	−	8.04572i	−0.624507	−	0.362729i
$493$	−3.55091			−0.159925
$494$		−	0.521083i		−	0.0234447i
$495$	−20.8663	+	11.9028i	−0.937872	+	0.534993i
$496$			10.4469i			0.469081i
$497$		−	14.3893i		−	0.645448i
$498$	2.49944	−	4.30325i	0.112002	−	0.192833i
$499$	33.2330			1.48771			0.743856	−	0.668340i	$-0.232995\pi$
$499$	33.2330			1.48771			0.743856	+	0.668340i	$0.232995\pi$
$500$		−	12.0259i		−	0.537817i
$501$	10.7615	+	6.25056i	0.480790	+	0.279254i
$502$		−	5.45388i		−	0.243419i
$503$	41.4063			1.84621			0.923107	−	0.384544i	$-0.125641\pi$
$503$	41.4063			1.84621			0.923107	+	0.384544i	$0.125641\pi$
$504$	5.32072	+	9.32752i	0.237004	+	0.415481i
$505$			18.7017i			0.832216i
$506$	−6.05242			−0.269063
$507$	11.1564	−	19.2078i	0.495472	−	0.853049i
$508$	−22.0994			−0.980503
$509$	−7.71730			−0.342063			−0.171032	−	0.985266i	$-0.554710\pi$
$509$	−7.71730			−0.342063			−0.171032	+	0.985266i	$0.554710\pi$
$510$	1.07268	−	1.84682i	0.0474990	−	0.0817786i
$511$			38.2632i			1.69266i
$512$	1.00000			0.0441942
$513$	−6.46349	−	0.0504523i	−0.285370	−	0.00222753i
$514$			20.1335i			0.888052i
$515$	2.65891			0.117165
$516$	−5.36578	−	3.11658i	−0.236215	−	0.137200i
$517$	40.4779			1.78022
$518$		−	21.5555i		−	0.947093i
$519$	−3.59102	+	6.18263i	−0.157628	+	0.271387i
$520$	−0.695430			−0.0304966
$521$		−	40.0700i		−	1.75550i	−0.479122	−	0.877748i	$-0.659045\pi$
$521$		−	40.0700i		−	1.75550i	0.479122	−	0.877748i	$-0.340955\pi$
$522$	12.4579	−	7.10640i	0.545268	−	0.311039i
$523$	1.42446			0.0622872			0.0311436	−	0.999515i	$-0.490085\pi$
$523$	1.42446			0.0622872			0.0311436	+	0.999515i	$0.490085\pi$
$524$	−13.6966			−0.598337
$525$	−6.98731	+	12.0300i	−0.304951	+	0.525031i
$526$			28.6271i			1.24820i
$527$	−7.75946			−0.338007
$528$	4.19599	−	7.22420i	0.182607	−	0.314393i
$529$	−21.4255			−0.931542
$530$	−16.0496			−0.697152
$531$	22.1748	+	6.26707i	0.962306	+	0.271968i
$532$	−4.45262			−0.193046
$533$	−3.87429			−0.167814
$534$	−13.9958	+	24.0965i	−0.605659	+	1.04276i
$535$	−0.0971579			−0.00420050
$536$			13.0941i			0.565578i
$537$	11.1121	−	19.1316i	0.479523	−	0.825589i
$538$	−5.51883			−0.237933
$539$	28.0361			1.20760
$540$	−0.0673329	+	8.62608i	−0.00289755	+	0.371207i
$541$		−	23.6082i		−	1.01500i	−0.861653	−	0.507498i	$-0.830571\pi$
$541$		−	23.6082i		−	1.01500i	0.861653	−	0.507498i	$-0.169429\pi$
$542$	−30.9726			−1.33039
$543$	−6.01563	+	10.3571i	−0.258156	+	0.444464i
$544$			0.742751i			0.0318452i
$545$	9.24382			0.395962
$546$	2.24576	+	1.30439i	0.0961097	+	0.0558229i
$547$	21.2284			0.907660			0.453830	−	0.891088i	$-0.350057\pi$
$547$	21.2284			0.907660			0.453830	+	0.891088i	$0.350057\pi$
$548$		−	7.16560i		−	0.306099i
$549$	23.6820	−	13.5090i	1.01073	−	0.576551i
$550$	10.8234			0.461511
$551$			5.94695i			0.253349i
$552$	−1.09159	+	1.87937i	−0.0464610	+	0.0799914i
$553$	−12.7347			−0.541536
$554$	19.9781			0.848790
$555$	8.69695	−	14.9734i	0.369165	−	0.635587i
$556$	5.20504			0.220743
$557$		−	27.9493i		−	1.18425i	−0.805846	−	0.592126i	$-0.798289\pi$
$557$		−	27.9493i		−	1.18425i	0.805846	−	0.592126i	$-0.201711\pi$
$558$	27.2231	−	15.5289i	1.15244	−	0.657392i
$559$	−1.50074			−0.0634745
$560$			5.94240i			0.251112i
$561$	5.36578	+	3.11658i	0.226543	+	0.131582i
$562$			23.4938i			0.991027i
$563$	−39.1650			−1.65061			−0.825304	−	0.564689i	$-0.808996\pi$
$563$	−39.1650			−1.65061			−0.825304	+	0.564689i	$0.808996\pi$
$564$	7.30040	−	12.5690i	0.307402	−	0.529252i
$565$		−	5.70752i		−	0.240117i
$566$		−	13.7557i		−	0.578196i
$567$	16.3970	−	27.7300i	0.688611	−	1.16455i
$568$			4.01996i			0.168674i
$569$	−7.87708			−0.330224			−0.165112	−	0.986275i	$-0.552799\pi$
$569$	−7.87708			−0.330224			−0.165112	+	0.986275i	$0.552799\pi$
$570$	−3.09300	−	1.79649i	−0.129551	−	0.0752467i
$571$			21.5046i			0.899939i	0.893044	+	0.449969i	$0.148565\pi$
$571$			21.5046i			0.899939i	−0.893044	+	0.449969i	$0.851435\pi$
$572$		−	2.02051i		−	0.0844819i
$573$	3.21804	−	5.54046i	0.134435	−	0.231456i
$574$			33.1055i			1.38180i
$575$	−2.81570			−0.117423
$576$	−1.48646	−	2.60585i	−0.0619358	−	0.108577i
$577$	33.8946			1.41105			0.705526	−	0.708684i	$-0.250711\pi$
$577$	33.8946			1.41105			0.705526	+	0.708684i	$0.250711\pi$
$578$	16.4483			0.684160
$579$	−10.4143	+	17.9301i	−0.432802	+	0.745151i
$580$	7.93672			0.329554
$581$	−10.2844			−0.426667
$582$	−17.2652	−	10.0280i	−0.715663	−	0.415675i
$583$		−	46.6309i		−	1.93125i
$584$		−	10.6897i		−	0.442341i
$585$	1.03373	+	1.81218i	0.0427394	+	0.0749246i
$586$		−	19.3118i		−	0.797762i
$587$	−7.95528			−0.328349			−0.164175	−	0.986431i	$-0.552496\pi$
$587$	−7.95528			−0.328349			−0.164175	+	0.986431i	$0.552496\pi$
$588$	5.05647	−	8.70567i	0.208525	−	0.359016i
$589$			12.9953i			0.535463i
$590$	8.94049	+	9.09259i	0.368074	+	0.374336i
$591$	−19.1265	−	11.1091i	−0.786759	−	0.456969i
$592$			6.02199i			0.247502i
$593$			5.58810i			0.229476i	0.993396	+	0.114738i	$0.0366028\pi$
$593$			5.58810i			0.229476i	−0.993396	+	0.114738i	$0.963397\pi$
$594$	−25.0623	−	0.195630i	−1.02832	−	0.00802680i
$595$	−4.41372			−0.180945
$596$	8.82075			0.361312
$597$	6.64038	−	11.4327i	0.271773	−	0.467908i
$598$			0.525636i			0.0214948i
$599$		−	32.0609i		−	1.30997i	−0.755640	−	0.654987i	$-0.772674\pi$
$599$		−	32.0609i		−	1.30997i	0.755640	−	0.654987i	$-0.227326\pi$
$600$	1.95206	−	3.36084i	0.0796924	−	0.137206i
$601$		−	21.2151i		−	0.865383i	−0.901542	−	0.432691i	$-0.857564\pi$
$601$		−	21.2151i		−	0.865383i	0.901542	−	0.432691i	$-0.142436\pi$
$602$			12.8237i			0.522655i
$603$	34.1211	−	19.4638i	1.38952	−	0.792628i
$604$			0.872794i			0.0355135i
$605$		−	20.3619i		−	0.827827i
$606$	−9.79984	+	16.8723i	−0.398091	+	0.685390i
$607$	21.2904			0.864151			0.432076	−	0.901837i	$-0.357781\pi$
$607$	21.2904			0.864151			0.432076	+	0.901837i	$0.357781\pi$
$608$	1.24394			0.0504483
$609$	−25.6301	−	14.8866i	−1.03858	−	0.603236i
$610$	15.0874			0.610872
$611$		−	3.51539i		−	0.142218i
$612$	1.93549	−	1.10407i	0.0782377	−	0.0446293i
$613$		−	9.86776i		−	0.398555i	−0.979943	−	0.199277i	$-0.936140\pi$
$613$		−	9.86776i		−	0.398555i	0.979943	−	0.199277i	$-0.0638595\pi$
$614$	−26.6117			−1.07396
$615$	−13.3570	+	22.9967i	−0.538607	+	0.927314i
$616$	−17.2652			−0.695633
$617$		−	26.3747i		−	1.06181i	−0.847432	−	0.530904i	$-0.821853\pi$
$617$		−	26.3747i		−	1.06181i	0.847432	−	0.530904i	$-0.178147\pi$
$618$	2.39881	+	1.39329i	0.0964941	+	0.0560462i
$619$	7.99178			0.321217			0.160608	−	0.987018i	$-0.448654\pi$
$619$	7.99178			0.321217			0.160608	+	0.987018i	$0.448654\pi$
$620$	17.3434			0.696526
$621$	6.51995	+	0.0508931i	0.261637	+	0.00204227i
$622$		−	13.4625i		−	0.539798i
$623$	57.5883			2.30723
$624$	−0.627402	−	0.364411i	−0.0251162	−	0.0145881i
$625$	−8.74506			−0.349803
$626$			4.24421i			0.169633i
$627$	5.21955	−	8.98645i	0.208449	−	0.358884i
$628$		−	23.3287i		−	0.930917i
$629$	−4.47284			−0.178344
$630$	15.4850	−	8.83314i	0.616937	−	0.351921i
$631$	−25.0296			−0.996411			−0.498206	−	0.867059i	$-0.666008\pi$
$631$	−25.0296			−0.996411			−0.498206	+	0.867059i	$0.666008\pi$
$632$	3.55772			0.141519
$633$	27.4869	+	15.9651i	1.09251	+	0.634555i
$634$		−	5.48243i		−	0.217735i
$635$			36.6881i			1.45592i
$636$	−14.4796	−	8.41013i	−0.574155	−	0.333483i
$637$		−	2.43486i		−	0.0964727i
$638$			23.0595i			0.912933i
$639$	10.4754	−	5.97551i	0.414400	−	0.236388i
$640$		−	1.66014i		−	0.0656228i
$641$			9.52542i			0.376232i	0.982147	+	0.188116i	$0.0602380\pi$
$641$			9.52542i			0.376232i	−0.982147	+	0.188116i	$0.939762\pi$
$642$	−0.0876537	−	0.0509114i	−0.00345942	−	0.00200931i
$643$	23.2413			0.916547			0.458273	−	0.888811i	$-0.348468\pi$
$643$	23.2413			0.916547			0.458273	+	0.888811i	$0.348468\pi$
$644$	4.49152			0.176991
$645$	−5.17395	+	8.90794i	−0.203724	+	0.350750i
$646$			0.923935i			0.0363517i
$647$		−	8.94338i		−	0.351601i	−0.984426	−	0.175800i	$-0.943749\pi$
$647$		−	8.94338i		−	0.351601i	0.984426	−	0.175800i	$-0.0562513\pi$
$648$	−4.58087	+	7.74697i	−0.179954	+	0.304330i
$649$	−26.4178	+	25.9759i	−1.03699	+	1.01964i
$650$		−	0.939982i		−	0.0368691i
$651$	−56.0071	−	32.5303i	−2.19509	−	1.27496i
$652$	4.74255			0.185732
$653$			16.9383i			0.662846i	0.943482	+	0.331423i	$0.107529\pi$
$653$			16.9383i			0.662846i	−0.943482	+	0.331423i	$0.892471\pi$
$654$	8.33957	+	4.84383i	0.326103	+	0.189409i
$655$			22.7382i			0.888455i
$656$		−	9.24875i		−	0.361103i
$657$	−27.8556	+	15.8898i	−1.08675	+	0.619918i
$658$	−30.0388			−1.17103
$659$	−14.0859			−0.548709			−0.274354	−	0.961629i	$-0.588464\pi$
$659$	−14.0859			−0.548709			−0.274354	+	0.961629i	$0.588464\pi$
$660$	−11.9932	−	6.96594i	−0.466834	−	0.271149i
$661$	0.840963			0.0327097			0.0163548	−	0.999866i	$-0.494794\pi$
$661$	0.840963			0.0327097			0.0163548	+	0.999866i	$0.494794\pi$
$662$	32.1662			1.25018
$663$	0.270666	−	0.466003i	0.0105118	−	0.0180981i
$664$	2.87316			0.111500
$665$			7.39197i			0.286648i
$666$	15.6924	−	8.95145i	0.608068	−	0.346862i
$667$		−	5.99891i		−	0.232279i
$668$			7.18517i			0.278003i
$669$	−10.3615	+	17.8393i	−0.400599	+	0.689708i
$670$	21.7380			0.839812
$671$			43.8352i			1.69224i
$672$	−3.11386	+	5.36111i	−0.120120	+	0.206809i
$673$			26.8836i			1.03629i	0.855293	+	0.518144i	$0.173377\pi$
$673$			26.8836i			1.03629i	−0.855293	+	0.518144i	$0.826623\pi$
$674$			17.9638i			0.691940i
$675$	−11.6595	−	0.0910109i	−0.448774	−	0.00350301i
$676$	12.8245			0.493251
$677$			9.79922i			0.376615i	0.982110	+	0.188307i	$0.0603001\pi$
$677$			9.79922i			0.376615i	−0.982110	+	0.188307i	$0.939700\pi$
$678$	2.99078	−	5.14920i	0.114860	−	0.197754i
$679$			41.2621i			1.58349i
$680$	1.23307			0.0472861
$681$	−7.57107	+	13.0350i	−0.290124	+	0.499504i
$682$			50.3896i			1.92952i
$683$	−31.2678			−1.19643			−0.598215	−	0.801336i	$-0.704123\pi$
$683$	−31.2678			−1.19643			−0.598215	+	0.801336i	$0.704123\pi$
$684$	−1.84906	−	3.24151i	−0.0707007	−	0.123942i
$685$	−11.8959			−0.454519
$686$	4.25050			0.162285
$687$	−25.5109	−	14.8174i	−0.973302	−	0.565318i
$688$		−	3.58258i		−	0.136585i
$689$	−4.04977			−0.154284
$690$	3.12002	+	1.81218i	0.118777	+	0.0689887i
$691$		−	32.2762i		−	1.22784i	−0.789366	−	0.613922i	$-0.789591\pi$
$691$		−	32.2762i		−	1.22784i	0.789366	−	0.613922i	$-0.210409\pi$
$692$	−4.12797			−0.156922
$693$	25.6640	+	44.9903i	0.974893	+	1.70904i
$694$	−30.2193			−1.14711
$695$		−	8.64109i		−	0.327775i
$696$	7.16033	+	4.15890i	0.271412	+	0.157643i
$697$	6.86952			0.260201
$698$			27.1281i			1.02681i
$699$	−8.59463	+	14.7973i	−0.325079	+	0.559685i
$700$	−8.03208			−0.303584
$701$	−50.5534			−1.90938			−0.954688	−	0.297607i	$-0.903811\pi$
$701$	−50.5534			−1.90938			−0.954688	+	0.297607i	$0.903811\pi$
$702$	−0.0169899	+	2.17660i	−0.000641244	+	0.0821503i
$703$			7.49098i			0.282528i
$704$	4.82340			0.181789
$705$	−20.8663	−	12.1197i	−0.785872	−	0.456454i
$706$	15.5292			0.584448
$707$	40.3231			1.51651
$708$	3.30133	+	12.8880i	0.124072	+	0.484362i
$709$	17.5937			0.660746			0.330373	−	0.943850i	$-0.392825\pi$
$709$	17.5937			0.660746			0.330373	+	0.943850i	$0.392825\pi$
$710$	6.67370			0.250459
$711$	−5.28842	−	9.27089i	−0.198331	−	0.347685i
$712$	−16.0885			−0.602944
$713$		−	13.1088i		−	0.490930i
$714$	−3.98196	−	2.31282i	−0.149021	−	0.0865552i
$715$	−3.35434			−0.125445
$716$	12.7736			0.477373
$717$	−9.20767	−	5.34804i	−0.343867	−	0.199726i
$718$		−	9.70378i		−	0.362142i
$719$	−51.0870			−1.90522			−0.952612	−	0.304187i	$-0.901615\pi$
$719$	−51.0870			−1.90522			−0.952612	+	0.304187i	$0.901615\pi$
$720$	−4.32607	+	2.46773i	−0.161223	+	0.0919669i
$721$		−	5.73292i		−	0.213505i
$722$	−17.4526			−0.649519
$723$	14.2751	−	24.5773i	0.530896	−	0.914039i
$724$	−6.91511			−0.256998
$725$			10.7277i			0.398417i
$726$	10.6698	−	18.3700i	0.395992	−	0.681776i
$727$	27.9108			1.03515			0.517577	−	0.855636i	$-0.326834\pi$
$727$	27.9108			1.03515			0.517577	+	0.855636i	$0.326834\pi$
$728$			1.49943i			0.0555726i
$729$	26.9967	+	0.421485i	0.999878	+	0.0156105i
$730$	−17.7463			−0.656821
$731$	2.66096			0.0984193
$732$	13.6115	+	7.90592i	0.503097	+	0.292211i
$733$	24.5303			0.906047			0.453024	−	0.891498i	$-0.350345\pi$
$733$	24.5303			0.906047			0.453024	+	0.891498i	$0.350345\pi$
$734$			21.1320i			0.779997i
$735$	−14.4526	−	8.39444i	−0.533093	−	0.309634i
$736$	−1.25480			−0.0462527
$737$			63.1579i			2.32645i
$738$	−24.1008	+	13.7479i	−0.887164	+	0.506067i
$739$		−	17.0899i		−	0.628661i	−0.949314	−	0.314331i	$-0.898220\pi$
$739$		−	17.0899i		−	0.628661i	0.949314	−	0.314331i	$-0.101780\pi$
$740$	9.99735			0.367510
$741$	−0.780448	−	0.453304i	−0.0286705	−	0.0166525i
$742$			34.6050i			1.27039i
$743$		−	1.24732i		−	0.0457597i	−0.999738	−	0.0228798i	$-0.992716\pi$
$743$		−	1.24732i		−	0.0457597i	0.999738	−	0.0228798i	$-0.00728352\pi$
$744$	15.6468	+	9.08804i	0.573639	+	0.333184i
$745$		−	14.6437i		−	0.536502i
$746$	−26.4779			−0.969424
$747$	−4.27084	−	7.48702i	−0.156262	−	0.273936i
$748$			3.58258i			0.130992i
$749$			0.209484i			0.00765438i
$750$	−18.0118	−	10.4617i	−0.657696	−	0.382006i
$751$			42.5159i			1.55143i	0.631085	+	0.775714i	$0.282610\pi$
$751$			42.5159i			1.55143i	−0.631085	+	0.775714i	$0.717390\pi$
$752$	8.39199			0.306024
$753$	−8.16850	−	4.74447i	−0.297677	−	0.172898i
$754$	2.00265			0.0729322
$755$	1.44896			0.0527331
$756$	18.5988	+	0.145178i	0.676434	+	0.00528007i
$757$	−15.0798			−0.548086			−0.274043	−	0.961717i	$-0.588361\pi$
$757$	−15.0798			−0.548086			−0.274043	+	0.961717i	$0.588361\pi$
$758$	2.78409			0.101123
$759$	−5.26515	+	9.06496i	−0.191113	+	0.329037i
$760$		−	2.06511i		−	0.0749094i
$761$			19.8632i			0.720039i	0.932945	+	0.360019i	$0.117230\pi$
$761$			19.8632i			0.720039i	−0.932945	+	0.360019i	$0.882770\pi$
$762$	−19.2248	+	33.0992i	−0.696442	+	1.19906i
$763$		−	19.9308i		−	0.721543i
$764$	3.69921			0.133833
$765$	−1.83291	−	3.21319i	−0.0662690	−	0.116173i
$766$		−	35.3588i		−	1.27756i
$767$	2.25593	+	2.29431i	0.0814570	+	0.0828428i
$768$	0.869925	−	1.49774i	0.0313907	−	0.0540451i
$769$		−	34.3092i		−	1.23722i	−0.785698	−	0.618610i	$-0.787696\pi$
$769$		−	34.3092i		−	1.23722i	0.785698	−	0.618610i	$-0.212304\pi$
$770$			28.6626i			1.03293i
$771$	30.1548	+	17.5147i	1.08600	+	0.630775i
$772$	−11.9714			−0.430862
$773$	1.83830			0.0661190			0.0330595	−	0.999453i	$-0.489475\pi$
$773$	1.83830			0.0661190			0.0330595	+	0.999453i	$0.489475\pi$
$774$	−9.33565	+	5.32536i	−0.335563	+	0.191416i
$775$			23.4422i			0.842070i
$776$		−	11.5275i		−	0.413812i
$777$	−32.2845	−	18.7517i	−1.15820	−	0.672712i
$778$		−	12.5625i		−	0.450387i
$779$		−	11.5049i		−	0.412204i
$780$	−0.604972	+	1.04157i	−0.0216615	+	0.0372944i
$781$			19.3899i			0.693824i
$782$		−	0.932006i		−	0.0333285i
$783$	0.193901	−	24.8408i	0.00692944	−	0.887736i
$784$	5.81253			0.207590
$785$	−38.7289			−1.38229
$786$	−11.9150	+	20.5139i	−0.424993	+	0.731707i
$787$	−13.2050			−0.470709			−0.235354	−	0.971910i	$-0.575625\pi$
$787$	−13.2050			−0.470709			−0.235354	+	0.971910i	$0.575625\pi$
$788$		−	12.7702i		−	0.454920i
$789$	42.8760	+	24.9035i	1.52643	+	0.886586i
$790$		−	5.90632i		−	0.210137i
$791$	−12.3061			−0.437554
$792$	−7.16979	−	12.5690i	−0.254767	−	0.446621i
$793$	3.80697			0.135189
$794$			32.5653i			1.15570i
$795$	−13.9620	+	24.0382i	−0.495181	+	0.852548i
$796$	7.63327			0.270554
$797$	25.7748			0.912989			0.456494	−	0.889726i	$-0.349105\pi$
$797$	25.7748			0.912989			0.456494	+	0.889726i	$0.349105\pi$
$798$	−3.87345	+	6.66888i	−0.137119	+	0.236076i
$799$			6.23315i			0.220513i
$800$	2.24394			0.0793351
$801$	23.9150	+	41.9243i	0.844994	+	1.48132i
$802$	25.7353			0.908746
$803$		−	51.5605i		−	1.81953i
$804$	19.6115	+	11.3909i	0.691646	+	0.401725i
$805$		−	7.45655i		−	0.262809i
$806$	4.37620			0.154145
$807$	−4.80097	+	8.26578i	−0.169002	+	0.290969i
$808$	−11.2652			−0.396307
$809$	29.8058			1.04792			0.523959	−	0.851744i	$-0.324455\pi$
$809$	29.8058			1.04792			0.523959	+	0.851744i	$0.324455\pi$
$810$	12.8611	+	7.60489i	0.451891	+	0.267209i
$811$		−	17.7097i		−	0.621872i	−0.950431	−	0.310936i	$-0.899357\pi$
$811$		−	17.7097i		−	0.621872i	0.950431	−	0.310936i	$-0.100643\pi$
$812$		−	17.1125i		−	0.600531i
$813$	−26.9438	+	46.3889i	−0.944961	+	1.62693i
$814$			29.0465i			1.01808i
$815$		−	7.87329i		−	0.275789i
$816$	1.11245	+	0.646138i	0.0389435	+	0.0226193i
$817$		−	4.45650i		−	0.155913i
$818$		−	2.79568i		−	0.0977485i
$819$	3.90729	−	2.22884i	0.136532	−	0.0778821i
$820$	−15.3542			−0.536193
$821$	14.4107			0.502936			0.251468	−	0.967866i	$-0.419087\pi$
$821$	14.4107			0.502936			0.251468	+	0.967866i	$0.419087\pi$
$822$	−10.7322	−	6.23354i	−0.374329	−	0.217420i
$823$		−	35.1384i		−	1.22485i	−0.790529	−	0.612425i	$-0.790194\pi$
$823$		−	35.1384i		−	1.22485i	0.790529	−	0.612425i	$-0.209806\pi$
$824$			1.60162i			0.0557949i
$825$	9.41555	−	16.2107i	0.327807	−	0.564382i
$826$	19.6047	−	19.2768i	0.682136	−	0.670725i
$827$		−	24.7747i		−	0.861499i	−0.902471	−	0.430750i	$-0.858249\pi$
$827$		−	24.7747i		−	0.861499i	0.902471	−	0.430750i	$-0.141751\pi$
$828$	1.86522	+	3.26983i	0.0648207	+	0.113634i
$829$	1.97335			0.0685372			0.0342686	−	0.999413i	$-0.489090\pi$
$829$	1.97335			0.0685372			0.0342686	+	0.999413i	$0.489090\pi$
$830$		−	4.76985i		−	0.165564i
$831$	17.3795	−	29.9221i	0.602888	−	1.03799i
$832$		−	0.418899i		−	0.0145227i
$833$			4.31726i			0.149584i
$834$	4.52799	−	7.79580i	0.156792	−	0.269947i
$835$	11.9284			0.412799
$836$	6.00000			0.207514
$837$	0.423713	−	54.2822i	0.0146456	−	1.87627i
$838$	26.4494			0.913681
$839$	−3.80927			−0.131511			−0.0657553	−	0.997836i	$-0.520946\pi$
$839$	−3.80927			−0.131511			−0.0657553	+	0.997836i	$0.520946\pi$
$840$	8.90018	+	5.16945i	0.307085	+	0.178363i
$841$	6.14441			0.211876
$842$			11.9509i			0.411855i
$843$	35.1877	+	20.4379i	1.21193	+	0.703917i
$844$			18.3522i			0.631710i
$845$		−	21.2905i		−	0.732415i
$846$	−12.4744	−	21.8682i	−0.428877	−	0.751845i
$847$	−43.9026			−1.50851
$848$		−	9.66765i		−	0.331988i
$849$	−20.6025	−	11.9664i	−0.707076	−	0.410687i
$850$			1.66669i			0.0571668i
$851$		−	7.55642i		−	0.259031i
$852$	6.02086	+	3.49707i	0.206271	+	0.119807i
$853$	−51.2486			−1.75472			−0.877359	−	0.479834i	$-0.840697\pi$
$853$	−51.2486			−1.75472			−0.877359	+	0.479834i	$0.840697\pi$
$854$		−	32.5303i		−	1.11316i
$855$	−5.38136	+	3.06970i	−0.184039	+	0.104982i
$856$		−	0.0585239i		−	0.00200031i
$857$	−0.987887			−0.0337456			−0.0168728	−	0.999858i	$-0.505371\pi$
$857$	−0.987887			−0.0337456			−0.0168728	+	0.999858i	$0.505371\pi$
$858$	−3.02621	−	1.75770i	−0.103313	−	0.0600068i
$859$			49.0308i			1.67291i	0.548037	+	0.836454i	$0.315375\pi$
$859$			49.0308i			1.67291i	−0.548037	+	0.836454i	$0.684625\pi$
$860$	−5.94758			−0.202811
$861$	49.5835	+	28.7993i	1.68980	+	0.981479i
$862$	−11.5375			−0.392969
$863$	−17.2465			−0.587077			−0.293538	−	0.955947i	$-0.594833\pi$
$863$	−17.2465			−0.587077			−0.293538	+	0.955947i	$0.594833\pi$
$864$	−5.19599	−	0.0405586i	−0.176771	−	0.00137983i
$865$			6.85300i			0.233009i
$866$	−36.2956			−1.23337
$867$	14.3088	−	24.6353i	0.485953	−	0.836660i
$868$		−	37.3943i		−	1.26925i
$869$	17.1603			0.582124
$870$	6.90435	−	11.8872i	0.234079	−	0.403012i
$871$	5.48509			0.185855
$872$			5.56810i			0.188560i
$873$	−30.0388	+	17.1351i	−1.01666	+	0.579935i
$874$	−1.56090			−0.0527981
$875$			43.0464i			1.45523i
$876$	−16.0103	−	9.29920i	−0.540939	−	0.314191i
$877$	4.86999			0.164448			0.0822239	−	0.996614i	$-0.473798\pi$
$877$	4.86999			0.164448			0.0822239	+	0.996614i	$0.473798\pi$
$878$	11.5445			0.389607
$879$	−28.9240	−	16.7998i	−0.975584	−	0.566643i
$880$		−	8.00751i		−	0.269933i
$881$	14.3475			0.483380			0.241690	−	0.970353i	$-0.422298\pi$
$881$	14.3475			0.483380			0.241690	+	0.970353i	$0.422298\pi$
$882$	−8.64009	−	15.1466i	−0.290927	−	0.510011i
$883$	26.9717			0.907671			0.453835	−	0.891086i	$-0.350055\pi$
$883$	26.9717			0.907671			0.453835	+	0.891086i	$0.350055\pi$
$884$	0.311137			0.0104647
$885$	21.3959	−	5.48067i	0.719216	−	0.184231i
$886$	−12.3499			−0.414904
$887$	−20.8782			−0.701022			−0.350511	−	0.936559i	$-0.613992\pi$
$887$	−20.8782			−0.701022			−0.350511	+	0.936559i	$0.613992\pi$
$888$	9.01939	+	5.23868i	0.302671	+	0.175799i
$889$	79.1040			2.65306
$890$			26.7092i			0.895295i
$891$	−22.0954	+	37.3667i	−0.740223	+	1.25183i
$892$	−11.9108			−0.398804
$893$	10.4391			0.349331
$894$	7.67339	−	13.2112i	0.256637	−	0.441849i
$895$		−	21.2060i		−	0.708839i
$896$	−3.57946			−0.119581
$897$	0.787267	+	0.457264i	0.0262861	+	0.0152676i
$898$			28.4979i			0.950988i
$899$	−49.9442			−1.66573
$900$	−3.33552	−	5.84736i	−0.111184	−	0.194912i
$901$	7.18065			0.239222
$902$		−	44.6104i		−	1.48536i
$903$	19.2066	+	11.1557i	0.639155	+	0.371237i
$904$	3.43798			0.114345
$905$			11.4801i			0.381610i
$906$	1.30722	+	0.759266i	0.0434295	+	0.0252249i
$907$	−6.35574			−0.211039			−0.105519	−	0.994417i	$-0.533651\pi$
$907$	−6.35574			−0.211039			−0.105519	+	0.994417i	$0.533651\pi$
$908$	−8.70313			−0.288823
$909$	16.7452	+	29.3553i	0.555403	+	0.973652i
$910$	2.48926			0.0825183
$911$			21.1718i			0.701452i	0.936478	+	0.350726i	$0.114065\pi$
$911$			21.1718i			0.701452i	−0.936478	+	0.350726i	$0.885935\pi$
$912$	1.08213	−	1.86310i	0.0358330	−	0.0616933i
$913$	13.8584			0.458646
$914$			22.4605i			0.742926i
$915$	13.1249	−	22.5971i	0.433897	−	0.747036i
$916$		−	17.0329i		−	0.562783i
$917$	49.0263			1.61899
$918$	0.0301249	−	3.85933i	0.000994271	−	0.127377i
$919$		−	21.0620i		−	0.694772i	−0.937722	−	0.347386i	$-0.887069\pi$
$919$		−	21.0620i		−	0.694772i	0.937722	−	0.347386i	$-0.112931\pi$
$920$			2.08315i			0.0686794i
$921$	−23.1502	+	39.8574i	−0.762824	+	1.31335i
$922$			6.76019i			0.222635i
$923$	1.68396			0.0554281
$924$	−15.0194	+	25.8587i	−0.494102	+	0.850690i
$925$			13.5130i			0.444304i
$926$		−	32.1740i		−	1.05730i
$927$	4.17356	−	2.38074i	0.137078	−	0.0781937i
$928$			4.78075i			0.156936i
$929$	32.5664			1.06847			0.534235	−	0.845336i	$-0.320600\pi$
$929$	32.5664			1.06847			0.534235	+	0.845336i	$0.320600\pi$
$930$	15.0874	−	25.9759i	0.494736	−	0.851782i
$931$	7.23042			0.236967
$932$	−9.87973			−0.323621
$933$	−20.1634	−	11.7114i	−0.660119	−	0.383414i
$934$	29.7721			0.974173
$935$	5.94758			0.194507
$936$	−1.09159	+	0.622676i	−0.0356796	+	0.0203528i
$937$		−	28.2471i		−	0.922792i	−0.887194	−	0.461396i	$-0.847349\pi$
$937$		−	28.2471i		−	0.922792i	0.887194	−	0.461396i	$-0.152651\pi$
$938$		−	46.8697i		−	1.53035i
$939$	6.35674	+	3.69215i	0.207444	+	0.120489i
$940$		−	13.9319i		−	0.454408i
$941$	24.1748			0.788077			0.394039	−	0.919094i	$-0.371078\pi$
$941$	24.1748			0.788077			0.394039	+	0.919094i	$0.371078\pi$
$942$	−34.9404	−	20.2942i	−1.13842	−	0.661222i
$943$			11.6054i			0.377923i
$944$	−5.47701	+	5.38539i	−0.178261	+	0.175279i
$945$	0.241016	−	30.8767i	0.00784023	−	1.00442i
$946$		−	17.2802i		−	0.561828i
$947$			12.7052i			0.412863i	0.978461	+	0.206431i	$0.0661850\pi$
$947$			12.7052i			0.412863i	−0.978461	+	0.206431i	$0.933815\pi$
$948$	3.09495	−	5.32855i	0.100519	−	0.173063i
$949$	−4.47788			−0.145358
$950$	2.79132			0.0905622
$951$	−8.21126	−	4.76930i	−0.266268	−	0.154655i
$952$		−	2.65865i		−	0.0861672i
$953$		−	19.7288i		−	0.639078i	−0.947573	−	0.319539i	$-0.896472\pi$
$953$		−	19.7288i		−	0.639078i	0.947573	−	0.319539i	$-0.103528\pi$
$954$	−25.1924	+	14.3706i	−0.815634	+	0.465265i
$955$		−	6.14120i		−	0.198725i
$956$		−	6.14770i		−	0.198831i
$957$	34.5371	+	20.0600i	1.11643	+	0.648448i
$958$			11.4600i			0.370257i
$959$			25.6490i			0.828249i
$960$	−2.48646	−	1.44420i	−0.0802502	−	0.0466113i
$961$	−78.1382			−2.52059
$962$	2.52261			0.0813321
$963$	−0.152504	+	0.0869935i	−0.00491439	+	0.00280333i
$964$	16.4096			0.528516
$965$			19.8743i			0.639775i
$966$	3.90729	−	6.72714i	0.125715	−	0.216442i
$967$		−	43.7060i		−	1.40549i	−0.711441	−	0.702745i	$-0.751957\pi$
$967$		−	43.7060i		−	1.40549i	0.711441	−	0.702745i	$-0.248043\pi$
$968$	12.2652			0.394217
$969$	1.38382	+	0.803754i	0.0444546	+	0.0258203i
$970$	−19.1372			−0.614458
$971$		−	38.0875i		−	1.22229i	−0.791521	−	0.611143i	$-0.790710\pi$
$971$		−	38.0875i		−	1.22229i	0.791521	−	0.611143i	$-0.209290\pi$
$972$	7.61795	+	13.6003i	0.244346	+	0.436228i
$973$	−18.6312			−0.597290
$974$	8.42054			0.269812
$975$	−1.40785	−	0.817714i	−0.0450873	−	0.0261878i
$976$			9.08804i			0.290901i
$977$	6.63591			0.212302			0.106151	−	0.994350i	$-0.466147\pi$
$977$	6.63591			0.212302			0.106151	+	0.994350i	$0.466147\pi$
$978$	4.12566	−	7.10311i	0.131924	−	0.227132i
$979$	−77.6014			−2.48015
$980$		−	9.64961i		−	0.308245i
$981$	14.5096	−	8.27675i	0.463256	−	0.264256i
$982$			7.10664i			0.226782i
$983$	39.0530			1.24560			0.622799	−	0.782382i	$-0.285995\pi$
$983$	39.0530			1.24560			0.622799	+	0.782382i	$0.285995\pi$
$984$	−13.8522	−	8.04572i	−0.441593	−	0.256488i
$985$	−21.2004			−0.675499
$986$	−3.55091			−0.113084
$987$	−26.1315	+	44.9903i	−0.831775	+	1.43206i
$988$		−	0.521083i		−	0.0165779i
$989$			4.49544i			0.142947i
$990$	−20.8663	+	11.9028i	−0.663176	+	0.378297i
$991$			28.3842i			0.901654i	0.892611	+	0.450827i	$0.148871\pi$
$991$			28.3842i			0.901654i	−0.892611	+	0.450827i	$0.851129\pi$
$992$			10.4469i			0.331690i
$993$	27.9822	−	48.1767i	0.887989	−	1.52884i
$994$		−	14.3893i		−	0.456400i
$995$		−	12.6723i		−	0.401739i
$996$	2.49944	−	4.30325i	0.0791977	−	0.136354i
$997$	−0.641094			−0.0203037			−0.0101518	−	0.999948i	$-0.503231\pi$
$997$	−0.641094			−0.0203037			−0.0101518	+	0.999948i	$0.503231\pi$
$998$	33.2330			1.05197
$999$	0.244244	−	31.2902i	0.00772753	−	0.989979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.c.b.353.7	yes	10
3.2	odd	2		354.2.c.a.353.8	yes	10
59.58	odd	2		354.2.c.a.353.7	✓	10
177.176	even	2	inner	354.2.c.b.353.8	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.c.a.353.7	✓	10	59.58	odd	2
354.2.c.a.353.8	yes	10	3.2	odd	2
354.2.c.b.353.7	yes	10	1.1	even	1	trivial
354.2.c.b.353.8	yes	10	177.176	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.869925 - 1.49774i) q^{3} +1.00000 q^{4} -1.66014i q^{5} +(0.869925 - 1.49774i) q^{6} -3.57946 q^{7} +1.00000 q^{8} +(-1.48646 - 2.60585i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.869925 - 1.49774i) q^{3} +1.00000 q^{4} -1.66014i q^{5} +(0.869925 - 1.49774i) q^{6} -3.57946 q^{7} +1.00000 q^{8} +(-1.48646 - 2.60585i) q^{9} -1.66014i q^{10} +4.82340 q^{11} +(0.869925 - 1.49774i) q^{12} -0.418899i q^{13} -3.57946 q^{14} +(-2.48646 - 1.44420i) q^{15} +1.00000 q^{16} +0.742751i q^{17} +(-1.48646 - 2.60585i) q^{18} +1.24394 q^{19} -1.66014i q^{20} +(-3.11386 + 5.36111i) q^{21} +4.82340 q^{22} -1.25480 q^{23} +(0.869925 - 1.49774i) q^{24} +2.24394 q^{25} -0.418899i q^{26} +(-5.19599 - 0.0405586i) q^{27} -3.57946 q^{28} +4.78075i q^{29} +(-2.48646 - 1.44420i) q^{30} +10.4469i q^{31} +1.00000 q^{32} +(4.19599 - 7.22420i) q^{33} +0.742751i q^{34} +5.94240i q^{35} +(-1.48646 - 2.60585i) q^{36} +6.02199i q^{37} +1.24394 q^{38} +(-0.627402 - 0.364411i) q^{39} -1.66014i q^{40} -9.24875i q^{41} +(-3.11386 + 5.36111i) q^{42} -3.58258i q^{43} +4.82340 q^{44} +(-4.32607 + 2.46773i) q^{45} -1.25480 q^{46} +8.39199 q^{47} +(0.869925 - 1.49774i) q^{48} +5.81253 q^{49} +2.24394 q^{50} +(1.11245 + 0.646138i) q^{51} -0.418899i q^{52} -9.66765i q^{53} +(-5.19599 - 0.0405586i) q^{54} -8.00751i q^{55} -3.57946 q^{56} +(1.08213 - 1.86310i) q^{57} +4.78075i q^{58} +(-5.47701 + 5.38539i) q^{59} +(-2.48646 - 1.44420i) q^{60} +9.08804i q^{61} +10.4469i q^{62} +(5.32072 + 9.32752i) q^{63} +1.00000 q^{64} -0.695430 q^{65} +(4.19599 - 7.22420i) q^{66} +13.0941i q^{67} +0.742751i q^{68} +(-1.09159 + 1.87937i) q^{69} +5.94240i q^{70} +4.01996i q^{71} +(-1.48646 - 2.60585i) q^{72} -10.6897i q^{73} +6.02199i q^{74} +(1.95206 - 3.36084i) q^{75} +1.24394 q^{76} -17.2652 q^{77} +(-0.627402 - 0.364411i) q^{78} +3.55772 q^{79} -1.66014i q^{80} +(-4.58087 + 7.74697i) q^{81} -9.24875i q^{82} +2.87316 q^{83} +(-3.11386 + 5.36111i) q^{84} +1.23307 q^{85} -3.58258i q^{86} +(7.16033 + 4.15890i) q^{87} +4.82340 q^{88} -16.0885 q^{89} +(-4.32607 + 2.46773i) q^{90} +1.49943i q^{91} -1.25480 q^{92} +(15.6468 + 9.08804i) q^{93} +8.39199 q^{94} -2.06511i q^{95} +(0.869925 - 1.49774i) q^{96} -11.5275i q^{97} +5.81253 q^{98} +(-7.16979 - 12.5690i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} - q^{6} - 2 q^{7} + 10 q^{8} + 3 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 - q^6 - 2 * q^7 + 10 * q^8 + 3 * q^9	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} - q^{6} - 2 q^{7} + 10 q^{8} + 3 q^{9} - 4 q^{11} - q^{12} - 2 q^{14} - 7 q^{15} + 10 q^{16} + 3 q^{18} - 6 q^{19} - 3 q^{21} - 4 q^{22} + 8 q^{23} - q^{24} + 4 q^{25} - 10 q^{27} - 2 q^{28} - 7 q^{30} + 10 q^{32} + 3 q^{36} - 6 q^{38} + 4 q^{39} - 3 q^{42} - 4 q^{44} - 11 q^{45} + 8 q^{46} - q^{48} + 8 q^{49} + 4 q^{50} + 2 q^{51} - 10 q^{54} - 2 q^{56} - 3 q^{57} - 20 q^{59} - 7 q^{60} - 19 q^{63} + 10 q^{64} - 16 q^{65} - 14 q^{69} + 3 q^{72} - 4 q^{75} - 6 q^{76} - 48 q^{77} + 4 q^{78} + 6 q^{79} + 7 q^{81} - 12 q^{83} - 3 q^{84} - 4 q^{85} - 15 q^{87} - 4 q^{88} + 16 q^{89} - 11 q^{90} + 8 q^{92} + 52 q^{93} - q^{96} + 8 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 - q^6 - 2 * q^7 + 10 * q^8 + 3 * q^9 - 4 * q^11 - q^12 - 2 * q^14 - 7 * q^15 + 10 * q^16 + 3 * q^18 - 6 * q^19 - 3 * q^21 - 4 * q^22 + 8 * q^23 - q^24 + 4 * q^25 - 10 * q^27 - 2 * q^28 - 7 * q^30 + 10 * q^32 + 3 * q^36 - 6 * q^38 + 4 * q^39 - 3 * q^42 - 4 * q^44 - 11 * q^45 + 8 * q^46 - q^48 + 8 * q^49 + 4 * q^50 + 2 * q^51 - 10 * q^54 - 2 * q^56 - 3 * q^57 - 20 * q^59 - 7 * q^60 - 19 * q^63 + 10 * q^64 - 16 * q^65 - 14 * q^69 + 3 * q^72 - 4 * q^75 - 6 * q^76 - 48 * q^77 + 4 * q^78 + 6 * q^79 + 7 * q^81 - 12 * q^83 - 3 * q^84 - 4 * q^85 - 15 * q^87 - 4 * q^88 + 16 * q^89 - 11 * q^90 + 8 * q^92 + 52 * q^93 - q^96 + 8 * q^98 - 2 * q^99

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