LMFDB - Embedded newform 1155.2.c.f.694.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(694,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.694");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15210 x^{12} + 40640 x^{10} + 63865 x^{8} + 55281 x^{6} + \cdots + 4 $ x^20 + 33x^18 + 456x^16 + 3426x^14 + 15210x^12 + 40640x^10 + 63865x^8 + 55281x^6 + 22984x^4 + 3428*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.11
Root			$0.0342944i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.f.694.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0342944i q^{2} -1.00000i q^{3} +1.99882 q^{4} +(-1.84220 + 1.26739i) q^{5} +0.0342944 q^{6} -1.00000i q^{7} +0.137137i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+0.0342944i q^{2} -1.00000i q^{3} +1.99882 q^{4} +(-1.84220 + 1.26739i) q^{5} +0.0342944 q^{6} -1.00000i q^{7} +0.137137i q^{8} -1.00000 q^{9} +(-0.0434646 - 0.0631773i) q^{10} +1.00000 q^{11} -1.99882i q^{12} +5.23302i q^{13} +0.0342944 q^{14} +(1.26739 + 1.84220i) q^{15} +3.99294 q^{16} +5.86667i q^{17} -0.0342944i q^{18} -1.91588 q^{19} +(-3.68224 + 2.53330i) q^{20} -1.00000 q^{21} +0.0342944i q^{22} +2.87247i q^{23} +0.137137 q^{24} +(1.78742 - 4.66959i) q^{25} -0.179464 q^{26} +1.00000i q^{27} -1.99882i q^{28} +6.16600 q^{29} +(-0.0631773 + 0.0434646i) q^{30} +8.30169 q^{31} +0.411211i q^{32} -1.00000i q^{33} -0.201194 q^{34} +(1.26739 + 1.84220i) q^{35} -1.99882 q^{36} -8.61106i q^{37} -0.0657039i q^{38} +5.23302 q^{39} +(-0.173807 - 0.252635i) q^{40} -1.69244 q^{41} -0.0342944i q^{42} +6.55683i q^{43} +1.99882 q^{44} +(1.84220 - 1.26739i) q^{45} -0.0985097 q^{46} +6.80222i q^{47} -3.99294i q^{48} -1.00000 q^{49} +(0.160141 + 0.0612987i) q^{50} +5.86667 q^{51} +10.4599i q^{52} +2.02461i q^{53} -0.0342944 q^{54} +(-1.84220 + 1.26739i) q^{55} +0.137137 q^{56} +1.91588i q^{57} +0.211460i q^{58} -6.11472 q^{59} +(2.53330 + 3.68224i) q^{60} +12.1948 q^{61} +0.284702i q^{62} +1.00000i q^{63} +7.97179 q^{64} +(-6.63230 - 9.64029i) q^{65} +0.0342944 q^{66} +0.347338i q^{67} +11.7264i q^{68} +2.87247 q^{69} +(-0.0631773 + 0.0434646i) q^{70} -15.6510 q^{71} -0.137137i q^{72} -12.7172i q^{73} +0.295312 q^{74} +(-4.66959 - 1.78742i) q^{75} -3.82950 q^{76} -1.00000i q^{77} +0.179464i q^{78} +1.95864 q^{79} +(-7.35581 + 5.06064i) q^{80} +1.00000 q^{81} -0.0580412i q^{82} +3.09388i q^{83} -1.99882 q^{84} +(-7.43539 - 10.8076i) q^{85} -0.224863 q^{86} -6.16600i q^{87} +0.137137i q^{88} +9.12512 q^{89} +(0.0434646 + 0.0631773i) q^{90} +5.23302 q^{91} +5.74156i q^{92} -8.30169i q^{93} -0.233278 q^{94} +(3.52943 - 2.42817i) q^{95} +0.411211 q^{96} +10.8973i q^{97} -0.0342944i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	$ 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} + 2 q^{10} + 20 q^{11} + 6 q^{14} - 2 q^{15} + 38 q^{16} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 q^{95} + 62 q^{96} - 20 q^{99}+O(q^{100}) $ 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 + 2 * q^10 + 20 * q^11 + 6 * q^14 - 2 * q^15 + 38 * q^16 - 34 * q^19 + 4 * q^20 - 20 * q^21 - 18 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^29 - 6 * q^30 + 12 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 - 2 * q^40 + 52 * q^41 - 26 * q^44 + 2 * q^45 + 40 * q^46 - 20 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^54 - 2 * q^55 - 18 * q^56 - 14 * q^59 - 28 * q^60 + 78 * q^61 - 26 * q^64 - 4 * q^65 + 6 * q^66 - 18 * q^69 - 6 * q^70 - 8 * q^74 - 8 * q^75 + 84 * q^76 - 52 * q^79 - 40 * q^80 + 20 * q^81 + 26 * q^84 - 24 * q^85 + 4 * q^86 - 10 * q^89 - 2 * q^90 - 96 * q^94 - 30 * q^95 + 62 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$			0.0342944i			0.0242498i	0.999926	+	0.0121249i	$0.00385958\pi$
$2$			0.0342944i			0.0242498i	−0.999926	+	0.0121249i	$0.996140\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.99882			0.999412
$5$	−1.84220	+	1.26739i	−0.823858	+	0.566796i
$5$	−1.84220	+	1.26739i	−0.823858	+	0.566796i
$6$	0.0342944			0.0140007
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			0.137137i			0.0484854i
$9$	−1.00000			−0.333333
$10$	−0.0434646	−	0.0631773i	−0.0137447	−	0.0199784i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		−	1.99882i		−	0.577011i
$13$			5.23302i			1.45138i	0.688022	+	0.725690i	$0.258479\pi$
$13$			5.23302i			1.45138i	−0.688022	+	0.725690i	$0.741521\pi$
$14$	0.0342944			0.00916558
$15$	1.26739	+	1.84220i	0.327240	+	0.475655i
$16$	3.99294			0.998236
$17$			5.86667i			1.42288i	0.702748	+	0.711439i	$0.251956\pi$
$17$			5.86667i			1.42288i	−0.702748	+	0.711439i	$0.748044\pi$
$18$		−	0.0342944i		−	0.00808328i
$19$	−1.91588			−0.439532			−0.219766	−	0.975553i	$-0.570529\pi$
$19$	−1.91588			−0.439532			−0.219766	+	0.975553i	$0.570529\pi$
$20$	−3.68224	+	2.53330i	−0.823374	+	0.566463i
$21$	−1.00000			−0.218218
$22$			0.0342944i			0.00731160i
$23$			2.87247i			0.598951i	0.954104	+	0.299476i	$0.0968117\pi$
$23$			2.87247i			0.598951i	−0.954104	+	0.299476i	$0.903188\pi$
$24$	0.137137			0.0279931
$25$	1.78742	−	4.66959i	0.357485	−	0.933919i
$26$	−0.179464			−0.0351957
$27$			1.00000i			0.192450i
$28$		−	1.99882i		−	0.377742i
$29$	6.16600			1.14500			0.572499	−	0.819905i	$-0.305974\pi$
$29$	6.16600			1.14500			0.572499	+	0.819905i	$0.305974\pi$
$30$	−0.0631773	+	0.0434646i	−0.0115346	+	0.00793551i
$31$	8.30169			1.49103			0.745514	−	0.666490i	$-0.232204\pi$
$31$	8.30169			1.49103			0.745514	+	0.666490i	$0.232204\pi$
$32$			0.411211i			0.0726925i
$33$		−	1.00000i		−	0.174078i
$34$	−0.201194			−0.0345045
$35$	1.26739	+	1.84220i	0.214229	+	0.311389i
$36$	−1.99882			−0.333137
$37$		−	8.61106i		−	1.41565i	−0.706388	−	0.707825i	$-0.749677\pi$
$37$		−	8.61106i		−	1.41565i	0.706388	−	0.707825i	$-0.250323\pi$
$38$		−	0.0657039i		−	0.0106586i
$39$	5.23302			0.837954
$40$	−0.173807	−	0.252635i	−0.0274813	−	0.0399451i
$41$	−1.69244			−0.264314			−0.132157	−	0.991229i	$-0.542190\pi$
$41$	−1.69244			−0.264314			−0.132157	+	0.991229i	$0.542190\pi$
$42$		−	0.0342944i		−	0.00529175i
$43$			6.55683i			0.999907i	0.866052	+	0.499954i	$0.166650\pi$
$43$			6.55683i			0.999907i	−0.866052	+	0.499954i	$0.833350\pi$
$44$	1.99882			0.301334
$45$	1.84220	−	1.26739i	0.274619	−	0.188932i
$46$	−0.0985097			−0.0145245
$47$			6.80222i			0.992206i	0.868264	+	0.496103i	$0.165236\pi$
$47$			6.80222i			0.992206i	−0.868264	+	0.496103i	$0.834764\pi$
$48$		−	3.99294i		−	0.576332i
$49$	−1.00000			−0.142857
$50$	0.160141	+	0.0612987i	0.0226474	+	0.00866895i
$51$	5.86667			0.821499
$52$			10.4599i			1.45053i
$53$			2.02461i			0.278101i	0.990285	+	0.139051i	$0.0444050\pi$
$53$			2.02461i			0.278101i	−0.990285	+	0.139051i	$0.955595\pi$
$54$	−0.0342944			−0.00466688
$55$	−1.84220	+	1.26739i	−0.248403	+	0.170895i
$56$	0.137137			0.0183258
$57$			1.91588i			0.253764i
$58$			0.211460i			0.0277660i
$59$	−6.11472			−0.796068			−0.398034	−	0.917371i	$-0.630307\pi$
$59$	−6.11472			−0.796068			−0.398034	+	0.917371i	$0.630307\pi$
$60$	2.53330	+	3.68224i	0.327047	+	0.475375i
$61$	12.1948			1.56138			0.780689	−	0.624919i	$-0.214868\pi$
$61$	12.1948			1.56138			0.780689	+	0.624919i	$0.214868\pi$
$62$			0.284702i			0.0361572i
$63$			1.00000i			0.125988i
$64$	7.97179			0.996473
$65$	−6.63230	−	9.64029i	−0.822636	−	1.19573i
$66$	0.0342944			0.00422135
$67$			0.347338i			0.0424340i	0.999775	+	0.0212170i	$0.00675409\pi$
$67$			0.347338i			0.0424340i	−0.999775	+	0.0212170i	$0.993246\pi$
$68$			11.7264i			1.42204i
$69$	2.87247			0.345805
$70$	−0.0631773	+	0.0434646i	−0.00755114	+	0.00519501i
$71$	−15.6510			−1.85743			−0.928717	−	0.370790i	$-0.879087\pi$
$71$	−15.6510			−1.85743			−0.928717	+	0.370790i	$0.879087\pi$
$72$		−	0.137137i		−	0.0161618i
$73$		−	12.7172i		−	1.48844i	−0.667935	−	0.744219i	$-0.732822\pi$
$73$		−	12.7172i		−	1.48844i	0.667935	−	0.744219i	$-0.267178\pi$
$74$	0.295312			0.0343293
$75$	−4.66959	−	1.78742i	−0.539198	−	0.206394i
$76$	−3.82950			−0.439273
$77$		−	1.00000i		−	0.113961i
$78$			0.179464i			0.0203203i
$79$	1.95864			0.220364			0.110182	−	0.993911i	$-0.464857\pi$
$79$	1.95864			0.220364			0.110182	+	0.993911i	$0.464857\pi$
$80$	−7.35581	+	5.06064i	−0.822405	+	0.565796i
$81$	1.00000			0.111111
$82$		−	0.0580412i		−	0.00640958i
$83$			3.09388i			0.339597i	0.985479	+	0.169799i	$0.0543117\pi$
$83$			3.09388i			0.339597i	−0.985479	+	0.169799i	$0.945688\pi$
$84$	−1.99882			−0.218090
$85$	−7.43539	−	10.8076i	−0.806481	−	1.17225i
$86$	−0.224863			−0.0242476
$87$		−	6.16600i		−	0.661065i
$88$			0.137137i			0.0146189i
$89$	9.12512			0.967261			0.483630	−	0.875272i	$-0.339318\pi$
$89$	9.12512			0.967261			0.483630	+	0.875272i	$0.339318\pi$
$90$	0.0434646	+	0.0631773i	0.00458157	+	0.00665948i
$91$	5.23302			0.548570
$92$			5.74156i			0.598599i
$93$		−	8.30169i		−	0.860846i
$94$	−0.233278			−0.0240608
$95$	3.52943	−	2.42817i	0.362112	−	0.249125i
$96$	0.411211			0.0419690
$97$			10.8973i			1.10646i	0.833029	+	0.553229i	$0.186604\pi$
$97$			10.8973i			1.10646i	−0.833029	+	0.553229i	$0.813396\pi$
$98$		−	0.0342944i		−	0.00346426i
$99$	−1.00000			−0.100504
$100$	3.57274	−	9.33370i	0.357274	−	0.933370i
$101$	10.2602			1.02092			0.510462	−	0.859900i	$-0.329474\pi$
$101$	10.2602			1.02092			0.510462	+	0.859900i	$0.329474\pi$
$102$			0.201194i			0.0199212i
$103$			2.96638i			0.292286i	0.989263	+	0.146143i	$0.0466860\pi$
$103$			2.96638i			0.292286i	−0.989263	+	0.146143i	$0.953314\pi$
$104$	−0.717643			−0.0703707
$105$	1.84220	−	1.26739i	0.179781	−	0.123685i
$106$	−0.0694327			−0.00674390
$107$			4.71311i			0.455633i	0.973704	+	0.227817i	$0.0731587\pi$
$107$			4.71311i			0.455633i	−0.973704	+	0.227817i	$0.926841\pi$
$108$			1.99882i			0.192337i
$109$	2.65673			0.254469			0.127234	−	0.991873i	$-0.459390\pi$
$109$	2.65673			0.254469			0.127234	+	0.991873i	$0.459390\pi$
$110$	−0.0434646	−	0.0631773i	−0.00414419	−	0.00602372i
$111$	−8.61106			−0.817326
$112$		−	3.99294i		−	0.377298i
$113$		−	13.1235i		−	1.23455i	−0.786746	−	0.617277i	$-0.788236\pi$
$113$		−	13.1235i		−	1.23455i	0.786746	−	0.617277i	$-0.211764\pi$
$114$	−0.0657039			−0.00615373
$115$	−3.64055	−	5.29167i	−0.339483	−	0.493451i
$116$	12.3248			1.14433
$117$		−	5.23302i		−	0.483793i
$118$		−	0.209701i		−	0.0193045i
$119$	5.86667			0.537797
$120$	−0.252635	+	0.173807i	−0.0230623	+	0.0158664i
$121$	1.00000			0.0909091
$122$			0.418212i			0.0378632i
$123$			1.69244i			0.152602i
$124$	16.5936			1.49015
$125$	2.62542	+	10.8677i	0.234825	+	0.972038i
$126$	−0.0342944			−0.00305519
$127$			14.3580i			1.27407i	0.770835	+	0.637035i	$0.219839\pi$
$127$			14.3580i			1.27407i	−0.770835	+	0.637035i	$0.780161\pi$
$128$			1.09581i			0.0968568i
$129$	6.55683			0.577297
$130$	0.330608	−	0.227451i	0.0289963	−	0.0199488i
$131$	3.97822			0.347578			0.173789	−	0.984783i	$-0.444399\pi$
$131$	3.97822			0.347578			0.173789	+	0.984783i	$0.444399\pi$
$132$		−	1.99882i		−	0.173975i
$133$			1.91588i			0.166127i
$134$	−0.0119117			−0.00102902
$135$	−1.26739	−	1.84220i	−0.109080	−	0.158552i
$136$	−0.804541			−0.0689888
$137$		−	6.06514i		−	0.518180i	−0.965853	−	0.259090i	$-0.916577\pi$
$137$		−	6.06514i		−	0.518180i	0.965853	−	0.259090i	$-0.0834226\pi$
$138$			0.0985097i			0.00838571i
$139$	−22.4906			−1.90762			−0.953812	−	0.300405i	$-0.902878\pi$
$139$	−22.4906			−1.90762			−0.953812	+	0.300405i	$0.902878\pi$
$140$	2.53330	+	3.68224i	0.214103	+	0.311206i
$141$	6.80222			0.572850
$142$		−	0.536743i		−	0.0450425i
$143$			5.23302i			0.437607i
$144$	−3.99294			−0.332745
$145$	−11.3590	+	7.81476i	−0.943316	+	0.648980i
$146$	0.436130			0.0360944
$147$			1.00000i			0.0824786i
$148$		−	17.2120i		−	1.41482i
$149$	−16.1527			−1.32328			−0.661641	−	0.749820i	$-0.730140\pi$
$149$	−16.1527			−1.32328			−0.661641	+	0.749820i	$0.730140\pi$
$150$	0.0612987	−	0.160141i	0.00500502	−	0.0130755i
$151$	0.0343257			0.00279339			0.00139669	−	0.999999i	$-0.499555\pi$
$151$	0.0343257			0.00279339			0.00139669	+	0.999999i	$0.499555\pi$
$152$		−	0.262738i		−	0.0213109i
$153$		−	5.86667i		−	0.474292i
$154$	0.0342944			0.00276353
$155$	−15.2934	+	10.5215i	−1.22840	+	0.845109i
$156$	10.4599			0.837461
$157$		−	3.89435i		−	0.310803i	−0.987851	−	0.155402i	$-0.950333\pi$
$157$		−	3.89435i		−	0.310803i	0.987851	−	0.155402i	$-0.0496672\pi$
$158$			0.0671704i			0.00534379i
$159$	2.02461			0.160562
$160$	−0.521166	−	0.757534i	−0.0412018	−	0.0598883i
$161$	2.87247			0.226382
$162$			0.0342944i			0.00269443i
$163$		−	14.3538i		−	1.12427i	−0.827044	−	0.562137i	$-0.809979\pi$
$163$		−	14.3538i		−	1.12427i	0.827044	−	0.562137i	$-0.190021\pi$
$164$	−3.38288			−0.264159
$165$	1.26739	+	1.84220i	0.0986665	+	0.143415i
$166$	−0.106103			−0.00823517
$167$			6.00284i			0.464513i	0.972655	+	0.232257i	$0.0746109\pi$
$167$			6.00284i			0.464513i	−0.972655	+	0.232257i	$0.925389\pi$
$168$		−	0.137137i		−	0.0105804i
$169$	−14.3845			−1.10650
$170$	0.370641	−	0.254993i	0.0284269	−	0.0195570i
$171$	1.91588			0.146511
$172$			13.1060i			0.999319i
$173$		−	15.0489i		−	1.14415i	−0.820202	−	0.572075i	$-0.806139\pi$
$173$		−	15.0489i		−	1.14415i	0.820202	−	0.572075i	$-0.193861\pi$
$174$	0.211460			0.0160307
$175$	−4.66959	−	1.78742i	−0.352988	−	0.135117i
$176$	3.99294			0.300980
$177$			6.11472i			0.459610i
$178$			0.312941i			0.0234559i
$179$	−12.4166			−0.928061			−0.464030	−	0.885819i	$-0.653597\pi$
$179$	−12.4166			−0.928061			−0.464030	+	0.885819i	$0.653597\pi$
$180$	3.68224	−	2.53330i	0.274458	−	0.188821i
$181$	−15.0557			−1.11908			−0.559541	−	0.828802i	$-0.689023\pi$
$181$	−15.0557			−1.11908			−0.559541	+	0.828802i	$0.689023\pi$
$182$			0.179464i			0.0133027i
$183$		−	12.1948i		−	0.901462i
$184$	−0.393923			−0.0290404
$185$	10.9136	+	15.8633i	0.802384	+	1.16629i
$186$	0.284702			0.0208754
$187$			5.86667i			0.429014i
$188$			13.5964i			0.991622i
$189$	1.00000			0.0727393
$190$	0.0832727	+	0.121040i	0.00604124	+	0.00878116i
$191$	23.8192			1.72350			0.861750	−	0.507333i	$-0.169369\pi$
$191$	23.8192			1.72350			0.861750	+	0.507333i	$0.169369\pi$
$192$		−	7.97179i		−	0.575314i
$193$			10.5596i			0.760094i	0.924967	+	0.380047i	$0.124092\pi$
$193$			10.5596i			0.760094i	−0.924967	+	0.380047i	$0.875908\pi$
$194$	−0.373718			−0.0268314
$195$	−9.64029	+	6.63230i	−0.690355	+	0.474949i
$196$	−1.99882			−0.142773
$197$		−	24.3156i		−	1.73241i	−0.499685	−	0.866207i	$-0.666551\pi$
$197$		−	24.3156i		−	1.73241i	0.499685	−	0.866207i	$-0.333449\pi$
$198$		−	0.0342944i		−	0.00243720i
$199$	−17.2427			−1.22230			−0.611150	−	0.791515i	$-0.709293\pi$
$199$	−17.2427			−1.22230			−0.611150	+	0.791515i	$0.709293\pi$
$200$	0.640376	+	0.245123i	0.0452814	+	0.0173328i
$201$	0.347338			0.0244993
$202$			0.351867i			0.0247573i
$203$		−	6.16600i		−	0.432769i
$204$	11.7264			0.821016
$205$	3.11781	−	2.14499i	0.217758	−	0.149812i
$206$	−0.101730			−0.00708790
$207$		−	2.87247i		−	0.199650i
$208$			20.8952i			1.44882i
$209$	−1.91588			−0.132524
$210$	0.0434646	+	0.0631773i	0.00299934	+	0.00435965i
$211$	27.3582			1.88342			0.941709	−	0.336428i	$-0.109219\pi$
$211$	27.3582			1.88342			0.941709	+	0.336428i	$0.109219\pi$
$212$			4.04683i			0.277937i
$213$			15.6510i			1.07239i
$214$	−0.161633			−0.0110490
$215$	−8.31009	−	12.0790i	−0.566744	−	0.823782i
$216$	−0.137137			−0.00933102
$217$		−	8.30169i		−	0.563556i
$218$			0.0911112i			0.00617083i
$219$	−12.7172			−0.859351
$220$	−3.68224	+	2.53330i	−0.248257	+	0.170795i
$221$	−30.7004			−2.06513
$222$		−	0.295312i		−	0.0198200i
$223$			0.745973i			0.0499541i	0.999688	+	0.0249770i	$0.00795126\pi$
$223$			0.745973i			0.0499541i	−0.999688	+	0.0249770i	$0.992049\pi$
$224$	0.411211			0.0274752
$225$	−1.78742	+	4.66959i	−0.119162	+	0.311306i
$226$	0.450063			0.0299378
$227$			0.0917717i			0.00609110i	0.999995	+	0.00304555i	$0.000969430\pi$
$227$			0.0917717i			0.00609110i	−0.999995	+	0.00304555i	$0.999031\pi$
$228$			3.82950i			0.253615i
$229$	−13.5990			−0.898644			−0.449322	−	0.893370i	$-0.648334\pi$
$229$	−13.5990			−0.898644			−0.449322	+	0.893370i	$0.648334\pi$
$230$	0.181475	−	0.124851i	0.0119661	−	0.00823241i
$231$	−1.00000			−0.0657952
$232$			0.845590i			0.0555157i
$233$			2.78159i			0.182228i	0.995840	+	0.0911141i	$0.0290428\pi$
$233$			2.78159i			0.182228i	−0.995840	+	0.0911141i	$0.970957\pi$
$234$	0.179464			0.0117319
$235$	−8.62109	−	12.5311i	−0.562378	−	0.817437i
$236$	−12.2222			−0.795600
$237$		−	1.95864i		−	0.127227i
$238$			0.201194i			0.0130415i
$239$	−1.51283			−0.0978568			−0.0489284	−	0.998802i	$-0.515581\pi$
$239$	−1.51283			−0.0978568			−0.0489284	+	0.998802i	$0.515581\pi$
$240$	5.06064	+	7.35581i	0.326663	+	0.474816i
$241$	−2.76617			−0.178185			−0.0890923	−	0.996023i	$-0.528397\pi$
$241$	−2.76617			−0.178185			−0.0890923	+	0.996023i	$0.528397\pi$
$242$			0.0342944i			0.00220453i
$243$		−	1.00000i		−	0.0641500i
$244$	24.3752			1.56046
$245$	1.84220	−	1.26739i	0.117694	−	0.0809708i
$246$	−0.0580412			−0.00370057
$247$		−	10.0258i		−	0.637927i
$248$			1.13847i			0.0722931i
$249$	3.09388			0.196066
$250$	−0.372702	+	0.0900374i	−0.0235718	+	0.00569446i
$251$	−5.44624			−0.343764			−0.171882	−	0.985118i	$-0.554985\pi$
$251$	−5.44624			−0.343764			−0.171882	+	0.985118i	$0.554985\pi$
$252$			1.99882i			0.125914i
$253$			2.87247i			0.180591i
$254$	−0.492401			−0.0308960
$255$	−10.8076	+	7.43539i	−0.676798	+	0.465622i
$256$	15.9060			0.994125
$257$		−	23.6554i		−	1.47558i	−0.675029	−	0.737791i	$-0.735869\pi$
$257$		−	23.6554i		−	1.47558i	0.675029	−	0.737791i	$-0.264131\pi$
$258$			0.224863i			0.0139994i
$259$	−8.61106			−0.535065
$260$	−13.2568	−	19.2692i	−0.822152	−	1.19503i
$261$	−6.16600			−0.381666
$262$			0.136431i			0.00842872i
$263$			5.94283i			0.366450i	0.983071	+	0.183225i	$0.0586537\pi$
$263$			5.94283i			0.366450i	−0.983071	+	0.183225i	$0.941346\pi$
$264$	0.137137			0.00844023
$265$	−2.56597	−	3.72974i	−0.157627	−	0.229116i
$266$	−0.0657039			−0.00402856
$267$		−	9.12512i		−	0.558448i
$268$			0.694267i			0.0424091i
$269$	−28.5670			−1.74176			−0.870880	−	0.491496i	$-0.836450\pi$
$269$	−28.5670			−1.74176			−0.870880	+	0.491496i	$0.836450\pi$
$270$	0.0631773	−	0.0434646i	0.00384485	−	0.00264517i
$271$	4.44331			0.269912			0.134956	−	0.990852i	$-0.456911\pi$
$271$	4.44331			0.269912			0.134956	+	0.990852i	$0.456911\pi$
$272$			23.4253i			1.42037i
$273$		−	5.23302i		−	0.316717i
$274$	0.208001			0.0125658
$275$	1.78742	−	4.66959i	0.107786	−	0.281587i
$276$	5.74156			0.345601
$277$		−	12.0179i		−	0.722086i	−0.932549	−	0.361043i	$-0.882421\pi$
$277$		−	12.0179i		−	0.722086i	0.932549	−	0.361043i	$-0.117579\pi$
$278$		−	0.771301i		−	0.0462596i
$279$	−8.30169			−0.497009
$280$	−0.252635	+	0.173807i	−0.0150978	+	0.0103870i
$281$	22.4119			1.33698			0.668492	−	0.743719i	$-0.266940\pi$
$281$	22.4119			1.33698			0.668492	+	0.743719i	$0.266940\pi$
$282$			0.233278i			0.0138915i
$283$		−	6.86368i		−	0.408003i	−0.978971	−	0.204002i	$-0.934605\pi$
$283$		−	6.86368i		−	0.408003i	0.978971	−	0.204002i	$-0.0653948\pi$
$284$	−31.2836			−1.85634
$285$	−2.42817	−	3.52943i	−0.143832	−	0.209065i
$286$	−0.179464			−0.0106119
$287$			1.69244i			0.0999014i
$288$		−	0.411211i		−	0.0242308i
$289$	−17.4179			−1.02458
$290$	−0.268003	−	0.389552i	−0.0157377	−	0.0228753i
$291$	10.8973			0.638814
$292$		−	25.4195i		−	1.48756i
$293$		−	5.41903i		−	0.316583i	−0.987392	−	0.158292i	$-0.949401\pi$
$293$		−	5.41903i		−	0.316583i	0.987392	−	0.158292i	$-0.0505986\pi$
$294$	−0.0342944			−0.00200009
$295$	11.2646	−	7.74976i	0.655847	−	0.451208i
$296$	1.18090			0.0686384
$297$			1.00000i			0.0580259i
$298$		−	0.553949i		−	0.0320894i
$299$	−15.0317			−0.869305
$300$	−9.33370	−	3.57274i	−0.538881	−	0.206273i
$301$	6.55683			0.377930
$302$			0.00117718i			6.77392e-5i
$303$		−	10.2602i		−	0.589431i
$304$	−7.64998			−0.438757
$305$	−22.4652	+	15.4556i	−1.28635	+	0.884983i
$306$	0.201194			0.0115015
$307$		−	8.13574i		−	0.464331i	−0.972676	−	0.232165i	$-0.925419\pi$
$307$		−	8.13574i		−	0.464331i	0.972676	−	0.232165i	$-0.0745811\pi$
$308$		−	1.99882i		−	0.113894i
$309$	2.96638			0.168752
$310$	−0.360830	−	0.524479i	−0.0204938	−	0.0297884i
$311$	11.0205			0.624913			0.312456	−	0.949932i	$-0.398848\pi$
$311$	11.0205			0.624913			0.312456	+	0.949932i	$0.398848\pi$
$312$			0.717643i			0.0406286i
$313$			12.7571i			0.721071i	0.932745	+	0.360536i	$0.117406\pi$
$313$			12.7571i			0.721071i	−0.932745	+	0.360536i	$0.882594\pi$
$314$	0.133555			0.00753693
$315$	−1.26739	−	1.84220i	−0.0714096	−	0.103796i
$316$	3.91497			0.220234
$317$		−	22.4073i		−	1.25852i	−0.777195	−	0.629260i	$-0.783358\pi$
$317$		−	22.4073i		−	1.25852i	0.777195	−	0.629260i	$-0.216642\pi$
$318$			0.0694327i			0.00389360i
$319$	6.16600			0.345230
$320$	−14.6857	+	10.1034i	−0.820953	+	0.564797i
$321$	4.71311			0.263060
$322$			0.0985097i			0.00548973i
$323$		−	11.2398i		−	0.625400i
$324$	1.99882			0.111046
$325$	24.4361	+	9.35363i	1.35547	+	0.518846i
$326$	0.492255			0.0272635
$327$		−	2.65673i		−	0.146918i
$328$		−	0.232097i		−	0.0128154i
$329$	6.80222			0.375019
$330$	−0.0631773	+	0.0434646i	−0.00347780	+	0.00239265i
$331$	−26.0154			−1.42994			−0.714969	−	0.699157i	$-0.753559\pi$
$331$	−26.0154			−1.42994			−0.714969	+	0.699157i	$0.753559\pi$
$332$			6.18411i			0.339397i
$333$			8.61106i			0.471883i
$334$	−0.205864			−0.0112644
$335$	−0.440214	−	0.639866i	−0.0240514	−	0.0349596i
$336$	−3.99294			−0.217833
$337$			27.1497i			1.47894i	0.673190	+	0.739469i	$0.264923\pi$
$337$			27.1497i			1.47894i	−0.673190	+	0.739469i	$0.735077\pi$
$338$		−	0.493309i		−	0.0268325i
$339$	−13.1235			−0.712771
$340$	−14.8620	−	21.6025i	−0.806007	−	1.17156i
$341$	8.30169			0.449562
$342$			0.0657039i			0.00355286i
$343$			1.00000i			0.0539949i
$344$	−0.899187			−0.0484809
$345$	−5.29167	+	3.64055i	−0.284894	+	0.196001i
$346$	0.516095			0.0277454
$347$			13.6560i			0.733090i	0.930400	+	0.366545i	$0.119459\pi$
$347$			13.6560i			0.733090i	−0.930400	+	0.366545i	$0.880541\pi$
$348$		−	12.3248i		−	0.660676i
$349$	−0.108061			−0.00578436			−0.00289218	−	0.999996i	$-0.500921\pi$
$349$	−0.108061			−0.00578436			−0.00289218	+	0.999996i	$0.500921\pi$
$350$	0.0612987	−	0.160141i	0.00327655	−	0.00855991i
$351$	−5.23302			−0.279318
$352$			0.411211i			0.0219176i
$353$		−	25.5801i		−	1.36149i	−0.732521	−	0.680744i	$-0.761656\pi$
$353$		−	25.5801i		−	1.36149i	0.732521	−	0.680744i	$-0.238344\pi$
$354$	−0.209701			−0.0111455
$355$	28.8323	−	19.8360i	1.53026	−	1.05279i
$356$	18.2395			0.966692
$357$		−	5.86667i		−	0.310497i
$358$		−	0.425821i		−	0.0225053i
$359$	−4.10107			−0.216446			−0.108223	−	0.994127i	$-0.534516\pi$
$359$	−4.10107			−0.216446			−0.108223	+	0.994127i	$0.534516\pi$
$360$	0.173807	+	0.252635i	0.00916045	+	0.0133150i
$361$	−15.3294			−0.806812
$362$		−	0.516328i		−	0.0271376i
$363$		−	1.00000i		−	0.0524864i
$364$	10.4599			0.548247
$365$	16.1177	+	23.4277i	0.843641	+	1.22626i
$366$	0.418212			0.0218603
$367$		−	31.4421i		−	1.64126i	−0.571457	−	0.820632i	$-0.693622\pi$
$367$		−	31.4421i		−	1.64126i	0.571457	−	0.820632i	$-0.306378\pi$
$368$			11.4696i			0.597895i
$369$	1.69244			0.0881048
$370$	−0.544024	+	0.374276i	−0.0282825	+	0.0194577i
$371$	2.02461			0.105112
$372$		−	16.5936i		−	0.860339i
$373$		−	16.9310i		−	0.876655i	−0.898815	−	0.438327i	$-0.855571\pi$
$373$		−	16.9310i		−	0.876655i	0.898815	−	0.438327i	$-0.144429\pi$
$374$	−0.201194			−0.0104035
$375$	10.8677	−	2.62542i	0.561206	−	0.135576i
$376$	−0.932839			−0.0481075
$377$			32.2668i			1.66183i
$378$			0.0342944i			0.00176392i
$379$	16.7989			0.862900			0.431450	−	0.902137i	$-0.358002\pi$
$379$	16.7989			0.862900			0.431450	+	0.902137i	$0.358002\pi$
$380$	7.05471	−	4.85348i	0.361899	−	0.248978i
$381$	14.3580			0.735585
$382$			0.816868i			0.0417946i
$383$		−	17.6213i		−	0.900404i	−0.892927	−	0.450202i	$-0.851352\pi$
$383$		−	17.6213i		−	0.900404i	0.892927	−	0.450202i	$-0.148648\pi$
$384$	1.09581			0.0559203
$385$	1.26739	+	1.84220i	0.0645924	+	0.0938874i
$386$	−0.362135			−0.0184322
$387$		−	6.55683i		−	0.333302i
$388$			21.7819i			1.10581i
$389$	−16.2497			−0.823890			−0.411945	−	0.911209i	$-0.635150\pi$
$389$	−16.2497			−0.823890			−0.411945	+	0.911209i	$0.635150\pi$
$390$	−0.227451	−	0.330608i	−0.0115174	−	0.0167410i
$391$	−16.8518			−0.852234
$392$		−	0.137137i		−	0.00692649i
$393$		−	3.97822i		−	0.200675i
$394$	0.833890			0.0420108
$395$	−3.60821	+	2.48237i	−0.181549	+	0.124901i
$396$	−1.99882			−0.100445
$397$		−	26.9634i		−	1.35325i	−0.736326	−	0.676627i	$-0.763441\pi$
$397$		−	26.9634i		−	1.35325i	0.736326	−	0.676627i	$-0.236559\pi$
$398$		−	0.591328i		−	0.0296406i
$399$	1.91588			0.0959137
$400$	7.13708	−	18.6454i	0.356854	−	0.932272i
$401$	29.5783			1.47707			0.738535	−	0.674216i	$-0.235518\pi$
$401$	29.5783			1.47707			0.738535	+	0.674216i	$0.235518\pi$
$402$			0.0119117i			0.000594104i
$403$			43.4429i			2.16405i
$404$	20.5083			1.02032
$405$	−1.84220	+	1.26739i	−0.0915398	+	0.0629773i
$406$	0.211460			0.0104946
$407$		−	8.61106i		−	0.426834i
$408$			0.804541i			0.0398307i
$409$	24.4183			1.20741			0.603704	−	0.797208i	$-0.293691\pi$
$409$	24.4183			1.20741			0.603704	+	0.797208i	$0.293691\pi$
$410$	0.0735611	+	0.106924i	0.00363292	+	0.00528059i
$411$	−6.06514			−0.299171
$412$			5.92928i			0.292114i
$413$			6.11472i			0.300886i
$414$	0.0985097			0.00484149
$415$	−3.92116	−	5.69955i	−0.192482	−	0.279780i
$416$	−2.15187			−0.105504
$417$			22.4906i			1.10137i
$418$		−	0.0657039i		−	0.00321368i
$419$	−18.1348			−0.885942			−0.442971	−	0.896536i	$-0.646076\pi$
$419$	−18.1348			−0.885942			−0.442971	+	0.896536i	$0.646076\pi$
$420$	3.68224	−	2.53330i	0.179675	−	0.123612i
$421$	9.62527			0.469107			0.234554	−	0.972103i	$-0.424637\pi$
$421$	9.62527			0.469107			0.234554	+	0.972103i	$0.424637\pi$
$422$			0.938236i			0.0456726i
$423$		−	6.80222i		−	0.330735i
$424$	−0.277649			−0.0134838
$425$	27.3950	+	10.4862i	1.32885	+	0.508657i
$426$	−0.536743			−0.0260053
$427$		−	12.1948i		−	0.590146i
$428$			9.42067i			0.455365i
$429$	5.23302			0.252653
$430$	0.414243	−	0.284990i	0.0199766	−	0.0137434i
$431$	−28.0611			−1.35166			−0.675828	−	0.737059i	$-0.736214\pi$
$431$	−28.0611			−1.35166			−0.675828	+	0.737059i	$0.736214\pi$
$432$			3.99294i			0.192111i
$433$			1.87390i			0.0900537i	0.998986	+	0.0450269i	$0.0143373\pi$
$433$			1.87390i			0.0900537i	−0.998986	+	0.0450269i	$0.985663\pi$
$434$	0.284702			0.0136661
$435$	7.81476	+	11.3590i	0.374689	+	0.544624i
$436$	5.31034			0.254319
$437$		−	5.50329i		−	0.263258i
$438$		−	0.436130i		−	0.0208391i
$439$	−40.1386			−1.91571			−0.957855	−	0.287252i	$-0.907258\pi$
$439$	−40.1386			−1.91571			−0.957855	+	0.287252i	$0.907258\pi$
$440$	−0.173807	−	0.252635i	−0.00828593	−	0.0120439i
$441$	1.00000			0.0476190
$442$		−	1.05285i		−	0.0500792i
$443$			17.9585i			0.853232i	0.904433	+	0.426616i	$0.140294\pi$
$443$			17.9585i			0.853232i	−0.904433	+	0.426616i	$0.859706\pi$
$444$	−17.2120			−0.816845
$445$	−16.8103	+	11.5651i	−0.796886	+	0.548239i
$446$	−0.0255827			−0.00121138
$447$			16.1527i			0.763998i
$448$		−	7.97179i		−	0.376632i
$449$	−0.845740			−0.0399129			−0.0199565	−	0.999801i	$-0.506353\pi$
$449$	−0.845740			−0.0399129			−0.0199565	+	0.999801i	$0.506353\pi$
$450$	−0.160141	−	0.0612987i	−0.00754913	−	0.00288965i
$451$	−1.69244			−0.0796938
$452$		−	26.2316i		−	1.23383i
$453$		−	0.0343257i		−	0.00161276i
$454$	−0.00314726			−0.000147708
$455$	−9.64029	+	6.63230i	−0.451944	+	0.310927i
$456$	−0.262738			−0.0123038
$457$			36.6739i			1.71553i	0.514042	+	0.857765i	$0.328148\pi$
$457$			36.6739i			1.71553i	−0.514042	+	0.857765i	$0.671852\pi$
$458$		−	0.466369i		−	0.0217920i
$459$	−5.86667			−0.273833
$460$	−7.27682	−	10.5771i	−0.339283	−	0.493161i
$461$	10.5896			0.493206			0.246603	−	0.969117i	$-0.420686\pi$
$461$	10.5896			0.493206			0.246603	+	0.969117i	$0.420686\pi$
$462$		−	0.0342944i		−	0.00159552i
$463$		−	33.0173i		−	1.53444i	−0.641381	−	0.767222i	$-0.721638\pi$
$463$		−	33.0173i		−	1.53444i	0.641381	−	0.767222i	$-0.278362\pi$
$464$	24.6205			1.14298
$465$	10.5215	+	15.2934i	0.487924	+	0.709215i
$466$	−0.0953932			−0.00441901
$467$		−	7.92985i		−	0.366950i	−0.983024	−	0.183475i	$-0.941265\pi$
$467$		−	7.92985i		−	0.366950i	0.983024	−	0.183475i	$-0.0587346\pi$
$468$		−	10.4599i		−	0.483509i
$469$	0.347338			0.0160386
$470$	0.429746	−	0.295656i	0.0198227	−	0.0136376i
$471$	−3.89435			−0.179442
$472$		−	0.838557i		−	0.0385977i
$473$			6.55683i			0.301483i
$474$	0.0671704			0.00308524
$475$	−3.42448	+	8.94636i	−0.157126	+	0.410487i
$476$	11.7264			0.537481
$477$		−	2.02461i		−	0.0927003i
$478$		−	0.0518816i		−	0.00237301i
$479$	27.6995			1.26562			0.632812	−	0.774306i	$-0.281901\pi$
$479$	27.6995			1.26562			0.632812	+	0.774306i	$0.281901\pi$
$480$	−0.757534	+	0.521166i	−0.0345765	+	0.0237879i
$481$	45.0619			2.05464
$482$		−	0.0948643i		−	0.00432095i
$483$		−	2.87247i		−	0.130702i
$484$	1.99882			0.0908556
$485$	−13.8112	−	20.0751i	−0.627136	−	0.911564i
$486$	0.0342944			0.00155563
$487$			10.7360i			0.486493i	0.969964	+	0.243247i	$0.0782125\pi$
$487$			10.7360i			0.486493i	−0.969964	+	0.243247i	$0.921788\pi$
$488$			1.67236i			0.0757041i
$489$	−14.3538			−0.649100
$490$	0.0434646	+	0.0631773i	0.00196353	+	0.00285406i
$491$	−3.63086			−0.163859			−0.0819293	−	0.996638i	$-0.526108\pi$
$491$	−3.63086			−0.163859			−0.0819293	+	0.996638i	$0.526108\pi$
$492$			3.38288i			0.152512i
$493$			36.1739i			1.62919i
$494$	0.343830			0.0154696
$495$	1.84220	−	1.26739i	0.0828009	−	0.0569651i
$496$	33.1482			1.48840
$497$			15.6510i			0.702044i
$498$			0.106103i			0.00475458i
$499$	33.4207			1.49612			0.748059	−	0.663633i	$-0.230986\pi$
$499$	33.4207			1.49612			0.748059	+	0.663633i	$0.230986\pi$
$500$	5.24775	+	21.7226i	0.234687	+	0.971466i
$501$	6.00284			0.268187
$502$		−	0.186776i		−	0.00833621i
$503$			19.3879i			0.864462i	0.901763	+	0.432231i	$0.142273\pi$
$503$			19.3879i			0.864462i	−0.901763	+	0.432231i	$0.857727\pi$
$504$	−0.137137			−0.00610859
$505$	−18.9013	+	13.0037i	−0.841097	+	0.578656i
$506$	−0.0985097			−0.00437929
$507$			14.3845i			0.638839i
$508$			28.6992i			1.27332i
$509$	9.11914			0.404199			0.202099	−	0.979365i	$-0.435224\pi$
$509$	9.11914			0.404199			0.202099	+	0.979365i	$0.435224\pi$
$510$	−0.254993	−	0.370641i	−0.0112913	−	0.0164123i
$511$	−12.7172			−0.562577
$512$			2.73711i			0.120964i
$513$		−	1.91588i		−	0.0845880i
$514$	0.811248			0.0357826
$515$	−3.75958	−	5.46468i	−0.165667	−	0.240803i
$516$	13.1060			0.576957
$517$			6.80222i			0.299161i
$518$		−	0.295312i		−	0.0129752i
$519$	−15.0489			−0.660575
$520$	1.32204	−	0.909537i	0.0579755	−	0.0398858i
$521$	32.6812			1.43179			0.715895	−	0.698208i	$-0.246019\pi$
$521$	32.6812			1.43179			0.715895	+	0.698208i	$0.246019\pi$
$522$		−	0.211460i		−	0.00925534i
$523$			28.9776i			1.26710i	0.773701	+	0.633551i	$0.218403\pi$
$523$			28.9776i			1.26710i	−0.773701	+	0.633551i	$0.781597\pi$
$524$	7.95176			0.347374
$525$	−1.78742	+	4.66959i	−0.0780096	+	0.203798i
$526$	−0.203806			−0.00888636
$527$			48.7033i			2.12155i
$528$		−	3.99294i		−	0.173771i
$529$	14.7489			0.641257
$530$	0.127909	−	0.0879987i	0.00555602	−	0.00382242i
$531$	6.11472			0.265356
$532$			3.82950i			0.166030i
$533$		−	8.85656i		−	0.383620i
$534$	0.312941			0.0135423
$535$	−5.97337	−	8.68250i	−0.258251	−	0.375377i
$536$	−0.0476330			−0.00205743
$537$			12.4166i			0.535816i
$538$		−	0.979689i		−	0.0422374i
$539$	−1.00000			−0.0430730
$540$	−2.53330	−	3.68224i	−0.109016	−	0.158458i
$541$	26.5551			1.14169			0.570846	−	0.821057i	$-0.306615\pi$
$541$	26.5551			1.14169			0.570846	+	0.821057i	$0.306615\pi$
$542$			0.152381i			0.00654533i
$543$			15.0557i			0.646103i
$544$	−2.41244			−0.103432
$545$	−4.89424	+	3.36713i	−0.209646	+	0.144232i
$546$	0.179464			0.00768033
$547$			5.73433i			0.245182i	0.992457	+	0.122591i	$0.0391204\pi$
$547$			5.73433i			0.245182i	−0.992457	+	0.122591i	$0.960880\pi$
$548$		−	12.1231i		−	0.517875i
$549$	−12.1948			−0.520459
$550$	0.160141	+	0.0612987i	0.00682844	+	0.00261379i
$551$	−11.8133			−0.503263
$552$			0.393923i			0.0167665i
$553$		−	1.95864i		−	0.0832897i
$554$	0.412147			0.0175105
$555$	15.8633	−	10.9136i	0.673360	−	0.463257i
$556$	−44.9547			−1.90650
$557$		−	22.8839i		−	0.969620i	−0.874619	−	0.484810i	$-0.838889\pi$
$557$		−	22.8839i		−	0.969620i	0.874619	−	0.484810i	$-0.161111\pi$
$558$		−	0.284702i		−	0.0120524i
$559$	−34.3120			−1.45124
$560$	5.06064	+	7.35581i	0.213851	+	0.310840i
$561$	5.86667			0.247691
$562$			0.768605i			0.0324216i
$563$		−	31.8215i		−	1.34112i	−0.741857	−	0.670558i	$-0.766055\pi$
$563$		−	31.8215i		−	1.34112i	0.741857	−	0.670558i	$-0.233945\pi$
$564$	13.5964			0.572513
$565$	16.6326	+	24.1761i	0.699741	+	1.01710i
$566$	0.235386			0.00989401
$567$		−	1.00000i		−	0.0419961i
$568$		−	2.14634i		−	0.0900584i
$569$	11.4866			0.481543			0.240772	−	0.970582i	$-0.422600\pi$
$569$	11.4866			0.481543			0.240772	+	0.970582i	$0.422600\pi$
$570$	0.121040	−	0.0832727i	0.00506980	−	0.00348791i
$571$	42.3069			1.77049			0.885244	−	0.465127i	$-0.153991\pi$
$571$	42.3069			1.77049			0.885244	+	0.465127i	$0.153991\pi$
$572$			10.4599i			0.437350i
$573$		−	23.8192i		−	0.995063i
$574$	−0.0580412			−0.00242259
$575$	13.4133	+	5.13432i	0.559372	+	0.214116i
$576$	−7.97179			−0.332158
$577$			15.4645i			0.643796i	0.946774	+	0.321898i	$0.104321\pi$
$577$			15.4645i			0.643796i	−0.946774	+	0.321898i	$0.895679\pi$
$578$		−	0.597336i		−	0.0248459i
$579$	10.5596			0.438841
$580$	−22.7047	+	15.6203i	−0.942762	+	0.648599i
$581$	3.09388			0.128356
$582$			0.373718i			0.0154911i
$583$			2.02461i			0.0838506i
$584$	1.74401			0.0721676
$585$	6.63230	+	9.64029i	0.274212	+	0.398577i
$586$	0.185843			0.00767709
$587$			29.6514i			1.22384i	0.790918	+	0.611922i	$0.209604\pi$
$587$			29.6514i			1.22384i	−0.790918	+	0.611922i	$0.790396\pi$
$588$			1.99882i			0.0824301i
$589$	−15.9050			−0.655354
$590$	0.265774	+	0.386312i	0.0109417	+	0.0159042i
$591$	−24.3156			−1.00021
$592$		−	34.3835i		−	1.41315i
$593$		−	27.7265i		−	1.13859i	−0.822133	−	0.569296i	$-0.807216\pi$
$593$		−	27.7265i		−	1.13859i	0.822133	−	0.569296i	$-0.192784\pi$
$594$	−0.0342944			−0.00140712
$595$	−10.8076	+	7.43539i	−0.443069	+	0.304821i
$596$	−32.2865			−1.32250
$597$			17.2427i			0.705696i
$598$		−	0.515504i		−	0.0210805i
$599$	1.74332			0.0712302			0.0356151	−	0.999366i	$-0.488661\pi$
$599$	1.74332			0.0712302			0.0356151	+	0.999366i	$0.488661\pi$
$600$	0.245123	−	0.640376i	0.0100071	−	0.0261433i
$601$	−0.926650			−0.0377988			−0.0188994	−	0.999821i	$-0.506016\pi$
$601$	−0.926650			−0.0377988			−0.0188994	+	0.999821i	$0.506016\pi$
$602$			0.224863i			0.00916473i
$603$		−	0.347338i		−	0.0141447i
$604$	0.0686111			0.00279174
$605$	−1.84220	+	1.26739i	−0.0748962	+	0.0515269i
$606$	0.351867			0.0142936
$607$		−	21.8891i		−	0.888452i	−0.895915	−	0.444226i	$-0.853479\pi$
$607$		−	21.8891i		−	0.888452i	0.895915	−	0.444226i	$-0.146521\pi$
$608$		−	0.787828i		−	0.0319507i
$609$	−6.16600			−0.249859
$610$	−0.530040	−	0.770432i	−0.0214607	−	0.0311939i
$611$	−35.5962			−1.44007
$612$		−	11.7264i		−	0.474014i
$613$			28.4545i			1.14927i	0.818411	+	0.574633i	$0.194855\pi$
$613$			28.4545i			1.14927i	−0.818411	+	0.574633i	$0.805145\pi$
$614$	0.279011			0.0112600
$615$	−2.14499	−	3.11781i	−0.0864942	−	0.125722i
$616$	0.137137			0.00552543
$617$		−	30.3870i		−	1.22334i	−0.791115	−	0.611668i	$-0.790499\pi$
$617$		−	30.3870i		−	1.22334i	0.791115	−	0.611668i	$-0.209501\pi$
$618$			0.101730i			0.00409220i
$619$	3.04886			0.122544			0.0612720	−	0.998121i	$-0.480484\pi$
$619$	3.04886			0.122544			0.0612720	+	0.998121i	$0.480484\pi$
$620$	−30.5688	+	21.0307i	−1.22767	+	0.844612i
$621$	−2.87247			−0.115268
$622$			0.377941i			0.0151540i
$623$		−	9.12512i		−	0.365590i
$624$	20.8952			0.836476
$625$	−18.6102	−	16.6931i	−0.744409	−	0.667724i
$626$	−0.437496			−0.0174859
$627$			1.91588i			0.0765127i
$628$		−	7.78413i		−	0.310620i
$629$	50.5183			2.01430
$630$	0.0631773	−	0.0434646i	0.00251705	−	0.00173167i
$631$	21.9237			0.872770			0.436385	−	0.899760i	$-0.356259\pi$
$631$	21.9237			0.872770			0.436385	+	0.899760i	$0.356259\pi$
$632$			0.268603i			0.0106844i
$633$		−	27.3582i		−	1.08739i
$634$	0.768447			0.0305189
$635$	−18.1973	−	26.4504i	−0.722138	−	1.04965i
$636$	4.04683			0.160467
$637$		−	5.23302i		−	0.207340i
$638$			0.211460i			0.00837177i
$639$	15.6510			0.619145
$640$	−1.38882	−	2.01870i	−0.0548980	−	0.0797963i
$641$	10.4733			0.413669			0.206834	−	0.978376i	$-0.433684\pi$
$641$	10.4733			0.413669			0.206834	+	0.978376i	$0.433684\pi$
$642$			0.161633i			0.00637916i
$643$			11.8610i			0.467754i	0.972266	+	0.233877i	$0.0751413\pi$
$643$			11.8610i			0.467754i	−0.972266	+	0.233877i	$0.924859\pi$
$644$	5.74156			0.226249
$645$	−12.0790	+	8.31009i	−0.475611	+	0.327210i
$646$	0.385463			0.0151658
$647$		−	38.6528i		−	1.51960i	−0.650157	−	0.759800i	$-0.725297\pi$
$647$		−	38.6528i		−	1.51960i	0.650157	−	0.759800i	$-0.274703\pi$
$648$			0.137137i			0.00538727i
$649$	−6.11472			−0.240024
$650$	−0.320777	+	0.838022i	−0.0125819	+	0.0328699i
$651$	−8.30169			−0.325369
$652$		−	28.6907i		−	1.12361i
$653$		−	32.2265i		−	1.26112i	−0.776140	−	0.630560i	$-0.782825\pi$
$653$		−	32.2265i		−	1.26112i	0.776140	−	0.630560i	$-0.217175\pi$
$654$	0.0911112			0.00356273
$655$	−7.32868	+	5.04197i	−0.286355	+	0.197006i
$656$	−6.75781			−0.263848
$657$			12.7172i			0.496146i
$658$			0.233278i			0.00909414i
$659$	30.9426			1.20535			0.602676	−	0.797986i	$-0.294101\pi$
$659$	30.9426			1.20535			0.602676	+	0.797986i	$0.294101\pi$
$660$	2.53330	+	3.68224i	0.0986085	+	0.143331i
$661$	−39.9799			−1.55504			−0.777519	−	0.628860i	$-0.783522\pi$
$661$	−39.9799			−1.55504			−0.777519	+	0.628860i	$0.783522\pi$
$662$		−	0.892185i		−	0.0346757i
$663$			30.7004i			1.19231i
$664$	−0.424286			−0.0164655
$665$	−2.42817	−	3.52943i	−0.0941604	−	0.136865i
$666$	−0.295312			−0.0114431
$667$			17.7117i			0.685798i
$668$			11.9986i			0.464240i
$669$	0.745973			0.0288410
$670$	0.0219439	−	0.0150969i	0.000847765	−	0.000583243i
$671$	12.1948			0.470773
$672$		−	0.411211i		−	0.0158628i
$673$			30.3413i			1.16957i	0.811187	+	0.584786i	$0.198822\pi$
$673$			30.3413i			1.16957i	−0.811187	+	0.584786i	$0.801178\pi$
$674$	−0.931084			−0.0358640
$675$	4.66959	+	1.78742i	0.179733	+	0.0687980i
$676$	−28.7521			−1.10585
$677$		−	18.5283i		−	0.712102i	−0.934467	−	0.356051i	$-0.884123\pi$
$677$		−	18.5283i		−	0.712102i	0.934467	−	0.356051i	$-0.115877\pi$
$678$		−	0.450063i		−	0.0172846i
$679$	10.8973			0.418202
$680$	1.48213	−	1.01967i	0.0568370	−	0.0391026i
$681$	0.0917717			0.00351670
$682$			0.284702i			0.0109018i
$683$		−	8.62720i		−	0.330111i	−0.986284	−	0.165055i	$-0.947220\pi$
$683$		−	8.62720i		−	0.330111i	0.986284	−	0.165055i	$-0.0527803\pi$
$684$	3.82950			0.146424
$685$	7.68692	+	11.1732i	0.293702	+	0.426907i
$686$	−0.0342944			−0.00130937
$687$			13.5990i			0.518833i
$688$			26.1811i			0.998144i
$689$	−10.5948			−0.403630
$690$	−0.124851	−	0.181475i	−0.00475298	−	0.00690863i
$691$	11.4883			0.437036			0.218518	−	0.975833i	$-0.429878\pi$
$691$	11.4883			0.437036			0.218518	+	0.975833i	$0.429878\pi$
$692$		−	30.0802i		−	1.14348i
$693$			1.00000i			0.0379869i
$694$	−0.468324			−0.0177773
$695$	41.4322	−	28.5044i	1.57161	−	1.08123i
$696$	0.845590			0.0320520
$697$		−	9.92898i		−	0.376087i
$698$		−	0.00370589i		−	0.000140270i
$699$	2.78159			0.105210
$700$	−9.33370	−	3.57274i	−0.352781	−	0.135037i
$701$	32.6489			1.23313			0.616565	−	0.787304i	$-0.288524\pi$
$701$	32.6489			1.23313			0.616565	+	0.787304i	$0.288524\pi$
$702$		−	0.179464i		−	0.00677342i
$703$			16.4977i			0.622223i
$704$	7.97179			0.300448
$705$	−12.5311	+	8.62109i	−0.471947	+	0.324689i
$706$	0.877254			0.0330159
$707$		−	10.2602i		−	0.385873i
$708$			12.2222i			0.459340i
$709$	43.1053			1.61885			0.809426	−	0.587221i	$-0.199778\pi$
$709$	43.1053			1.61885			0.809426	+	0.587221i	$0.199778\pi$
$710$	0.680265	+	0.988789i	0.0255299	+	0.0371086i
$711$	−1.95864			−0.0734547
$712$			1.25140i			0.0468980i
$713$			23.8464i			0.893053i
$714$	0.201194			0.00752951
$715$	−6.63230	−	9.64029i	−0.248034	−	0.360526i
$716$	−24.8186			−0.927515
$717$			1.51283i			0.0564976i
$718$		−	0.140644i		−	0.00524878i
$719$	−10.3189			−0.384829			−0.192415	−	0.981314i	$-0.561632\pi$
$719$	−10.3189			−0.384829			−0.192415	+	0.981314i	$0.561632\pi$
$720$	7.35581	−	5.06064i	0.274135	−	0.188599i
$721$	2.96638			0.110474
$722$		−	0.525714i		−	0.0195651i
$723$			2.76617i			0.102875i
$724$	−30.0937			−1.11842
$725$	11.0213	−	28.7927i	0.409319	−	1.06934i
$726$	0.0342944			0.00127279
$727$		−	21.6176i		−	0.801752i	−0.916132	−	0.400876i	$-0.868706\pi$
$727$		−	21.6176i		−	0.801752i	0.916132	−	0.400876i	$-0.131294\pi$
$728$			0.717643i			0.0265976i
$729$	−1.00000			−0.0370370
$730$	−0.803441	+	0.552749i	−0.0297367	+	0.0204582i
$731$	−38.4668			−1.42275
$732$		−	24.3752i		−	0.900932i
$733$			10.0439i			0.370980i	0.982646	+	0.185490i	$0.0593872\pi$
$733$			10.0439i			0.370980i	−0.982646	+	0.185490i	$0.940613\pi$
$734$	1.07829			0.0398004
$735$	−1.26739	−	1.84220i	−0.0467485	−	0.0679507i
$736$	−1.18119			−0.0435393
$737$			0.347338i			0.0127943i
$738$			0.0580412i			0.00213653i
$739$	17.9428			0.660037			0.330018	−	0.943975i	$-0.392945\pi$
$739$	17.9428			0.660037			0.330018	+	0.943975i	$0.392945\pi$
$740$	21.8144	+	31.7080i	0.801913	+	1.16561i
$741$	−10.0258			−0.368308
$742$			0.0694327i			0.00254896i
$743$		−	17.1920i		−	0.630712i	−0.948973	−	0.315356i	$-0.897876\pi$
$743$		−	17.1920i		−	0.630712i	0.948973	−	0.315356i	$-0.102124\pi$
$744$	1.13847			0.0417385
$745$	29.7566	−	20.4719i	1.09020	−	0.750031i
$746$	0.580640			0.0212587
$747$		−	3.09388i		−	0.113199i
$748$			11.7264i			0.428761i
$749$	4.71311			0.172213
$750$	0.0900374	+	0.372702i	0.00328770	+	0.0136092i
$751$	30.1869			1.10153			0.550767	−	0.834659i	$-0.314335\pi$
$751$	30.1869			1.10153			0.550767	+	0.834659i	$0.314335\pi$
$752$			27.1609i			0.990456i
$753$			5.44624i			0.198472i
$754$	−1.10657			−0.0402990
$755$	−0.0632349	+	0.0435042i	−0.00230135	+	0.00158328i
$756$	1.99882			0.0726965
$757$		−	12.5326i		−	0.455506i	−0.973719	−	0.227753i	$-0.926862\pi$
$757$		−	12.5326i		−	0.455506i	0.973719	−	0.227753i	$-0.0731378\pi$
$758$			0.576108i			0.0209252i
$759$	2.87247			0.104264
$760$	0.332993	+	0.484017i	0.0120789	+	0.0175571i
$761$	39.6608			1.43770			0.718852	−	0.695163i	$-0.244668\pi$
$761$	39.6608			1.43770			0.718852	+	0.695163i	$0.244668\pi$
$762$			0.492401i			0.0178378i
$763$		−	2.65673i		−	0.0961802i
$764$	47.6105			1.72249
$765$	7.43539	+	10.8076i	0.268827	+	0.390750i
$766$	0.604311			0.0218347
$767$		−	31.9984i		−	1.15540i
$768$		−	15.9060i		−	0.573958i
$769$	−33.5820			−1.21100			−0.605498	−	0.795847i	$-0.707026\pi$
$769$	−33.5820			−1.21100			−0.605498	+	0.795847i	$0.707026\pi$
$770$	−0.0631773	+	0.0434646i	−0.00227675	+	0.00156636i
$771$	−23.6554			−0.851928
$772$			21.1067i			0.759647i
$773$			29.8169i			1.07244i	0.844078	+	0.536220i	$0.180148\pi$
$773$			29.8169i			1.07244i	−0.844078	+	0.536220i	$0.819852\pi$
$774$	0.224863			0.00808253
$775$	14.8386	−	38.7655i	0.533020	−	1.39250i
$776$	−1.49443			−0.0536471
$777$			8.61106i			0.308920i
$778$		−	0.557273i		−	0.0199792i
$779$	3.24250			0.116175
$780$	−19.2692	+	13.2568i	−0.689949	+	0.474670i
$781$	−15.6510			−0.560037
$782$		−	0.577925i		−	0.0206665i
$783$			6.16600i			0.220355i
$784$	−3.99294			−0.142605
$785$	4.93568	+	7.17419i	0.176162	+	0.256058i
$786$	0.136431			0.00486632
$787$			1.58708i			0.0565731i	0.999600	+	0.0282866i	$0.00900509\pi$
$787$			1.58708i			0.0565731i	−0.999600	+	0.0282866i	$0.990995\pi$
$788$		−	48.6026i		−	1.73140i
$789$	5.94283			0.211570
$790$	−0.0851314	−	0.123742i	−0.00302884	−	0.00440253i
$791$	−13.1235			−0.466618
$792$		−	0.137137i		−	0.00487297i
$793$			63.8154i			2.26615i
$794$	0.924694			0.0328162
$795$	−3.72974	+	2.56597i	−0.132280	+	0.0910057i
$796$	−34.4651			−1.22158
$797$			42.9492i			1.52134i	0.649140	+	0.760669i	$0.275129\pi$
$797$			42.9492i			1.52134i	−0.649140	+	0.760669i	$0.724871\pi$
$798$			0.0657039i			0.00232589i
$799$	−39.9064			−1.41179
$800$	1.92019	+	0.735008i	0.0678889	+	0.0259865i
$801$	−9.12512			−0.322420
$802$			1.01437i			0.0358187i
$803$		−	12.7172i		−	0.448781i
$804$	0.694267			0.0244849
$805$	−5.29167	+	3.64055i	−0.186507	+	0.128313i
$806$	−1.48985			−0.0524778
$807$			28.5670i			1.00561i
$808$			1.40705i			0.0494999i
$809$	22.2866			0.783554			0.391777	−	0.920060i	$-0.371860\pi$
$809$	22.2866			0.783554			0.391777	+	0.920060i	$0.371860\pi$
$810$	−0.0434646	−	0.0631773i	−0.00152719	−	0.00221983i
$811$	−47.6327			−1.67261			−0.836304	−	0.548265i	$-0.815288\pi$
$811$	−47.6327			−1.67261			−0.836304	+	0.548265i	$0.815288\pi$
$812$		−	12.3248i		−	0.432514i
$813$		−	4.44331i		−	0.155834i
$814$	0.295312			0.0103507
$815$	18.1919	+	26.4426i	0.637234	+	0.926243i
$816$	23.4253			0.820050
$817$		−	12.5621i		−	0.439491i
$818$			0.837413i			0.0292795i
$819$	−5.23302			−0.182857
$820$	6.23196	−	4.28745i	0.217629	−	0.149724i
$821$	−3.58177			−0.125005			−0.0625023	−	0.998045i	$-0.519908\pi$
$821$	−3.58177			−0.125005			−0.0625023	+	0.998045i	$0.519908\pi$
$822$		−	0.208001i		−	0.00725485i
$823$			29.9446i			1.04380i	0.853006	+	0.521902i	$0.174777\pi$
$823$			29.9446i			1.04380i	−0.853006	+	0.521902i	$0.825223\pi$
$824$	−0.406802			−0.0141716
$825$	−4.66959	−	1.78742i	−0.162574	−	0.0622301i
$826$	−0.209701			−0.00729643
$827$			28.3922i			0.987292i	0.869663	+	0.493646i	$0.164336\pi$
$827$			28.3922i			0.987292i	−0.869663	+	0.493646i	$0.835664\pi$
$828$		−	5.74156i		−	0.199533i
$829$	−5.31967			−0.184760			−0.0923799	−	0.995724i	$-0.529447\pi$
$829$	−5.31967			−0.184760			−0.0923799	+	0.995724i	$0.529447\pi$
$830$	0.195463	−	0.134474i	0.00678462	−	0.00466766i
$831$	−12.0179			−0.416896
$832$			41.7165i			1.44626i
$833$		−	5.86667i		−	0.203268i
$834$	−0.771301			−0.0267080
$835$	−7.60796	−	11.0584i	−0.263284	−	0.382693i
$836$	−3.82950			−0.132446
$837$			8.30169i			0.286949i
$838$		−	0.621922i		−	0.0214839i
$839$	42.3351			1.46157			0.730786	−	0.682607i	$-0.239154\pi$
$839$	42.3351			1.46157			0.730786	+	0.682607i	$0.239154\pi$
$840$	0.173807	+	0.252635i	0.00599692	+	0.00871674i
$841$	9.01962			0.311021
$842$			0.330093i			0.0113758i
$843$		−	22.4119i		−	0.771908i
$844$	54.6843			1.88231
$845$	26.4992	−	18.2309i	0.911600	−	0.627160i
$846$	0.233278			0.00802028
$847$		−	1.00000i		−	0.0343604i
$848$			8.08414i			0.277610i
$849$	−6.86368			−0.235561
$850$	−0.359620	+	0.939496i	−0.0123348	+	0.0322245i
$851$	24.7350			0.847905
$852$			31.2836i			1.07176i
$853$		−	10.9376i		−	0.374497i	−0.982313	−	0.187248i	$-0.940043\pi$
$853$		−	10.9376i		−	0.374497i	0.982313	−	0.187248i	$-0.0599569\pi$
$854$	0.418212			0.0143109
$855$	−3.52943	+	2.42817i	−0.120704	+	0.0830416i
$856$	−0.646344			−0.0220916
$857$			11.1742i			0.381705i	0.981619	+	0.190852i	$0.0611252\pi$
$857$			11.1742i			0.381705i	−0.981619	+	0.190852i	$0.938875\pi$
$858$			0.179464i			0.00612679i
$859$	7.95429			0.271397			0.135698	−	0.990750i	$-0.456672\pi$
$859$	7.95429			0.271397			0.135698	+	0.990750i	$0.456672\pi$
$860$	−16.6104	−	24.1438i	−0.566410	−	0.823298i
$861$	1.69244			0.0576781
$862$		−	0.962340i		−	0.0327774i
$863$		−	36.4050i		−	1.23924i	−0.784901	−	0.619621i	$-0.787286\pi$
$863$		−	36.4050i		−	1.23924i	0.784901	−	0.619621i	$-0.212714\pi$
$864$	−0.411211			−0.0139897
$865$	19.0729	+	27.7232i	0.648499	+	0.942617i
$866$	−0.0642642			−0.00218379
$867$			17.4179i			0.591542i
$868$		−	16.5936i		−	0.563224i
$869$	1.95864			0.0664422
$870$	−0.389552	+	0.268003i	−0.0132070	+	0.00908615i
$871$	−1.81762			−0.0615879
$872$			0.364338i			0.0123380i
$873$		−	10.8973i		−	0.368819i
$874$	0.188732			0.00638397
$875$	10.8677	−	2.62542i	0.367396	−	0.0887554i
$876$	−25.4195			−0.858845
$877$		−	48.3041i		−	1.63111i	−0.578677	−	0.815557i	$-0.696431\pi$
$877$		−	48.3041i		−	1.63111i	0.578677	−	0.815557i	$-0.303569\pi$
$878$		−	1.37653i		−	0.0464557i
$879$	−5.41903			−0.182779
$880$	−7.35581	+	5.06064i	−0.247964	+	0.170594i
$881$	45.2084			1.52311			0.761554	−	0.648101i	$-0.224437\pi$
$881$	45.2084			1.52311			0.761554	+	0.648101i	$0.224437\pi$
$882$			0.0342944i			0.00115475i
$883$			1.32214i			0.0444936i	0.999753	+	0.0222468i	$0.00708196\pi$
$883$			1.32214i			0.0444936i	−0.999753	+	0.0222468i	$0.992918\pi$
$884$	−61.3648			−2.06392
$885$	−7.74976	−	11.2646i	−0.260505	−	0.378654i
$886$	−0.615875			−0.0206907
$887$			1.17920i			0.0395936i	0.999804	+	0.0197968i	$0.00630194\pi$
$887$			1.17920i			0.0395936i	−0.999804	+	0.0197968i	$0.993698\pi$
$888$		−	1.18090i		−	0.0396284i
$889$	14.3580			0.481553
$890$	−0.396620	−	0.576501i	−0.0132947	−	0.0193243i
$891$	1.00000			0.0335013
$892$			1.49107i			0.0499247i
$893$		−	13.0322i		−	0.436106i
$894$	−0.553949			−0.0185268
$895$	22.8739	−	15.7367i	0.764590	−	0.526021i
$896$	1.09581			0.0366084
$897$			15.0317i			0.501894i
$898$		−	0.0290042i		−	0.000967883i
$899$	51.1883			1.70722
$900$	−3.57274	+	9.33370i	−0.119091	+	0.311123i
$901$	−11.8777			−0.395704
$902$		−	0.0580412i		−	0.00193256i
$903$		−	6.55683i		−	0.218198i
$904$	1.79972			0.0598579
$905$	27.7357	−	19.0815i	0.921966	−	0.634292i
$906$	0.00117718			3.91092e−5
$907$			17.6627i			0.586480i	0.956039	+	0.293240i	$0.0947334\pi$
$907$			17.6627i			0.586480i	−0.956039	+	0.293240i	$0.905267\pi$
$908$			0.183435i			0.00608752i
$909$	−10.2602			−0.340308
$910$	−0.227451	−	0.330608i	−0.00753993	−	0.0109596i
$911$	−15.5313			−0.514575			−0.257287	−	0.966335i	$-0.582829\pi$
$911$	−15.5313			−0.514575			−0.257287	+	0.966335i	$0.582829\pi$
$912$			7.64998i			0.253316i
$913$			3.09388i			0.102392i
$914$	−1.25771			−0.0416013
$915$	15.4556	+	22.4652i	0.510945	+	0.742677i
$916$	−27.1819			−0.898116
$917$		−	3.97822i		−	0.131372i
$918$		−	0.201194i		−	0.00664040i
$919$	−14.2932			−0.471490			−0.235745	−	0.971815i	$-0.575753\pi$
$919$	−14.2932			−0.471490			−0.235745	+	0.971815i	$0.575753\pi$
$920$	0.725686	−	0.499256i	0.0239252	−	0.0164600i
$921$	−8.13574			−0.268082
$922$			0.363164i			0.0119602i
$923$		−	81.9021i		−	2.69584i
$924$	−1.99882			−0.0657565
$925$	−40.2102	−	15.3916i	−1.32210	−	0.506073i
$926$	1.13231			0.0372100
$927$		−	2.96638i		−	0.0974288i
$928$			2.53553i			0.0832328i
$929$	−55.7961			−1.83061			−0.915306	−	0.402759i	$-0.868051\pi$
$929$	−55.7961			−1.83061			−0.915306	+	0.402759i	$0.868051\pi$
$930$	−0.524479	+	0.360830i	−0.0171983	+	0.0118321i
$931$	1.91588			0.0627903
$932$			5.55992i			0.182121i
$933$		−	11.0205i		−	0.360794i
$934$	0.271950			0.00889847
$935$	−7.43539	−	10.8076i	−0.243163	−	0.353446i
$936$	0.717643			0.0234569
$937$			13.0686i			0.426934i	0.976950	+	0.213467i	$0.0684756\pi$
$937$			13.0686i			0.426934i	−0.976950	+	0.213467i	$0.931524\pi$
$938$			0.0119117i			0.000388932i
$939$	12.7571			0.416311
$940$	−17.2320	−	25.0474i	−0.562047	−	0.816956i
$941$	48.2709			1.57359			0.786793	−	0.617217i	$-0.211740\pi$
$941$	48.2709			1.57359			0.786793	+	0.617217i	$0.211740\pi$
$942$		−	0.133555i		−	0.00435145i
$943$		−	4.86147i		−	0.158311i
$944$	−24.4157			−0.794664
$945$	−1.84220	+	1.26739i	−0.0599269	+	0.0412283i
$946$	−0.224863			−0.00731092
$947$		−	19.1949i		−	0.623750i	−0.950123	−	0.311875i	$-0.899043\pi$
$947$		−	19.1949i		−	0.623750i	0.950123	−	0.311875i	$-0.100957\pi$
$948$		−	3.91497i		−	0.127152i
$949$	66.5495			2.16029
$950$	−0.306811	−	0.117441i	−0.00995425	−	0.00381028i
$951$	−22.4073			−0.726607
$952$			0.804541i			0.0260753i
$953$			25.7683i			0.834717i	0.908742	+	0.417359i	$0.137044\pi$
$953$			25.7683i			0.834717i	−0.908742	+	0.417359i	$0.862956\pi$
$954$	0.0694327			0.00224797
$955$	−43.8799	+	30.1884i	−1.41992	+	0.976873i
$956$	−3.02388			−0.0977992
$957$		−	6.16600i		−	0.199319i
$958$			0.949940i			0.0306912i
$959$	−6.06514			−0.195854
$960$	10.1034	+	14.6857i	0.326086	+	0.473977i
$961$	37.9181			1.22317
$962$			1.54537i			0.0498248i
$963$		−	4.71311i		−	0.151878i
$964$	−5.52909			−0.178080
$965$	−13.3831	−	19.4529i	−0.430818	−	0.626210i
$966$	0.0985097			0.00316950
$967$			19.1756i			0.616646i	0.951282	+	0.308323i	$0.0997678\pi$
$967$			19.1756i			0.616646i	−0.951282	+	0.308323i	$0.900232\pi$
$968$			0.137137i			0.00440776i
$969$	−11.2398			−0.361075
$970$	0.688465	−	0.473649i	0.0221053	−	0.0152079i
$971$	−55.1464			−1.76973			−0.884866	−	0.465846i	$-0.845750\pi$
$971$	−55.1464			−1.76973			−0.884866	+	0.465846i	$0.845750\pi$
$972$		−	1.99882i		−	0.0641123i
$973$			22.4906i			0.721014i
$974$	−0.368184			−0.0117974
$975$	9.35363	−	24.4361i	0.299556	−	0.782581i
$976$	48.6930			1.55862
$977$			4.68145i			0.149773i	0.997192	+	0.0748865i	$0.0238594\pi$
$977$			4.68145i			0.149773i	−0.997192	+	0.0748865i	$0.976141\pi$
$978$		−	0.492255i		−	0.0157406i
$979$	9.12512			0.291640
$980$	3.68224	−	2.53330i	0.117625	−	0.0809232i
$981$	−2.65673			−0.0848230
$982$		−	0.124519i		−	0.00397355i
$983$		−	32.5791i		−	1.03911i	−0.854436	−	0.519556i	$-0.826097\pi$
$983$		−	32.5791i		−	1.03911i	0.854436	−	0.519556i	$-0.173903\pi$
$984$	−0.232097			−0.00739897
$985$	30.8174	+	44.7943i	0.981925	+	1.42726i
$986$	−1.24057			−0.0395076
$987$		−	6.80222i		−	0.216517i
$988$		−	20.0398i		−	0.637552i
$989$	−18.8343			−0.598896
$990$	0.0434646	+	0.0631773i	0.00138140	+	0.00200791i
$991$	−35.6870			−1.13363			−0.566817	−	0.823843i	$-0.691826\pi$
$991$	−35.6870			−1.13363			−0.566817	+	0.823843i	$0.691826\pi$
$992$			3.41375i			0.108387i
$993$			26.0154i			0.825575i
$994$	−0.536743			−0.0170245
$995$	31.7645	−	21.8533i	1.00700	−	0.692795i
$996$	6.18411			0.195951
$997$		−	33.0569i		−	1.04692i	−0.852050	−	0.523461i	$-0.824641\pi$
$997$		−	33.0569i		−	1.04692i	0.852050	−	0.523461i	$-0.175359\pi$
$998$			1.14615i			0.0362806i
$999$	8.61106			0.272442

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.f.694.11	yes	20
5.2	odd	4		5775.2.a.cn.1.6		10
5.3	odd	4		5775.2.a.co.1.5		10
5.4	even	2	inner	1155.2.c.f.694.10	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.f.694.10	✓	20	5.4	even	2	inner
1155.2.c.f.694.11	yes	20	1.1	even	1	trivial
5775.2.a.cn.1.6		10	5.2	odd	4
5775.2.a.co.1.5		10	5.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.0342944i q^{2} -1.00000i q^{3} +1.99882 q^{4} +(-1.84220 + 1.26739i) q^{5} +0.0342944 q^{6} -1.00000i q^{7} +0.137137i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+0.0342944i q^{2} -1.00000i q^{3} +1.99882 q^{4} +(-1.84220 + 1.26739i) q^{5} +0.0342944 q^{6} -1.00000i q^{7} +0.137137i q^{8} -1.00000 q^{9} +(-0.0434646 - 0.0631773i) q^{10} +1.00000 q^{11} -1.99882i q^{12} +5.23302i q^{13} +0.0342944 q^{14} +(1.26739 + 1.84220i) q^{15} +3.99294 q^{16} +5.86667i q^{17} -0.0342944i q^{18} -1.91588 q^{19} +(-3.68224 + 2.53330i) q^{20} -1.00000 q^{21} +0.0342944i q^{22} +2.87247i q^{23} +0.137137 q^{24} +(1.78742 - 4.66959i) q^{25} -0.179464 q^{26} +1.00000i q^{27} -1.99882i q^{28} +6.16600 q^{29} +(-0.0631773 + 0.0434646i) q^{30} +8.30169 q^{31} +0.411211i q^{32} -1.00000i q^{33} -0.201194 q^{34} +(1.26739 + 1.84220i) q^{35} -1.99882 q^{36} -8.61106i q^{37} -0.0657039i q^{38} +5.23302 q^{39} +(-0.173807 - 0.252635i) q^{40} -1.69244 q^{41} -0.0342944i q^{42} +6.55683i q^{43} +1.99882 q^{44} +(1.84220 - 1.26739i) q^{45} -0.0985097 q^{46} +6.80222i q^{47} -3.99294i q^{48} -1.00000 q^{49} +(0.160141 + 0.0612987i) q^{50} +5.86667 q^{51} +10.4599i q^{52} +2.02461i q^{53} -0.0342944 q^{54} +(-1.84220 + 1.26739i) q^{55} +0.137137 q^{56} +1.91588i q^{57} +0.211460i q^{58} -6.11472 q^{59} +(2.53330 + 3.68224i) q^{60} +12.1948 q^{61} +0.284702i q^{62} +1.00000i q^{63} +7.97179 q^{64} +(-6.63230 - 9.64029i) q^{65} +0.0342944 q^{66} +0.347338i q^{67} +11.7264i q^{68} +2.87247 q^{69} +(-0.0631773 + 0.0434646i) q^{70} -15.6510 q^{71} -0.137137i q^{72} -12.7172i q^{73} +0.295312 q^{74} +(-4.66959 - 1.78742i) q^{75} -3.82950 q^{76} -1.00000i q^{77} +0.179464i q^{78} +1.95864 q^{79} +(-7.35581 + 5.06064i) q^{80} +1.00000 q^{81} -0.0580412i q^{82} +3.09388i q^{83} -1.99882 q^{84} +(-7.43539 - 10.8076i) q^{85} -0.224863 q^{86} -6.16600i q^{87} +0.137137i q^{88} +9.12512 q^{89} +(0.0434646 + 0.0631773i) q^{90} +5.23302 q^{91} +5.74156i q^{92} -8.30169i q^{93} -0.233278 q^{94} +(3.52943 - 2.42817i) q^{95} +0.411211 q^{96} +10.8973i q^{97} -0.0342944i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9}+O(q^{10}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9	\( 20 q - 26 q^{4} - 2 q^{5} + 6 q^{6} - 20 q^{9} + 2 q^{10} + 20 q^{11} + 6 q^{14} - 2 q^{15} + 38 q^{16} - 34 q^{19} + 4 q^{20} - 20 q^{21} - 18 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{29} - 6 q^{30} + 12 q^{31} - 32 q^{34} - 2 q^{35} + 26 q^{36} - 2 q^{40} + 52 q^{41} - 26 q^{44} + 2 q^{45} + 40 q^{46} - 20 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{54} - 2 q^{55} - 18 q^{56} - 14 q^{59} - 28 q^{60} + 78 q^{61} - 26 q^{64} - 4 q^{65} + 6 q^{66} - 18 q^{69} - 6 q^{70} - 8 q^{74} - 8 q^{75} + 84 q^{76} - 52 q^{79} - 40 q^{80} + 20 q^{81} + 26 q^{84} - 24 q^{85} + 4 q^{86} - 10 q^{89} - 2 q^{90} - 96 q^{94} - 30 q^{95} + 62 q^{96} - 20 q^{99}+O(q^{100}) \) 20 * q - 26 * q^4 - 2 * q^5 + 6 * q^6 - 20 * q^9 + 2 * q^10 + 20 * q^11 + 6 * q^14 - 2 * q^15 + 38 * q^16 - 34 * q^19 + 4 * q^20 - 20 * q^21 - 18 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^29 - 6 * q^30 + 12 * q^31 - 32 * q^34 - 2 * q^35 + 26 * q^36 - 2 * q^40 + 52 * q^41 - 26 * q^44 + 2 * q^45 + 40 * q^46 - 20 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^54 - 2 * q^55 - 18 * q^56 - 14 * q^59 - 28 * q^60 + 78 * q^61 - 26 * q^64 - 4 * q^65 + 6 * q^66 - 18 * q^69 - 6 * q^70 - 8 * q^74 - 8 * q^75 + 84 * q^76 - 52 * q^79 - 40 * q^80 + 20 * q^81 + 26 * q^84 - 24 * q^85 + 4 * q^86 - 10 * q^89 - 2 * q^90 - 96 * q^94 - 30 * q^95 + 62 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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