LMFDB - Embedded newform 1155.2.i.c.76.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(76,1155)]

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, 0, 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("1155.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.i (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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.7
Root			$0.917186 - 1.66637i$ of defining polynomial
Character	$\chi$	$=$	1155.76
Dual form			1155.2.i.c.76.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.474903i q^{2} -1.00000i q^{3} +1.77447 q^{4} +1.00000i q^{5} -0.474903 q^{6} +(0.474903 - 2.60278i) q^{7} -1.79251i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.474903i q^{2} -1.00000i q^{3} +1.77447 q^{4} +1.00000i q^{5} -0.474903 q^{6} +(0.474903 - 2.60278i) q^{7} -1.79251i q^{8} -1.00000 q^{9} +0.474903 q^{10} +(3.23607 - 0.726543i) q^{11} -1.77447i q^{12} -0.814323 q^{13} +(-1.23607 - 0.225533i) q^{14} +1.00000 q^{15} +2.69767 q^{16} +6.40701 q^{17} +0.474903i q^{18} -4.95392 q^{19} +1.77447i q^{20} +(-2.60278 - 0.474903i) q^{21} +(-0.345037 - 1.53682i) q^{22} -0.774467 q^{23} -1.79251 q^{24} -1.00000 q^{25} +0.386724i q^{26} +1.00000i q^{27} +(0.842700 - 4.61855i) q^{28} -2.51905i q^{29} -0.474903i q^{30} +5.42943i q^{31} -4.86614i q^{32} +(-0.726543 - 3.23607i) q^{33} -3.04271i q^{34} +(2.60278 + 0.474903i) q^{35} -1.77447 q^{36} -5.42943 q^{37} +2.35263i q^{38} +0.814323i q^{39} +1.79251 q^{40} +2.77069 q^{41} +(-0.225533 + 1.23607i) q^{42} -6.55058i q^{43} +(5.74230 - 1.28923i) q^{44} -1.00000i q^{45} +0.367797i q^{46} -4.57057i q^{47} -2.69767i q^{48} +(-6.54893 - 2.47214i) q^{49} +0.474903i q^{50} -6.40701i q^{51} -1.44499 q^{52} +9.63333 q^{53} +0.474903 q^{54} +(0.726543 + 3.23607i) q^{55} +(-4.66550 - 0.851266i) q^{56} +4.95392i q^{57} -1.19630 q^{58} +3.34504i q^{59} +1.77447 q^{60} -8.03565 q^{61} +2.57845 q^{62} +(-0.474903 + 2.60278i) q^{63} +3.08439 q^{64} -0.814323i q^{65} +(-1.53682 + 0.345037i) q^{66} +16.0211 q^{67} +11.3690 q^{68} +0.774467i q^{69} +(0.225533 - 1.23607i) q^{70} -3.04271 q^{71} +1.79251i q^{72} -9.23710 q^{73} +2.57845i q^{74} +1.00000i q^{75} -8.79057 q^{76} +(-0.354213 - 8.76781i) q^{77} +0.386724 q^{78} +7.97625i q^{79} +2.69767i q^{80} +1.00000 q^{81} -1.31581i q^{82} +6.58257 q^{83} +(-4.61855 - 0.842700i) q^{84} +6.40701i q^{85} -3.11089 q^{86} -2.51905 q^{87} +(-1.30233 - 5.80067i) q^{88} -1.12710i q^{89} -0.474903 q^{90} +(-0.386724 + 2.11950i) q^{91} -1.37427 q^{92} +5.42943 q^{93} -2.17058 q^{94} -4.95392i q^{95} -4.86614 q^{96} -12.2039i q^{97} +(-1.17402 + 3.11011i) q^{98} +(-3.23607 + 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) $ 16 * q - 24 * q^4 - 16 * q^9	$ 16 q - 24 q^{4} - 16 q^{9} + 16 q^{11} + 16 q^{14} + 16 q^{15} + 24 q^{16} + 40 q^{23} - 16 q^{25} + 24 q^{36} - 40 q^{37} - 56 q^{42} - 24 q^{44} + 8 q^{53} + 8 q^{56} + 72 q^{58} - 24 q^{60} + 8 q^{64} + 80 q^{67} + 56 q^{70} - 24 q^{71} - 16 q^{78} + 16 q^{81} - 8 q^{86} - 40 q^{88} + 16 q^{91} - 160 q^{92} + 40 q^{93} - 16 q^{99}+O(q^{100}) $ 16 * q - 24 * q^4 - 16 * q^9 + 16 * q^11 + 16 * q^14 + 16 * q^15 + 24 * q^16 + 40 * q^23 - 16 * q^25 + 24 * q^36 - 40 * q^37 - 56 * q^42 - 24 * q^44 + 8 * q^53 + 8 * q^56 + 72 * q^58 - 24 * q^60 + 8 * q^64 + 80 * q^67 + 56 * q^70 - 24 * q^71 - 16 * q^78 + 16 * q^81 - 8 * q^86 - 40 * q^88 + 16 * q^91 - 160 * q^92 + 40 * q^93 - 16 * 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 $

$2$		−	0.474903i		−	0.335807i	−0.985803	−	0.167904i	$-0.946300\pi$
$2$		−	0.474903i		−	0.335807i	0.985803	−	0.167904i	$-0.0536997\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.77447			0.887234
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.474903			−0.193878
$7$	0.474903	−	2.60278i	0.179496	−	0.983759i
$7$	0.474903	−	2.60278i	0.179496	−	0.983759i
$8$		−	1.79251i		−	0.633746i
$9$	−1.00000			−0.333333
$10$	0.474903			0.150177
$11$	3.23607	−	0.726543i	0.975711	−	0.219061i
$11$	3.23607	−	0.726543i	0.975711	−	0.219061i
$12$		−	1.77447i		−	0.512245i
$13$	−0.814323			−0.225853			−0.112926	−	0.993603i	$-0.536022\pi$
$13$	−0.814323			−0.225853			−0.112926	+	0.993603i	$0.536022\pi$
$14$	−1.23607	−	0.225533i	−0.330353	−	0.0602762i
$15$	1.00000			0.258199
$16$	2.69767			0.674417
$17$	6.40701			1.55393			0.776964	−	0.629545i	$-0.216759\pi$
$17$	6.40701			1.55393			0.776964	+	0.629545i	$0.216759\pi$
$18$			0.474903i			0.111936i
$19$	−4.95392			−1.13651			−0.568254	−	0.822853i	$-0.692381\pi$
$19$	−4.95392			−1.13651			−0.568254	+	0.822853i	$0.692381\pi$
$20$			1.77447i			0.396783i
$21$	−2.60278	−	0.474903i	−0.567973	−	0.103632i
$22$	−0.345037	−	1.53682i	−0.0735622	−	0.327651i
$23$	−0.774467			−0.161488			−0.0807438	−	0.996735i	$-0.525730\pi$
$23$	−0.774467			−0.161488			−0.0807438	+	0.996735i	$0.525730\pi$
$24$	−1.79251			−0.365894
$25$	−1.00000			−0.200000
$26$			0.386724i			0.0758429i
$27$			1.00000i			0.192450i
$28$	0.842700	−	4.61855i	0.159255	−	0.872824i
$29$		−	2.51905i		−	0.467775i	−0.972264	−	0.233888i	$-0.924855\pi$
$29$		−	2.51905i		−	0.467775i	0.972264	−	0.233888i	$-0.0751448\pi$
$30$		−	0.474903i		−	0.0867050i
$31$			5.42943i			0.975154i	0.873080	+	0.487577i	$0.162119\pi$
$31$			5.42943i			0.975154i	−0.873080	+	0.487577i	$0.837881\pi$
$32$		−	4.86614i		−	0.860220i
$33$	−0.726543	−	3.23607i	−0.126475	−	0.563327i
$34$		−	3.04271i		−	0.521820i
$35$	2.60278	+	0.474903i	0.439950	+	0.0802732i
$36$	−1.77447			−0.295745
$37$	−5.42943			−0.892593			−0.446296	−	0.894885i	$-0.647257\pi$
$37$	−5.42943			−0.892593			−0.446296	+	0.894885i	$0.647257\pi$
$38$			2.35263i			0.381647i
$39$			0.814323i			0.130396i
$40$	1.79251			0.283420
$41$	2.77069			0.432709			0.216354	−	0.976315i	$-0.430583\pi$
$41$	2.77069			0.432709			0.216354	+	0.976315i	$0.430583\pi$
$42$	−0.225533	+	1.23607i	−0.0348005	+	0.190729i
$43$		−	6.55058i		−	0.998955i	−0.866327	−	0.499477i	$-0.833525\pi$
$43$		−	6.55058i		−	0.998955i	0.866327	−	0.499477i	$-0.166475\pi$
$44$	5.74230	−	1.28923i	0.865684	−	0.194358i
$45$		−	1.00000i		−	0.149071i
$46$			0.367797i			0.0542287i
$47$		−	4.57057i		−	0.666686i	−0.942806	−	0.333343i	$-0.891823\pi$
$47$		−	4.57057i		−	0.666686i	0.942806	−	0.333343i	$-0.108177\pi$
$48$		−	2.69767i		−	0.389375i
$49$	−6.54893	−	2.47214i	−0.935562	−	0.353162i
$50$			0.474903i			0.0671614i
$51$		−	6.40701i		−	0.897160i
$52$	−1.44499			−0.200384
$53$	9.63333			1.32324			0.661620	−	0.749840i	$-0.269869\pi$
$53$	9.63333			1.32324			0.661620	+	0.749840i	$0.269869\pi$
$54$	0.474903			0.0646261
$55$	0.726543	+	3.23607i	0.0979670	+	0.436351i
$56$	−4.66550	−	0.851266i	−0.623453	−	0.113755i
$57$			4.95392i			0.656163i
$58$	−1.19630			−0.157082
$59$			3.34504i			0.435487i	0.976006	+	0.217743i	$0.0698696\pi$
$59$			3.34504i			0.435487i	−0.976006	+	0.217743i	$0.930130\pi$
$60$	1.77447			0.229083
$61$	−8.03565			−1.02886			−0.514430	−	0.857532i	$-0.671996\pi$
$61$	−8.03565			−1.02886			−0.514430	+	0.857532i	$0.671996\pi$
$62$	2.57845			0.327464
$63$	−0.474903	+	2.60278i	−0.0598321	+	0.327920i
$64$	3.08439			0.385549
$65$		−	0.814323i		−	0.101004i
$66$	−1.53682	+	0.345037i	−0.189169	+	0.0424711i
$67$	16.0211			1.95729			0.978643	−	0.205569i	$-0.0659045\pi$
$67$	16.0211			1.95729			0.978643	+	0.205569i	$0.0659045\pi$
$68$	11.3690			1.37870
$69$			0.774467i			0.0932349i
$70$	0.225533	−	1.23607i	0.0269563	−	0.147738i
$71$	−3.04271			−0.361103			−0.180551	−	0.983566i	$-0.557788\pi$
$71$	−3.04271			−0.361103			−0.180551	+	0.983566i	$0.557788\pi$
$72$			1.79251i			0.211249i
$73$	−9.23710			−1.08112			−0.540560	−	0.841305i	$-0.681788\pi$
$73$	−9.23710			−1.08112			−0.540560	+	0.841305i	$0.681788\pi$
$74$			2.57845i			0.299739i
$75$			1.00000i			0.115470i
$76$	−8.79057			−1.00835
$77$	−0.354213	−	8.76781i	−0.0403663	−	0.999185i
$78$	0.386724			0.0437879
$79$			7.97625i			0.897398i	0.893683	+	0.448699i	$0.148112\pi$
$79$			7.97625i			0.897398i	−0.893683	+	0.448699i	$0.851888\pi$
$80$			2.69767i			0.301609i
$81$	1.00000			0.111111
$82$		−	1.31581i		−	0.145307i
$83$	6.58257			0.722531			0.361265	−	0.932463i	$-0.382345\pi$
$83$	6.58257			0.722531			0.361265	+	0.932463i	$0.382345\pi$
$84$	−4.61855	−	0.842700i	−0.503925	−	0.0919461i
$85$			6.40701i			0.694937i
$86$	−3.11089			−0.335456
$87$	−2.51905			−0.270070
$88$	−1.30233	−	5.80067i	−0.138829	−	0.618353i
$89$		−	1.12710i		−	0.119472i	−0.998214	−	0.0597361i	$-0.980974\pi$
$89$		−	1.12710i		−	0.119472i	0.998214	−	0.0597361i	$-0.0190259\pi$
$90$	−0.474903			−0.0500592
$91$	−0.386724	+	2.11950i	−0.0405397	+	0.222184i
$92$	−1.37427			−0.143277
$93$	5.42943			0.563006
$94$	−2.17058			−0.223878
$95$		−	4.95392i		−	0.508262i
$96$	−4.86614			−0.496648
$97$		−	12.2039i		−	1.23912i	−0.784950	−	0.619559i	$-0.787311\pi$
$97$		−	12.2039i		−	1.23912i	0.784950	−	0.619559i	$-0.212689\pi$
$98$	−1.17402	+	3.11011i	−0.118594	+	0.314168i
$99$	−3.23607	+	0.726543i	−0.325237	+	0.0730203i
$100$	−1.77447			−0.177447
$101$	−6.15537			−0.612482			−0.306241	−	0.951954i	$-0.599071\pi$
$101$	−6.15537			−0.612482			−0.306241	+	0.951954i	$0.599071\pi$
$102$	−3.04271			−0.301273
$103$		−	1.57816i		−	0.155501i	−0.996973	−	0.0777506i	$-0.975226\pi$
$103$		−	1.57816i		−	0.155501i	0.996973	−	0.0777506i	$-0.0247738\pi$
$104$			1.45968i			0.143133i
$105$	0.474903	−	2.60278i	0.0463458	−	0.254005i
$106$		−	4.57489i		−	0.444353i
$107$			6.29895i			0.608942i	0.952522	+	0.304471i	$0.0984797\pi$
$107$			6.29895i			0.608942i	−0.952522	+	0.304471i	$0.901520\pi$
$108$			1.77447i			0.170748i
$109$			8.92605i			0.854961i	0.904025	+	0.427480i	$0.140599\pi$
$109$			8.92605i			0.854961i	−0.904025	+	0.427480i	$0.859401\pi$
$110$	1.53682	−	0.345037i	0.146530	−	0.0328980i
$111$			5.42943i			0.515339i
$112$	1.28113	−	7.02144i	0.121055	−	0.663464i
$113$	−9.46454			−0.890349			−0.445175	−	0.895444i	$-0.646858\pi$
$113$	−9.46454			−0.890349			−0.445175	+	0.895444i	$0.646858\pi$
$114$	2.35263			0.220344
$115$		−	0.774467i		−	0.0722194i
$116$		−	4.46997i		−	0.415026i
$117$	0.814323			0.0752842
$118$	1.58857			0.146240
$119$	3.04271	−	16.6760i	0.278924	−	1.52869i
$120$		−	1.79251i		−	0.163633i
$121$	9.94427	−	4.70228i	0.904025	−	0.427480i
$122$			3.81615i			0.345498i
$123$		−	2.77069i		−	0.249824i
$124$			9.63435i			0.865190i
$125$		−	1.00000i		−	0.0894427i
$126$	1.23607	+	0.225533i	0.110118	+	0.0200921i
$127$			1.51249i			0.134212i	0.997746	+	0.0671059i	$0.0213765\pi$
$127$			1.51249i			0.134212i	−0.997746	+	0.0671059i	$0.978623\pi$
$128$		−	11.1971i		−	0.989690i
$129$	−6.55058			−0.576747
$130$	−0.386724			−0.0339180
$131$	9.19702			0.803547			0.401774	−	0.915739i	$-0.368394\pi$
$131$	9.19702			0.803547			0.401774	+	0.915739i	$0.368394\pi$
$132$	−1.28923	−	5.74230i	−0.112213	−	0.499803i
$133$	−2.35263	+	12.8940i	−0.203999	+	1.11805i
$134$		−	7.60845i		−	0.657270i
$135$	−1.00000			−0.0860663
$136$		−	11.4846i		−	0.984796i
$137$	−12.7263			−1.08728			−0.543642	−	0.839317i	$-0.682955\pi$
$137$	−12.7263			−1.08728			−0.543642	+	0.839317i	$0.682955\pi$
$138$	0.367797			0.0313089
$139$	−10.6902			−0.906730			−0.453365	−	0.891325i	$-0.649776\pi$
$139$	−10.6902			−0.906730			−0.453365	+	0.891325i	$0.649776\pi$
$140$	4.61855	+	0.842700i	0.390339	+	0.0712211i
$141$	−4.57057			−0.384911
$142$			1.44499i			0.121261i
$143$	−2.63520	+	0.591640i	−0.220367	+	0.0494755i
$144$	−2.69767			−0.224806
$145$	2.51905			0.209196
$146$			4.38672i			0.363048i
$147$	−2.47214	+	6.54893i	−0.203898	+	0.540147i
$148$	−9.63435			−0.791938
$149$			3.07364i			0.251802i	0.992043	+	0.125901i	$0.0401822\pi$
$149$			3.07364i			0.251802i	−0.992043	+	0.125901i	$0.959818\pi$
$150$	0.474903			0.0387757
$151$			9.28384i			0.755509i	0.925906	+	0.377754i	$0.123304\pi$
$151$			9.28384i			0.755509i	−0.925906	+	0.377754i	$0.876696\pi$
$152$			8.87993i			0.720257i
$153$	−6.40701			−0.517976
$154$	−4.16386	+	0.168217i	−0.335533	+	0.0135553i
$155$	−5.42943			−0.436102
$156$			1.44499i			0.115692i
$157$			22.6971i			1.81143i	0.423891	+	0.905713i	$0.360664\pi$
$157$			22.6971i			1.81143i	−0.423891	+	0.905713i	$0.639336\pi$
$158$	3.78794			0.301353
$159$		−	9.63333i		−	0.763973i
$160$	4.86614			0.384702
$161$	−0.367797	+	2.01577i	−0.0289864	+	0.158865i
$162$		−	0.474903i		−	0.0373119i
$163$	1.19630			0.0937017			0.0468508	−	0.998902i	$-0.485081\pi$
$163$	1.19630			0.0937017			0.0468508	+	0.998902i	$0.485081\pi$
$164$	4.91649			0.383914
$165$	3.23607	−	0.726543i	0.251928	−	0.0565613i
$166$		−	3.12608i		−	0.242631i
$167$	20.0947			1.55498			0.777489	−	0.628896i	$-0.216493\pi$
$167$	20.0947			1.55498			0.777489	+	0.628896i	$0.216493\pi$
$168$	−0.851266	+	4.66550i	−0.0656766	+	0.359951i
$169$	−12.3369			−0.948991
$170$	3.04271			0.233365
$171$	4.95392			0.378836
$172$		−	11.6238i		−	0.886306i
$173$	−14.0429			−1.06766			−0.533830	−	0.845592i	$-0.679248\pi$
$173$	−14.0429			−1.06766			−0.533830	+	0.845592i	$0.679248\pi$
$174$			1.19630i			0.0906915i
$175$	−0.474903	+	2.60278i	−0.0358993	+	0.196752i
$176$	8.72984	−	1.95997i	0.658036	−	0.147738i
$177$	3.34504			0.251428
$178$	−0.535262			−0.0401196
$179$	3.88638			0.290481			0.145241	−	0.989396i	$-0.453604\pi$
$179$	3.88638			0.290481			0.145241	+	0.989396i	$0.453604\pi$
$180$		−	1.77447i		−	0.132261i
$181$			4.60466i			0.342262i	0.985248	+	0.171131i	$0.0547421\pi$
$181$			4.60466i			0.342262i	−0.985248	+	0.171131i	$0.945258\pi$
$182$	1.00656	+	0.183657i	0.0746111	+	0.0136135i
$183$			8.03565i			0.594013i
$184$			1.38824i			0.102342i
$185$		−	5.42943i		−	0.399180i
$186$		−	2.57845i		−	0.189061i
$187$	20.7335	−	4.65496i	1.51618	−	0.340405i
$188$		−	8.11033i		−	0.591506i
$189$	2.60278	+	0.474903i	0.189324	+	0.0345441i
$190$	−2.35263			−0.170678
$191$	14.1747			1.02564			0.512821	−	0.858495i	$-0.328600\pi$
$191$	14.1747			1.02564			0.512821	+	0.858495i	$0.328600\pi$
$192$		−	3.08439i		−	0.222597i
$193$			0.949806i			0.0683685i	0.999416	+	0.0341843i	$0.0108833\pi$
$193$			0.949806i			0.0683685i	−0.999416	+	0.0341843i	$0.989117\pi$
$194$	−5.79567			−0.416105
$195$	−0.814323			−0.0583149
$196$	−11.6209	−	4.38672i	−0.830062	−	0.313337i
$197$			14.1068i			1.00507i	0.864557	+	0.502536i	$0.167599\pi$
$197$			14.1068i			1.00507i	−0.864557	+	0.502536i	$0.832401\pi$
$198$	0.345037	+	1.53682i	0.0245207	+	0.109217i
$199$			3.30993i			0.234634i	0.993094	+	0.117317i	$0.0374294\pi$
$199$			3.30993i			0.234634i	−0.993094	+	0.117317i	$0.962571\pi$
$200$			1.79251i			0.126749i
$201$		−	16.0211i		−	1.13004i
$202$			2.92320i			0.205676i
$203$	−6.55653	−	1.19630i	−0.460178	−	0.0839640i
$204$		−	11.3690i		−	0.795991i
$205$			2.77069i			0.193513i
$206$	−0.749475			−0.0522184
$207$	0.774467			0.0538292
$208$	−2.19677			−0.152319
$209$	−16.0312	+	3.59923i	−1.10890	+	0.248964i
$210$	−1.23607	−	0.225533i	−0.0852968	−	0.0155632i
$211$			26.5392i			1.82703i	0.406802	+	0.913516i	$0.366644\pi$
$211$			26.5392i			1.82703i	−0.406802	+	0.913516i	$0.633356\pi$
$212$	17.0940			1.17402
$213$			3.04271i			0.208483i
$214$	2.99139			0.204487
$215$	6.55058			0.446746
$216$	1.79251			0.121965
$217$	14.1316	+	2.57845i	0.959317	+	0.175037i
$218$	4.23901			0.287102
$219$			9.23710i			0.624185i
$220$	1.28923	+	5.74230i	0.0869196	+	0.387146i
$221$	−5.21737			−0.350959
$222$	2.57845			0.173054
$223$		−	12.6760i		−	0.848850i	−0.905463	−	0.424425i	$-0.860476\pi$
$223$		−	12.6760i		−	0.848850i	0.905463	−	0.424425i	$-0.139524\pi$
$224$	−12.6655	−	2.31094i	−0.846249	−	0.154406i
$225$	1.00000			0.0666667
$226$			4.49474i			0.298986i
$227$	22.8060			1.51369			0.756845	−	0.653595i	$-0.226740\pi$
$227$	22.8060			1.51369			0.756845	+	0.653595i	$0.226740\pi$
$228$			8.79057i			0.582170i
$229$		−	15.2326i		−	1.00660i	−0.864113	−	0.503298i	$-0.832120\pi$
$229$		−	15.2326i		−	1.00660i	0.864113	−	0.503298i	$-0.167880\pi$
$230$	−0.367797			−0.0242518
$231$	−8.76781	+	0.354213i	−0.576880	+	0.0233055i
$232$	−4.51541			−0.296451
$233$			19.5595i			1.28138i	0.767798	+	0.640692i	$0.221353\pi$
$233$			19.5595i			1.28138i	−0.767798	+	0.640692i	$0.778647\pi$
$234$		−	0.386724i		−	0.0252810i
$235$	4.57057			0.298151
$236$			5.93566i			0.386378i
$237$	7.97625			0.518113
$238$	−7.91950	−	1.44499i	−0.513345	−	0.0936648i
$239$			23.6204i			1.52787i	0.645291	+	0.763937i	$0.276736\pi$
$239$			23.6204i			1.52787i	−0.645291	+	0.763937i	$0.723264\pi$
$240$	2.69767			0.174134
$241$	27.7113			1.78504			0.892521	−	0.451006i	$-0.148935\pi$
$241$	27.7113			1.78504			0.892521	+	0.451006i	$0.148935\pi$
$242$	−2.23313	−	4.72256i	−0.143551	−	0.303578i
$243$		−	1.00000i		−	0.0641500i
$244$	−14.2590			−0.912839
$245$	2.47214	−	6.54893i	0.157939	−	0.418396i
$246$	−1.31581			−0.0838928
$247$	4.03409			0.256683
$248$	9.73228			0.618001
$249$		−	6.58257i		−	0.417153i
$250$	−0.474903			−0.0300355
$251$			20.4289i			1.28946i	0.764411	+	0.644729i	$0.223030\pi$
$251$			20.4289i			1.28946i	−0.764411	+	0.644729i	$0.776970\pi$
$252$	−0.842700	+	4.61855i	−0.0530851	+	0.290941i
$253$	−2.50623	+	0.562683i	−0.157565	+	0.0353756i
$254$	0.718285			0.0450692
$255$	6.40701			0.401222
$256$	0.851266			0.0532041
$257$			20.2883i			1.26555i	0.774336	+	0.632774i	$0.218084\pi$
$257$			20.2883i			1.26555i	−0.774336	+	0.632774i	$0.781916\pi$
$258$			3.11089i			0.193676i
$259$	−2.57845	+	14.1316i	−0.160217	+	0.878096i
$260$		−	1.44499i		−	0.0896145i
$261$			2.51905i			0.155925i
$262$		−	4.36769i		−	0.269837i
$263$			25.6361i			1.58079i	0.612597	+	0.790396i	$0.290125\pi$
$263$			25.6361i			1.58079i	−0.612597	+	0.790396i	$0.709875\pi$
$264$	−5.80067	+	1.30233i	−0.357006	+	0.0801530i
$265$			9.63333i			0.591771i
$266$	6.12338	+	1.11727i	0.375449	+	0.0685043i
$267$	−1.12710			−0.0689773
$268$	28.4289			1.73657
$269$			15.5197i			0.946253i	0.880994	+	0.473127i	$0.156875\pi$
$269$			15.5197i			0.946253i	−0.880994	+	0.473127i	$0.843125\pi$
$270$			0.474903i			0.0289017i
$271$	1.42566			0.0866029			0.0433015	−	0.999062i	$-0.486212\pi$
$271$	1.42566			0.0866029			0.0433015	+	0.999062i	$0.486212\pi$
$272$	17.2840			1.04800
$273$	2.11950	+	0.386724i	0.128278	+	0.0234056i
$274$			6.04377i			0.365118i
$275$	−3.23607	+	0.726543i	−0.195142	+	0.0438122i
$276$			1.37427i			0.0827211i
$277$			3.29785i			0.198149i	0.995080	+	0.0990744i	$0.0315882\pi$
$277$			3.29785i			0.198149i	−0.995080	+	0.0990744i	$0.968412\pi$
$278$			5.07680i			0.304486i
$279$		−	5.42943i		−	0.325051i
$280$	0.851266	−	4.66550i	0.0508729	−	0.278817i
$281$		−	6.26696i		−	0.373856i	−0.982374	−	0.186928i	$-0.940147\pi$
$281$		−	6.26696i		−	0.373856i	0.982374	−	0.186928i	$-0.0598530\pi$
$282$			2.17058i			0.129256i
$283$	−25.9472			−1.54240			−0.771199	−	0.636594i	$-0.780343\pi$
$283$	−25.9472			−1.54240			−0.771199	+	0.636594i	$0.780343\pi$
$284$	−5.39918			−0.320383
$285$	−4.95392			−0.293445
$286$	0.280972	+	1.25147i	0.0166142	+	0.0740008i
$287$	1.31581	−	7.21149i	0.0776697	−	0.425681i
$288$			4.86614i			0.286740i
$289$	24.0497			1.41469
$290$		−	1.19630i		−	0.0702493i
$291$	−12.2039			−0.715405
$292$	−16.3909			−0.959207
$293$	−25.6554			−1.49881			−0.749404	−	0.662113i	$-0.769660\pi$
$293$	−25.6554			−1.49881			−0.749404	+	0.662113i	$0.769660\pi$
$294$	3.11011	+	1.17402i	0.181385	+	0.0684705i
$295$	−3.34504			−0.194756
$296$			9.73228i			0.565677i
$297$	0.726543	+	3.23607i	0.0421583	+	0.187776i
$298$	1.45968			0.0845569
$299$	0.630667			0.0364724
$300$			1.77447i			0.102449i
$301$	−17.0497	−	3.11089i	−0.982730	−	0.179309i
$302$	4.40892			0.253705
$303$			6.15537i			0.353617i
$304$	−13.3640			−0.766480
$305$		−	8.03565i		−	0.460120i
$306$			3.04271i			0.173940i
$307$	17.7954			1.01563			0.507817	−	0.861465i	$-0.330452\pi$
$307$	17.7954			1.01563			0.507817	+	0.861465i	$0.330452\pi$
$308$	−0.628539	−	15.5582i	−0.0358143	−	0.886510i
$309$	−1.57816			−0.0897786
$310$			2.57845i			0.146446i
$311$		−	27.2195i		−	1.54348i	−0.635939	−	0.771739i	$-0.719387\pi$
$311$		−	27.2195i		−	1.54348i	0.635939	−	0.771739i	$-0.280613\pi$
$312$	1.45968			0.0826380
$313$		−	10.4581i		−	0.591126i	−0.955323	−	0.295563i	$-0.904493\pi$
$313$		−	10.4581i		−	0.591126i	0.955323	−	0.295563i	$-0.0955073\pi$
$314$	10.7789			0.608290
$315$	−2.60278	−	0.474903i	−0.146650	−	0.0267577i
$316$			14.1536i			0.796202i
$317$	11.7821			0.661747			0.330873	−	0.943675i	$-0.392657\pi$
$317$	11.7821			0.661747			0.330873	+	0.943675i	$0.392657\pi$
$318$	−4.57489			−0.256547
$319$	−1.83020	−	8.15181i	−0.102471	−	0.456414i
$320$			3.08439i			0.172423i
$321$	6.29895			0.351573
$322$	0.957294	+	0.174668i	0.0533479	+	0.00973385i
$323$	−31.7398			−1.76605
$324$	1.77447			0.0985815
$325$	0.814323			0.0451705
$326$		−	0.568128i		−	0.0314657i
$327$	8.92605			0.493612
$328$		−	4.96647i		−	0.274228i
$329$	−11.8962	−	2.17058i	−0.655858	−	0.119668i
$330$	−0.345037	−	1.53682i	−0.0189937	−	0.0845990i
$331$	−18.5987			−1.02228			−0.511138	−	0.859499i	$-0.670776\pi$
$331$	−18.5987			−1.02228			−0.511138	+	0.859499i	$0.670776\pi$
$332$	11.6806			0.641054
$333$	5.42943			0.297531
$334$		−	9.54305i		−	0.522173i
$335$			16.0211i			0.875325i
$336$	−7.02144	−	1.28113i	−0.383051	−	0.0698914i
$337$		−	16.6826i		−	0.908762i	−0.890808	−	0.454381i	$-0.849861\pi$
$337$		−	16.6826i		−	0.908762i	0.890808	−	0.454381i	$-0.150139\pi$
$338$			5.85882i			0.318678i
$339$			9.46454i			0.514043i
$340$			11.3690i			0.616572i
$341$	3.94471	+	17.5700i	0.213618	+	0.951469i
$342$		−	2.35263i		−	0.127216i
$343$	−9.54454	+	15.8714i	−0.515356	+	0.856976i
$344$	−11.7420			−0.633084
$345$	−0.774467			−0.0416959
$346$			6.66900i			0.358528i
$347$			26.9136i			1.44480i	0.691475	+	0.722400i	$0.256961\pi$
$347$			26.9136i			1.44480i	−0.691475	+	0.722400i	$0.743039\pi$
$348$	−4.46997			−0.239615
$349$	−5.84889			−0.313084			−0.156542	−	0.987671i	$-0.550035\pi$
$349$	−5.84889			−0.313084			−0.156542	+	0.987671i	$0.550035\pi$
$350$	1.23607	+	0.225533i	0.0660706	+	0.0120552i
$351$		−	0.814323i		−	0.0434654i
$352$	−3.53546	−	15.7472i	−0.188441	−	0.839327i
$353$		−	32.0573i		−	1.70624i	−0.521715	−	0.853120i	$-0.674708\pi$
$353$		−	32.0573i		−	1.70624i	0.521715	−	0.853120i	$-0.325292\pi$
$354$		−	1.58857i		−	0.0844314i
$355$		−	3.04271i		−	0.161490i
$356$		−	2.00000i		−	0.106000i
$357$	−16.6760	−	3.04271i	−0.882589	−	0.161037i
$358$		−	1.84565i		−	0.0975457i
$359$		−	8.34861i		−	0.440623i	−0.975430	−	0.220311i	$-0.929293\pi$
$359$		−	8.34861i		−	0.440623i	0.975430	−	0.220311i	$-0.0707073\pi$
$360$	−1.79251			−0.0944733
$361$	5.54134			0.291649
$362$	2.18677			0.114934
$363$	−4.70228	−	9.94427i	−0.246806	−	0.521939i
$364$	−0.686230	+	3.76099i	−0.0359682	+	0.197130i
$365$		−	9.23710i		−	0.483492i
$366$	3.81615			0.199474
$367$		−	9.51970i		−	0.496925i	−0.968642	−	0.248462i	$-0.920075\pi$
$367$		−	9.51970i		−	0.496925i	0.968642	−	0.248462i	$-0.0799252\pi$
$368$	−2.08926			−0.108910
$369$	−2.77069			−0.144236
$370$	−2.57845			−0.134047
$371$	4.57489	−	25.0734i	0.237517	−	1.30175i
$372$	9.63435			0.499518
$373$			3.36535i			0.174251i	0.996197	+	0.0871257i	$0.0277682\pi$
$373$			3.36535i			0.174251i	−0.996197	+	0.0871257i	$0.972232\pi$
$374$	−2.21066	−	9.84640i	−0.114310	−	0.509145i
$375$	−1.00000			−0.0516398
$376$	−8.19277			−0.422510
$377$			2.05132i			0.105648i
$378$	0.225533	−	1.23607i	0.0116002	−	0.0635765i
$379$	−16.2742			−0.835952			−0.417976	−	0.908458i	$-0.637260\pi$
$379$	−16.2742			−0.835952			−0.417976	+	0.908458i	$0.637260\pi$
$380$		−	8.79057i		−	0.450947i
$381$	1.51249			0.0774872
$382$		−	6.73159i		−	0.344418i
$383$			28.6127i			1.46204i	0.682355	+	0.731021i	$0.260956\pi$
$383$			28.6127i			1.46204i	−0.682355	+	0.731021i	$0.739044\pi$
$384$	−11.1971			−0.571398
$385$	8.76781	−	0.354213i	0.446849	−	0.0180524i
$386$	0.451065			0.0229586
$387$			6.55058i			0.332985i
$388$		−	21.6554i		−	1.09939i
$389$	28.6279			1.45149			0.725746	−	0.687963i	$-0.241495\pi$
$389$	28.6279			1.45149			0.725746	+	0.687963i	$0.241495\pi$
$390$			0.386724i			0.0195825i
$391$	−4.96202			−0.250940
$392$	−4.43132	+	11.7390i	−0.223815	+	0.592909i
$393$		−	9.19702i		−	0.463928i
$394$	6.69938			0.337510
$395$	−7.97625			−0.401329
$396$	−5.74230	+	1.28923i	−0.288561	+	0.0647860i
$397$		−	8.00588i		−	0.401804i	−0.979611	−	0.200902i	$-0.935613\pi$
$397$		−	8.00588i		−	0.401804i	0.979611	−	0.200902i	$-0.0643872\pi$
$398$	1.57189			0.0787919
$399$	12.8940	+	2.35263i	0.645506	+	0.117779i
$400$	−2.69767			−0.134883
$401$	29.7106			1.48368			0.741838	−	0.670579i	$-0.233954\pi$
$401$	29.7106			1.48368			0.741838	+	0.670579i	$0.233954\pi$
$402$	−7.60845			−0.379475
$403$		−	4.42131i		−	0.220241i
$404$	−10.9225			−0.543415
$405$			1.00000i			0.0496904i
$406$	−0.568128	+	3.11371i	−0.0281957	+	0.154531i
$407$	−17.5700	+	3.94471i	−0.870913	+	0.195532i
$408$	−11.4846			−0.568572
$409$	−25.5245			−1.26211			−0.631053	−	0.775739i	$-0.717377\pi$
$409$	−25.5245			−1.26211			−0.631053	+	0.775739i	$0.717377\pi$
$410$	1.31581			0.0649831
$411$			12.7263i			0.627744i
$412$		−	2.80040i		−	0.137966i
$413$	8.70640	+	1.58857i	0.428414	+	0.0781683i
$414$		−	0.367797i		−	0.0180762i
$415$			6.58257i			0.323126i
$416$			3.96261i			0.194283i
$417$			10.6902i			0.523501i
$418$	1.70929	+	7.61328i	0.0836040	+	0.372377i
$419$			9.79610i			0.478571i	0.970949	+	0.239285i	$0.0769132\pi$
$419$			9.79610i			0.478571i	−0.970949	+	0.239285i	$0.923087\pi$
$420$	0.842700	−	4.61855i	0.0411195	−	0.225362i
$421$	−3.20446			−0.156176			−0.0780880	−	0.996946i	$-0.524882\pi$
$421$	−3.20446			−0.156176			−0.0780880	+	0.996946i	$0.524882\pi$
$422$	12.6035			0.613530
$423$			4.57057i			0.222229i
$424$		−	17.2678i		−	0.838598i
$425$	−6.40701			−0.310785
$426$	1.44499			0.0700100
$427$	−3.81615	+	20.9150i	−0.184677	+	1.01215i
$428$			11.1773i			0.540274i
$429$	0.591640	+	2.63520i	0.0285647	+	0.127229i
$430$		−	3.11089i		−	0.150021i
$431$			13.2057i			0.636096i	0.948075	+	0.318048i	$0.103027\pi$
$431$			13.2057i			0.636096i	−0.948075	+	0.318048i	$0.896973\pi$
$432$			2.69767i			0.129792i
$433$			18.1217i			0.870872i	0.900220	+	0.435436i	$0.143406\pi$
$433$			18.1217i			0.870872i	−0.900220	+	0.435436i	$0.856594\pi$
$434$	1.22451	−	6.71114i	0.0587786	−	0.322145i
$435$		−	2.51905i		−	0.120779i
$436$			15.8390i			0.758550i
$437$	3.83665			0.183532
$438$	4.38672			0.209606
$439$	28.9147			1.38002			0.690011	−	0.723799i	$-0.257606\pi$
$439$	28.9147			1.38002			0.690011	+	0.723799i	$0.257606\pi$
$440$	5.80067	−	1.30233i	0.276536	−	0.0620862i
$441$	6.54893	+	2.47214i	0.311854	+	0.117721i
$442$			2.47775i			0.117854i
$443$	8.10648			0.385151			0.192575	−	0.981282i	$-0.438316\pi$
$443$	8.10648			0.385151			0.192575	+	0.981282i	$0.438316\pi$
$444$			9.63435i			0.457226i
$445$	1.12710			0.0534296
$446$	−6.01988			−0.285050
$447$	3.07364			0.145378
$448$	1.46479	−	8.02800i	0.0692047	−	0.379287i
$449$	−10.6127			−0.500845			−0.250422	−	0.968137i	$-0.580569\pi$
$449$	−10.6127			−0.500845			−0.250422	+	0.968137i	$0.580569\pi$
$450$		−	0.474903i		−	0.0223871i
$451$	8.96613	−	2.01302i	0.422199	−	0.0947895i
$452$	−16.7945			−0.789948
$453$	9.28384			0.436193
$454$		−	10.8306i		−	0.508308i
$455$	−2.11950	−	0.386724i	−0.0993639	−	0.0181299i
$456$	8.87993			0.415841
$457$		−	39.1722i		−	1.83240i	−0.400724	−	0.916199i	$-0.631241\pi$
$457$		−	39.1722i		−	1.83240i	0.400724	−	0.916199i	$-0.368759\pi$
$458$	−7.23399			−0.338022
$459$			6.40701i			0.299053i
$460$		−	1.37427i		−	0.0640755i
$461$	−6.71349			−0.312678			−0.156339	−	0.987703i	$-0.549969\pi$
$461$	−6.71349			−0.312678			−0.156339	+	0.987703i	$0.549969\pi$
$462$	0.168217	+	4.16386i	0.00782615	+	0.193720i
$463$	−19.4164			−0.902357			−0.451178	−	0.892434i	$-0.648996\pi$
$463$	−19.4164			−0.902357			−0.451178	+	0.892434i	$0.648996\pi$
$464$		−	6.79556i		−	0.315476i
$465$			5.42943i			0.251784i
$466$	9.28886			0.430298
$467$		−	21.2515i		−	0.983401i	−0.870765	−	0.491700i	$-0.836376\pi$
$467$		−	21.2515i		−	0.983401i	0.870765	−	0.491700i	$-0.163624\pi$
$468$	1.44499			0.0667947
$469$	7.60845	−	41.6993i	0.351326	−	1.92550i
$470$		−	2.17058i		−	0.100121i
$471$	22.6971			1.04583
$472$	5.99600			0.275988
$473$	−4.75928	−	21.1981i	−0.218832	−	0.974691i
$474$		−	3.78794i		−	0.173986i
$475$	4.95392			0.227302
$476$	5.39918	−	29.5911i	0.247471	−	1.35630i
$477$	−9.63333			−0.441080
$478$	11.2174			0.513071
$479$	−6.81032			−0.311171			−0.155586	−	0.987822i	$-0.549726\pi$
$479$	−6.81032			−0.311171			−0.155586	+	0.987822i	$0.549726\pi$
$480$		−	4.86614i		−	0.222108i
$481$	4.42131			0.201594
$482$		−	13.1602i		−	0.599429i
$483$	2.01577	+	0.367797i	0.0917206	+	0.0167353i
$484$	17.6458	−	8.34405i	0.802081	−	0.379275i
$485$	12.2039			0.554150
$486$	−0.474903			−0.0215420
$487$	5.26281			0.238481			0.119240	−	0.992865i	$-0.461954\pi$
$487$	5.26281			0.238481			0.119240	+	0.992865i	$0.461954\pi$
$488$			14.4040i			0.652036i
$489$		−	1.19630i		−	0.0540987i
$490$	−3.11011	−	1.17402i	−0.140500	−	0.0530370i
$491$		−	42.5430i		−	1.91994i	−0.280106	−	0.959969i	$-0.590370\pi$
$491$		−	42.5430i		−	1.91994i	0.280106	−	0.959969i	$-0.409630\pi$
$492$		−	4.91649i		−	0.221653i
$493$		−	16.1396i		−	0.726889i
$494$		−	1.91580i		−	0.0861960i
$495$	−0.726543	−	3.23607i	−0.0326557	−	0.145450i
$496$			14.6468i			0.657661i
$497$	−1.44499	+	7.91950i	−0.0648166	+	0.355238i
$498$	−3.12608			−0.140083
$499$	7.33201			0.328226			0.164113	−	0.986442i	$-0.447524\pi$
$499$	7.33201			0.328226			0.164113	+	0.986442i	$0.447524\pi$
$500$		−	1.77447i		−	0.0793566i
$501$		−	20.0947i		−	0.897767i
$502$	9.70173			0.433009
$503$	−8.59569			−0.383263			−0.191631	−	0.981467i	$-0.561378\pi$
$503$	−8.59569			−0.383263			−0.191631	+	0.981467i	$0.561378\pi$
$504$	4.66550	+	0.851266i	0.207818	+	0.0379184i
$505$		−	6.15537i		−	0.273910i
$506$	0.267220	+	1.19022i	0.0118794	+	0.0529115i
$507$			12.3369i			0.547900i
$508$			2.68386i			0.119077i
$509$			8.12437i			0.360106i	0.983657	+	0.180053i	$0.0576270\pi$
$509$			8.12437i			0.360106i	−0.983657	+	0.180053i	$0.942373\pi$
$510$		−	3.04271i		−	0.134733i
$511$	−4.38672	+	24.0421i	−0.194057	+	1.06356i
$512$		−	22.7984i		−	1.00756i
$513$		−	4.95392i		−	0.218721i
$514$	9.63497			0.424980
$515$	1.57816			0.0695422
$516$	−11.6238			−0.511709
$517$	−3.32071	−	14.7907i	−0.146045	−	0.650493i
$518$	6.71114	+	1.22451i	0.294871	+	0.0538021i
$519$			14.0429i			0.616414i
$520$	−1.45968			−0.0640111
$521$		−	33.4082i		−	1.46364i	−0.681497	−	0.731821i	$-0.738671\pi$
$521$		−	33.4082i		−	1.46364i	0.681497	−	0.731821i	$-0.261329\pi$
$522$	1.19630			0.0523608
$523$	23.4555			1.02564			0.512820	−	0.858496i	$-0.328601\pi$
$523$	23.4555			1.02564			0.512820	+	0.858496i	$0.328601\pi$
$524$	16.3198			0.712934
$525$	2.60278	+	0.474903i	0.113595	+	0.0207265i
$526$	12.1747			0.530841
$527$			34.7864i			1.51532i
$528$	−1.95997	−	8.72984i	−0.0852968	−	0.379917i
$529$	−22.4002			−0.973922
$530$	4.57489			0.198721
$531$		−	3.34504i		−	0.145162i
$532$	−4.17467	+	22.8799i	−0.180995	+	0.991971i
$533$	−2.25623			−0.0977284
$534$			0.535262i			0.0231631i
$535$	−6.29895			−0.272327
$536$		−	28.7179i		−	1.24042i
$537$		−	3.88638i		−	0.167710i
$538$	7.37035			0.317758
$539$	−22.9889	−	3.24192i	−0.990202	−	0.139639i
$540$	−1.77447			−0.0763609
$541$			22.0272i			0.947024i	0.880787	+	0.473512i	$0.157014\pi$
$541$			22.0272i			0.947024i	−0.880787	+	0.473512i	$0.842986\pi$
$542$		−	0.677052i		−	0.0290819i
$543$	4.60466			0.197605
$544$		−	31.1774i		−	1.33672i
$545$	−8.92605			−0.382350
$546$	0.183657	−	1.00656i	0.00785977	−	0.0430767i
$547$		−	45.2889i		−	1.93641i	−0.250151	−	0.968207i	$-0.580480\pi$
$547$		−	45.2889i		−	1.93641i	0.250151	−	0.968207i	$-0.419520\pi$
$548$	−22.5825			−0.964675
$549$	8.03565			0.342953
$550$	0.345037	+	1.53682i	0.0147124	+	0.0655301i
$551$			12.4792i			0.531630i
$552$	1.38824			0.0590873
$553$	20.7604	+	3.78794i	0.882823	+	0.161080i
$554$	1.56616			0.0665398
$555$	−5.42943			−0.230466
$556$	−18.9694			−0.804481
$557$		−	31.9590i		−	1.35414i	−0.735917	−	0.677072i	$-0.763248\pi$
$557$		−	31.9590i		−	1.35414i	0.735917	−	0.677072i	$-0.236752\pi$
$558$	−2.57845			−0.109155
$559$			5.33429i			0.225617i
$560$	7.02144	+	1.28113i	0.296710	+	0.0541376i
$561$	−4.65496	−	20.7335i	−0.196533	−	0.875369i
$562$	−2.97620			−0.125543
$563$	−7.22589			−0.304535			−0.152268	−	0.988339i	$-0.548658\pi$
$563$	−7.22589			−0.304535			−0.152268	+	0.988339i	$0.548658\pi$
$564$	−8.11033			−0.341506
$565$		−	9.46454i		−	0.398176i
$566$			12.3224i			0.517948i
$567$	0.474903	−	2.60278i	0.0199440	−	0.109307i
$568$			5.45407i			0.228848i
$569$		−	14.1104i		−	0.591538i	−0.955260	−	0.295769i	$-0.904424\pi$
$569$		−	14.1104i		−	0.591538i	0.955260	−	0.295769i	$-0.0955758\pi$
$570$			2.35263i			0.0985409i
$571$			33.9554i			1.42099i	0.703703	+	0.710495i	$0.251529\pi$
$571$			33.9554i			1.42099i	−0.703703	+	0.710495i	$0.748471\pi$
$572$	−4.67608	+	1.04985i	−0.195517	+	0.0438963i
$573$		−	14.1747i		−	0.592155i
$574$	−3.42476	−	0.624881i	−0.142947	−	0.0260820i
$575$	0.774467			0.0322975
$576$	−3.08439			−0.128516
$577$			12.8097i			0.533275i	0.963797	+	0.266638i	$0.0859127\pi$
$577$			12.8097i			0.533275i	−0.963797	+	0.266638i	$0.914087\pi$
$578$		−	11.4213i		−	0.475063i
$579$	0.949806			0.0394726
$580$	4.46997			0.185605
$581$	3.12608	−	17.1330i	0.129692	−	0.710796i
$582$			5.79567i			0.240238i
$583$	31.1741	−	6.99902i	1.29110	−	0.289870i
$584$			16.5575i			0.685156i
$585$			0.814323i			0.0336681i
$586$			12.1838i			0.503310i
$587$			3.45751i			0.142707i	0.997451	+	0.0713534i	$0.0227318\pi$
$587$			3.45751i			0.142707i	−0.997451	+	0.0713534i	$0.977268\pi$
$588$	−4.38672	+	11.6209i	−0.180905	+	0.479237i
$589$		−	26.8970i		−	1.10827i
$590$			1.58857i			0.0654003i
$591$	14.1068			0.580278
$592$	−14.6468			−0.601980
$593$	−16.9490			−0.696014			−0.348007	−	0.937492i	$-0.613141\pi$
$593$	−16.9490			−0.696014			−0.348007	+	0.937492i	$0.613141\pi$
$594$	1.53682	−	0.345037i	0.0630564	−	0.0141570i
$595$	16.6760	+	3.04271i	0.683651	+	0.124739i
$596$			5.45407i			0.223407i
$597$	3.30993			0.135466
$598$		−	0.299505i		−	0.0122477i
$599$	0.684193			0.0279554			0.0139777	−	0.999902i	$-0.495551\pi$
$599$	0.684193			0.0279554			0.0139777	+	0.999902i	$0.495551\pi$
$600$	1.79251			0.0731787
$601$	24.6102			1.00387			0.501936	−	0.864905i	$-0.332621\pi$
$601$	24.6102			1.00387			0.501936	+	0.864905i	$0.332621\pi$
$602$	−1.47737	+	8.09697i	−0.0602132	+	0.330008i
$603$	−16.0211			−0.652428
$604$			16.4739i			0.670313i
$605$	4.70228	+	9.94427i	0.191175	+	0.404292i
$606$	2.92320			0.118747
$607$	−11.5771			−0.469898			−0.234949	−	0.972008i	$-0.575492\pi$
$607$	−11.5771			−0.469898			−0.234949	+	0.972008i	$0.575492\pi$
$608$			24.1065i			0.977647i
$609$	−1.19630	+	6.55653i	−0.0484766	+	0.265684i
$610$	−3.81615			−0.154512
$611$			3.72192i			0.150573i
$612$	−11.3690			−0.459566
$613$			4.12694i			0.166686i	0.996521	+	0.0833428i	$0.0265596\pi$
$613$			4.12694i			0.166686i	−0.996521	+	0.0833428i	$0.973440\pi$
$614$		−	8.45107i		−	0.341057i
$615$	2.77069			0.111725
$616$	−15.7163	+	0.634929i	−0.633230	+	0.0255820i
$617$	0.965342			0.0388632			0.0194316	−	0.999811i	$-0.493814\pi$
$617$	0.965342			0.0388632			0.0194316	+	0.999811i	$0.493814\pi$
$618$			0.749475i			0.0301483i
$619$			46.5505i			1.87102i	0.353295	+	0.935512i	$0.385061\pi$
$619$			46.5505i			1.87102i	−0.353295	+	0.935512i	$0.614939\pi$
$620$	−9.63435			−0.386925
$621$		−	0.774467i		−	0.0310783i
$622$	−12.9266			−0.518311
$623$	−2.93359	−	0.535262i	−0.117532	−	0.0214448i
$624$			2.19677i			0.0879413i
$625$	1.00000			0.0400000
$626$	−4.96658			−0.198504
$627$	3.59923	+	16.0312i	0.143740	+	0.640226i
$628$			40.2753i			1.60716i
$629$	−34.7864			−1.38702
$630$	−0.225533	+	1.23607i	−0.00898544	+	0.0492461i
$631$	−41.6284			−1.65720			−0.828599	−	0.559842i	$-0.810862\pi$
$631$	−41.6284			−1.65720			−0.828599	+	0.559842i	$0.810862\pi$
$632$	14.2975			0.568723
$633$	26.5392			1.05484
$634$		−	5.59533i		−	0.222219i
$635$	−1.51249			−0.0600213
$636$		−	17.0940i		−	0.677822i
$637$	5.33295	+	2.01312i	0.211299	+	0.0797626i
$638$	−3.87132	+	0.869165i	−0.153267	+	0.0344106i
$639$	3.04271			0.120368
$640$	11.1971			0.442603
$641$	−22.0702			−0.871721			−0.435861	−	0.900014i	$-0.643556\pi$
$641$	−22.0702			−0.871721			−0.435861	+	0.900014i	$0.643556\pi$
$642$		−	2.99139i		−	0.118061i
$643$		−	31.7057i		−	1.25035i	−0.780484	−	0.625176i	$-0.785027\pi$
$643$		−	31.7057i		−	1.25035i	0.780484	−	0.625176i	$-0.214973\pi$
$644$	−0.652643	+	3.57692i	−0.0257177	+	0.140950i
$645$		−	6.55058i		−	0.257929i
$646$			15.0733i			0.593052i
$647$			8.53648i			0.335604i	0.985821	+	0.167802i	$0.0536669\pi$
$647$			8.53648i			0.335604i	−0.985821	+	0.167802i	$0.946333\pi$
$648$		−	1.79251i		−	0.0704163i
$649$	2.43031	+	10.8248i	0.0953981	+	0.424909i
$650$		−	0.386724i		−	0.0151686i
$651$	2.57845	−	14.1316i	0.101057	−	0.553862i
$652$	2.12280			0.0831353
$653$	−13.4224			−0.525259			−0.262630	−	0.964897i	$-0.584590\pi$
$653$	−13.4224			−0.525259			−0.262630	+	0.964897i	$0.584590\pi$
$654$		−	4.23901i		−	0.165758i
$655$			9.19702i			0.359357i
$656$	7.47440			0.291826
$657$	9.23710			0.360374
$658$	−1.03081	+	5.64954i	−0.0401853	+	0.220242i
$659$			26.5905i			1.03582i	0.855436	+	0.517909i	$0.173290\pi$
$659$			26.5905i			1.03582i	−0.855436	+	0.517909i	$0.826710\pi$
$660$	5.74230	−	1.28923i	0.223519	−	0.0501831i
$661$		−	47.0053i		−	1.82829i	−0.405382	−	0.914147i	$-0.632861\pi$
$661$		−	47.0053i		−	1.82829i	0.405382	−	0.914147i	$-0.367139\pi$
$662$			8.83256i			0.343287i
$663$			5.21737i			0.202626i
$664$		−	11.7993i		−	0.457901i
$665$	−12.8940	−	2.35263i	−0.500007	−	0.0912311i
$666$		−	2.57845i		−	0.0999130i
$667$			1.95092i			0.0755399i
$668$	35.6575			1.37963
$669$	−12.6760			−0.490084
$670$	7.60845			0.293940
$671$	−26.0039	+	5.83824i	−1.00387	+	0.225383i
$672$	−2.31094	+	12.6655i	−0.0891466	+	0.488582i
$673$			15.6212i			0.602155i	0.953600	+	0.301077i	$0.0973463\pi$
$673$			15.6212i			0.602155i	−0.953600	+	0.301077i	$0.902654\pi$
$674$	−7.92264			−0.305169
$675$		−	1.00000i		−	0.0384900i
$676$	−21.8914			−0.841976
$677$	−36.8022			−1.41442			−0.707211	−	0.707003i	$-0.750047\pi$
$677$	−36.8022			−1.41442			−0.707211	+	0.707003i	$0.750047\pi$
$678$	4.49474			0.172619
$679$	−31.7641	−	5.79567i	−1.21899	−	0.222417i
$680$	11.4846			0.440414
$681$		−	22.8060i		−	0.873929i
$682$	8.34405	−	1.87335i	0.319510	−	0.0717345i
$683$	21.6534			0.828544			0.414272	−	0.910153i	$-0.364036\pi$
$683$	21.6534			0.828544			0.414272	+	0.910153i	$0.364036\pi$
$684$	8.79057			0.336116
$685$		−	12.7263i		−	0.486248i
$686$	7.53738	+	4.53273i	0.287779	+	0.173060i
$687$	−15.2326			−0.581159
$688$		−	17.6713i		−	0.673712i
$689$	−7.84464			−0.298857
$690$			0.367797i			0.0140018i
$691$			0.111456i			0.00423999i	0.999998	+	0.00212000i	$0.000674816\pi$
$691$			0.111456i			0.00423999i	−0.999998	+	0.00212000i	$0.999325\pi$
$692$	−24.9186			−0.947264
$693$	0.354213	+	8.76781i	0.0134554	+	0.333062i
$694$	12.7814			0.485174
$695$		−	10.6902i		−	0.405502i
$696$			4.51541i			0.171156i
$697$	17.7518			0.672398
$698$			2.77765i			0.105136i
$699$	19.5595			0.739808
$700$	−0.842700	+	4.61855i	−0.0318511	+	0.174565i
$701$			11.9236i			0.450349i	0.974318	+	0.225174i	$0.0722952\pi$
$701$			11.9236i			0.450349i	−0.974318	+	0.225174i	$0.927705\pi$
$702$	−0.386724			−0.0145960
$703$	26.8970			1.01444
$704$	9.98131	−	2.24094i	0.376185	−	0.0844587i
$705$		−	4.57057i		−	0.172138i
$706$	−15.2241			−0.572967
$707$	−2.92320	+	16.0211i	−0.109938	+	0.602534i
$708$	5.93566			0.223076
$709$	19.5862			0.735576			0.367788	−	0.929910i	$-0.380115\pi$
$709$	19.5862			0.735576			0.367788	+	0.929910i	$0.380115\pi$
$710$	−1.44499			−0.0542295
$711$		−	7.97625i		−	0.299133i
$712$	−2.02033			−0.0757151
$713$		−	4.20492i		−	0.157475i
$714$	−1.44499	+	7.91950i	−0.0540774	+	0.296380i
$715$	−0.591640	−	2.63520i	−0.0221261	−	0.0985511i
$716$	6.89625			0.257725
$717$	23.6204			0.882118
$718$	−3.96478			−0.147964
$719$		−	37.2055i		−	1.38753i	−0.720201	−	0.693765i	$-0.755950\pi$
$719$		−	37.2055i		−	1.38753i	0.720201	−	0.693765i	$-0.244050\pi$
$720$		−	2.69767i		−	0.100536i
$721$	−4.10762	−	0.749475i	−0.152976	−	0.0279119i
$722$		−	2.63160i		−	0.0979379i
$723$		−	27.7113i		−	1.03059i
$724$			8.17082i			0.303666i
$725$			2.51905i			0.0935551i
$726$	−4.72256	+	2.23313i	−0.175271	+	0.0828791i
$727$		−	5.74695i		−	0.213143i	−0.994305	−	0.106571i	$-0.966013\pi$
$727$		−	5.74695i		−	0.213143i	0.994305	−	0.106571i	$-0.0339872\pi$
$728$	3.79922	+	0.693205i	0.140809	+	0.0256919i
$729$	−1.00000			−0.0370370
$730$	−4.38672			−0.162360
$731$		−	41.9696i		−	1.55230i
$732$			14.2590i			0.527028i
$733$	−21.6027			−0.797913			−0.398956	−	0.916970i	$-0.630628\pi$
$733$	−21.6027			−0.797913			−0.398956	+	0.916970i	$0.630628\pi$
$734$	−4.52094			−0.166871
$735$	−6.54893	−	2.47214i	−0.241561	−	0.0911861i
$736$			3.76867i			0.138915i
$737$	51.8453	−	11.6400i	1.90975	−	0.428765i
$738$			1.31581i			0.0484355i
$739$		−	43.4396i		−	1.59795i	−0.601364	−	0.798975i	$-0.705376\pi$
$739$		−	43.4396i		−	1.59795i	0.601364	−	0.798975i	$-0.294624\pi$
$740$		−	9.63435i		−	0.354166i
$741$		−	4.03409i		−	0.148196i
$742$	−11.9074	−	2.17263i	−0.437136	−	0.0797598i
$743$		−	39.7439i		−	1.45806i	−0.684481	−	0.729030i	$-0.739971\pi$
$743$		−	39.7439i		−	1.45806i	0.684481	−	0.729030i	$-0.260029\pi$
$744$		−	9.73228i		−	0.356803i
$745$	−3.07364			−0.112609
$746$	1.59822			0.0585149
$747$	−6.58257			−0.240844
$748$	36.7909	−	8.26008i	1.34521	−	0.302018i
$749$	16.3948	+	2.99139i	0.599052	+	0.109303i
$750$			0.474903i			0.0173410i
$751$	−10.9222			−0.398556			−0.199278	−	0.979943i	$-0.563860\pi$
$751$	−10.9222			−0.398556			−0.199278	+	0.979943i	$0.563860\pi$
$752$		−	12.3299i		−	0.449625i
$753$	20.4289			0.744469
$754$	0.974177			0.0354774
$755$	−9.28384			−0.337874
$756$	4.61855	+	0.842700i	0.167975	+	0.0306487i
$757$	32.6738			1.18755			0.593774	−	0.804632i	$-0.297637\pi$
$757$	32.6738			1.18755			0.593774	+	0.804632i	$0.297637\pi$
$758$			7.72869i			0.280719i
$759$	0.562683	+	2.50623i	0.0204241	+	0.0909703i
$760$	−8.87993			−0.322109
$761$	−41.0691			−1.48876			−0.744378	−	0.667759i	$-0.767254\pi$
$761$	−41.0691			−1.48876			−0.744378	+	0.667759i	$0.767254\pi$
$762$		−	0.718285i		−	0.0260207i
$763$	23.2326	+	4.23901i	0.841075	+	0.153462i
$764$	25.1525			0.909985
$765$		−	6.40701i		−	0.231646i
$766$	13.5883			0.490964
$767$		−	2.72394i		−	0.0983558i
$768$		−	0.851266i		−	0.0307174i
$769$	37.8727			1.36572			0.682862	−	0.730547i	$-0.260735\pi$
$769$	37.8727			1.36572			0.682862	+	0.730547i	$0.260735\pi$
$770$	−0.168217	−	4.16386i	−0.00606211	−	0.150055i
$771$	20.2883			0.730665
$772$			1.68540i			0.0606588i
$773$		−	14.2694i		−	0.513234i	−0.966513	−	0.256617i	$-0.917392\pi$
$773$		−	14.2694i		−	0.513234i	0.966513	−	0.256617i	$-0.0826079\pi$
$774$	3.11089			0.111819
$775$		−	5.42943i		−	0.195031i
$776$	−21.8756			−0.785287
$777$	14.1316	+	2.57845i	0.506969	+	0.0925014i
$778$		−	13.5955i		−	0.487421i
$779$	−13.7258			−0.491777
$780$	−1.44499			−0.0517389
$781$	−9.84640	+	2.21066i	−0.352332	+	0.0791035i
$782$			2.35648i			0.0842674i
$783$	2.51905			0.0900234
$784$	−17.6669	−	6.66900i	−0.630959	−	0.238179i
$785$	−22.6971			−0.810094
$786$	−4.36769			−0.155790
$787$	−55.7594			−1.98761			−0.993805	−	0.111142i	$-0.964549\pi$
$787$	−55.7594			−1.98761			−0.993805	+	0.111142i	$0.964549\pi$
$788$			25.0321i			0.891733i
$789$	25.6361			0.912670
$790$			3.78794i			0.134769i
$791$	−4.49474	+	24.6341i	−0.159814	+	0.875889i
$792$	1.30233	+	5.80067i	0.0462763	+	0.206118i
$793$	6.54362			0.232371
$794$	−3.80202			−0.134929
$795$	9.63333			0.341659
$796$			5.87335i			0.208176i
$797$			37.1400i			1.31557i	0.753207	+	0.657783i	$0.228506\pi$
$797$			37.1400i			1.31557i	−0.753207	+	0.657783i	$0.771494\pi$
$798$	1.11727	−	6.12338i	0.0395510	−	0.216765i
$799$		−	29.2837i		−	1.03598i
$800$			4.86614i			0.172044i
$801$			1.12710i			0.0398241i
$802$		−	14.1096i		−	0.498229i
$803$	−29.8919	+	6.71114i	−1.05486	+	0.236831i
$804$		−	28.4289i		−	1.00261i
$805$	−2.01577	−	0.367797i	−0.0710465	−	0.0129631i
$806$	−2.09969			−0.0739585
$807$	15.5197			0.546319
$808$			11.0335i			0.388158i
$809$		−	20.4773i		−	0.719944i	−0.932963	−	0.359972i	$-0.882786\pi$
$809$		−	20.4773i		−	0.719944i	0.932963	−	0.359972i	$-0.117214\pi$
$810$	0.474903			0.0166864
$811$	11.2321			0.394413			0.197206	−	0.980362i	$-0.436813\pi$
$811$	11.2321			0.394413			0.197206	+	0.980362i	$0.436813\pi$
$812$	−11.6343	−	2.12280i	−0.408286	−	0.0744957i
$813$		−	1.42566i		−	0.0500002i
$814$	1.87335	+	8.34405i	0.0656611	+	0.292459i
$815$			1.19630i			0.0419047i
$816$		−	17.2840i		−	0.605060i
$817$			32.4511i			1.13532i
$818$			12.1217i			0.423824i
$819$	0.386724	−	2.11950i	0.0135132	−	0.0740615i
$820$			4.91649i			0.171691i
$821$		−	36.1005i		−	1.25991i	−0.776630	−	0.629957i	$-0.783072\pi$
$821$		−	36.1005i		−	1.25991i	0.776630	−	0.629957i	$-0.216928\pi$
$822$	6.04377			0.210801
$823$	−7.42012			−0.258649			−0.129325	−	0.991602i	$-0.541281\pi$
$823$	−7.42012			−0.258649			−0.129325	+	0.991602i	$0.541281\pi$
$824$	−2.82887			−0.0985483
$825$	0.726543	+	3.23607i	0.0252950	+	0.112665i
$826$	0.754415	−	4.13469i	0.0262495	−	0.143864i
$827$			8.28729i			0.288177i	0.989565	+	0.144089i	$0.0460251\pi$
$827$			8.28729i			0.288177i	−0.989565	+	0.144089i	$0.953975\pi$
$828$	1.37427			0.0477591
$829$			39.1704i			1.36044i	0.733006	+	0.680222i	$0.238117\pi$
$829$			39.1704i			1.36044i	−0.733006	+	0.680222i	$0.761883\pi$
$830$	3.12608			0.108508
$831$	3.29785			0.114401
$832$	−2.51169			−0.0870773
$833$	−41.9591	−	15.8390i	−1.45380	−	0.548789i
$834$	5.07680			0.175795
$835$			20.0947i			0.695407i
$836$	−28.4469	+	6.38672i	−0.983856	+	0.220889i
$837$	−5.42943			−0.187669
$838$	4.65220			0.160707
$839$		−	2.69823i		−	0.0931534i	−0.998915	−	0.0465767i	$-0.985169\pi$
$839$		−	2.69823i		−	0.0931534i	0.998915	−	0.0465767i	$-0.0148312\pi$
$840$	−4.66550	−	0.851266i	−0.160975	−	0.0293715i
$841$	22.6544			0.781186
$842$			1.52181i			0.0524450i
$843$	−6.26696			−0.215846
$844$			47.0929i			1.62100i
$845$		−	12.3369i		−	0.424402i
$846$	2.17058			0.0746260
$847$	−7.51645	−	28.1159i	−0.258268	−	0.966073i
$848$	25.9875			0.892415
$849$			25.9472i			0.890504i
$850$			3.04271i			0.104364i
$851$	4.20492			0.144143
$852$			5.39918i			0.184973i
$853$	−13.5735			−0.464748			−0.232374	−	0.972627i	$-0.574649\pi$
$853$	−13.5735			−0.464748			−0.232374	+	0.972627i	$0.574649\pi$
$854$	9.93261	+	1.81230i	0.339887	+	0.0620157i
$855$			4.95392i			0.169421i
$856$	11.2909			0.385915
$857$	−43.4406			−1.48390			−0.741951	−	0.670454i	$-0.766099\pi$
$857$	−43.4406			−1.48390			−0.741951	+	0.670454i	$0.766099\pi$
$858$	1.25147	−	0.280972i	0.0427244	−	0.00959222i
$859$		−	22.6431i		−	0.772572i	−0.922379	−	0.386286i	$-0.873758\pi$
$859$		−	22.6431i		−	0.772572i	0.922379	−	0.386286i	$-0.126242\pi$
$860$	11.6238			0.396368
$861$	−7.21149	−	1.31581i	−0.245767	−	0.0448426i
$862$	6.27142			0.213606
$863$	−15.8723			−0.540301			−0.270150	−	0.962818i	$-0.587073\pi$
$863$	−15.8723			−0.540301			−0.270150	+	0.962818i	$0.587073\pi$
$864$	4.86614			0.165549
$865$		−	14.0429i		−	0.477472i
$866$	8.60603			0.292445
$867$		−	24.0497i		−	0.816772i
$868$	25.0761	+	4.57538i	0.851138	+	0.155298i
$869$	5.79508	+	25.8117i	0.196585	+	0.875601i
$870$	−1.19630			−0.0405585
$871$	−13.0463			−0.442058
$872$	16.0000			0.541828
$873$			12.2039i			0.413039i
$874$		−	1.82204i		−	0.0616313i
$875$	−2.60278	−	0.474903i	−0.0879900	−	0.0160546i
$876$			16.3909i			0.553798i
$877$		−	2.06252i		−	0.0696462i	−0.999393	−	0.0348231i	$-0.988913\pi$
$877$		−	2.06252i		−	0.0696462i	0.999393	−	0.0348231i	$-0.0110868\pi$
$878$		−	13.7317i		−	0.463421i
$879$			25.6554i			0.865337i
$880$	1.95997	+	8.72984i	0.0660706	+	0.294283i
$881$			23.7891i			0.801475i	0.916193	+	0.400737i	$0.131246\pi$
$881$			23.7891i			0.801475i	−0.916193	+	0.400737i	$0.868754\pi$
$882$	1.17402	−	3.11011i	0.0395315	−	0.104723i
$883$	−24.7263			−0.832107			−0.416054	−	0.909340i	$-0.636587\pi$
$883$	−24.7263			−0.832107			−0.416054	+	0.909340i	$0.636587\pi$
$884$	−9.25806			−0.311382
$885$			3.34504i			0.112442i
$886$		−	3.84979i		−	0.129336i
$887$	−51.4590			−1.72783			−0.863913	−	0.503642i	$-0.831993\pi$
$887$	−51.4590			−1.72783			−0.863913	+	0.503642i	$0.831993\pi$
$888$	9.73228			0.326594
$889$	3.93668	+	0.718285i	0.132032	+	0.0240905i
$890$		−	0.535262i		−	0.0179420i
$891$	3.23607	−	0.726543i	0.108412	−	0.0243401i
$892$		−	22.4932i		−	0.753128i
$893$			22.6422i			0.757694i
$894$		−	1.45968i		−	0.0488189i
$895$			3.88638i			0.129907i
$896$	−29.1435	−	5.31752i	−0.973617	−	0.177646i
$897$		−	0.630667i		−	0.0210573i
$898$			5.04001i			0.168187i
$899$	13.6770			0.456153
$900$	1.77447			0.0591489
$901$	61.7208			2.05622
$902$	−0.955990	−	4.25804i	−0.0318310	−	0.141777i
$903$	−3.11089	+	17.0497i	−0.103524	+	0.567380i
$904$			16.9652i			0.564256i
$905$	−4.60466			−0.153064
$906$		−	4.40892i		−	0.146477i
$907$	16.6220			0.551925			0.275963	−	0.961168i	$-0.411003\pi$
$907$	16.6220			0.551925			0.275963	+	0.961168i	$0.411003\pi$
$908$	40.4686			1.34300
$909$	6.15537			0.204161
$910$	−0.183657	+	1.00656i	−0.00608815	+	0.0333671i
$911$	33.6402			1.11455			0.557275	−	0.830328i	$-0.311847\pi$
$911$	33.6402			1.11455			0.557275	+	0.830328i	$0.311847\pi$
$912$			13.3640i			0.442528i
$913$	21.3016	−	4.78252i	0.704981	−	0.158278i
$914$	−18.6030			−0.615332
$915$	−8.03565			−0.265650
$916$		−	27.0297i		−	0.893086i
$917$	4.36769	−	23.9378i	0.144234	−	0.790497i
$918$	3.04271			0.100424
$919$		−	16.0146i		−	0.528271i	−0.964486	−	0.264136i	$-0.914913\pi$
$919$		−	16.0146i		−	0.528271i	0.964486	−	0.264136i	$-0.0850867\pi$
$920$	−1.38824			−0.0457688
$921$		−	17.7954i		−	0.586377i
$922$			3.18825i			0.105000i
$923$	2.47775			0.0815560
$924$	−15.5582	+	0.628539i	−0.511827	+	0.0206774i
$925$	5.42943			0.178519
$926$			9.22091i			0.303018i
$927$			1.57816i			0.0518337i
$928$	−12.2580			−0.402390
$929$			1.93181i			0.0633808i	0.999498	+	0.0316904i	$0.0100891\pi$
$929$			1.93181i			0.0633808i	−0.999498	+	0.0316904i	$0.989911\pi$
$930$	2.57845			0.0845508
$931$	32.4429	+	12.2468i	1.06327	+	0.401372i
$932$			34.7077i			1.13689i
$933$	−27.2195			−0.891128
$934$	−10.0924			−0.330233
$935$	4.65496	+	20.7335i	0.152234	+	0.678058i
$936$		−	1.45968i		−	0.0477111i
$937$	44.3331			1.44830			0.724150	−	0.689643i	$-0.242232\pi$
$937$	44.3331			1.44830			0.724150	+	0.689643i	$0.242232\pi$
$938$	−19.8031	−	3.61328i	−0.646595	−	0.117978i
$939$	−10.4581			−0.341287
$940$	8.11033			0.264530
$941$	0.677413			0.0220830			0.0110415	−	0.999939i	$-0.496485\pi$
$941$	0.677413			0.0220830			0.0110415	+	0.999939i	$0.496485\pi$
$942$		−	10.7789i		−	0.351196i
$943$	−2.14581			−0.0698771
$944$			9.02380i			0.293700i
$945$	−0.474903	+	2.60278i	−0.0154486	+	0.0846685i
$946$	−10.0671	+	2.26019i	−0.327308	+	0.0734853i
$947$	−49.5219			−1.60924			−0.804622	−	0.593787i	$-0.797632\pi$
$947$	−49.5219			−1.60924			−0.804622	+	0.593787i	$0.797632\pi$
$948$	14.1536			0.459687
$949$	7.52198			0.244174
$950$		−	2.35263i		−	0.0763294i
$951$		−	11.7821i		−	0.382060i
$952$	−29.8919	−	5.45407i	−0.968801	−	0.176767i
$953$		−	32.2848i		−	1.04581i	−0.852392	−	0.522903i	$-0.824849\pi$
$953$		−	32.2848i		−	1.04581i	0.852392	−	0.522903i	$-0.175151\pi$
$954$			4.57489i			0.148118i
$955$			14.1747i			0.458681i
$956$			41.9135i			1.35558i
$957$	−8.15181	+	1.83020i	−0.263511	+	0.0591618i
$958$			3.23424i			0.104494i
$959$	−6.04377	+	33.1239i	−0.195164	+	1.06963i
$960$	3.08439			0.0995484
$961$	1.52129			0.0490738
$962$		−	2.09969i		−	0.0676968i
$963$		−	6.29895i		−	0.202981i
$964$	49.1728			1.58375
$965$	−0.949806			−0.0305753
$966$	0.174668	−	0.957294i	0.00561984	−	0.0308004i
$967$			16.1326i			0.518790i	0.965771	+	0.259395i	$0.0835232\pi$
$967$			16.1326i			0.518790i	−0.965771	+	0.259395i	$0.916477\pi$
$968$	−8.42887	−	17.8252i	−0.270914	−	0.572922i
$969$			31.7398i			1.01963i
$970$		−	5.79567i		−	0.186088i
$971$		−	11.9237i		−	0.382648i	−0.981527	−	0.191324i	$-0.938722\pi$
$971$		−	11.9237i		−	0.382648i	0.981527	−	0.191324i	$-0.0612782\pi$
$972$		−	1.77447i		−	0.0569161i
$973$	−5.07680	+	27.8242i	−0.162755	+	0.892003i
$974$		−	2.49932i		−	0.0800835i
$975$		−	0.814323i		−	0.0260792i
$976$	−21.6775			−0.693881
$977$	−10.6478			−0.340654			−0.170327	−	0.985388i	$-0.554482\pi$
$977$	−10.6478			−0.340654			−0.170327	+	0.985388i	$0.554482\pi$
$978$	−0.568128			−0.0181667
$979$	−0.818885	−	3.64737i	−0.0261717	−	0.116570i
$980$	4.38672	−	11.6209i	0.140129	−	0.371215i
$981$		−	8.92605i		−	0.284987i
$982$	−20.2038			−0.644729
$983$		−	59.3412i		−	1.89269i	−0.323157	−	0.946345i	$-0.604744\pi$
$983$		−	59.3412i		−	1.89269i	0.323157	−	0.946345i	$-0.395256\pi$
$984$	−4.96647			−0.158325
$985$	−14.1068			−0.449481
$986$	−7.66472			−0.244094
$987$	−2.17058	+	11.8962i	−0.0690902	+	0.378660i
$988$	7.15837			0.227738
$989$			5.07321i			0.161319i
$990$	−1.53682	+	0.345037i	−0.0488433	+	0.0109660i
$991$	39.7659			1.26320			0.631602	−	0.775293i	$-0.282398\pi$
$991$	39.7659			1.26320			0.631602	+	0.775293i	$0.282398\pi$
$992$	26.4204			0.838848
$993$			18.5987i			0.590211i
$994$	3.76099	+	0.686230i	0.119291	+	0.0217659i
$995$	−3.30993			−0.104932
$996$		−	11.6806i		−	0.370112i
$997$	−7.48964			−0.237199			−0.118600	−	0.992942i	$-0.537841\pi$
$997$	−7.48964			−0.237199			−0.118600	+	0.992942i	$0.537841\pi$
$998$		−	3.48199i		−	0.110221i
$999$		−	5.42943i		−	0.171780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.i.c.76.7	✓	16
7.6	odd	2	inner	1155.2.i.c.76.8	yes	16
11.10	odd	2	inner	1155.2.i.c.76.9	yes	16
77.76	even	2	inner	1155.2.i.c.76.10	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.i.c.76.7	✓	16	1.1	even	1	trivial
1155.2.i.c.76.8	yes	16	7.6	odd	2	inner
1155.2.i.c.76.9	yes	16	11.10	odd	2	inner
1155.2.i.c.76.10	yes	16	77.76	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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.474903i q^{2} -1.00000i q^{3} +1.77447 q^{4} +1.00000i q^{5} -0.474903 q^{6} +(0.474903 - 2.60278i) q^{7} -1.79251i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.474903i q^{2} -1.00000i q^{3} +1.77447 q^{4} +1.00000i q^{5} -0.474903 q^{6} +(0.474903 - 2.60278i) q^{7} -1.79251i q^{8} -1.00000 q^{9} +0.474903 q^{10} +(3.23607 - 0.726543i) q^{11} -1.77447i q^{12} -0.814323 q^{13} +(-1.23607 - 0.225533i) q^{14} +1.00000 q^{15} +2.69767 q^{16} +6.40701 q^{17} +0.474903i q^{18} -4.95392 q^{19} +1.77447i q^{20} +(-2.60278 - 0.474903i) q^{21} +(-0.345037 - 1.53682i) q^{22} -0.774467 q^{23} -1.79251 q^{24} -1.00000 q^{25} +0.386724i q^{26} +1.00000i q^{27} +(0.842700 - 4.61855i) q^{28} -2.51905i q^{29} -0.474903i q^{30} +5.42943i q^{31} -4.86614i q^{32} +(-0.726543 - 3.23607i) q^{33} -3.04271i q^{34} +(2.60278 + 0.474903i) q^{35} -1.77447 q^{36} -5.42943 q^{37} +2.35263i q^{38} +0.814323i q^{39} +1.79251 q^{40} +2.77069 q^{41} +(-0.225533 + 1.23607i) q^{42} -6.55058i q^{43} +(5.74230 - 1.28923i) q^{44} -1.00000i q^{45} +0.367797i q^{46} -4.57057i q^{47} -2.69767i q^{48} +(-6.54893 - 2.47214i) q^{49} +0.474903i q^{50} -6.40701i q^{51} -1.44499 q^{52} +9.63333 q^{53} +0.474903 q^{54} +(0.726543 + 3.23607i) q^{55} +(-4.66550 - 0.851266i) q^{56} +4.95392i q^{57} -1.19630 q^{58} +3.34504i q^{59} +1.77447 q^{60} -8.03565 q^{61} +2.57845 q^{62} +(-0.474903 + 2.60278i) q^{63} +3.08439 q^{64} -0.814323i q^{65} +(-1.53682 + 0.345037i) q^{66} +16.0211 q^{67} +11.3690 q^{68} +0.774467i q^{69} +(0.225533 - 1.23607i) q^{70} -3.04271 q^{71} +1.79251i q^{72} -9.23710 q^{73} +2.57845i q^{74} +1.00000i q^{75} -8.79057 q^{76} +(-0.354213 - 8.76781i) q^{77} +0.386724 q^{78} +7.97625i q^{79} +2.69767i q^{80} +1.00000 q^{81} -1.31581i q^{82} +6.58257 q^{83} +(-4.61855 - 0.842700i) q^{84} +6.40701i q^{85} -3.11089 q^{86} -2.51905 q^{87} +(-1.30233 - 5.80067i) q^{88} -1.12710i q^{89} -0.474903 q^{90} +(-0.386724 + 2.11950i) q^{91} -1.37427 q^{92} +5.42943 q^{93} -2.17058 q^{94} -4.95392i q^{95} -4.86614 q^{96} -12.2039i q^{97} +(-1.17402 + 3.11011i) q^{98} +(-3.23607 + 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) \) 16 * q - 24 * q^4 - 16 * q^9	\( 16 q - 24 q^{4} - 16 q^{9} + 16 q^{11} + 16 q^{14} + 16 q^{15} + 24 q^{16} + 40 q^{23} - 16 q^{25} + 24 q^{36} - 40 q^{37} - 56 q^{42} - 24 q^{44} + 8 q^{53} + 8 q^{56} + 72 q^{58} - 24 q^{60} + 8 q^{64} + 80 q^{67} + 56 q^{70} - 24 q^{71} - 16 q^{78} + 16 q^{81} - 8 q^{86} - 40 q^{88} + 16 q^{91} - 160 q^{92} + 40 q^{93} - 16 q^{99}+O(q^{100}) \) 16 * q - 24 * q^4 - 16 * q^9 + 16 * q^11 + 16 * q^14 + 16 * q^15 + 24 * q^16 + 40 * q^23 - 16 * q^25 + 24 * q^36 - 40 * q^37 - 56 * q^42 - 24 * q^44 + 8 * q^53 + 8 * q^56 + 72 * q^58 - 24 * q^60 + 8 * q^64 + 80 * q^67 + 56 * q^70 - 24 * q^71 - 16 * q^78 + 16 * q^81 - 8 * q^86 - 40 * q^88 + 16 * q^91 - 160 * q^92 + 40 * q^93 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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