LMFDB - Embedded newform 108.2.i.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,2,Mod(13,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, 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:	$0.862384341830$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 $ x^18 - 6x^17 + 24x^16 - 66x^15 + 153x^14 - 315x^13 + 651x^12 - 1350x^11 + 2700x^10 - 4941x^9 + 8100x^8 - 12150x^7 + 17577x^6 - 25515x^5 + 37179x^4 - 48114x^3 + 52488x^2 - 39366*x + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.1
Root			$1.68668 - 0.393823i$ of defining polynomial
Character	$\chi$	$=$	108.49
Dual form			108.2.i.a.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54522 - 0.782494i) q^{3} +(2.29878 - 0.836687i) q^{5} +(-0.775345 - 4.39720i) q^{7} +(1.77541 + 2.41825i) q^{9} +O(q^{10})$	\(q+(-1.54522 - 0.782494i) q^{3} +(2.29878 - 0.836687i) q^{5} +(-0.775345 - 4.39720i) q^{7} +(1.77541 + 2.41825i) q^{9} +(2.73892 + 0.996887i) q^{11} +(-2.01596 - 1.69159i) q^{13} +(-4.20682 - 0.505915i) q^{15} +(-1.67030 + 2.89305i) q^{17} +(1.02319 + 1.77222i) q^{19} +(-2.24270 + 7.40135i) q^{21} +(-1.60711 + 9.11438i) q^{23} +(0.754121 - 0.632782i) q^{25} +(-0.851129 - 5.12597i) q^{27} +(5.30671 - 4.45286i) q^{29} +(-0.380324 + 2.15692i) q^{31} +(-3.45218 - 3.68360i) q^{33} +(-5.46143 - 9.45948i) q^{35} +(0.708571 - 1.22728i) q^{37} +(1.79144 + 4.19136i) q^{39} +(3.13541 + 2.63092i) q^{41} +(4.42467 + 1.61045i) q^{43} +(6.10459 + 4.07356i) q^{45} +(-1.03917 - 5.89344i) q^{47} +(-12.1564 + 4.42456i) q^{49} +(4.84477 - 3.16339i) q^{51} +1.97011 q^{53} +7.13026 q^{55} +(-0.194305 - 3.53911i) q^{57} +(-6.20572 + 2.25870i) q^{59} +(-1.25433 - 7.11368i) q^{61} +(9.25698 - 9.68180i) q^{63} +(-6.04958 - 2.20187i) q^{65} +(2.37884 + 1.99608i) q^{67} +(9.61529 - 12.8262i) q^{69} +(-6.60947 + 11.4479i) q^{71} +(6.40266 + 11.0897i) q^{73} +(-1.66043 + 0.387693i) q^{75} +(2.25990 - 12.8165i) q^{77} +(1.57726 - 1.32348i) q^{79} +(-2.69586 + 8.58675i) q^{81} +(-1.20111 + 1.00785i) q^{83} +(-1.41908 + 8.04800i) q^{85} +(-11.6844 + 2.72818i) q^{87} +(-6.88694 - 11.9285i) q^{89} +(-5.87520 + 10.1761i) q^{91} +(2.27546 - 3.03532i) q^{93} +(3.83488 + 3.21785i) q^{95} +(-13.9332 - 5.07127i) q^{97} +(2.45198 + 8.39328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 18 * q + 3 * q^5 + 6 * q^9	$ 18 q + 3 q^{5} + 6 q^{9} + 3 q^{11} - 9 q^{15} - 12 q^{17} - 30 q^{21} - 30 q^{23} + 9 q^{25} - 27 q^{27} - 24 q^{29} + 9 q^{31} - 18 q^{33} - 21 q^{35} + 3 q^{39} + 21 q^{41} - 9 q^{43} + 45 q^{45} + 45 q^{47} - 18 q^{49} + 63 q^{51} + 66 q^{53} + 54 q^{57} + 60 q^{59} - 18 q^{61} + 57 q^{63} + 33 q^{65} - 27 q^{67} - 9 q^{69} - 12 q^{71} + 9 q^{73} - 33 q^{75} - 75 q^{77} - 36 q^{79} - 54 q^{81} - 45 q^{83} - 36 q^{85} - 63 q^{87} - 48 q^{89} + 9 q^{91} - 33 q^{93} + 6 q^{95} - 27 q^{97} + 27 q^{99}+O(q^{100}) $ 18 * q + 3 * q^5 + 6 * q^9 + 3 * q^11 - 9 * q^15 - 12 * q^17 - 30 * q^21 - 30 * q^23 + 9 * q^25 - 27 * q^27 - 24 * q^29 + 9 * q^31 - 18 * q^33 - 21 * q^35 + 3 * q^39 + 21 * q^41 - 9 * q^43 + 45 * q^45 + 45 * q^47 - 18 * q^49 + 63 * q^51 + 66 * q^53 + 54 * q^57 + 60 * q^59 - 18 * q^61 + 57 * q^63 + 33 * q^65 - 27 * q^67 - 9 * q^69 - 12 * q^71 + 9 * q^73 - 33 * q^75 - 75 * q^77 - 36 * q^79 - 54 * q^81 - 45 * q^83 - 36 * q^85 - 63 * q^87 - 48 * q^89 + 9 * q^91 - 33 * q^93 + 6 * q^95 - 27 * q^97 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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			0
$2$		0			0
$3$	−1.54522	−	0.782494i	−0.892133	−	0.451773i
$3$	−1.54522	−	0.782494i	−0.892133	−	0.451773i
$4$		0			0
$5$	2.29878	−	0.836687i	1.02805	−	0.374178i	0.227709	−	0.973729i	$-0.426876\pi$
$5$	2.29878	−	0.836687i	1.02805	−	0.374178i	0.800336	+	0.599551i	$0.204654\pi$
$6$		0			0
$7$	−0.775345	−	4.39720i	−0.293053	−	1.66199i	−0.675012	−	0.737807i	$-0.735862\pi$
$7$	−0.775345	−	4.39720i	−0.293053	−	1.66199i	0.381959	−	0.924179i	$-0.375250\pi$
$8$		0			0
$9$	1.77541	+	2.41825i	0.591802	+	0.806083i
$10$		0			0
$11$	2.73892	+	0.996887i	0.825816	+	0.300573i	0.720141	−	0.693828i	$-0.244077\pi$
$11$	2.73892	+	0.996887i	0.825816	+	0.300573i	0.105676	+	0.994401i	$0.466299\pi$
$12$		0			0
$13$	−2.01596	−	1.69159i	−0.559127	−	0.469163i	0.318891	−	0.947791i	$-0.396690\pi$
$13$	−2.01596	−	1.69159i	−0.559127	−	0.469163i	−0.878018	+	0.478628i	$0.841134\pi$
$14$		0			0
$15$	−4.20682	−	0.505915i	−1.08620	−	0.130627i
$16$		0			0
$17$	−1.67030	+	2.89305i	−0.405108	+	0.701667i	−0.994334	−	0.106301i	$-0.966099\pi$
$17$	−1.67030	+	2.89305i	−0.405108	+	0.701667i	0.589226	+	0.807968i	$0.299433\pi$
$18$		0			0
$19$	1.02319	+	1.77222i	0.234736	+	0.406575i	0.959196	−	0.282742i	$-0.0912441\pi$
$19$	1.02319	+	1.77222i	0.234736	+	0.406575i	−0.724460	+	0.689317i	$0.757911\pi$
$20$		0			0
$21$	−2.24270	+	7.40135i	−0.489398	+	1.61511i
$22$		0			0
$23$	−1.60711	+	9.11438i	−0.335106	+	1.90048i	0.0910783	+	0.995844i	$0.470969\pi$
$23$	−1.60711	+	9.11438i	−0.335106	+	1.90048i	−0.426184	+	0.904636i	$0.640142\pi$
$24$		0			0
$25$	0.754121	−	0.632782i	0.150824	−	0.126556i
$26$		0			0
$27$	−0.851129	−	5.12597i	−0.163800	−	0.986494i
$28$		0			0
$29$	5.30671	−	4.45286i	0.985431	−	0.826875i	0.000531132	−	1.00000i	$-0.499831\pi$
$29$	5.30671	−	4.45286i	0.985431	−	0.826875i	0.984900	+	0.173125i	$0.0553865\pi$
$30$		0			0
$31$	−0.380324	+	2.15692i	−0.0683082	+	0.387395i	0.931417	+	0.363954i	$0.118573\pi$
$31$	−0.380324	+	2.15692i	−0.0683082	+	0.387395i	−0.999725	+	0.0234413i	$0.992538\pi$
$32$		0			0
$33$	−3.45218	−	3.68360i	−0.600947	−	0.641232i
$34$		0			0
$35$	−5.46143	−	9.45948i	−0.923151	−	1.59894i
$36$		0			0
$37$	0.708571	−	1.22728i	0.116488	−	0.201764i	−0.801885	−	0.597478i	$-0.796170\pi$
$37$	0.708571	−	1.22728i	0.116488	−	0.201764i	0.918374	+	0.395714i	$0.129503\pi$
$38$		0			0
$39$	1.79144	+	4.19136i	0.286860	+	0.671154i
$40$		0			0
$41$	3.13541	+	2.63092i	0.489669	+	0.410881i	0.853908	−	0.520424i	$-0.174226\pi$
$41$	3.13541	+	2.63092i	0.489669	+	0.410881i	−0.364238	+	0.931306i	$0.618671\pi$
$42$		0			0
$43$	4.42467	+	1.61045i	0.674755	+	0.245591i	0.656594	−	0.754244i	$-0.271997\pi$
$43$	4.42467	+	1.61045i	0.674755	+	0.245591i	0.0181613	+	0.999835i	$0.494219\pi$
$44$		0			0
$45$	6.10459	+	4.07356i	0.910018	+	0.607251i
$46$		0			0
$47$	−1.03917	−	5.89344i	−0.151579	−	0.859647i	−0.961847	−	0.273588i	$-0.911790\pi$
$47$	−1.03917	−	5.89344i	−0.151579	−	0.859647i	0.810268	−	0.586059i	$-0.199321\pi$
$48$		0			0
$49$	−12.1564	+	4.42456i	−1.73663	+	0.632080i
$50$		0			0
$51$	4.84477	−	3.16339i	0.678404	−	0.442964i
$52$		0			0
$53$	1.97011			0.270616			0.135308	−	0.990804i	$-0.456798\pi$
$53$	1.97011			0.270616			0.135308	+	0.990804i	$0.456798\pi$
$54$		0			0
$55$	7.13026			0.961445
$56$		0			0
$57$	−0.194305	−	3.53911i	−0.0257363	−	0.468766i
$58$		0			0
$59$	−6.20572	+	2.25870i	−0.807916	+	0.294057i	−0.712763	−	0.701405i	$-0.752556\pi$
$59$	−6.20572	+	2.25870i	−0.807916	+	0.294057i	−0.0951531	+	0.995463i	$0.530334\pi$
$60$		0			0
$61$	−1.25433	−	7.11368i	−0.160601	−	0.910814i	−0.953485	−	0.301441i	$-0.902532\pi$
$61$	−1.25433	−	7.11368i	−0.160601	−	0.910814i	0.792884	−	0.609373i	$-0.208579\pi$
$62$		0			0
$63$	9.25698	−	9.68180i	1.16627	−	1.21979i
$64$		0			0
$65$	−6.04958	−	2.20187i	−0.750358	−	0.273108i
$66$		0			0
$67$	2.37884	+	1.99608i	0.290621	+	0.243860i	0.776428	−	0.630206i	$-0.217030\pi$
$67$	2.37884	+	1.99608i	0.290621	+	0.243860i	−0.485807	+	0.874066i	$0.661474\pi$
$68$		0			0
$69$	9.61529	−	12.8262i	1.15754	−	1.54409i
$70$		0			0
$71$	−6.60947	+	11.4479i	−0.784400	+	1.35862i	0.144958	+	0.989438i	$0.453695\pi$
$71$	−6.60947	+	11.4479i	−0.784400	+	1.35862i	−0.929357	+	0.369182i	$0.879638\pi$
$72$		0			0
$73$	6.40266	+	11.0897i	0.749374	+	1.29795i	0.948123	+	0.317904i	$0.102979\pi$
$73$	6.40266	+	11.0897i	0.749374	+	1.29795i	−0.198749	+	0.980051i	$0.563688\pi$
$74$		0			0
$75$	−1.66043	+	0.387693i	−0.191730	+	0.0447669i
$76$		0			0
$77$	2.25990	−	12.8165i	0.257540	−	1.46058i
$78$		0			0
$79$	1.57726	−	1.32348i	0.177456	−	0.148903i	−0.549733	−	0.835340i	$-0.685271\pi$
$79$	1.57726	−	1.32348i	0.177456	−	0.148903i	0.727189	+	0.686437i	$0.240826\pi$
$80$		0			0
$81$	−2.69586	+	8.58675i	−0.299540	+	0.954084i
$82$		0			0
$83$	−1.20111	+	1.00785i	−0.131839	+	0.110626i	−0.706323	−	0.707890i	$-0.749647\pi$
$83$	−1.20111	+	1.00785i	−0.131839	+	0.110626i	0.574484	+	0.818516i	$0.305203\pi$
$84$		0			0
$85$	−1.41908	+	8.04800i	−0.153921	+	0.872928i
$86$		0			0
$87$	−11.6844	+	2.72818i	−1.25270	+	0.292491i
$88$		0			0
$89$	−6.88694	−	11.9285i	−0.730014	−	1.26442i	−0.956877	−	0.290495i	$-0.906180\pi$
$89$	−6.88694	−	11.9285i	−0.730014	−	1.26442i	0.226862	−	0.973927i	$-0.427153\pi$
$90$		0			0
$91$	−5.87520	+	10.1761i	−0.615889	+	1.06675i
$92$		0			0
$93$	2.27546	−	3.03532i	0.235955	−	0.314748i
$94$		0			0
$95$	3.83488	+	3.21785i	0.393451	+	0.330144i
$96$		0			0
$97$	−13.9332	−	5.07127i	−1.41470	−	0.514909i	−0.482195	−	0.876064i	$-0.660160\pi$
$97$	−13.9332	−	5.07127i	−1.41470	−	0.514909i	−0.932506	+	0.361155i	$0.882383\pi$
$98$		0			0
$99$	2.45198	+	8.39328i	0.246434	+	0.843556i
$100$		0			0
$101$	0.515693	+	2.92464i	0.0513134	+	0.291013i	0.999656	−	0.0262361i	$-0.00835216\pi$
$101$	0.515693	+	2.92464i	0.0513134	+	0.291013i	−0.948342	+	0.317249i	$0.897241\pi$
$102$		0			0
$103$	10.5040	−	3.82316i	1.03499	−	0.376707i	0.232013	−	0.972713i	$-0.425469\pi$
$103$	10.5040	−	3.82316i	1.03499	−	0.376707i	0.802980	+	0.596006i	$0.203247\pi$
$104$		0			0
$105$	1.03713	+	18.8905i	0.101214	+	1.84352i
$106$		0			0
$107$	4.88974			0.472709			0.236355	−	0.971667i	$-0.424047\pi$
$107$	4.88974			0.472709			0.236355	+	0.971667i	$0.424047\pi$
$108$		0			0
$109$	−3.68231			−0.352701			−0.176351	−	0.984327i	$-0.556429\pi$
$109$	−3.68231			−0.352701			−0.176351	+	0.984327i	$0.556429\pi$
$110$		0			0
$111$	−2.05524	+	1.34197i	−0.195074	+	0.127374i
$112$		0			0
$113$	−6.55548	+	2.38600i	−0.616688	+	0.224456i	−0.631427	−	0.775435i	$-0.717530\pi$
$113$	−6.55548	+	2.38600i	−0.616688	+	0.224456i	0.0147393	+	0.999891i	$0.495308\pi$
$114$		0			0
$115$	3.93149	+	22.2966i	0.366614	+	2.07917i
$116$		0			0
$117$	0.511539	−	7.87836i	0.0472918	−	0.728354i
$118$		0			0
$119$	14.0164	+	5.10154i	1.28488	+	0.467658i
$120$		0			0
$121$	−1.91857	−	1.60987i	−0.174416	−	0.146352i
$122$		0			0
$123$	−2.78622	−	6.51880i	−0.251225	−	0.587780i
$124$		0			0
$125$	−4.91166	+	8.50724i	−0.439312	+	0.760911i
$126$		0			0
$127$	−9.67931	−	16.7651i	−0.858900	−	1.48766i	−0.872979	−	0.487757i	$-0.837815\pi$
$127$	−9.67931	−	16.7651i	−0.858900	−	1.48766i	0.0140793	−	0.999901i	$-0.495518\pi$
$128$		0			0
$129$	−5.57692	−	5.95077i	−0.491020	−	0.523936i
$130$		0			0
$131$	−0.481816	+	2.73252i	−0.0420965	+	0.238741i	−0.998595	−	0.0529973i	$-0.983123\pi$
$131$	−0.481816	+	2.73252i	−0.0420965	+	0.238741i	0.956498	+	0.291738i	$0.0942336\pi$
$132$		0			0
$133$	6.99947	−	5.87326i	0.606931	−	0.509276i
$134$		0			0
$135$	−6.24539	−	11.0713i	−0.537518	−	0.952870i
$136$		0			0
$137$	−5.21498	+	4.37589i	−0.445546	+	0.373858i	−0.837780	−	0.546008i	$-0.816147\pi$
$137$	−5.21498	+	4.37589i	−0.445546	+	0.373858i	0.392234	+	0.919865i	$0.371702\pi$
$138$		0			0
$139$	3.23814	−	18.3644i	0.274656	−	1.55765i	−0.465398	−	0.885102i	$-0.654089\pi$
$139$	3.23814	−	18.3644i	0.274656	−	1.55765i	0.740053	−	0.672548i	$-0.234800\pi$
$140$		0			0
$141$	−3.00583	+	9.91981i	−0.253137	+	0.835398i
$142$		0			0
$143$	−3.83523	−	6.64282i	−0.320718	−	0.555501i
$144$		0			0
$145$	8.47330	−	14.6762i	0.703670	−	1.21879i
$146$		0			0
$147$	22.2465	+	2.67537i	1.83486	+	0.220661i
$148$		0			0
$149$	0.277361	+	0.232733i	0.0227223	+	0.0190662i	0.654078	−	0.756427i	$-0.273057\pi$
$149$	0.277361	+	0.232733i	0.0227223	+	0.0190662i	−0.631356	+	0.775493i	$0.717501\pi$
$150$		0			0
$151$	3.32130	+	1.20886i	0.270284	+	0.0983752i	0.473607	−	0.880737i	$-0.342952\pi$
$151$	3.32130	+	1.20886i	0.270284	+	0.0983752i	−0.203323	+	0.979112i	$0.565174\pi$
$152$		0			0
$153$	−9.96158	+	1.09713i	−0.805346	+	0.0886978i
$154$		0			0
$155$	0.930390	+	5.27651i	0.0747308	+	0.423819i
$156$		0			0
$157$	11.7131	−	4.26323i	0.934810	−	0.340243i	0.170696	−	0.985324i	$-0.445398\pi$
$157$	11.7131	−	4.26323i	0.934810	−	0.340243i	0.764114	+	0.645081i	$0.223176\pi$
$158$		0			0
$159$	−3.04425	−	1.54160i	−0.241425	−	0.122257i
$160$		0			0
$161$	41.3238			3.25678
$162$		0			0
$163$	−16.1125			−1.26203			−0.631016	−	0.775770i	$-0.717362\pi$
$163$	−16.1125			−1.26203			−0.631016	+	0.775770i	$0.717362\pi$
$164$		0			0
$165$	−11.0178	−	5.57939i	−0.857736	−	0.434355i
$166$		0			0
$167$	16.7783	−	6.10681i	1.29835	−	0.472559i	0.401889	−	0.915689i	$-0.368354\pi$
$167$	16.7783	−	6.10681i	1.29835	−	0.472559i	0.896458	+	0.443129i	$0.146132\pi$
$168$		0			0
$169$	−1.05481	−	5.98214i	−0.0811395	−	0.460165i
$170$		0			0
$171$	−2.46909	+	5.62074i	−0.188816	+	0.429829i
$172$		0			0
$173$	−13.9855	−	5.09032i	−1.06330	−	0.387010i	−0.249633	−	0.968340i	$-0.580310\pi$
$173$	−13.9855	−	5.09032i	−1.06330	−	0.387010i	−0.813667	+	0.581331i	$0.802532\pi$
$174$		0			0
$175$	−3.36718	−	2.82540i	−0.254535	−	0.213580i
$176$		0			0
$177$	11.3566	+	1.36575i	0.853615	+	0.102656i
$178$		0			0
$179$	0.817468	−	1.41590i	0.0611004	−	0.105829i	−0.833857	−	0.551980i	$-0.813872\pi$
$179$	0.817468	−	1.41590i	0.0611004	−	0.105829i	0.894958	+	0.446151i	$0.147206\pi$
$180$		0			0
$181$	−2.16838	−	3.75574i	−0.161174	−	0.279162i	0.774116	−	0.633044i	$-0.218195\pi$
$181$	−2.16838	−	3.75574i	−0.161174	−	0.279162i	−0.935290	+	0.353882i	$0.884861\pi$
$182$		0			0
$183$	−3.62819	+	11.9737i	−0.268204	+	0.885122i
$184$		0			0
$185$	0.601998	−	3.41410i	0.0442598	−	0.251010i
$186$		0			0
$187$	−7.45887	+	6.25873i	−0.545447	+	0.457684i
$188$		0			0
$189$	−21.8800	+	7.71698i	−1.59154	+	0.561328i
$190$		0			0
$191$	0.661413	−	0.554991i	0.0478582	−	0.0401578i	−0.618545	−	0.785749i	$-0.712277\pi$
$191$	0.661413	−	0.554991i	0.0478582	−	0.0401578i	0.666403	+	0.745592i	$0.267833\pi$
$192$		0			0
$193$	−0.904508	+	5.12972i	−0.0651079	+	0.369245i	0.934793	+	0.355192i	$0.115585\pi$
$193$	−0.904508	+	5.12972i	−0.0651079	+	0.369245i	−0.999901	+	0.0140533i	$0.995527\pi$
$194$		0			0
$195$	7.62498	+	8.13613i	0.546036	+	0.582640i
$196$		0			0
$197$	13.1550	+	22.7852i	0.937257	+	1.62338i	0.770559	+	0.637368i	$0.219977\pi$
$197$	13.1550	+	22.7852i	0.937257	+	1.62338i	0.166697	+	0.986008i	$0.446690\pi$
$198$		0			0
$199$	5.38490	−	9.32692i	0.381725	−	0.661168i	−0.609584	−	0.792722i	$-0.708663\pi$
$199$	5.38490	−	9.32692i	0.381725	−	0.661168i	0.991309	+	0.131554i	$0.0419967\pi$
$200$		0			0
$201$	−2.11390	−	4.94580i	−0.149103	−	0.348850i
$202$		0			0
$203$	−23.6946	−	19.8822i	−1.66304	−	1.39545i
$204$		0			0
$205$	9.40889	+	3.42456i	0.657145	+	0.239181i
$206$		0			0
$207$	−24.8941	+	12.2953i	−1.73026	+	0.854585i
$208$		0			0
$209$	1.03574	+	5.87397i	0.0716436	+	0.406311i
$210$		0			0
$211$	−3.45213	+	1.25647i	−0.237654	+	0.0864990i	−0.458102	−	0.888900i	$-0.651470\pi$
$211$	−3.45213	+	1.25647i	−0.237654	+	0.0864990i	0.220448	+	0.975399i	$0.429248\pi$
$212$		0			0
$213$	19.1710	−	12.5177i	1.31358	−	0.857699i
$214$		0			0
$215$	11.5188			0.785574
$216$		0			0
$217$	9.77931			0.663863
$218$		0			0
$219$	−1.21587	−	22.1461i	−0.0821608	−	1.49650i
$220$		0			0
$221$	8.26111	−	3.00680i	0.555703	−	0.202259i
$222$		0			0
$223$	0.863453	+	4.89688i	0.0578211	+	0.327920i	0.999974	−	0.00726484i	$-0.00231249\pi$
$223$	0.863453	+	4.89688i	0.0578211	+	0.327920i	−0.942153	+	0.335184i	$0.891201\pi$
$224$		0			0
$225$	2.86910	+	0.700205i	0.191273	+	0.0466804i
$226$		0			0
$227$	−9.99997	−	3.63969i	−0.663721	−	0.241575i	−0.0118791	−	0.999929i	$-0.503781\pi$
$227$	−9.99997	−	3.63969i	−0.663721	−	0.241575i	−0.651842	+	0.758355i	$0.726004\pi$
$228$		0			0
$229$	10.9102	+	9.15476i	0.720967	+	0.604963i	0.927653	−	0.373444i	$-0.121823\pi$
$229$	10.9102	+	9.15476i	0.720967	+	0.604963i	−0.206685	+	0.978407i	$0.566268\pi$
$230$		0			0
$231$	−13.5209	+	18.0360i	−0.889610	+	1.18668i
$232$		0			0
$233$	−7.93762	+	13.7484i	−0.520011	+	0.900685i	0.479719	+	0.877422i	$0.340739\pi$
$233$	−7.93762	+	13.7484i	−0.520011	+	0.900685i	−0.999729	+	0.0232627i	$0.992595\pi$
$234$		0			0
$235$	−7.31980	−	12.6783i	−0.477491	−	0.827039i
$236$		0			0
$237$	−3.47283	+	0.810869i	−0.225584	+	0.0526716i
$238$		0			0
$239$	−1.85681	+	10.5305i	−0.120107	+	0.681160i	0.863988	+	0.503513i	$0.167959\pi$
$239$	−1.85681	+	10.5305i	−0.120107	+	0.681160i	−0.984094	+	0.177646i	$0.943152\pi$
$240$		0			0
$241$	−11.5594	+	9.69950i	−0.744607	+	0.624800i	−0.934071	−	0.357088i	$-0.883770\pi$
$241$	−11.5594	+	9.69950i	−0.744607	+	0.624800i	0.189463	+	0.981888i	$0.439325\pi$
$242$		0			0
$243$	10.8848	−	11.1589i	0.698259	−	0.715846i
$244$		0			0
$245$	−24.2429	+	20.3422i	−1.54882	+	1.29961i
$246$		0			0
$247$	0.935157	−	5.30354i	0.0595026	−	0.337456i
$248$		0			0
$249$	2.64461	−	0.617489i	0.167596	−	0.0391318i
$250$		0			0
$251$	−8.07700	−	13.9898i	−0.509816	−	0.883027i	−0.999935	−	0.0113719i	$-0.996380\pi$
$251$	−8.07700	−	13.9898i	−0.509816	−	0.883027i	0.490119	−	0.871655i	$-0.336953\pi$
$252$		0			0
$253$	−13.4878	+	23.3615i	−0.847968	+	1.46872i
$254$		0			0
$255$	8.49030	−	11.3255i	0.531683	−	0.709231i
$256$		0			0
$257$	−1.39647	−	1.17178i	−0.0871096	−	0.0730936i	0.598193	−	0.801352i	$-0.295886\pi$
$257$	−1.39647	−	1.17178i	−0.0871096	−	0.0730936i	−0.685303	+	0.728258i	$0.740330\pi$
$258$		0			0
$259$	−5.94599	−	2.16416i	−0.369466	−	0.134475i
$260$		0			0
$261$	20.1897	+	4.92731i	1.24971	+	0.304993i
$262$		0			0
$263$	2.36051	+	13.3871i	0.145556	+	0.825487i	0.966919	+	0.255082i	$0.0821025\pi$
$263$	2.36051	+	13.3871i	0.145556	+	0.825487i	−0.821364	+	0.570405i	$0.806786\pi$
$264$		0			0
$265$	4.52885	−	1.64837i	0.278205	−	0.101258i
$266$		0			0
$267$	1.30784	+	23.8212i	0.0800382	+	1.45783i
$268$		0			0
$269$	−16.0603			−0.979212			−0.489606	−	0.871944i	$-0.662859\pi$
$269$	−16.0603			−0.979212			−0.489606	+	0.871944i	$0.662859\pi$
$270$		0			0
$271$	−16.0822			−0.976924			−0.488462	−	0.872585i	$-0.662442\pi$
$271$	−16.0822			−0.976924			−0.488462	+	0.872585i	$0.662442\pi$
$272$		0			0
$273$	17.0413	−	11.1271i	1.03138	−	0.673441i
$274$		0			0
$275$	2.69629	−	0.981370i	0.162592	−	0.0591788i
$276$		0			0
$277$	2.62263	+	14.8737i	0.157578	+	0.893672i	0.956390	+	0.292091i	$0.0943511\pi$
$277$	2.62263	+	14.8737i	0.157578	+	0.893672i	−0.798812	+	0.601581i	$0.794538\pi$
$278$		0			0
$279$	−5.89121	+	2.90970i	−0.352698	+	0.174199i
$280$		0			0
$281$	5.84548	+	2.12758i	0.348712	+	0.126921i	0.510437	−	0.859915i	$-0.329484\pi$
$281$	5.84548	+	2.12758i	0.348712	+	0.126921i	−0.161725	+	0.986836i	$0.551706\pi$
$282$		0			0
$283$	7.75911	+	6.51066i	0.461231	+	0.387019i	0.843584	−	0.536998i	$-0.180442\pi$
$283$	7.75911	+	6.51066i	0.461231	+	0.387019i	−0.382353	+	0.924016i	$0.624886\pi$
$284$		0			0
$285$	−3.40779	−	7.97305i	−0.201860	−	0.472283i
$286$		0			0
$287$	9.13768	−	15.8269i	0.539380	−	0.934234i
$288$		0			0
$289$	2.92018	+	5.05791i	0.171776	+	0.297524i
$290$		0			0
$291$	17.5616	+	18.7388i	1.02948	+	1.09849i
$292$		0			0
$293$	5.02648	−	28.5066i	0.293650	−	1.66537i	−0.378989	−	0.925401i	$-0.623728\pi$
$293$	5.02648	−	28.5066i	0.293650	−	1.66537i	0.672639	−	0.739971i	$-0.265161\pi$
$294$		0			0
$295$	−12.3758	+	10.3845i	−0.720544	+	0.604609i
$296$		0			0
$297$	2.77883	−	14.8881i	0.161244	−	0.863896i
$298$		0			0
$299$	18.6577	−	15.6557i	1.07900	−	0.905390i
$300$		0			0
$301$	3.65081	−	20.7048i	0.210429	−	1.19340i
$302$		0			0
$303$	1.49165	−	4.92274i	0.0856932	−	0.282804i
$304$		0			0
$305$	−8.83537	−	15.3033i	−0.505912	−	0.876265i
$306$		0			0
$307$	−1.33981	+	2.32062i	−0.0764669	+	0.132445i	−0.901723	−	0.432314i	$-0.857697\pi$
$307$	−1.33981	+	2.32062i	−0.0764669	+	0.132445i	0.825256	+	0.564758i	$0.191031\pi$
$308$		0			0
$309$	−19.2226	−	2.31173i	−1.09354	−	0.131509i
$310$		0			0
$311$	−11.1610	−	9.36520i	−0.632883	−	0.531052i	0.268941	−	0.963157i	$-0.413326\pi$
$311$	−11.1610	−	9.36520i	−0.632883	−	0.531052i	−0.901823	+	0.432105i	$0.857771\pi$
$312$		0			0
$313$	24.9660	+	9.08687i	1.41116	+	0.513620i	0.931470	−	0.363818i	$-0.118527\pi$
$313$	24.9660	+	9.08687i	1.41116	+	0.513620i	0.479690	+	0.877438i	$0.340749\pi$
$314$		0			0
$315$	13.1791	−	30.0015i	0.742559	−	1.69039i
$316$		0			0
$317$	−3.59994	−	20.4163i	−0.202193	−	1.14669i	−0.901797	−	0.432161i	$-0.857751\pi$
$317$	−3.59994	−	20.4163i	−0.202193	−	1.14669i	0.699604	−	0.714531i	$-0.253360\pi$
$318$		0			0
$319$	18.9737	−	6.90585i	1.06232	−	0.386653i
$320$		0			0
$321$	−7.55572	−	3.82619i	−0.421719	−	0.213557i
$322$		0			0
$323$	−6.83615			−0.380373
$324$		0			0
$325$	−2.59069			−0.143705
$326$		0			0
$327$	5.68997	+	2.88138i	0.314656	+	0.159341i
$328$		0			0
$329$	−25.1089	+	9.13890i	−1.38430	+	0.503844i
$330$		0			0
$331$	−1.94118	−	11.0090i	−0.106697	−	0.605107i	−0.990529	−	0.137303i	$-0.956156\pi$
$331$	−1.94118	−	11.0090i	−0.106697	−	0.605107i	0.883832	−	0.467804i	$-0.154955\pi$
$332$		0			0
$333$	4.22587	−	0.465422i	0.231576	−	0.0255050i
$334$		0			0
$335$	7.13851	+	2.59821i	0.390019	+	0.141955i
$336$		0			0
$337$	6.44752	+	5.41011i	0.351219	+	0.294707i	0.801279	−	0.598291i	$-0.204153\pi$
$337$	6.44752	+	5.41011i	0.351219	+	0.294707i	−0.450061	+	0.892998i	$0.648598\pi$
$338$		0			0
$339$	11.9967	+	1.44273i	0.651570	+	0.0783582i
$340$		0			0
$341$	−3.19189	+	5.52851i	−0.172850	+	0.299386i
$342$		0			0
$343$	13.2534	+	22.9556i	0.715619	+	1.23949i
$344$		0			0
$345$	11.3719	−	37.5295i	0.612244	−	2.02052i
$346$		0			0
$347$	−1.44612	+	8.20137i	−0.0776319	+	0.440273i	0.921073	+	0.389391i	$0.127314\pi$
$347$	−1.44612	+	8.20137i	−0.0776319	+	0.440273i	−0.998705	+	0.0508820i	$0.983797\pi$
$348$		0			0
$349$	−2.14276	+	1.79799i	−0.114700	+	0.0962444i	−0.698334	−	0.715772i	$-0.746075\pi$
$349$	−2.14276	+	1.79799i	−0.114700	+	0.0962444i	0.583634	+	0.812017i	$0.301630\pi$
$350$		0			0
$351$	−6.95520	+	11.7735i	−0.371241	+	0.628424i
$352$		0			0
$353$	−7.96097	+	6.68005i	−0.423720	+	0.355543i	−0.829576	−	0.558394i	$-0.811418\pi$
$353$	−7.96097	+	6.68005i	−0.423720	+	0.355543i	0.405856	+	0.913937i	$0.366973\pi$
$354$		0			0
$355$	−5.61537	+	31.8463i	−0.298033	+	1.69023i
$356$		0			0
$357$	−17.6665	−	18.8507i	−0.935008	−	0.997686i
$358$		0			0
$359$	4.64987	+	8.05381i	0.245411	+	0.425064i	0.962247	−	0.272178i	$-0.0877439\pi$
$359$	4.64987	+	8.05381i	0.245411	+	0.425064i	−0.716836	+	0.697241i	$0.754411\pi$
$360$		0			0
$361$	7.40616	−	12.8278i	0.389798	−	0.675150i
$362$		0			0
$363$	1.70490	+	3.98888i	0.0894840	+	0.209362i
$364$		0			0
$365$	23.9969	+	20.1358i	1.25606	+	1.05396i
$366$		0			0
$367$	−2.86164	−	1.04155i	−0.149376	−	0.0543686i	0.266250	−	0.963904i	$-0.414215\pi$
$367$	−2.86164	−	1.04155i	−0.149376	−	0.0543686i	−0.415626	+	0.909535i	$0.636438\pi$
$368$		0			0
$369$	−0.795595	+	12.2532i	−0.0414170	+	0.637875i
$370$		0			0
$371$	−1.52752	−	8.66297i	−0.0793047	−	0.449759i
$372$		0			0
$373$	−18.8374	+	6.85625i	−0.975363	+	0.355003i	−0.780036	−	0.625735i	$-0.784799\pi$
$373$	−18.8374	+	6.85625i	−0.975363	+	0.355003i	−0.195327	+	0.980738i	$0.562577\pi$
$374$		0			0
$375$	14.2465	−	9.30222i	0.735684	−	0.480364i
$376$		0			0
$377$	−18.2305			−0.938920
$378$		0			0
$379$	5.89450			0.302780			0.151390	−	0.988474i	$-0.451625\pi$
$379$	5.89450			0.302780			0.151390	+	0.988474i	$0.451625\pi$
$380$		0			0
$381$	1.83811	+	33.4797i	0.0941691	+	1.71522i
$382$		0			0
$383$	−5.02364	+	1.82846i	−0.256696	+	0.0934298i	−0.467163	−	0.884171i	$-0.654724\pi$
$383$	−5.02364	+	1.82846i	−0.256696	+	0.0934298i	0.210467	+	0.977601i	$0.432502\pi$
$384$		0			0
$385$	−5.52842	−	31.3532i	−0.281754	−	1.59791i
$386$		0			0
$387$	3.96112	+	13.5591i	0.201355	+	0.689250i
$388$		0			0
$389$	−2.75979	−	1.00448i	−0.139927	−	0.0509293i	0.271107	−	0.962549i	$-0.412610\pi$
$389$	−2.75979	−	1.00448i	−0.139927	−	0.0509293i	−0.411034	+	0.911620i	$0.634832\pi$
$390$		0			0
$391$	−23.6840	−	19.8732i	−1.19775	−	1.00503i
$392$		0			0
$393$	2.88269	−	3.84532i	0.145412	−	0.193971i
$394$		0			0
$395$	2.51844	−	4.36206i	0.126716	−	0.219479i
$396$		0			0
$397$	−7.19815	−	12.4676i	−0.361265	−	0.625729i	0.626905	−	0.779096i	$-0.284322\pi$
$397$	−7.19815	−	12.4676i	−0.361265	−	0.625729i	−0.988169	+	0.153367i	$0.950988\pi$
$398$		0			0
$399$	−15.4115	+	3.59843i	−0.771541	+	0.180147i
$400$		0			0
$401$	2.55499	−	14.4901i	0.127590	−	0.723599i	−0.852146	−	0.523305i	$-0.824699\pi$
$401$	2.55499	−	14.4901i	0.127590	−	0.723599i	0.979736	−	0.200294i	$-0.0641899\pi$
$402$		0			0
$403$	4.41535	−	3.70492i	0.219944	−	0.184555i
$404$		0			0
$405$	0.987244	+	21.9946i	0.0490565	+	1.09292i
$406$		0			0
$407$	3.16418	−	2.65506i	0.156843	−	0.131607i
$408$		0			0
$409$	−4.83984	+	27.4481i	−0.239315	+	1.35722i	0.594018	+	0.804451i	$0.297541\pi$
$409$	−4.83984	+	27.4481i	−0.239315	+	1.35722i	−0.833333	+	0.552771i	$0.813570\pi$
$410$		0			0
$411$	11.4824	−	2.68102i	0.566385	−	0.132245i
$412$		0			0
$413$	14.7435	+	25.5365i	0.725481	+	1.25657i
$414$		0			0
$415$	−1.91783	+	3.32178i	−0.0941425	+	0.163060i
$416$		0			0
$417$	−19.3737	+	25.8432i	−0.948733	+	1.26555i
$418$		0			0
$419$	26.7631	+	22.4569i	1.30746	+	1.09709i	0.988804	+	0.149223i	$0.0476773\pi$
$419$	26.7631	+	22.4569i	1.30746	+	1.09709i	0.318660	+	0.947869i	$0.396767\pi$
$420$		0			0
$421$	−8.75763	−	3.18752i	−0.426821	−	0.155350i	0.119673	−	0.992813i	$-0.461815\pi$
$421$	−8.75763	−	3.18752i	−0.426821	−	0.155350i	−0.546493	+	0.837463i	$0.684038\pi$
$422$		0			0
$423$	12.4069	−	12.9762i	0.603242	−	0.630926i
$424$		0			0
$425$	0.571060	+	3.23865i	0.0277005	+	0.157097i
$426$		0			0
$427$	−30.3078	+	11.0311i	−1.46670	+	0.533833i
$428$		0			0
$429$	0.728314	+	13.2657i	0.0351633	+	0.640472i
$430$		0			0
$431$	3.92496			0.189058			0.0945292	−	0.995522i	$-0.469865\pi$
$431$	3.92496			0.189058			0.0945292	+	0.995522i	$0.469865\pi$
$432$		0			0
$433$	40.3617			1.93966			0.969829	−	0.243786i	$-0.0783894\pi$
$433$	40.3617			1.93966			0.969829	+	0.243786i	$0.0783894\pi$
$434$		0			0
$435$	−24.5771	+	16.0476i	−1.17838	+	0.769425i
$436$		0			0
$437$	−17.7971	+	6.47760i	−0.851349	+	0.309866i
$438$		0			0
$439$	−0.759264	−	4.30600i	−0.0362377	−	0.205514i	0.961313	−	0.275457i	$-0.0888293\pi$
$439$	−0.759264	−	4.30600i	−0.0362377	−	0.205514i	−0.997551	+	0.0699432i	$0.977718\pi$
$440$		0			0
$441$	−32.2822	−	21.5418i	−1.53725	−	1.02580i
$442$		0			0
$443$	−26.3212	−	9.58012i	−1.25056	−	0.455165i	−0.369967	−	0.929045i	$-0.620631\pi$
$443$	−26.3212	−	9.58012i	−1.25056	−	0.455165i	−0.880590	+	0.473880i	$0.842853\pi$
$444$		0			0
$445$	−25.8120	−	21.6589i	−1.22361	−	1.02673i
$446$		0			0
$447$	−0.246471	−	0.576657i	−0.0116577	−	0.0272749i
$448$		0			0
$449$	14.0254	−	24.2927i	0.661899	−	1.14644i	−0.318217	−	0.948018i	$-0.603084\pi$
$449$	14.0254	−	24.2927i	0.661899	−	1.14644i	0.980116	−	0.198425i	$-0.0635826\pi$
$450$		0			0
$451$	5.96493	+	10.3316i	0.280877	+	0.486494i
$452$		0			0
$453$	−4.18622	−	4.46684i	−0.196686	−	0.209871i
$454$		0			0
$455$	−4.99154	+	28.3084i	−0.234007	+	1.32712i
$456$		0			0
$457$	25.3932	−	21.3074i	1.18784	−	0.996718i	0.187948	−	0.982179i	$-0.439816\pi$
$457$	25.3932	−	21.3074i	1.18784	−	0.996718i	0.999894	−	0.0145393i	$-0.00462816\pi$
$458$		0			0
$459$	16.2513	+	6.09956i	0.758547	+	0.284703i
$460$		0			0
$461$	17.7916	−	14.9290i	0.828639	−	0.695311i	−0.126339	−	0.991987i	$-0.540323\pi$
$461$	17.7916	−	14.9290i	0.828639	−	0.695311i	0.954978	+	0.296676i	$0.0958782\pi$
$462$		0			0
$463$	2.87203	−	16.2881i	0.133475	−	0.756972i	−0.842435	−	0.538798i	$-0.818879\pi$
$463$	2.87203	−	16.2881i	0.133475	−	0.756972i	0.975910	−	0.218174i	$-0.0700102\pi$
$464$		0			0
$465$	2.69118	−	8.88139i	0.124800	−	0.411864i
$466$		0			0
$467$	8.44277	+	14.6233i	0.390685	+	0.676686i	0.992540	−	0.121919i	$-0.0389049\pi$
$467$	8.44277	+	14.6233i	0.390685	+	0.676686i	−0.601855	+	0.798605i	$0.705572\pi$
$468$		0			0
$469$	6.93275	−	12.0079i	0.320125	−	0.554472i
$470$		0			0
$471$	−21.4353	−	2.57782i	−0.987688	−	0.118780i
$472$		0			0
$473$	10.5134	+	8.82178i	0.483406	+	0.405626i
$474$		0			0
$475$	1.89304	+	0.689009i	0.0868585	+	0.0316139i
$476$		0			0
$477$	3.49775	+	4.76422i	0.160151	+	0.218139i
$478$		0			0
$479$	0.572645	+	3.24763i	0.0261648	+	0.148388i	0.995091	−	0.0989606i	$-0.0315518\pi$
$479$	0.572645	+	3.24763i	0.0261648	+	0.148388i	−0.968927	+	0.247349i	$0.920441\pi$
$480$		0			0
$481$	−3.50451	+	1.27554i	−0.159792	+	0.0581594i
$482$		0			0
$483$	−63.8544	−	32.3357i	−2.90548	−	1.47132i
$484$		0			0
$485$	−36.2724			−1.64704
$486$		0			0
$487$	−8.40222			−0.380741			−0.190370	−	0.981712i	$-0.560969\pi$
$487$	−8.40222			−0.380741			−0.190370	+	0.981712i	$0.560969\pi$
$488$		0			0
$489$	24.8974	+	12.6080i	1.12590	+	0.570152i
$490$		0			0
$491$	31.7943	−	11.5722i	1.43486	−	0.522246i	0.496538	−	0.868015i	$-0.334604\pi$
$491$	31.7943	−	11.5722i	1.43486	−	0.522246i	0.938320	+	0.345769i	$0.112382\pi$
$492$		0			0
$493$	4.01852	+	22.7902i	0.180985	+	1.02642i
$494$		0			0
$495$	12.6591	+	17.2428i	0.568985	+	0.775004i
$496$		0			0
$497$	55.4635	+	20.1871i	2.48788	+	0.905513i
$498$		0			0
$499$	28.6162	+	24.0118i	1.28103	+	1.07492i	0.993101	+	0.117266i	$0.0374129\pi$
$499$	28.6162	+	24.0118i	1.28103	+	1.07492i	0.287934	+	0.957650i	$0.407031\pi$
$500$		0			0
$501$	−30.7048	−	3.69257i	−1.37179	−	0.164972i
$502$		0			0
$503$	−0.0186236	+	0.0322570i	−0.000830385	+	0.00143827i	−0.866440	−	0.499281i	$-0.833598\pi$
$503$	−0.0186236	+	0.0322570i	−0.000830385	+	0.00143827i	0.865610	+	0.500719i	$0.166931\pi$
$504$		0			0
$505$	3.63247	+	6.29163i	0.161643	+	0.279974i
$506$		0			0
$507$	−3.05107	+	10.0691i	−0.135503	+	0.447185i
$508$		0			0
$509$	−3.22655	+	18.2987i	−0.143014	+	0.811074i	0.825926	+	0.563779i	$0.190653\pi$
$509$	−3.22655	+	18.2987i	−0.143014	+	0.811074i	−0.968940	+	0.247295i	$0.920458\pi$
$510$		0			0
$511$	43.7995	−	36.7521i	1.93758	−	1.62582i
$512$		0			0
$513$	8.21347	−	6.75323i	0.362634	−	0.298162i
$514$		0			0
$515$	20.9477	−	17.5772i	0.923065	−	0.774543i
$516$		0			0
$517$	3.02888	−	17.1776i	0.133210	−	0.755471i
$518$		0			0
$519$	17.6276	+	18.8093i	0.773765	+	0.825635i
$520$		0			0
$521$	−8.96816	−	15.5333i	−0.392902	−	0.680526i	0.599929	−	0.800053i	$-0.295196\pi$
$521$	−8.96816	−	15.5333i	−0.392902	−	0.680526i	−0.992831	+	0.119527i	$0.961862\pi$
$522$		0			0
$523$	2.28323	−	3.95468i	0.0998388	−	0.172926i	−0.811779	−	0.583965i	$-0.801501\pi$
$523$	2.28323	−	3.95468i	0.0998388	−	0.172926i	0.911618	+	0.411039i	$0.134834\pi$
$524$		0			0
$525$	2.99217	+	7.00065i	0.130589	+	0.305534i
$526$		0			0
$527$	−5.60483	−	4.70301i	−0.244150	−	0.204866i
$528$		0			0
$529$	−58.8762	−	21.4292i	−2.55984	−	0.931704i
$530$		0			0
$531$	−16.4798	−	10.9969i	−0.715161	−	0.477223i
$532$		0			0
$533$	−1.87042	−	10.6077i	−0.0810169	−	0.459470i
$534$		0			0
$535$	11.2404	−	4.09119i	0.485967	−	0.176877i
$536$		0			0
$537$	−2.37110	+	1.54821i	−0.102320	+	0.0668101i
$538$		0			0
$539$	−37.7062			−1.62412
$540$		0			0
$541$	−13.3230			−0.572802			−0.286401	−	0.958110i	$-0.592459\pi$
$541$	−13.3230			−0.572802			−0.286401	+	0.958110i	$0.592459\pi$
$542$		0			0
$543$	0.411776	+	7.50018i	0.0176710	+	0.321863i
$544$		0			0
$545$	−8.46481	+	3.08094i	−0.362593	+	0.131973i
$546$		0			0
$547$	−5.06345	−	28.7162i	−0.216497	−	1.22782i	−0.878289	−	0.478130i	$-0.841315\pi$
$547$	−5.06345	−	28.7162i	−0.216497	−	1.22782i	0.661792	−	0.749688i	$-0.269796\pi$
$548$		0			0
$549$	14.9757	−	15.6630i	0.639147	−	0.668480i
$550$		0			0
$551$	13.3212	+	4.84852i	0.567503	+	0.206554i
$552$		0			0
$553$	−7.04253	−	5.90938i	−0.299479	−	0.251292i
$554$		0			0
$555$	−3.60173	+	4.80447i	−0.152885	+	0.203939i
$556$		0			0
$557$	16.7045	−	28.9330i	0.707791	−	1.22593i	−0.257884	−	0.966176i	$-0.583025\pi$
$557$	16.7045	−	28.9330i	0.707791	−	1.22593i	0.965675	−	0.259753i	$-0.0836413\pi$
$558$		0			0
$559$	−6.19573	−	10.7313i	−0.262051	−	0.453886i
$560$		0			0
$561$	16.4230	−	3.83460i	0.693380	−	0.161897i
$562$		0			0
$563$	−3.01400	+	17.0933i	−0.127025	+	0.720395i	0.853059	+	0.521814i	$0.174744\pi$
$563$	−3.01400	+	17.0933i	−0.127025	+	0.720395i	−0.980084	+	0.198581i	$0.936367\pi$
$564$		0			0
$565$	−13.0733	+	10.9698i	−0.549996	+	0.461502i
$566$		0			0
$567$	39.8479	+	5.19653i	1.67346	+	0.218234i
$568$		0			0
$569$	34.5890	−	29.0236i	1.45004	−	1.21673i	0.517498	−	0.855685i	$-0.326864\pi$
$569$	34.5890	−	29.0236i	1.45004	−	1.21673i	0.932547	−	0.361047i	$-0.117581\pi$
$570$		0			0
$571$	4.85742	−	27.5478i	0.203277	−	1.15284i	−0.696851	−	0.717215i	$-0.745416\pi$
$571$	4.85742	−	27.5478i	0.203277	−	1.15284i	0.900128	−	0.435625i	$-0.143473\pi$
$572$		0			0
$573$	−1.45631	+	0.340032i	−0.0608380	+	0.0142050i
$574$		0			0
$575$	4.55547	+	7.89030i	0.189976	+	0.329048i
$576$		0			0
$577$	−16.9009	+	29.2732i	−0.703593	+	1.21866i	0.263603	+	0.964631i	$0.415089\pi$
$577$	−16.9009	+	29.2732i	−0.703593	+	1.21866i	−0.967197	+	0.254028i	$0.918244\pi$
$578$		0			0
$579$	5.41164	−	7.21877i	0.224900	−	0.300002i
$580$		0			0
$581$	5.36299	+	4.50009i	0.222494	+	0.186695i
$582$		0			0
$583$	5.39598	+	1.96398i	0.223479	+	0.0813396i
$584$		0			0
$585$	−5.41581	−	18.5386i	−0.223916	−	0.766477i
$586$		0			0
$587$	1.35230	+	7.66925i	0.0558152	+	0.316544i	0.999914	−	0.0131190i	$-0.00417603\pi$
$587$	1.35230	+	7.66925i	0.0558152	+	0.316544i	−0.944099	+	0.329663i	$0.893065\pi$
$588$		0			0
$589$	−4.21168	+	1.53293i	−0.173539	+	0.0631632i
$590$		0			0
$591$	−2.49815	−	45.5018i	−0.102760	−	1.87169i
$592$		0			0
$593$	−18.2877			−0.750986			−0.375493	−	0.926825i	$-0.622527\pi$
$593$	−18.2877			−0.750986			−0.375493	+	0.926825i	$0.622527\pi$
$594$		0			0
$595$	36.4890			1.49590
$596$		0			0
$597$	−15.6191	+	10.1985i	−0.639247	+	0.417396i
$598$		0			0
$599$	20.3587	−	7.40994i	0.831832	−	0.302762i	0.109221	−	0.994017i	$-0.465164\pi$
$599$	20.3587	−	7.40994i	0.831832	−	0.302762i	0.722611	+	0.691255i	$0.242942\pi$
$600$		0			0
$601$	0.0948417	+	0.537874i	0.00386867	+	0.0219403i	0.986681	−	0.162667i	$-0.0520097\pi$
$601$	0.0948417	+	0.537874i	0.00386867	+	0.0219403i	−0.982812	+	0.184608i	$0.940899\pi$
$602$		0			0
$603$	−0.603617	+	9.29647i	−0.0245812	+	0.378582i
$604$		0			0
$605$	−5.75733	−	2.09550i	−0.234069	−	0.0851941i
$606$		0			0
$607$	−9.78443	−	8.21011i	−0.397138	−	0.333238i	0.422248	−	0.906480i	$-0.361241\pi$
$607$	−9.78443	−	8.21011i	−0.397138	−	0.333238i	−0.819386	+	0.573242i	$0.805685\pi$
$608$		0			0
$609$	21.0558	+	49.2632i	0.853222	+	1.99625i
$610$		0			0
$611$	−7.87436	+	13.6388i	−0.318563	+	0.551767i
$612$		0			0
$613$	7.48439	+	12.9634i	0.302292	+	0.523585i	0.976655	−	0.214815i	$-0.0689150\pi$
$613$	7.48439	+	12.9634i	0.302292	+	0.523585i	−0.674363	+	0.738400i	$0.735582\pi$
$614$		0			0
$615$	−11.8591	−	12.6541i	−0.478205	−	0.510262i
$616$		0			0
$617$	−3.91960	+	22.2292i	−0.157797	+	0.894912i	0.798387	+	0.602145i	$0.205687\pi$
$617$	−3.91960	+	22.2292i	−0.157797	+	0.894912i	−0.956184	+	0.292767i	$0.905424\pi$
$618$		0			0
$619$	−24.0226	+	20.1574i	−0.965551	+	0.810193i	−0.981847	−	0.189674i	$-0.939257\pi$
$619$	−24.0226	+	20.1574i	−0.965551	+	0.810193i	0.0162965	+	0.999867i	$0.494812\pi$
$620$		0			0
$621$	48.0879	+	0.480490i	1.92970	+	0.0192814i
$622$		0			0
$623$	−47.1124	+	39.5320i	−1.88752	+	1.58382i
$624$		0			0
$625$	−5.02765	+	28.5132i	−0.201106	+	1.14053i
$626$		0			0
$627$	2.99590	−	9.88704i	0.119645	−	0.394850i
$628$		0			0
$629$	2.36705	+	4.09986i	0.0943806	+	0.163472i
$630$		0			0
$631$	3.23348	−	5.60055i	0.128723	−	0.222955i	−0.794459	−	0.607318i	$-0.792246\pi$
$631$	3.23348	−	5.60055i	0.128723	−	0.222955i	0.923182	+	0.384363i	$0.125579\pi$
$632$		0			0
$633$	6.31747	+	0.759743i	0.251097	+	0.0301971i
$634$		0			0
$635$	−36.2777	−	30.4406i	−1.43964	−	1.20800i
$636$		0			0
$637$	31.9913	+	11.6439i	1.26754	+	0.461348i
$638$		0			0
$639$	−39.4185	+	4.34140i	−1.55937	+	0.171743i
$640$		0			0
$641$	2.29933	+	13.0401i	0.0908180	+	0.515055i	0.995949	+	0.0899216i	$0.0286616\pi$
$641$	2.29933	+	13.0401i	0.0908180	+	0.515055i	−0.905131	+	0.425133i	$0.860227\pi$
$642$		0			0
$643$	−14.5304	+	5.28864i	−0.573024	+	0.208564i	−0.612247	−	0.790667i	$-0.709734\pi$
$643$	−14.5304	+	5.28864i	−0.573024	+	0.208564i	0.0392228	+	0.999230i	$0.487512\pi$
$644$		0			0
$645$	−17.7990	−	9.01337i	−0.700836	−	0.354901i
$646$		0			0
$647$	−43.4105			−1.70664			−0.853321	−	0.521386i	$-0.825415\pi$
$647$	−43.4105			−1.70664			−0.853321	+	0.521386i	$0.825415\pi$
$648$		0			0
$649$	−19.2486			−0.755576
$650$		0			0
$651$	−15.1112	−	7.65225i	−0.592254	−	0.299915i
$652$		0			0
$653$	13.3043	−	4.84239i	0.520639	−	0.189497i	−0.0683146	−	0.997664i	$-0.521762\pi$
$653$	13.3043	−	4.84239i	0.520639	−	0.189497i	0.588954	+	0.808167i	$0.299540\pi$
$654$		0			0
$655$	1.17867	+	6.68458i	0.0460545	+	0.261188i
$656$		0			0
$657$	−15.4504	+	35.1720i	−0.602778	+	1.37219i
$658$		0			0
$659$	−28.4190	−	10.3437i	−1.10705	−	0.402933i	−0.277138	−	0.960830i	$-0.589386\pi$
$659$	−28.4190	−	10.3437i	−1.10705	−	0.402933i	−0.829910	+	0.557897i	$0.811608\pi$
$660$		0			0
$661$	25.2334	+	21.1734i	0.981467	+	0.823548i	0.984310	−	0.176448i	$-0.0564607\pi$
$661$	25.2334	+	21.1734i	0.981467	+	0.823548i	−0.00284345	+	0.999996i	$0.500905\pi$
$662$		0			0
$663$	−15.1180	−	1.81810i	−0.587136	−	0.0706093i
$664$		0			0
$665$	11.1762	−	19.3577i	0.433393	−	0.750659i
$666$		0			0
$667$	32.0566	+	55.5236i	1.24124	+	2.14988i
$668$		0			0
$669$	2.49756	−	8.24241i	0.0965611	−	0.318670i
$670$		0			0
$671$	3.65601	−	20.7343i	0.141139	−	0.800437i
$672$		0			0
$673$	24.6823	−	20.7109i	0.951435	−	0.798348i	−0.0281040	−	0.999605i	$-0.508947\pi$
$673$	24.6823	−	20.7109i	0.951435	−	0.798348i	0.979539	+	0.201257i	$0.0645025\pi$
$674$		0			0
$675$	−3.88548	−	3.32702i	−0.149552	−	0.128057i
$676$		0			0
$677$	−14.7327	+	12.3622i	−0.566224	+	0.475119i	−0.880391	−	0.474249i	$-0.842720\pi$
$677$	−14.7327	+	12.3622i	−0.566224	+	0.475119i	0.314166	+	0.949368i	$0.398275\pi$
$678$		0			0
$679$	−11.4963	+	65.1990i	−0.441189	+	2.50211i
$680$		0			0
$681$	12.6041	+	13.4490i	0.482991	+	0.515368i
$682$		0			0
$683$	19.7531	+	34.2134i	0.755832	+	1.30914i	0.944960	+	0.327186i	$0.106100\pi$
$683$	19.7531	+	34.2134i	0.755832	+	1.30914i	−0.189128	+	0.981952i	$0.560566\pi$
$684$		0			0
$685$	−8.32684	+	14.4225i	−0.318152	+	0.551056i
$686$		0			0
$687$	−9.69514	−	22.6833i	−0.369893	−	0.865421i
$688$		0			0
$689$	−3.97166	−	3.33262i	−0.151308	−	0.126963i
$690$		0			0
$691$	−10.3604	−	3.77088i	−0.394128	−	0.143451i	0.137351	−	0.990522i	$-0.456141\pi$
$691$	−10.3604	−	3.77088i	−0.394128	−	0.143451i	−0.531479	+	0.847072i	$0.678363\pi$
$692$		0			0
$693$	35.0058	−	17.2896i	1.32976	−	0.656776i
$694$		0			0
$695$	−7.92150	−	44.9251i	−0.300480	−	1.70411i
$696$		0			0
$697$	−12.8485	+	4.67646i	−0.486671	+	0.177134i
$698$		0			0
$699$	23.0234	−	15.0331i	0.870824	−	0.568604i
$700$		0			0
$701$	19.4643			0.735157			0.367578	−	0.929993i	$-0.380187\pi$
$701$	19.4643			0.735157			0.367578	+	0.929993i	$0.380187\pi$
$702$		0			0
$703$	2.90001			0.109376
$704$		0			0
$705$	1.39003	+	25.3184i	0.0523517	+	0.953546i
$706$		0			0
$707$	12.4604	−	4.53521i	0.468621	−	0.170564i
$708$		0			0
$709$	3.68146	+	20.8786i	0.138260	+	0.784112i	0.972534	+	0.232761i	$0.0747761\pi$
$709$	3.68146	+	20.8786i	0.138260	+	0.784112i	−0.834274	+	0.551350i	$0.814113\pi$
$710$		0			0
$711$	6.00078	+	1.46450i	0.225047	+	0.0549229i
$712$		0			0
$713$	−19.0478	−	6.93284i	−0.713346	−	0.259637i
$714$		0			0
$715$	−14.3743	−	12.0615i	−0.537569	−	0.451074i
$716$		0			0
$717$	11.1092	−	14.8190i	0.414881	−	0.553424i
$718$		0			0
$719$	10.7055	−	18.5424i	0.399247	−	0.691516i	−0.594386	−	0.804180i	$-0.702605\pi$
$719$	10.7055	−	18.5424i	0.399247	−	0.691516i	0.993633	+	0.112664i	$0.0359383\pi$
$720$		0			0
$721$	−24.9554	−	43.2241i	−0.929389	−	1.60975i
$722$		0			0
$723$	25.4516	−	5.94269i	0.946557	−	0.221011i
$724$		0			0
$725$	1.18421	−	6.71598i	0.0439804	−	0.249425i
$726$		0			0
$727$	−19.1435	+	16.0633i	−0.709994	+	0.595756i	−0.924598	−	0.380945i	$-0.875599\pi$
$727$	−19.1435	+	16.0633i	−0.709994	+	0.595756i	0.214603	+	0.976701i	$0.431154\pi$
$728$		0			0
$729$	−25.5512	+	8.72573i	−0.946339	+	0.323175i
$730$		0			0
$731$	−12.0496	+	10.1108i	−0.445671	+	0.373963i
$732$		0			0
$733$	6.39490	−	36.2673i	0.236201	−	1.33956i	−0.603869	−	0.797084i	$-0.706375\pi$
$733$	6.39490	−	36.2673i	0.236201	−	1.33956i	0.840070	−	0.542478i	$-0.182514\pi$
$734$		0			0
$735$	53.3782	−	12.4632i	1.96888	−	0.459714i
$736$		0			0
$737$	4.52558	+	7.83854i	0.166702	+	0.288736i
$738$		0			0
$739$	24.0508	−	41.6573i	0.884724	−	1.53239i	0.0386947	−	0.999251i	$-0.487680\pi$
$739$	24.0508	−	41.6573i	0.884724	−	1.53239i	0.846029	−	0.533136i	$-0.178987\pi$
$740$		0			0
$741$	−5.59501	+	7.46338i	−0.205538	+	0.274174i
$742$		0			0
$743$	−30.1085	−	25.2640i	−1.10457	−	0.926846i	−0.106848	−	0.994275i	$-0.534076\pi$
$743$	−30.1085	−	25.2640i	−1.10457	−	0.926846i	−0.997724	+	0.0674292i	$0.978520\pi$
$744$		0			0
$745$	0.832316	+	0.302938i	0.0304937	+	0.0110988i
$746$		0			0
$747$	−4.56969	−	1.11524i	−0.167196	−	0.0408044i
$748$		0			0
$749$	−3.79124	−	21.5012i	−0.138529	−	0.785636i
$750$		0			0
$751$	−30.2087	+	10.9951i	−1.10233	+	0.401215i	−0.828174	−	0.560470i	$-0.810620\pi$
$751$	−30.2087	+	10.9951i	−1.10233	+	0.401215i	−0.274155	+	0.961685i	$0.588398\pi$
$752$		0			0
$753$	1.53383	+	27.9375i	0.0558958	+	1.01810i
$754$		0			0
$755$	8.64638			0.314674
$756$		0			0
$757$	−8.58106			−0.311884			−0.155942	−	0.987766i	$-0.549841\pi$
$757$	−8.58106			−0.311884			−0.155942	+	0.987766i	$0.549841\pi$
$758$		0			0
$759$	39.1218	−	25.5445i	1.42003	−	0.927208i
$760$		0			0
$761$	−36.1796	+	13.1683i	−1.31151	+	0.477350i	−0.900728	−	0.434384i	$-0.856966\pi$
$761$	−36.1796	+	13.1683i	−1.31151	+	0.477350i	−0.410781	+	0.911734i	$0.634744\pi$
$762$		0			0
$763$	2.85506	+	16.1918i	0.103360	+	0.586184i
$764$		0			0
$765$	−21.9815	+	10.8568i	−0.794743	+	0.392528i
$766$		0			0
$767$	16.3313	+	5.94410i	0.589688	+	0.214629i
$768$		0			0
$769$	−0.402488	−	0.337727i	−0.0145141	−	0.0121788i	0.635502	−	0.772099i	$-0.280793\pi$
$769$	−0.402488	−	0.337727i	−0.0145141	−	0.0121788i	−0.650016	+	0.759921i	$0.725238\pi$
$770$		0			0
$771$	1.24095	+	2.90339i	0.0446916	+	0.104563i
$772$		0			0
$773$	7.89821	−	13.6801i	0.284079	−	0.492039i	−0.688307	−	0.725420i	$-0.741646\pi$
$773$	7.89821	−	13.6801i	0.284079	−	0.492039i	0.972385	+	0.233381i	$0.0749789\pi$
$774$		0			0
$775$	1.07805	+	1.86724i	0.0387248	+	0.0670734i
$776$		0			0
$777$	7.49441	+	7.99680i	0.268861	+	0.286884i
$778$		0			0
$779$	−1.45445	+	8.24858i	−0.0521109	+	0.295536i
$780$		0			0
$781$	−29.5151	+	24.7661i	−1.05613	+	0.886202i
$782$		0			0
$783$	−27.3419	−	23.4121i	−0.977120	−	0.836679i
$784$		0			0
$785$	23.3589	−	19.6005i	0.833716	−	0.699571i
$786$		0			0
$787$	0.719048	−	4.07793i	0.0256313	−	0.145362i	−0.969306	−	0.245856i	$-0.920931\pi$
$787$	0.719048	−	4.07793i	0.0256313	−	0.145362i	0.994938	+	0.100493i	$0.0320421\pi$
$788$		0			0
$789$	6.82784	−	22.5332i	0.243078	−	0.802202i
$790$		0			0
$791$	15.5745	+	26.9758i	0.553765	+	0.959149i
$792$		0			0
$793$	−9.50476	+	16.4627i	−0.337524	+	0.584608i
$794$		0			0
$795$	−8.28791	−	0.996708i	−0.293942	−	0.0353496i
$796$		0			0
$797$	31.1285	+	26.1199i	1.10263	+	0.925215i	0.997599	−	0.0692544i	$-0.0220620\pi$
$797$	31.1285	+	26.1199i	1.10263	+	0.925215i	0.105029	+	0.994469i	$0.466506\pi$
$798$		0			0
$799$	18.7857	+	6.83745i	0.664592	+	0.241892i
$800$		0			0
$801$	16.6190	−	37.8323i	0.587205	−	1.33674i
$802$		0			0
$803$	6.48119	+	36.7566i	0.228716	+	1.29711i
$804$		0			0
$805$	94.9944	−	34.5751i	3.34811	−	1.21861i
$806$		0			0
$807$	24.8166	+	12.5671i	0.873587	+	0.442381i
$808$		0			0
$809$	−18.5974			−0.653851			−0.326925	−	0.945050i	$-0.606013\pi$
$809$	−18.5974			−0.653851			−0.326925	+	0.945050i	$0.606013\pi$
$810$		0			0
$811$	−16.3945			−0.575690			−0.287845	−	0.957677i	$-0.592939\pi$
$811$	−16.3945			−0.575690			−0.287845	+	0.957677i	$0.592939\pi$
$812$		0			0
$813$	24.8505	+	12.5842i	0.871546	+	0.441348i
$814$		0			0
$815$	−37.0392	+	13.4812i	−1.29743	+	0.472224i
$816$		0			0
$817$	1.67321	+	9.48927i	0.0585383	+	0.331987i
$818$		0			0
$819$	−35.0393	+	3.85910i	−1.22437	+	0.134848i
$820$		0			0
$821$	−48.0156	−	17.4762i	−1.67575	−	0.609925i	−0.683037	−	0.730384i	$-0.739341\pi$
$821$	−48.0156	−	17.4762i	−1.67575	−	0.609925i	−0.992718	+	0.120459i	$0.961563\pi$
$822$		0			0
$823$	25.2465	+	21.1843i	0.880038	+	0.738439i	0.966187	−	0.257843i	$-0.0830117\pi$
$823$	25.2465	+	21.1843i	0.880038	+	0.738439i	−0.0861493	+	0.996282i	$0.527456\pi$
$824$		0			0
$825$	−4.93428	−	0.593399i	−0.171790	−	0.0206595i
$826$		0			0
$827$	13.1025	−	22.6941i	0.455617	−	0.789152i	−0.543106	−	0.839664i	$-0.682752\pi$
$827$	13.1025	−	22.6941i	0.455617	−	0.789152i	0.998723	+	0.0505118i	$0.0160852\pi$
$828$		0			0
$829$	−21.8984	−	37.9291i	−0.760563	−	1.31733i	−0.942561	−	0.334035i	$-0.891590\pi$
$829$	−21.8984	−	37.9291i	−0.760563	−	1.31733i	0.181998	−	0.983299i	$-0.441744\pi$
$830$		0			0
$831$	7.58601	−	25.0353i	0.263156	−	0.868464i
$832$		0			0
$833$	7.50436	−	42.5593i	0.260011	−	1.47459i
$834$		0			0
$835$	33.4602	−	28.0764i	1.15794	−	0.971625i
$836$		0			0
$837$	11.3800	+	0.113708i	0.393352	+	0.00393033i
$838$		0			0
$839$	−11.6982	+	9.81599i	−0.403868	+	0.338886i	−0.821987	−	0.569507i	$-0.807134\pi$
$839$	−11.6982	+	9.81599i	−0.403868	+	0.338886i	0.418118	+	0.908393i	$0.362690\pi$
$840$		0			0
$841$	3.29742	−	18.7006i	0.113704	−	0.644848i
$842$		0			0
$843$	−7.36773	−	7.86162i	−0.253758	−	0.270769i
$844$		0			0
$845$	−7.42997	−	12.8691i	−0.255599	−	0.442710i
$846$		0			0
$847$	−5.59138	+	9.68455i	−0.192122	+	0.332765i
$848$		0			0
$849$	−6.89497	−	16.1319i	−0.236635	−	0.553644i
$850$		0			0
$851$	10.0472	+	8.43056i	0.344412	+	0.288996i
$852$		0			0
$853$	33.5924	+	12.2266i	1.15018	+	0.418632i	0.845581	−	0.533848i	$-0.179254\pi$
$853$	33.5924	+	12.2266i	1.15018	+	0.418632i	0.304602	+	0.952480i	$0.401477\pi$
$854$		0			0
$855$	−0.973082	+	14.9867i	−0.0332787	+	0.512534i
$856$		0			0
$857$	8.58863	+	48.7086i	0.293382	+	1.66385i	0.673706	+	0.738999i	$0.264701\pi$
$857$	8.58863	+	48.7086i	0.293382	+	1.66385i	−0.380324	+	0.924853i	$0.624188\pi$
$858$		0			0
$859$	28.7052	−	10.4479i	0.979410	−	0.356476i	0.197799	−	0.980243i	$-0.436621\pi$
$859$	28.7052	−	10.4479i	0.979410	−	0.356476i	0.781611	+	0.623766i	$0.214398\pi$
$860$		0			0
$861$	−26.5042	+	17.3059i	−0.903260	+	0.589783i
$862$		0			0
$863$	26.4315			0.899738			0.449869	−	0.893095i	$-0.351471\pi$
$863$	26.4315			0.899738			0.449869	+	0.893095i	$0.351471\pi$
$864$		0			0
$865$	−36.4087			−1.23793
$866$		0			0
$867$	−0.554545	−	10.1006i	−0.0188333	−	0.343034i
$868$		0			0
$869$	5.63935	−	2.05256i	0.191302	−	0.0696282i
$870$		0			0
$871$	−1.41909	−	8.04803i	−0.0480839	−	0.272697i
$872$		0			0
$873$	−12.4735	−	42.6975i	−0.422164	−	1.44509i
$874$		0			0
$875$	41.2163	+	15.0015i	1.39337	+	0.507144i
$876$		0			0
$877$	−24.7367	−	20.7565i	−0.835298	−	0.700898i	0.121203	−	0.992628i	$-0.461325\pi$
$877$	−24.7367	−	20.7565i	−0.835298	−	0.700898i	−0.956501	+	0.291729i	$0.905769\pi$
$878$		0			0
$879$	−30.0732	+	40.1157i	−1.01434	+	1.35307i
$880$		0			0
$881$	7.59147	−	13.1488i	0.255763	−	0.442995i	−0.709339	−	0.704867i	$-0.751007\pi$
$881$	7.59147	−	13.1488i	0.255763	−	0.442995i	0.965103	+	0.261872i	$0.0843400\pi$
$882$		0			0
$883$	−28.8015	−	49.8856i	−0.969246	−	1.67878i	−0.697746	−	0.716346i	$-0.745813\pi$
$883$	−28.8015	−	49.8856i	−0.969246	−	1.67878i	−0.271501	−	0.962438i	$-0.587520\pi$
$884$		0			0
$885$	27.2491	−	6.36237i	0.915967	−	0.213869i
$886$		0			0
$887$	4.36638	−	24.7630i	0.146609	−	0.831460i	−0.819453	−	0.573147i	$-0.805722\pi$
$887$	4.36638	−	24.7630i	0.146609	−	0.831460i	0.966061	−	0.258313i	$-0.0831665\pi$
$888$		0			0
$889$	−66.2145	+	55.5606i	−2.22076	+	1.86344i
$890$		0			0
$891$	−15.9438	+	20.8310i	−0.534136	+	0.697865i
$892$		0			0
$893$	9.38119	−	7.87175i	0.313930	−	0.263418i
$894$		0			0
$895$	0.694517	−	3.93880i	0.0232151	−	0.131660i
$896$		0			0
$897$	−41.0807	+	9.59190i	−1.37164	+	0.320264i
$898$		0			0
$899$	7.58621	+	13.1397i	0.253014	+	0.438233i
$900$		0			0
$901$	−3.29068	+	5.69962i	−0.109628	+	0.189882i
$902$		0			0
$903$	−21.8427	+	29.1367i	−0.726879	+	0.969609i
$904$		0			0
$905$	−8.12700	−	6.81936i	−0.270150	−	0.226683i
$906$		0			0
$907$	11.1517	+	4.05888i	0.370286	+	0.134773i	0.520459	−	0.853887i	$-0.325761\pi$
$907$	11.1517	+	4.05888i	0.370286	+	0.134773i	−0.150173	+	0.988660i	$0.547983\pi$
$908$		0			0
$909$	−6.15694	+	6.43950i	−0.204213	+	0.213585i
$910$		0			0
$911$	−1.83884	−	10.4286i	−0.0609234	−	0.345514i	−0.999998	−	0.00180148i	$-0.999427\pi$
$911$	−1.83884	−	10.4286i	−0.0609234	−	0.345514i	0.939075	−	0.343712i	$-0.111685\pi$
$912$		0			0
$913$	−4.29446	+	1.56305i	−0.142126	+	0.0517295i
$914$		0			0
$915$	1.67784	+	30.5606i	0.0554678	+	1.01030i
$916$		0			0
$917$	12.3890			0.409121
$918$		0			0
$919$	56.7884			1.87328			0.936639	−	0.350297i	$-0.113919\pi$
$919$	56.7884			1.87328			0.936639	+	0.350297i	$0.113919\pi$
$920$		0			0
$921$	3.88617	−	2.53747i	0.128054	−	0.0836125i
$922$		0			0
$923$	32.6896	−	11.8981i	1.07599	−	0.391629i
$924$		0			0
$925$	−0.242254	−	1.37389i	−0.00796525	−	0.0451732i
$926$		0			0
$927$	27.8943	+	18.6137i	0.916168	+	0.611355i
$928$		0			0
$929$	13.9543	+	5.07894i	0.457825	+	0.166635i	0.560629	−	0.828067i	$-0.310559\pi$
$929$	13.9543	+	5.07894i	0.457825	+	0.166635i	−0.102804	+	0.994702i	$0.532782\pi$
$930$		0			0
$931$	−20.2796	−	17.0166i	−0.664636	−	0.557696i
$932$		0			0
$933$	9.91800	+	23.2047i	0.324701	+	0.759688i
$934$		0			0
$935$	−11.9097	+	20.6282i	−0.389489	+	0.674614i
$936$		0			0
$937$	3.12589	+	5.41420i	0.102118	+	0.176874i	0.912557	−	0.408949i	$-0.134105\pi$
$937$	3.12589	+	5.41420i	0.102118	+	0.176874i	−0.810439	+	0.585823i	$0.800771\pi$
$938$		0			0
$939$	−31.4675	−	33.5769i	−1.02690	−	1.09574i
$940$		0			0
$941$	7.42421	−	42.1048i	0.242022	−	1.37258i	−0.585286	−	0.810827i	$-0.699018\pi$
$941$	7.42421	−	42.1048i	0.242022	−	1.37258i	0.827308	−	0.561749i	$-0.189871\pi$
$942$		0			0
$943$	−29.0182	+	24.3492i	−0.944963	+	0.792918i
$944$		0			0
$945$	−43.8406	+	36.0464i	−1.42614	+	1.17259i
$946$		0			0
$947$	−35.1099	+	29.4607i	−1.14092	+	0.957343i	−0.999468	−	0.0326022i	$-0.989621\pi$
$947$	−35.1099	+	29.4607i	−1.14092	+	0.957343i	−0.141449	+	0.989946i	$0.545176\pi$
$948$		0			0
$949$	5.85179	−	33.1871i	0.189957	−	1.07730i
$950$		0			0
$951$	−10.4129	+	34.3645i	−0.337662	+	1.11435i
$952$		0			0
$953$	14.9742	+	25.9361i	0.485062	+	0.840152i	0.999853	−	0.0171636i	$-0.00546362\pi$
$953$	14.9742	+	25.9361i	0.485062	+	0.840152i	−0.514790	+	0.857316i	$0.672130\pi$
$954$		0			0
$955$	1.05609	−	1.82920i	0.0341742	−	0.0591915i
$956$		0			0
$957$	−34.7223	−	4.17572i	−1.12241	−	0.134982i
$958$		0			0
$959$	23.2851	+	19.5385i	0.751915	+	0.630931i
$960$		0			0
$961$	24.6228	+	8.96196i	0.794284	+	0.289096i
$962$		0			0
$963$	8.68128	+	11.8246i	0.279750	+	0.381043i
$964$		0			0
$965$	2.21271	+	12.5489i	0.0712296	+	0.403963i
$966$		0			0
$967$	4.92520	−	1.79262i	0.158384	−	0.0576469i	−0.261612	−	0.965173i	$-0.584254\pi$
$967$	4.92520	−	1.79262i	0.158384	−	0.0576469i	0.419995	+	0.907526i	$0.362032\pi$
$968$		0			0
$969$	10.5634	+	5.34924i	0.339344	+	0.171842i
$970$		0			0
$971$	39.9453			1.28191			0.640953	−	0.767580i	$-0.278539\pi$
$971$	39.9453			1.28191			0.640953	+	0.767580i	$0.278539\pi$
$972$		0			0
$973$	−83.2627			−2.66928
$974$		0			0
$975$	4.00318	+	2.02720i	0.128204	+	0.0649222i
$976$		0			0
$977$	−41.6045	+	15.1428i	−1.33105	+	0.484462i	−0.906982	−	0.421170i	$-0.861620\pi$
$977$	−41.6045	+	15.1428i	−1.33105	+	0.484462i	−0.424065	+	0.905632i	$0.639397\pi$
$978$		0			0
$979$	−6.97141	−	39.5368i	−0.222807	−	1.26360i
$980$		0			0
$981$	−6.53759	−	8.90474i	−0.208729	−	0.284306i
$982$		0			0
$983$	−20.6361	−	7.51093i	−0.658189	−	0.239561i	−0.00873499	−	0.999962i	$-0.502780\pi$
$983$	−20.6361	−	7.51093i	−0.658189	−	0.239561i	−0.649454	+	0.760400i	$0.725003\pi$
$984$		0			0
$985$	49.3046	+	41.3714i	1.57097	+	1.31820i
$986$		0			0
$987$	45.9500	+	5.52597i	1.46260	+	0.175894i
$988$		0			0
$989$	−21.7892	+	37.7399i	−0.692855	+	1.20006i
$990$		0			0
$991$	19.6409	+	34.0190i	0.623912	+	1.08065i	0.988750	+	0.149577i	$0.0477911\pi$
$991$	19.6409	+	34.0190i	0.623912	+	1.08065i	−0.364838	+	0.931071i	$0.618876\pi$
$992$		0			0
$993$	−5.61490	+	18.5302i	−0.178183	+	0.588039i
$994$		0			0
$995$	4.57498	−	25.9460i	0.145037	−	0.822544i
$996$		0			0
$997$	20.1124	−	16.8763i	0.636967	−	0.534479i	−0.266118	−	0.963940i	$-0.585741\pi$
$997$	20.1124	−	16.8763i	0.636967	−	0.534479i	0.903085	+	0.429462i	$0.141297\pi$
$998$		0			0
$999$	−6.89409	−	2.58754i	−0.218119	−	0.0818661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.i.a.49.1	✓	18
3.2	odd	2		324.2.i.a.37.1		18
4.3	odd	2		432.2.u.d.49.3		18
9.2	odd	6		972.2.i.d.433.3		18
9.4	even	3		972.2.i.c.757.1		18
9.5	odd	6		972.2.i.b.757.3		18
9.7	even	3		972.2.i.a.433.1		18
27.2	odd	18		972.2.i.d.541.3		18
27.4	even	9		2916.2.a.d.1.1		9
27.5	odd	18		2916.2.e.d.973.1		18
27.7	even	9		972.2.i.c.217.1		18
27.11	odd	18		324.2.i.a.289.1		18
27.13	even	9		2916.2.e.c.1945.9		18
27.14	odd	18		2916.2.e.d.1945.1		18
27.16	even	9	inner	108.2.i.a.97.1	yes	18
27.20	odd	18		972.2.i.b.217.3		18
27.22	even	9		2916.2.e.c.973.9		18
27.23	odd	18		2916.2.a.c.1.9		9
27.25	even	9		972.2.i.a.541.1		18
108.43	odd	18		432.2.u.d.97.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.i.a.49.1	✓	18	1.1	even	1	trivial
108.2.i.a.97.1	yes	18	27.16	even	9	inner
324.2.i.a.37.1		18	3.2	odd	2
324.2.i.a.289.1		18	27.11	odd	18
432.2.u.d.49.3		18	4.3	odd	2
432.2.u.d.97.3		18	108.43	odd	18
972.2.i.a.433.1		18	9.7	even	3
972.2.i.a.541.1		18	27.25	even	9
972.2.i.b.217.3		18	27.20	odd	18
972.2.i.b.757.3		18	9.5	odd	6
972.2.i.c.217.1		18	27.7	even	9
972.2.i.c.757.1		18	9.4	even	3
972.2.i.d.433.3		18	9.2	odd	6
972.2.i.d.541.3		18	27.2	odd	18
2916.2.a.c.1.9		9	27.23	odd	18
2916.2.a.d.1.1		9	27.4	even	9
2916.2.e.c.973.9		18	27.22	even	9
2916.2.e.c.1945.9		18	27.13	even	9
2916.2.e.d.973.1		18	27.5	odd	18
2916.2.e.d.1945.1		18	27.14	odd	18

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54522 - 0.782494i) q^{3} +(2.29878 - 0.836687i) q^{5} +(-0.775345 - 4.39720i) q^{7} +(1.77541 + 2.41825i) q^{9} +O(q^{10})\)	\(q+(-1.54522 - 0.782494i) q^{3} +(2.29878 - 0.836687i) q^{5} +(-0.775345 - 4.39720i) q^{7} +(1.77541 + 2.41825i) q^{9} +(2.73892 + 0.996887i) q^{11} +(-2.01596 - 1.69159i) q^{13} +(-4.20682 - 0.505915i) q^{15} +(-1.67030 + 2.89305i) q^{17} +(1.02319 + 1.77222i) q^{19} +(-2.24270 + 7.40135i) q^{21} +(-1.60711 + 9.11438i) q^{23} +(0.754121 - 0.632782i) q^{25} +(-0.851129 - 5.12597i) q^{27} +(5.30671 - 4.45286i) q^{29} +(-0.380324 + 2.15692i) q^{31} +(-3.45218 - 3.68360i) q^{33} +(-5.46143 - 9.45948i) q^{35} +(0.708571 - 1.22728i) q^{37} +(1.79144 + 4.19136i) q^{39} +(3.13541 + 2.63092i) q^{41} +(4.42467 + 1.61045i) q^{43} +(6.10459 + 4.07356i) q^{45} +(-1.03917 - 5.89344i) q^{47} +(-12.1564 + 4.42456i) q^{49} +(4.84477 - 3.16339i) q^{51} +1.97011 q^{53} +7.13026 q^{55} +(-0.194305 - 3.53911i) q^{57} +(-6.20572 + 2.25870i) q^{59} +(-1.25433 - 7.11368i) q^{61} +(9.25698 - 9.68180i) q^{63} +(-6.04958 - 2.20187i) q^{65} +(2.37884 + 1.99608i) q^{67} +(9.61529 - 12.8262i) q^{69} +(-6.60947 + 11.4479i) q^{71} +(6.40266 + 11.0897i) q^{73} +(-1.66043 + 0.387693i) q^{75} +(2.25990 - 12.8165i) q^{77} +(1.57726 - 1.32348i) q^{79} +(-2.69586 + 8.58675i) q^{81} +(-1.20111 + 1.00785i) q^{83} +(-1.41908 + 8.04800i) q^{85} +(-11.6844 + 2.72818i) q^{87} +(-6.88694 - 11.9285i) q^{89} +(-5.87520 + 10.1761i) q^{91} +(2.27546 - 3.03532i) q^{93} +(3.83488 + 3.21785i) q^{95} +(-13.9332 - 5.07127i) q^{97} +(2.45198 + 8.39328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 18 * q + 3 * q^5 + 6 * q^9	\( 18 q + 3 q^{5} + 6 q^{9} + 3 q^{11} - 9 q^{15} - 12 q^{17} - 30 q^{21} - 30 q^{23} + 9 q^{25} - 27 q^{27} - 24 q^{29} + 9 q^{31} - 18 q^{33} - 21 q^{35} + 3 q^{39} + 21 q^{41} - 9 q^{43} + 45 q^{45} + 45 q^{47} - 18 q^{49} + 63 q^{51} + 66 q^{53} + 54 q^{57} + 60 q^{59} - 18 q^{61} + 57 q^{63} + 33 q^{65} - 27 q^{67} - 9 q^{69} - 12 q^{71} + 9 q^{73} - 33 q^{75} - 75 q^{77} - 36 q^{79} - 54 q^{81} - 45 q^{83} - 36 q^{85} - 63 q^{87} - 48 q^{89} + 9 q^{91} - 33 q^{93} + 6 q^{95} - 27 q^{97} + 27 q^{99}+O(q^{100}) \) 18 * q + 3 * q^5 + 6 * q^9 + 3 * q^11 - 9 * q^15 - 12 * q^17 - 30 * q^21 - 30 * q^23 + 9 * q^25 - 27 * q^27 - 24 * q^29 + 9 * q^31 - 18 * q^33 - 21 * q^35 + 3 * q^39 + 21 * q^41 - 9 * q^43 + 45 * q^45 + 45 * q^47 - 18 * q^49 + 63 * q^51 + 66 * q^53 + 54 * q^57 + 60 * q^59 - 18 * q^61 + 57 * q^63 + 33 * q^65 - 27 * q^67 - 9 * q^69 - 12 * q^71 + 9 * q^73 - 33 * q^75 - 75 * q^77 - 36 * q^79 - 54 * q^81 - 45 * q^83 - 36 * q^85 - 63 * q^87 - 48 * q^89 + 9 * q^91 - 33 * q^93 + 6 * q^95 - 27 * q^97 + 27 * q^99

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