LMFDB - Embedded newform 342.2.u.b.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(55,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("342.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.u (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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			289.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	342.289
Dual form			342.2.u.b.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.0923963 - 0.0775297i) q^{5} +(2.14543 - 3.71599i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.0923963 - 0.0775297i) q^{5} +(2.14543 - 3.71599i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.113341 - 0.0412527i) q^{10} +(1.28699 + 2.22913i) q^{11} +(0.141559 - 0.802823i) q^{13} +(3.28699 - 2.75811i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-0.439693 - 0.160035i) q^{17} +(3.16637 + 2.99568i) q^{19} +0.120615 q^{20} +(0.446967 + 2.53487i) q^{22} +(-4.25490 - 3.57029i) q^{23} +(-0.865715 + 4.90971i) q^{25} +(0.407604 - 0.705990i) q^{26} +(4.03209 - 1.46756i) q^{28} +(2.20574 - 0.802823i) q^{29} +(-2.67365 + 4.63089i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-0.358441 - 0.300767i) q^{34} +(-0.0898700 - 0.509678i) q^{35} -8.51754 q^{37} +(1.95084 + 3.89798i) q^{38} +(0.113341 + 0.0412527i) q^{40} +(-0.666374 - 3.77920i) q^{41} +(7.14930 - 5.99898i) q^{43} +(-0.446967 + 2.53487i) q^{44} +(-2.77719 - 4.81023i) q^{46} +(-8.90420 + 3.24086i) q^{47} +(-5.70574 - 9.88263i) q^{49} +(-2.49273 + 4.31753i) q^{50} +(0.624485 - 0.524005i) q^{52} +(-9.77379 - 8.20118i) q^{53} +(0.291737 + 0.106183i) q^{55} +4.29086 q^{56} +2.34730 q^{58} +(14.1420 + 5.14728i) q^{59} +(-1.31521 - 1.10359i) q^{61} +(-4.09627 + 3.43718i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-0.0491630 - 0.0851529i) q^{65} +(-10.7652 + 3.91820i) q^{67} +(-0.233956 - 0.405223i) q^{68} +(0.0898700 - 0.509678i) q^{70} +(-10.2135 + 8.57013i) q^{71} +(0.396459 + 2.24843i) q^{73} +(-8.00387 - 2.91317i) q^{74} +(0.500000 + 4.33013i) q^{76} +11.0446 q^{77} +(0.843426 + 4.78331i) q^{79} +(0.0923963 + 0.0775297i) q^{80} +(0.666374 - 3.77920i) q^{82} +(1.62449 - 2.81369i) q^{83} +(-0.0530334 + 0.0193026i) q^{85} +(8.76991 - 3.19199i) q^{86} +(-1.28699 + 2.22913i) q^{88} +(-0.595800 + 3.37895i) q^{89} +(-2.67958 - 2.24843i) q^{91} +(-0.964508 - 5.46999i) q^{92} -9.47565 q^{94} +(0.524815 + 0.0313013i) q^{95} +(-2.91400 - 1.06061i) q^{97} +(-1.98158 - 11.2381i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 3 * q^5 - 3 * q^7 + 3 * q^8	$ 6 q - 3 q^{5} - 3 q^{7} + 3 q^{8} - 6 q^{10} + 9 q^{13} + 12 q^{14} + 3 q^{17} + 12 q^{20} + 15 q^{22} - 27 q^{23} - 15 q^{25} + 6 q^{26} + 15 q^{28} + 3 q^{29} - 15 q^{31} + 6 q^{34} - 12 q^{35} - 6 q^{37} - 6 q^{40} + 15 q^{41} + 3 q^{43} - 15 q^{44} - 6 q^{46} - 15 q^{47} - 24 q^{49} + 3 q^{50} - 9 q^{52} - 6 q^{53} + 27 q^{55} - 6 q^{56} + 12 q^{58} + 27 q^{59} - 15 q^{61} + 3 q^{62} - 3 q^{64} - 12 q^{65} - 3 q^{67} - 6 q^{68} + 12 q^{70} - 3 q^{71} + 12 q^{73} - 24 q^{74} + 3 q^{76} + 42 q^{77} + 27 q^{79} - 3 q^{80} - 15 q^{82} - 3 q^{83} + 12 q^{85} + 24 q^{86} - 42 q^{89} - 42 q^{91} + 27 q^{92} - 18 q^{94} - 24 q^{95} + 18 q^{97}+O(q^{100}) $ 6 * q - 3 * q^5 - 3 * q^7 + 3 * q^8 - 6 * q^10 + 9 * q^13 + 12 * q^14 + 3 * q^17 + 12 * q^20 + 15 * q^22 - 27 * q^23 - 15 * q^25 + 6 * q^26 + 15 * q^28 + 3 * q^29 - 15 * q^31 + 6 * q^34 - 12 * q^35 - 6 * q^37 - 6 * q^40 + 15 * q^41 + 3 * q^43 - 15 * q^44 - 6 * q^46 - 15 * q^47 - 24 * q^49 + 3 * q^50 - 9 * q^52 - 6 * q^53 + 27 * q^55 - 6 * q^56 + 12 * q^58 + 27 * q^59 - 15 * q^61 + 3 * q^62 - 3 * q^64 - 12 * q^65 - 3 * q^67 - 6 * q^68 + 12 * q^70 - 3 * q^71 + 12 * q^73 - 24 * q^74 + 3 * q^76 + 42 * q^77 + 27 * q^79 - 3 * q^80 - 15 * q^82 - 3 * q^83 + 12 * q^85 + 24 * q^86 - 42 * q^89 - 42 * q^91 + 27 * q^92 - 18 * q^94 - 24 * q^95 + 18 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$		0			0
$3$		0			0
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.0923963	−	0.0775297i	0.0413209	−	0.0346723i	−0.621893	−	0.783102i	$-0.713636\pi$
$5$	0.0923963	−	0.0775297i	0.0413209	−	0.0346723i	0.663214	+	0.748430i	$0.269192\pi$
$6$		0			0
$7$	2.14543	−	3.71599i	0.810896	−	1.40451i	−0.101341	−	0.994852i	$-0.532313\pi$
$7$	2.14543	−	3.71599i	0.810896	−	1.40451i	0.912238	−	0.409662i	$-0.134353\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$		0			0
$10$	0.113341	−	0.0412527i	0.0358415	−	0.0130452i
$11$	1.28699	+	2.22913i	0.388042	+	0.672108i	0.992186	−	0.124767i	$-0.0398183\pi$
$11$	1.28699	+	2.22913i	0.388042	+	0.672108i	−0.604144	+	0.796875i	$0.706485\pi$
$12$		0			0
$13$	0.141559	−	0.802823i	0.0392615	−	0.222663i	−0.958864	−	0.283866i	$-0.908383\pi$
$13$	0.141559	−	0.802823i	0.0392615	−	0.222663i	0.998125	+	0.0612035i	$0.0194939\pi$
$14$	3.28699	−	2.75811i	0.878485	−	0.737136i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−0.439693	−	0.160035i	−0.106641	−	0.0388142i	0.288149	−	0.957586i	$-0.406960\pi$
$17$	−0.439693	−	0.160035i	−0.106641	−	0.0388142i	−0.394790	+	0.918772i	$0.629183\pi$
$18$		0			0
$19$	3.16637	+	2.99568i	0.726416	+	0.687255i
$19$	3.16637	+	2.99568i	0.726416	+	0.687255i
$20$	0.120615			0.0269703
$21$		0			0
$22$	0.446967	+	2.53487i	0.0952936	+	0.540437i
$23$	−4.25490	−	3.57029i	−0.887208	−	0.744456i	0.0804401	−	0.996759i	$-0.474367\pi$
$23$	−4.25490	−	3.57029i	−0.887208	−	0.744456i	−0.967648	+	0.252304i	$0.918812\pi$
$24$		0			0
$25$	−0.865715	+	4.90971i	−0.173143	+	0.981942i
$26$	0.407604	−	0.705990i	0.0799377	−	0.138456i
$27$		0			0
$28$	4.03209	−	1.46756i	0.761993	−	0.277343i
$29$	2.20574	−	0.802823i	0.409595	−	0.149080i	−0.129001	−	0.991644i	$-0.541177\pi$
$29$	2.20574	−	0.802823i	0.409595	−	0.149080i	0.538596	+	0.842564i	$0.318955\pi$
$30$		0			0
$31$	−2.67365	+	4.63089i	−0.480201	+	0.831733i	−0.999742	−	0.0227125i	$-0.992770\pi$
$31$	−2.67365	+	4.63089i	−0.480201	+	0.831733i	0.519541	+	0.854446i	$0.326103\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$		0			0
$34$	−0.358441	−	0.300767i	−0.0614721	−	0.0515812i
$35$	−0.0898700	−	0.509678i	−0.0151908	−	0.0861514i
$36$		0			0
$37$	−8.51754			−1.40028			−0.700138	−	0.714008i	$-0.746878\pi$
$37$	−8.51754			−1.40028			−0.700138	+	0.714008i	$0.746878\pi$
$38$	1.95084	+	3.89798i	0.316468	+	0.632336i
$39$		0			0
$40$	0.113341	+	0.0412527i	0.0179208	+	0.00652262i
$41$	−0.666374	−	3.77920i	−0.104070	−	0.590211i	−0.991588	−	0.129437i	$-0.958683\pi$
$41$	−0.666374	−	3.77920i	−0.104070	−	0.590211i	0.887517	−	0.460774i	$-0.152428\pi$
$42$		0			0
$43$	7.14930	−	5.99898i	1.09026	−	0.914835i	0.0935262	−	0.995617i	$-0.470186\pi$
$43$	7.14930	−	5.99898i	1.09026	−	0.914835i	0.996732	+	0.0807817i	$0.0257417\pi$
$44$	−0.446967	+	2.53487i	−0.0673827	+	0.382147i
$45$		0			0
$46$	−2.77719	−	4.81023i	−0.409474	−	0.709230i
$47$	−8.90420	+	3.24086i	−1.29881	+	0.472729i	−0.896609	−	0.442822i	$-0.853977\pi$
$47$	−8.90420	+	3.24086i	−1.29881	+	0.472729i	−0.402202	+	0.915551i	$0.631755\pi$
$48$		0			0
$49$	−5.70574	−	9.88263i	−0.815105	−	1.41180i
$50$	−2.49273	+	4.31753i	−0.352525	+	0.610591i
$51$		0			0
$52$	0.624485	−	0.524005i	0.0866005	−	0.0726665i
$53$	−9.77379	−	8.20118i	−1.34253	−	1.12652i	−0.980968	−	0.194172i	$-0.937798\pi$
$53$	−9.77379	−	8.20118i	−1.34253	−	1.12652i	−0.361565	−	0.932347i	$-0.617757\pi$
$54$		0			0
$55$	0.291737	+	0.106183i	0.0393378	+	0.0143178i
$56$	4.29086			0.573390
$57$		0			0
$58$	2.34730			0.308215
$59$	14.1420	+	5.14728i	1.84113	+	0.670118i	0.989220	+	0.146439i	$0.0467811\pi$
$59$	14.1420	+	5.14728i	1.84113	+	0.670118i	0.851915	+	0.523680i	$0.175441\pi$
$60$		0			0
$61$	−1.31521	−	1.10359i	−0.168395	−	0.141300i	0.554696	−	0.832053i	$-0.312835\pi$
$61$	−1.31521	−	1.10359i	−0.168395	−	0.141300i	−0.723091	+	0.690753i	$0.757279\pi$
$62$	−4.09627	+	3.43718i	−0.520226	+	0.436522i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.0491630	−	0.0851529i	−0.00609792	−	0.0105619i
$66$		0			0
$67$	−10.7652	+	3.91820i	−1.31517	+	0.478684i	−0.901909	−	0.431926i	$-0.857834\pi$
$67$	−10.7652	+	3.91820i	−1.31517	+	0.478684i	−0.413266	+	0.910611i	$0.635612\pi$
$68$	−0.233956	−	0.405223i	−0.0283713	−	0.0491405i
$69$		0			0
$70$	0.0898700	−	0.509678i	0.0107415	−	0.0609182i
$71$	−10.2135	+	8.57013i	−1.21212	+	1.01709i	−0.212918	+	0.977070i	$0.568297\pi$
$71$	−10.2135	+	8.57013i	−1.21212	+	1.01709i	−0.999199	+	0.0400167i	$0.987259\pi$
$72$		0			0
$73$	0.396459	+	2.24843i	0.0464021	+	0.263159i	0.999179	−	0.0405117i	$-0.0128988\pi$
$73$	0.396459	+	2.24843i	0.0464021	+	0.263159i	−0.952777	+	0.303671i	$0.901788\pi$
$74$	−8.00387	−	2.91317i	−0.930431	−	0.338649i
$75$		0			0
$76$	0.500000	+	4.33013i	0.0573539	+	0.496700i
$77$	11.0446			1.25865
$78$		0			0
$79$	0.843426	+	4.78331i	0.0948928	+	0.538164i	0.994780	+	0.102042i	$0.0325375\pi$
$79$	0.843426	+	4.78331i	0.0948928	+	0.538164i	−0.899887	+	0.436122i	$0.856351\pi$
$80$	0.0923963	+	0.0775297i	0.0103302	+	0.00866808i
$81$		0			0
$82$	0.666374	−	3.77920i	0.0735887	−	0.417342i
$83$	1.62449	−	2.81369i	0.178310	−	0.308843i	−0.762992	−	0.646408i	$-0.776270\pi$
$83$	1.62449	−	2.81369i	0.178310	−	0.308843i	0.941302	+	0.337566i	$0.109604\pi$
$84$		0			0
$85$	−0.0530334	+	0.0193026i	−0.00575228	+	0.00209366i
$86$	8.76991	−	3.19199i	0.945684	−	0.344201i
$87$		0			0
$88$	−1.28699	+	2.22913i	−0.137193	+	0.237626i
$89$	−0.595800	+	3.37895i	−0.0631547	+	0.358168i	0.936811	+	0.349837i	$0.113763\pi$
$89$	−0.595800	+	3.37895i	−0.0631547	+	0.358168i	−0.999965	+	0.00833100i	$0.997348\pi$
$90$		0			0
$91$	−2.67958	−	2.24843i	−0.280896	−	0.235700i
$92$	−0.964508	−	5.46999i	−0.100557	−	0.570286i
$93$		0			0
$94$	−9.47565			−0.977339
$95$	0.524815	+	0.0313013i	0.0538449	+	0.00321145i
$96$		0			0
$97$	−2.91400	−	1.06061i	−0.295872	−	0.107689i	0.189819	−	0.981819i	$-0.439210\pi$
$97$	−2.91400	−	1.06061i	−0.295872	−	0.107689i	−0.485691	+	0.874130i	$0.661432\pi$
$98$	−1.98158	−	11.2381i	−0.200170	−	1.13522i
$99$		0			0
$100$	−3.81908	+	3.20459i	−0.381908	+	0.320459i
$101$	2.90508	−	16.4755i	0.289066	−	1.63937i	−0.401323	−	0.915937i	$-0.631450\pi$
$101$	2.90508	−	16.4755i	0.289066	−	1.63937i	0.690389	−	0.723438i	$-0.257439\pi$
$102$		0			0
$103$	5.19846	+	9.00400i	0.512220	+	0.887191i	0.999900	+	0.0141681i	$0.00451001\pi$
$103$	5.19846	+	9.00400i	0.512220	+	0.887191i	−0.487680	+	0.873023i	$0.662157\pi$
$104$	0.766044	−	0.278817i	0.0751168	−	0.0273403i
$105$		0			0
$106$	−6.37939	−	11.0494i	−0.619621	−	1.07321i
$107$	−4.55690	+	7.89279i	−0.440533	+	0.763025i	−0.997729	−	0.0673560i	$-0.978544\pi$
$107$	−4.55690	+	7.89279i	−0.440533	+	0.763025i	0.557196	+	0.830381i	$0.311877\pi$
$108$		0			0
$109$	2.93376	−	2.46172i	0.281004	−	0.235790i	−0.491382	−	0.870944i	$-0.663508\pi$
$109$	2.93376	−	2.46172i	0.281004	−	0.235790i	0.772385	+	0.635154i	$0.219064\pi$
$110$	0.237826	+	0.199560i	0.0226758	+	0.0190273i
$111$		0			0
$112$	4.03209	+	1.46756i	0.380997	+	0.138671i
$113$	−5.41147			−0.509069			−0.254534	−	0.967064i	$-0.581922\pi$
$113$	−5.41147			−0.509069			−0.254534	+	0.967064i	$0.581922\pi$
$114$		0			0
$115$	−0.669940			−0.0624722
$116$	2.20574	+	0.802823i	0.204798	+	0.0745402i
$117$		0			0
$118$	11.5287	+	9.67372i	1.06130	+	0.890538i
$119$	−1.53802	+	1.29055i	−0.140990	+	0.118305i
$120$		0			0
$121$	2.18732	−	3.78855i	0.198847	−	0.344413i
$122$	−0.858441	−	1.48686i	−0.0777196	−	0.134614i
$123$		0			0
$124$	−5.02481	+	1.82888i	−0.451242	+	0.164239i
$125$	0.602196	+	1.04303i	0.0538621	+	0.0932919i
$126$		0			0
$127$	0.736482	−	4.17680i	0.0653522	−	0.370631i	−0.934539	−	0.355861i	$-0.884188\pi$
$127$	0.736482	−	4.17680i	0.0653522	−	0.370631i	0.999891	−	0.0147693i	$-0.00470138\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$		0			0
$130$	−0.0170741	−	0.0968323i	−0.00149750	−	0.00849275i
$131$	19.7738	+	7.19707i	1.72764	+	0.628811i	0.998458	−	0.0555055i	$-0.0176770\pi$
$131$	19.7738	+	7.19707i	1.72764	+	0.628811i	0.729185	+	0.684316i	$0.239899\pi$
$132$		0			0
$133$	17.9251	−	5.33921i	1.55431	−	0.462968i
$134$	−11.4561			−0.989652
$135$		0			0
$136$	−0.0812519	−	0.460802i	−0.00696729	−	0.0395135i
$137$	9.43835	+	7.91971i	0.806373	+	0.676627i	0.949739	−	0.313043i	$-0.101348\pi$
$137$	9.43835	+	7.91971i	0.806373	+	0.676627i	−0.143367	+	0.989670i	$0.545793\pi$
$138$		0			0
$139$	−0.970437	+	5.50362i	−0.0823114	+	0.466811i	0.915593	+	0.402106i	$0.131722\pi$
$139$	−0.970437	+	5.50362i	−0.0823114	+	0.466811i	−0.997904	+	0.0647050i	$0.979389\pi$
$140$	0.258770	−	0.448204i	0.0218701	−	0.0378801i
$141$		0			0
$142$	−12.5287	+	4.56007i	−1.05138	+	0.382672i
$143$	1.97178	−	0.717670i	0.164889	−	0.0600146i
$144$		0			0
$145$	0.141559	−	0.245188i	0.0117559	−	0.0203617i
$146$	−0.396459	+	2.24843i	−0.0328112	+	0.186082i
$147$		0			0
$148$	−6.52481	−	5.47497i	−0.536336	−	0.450040i
$149$	−1.92649	−	10.9257i	−0.157824	−	0.895065i	−0.956158	−	0.292850i	$-0.905396\pi$
$149$	−1.92649	−	10.9257i	−0.157824	−	0.895065i	0.798334	−	0.602215i	$-0.205715\pi$
$150$		0			0
$151$	12.5963			1.02507			0.512535	−	0.858666i	$-0.328707\pi$
$151$	12.5963			1.02507			0.512535	+	0.858666i	$0.328707\pi$
$152$	−1.01114	+	4.24000i	−0.0820146	+	0.343909i
$153$		0			0
$154$	10.3785	+	3.77747i	0.836324	+	0.304397i
$155$	0.111997	+	0.635164i	0.00899579	+	0.0510176i
$156$		0			0
$157$	−3.04710	+	2.55682i	−0.243185	+	0.204057i	−0.756231	−	0.654304i	$-0.772962\pi$
$157$	−3.04710	+	2.55682i	−0.243185	+	0.204057i	0.513046	+	0.858361i	$0.328517\pi$
$158$	−0.843426	+	4.78331i	−0.0670994	+	0.380539i
$159$		0			0
$160$	0.0603074	+	0.104455i	0.00476772	+	0.00825793i
$161$	−22.3957	+	8.15138i	−1.76503	+	0.642419i
$162$		0			0
$163$	−9.60014	−	16.6279i	−0.751941	−	1.30240i	−0.946881	−	0.321584i	$-0.895785\pi$
$163$	−9.60014	−	16.6279i	−0.751941	−	1.30240i	0.194940	−	0.980815i	$-0.437549\pi$
$164$	1.91875	−	3.32337i	0.149829	−	0.259512i
$165$		0			0
$166$	2.48886	−	2.08840i	0.193173	−	0.162091i
$167$	11.7777	+	9.88263i	0.911382	+	0.764741i	0.972381	−	0.233397i	$-0.0749842\pi$
$167$	11.7777	+	9.88263i	0.911382	+	0.764741i	−0.0609991	+	0.998138i	$0.519429\pi$
$168$		0			0
$169$	11.5915	+	4.21897i	0.891655	+	0.324536i
$170$	−0.0564370			−0.00432852
$171$		0			0
$172$	9.33275			0.711615
$173$	−6.19594	−	2.25514i	−0.471068	−	0.171455i	0.0955679	−	0.995423i	$-0.469533\pi$
$173$	−6.19594	−	2.25514i	−0.471068	−	0.171455i	−0.566636	+	0.823968i	$0.691756\pi$
$174$		0			0
$175$	16.3871	+	13.7504i	1.23875	+	1.03943i
$176$	−1.97178	+	1.65452i	−0.148629	+	0.124714i
$177$		0			0
$178$	−1.71554	+	2.97140i	−0.128585	+	0.222716i
$179$	0.620615	+	1.07494i	0.0463869	+	0.0803445i	0.888287	−	0.459290i	$-0.151896\pi$
$179$	0.620615	+	1.07494i	0.0463869	+	0.0803445i	−0.841900	+	0.539634i	$0.818563\pi$
$180$		0			0
$181$	−3.78699	+	1.37835i	−0.281485	+	0.102452i	−0.478905	−	0.877867i	$-0.658966\pi$
$181$	−3.78699	+	1.37835i	−0.281485	+	0.102452i	0.197420	+	0.980319i	$0.436744\pi$
$182$	−1.74897	−	3.02931i	−0.129642	−	0.224547i
$183$		0			0
$184$	0.964508	−	5.46999i	0.0711044	−	0.403253i
$185$	−0.786989	+	0.660362i	−0.0578606	+	0.0485508i
$186$		0			0
$187$	−0.209141	−	1.18610i	−0.0152939	−	0.0867359i
$188$	−8.90420	−	3.24086i	−0.649406	−	0.236364i
$189$		0			0
$190$	0.482459	+	0.208911i	0.0350013	+	0.0151560i
$191$	24.0847			1.74271			0.871354	−	0.490654i	$-0.163242\pi$
$191$	24.0847			1.74271			0.871354	+	0.490654i	$0.163242\pi$
$192$		0			0
$193$	−1.71213	−	9.70999i	−0.123242	−	0.698941i	−0.982336	−	0.187123i	$-0.940084\pi$
$193$	−1.71213	−	9.70999i	−0.123242	−	0.698941i	0.859094	−	0.511817i	$-0.171028\pi$
$194$	−2.37551	−	1.99329i	−0.170552	−	0.143110i
$195$		0			0
$196$	1.98158	−	11.2381i	0.141542	−	0.802722i
$197$	−3.22803	+	5.59110i	−0.229987	+	0.398350i	−0.957804	−	0.287422i	$-0.907202\pi$
$197$	−3.22803	+	5.59110i	−0.229987	+	0.398350i	0.727817	+	0.685772i	$0.240535\pi$
$198$		0			0
$199$	−23.2777	+	8.47237i	−1.65011	+	0.600591i	−0.988763	−	0.149490i	$-0.952237\pi$
$199$	−23.2777	+	8.47237i	−1.65011	+	0.600591i	−0.661346	+	0.750081i	$0.730015\pi$
$200$	−4.68479	+	1.70513i	−0.331265	+	0.120571i
$201$		0			0
$202$	8.36484	−	14.4883i	0.588548	−	1.01939i
$203$	1.74897	−	9.91890i	0.122754	−	0.696171i
$204$		0			0
$205$	−0.354570	−	0.297520i	−0.0247643	−	0.0207797i
$206$	1.80541	+	10.2390i	0.125789	+	0.713383i
$207$		0			0
$208$	0.815207			0.0565245
$209$	−2.60266	+	10.9137i	−0.180030	+	0.754914i
$210$		0			0
$211$	1.30066	+	0.473401i	0.0895411	+	0.0325903i	0.386402	−	0.922330i	$-0.373718\pi$
$211$	1.30066	+	0.473401i	0.0895411	+	0.0325903i	−0.296861	+	0.954921i	$0.595940\pi$
$212$	−2.21554	−	12.5649i	−0.152164	−	0.862963i
$213$		0			0
$214$	−6.98158	+	5.85824i	−0.477251	+	0.400461i
$215$	0.195470	−	1.10857i	0.0133309	−	0.0756036i
$216$		0			0
$217$	11.4722	+	19.8705i	0.778787	+	1.34890i
$218$	3.59879	−	1.30985i	0.243741	−	0.0887145i
$219$		0			0
$220$	0.155230	+	0.268866i	0.0104656	+	0.0181269i
$221$	−0.190722	+	0.330341i	−0.0128294	+	0.0222211i
$222$		0			0
$223$	17.0929	−	14.3426i	1.14462	−	0.960453i	0.145043	−	0.989425i	$-0.453668\pi$
$223$	17.0929	−	14.3426i	1.14462	−	0.960453i	0.999580	+	0.0289729i	$0.00922364\pi$
$224$	3.28699	+	2.75811i	0.219621	+	0.184284i
$225$		0			0
$226$	−5.08512	−	1.85083i	−0.338257	−	0.123116i
$227$	20.7665			1.37832			0.689161	−	0.724608i	$-0.257979\pi$
$227$	20.7665			1.37832			0.689161	+	0.724608i	$0.257979\pi$
$228$		0			0
$229$	5.51754			0.364609			0.182305	−	0.983242i	$-0.441644\pi$
$229$	5.51754			0.364609			0.182305	+	0.983242i	$0.441644\pi$
$230$	−0.629538	−	0.229133i	−0.0415105	−	0.0151086i
$231$		0			0
$232$	1.79813	+	1.50881i	0.118053	+	0.0990584i
$233$	11.5569	−	9.69739i	0.757118	−	0.635297i	−0.180257	−	0.983620i	$-0.557693\pi$
$233$	11.5569	−	9.69739i	0.757118	−	0.635297i	0.937375	+	0.348322i	$0.113248\pi$
$234$		0			0
$235$	−0.571452	+	0.989783i	−0.0372774	+	0.0645664i
$236$	7.52481	+	13.0334i	0.489824	+	0.848400i
$237$		0			0
$238$	−1.88666	+	0.686688i	−0.122294	+	0.0445114i
$239$	−14.4757	−	25.0726i	−0.936352	−	1.62181i	−0.772205	−	0.635374i	$-0.780846\pi$
$239$	−14.4757	−	25.0726i	−0.936352	−	1.62181i	−0.164147	−	0.986436i	$-0.552487\pi$
$240$		0			0
$241$	−3.36349	+	19.0753i	−0.216662	+	1.22875i	0.661338	+	0.750088i	$0.269989\pi$
$241$	−3.36349	+	19.0753i	−0.216662	+	1.22875i	−0.878000	+	0.478661i	$0.841122\pi$
$242$	3.35117	−	2.81196i	0.215421	−	0.180760i
$243$		0			0
$244$	−0.298133	−	1.69080i	−0.0190860	−	0.108242i
$245$	−1.29339	−	0.470754i	−0.0826314	−	0.0300754i
$246$		0			0
$247$	2.85323	−	2.11797i	0.181546	−	0.134763i
$248$	−5.34730			−0.339554
$249$		0			0
$250$	0.209141	+	1.18610i	0.0132272	+	0.0750153i
$251$	3.32635	+	2.79114i	0.209957	+	0.176175i	0.741702	−	0.670730i	$-0.234019\pi$
$251$	3.32635	+	2.79114i	0.209957	+	0.176175i	−0.531745	+	0.846905i	$0.678463\pi$
$252$		0			0
$253$	2.48262	−	14.0796i	0.156081	−	0.885180i
$254$	2.12061	−	3.67301i	0.133059	−	0.230465i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	16.6951	−	6.07650i	1.04141	−	0.379042i	0.235995	−	0.971754i	$-0.424165\pi$
$257$	16.6951	−	6.07650i	1.04141	−	0.379042i	0.805414	+	0.592712i	$0.201943\pi$
$258$		0			0
$259$	−18.2738	+	31.6511i	−1.13548	+	1.96671i
$260$	0.0170741	−	0.0968323i	0.00105889	−	0.00600528i
$261$		0			0
$262$	16.1197	+	13.5261i	0.995881	+	0.835643i
$263$	0.401674	+	2.27801i	0.0247683	+	0.140468i	0.994684	−	0.102972i	$-0.0328352\pi$
$263$	0.401674	+	2.27801i	0.0247683	+	0.140468i	−0.969916	+	0.243440i	$0.921724\pi$
$264$		0			0
$265$	−1.53890			−0.0945336
$266$	18.6702	+	1.11354i	1.14475	+	0.0682756i
$267$		0			0
$268$	−10.7652	−	3.91820i	−0.657587	−	0.239342i
$269$	0.489322	+	2.77509i	0.0298345	+	0.169200i	0.996084	−	0.0884063i	$-0.0281774\pi$
$269$	0.489322	+	2.77509i	0.0298345	+	0.169200i	−0.966250	+	0.257606i	$0.917066\pi$
$270$		0			0
$271$	−5.12449	+	4.29995i	−0.311290	+	0.261204i	−0.785025	−	0.619464i	$-0.787350\pi$
$271$	−5.12449	+	4.29995i	−0.311290	+	0.261204i	0.473735	+	0.880668i	$0.342906\pi$
$272$	0.0812519	−	0.460802i	0.00492662	−	0.0279403i
$273$		0			0
$274$	6.16044	+	10.6702i	0.372166	+	0.644611i
$275$	−12.0586	+	4.38895i	−0.727158	+	0.264664i
$276$		0			0
$277$	−4.12583	−	7.14615i	−0.247897	−	0.429370i	0.715045	−	0.699078i	$-0.246406\pi$
$277$	−4.12583	−	7.14615i	−0.247897	−	0.429370i	−0.962942	+	0.269708i	$0.913073\pi$
$278$	−2.79426	+	4.83981i	−0.167589	+	0.290272i
$279$		0			0
$280$	0.396459	−	0.332669i	0.0236930	−	0.0198808i
$281$	−21.4008	−	17.9574i	−1.27666	−	1.07125i	−0.993695	−	0.112120i	$-0.964236\pi$
$281$	−21.4008	−	17.9574i	−1.27666	−	1.07125i	−0.282970	−	0.959129i	$-0.591320\pi$
$282$		0			0
$283$	−2.27972	−	0.829748i	−0.135515	−	0.0493234i	0.273372	−	0.961908i	$-0.411861\pi$
$283$	−2.27972	−	0.829748i	−0.135515	−	0.0493234i	−0.408887	+	0.912585i	$0.634083\pi$
$284$	−13.3327			−0.791153
$285$		0			0
$286$	2.09833			0.124077
$287$	−15.4731	−	5.63176i	−0.913350	−	0.332432i
$288$		0			0
$289$	−12.8550	−	10.7867i	−0.756179	−	0.634509i
$290$	0.216881	−	0.181985i	0.0127357	−	0.0106865i
$291$		0			0
$292$	−1.14156	+	1.97724i	−0.0668047	+	0.115709i
$293$	−7.05051	−	12.2118i	−0.411895	−	0.713423i	0.583202	−	0.812327i	$-0.301800\pi$
$293$	−7.05051	−	12.2118i	−0.411895	−	0.713423i	−0.995097	+	0.0989041i	$0.968466\pi$
$294$		0			0
$295$	1.70574	−	0.620838i	0.0993119	−	0.0361466i
$296$	−4.25877	−	7.37641i	−0.247536	−	0.428745i
$297$		0			0
$298$	1.92649	−	10.9257i	0.111599	−	0.632907i
$299$	−3.46863	+	2.91052i	−0.200596	+	0.168320i
$300$		0			0
$301$	−6.95383	−	39.4371i	−0.400812	−	2.27312i
$302$	11.8366	+	4.30818i	0.681121	+	0.247908i
$303$		0			0
$304$	−2.40033	+	3.63846i	−0.137668	+	0.208680i
$305$	−0.207081			−0.0118574
$306$		0			0
$307$	−3.50892	−	19.9001i	−0.200265	−	1.13576i	−0.904719	−	0.426009i	$-0.859919\pi$
$307$	−3.50892	−	19.9001i	−0.200265	−	1.13576i	0.704454	−	0.709749i	$-0.251192\pi$
$308$	8.46064	+	7.09932i	0.482090	+	0.404521i
$309$		0			0
$310$	−0.111997	+	0.635164i	−0.00636098	+	0.0360749i
$311$	4.80928	−	8.32991i	0.272709	−	0.472346i	−0.696845	−	0.717221i	$-0.745414\pi$
$311$	4.80928	−	8.32991i	0.272709	−	0.472346i	0.969555	+	0.244875i	$0.0787470\pi$
$312$		0			0
$313$	−23.3871	+	8.51222i	−1.32192	+	0.481139i	−0.904073	−	0.427379i	$-0.859437\pi$
$313$	−23.3871	+	8.51222i	−1.32192	+	0.481139i	−0.417846	+	0.908518i	$0.637215\pi$
$314$	−3.73783	+	1.36046i	−0.210938	+	0.0767751i
$315$		0			0
$316$	−2.42855	+	4.20637i	−0.136617	+	0.236627i
$317$	−2.99778	+	17.0012i	−0.168372	+	0.954885i	0.777147	+	0.629319i	$0.216666\pi$
$317$	−2.99778	+	17.0012i	−0.168372	+	0.954885i	−0.945519	+	0.325566i	$0.894445\pi$
$318$		0			0
$319$	4.62836	+	3.88365i	0.259138	+	0.217443i
$320$	0.0209445	+	0.118782i	0.00117083	+	0.00664014i
$321$		0			0
$322$	−23.8331			−1.32816
$323$	−0.912818	−	1.82391i	−0.0507906	−	0.101485i
$324$		0			0
$325$	3.81908	+	1.39003i	0.211844	+	0.0771050i
$326$	−3.33409	−	18.9086i	−0.184658	−	1.04725i
$327$		0			0
$328$	2.93969	−	2.46669i	0.162317	−	0.136200i
$329$	−7.06031	+	40.0410i	−0.389247	+	2.20753i
$330$		0			0
$331$	−4.99525	−	8.65203i	−0.274564	−	0.475559i	0.695461	−	0.718564i	$-0.255200\pi$
$331$	−4.99525	−	8.65203i	−0.274564	−	0.475559i	−0.970025	+	0.243005i	$0.921867\pi$
$332$	3.05303	−	1.11121i	0.167557	−	0.0609858i
$333$		0			0
$334$	7.68732	+	13.3148i	0.420631	+	0.728555i
$335$	−0.690884	+	1.19665i	−0.0377470	+	0.0653798i
$336$		0			0
$337$	5.18139	−	4.34770i	0.282248	−	0.236834i	−0.490662	−	0.871350i	$-0.663245\pi$
$337$	5.18139	−	4.34770i	0.282248	−	0.236834i	0.772910	+	0.634516i	$0.218800\pi$
$338$	9.44949	+	7.92907i	0.513985	+	0.431284i
$339$		0			0
$340$	−0.0530334	−	0.0193026i	−0.00287614	−	0.00104683i
$341$	−13.7638			−0.745353
$342$		0			0
$343$	−18.9290			−1.02207
$344$	8.76991	+	3.19199i	0.472842	+	0.172100i
$345$		0			0
$346$	−5.05097	−	4.23827i	−0.271542	−	0.227851i
$347$	−18.8457	+	15.8134i	−1.01169	+	0.848909i	−0.988561	−	0.150823i	$-0.951808\pi$
$347$	−18.8457	+	15.8134i	−1.01169	+	0.848909i	−0.0231297	+	0.999732i	$0.507363\pi$
$348$		0			0
$349$	3.41740	−	5.91912i	0.182929	−	0.316843i	−0.759947	−	0.649985i	$-0.774775\pi$
$349$	3.41740	−	5.91912i	0.182929	−	0.316843i	0.942877	+	0.333141i	$0.108109\pi$
$350$	10.6959	+	18.5259i	0.571722	+	0.990251i
$351$		0			0
$352$	−2.41875	+	0.880352i	−0.128920	+	0.0469229i
$353$	−2.54189	−	4.40268i	−0.135291	−	0.234331i	0.790418	−	0.612568i	$-0.209864\pi$
$353$	−2.54189	−	4.40268i	−0.135291	−	0.234331i	−0.925709	+	0.378237i	$0.876530\pi$
$354$		0			0
$355$	−0.279248	+	1.58370i	−0.0148210	+	0.0840538i
$356$	−2.62836	+	2.20545i	−0.139303	+	0.116889i
$357$		0			0
$358$	0.215537	+	1.22237i	0.0113915	+	0.0646044i
$359$	−2.69459	−	0.980752i	−0.142215	−	0.0517621i	0.269932	−	0.962879i	$-0.412999\pi$
$359$	−2.69459	−	0.980752i	−0.142215	−	0.0517621i	−0.412147	+	0.911117i	$0.635221\pi$
$360$		0			0
$361$	1.05185	+	18.9709i	0.0553606	+	0.998466i
$362$	−4.03003			−0.211814
$363$		0			0
$364$	−0.607411	−	3.44480i	−0.0318370	−	0.180557i
$365$	0.210952	+	0.177009i	0.0110417	+	0.00926510i
$366$		0			0
$367$	3.84507	−	21.8065i	0.200711	−	1.13829i	−0.703336	−	0.710858i	$-0.748307\pi$
$367$	3.84507	−	21.8065i	0.200711	−	1.13829i	0.904047	−	0.427433i	$-0.140582\pi$
$368$	2.77719	−	4.81023i	0.144771	−	0.250751i
$369$		0			0
$370$	−0.965385	+	0.351371i	−0.0501880	+	0.0182669i
$371$	−51.4445	+	18.7243i	−2.67087	+	0.972115i
$372$		0			0
$373$	−8.83662	+	15.3055i	−0.457543	+	0.792487i	−0.998830	−	0.0483501i	$-0.984604\pi$
$373$	−8.83662	+	15.3055i	−0.457543	+	0.792487i	0.541288	+	0.840837i	$0.317937\pi$
$374$	0.209141	−	1.18610i	0.0108144	−	0.0613315i
$375$		0			0
$376$	−7.25877	−	6.09083i	−0.374343	−	0.314111i
$377$	−0.332282	−	1.88446i	−0.0171134	−	0.0970548i
$378$		0			0
$379$	−9.75970			−0.501322			−0.250661	−	0.968075i	$-0.580648\pi$
$379$	−9.75970			−0.501322			−0.250661	+	0.968075i	$0.580648\pi$
$380$	0.381911	+	0.361323i	0.0195916	+	0.0185355i
$381$		0			0
$382$	22.6322	+	8.23746i	1.15797	+	0.421465i
$383$	3.87505	+	21.9765i	0.198006	+	1.12295i	0.908073	+	0.418812i	$0.137553\pi$
$383$	3.87505	+	21.9765i	0.198006	+	1.12295i	−0.710067	+	0.704134i	$0.751335\pi$
$384$		0			0
$385$	1.02048	−	0.856282i	0.0520084	−	0.0436402i
$386$	1.71213	−	9.70999i	0.0871453	−	0.494226i
$387$		0			0
$388$	−1.55051	−	2.68556i	−0.0787151	−	0.136339i
$389$	6.59879	−	2.40176i	0.334572	−	0.121774i	−0.169271	−	0.985570i	$-0.554141\pi$
$389$	6.59879	−	2.40176i	0.334572	−	0.121774i	0.503843	+	0.863795i	$0.331919\pi$
$390$		0			0
$391$	1.29948	+	2.25076i	0.0657174	+	0.113826i
$392$	5.70574	−	9.88263i	0.288183	−	0.499148i
$393$		0			0
$394$	−4.94562	+	4.14987i	−0.249157	+	0.209067i
$395$	0.448778	+	0.376569i	0.0225805	+	0.0189472i
$396$		0			0
$397$	18.7738	+	6.83310i	0.942229	+	0.342943i	0.767046	−	0.641592i	$-0.221726\pi$
$397$	18.7738	+	6.83310i	0.942229	+	0.342943i	0.175184	+	0.984536i	$0.443948\pi$
$398$	−24.7716			−1.24169
$399$		0			0
$400$	−4.98545			−0.249273
$401$	−1.11809	−	0.406951i	−0.0558347	−	0.0203222i	0.313952	−	0.949439i	$-0.398347\pi$
$401$	−1.11809	−	0.406951i	−0.0558347	−	0.0203222i	−0.369787	+	0.929117i	$0.620569\pi$
$402$		0			0
$403$	3.33931	+	2.80201i	0.166343	+	0.139578i
$404$	12.8157	−	10.7536i	0.637604	−	0.535013i
$405$		0			0
$406$	5.03596	−	8.72254i	0.249930	−	0.432892i
$407$	−10.9620	−	18.9867i	−0.543365	−	0.941136i
$408$		0			0
$409$	−8.91622	+	3.24524i	−0.440879	+	0.160467i	−0.552916	−	0.833237i	$-0.686485\pi$
$409$	−8.91622	+	3.24524i	−0.440879	+	0.160467i	0.112037	+	0.993704i	$0.464263\pi$
$410$	−0.231429	−	0.400847i	−0.0114295	−	0.0197964i
$411$		0			0
$412$	−1.80541	+	10.2390i	−0.0889460	+	0.504438i
$413$	49.4680	−	41.5086i	2.43416	−	2.04250i
$414$		0			0
$415$	−0.0680482	−	0.385920i	−0.00334035	−	0.0189441i
$416$	0.766044	+	0.278817i	0.0375584	+	0.0136701i
$417$		0			0
$418$	−6.17840	+	9.36532i	−0.302195	+	0.458073i
$419$	−4.72638			−0.230899			−0.115449	−	0.993313i	$-0.536831\pi$
$419$	−4.72638			−0.230899			−0.115449	+	0.993313i	$0.536831\pi$
$420$		0			0
$421$	0.240819	+	1.36575i	0.0117368	+	0.0665627i	0.990114	−	0.140268i	$-0.0447963\pi$
$421$	0.240819	+	1.36575i	0.0117368	+	0.0665627i	−0.978377	+	0.206830i	$0.933685\pi$
$422$	1.06031	+	0.889704i	0.0516150	+	0.0433101i
$423$		0			0
$424$	2.21554	−	12.5649i	0.107596	−	0.610207i
$425$	1.16637	−	2.02022i	0.0565775	−	0.0979950i
$426$		0			0
$427$	−6.92262	+	2.51963i	−0.335009	+	0.121933i
$428$	−8.56418	+	3.11711i	−0.413965	+	0.150671i
$429$		0			0
$430$	0.562834	−	0.974856i	0.0271422	−	0.0470117i
$431$	−0.470904	+	2.67063i	−0.0226827	+	0.128640i	−0.994046	−	0.108958i	$-0.965249\pi$
$431$	−0.470904	+	2.67063i	−0.0226827	+	0.128640i	0.971364	+	0.237597i	$0.0763599\pi$
$432$		0			0
$433$	−15.5057	−	13.0108i	−0.745155	−	0.625260i	0.189061	−	0.981965i	$-0.439455\pi$
$433$	−15.5057	−	13.0108i	−0.745155	−	0.625260i	−0.934217	+	0.356706i	$0.883900\pi$
$434$	3.98427	+	22.5959i	0.191251	+	1.08464i
$435$		0			0
$436$	3.82976			0.183412
$437$	−2.77719	−	24.0512i	−0.132851	−	1.15052i
$438$		0			0
$439$	17.1027	+	6.22486i	0.816266	+	0.297096i	0.716209	−	0.697885i	$-0.245876\pi$
$439$	17.1027	+	6.22486i	0.816266	+	0.297096i	0.100056	+	0.994982i	$0.468098\pi$
$440$	0.0539108	+	0.305743i	0.00257009	+	0.0145757i
$441$		0			0
$442$	−0.292204	+	0.245188i	−0.0138987	+	0.0116624i
$443$	6.20661	−	35.1995i	0.294885	−	1.67238i	−0.372784	−	0.927918i	$-0.621597\pi$
$443$	6.20661	−	35.1995i	0.294885	−	1.67238i	0.667669	−	0.744458i	$-0.267292\pi$
$444$		0			0
$445$	0.206919	+	0.358394i	0.00980891	+	0.0169895i
$446$	20.9675	−	7.63155i	0.992840	−	0.361364i
$447$		0			0
$448$	2.14543	+	3.71599i	0.101362	+	0.175564i
$449$	−9.49525	+	16.4463i	−0.448109	+	0.776147i	−0.998263	−	0.0589161i	$-0.981236\pi$
$449$	−9.49525	+	16.4463i	−0.448109	+	0.776147i	0.550154	+	0.835063i	$0.314569\pi$
$450$		0			0
$451$	7.56670	−	6.34922i	0.356302	−	0.298973i
$452$	−4.14543	−	3.47843i	−0.194985	−	0.163612i
$453$		0			0
$454$	19.5141	+	7.10257i	0.915844	+	0.333340i
$455$	−0.421903			−0.0197791
$456$		0			0
$457$	25.9632			1.21451			0.607253	−	0.794509i	$-0.292272\pi$
$457$	25.9632			1.21451			0.607253	+	0.794509i	$0.292272\pi$
$458$	5.18479	+	1.88711i	0.242269	+	0.0881789i
$459$		0			0
$460$	−0.513204	−	0.430629i	−0.0239282	−	0.0200782i
$461$	22.3949	−	18.7915i	1.04303	−	0.875209i	0.0506891	−	0.998714i	$-0.483858\pi$
$461$	22.3949	−	18.7915i	1.04303	−	0.875209i	0.992344	+	0.123506i	$0.0394138\pi$
$462$		0			0
$463$	10.5954	−	18.3518i	0.492410	−	0.852878i	−0.507552	−	0.861621i	$-0.669450\pi$
$463$	10.5954	−	18.3518i	0.492410	−	0.852878i	0.999962	+	0.00874269i	$0.00278292\pi$
$464$	1.17365	+	2.03282i	0.0544852	+	0.0943712i
$465$		0			0
$466$	14.1766	−	5.15988i	0.656720	−	0.239027i
$467$	−1.07263	−	1.85786i	−0.0496356	−	0.0859713i	0.840140	−	0.542369i	$-0.182473\pi$
$467$	−1.07263	−	1.85786i	−0.0496356	−	0.0859713i	−0.889776	+	0.456398i	$0.849139\pi$
$468$		0			0
$469$	−8.53590	+	48.4095i	−0.394151	+	2.23534i
$470$	−0.875515	+	0.734644i	−0.0403845	+	0.0338866i
$471$		0			0
$472$	2.61334	+	14.8210i	0.120289	+	0.682191i
$473$	22.5736	+	8.21611i	1.03793	+	0.377777i
$474$		0			0
$475$	−17.4491	+	12.9526i	−0.800619	+	0.594305i
$476$	−2.00774			−0.0920246
$477$		0			0
$478$	−5.02734	−	28.5115i	−0.229945	−	1.30408i
$479$	2.60220	+	2.18350i	0.118897	+	0.0997668i	0.700298	−	0.713851i	$-0.253051\pi$
$479$	2.60220	+	2.18350i	0.118897	+	0.0997668i	−0.581400	+	0.813618i	$0.697495\pi$
$480$		0			0
$481$	−1.20574	+	6.83807i	−0.0549769	+	0.311789i
$482$	−9.68479	+	16.7746i	−0.441130	+	0.764060i
$483$		0			0
$484$	4.11081	−	1.49621i	0.186855	−	0.0680097i
$485$	−0.351471	+	0.127925i	−0.0159595	+	0.00580878i
$486$		0			0
$487$	−9.89306	+	17.1353i	−0.448297	+	0.776473i	−0.998275	−	0.0587056i	$-0.981303\pi$
$487$	−9.89306	+	17.1353i	−0.448297	+	0.776473i	0.549978	+	0.835179i	$0.314636\pi$
$488$	0.298133	−	1.69080i	0.0134959	−	0.0765388i
$489$		0			0
$490$	−1.05438	−	0.884728i	−0.0476319	−	0.0399679i
$491$	−4.36618	−	24.7618i	−0.197043	−	1.11749i	−0.909479	−	0.415750i	$-0.863519\pi$
$491$	−4.36618	−	24.7618i	−0.197043	−	1.11749i	0.712436	−	0.701737i	$-0.247592\pi$
$492$		0			0
$493$	−1.09833			−0.0494661
$494$	3.40554	−	1.01438i	0.153223	−	0.0456392i
$495$		0			0
$496$	−5.02481	−	1.82888i	−0.225621	−	0.0821193i
$497$	9.93423	+	56.3398i	0.445611	+	2.52719i
$498$		0			0
$499$	26.9329	−	22.5994i	1.20568	−	1.01169i	0.206232	−	0.978503i	$-0.433880\pi$
$499$	26.9329	−	22.5994i	1.20568	−	1.01169i	0.999449	−	0.0331839i	$-0.0105647\pi$
$500$	−0.209141	+	1.18610i	−0.00935305	+	0.0530438i
$501$		0			0
$502$	2.17112	+	3.76049i	0.0969019	+	0.167839i
$503$	19.1186	−	6.95859i	0.852454	−	0.310268i	0.121414	−	0.992602i	$-0.461257\pi$
$503$	19.1186	−	6.95859i	0.852454	−	0.310268i	0.731041	+	0.682334i	$0.239035\pi$
$504$		0			0
$505$	−1.00892	−	1.74751i	−0.0448965	−	0.0777630i
$506$	7.14842	−	12.3814i	0.317786	−	0.550422i
$507$		0			0
$508$	3.24897	−	2.72621i	0.144150	−	0.120956i
$509$	10.0851	+	8.46242i	0.447015	+	0.375090i	0.838327	−	0.545168i	$-0.183534\pi$
$509$	10.0851	+	8.46242i	0.447015	+	0.375090i	−0.391312	+	0.920258i	$0.627979\pi$
$510$		0			0
$511$	9.20574	+	3.35061i	0.407238	+	0.148222i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	17.7665			0.783647
$515$	1.17840	+	0.428901i	0.0519263	+	0.0188996i
$516$		0			0
$517$	−18.6839	−	15.6777i	−0.821718	−	0.689503i
$518$	−27.9971	+	23.4923i	−1.23012	+	1.03219i
$519$		0			0
$520$	0.0491630	−	0.0851529i	0.00215594	−	0.00373420i
$521$	10.2456	+	17.7458i	0.448866	+	0.777459i	0.998313	−	0.0580697i	$-0.0184946\pi$
$521$	10.2456	+	17.7458i	0.448866	+	0.777459i	−0.549446	+	0.835529i	$0.685161\pi$
$522$		0			0
$523$	40.3312	−	14.6793i	1.76356	−	0.641883i	0.763566	−	0.645730i	$-0.223447\pi$
$523$	40.3312	−	14.6793i	1.76356	−	0.641883i	0.999993	+	0.00384740i	$0.00122467\pi$
$524$	10.5214	+	18.2236i	0.459630	+	0.796102i
$525$		0			0
$526$	−0.401674	+	2.27801i	−0.0175138	+	0.0993258i
$527$	1.91669	−	1.60829i	0.0834923	−	0.0700583i
$528$		0			0
$529$	1.36333	+	7.73183i	0.0592753	+	0.336167i
$530$	−1.44609	−	0.526333i	−0.0628141	−	0.0228625i
$531$		0			0
$532$	17.1634	+	7.43199i	0.744129	+	0.322217i
$533$	−3.12836			−0.135504
$534$		0			0
$535$	0.190884	+	1.08256i	0.00825265	+	0.0468031i
$536$	−8.77584	−	7.36381i	−0.379059	−	0.318068i
$537$		0			0
$538$	−0.489322	+	2.77509i	−0.0210962	+	0.119642i
$539$	14.6864	−	25.4377i	0.632590	−	1.09568i
$540$		0			0
$541$	13.6976	−	4.98551i	0.588905	−	0.214344i	−0.0303426	−	0.999540i	$-0.509660\pi$
$541$	13.6976	−	4.98551i	0.588905	−	0.214344i	0.619248	+	0.785196i	$0.287438\pi$
$542$	−6.28611	+	2.28796i	−0.270012	+	0.0982762i
$543$		0			0
$544$	0.233956	−	0.405223i	0.0100308	−	0.0173738i
$545$	0.0802124	−	0.454907i	0.00343592	−	0.0194861i
$546$		0			0
$547$	14.2246	+	11.9359i	0.608201	+	0.510341i	0.894070	−	0.447928i	$-0.147838\pi$
$547$	14.2246	+	11.9359i	0.608201	+	0.510341i	−0.285869	+	0.958269i	$0.592282\pi$
$548$	2.13950	+	12.1337i	0.0913949	+	0.518326i
$549$		0			0
$550$	−12.8324			−0.547177
$551$	9.38919	+	4.06564i	0.399993	+	0.173202i
$552$		0			0
$553$	19.5842	+	7.12808i	0.832807	+	0.303117i
$554$	−1.43289	−	8.12630i	−0.0608775	−	0.345253i
$555$		0			0
$556$	−4.28106	+	3.59224i	−0.181557	+	0.152345i
$557$	−2.69816	+	15.3020i	−0.114325	+	0.648367i	0.872758	+	0.488154i	$0.162329\pi$
$557$	−2.69816	+	15.3020i	−0.114325	+	0.648367i	−0.987082	+	0.160214i	$0.948782\pi$
$558$		0			0
$559$	−3.80406	−	6.58883i	−0.160895	−	0.278678i
$560$	0.486329	−	0.177009i	0.0205512	−	0.00748001i
$561$		0			0
$562$	−13.9684	−	24.1939i	−0.589220	−	1.02056i
$563$	−6.07785	+	10.5271i	−0.256151	+	0.443666i	−0.965207	−	0.261485i	$-0.915788\pi$
$563$	−6.07785	+	10.5271i	−0.256151	+	0.443666i	0.709057	+	0.705151i	$0.249121\pi$
$564$		0			0
$565$	−0.500000	+	0.419550i	−0.0210352	+	0.0176506i
$566$	−1.85844	−	1.55942i	−0.0781161	−	0.0655472i
$567$		0			0
$568$	−12.5287	−	4.56007i	−0.525692	−	0.191336i
$569$	−13.6709			−0.573113			−0.286556	−	0.958063i	$-0.592511\pi$
$569$	−13.6709			−0.573113			−0.286556	+	0.958063i	$0.592511\pi$
$570$		0			0
$571$	28.2003			1.18014			0.590072	−	0.807350i	$-0.299099\pi$
$571$	28.2003			1.18014			0.590072	+	0.807350i	$0.299099\pi$
$572$	1.97178	+	0.717670i	0.0824443	+	0.0300073i
$573$		0			0
$574$	−12.6138	−	10.5842i	−0.526490	−	0.441778i
$575$	21.2126	−	17.7995i	0.884627	−	0.742290i
$576$		0			0
$577$	−10.1095	+	17.5101i	−0.420863	+	0.728956i	−0.996024	−	0.0890843i	$-0.971606\pi$
$577$	−10.1095	+	17.5101i	−0.420863	+	0.728956i	0.575161	+	0.818040i	$0.304939\pi$
$578$	−8.39053	−	14.5328i	−0.349000	−	0.604486i
$579$		0			0
$580$	0.266044	−	0.0968323i	0.0110469	−	0.00402074i
$581$	−6.97044	−	12.0732i	−0.289182	−	0.500879i
$582$		0			0
$583$	5.70274	−	32.3419i	0.236184	−	1.33946i
$584$	−1.74897	+	1.46756i	−0.0723729	+	0.0607281i
$585$		0			0
$586$	−2.44862	−	13.8868i	−0.101151	−	0.573658i
$587$	−4.89306	−	1.78093i	−0.201958	−	0.0735067i	0.239061	−	0.971005i	$-0.423161\pi$
$587$	−4.89306	−	1.78093i	−0.201958	−	0.0735067i	−0.441019	+	0.897498i	$0.645383\pi$
$588$		0			0
$589$	−22.3384	+	6.65376i	−0.920439	+	0.274163i
$590$	1.81521			0.0747309
$591$		0			0
$592$	−1.47906	−	8.38814i	−0.0607888	−	0.344750i
$593$	33.3573	+	27.9901i	1.36982	+	1.14942i	0.972811	+	0.231602i	$0.0743966\pi$
$593$	33.3573	+	27.9901i	1.36982	+	1.14942i	0.397010	+	0.917814i	$0.370048\pi$
$594$		0			0
$595$	−0.0420512	+	0.238484i	−0.00172393	+	0.00977690i
$596$	5.54710	−	9.60787i	0.227218	−	0.393553i
$597$		0			0
$598$	−4.25490	+	1.54866i	−0.173996	+	0.0633293i
$599$	−30.7511	+	11.1925i	−1.25646	+	0.457312i	−0.882578	−	0.470166i	$-0.844194\pi$
$599$	−30.7511	+	11.1925i	−1.25646	+	0.457312i	−0.373877	+	0.927478i	$0.621972\pi$
$600$		0			0
$601$	10.3867	−	17.9902i	0.423681	−	0.733836i	−0.572616	−	0.819824i	$-0.694071\pi$
$601$	10.3867	−	17.9902i	0.423681	−	0.733836i	0.996296	+	0.0859876i	$0.0274045\pi$
$602$	6.95383	−	39.4371i	0.283417	−	1.60734i
$603$		0			0
$604$	9.64930	+	8.09672i	0.392624	+	0.329451i
$605$	−0.0916247	−	0.519630i	−0.00372508	−	0.0211260i
$606$		0			0
$607$	−23.0419			−0.935241			−0.467621	−	0.883929i	$-0.654889\pi$
$607$	−23.0419			−0.935241			−0.467621	+	0.883929i	$0.654889\pi$
$608$	−3.50000	+	2.59808i	−0.141944	+	0.105366i
$609$		0			0
$610$	−0.194593	−	0.0708260i	−0.00787883	−	0.00286766i
$611$	1.34137	+	7.60727i	0.0542659	+	0.307757i
$612$		0			0
$613$	16.2404	−	13.6273i	0.655942	−	0.550400i	−0.252926	−	0.967486i	$-0.581393\pi$
$613$	16.2404	−	13.6273i	0.655942	−	0.550400i	0.908867	+	0.417085i	$0.136948\pi$
$614$	3.50892	−	19.9001i	0.141609	−	0.803102i
$615$		0			0
$616$	5.52229	+	9.56488i	0.222499	+	0.385380i
$617$	−19.2472	+	7.00541i	−0.774864	+	0.282027i	−0.699029	−	0.715093i	$-0.746384\pi$
$617$	−19.2472	+	7.00541i	−0.774864	+	0.282027i	−0.0758345	+	0.997120i	$0.524162\pi$
$618$		0			0
$619$	7.87258	+	13.6357i	0.316426	+	0.548065i	0.979740	−	0.200276i	$-0.0641839\pi$
$619$	7.87258	+	13.6357i	0.316426	+	0.548065i	−0.663314	+	0.748341i	$0.730851\pi$
$620$	−0.322481	+	0.558554i	−0.0129512	+	0.0224321i
$621$		0			0
$622$	7.36824	−	6.18269i	0.295440	−	0.247903i
$623$	11.2779	+	9.46329i	0.451840	+	0.379139i
$624$		0			0
$625$	−23.2875	−	8.47594i	−0.931498	−	0.339038i
$626$	−24.8881			−0.994727
$627$		0			0
$628$	−3.97771			−0.158728
$629$	3.74510	+	1.36310i	0.149327	+	0.0543506i
$630$		0			0
$631$	−16.2041	−	13.5969i	−0.645077	−	0.541284i	0.260496	−	0.965475i	$-0.416114\pi$
$631$	−16.2041	−	13.5969i	−0.645077	−	0.541284i	−0.905573	+	0.424191i	$0.860558\pi$
$632$	−3.72075	+	3.12208i	−0.148004	+	0.124190i
$633$		0			0
$634$	−8.63176	+	14.9506i	−0.342811	+	0.593766i
$635$	−0.255777	−	0.443020i	−0.0101502	−	0.0175807i
$636$		0			0
$637$	−8.74170	+	3.18172i	−0.346359	+	0.126064i
$638$	3.02094	+	5.23243i	0.119600	+	0.207154i
$639$		0			0
$640$	−0.0209445	+	0.118782i	−0.000827905	+	0.00469528i
$641$	−6.30200	+	5.28801i	−0.248914	+	0.208864i	−0.758705	−	0.651435i	$-0.774167\pi$
$641$	−6.30200	+	5.28801i	−0.248914	+	0.208864i	0.509790	+	0.860299i	$0.329723\pi$
$642$		0			0
$643$	−0.742574	−	4.21134i	−0.0292842	−	0.166079i	0.966658	−	0.256069i	$-0.0824276\pi$
$643$	−0.742574	−	4.21134i	−0.0292842	−	0.166079i	−0.995943	+	0.0899901i	$0.971316\pi$
$644$	−22.3957	−	8.15138i	−0.882516	−	0.321210i
$645$		0			0
$646$	−0.233956	−	2.02611i	−0.00920486	−	0.0797164i
$647$	−0.947682			−0.0372572			−0.0186286	−	0.999826i	$-0.505930\pi$
$647$	−0.947682			−0.0372572			−0.0186286	+	0.999826i	$0.505930\pi$
$648$		0			0
$649$	6.72668	+	38.1489i	0.264045	+	1.49748i
$650$	3.11334	+	2.61240i	0.122115	+	0.102467i
$651$		0			0
$652$	3.33409	−	18.9086i	0.130573	−	0.740517i
$653$	−16.4217	+	28.4433i	−0.642632	+	1.11307i	0.342211	+	0.939623i	$0.388824\pi$
$653$	−16.4217	+	28.4433i	−0.642632	+	1.11307i	−0.984843	+	0.173449i	$0.944509\pi$
$654$		0			0
$655$	2.38501	−	0.868073i	0.0931901	−	0.0339184i
$656$	3.60607	−	1.31250i	0.140793	−	0.0512446i
$657$		0			0
$658$	−20.3293	+	35.2115i	−0.792520	+	1.37269i
$659$	−0.823826	+	4.67215i	−0.0320917	+	0.182001i	−0.996640	−	0.0819047i	$-0.973900\pi$
$659$	−0.823826	+	4.67215i	−0.0320917	+	0.182001i	0.964548	+	0.263906i	$0.0850108\pi$
$660$		0			0
$661$	30.1864	+	25.3294i	1.17412	+	0.985201i	1.00000		0.000475674i	$0.000151412\pi$
$661$	30.1864	+	25.3294i	1.17412	+	0.985201i	0.174117	+	0.984725i	$0.444293\pi$
$662$	−1.73483	−	9.83873i	−0.0674262	−	0.382393i
$663$		0			0
$664$	3.24897			0.126085
$665$	1.24227	−	1.88305i	0.0481731	−	0.0730217i
$666$		0			0
$667$	−12.2515	−	4.45918i	−0.474380	−	0.172660i
$668$	2.66978	+	15.1411i	0.103297	+	0.585825i
$669$		0			0
$670$	−1.05850	+	0.888184i	−0.0408933	+	0.0343135i
$671$	0.767389	−	4.35208i	0.0296247	−	0.168010i
$672$		0			0
$673$	−8.57145	−	14.8462i	−0.330405	−	0.572279i	0.652186	−	0.758059i	$-0.273852\pi$
$673$	−8.57145	−	14.8462i	−0.330405	−	0.572279i	−0.982591	+	0.185780i	$0.940519\pi$
$674$	6.35591	−	2.31336i	0.244821	−	0.0891074i
$675$		0			0
$676$	6.16772	+	10.6828i	0.237220	+	0.410877i
$677$	3.56506	−	6.17486i	0.137016	−	0.237319i	−0.789350	−	0.613944i	$-0.789582\pi$
$677$	3.56506	−	6.17486i	0.137016	−	0.237319i	0.926366	+	0.376625i	$0.122915\pi$
$678$		0			0
$679$	−10.1930	+	8.55294i	−0.391171	+	0.328232i
$680$	−0.0432332	−	0.0362770i	−0.00165792	−	0.00139116i
$681$		0			0
$682$	−12.9338	−	4.70750i	−0.495259	−	0.180260i
$683$	26.0000			0.994862			0.497431	−	0.867503i	$-0.334277\pi$
$683$	26.0000			0.994862			0.497431	+	0.867503i	$0.334277\pi$
$684$		0			0
$685$	1.48608			0.0567802
$686$	−17.7875	−	6.47410i	−0.679128	−	0.247182i
$687$		0			0
$688$	7.14930	+	5.99898i	0.272565	+	0.228709i
$689$	−7.96766	+	6.68566i	−0.303544	+	0.254703i
$690$		0			0
$691$	−19.6857	+	34.0967i	−0.748880	+	1.29710i	0.199479	+	0.979902i	$0.436075\pi$
$691$	−19.6857	+	34.0967i	−0.748880	+	1.29710i	−0.948360	+	0.317197i	$0.897258\pi$
$692$	−3.29679	−	5.71021i	−0.125325	−	0.217069i
$693$		0			0
$694$	−23.1177	+	8.41415i	−0.877535	+	0.319397i
$695$	0.337029	+	0.583752i	0.0127843	+	0.0221430i
$696$		0			0
$697$	−0.311804	+	1.76833i	−0.0118104	+	0.0669802i
$698$	5.23577	−	4.39333i	0.198177	−	0.166290i
$699$		0			0
$700$	3.71466	+	21.0669i	0.140401	+	0.796253i
$701$	5.29426	+	1.92695i	0.199962	+	0.0727801i	0.440060	−	0.897969i	$-0.354957\pi$
$701$	5.29426	+	1.92695i	0.199962	+	0.0727801i	−0.240098	+	0.970749i	$0.577180\pi$
$702$		0			0
$703$	−26.9697	−	25.5158i	−1.01718	−	0.962346i
$704$	−2.57398			−0.0970104
$705$		0			0
$706$	−0.882789	−	5.00654i	−0.0332242	−	0.188424i
$707$	−54.9903	−	46.1423i	−2.06812	−	1.73536i
$708$		0			0
$709$	5.32517	−	30.2005i	0.199991	−	1.13421i	−0.705139	−	0.709069i	$-0.749115\pi$
$709$	5.32517	−	30.2005i	0.199991	−	1.13421i	0.905130	−	0.425136i	$-0.139774\pi$
$710$	−0.804063	+	1.39268i	−0.0301760	+	0.0522663i
$711$		0			0
$712$	−3.22416	+	1.17350i	−0.120830	+	0.0439786i
$713$	27.9097	−	10.1583i	1.04523	−	0.380432i
$714$		0			0
$715$	0.126545	−	0.219182i	0.00473250	−	0.00819693i
$716$	−0.215537	+	1.22237i	−0.00805500	+	0.0456822i
$717$		0			0
$718$	−2.19665	−	1.84321i	−0.0819783	−	0.0687880i
$719$	−1.10085	−	6.24324i	−0.0410549	−	0.232834i	0.957375	−	0.288847i	$-0.0932720\pi$
$719$	−1.10085	−	6.24324i	−0.0410549	−	0.232834i	−0.998430	+	0.0560138i	$0.982161\pi$
$720$		0			0
$721$	44.6117			1.66143
$722$	−5.50000	+	18.1865i	−0.204689	+	0.676833i
$723$		0			0
$724$	−3.78699	−	1.37835i	−0.140742	−	0.0512260i
$725$	2.03209	+	11.5245i	0.0754699	+	0.428011i
$726$		0			0
$727$	−17.8806	+	15.0036i	−0.663154	+	0.556452i	−0.911030	−	0.412340i	$-0.864712\pi$
$727$	−17.8806	+	15.0036i	−0.663154	+	0.556452i	0.247877	+	0.968792i	$0.420267\pi$
$728$	0.607411	−	3.44480i	0.0225121	−	0.127673i
$729$		0			0
$730$	0.137689	+	0.238484i	0.00509609	+	0.00882670i
$731$	−4.10354	+	1.49357i	−0.151775	+	0.0552416i
$732$		0			0
$733$	−0.794730	−	1.37651i	−0.0293540	−	0.0508426i	0.850975	−	0.525206i	$-0.176012\pi$
$733$	−0.794730	−	1.37651i	−0.0293540	−	0.0508426i	−0.880329	+	0.474363i	$0.842678\pi$
$734$	11.0715	−	19.1763i	0.408655	−	0.707811i
$735$		0			0
$736$	4.25490	−	3.57029i	0.156838	−	0.131602i
$737$	−22.5888	−	18.9543i	−0.832070	−	0.698190i
$738$		0			0
$739$	−3.43882	−	1.25163i	−0.126499	−	0.0460418i	0.277995	−	0.960582i	$-0.410330\pi$
$739$	−3.43882	−	1.25163i	−0.126499	−	0.0460418i	−0.404494	+	0.914541i	$0.632552\pi$
$740$	−1.02734			−0.0377658
$741$		0			0
$742$	−54.7461			−2.00979
$743$	−17.2716	−	6.28634i	−0.633632	−	0.230623i	0.00517924	−	0.999987i	$-0.498351\pi$
$743$	−17.2716	−	6.28634i	−0.633632	−	0.230623i	−0.638811	+	0.769363i	$0.720574\pi$
$744$		0			0
$745$	−1.02506	−	0.860130i	−0.0375554	−	0.0315127i
$746$	−13.5385	+	11.3601i	−0.495679	+	0.415924i
$747$		0			0
$748$	0.602196	−	1.04303i	0.0220185	−	0.0381371i
$749$	19.5530	+	33.8668i	0.714452	+	1.23747i
$750$		0			0
$751$	−28.8161	+	10.4882i	−1.05152	+	0.382720i	−0.809235	−	0.587486i	$-0.800118\pi$
$751$	−28.8161	+	10.4882i	−1.05152	+	0.382720i	−0.242281	+	0.970206i	$0.577896\pi$
$752$	−4.73783	−	8.20616i	−0.172771	−	0.299248i
$753$		0			0
$754$	0.332282	−	1.88446i	0.0121010	−	0.0686281i
$755$	1.16385	−	0.976584i	0.0423568	−	0.0355415i
$756$		0			0
$757$	−1.35235	−	7.66955i	−0.0491520	−	0.278755i	0.950319	−	0.311278i	$-0.100757\pi$
$757$	−1.35235	−	7.66955i	−0.0491520	−	0.278755i	−0.999471	+	0.0325230i	$0.989646\pi$
$758$	−9.17112	−	3.33802i	−0.333110	−	0.121242i
$759$		0			0
$760$	0.235300	+	0.470154i	0.00853522	+	0.0170543i
$761$	−28.3969			−1.02939			−0.514694	−	0.857374i	$-0.672094\pi$
$761$	−28.3969			−1.02939			−0.514694	+	0.857374i	$0.672094\pi$
$762$		0			0
$763$	−2.85355	−	16.1833i	−0.103305	−	0.585874i
$764$	18.4500	+	15.4814i	0.667496	+	0.560096i
$765$		0			0
$766$	−3.87505	+	21.9765i	−0.140011	+	0.794043i
$767$	6.13429	−	10.6249i	0.221496	−	0.383643i
$768$		0			0
$769$	−33.1095	+	12.0509i	−1.19396	+	0.434566i	−0.861112	−	0.508415i	$-0.830232\pi$
$769$	−33.1095	+	12.0509i	−1.19396	+	0.434566i	−0.332848	+	0.942981i	$0.608010\pi$
$770$	1.25180	−	0.455618i	0.0451118	−	0.0164193i
$771$		0			0
$772$	4.92989	−	8.53882i	0.177431	−	0.307319i
$773$	3.49092	−	19.7980i	0.125559	−	0.712083i	−0.855415	−	0.517944i	$-0.826698\pi$
$773$	3.49092	−	19.7980i	0.125559	−	0.712083i	0.980974	−	0.194139i	$-0.0621913\pi$
$774$		0			0
$775$	−20.4217	−	17.1359i	−0.733571	−	0.615539i
$776$	−0.538485	−	3.05390i	−0.0193305	−	0.109629i
$777$		0			0
$778$	7.02229			0.251761
$779$	9.21126	−	13.9626i	0.330028	−	0.500262i
$780$		0			0
$781$	−32.2486	−	11.7375i	−1.15394	−	0.420001i
$782$	0.451304	+	2.55947i	0.0161386	+	0.0915265i
$783$		0			0
$784$	8.74170	−	7.33515i	0.312203	−	0.261970i
$785$	−0.0833113	+	0.472482i	−0.00297351	+	0.0168636i
$786$		0			0
$787$	11.9265	+	20.6573i	0.425133	+	0.736353i	0.996433	−	0.0843890i	$-0.0268938\pi$
$787$	11.9265	+	20.6573i	0.425133	+	0.736353i	−0.571299	+	0.820742i	$0.693561\pi$
$788$	−6.06670	+	2.20810i	−0.216117	+	0.0786603i
$789$		0			0
$790$	0.292919	+	0.507350i	0.0104216	+	0.0180507i
$791$	−11.6099	+	20.1090i	−0.412802	+	0.714994i
$792$		0			0
$793$	−1.07217	+	0.899655i	−0.0380738	+	0.0319477i
$794$	15.3045	+	12.8420i	0.543137	+	0.455746i
$795$		0			0
$796$	−23.2777	−	8.47237i	−0.825055	−	0.300295i
$797$	28.5262			1.01045			0.505225	−	0.862988i	$-0.331409\pi$
$797$	28.5262			1.01045			0.505225	+	0.862988i	$0.331409\pi$
$798$		0			0
$799$	4.43376			0.156855
$800$	−4.68479	−	1.70513i	−0.165632	−	0.0602853i
$801$		0			0
$802$	−0.911474	−	0.764818i	−0.0321853	−	0.0270066i
$803$	−4.50181	+	3.77747i	−0.158865	+	0.133304i
$804$		0			0
$805$	−1.43731	+	2.48949i	−0.0506585	+	0.0877431i
$806$	2.17958	+	3.77514i	0.0767724	+	0.132974i
$807$		0			0
$808$	15.7208	−	5.72189i	0.553054	−	0.201295i
$809$	12.4645	+	21.5892i	0.438229	+	0.759034i	0.997553	−	0.0699145i	$-0.0222727\pi$
$809$	12.4645	+	21.5892i	0.438229	+	0.759034i	−0.559324	+	0.828949i	$0.688939\pi$
$810$		0			0
$811$	3.21672	−	18.2429i	0.112954	−	0.640596i	−0.874788	−	0.484505i	$-0.839000\pi$
$811$	3.21672	−	18.2429i	0.112954	−	0.640596i	0.987743	−	0.156091i	$-0.0498892\pi$
$812$	7.71554	−	6.47410i	0.270762	−	0.227197i
$813$		0			0
$814$	−3.80706	−	21.5909i	−0.133437	−	0.756760i
$815$	−2.17617	−	0.792063i	−0.0762281	−	0.0277447i
$816$		0			0
$817$	40.6083	+	2.42199i	1.42071	+	0.0847346i
$818$	−9.48845			−0.331756
$819$		0			0
$820$	−0.0803746	−	0.455827i	−0.00280680	−	0.0159182i
$821$	−27.2415	−	22.8584i	−0.950736	−	0.797762i	0.0286853	−	0.999588i	$-0.490868\pi$
$821$	−27.2415	−	22.8584i	−0.950736	−	0.797762i	−0.979421	+	0.201826i	$0.935312\pi$
$822$		0			0
$823$	−3.21167	+	18.2143i	−0.111952	+	0.634909i	0.876263	+	0.481834i	$0.160029\pi$
$823$	−3.21167	+	18.2143i	−0.111952	+	0.634909i	−0.988214	+	0.153076i	$0.951082\pi$
$824$	−5.19846	+	9.00400i	−0.181097	+	0.313669i
$825$		0			0
$826$	60.6814	−	22.0862i	2.11138	−	0.768479i
$827$	29.6891	−	10.8060i	1.03239	−	0.375760i	0.230401	−	0.973096i	$-0.425996\pi$
$827$	29.6891	−	10.8060i	1.03239	−	0.375760i	0.801991	+	0.597336i	$0.203774\pi$
$828$		0			0
$829$	20.5719	−	35.6316i	0.714492	−	1.23754i	−0.248663	−	0.968590i	$-0.579991\pi$
$829$	20.5719	−	35.6316i	0.714492	−	1.23754i	0.963155	−	0.268947i	$-0.0866756\pi$
$830$	0.0680482	−	0.385920i	0.00236199	−	0.0133955i
$831$		0			0
$832$	0.624485	+	0.524005i	0.0216501	+	0.0181666i
$833$	0.927204	+	5.25844i	0.0321257	+	0.182194i
$834$		0			0
$835$	1.85441			0.0641744
$836$	−9.00892	+	6.68739i	−0.311580	+	0.231288i
$837$		0			0
$838$	−4.44134	−	1.61652i	−0.153424	−	0.0558416i
$839$	−3.46956	−	19.6769i	−0.119783	−	0.679320i	−0.984271	−	0.176667i	$-0.943468\pi$
$839$	−3.46956	−	19.6769i	−0.119783	−	0.679320i	0.864488	−	0.502653i	$-0.167643\pi$
$840$		0			0
$841$	−17.9945	+	15.0992i	−0.620501	+	0.520662i
$842$	−0.240819	+	1.36575i	−0.00829917	+	0.0470669i
$843$		0			0
$844$	0.692066	+	1.19869i	0.0238219	+	0.0412608i
$845$	1.39811	−	0.508870i	0.0480964	−	0.0175057i
$846$		0			0
$847$	−9.38548	−	16.2561i	−0.322489	−	0.558567i
$848$	6.37939	−	11.0494i	0.219069	−	0.379439i
$849$		0			0
$850$	1.78699	−	1.49946i	0.0612932	−	0.0514311i
$851$	36.2413	+	30.4100i	1.24234	+	1.04244i
$852$		0			0
$853$	17.7939	+	6.47643i	0.609250	+	0.221749i	0.628175	−	0.778072i	$-0.283802\pi$
$853$	17.7939	+	6.47643i	0.609250	+	0.221749i	−0.0189251	+	0.999821i	$0.506024\pi$
$854$	−7.36690			−0.252090
$855$		0			0
$856$	−9.11381			−0.311504
$857$	−20.0532	−	7.29877i	−0.685004	−	0.249321i	−0.0240095	−	0.999712i	$-0.507643\pi$
$857$	−20.0532	−	7.29877i	−0.685004	−	0.249321i	−0.660995	+	0.750391i	$0.729865\pi$
$858$		0			0
$859$	35.1129	+	29.4632i	1.19804	+	1.00527i	0.999684	+	0.0251425i	$0.00800396\pi$
$859$	35.1129	+	29.4632i	1.19804	+	1.00527i	0.198354	+	0.980130i	$0.436440\pi$
$860$	0.862311	−	0.723565i	0.0294046	−	0.0246734i
$861$		0			0
$862$	−1.35591	+	2.34851i	−0.0461826	+	0.0799907i
$863$	7.62970	+	13.2150i	0.259718	+	0.449845i	0.966166	−	0.257920i	$-0.0830371\pi$
$863$	7.62970	+	13.2150i	0.259718	+	0.449845i	−0.706448	+	0.707765i	$0.749704\pi$
$864$		0			0
$865$	−0.747321	+	0.272003i	−0.0254097	+	0.00924837i
$866$	−10.1206	−	17.5294i	−0.343912	−	0.595674i
$867$		0			0
$868$	−3.98427	+	22.5959i	−0.135235	+	0.766955i
$869$	−9.57713	+	8.03617i	−0.324882	+	0.272608i
$870$		0			0
$871$	1.62171	+	9.19718i	0.0549496	+	0.311634i
$872$	3.59879	+	1.30985i	0.121871	+	0.0443572i
$873$		0			0
$874$	5.61628	−	23.5506i	0.189973	−	0.796609i
$875$	5.16788			0.174706
$876$		0			0
$877$	3.88635	+	22.0406i	0.131233	+	0.744259i	0.977409	+	0.211356i	$0.0677878\pi$
$877$	3.88635	+	22.0406i	0.131233	+	0.744259i	−0.846176	+	0.532903i	$0.821101\pi$
$878$	13.9422	+	11.6989i	0.470527	+	0.394819i
$879$		0			0
$880$	−0.0539108	+	0.305743i	−0.00181733	+	0.0103066i
$881$	−13.5052	+	23.3917i	−0.455002	+	0.788087i	−0.998688	−	0.0512016i	$-0.983695\pi$
$881$	−13.5052	+	23.3917i	−0.455002	+	0.788087i	0.543686	+	0.839289i	$0.317028\pi$
$882$		0			0
$883$	−16.3640	+	5.95599i	−0.550691	+	0.200435i	−0.602354	−	0.798229i	$-0.705770\pi$
$883$	−16.3640	+	5.95599i	−0.550691	+	0.200435i	0.0516624	+	0.998665i	$0.483548\pi$
$884$	−0.358441	+	0.130462i	−0.0120557	+	0.00438790i
$885$		0			0
$886$	17.8712	−	30.9539i	0.600396	−	1.03992i
$887$	−10.1718	+	57.6869i	−0.341534	+	1.93694i	0.00788527	+	0.999969i	$0.497490\pi$
$887$	−10.1718	+	57.6869i	−0.341534	+	1.93694i	−0.349419	+	0.936966i	$0.613621\pi$
$888$		0			0
$889$	−13.9409	−	11.6978i	−0.467562	−	0.392331i
$890$	0.0718623	+	0.407551i	0.00240883	+	0.0136611i
$891$		0			0
$892$	22.3131			0.747099
$893$	−37.9026	−	16.4123i	−1.26836	−	0.549217i
$894$		0			0
$895$	0.140682	+	0.0512040i	0.00470248	+	0.00171156i
$896$	0.745100	+	4.22567i	0.0248920	+	0.141170i
$897$		0			0
$898$	−14.5476	+	12.2069i	−0.485459	+	0.407348i
$899$	−2.17958	+	12.3610i	−0.0726930	+	0.412262i
$900$		0			0
$901$	2.98499	+	5.17015i	0.0994443	+	0.172243i
$902$	9.28194	−	3.37835i	0.309055	−	0.112487i
$903$		0			0
$904$	−2.70574	−	4.68647i	−0.0899915	−	0.155870i
$905$	−0.243041	+	0.420959i	−0.00807894	+	0.0139931i
$906$		0			0
$907$	−7.55896	+	6.34272i	−0.250991	+	0.210607i	−0.759599	−	0.650392i	$-0.774605\pi$
$907$	−7.55896	+	6.34272i	−0.250991	+	0.210607i	0.508608	+	0.860998i	$0.330160\pi$
$908$	15.9081	+	13.3485i	0.527928	+	0.442984i
$909$		0			0
$910$	−0.396459	−	0.144299i	−0.0131425	−	0.00478348i
$911$	13.9813			0.463222			0.231611	−	0.972808i	$-0.425600\pi$
$911$	13.9813			0.463222			0.231611	+	0.972808i	$0.425600\pi$
$912$		0			0
$913$	8.36278			0.276768
$914$	24.3974	+	8.87992i	0.806994	+	0.293722i
$915$		0			0
$916$	4.22668	+	3.54661i	0.139653	+	0.117183i
$917$	69.1675	−	58.0384i	2.28411	−	1.91660i
$918$		0			0
$919$	6.36231	−	11.0198i	0.209873	−	0.363511i	−0.741801	−	0.670620i	$-0.766028\pi$
$919$	6.36231	−	11.0198i	0.209873	−	0.363511i	0.951674	+	0.307109i	$0.0993615\pi$
$920$	−0.334970	−	0.580185i	−0.0110436	−	0.0191281i
$921$		0			0
$922$	27.4714	−	9.99876i	0.904721	−	0.329292i
$923$	5.43448	+	9.41279i	0.178878	+	0.309826i
$924$		0			0
$925$	7.37376	−	41.8187i	0.242448	−	1.37499i
$926$	16.2331	−	13.6212i	0.533452	−	0.447619i
$927$		0			0
$928$	0.407604	+	2.31164i	0.0133802	+	0.0758832i
$929$	19.6830	+	7.16404i	0.645780	+	0.235045i	0.644085	−	0.764954i	$-0.277238\pi$
$929$	19.6830	+	7.16404i	0.645780	+	0.235045i	0.00169466	+	0.999999i	$0.499461\pi$
$930$		0			0
$931$	11.5386	−	48.3846i	0.378164	−	1.58574i
$932$	15.0865			0.494174
$933$		0			0
$934$	−0.372522	−	2.11268i	−0.0121893	−	0.0691289i
$935$	−0.111281	−	0.0933762i	−0.00363929	−	0.00305373i
$936$		0			0
$937$	−1.68866	+	9.57688i	−0.0551662	+	0.312863i	−0.999887	−	0.0150119i	$-0.995221\pi$
$937$	−1.68866	+	9.57688i	−0.0551662	+	0.312863i	0.944721	+	0.327875i	$0.106332\pi$
$938$	−24.5782	+	42.5706i	−0.802505	+	1.38998i
$939$		0			0
$940$	−1.07398	+	0.390896i	−0.0350293	+	0.0127496i
$941$	−21.7875	+	7.92999i	−0.710251	+	0.258510i	−0.671781	−	0.740750i	$-0.734470\pi$
$941$	−21.7875	+	7.92999i	−0.710251	+	0.258510i	−0.0384696	+	0.999260i	$0.512248\pi$
$942$		0			0
$943$	−10.6575	+	18.4592i	−0.347054	+	0.601116i
$944$	−2.61334	+	14.8210i	−0.0850570	+	0.482382i
$945$		0			0
$946$	18.4021	+	15.4412i	0.598305	+	0.502038i
$947$	−4.77900	−	27.1031i	−0.155297	−	0.880731i	−0.958514	−	0.285045i	$-0.907991\pi$
$947$	−4.77900	−	27.1031i	−0.155297	−	0.880731i	0.803217	−	0.595686i	$-0.203120\pi$
$948$		0			0
$949$	1.86122			0.0604176
$950$	−20.8268	+	6.20351i	−0.675711	+	0.201268i
$951$		0			0
$952$	−1.88666	−	0.686688i	−0.0611470	−	0.0222557i
$953$	−8.75608	−	49.6582i	−0.283637	−	1.60859i	−0.710113	−	0.704088i	$-0.751356\pi$
$953$	−8.75608	−	49.6582i	−0.283637	−	1.60859i	0.426475	−	0.904499i	$-0.359755\pi$
$954$		0			0
$955$	2.22534	−	1.86728i	0.0720102	−	0.0604238i
$956$	5.02734	−	28.5115i	0.162596	−	0.922127i
$957$		0			0
$958$	1.69846	+	2.94182i	0.0548749	+	0.0950460i
$959$	49.6789	−	18.0816i	1.60422	−	0.583887i
$960$		0			0
$961$	1.20321	+	2.08402i	0.0388133	+	0.0672265i
$962$	−3.47178	+	6.01330i	−0.111935	+	0.193877i
$963$		0			0
$964$	−14.8380	+	12.4505i	−0.477899	+	0.401005i
$965$	−0.911007	−	0.764426i	−0.0293264	−	0.0246077i
$966$		0			0
$967$	−29.9424	−	10.8981i	−0.962882	−	0.350460i	−0.187720	−	0.982223i	$-0.560110\pi$
$967$	−29.9424	−	10.8981i	−0.962882	−	0.350460i	−0.775162	+	0.631762i	$0.782332\pi$
$968$	4.37464			0.140606
$969$		0			0
$970$	−0.374028			−0.0120093
$971$	−2.10607	−	0.766546i	−0.0675869	−	0.0245996i	0.308005	−	0.951385i	$-0.400338\pi$
$971$	−2.10607	−	0.766546i	−0.0675869	−	0.0245996i	−0.375592	+	0.926785i	$0.622561\pi$
$972$		0			0
$973$	18.3694	+	15.4138i	0.588897	+	0.494143i
$974$	−15.1570	+	12.7183i	−0.485663	+	0.407520i
$975$		0			0
$976$	0.858441	−	1.48686i	0.0274780	−	0.0475933i
$977$	−0.733956	−	1.27125i	−0.0234813	−	0.0406708i	0.854046	−	0.520198i	$-0.174142\pi$
$977$	−0.733956	−	1.27125i	−0.0234813	−	0.0406708i	−0.877527	+	0.479527i	$0.840808\pi$
$978$		0			0
$979$	−8.29890	+	3.02055i	−0.265234	+	0.0965373i
$980$	−0.688196	−	1.19199i	−0.0219836	−	0.0380767i
$981$		0			0
$982$	4.36618	−	24.7618i	0.139330	−	0.790182i
$983$	−22.9957	+	19.2957i	−0.733450	+	0.615437i	−0.931070	−	0.364841i	$-0.881123\pi$
$983$	−22.9957	+	19.2957i	−0.733450	+	0.615437i	0.197620	+	0.980279i	$0.436679\pi$
$984$		0			0
$985$	0.135219	+	0.766865i	0.00430844	+	0.0244343i
$986$	−1.03209	−	0.375650i	−0.0328684	−	0.0119631i
$987$		0			0
$988$	3.54710	+	0.211558i	0.112848	+	0.00673057i
$989$	−51.8376			−1.64834
$990$		0			0
$991$	9.50464	+	53.9035i	0.301925	+	1.71230i	0.637637	+	0.770337i	$0.279912\pi$
$991$	9.50464	+	53.9035i	0.301925	+	1.71230i	−0.335712	+	0.941965i	$0.608977\pi$
$992$	−4.09627	−	3.43718i	−0.130057	−	0.109130i
$993$		0			0
$994$	−9.93423	+	56.3398i	−0.315095	+	1.78699i
$995$	−1.49391	+	2.58752i	−0.0473601	+	0.0820300i
$996$		0			0
$997$	45.6896	−	16.6297i	1.44700	−	0.526666i	0.505251	−	0.862972i	$-0.331400\pi$
$997$	45.6896	−	16.6297i	1.44700	−	0.526666i	0.941753	+	0.336306i	$0.109178\pi$
$998$	33.0381	−	12.0249i	1.04580	−	0.380641i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.u.b.289.1		6
3.2	odd	2		114.2.i.c.61.1	yes	6
12.11	even	2		912.2.bo.d.289.1		6
19.5	even	9	inner	342.2.u.b.271.1		6
19.9	even	9		6498.2.a.bp.1.1		3
19.10	odd	18		6498.2.a.bu.1.1		3
57.5	odd	18		114.2.i.c.43.1	✓	6
57.29	even	18		2166.2.a.p.1.3		3
57.47	odd	18		2166.2.a.r.1.3		3
228.119	even	18		912.2.bo.d.385.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.c.43.1	✓	6	57.5	odd	18
114.2.i.c.61.1	yes	6	3.2	odd	2
342.2.u.b.271.1		6	19.5	even	9	inner
342.2.u.b.289.1		6	1.1	even	1	trivial
912.2.bo.d.289.1		6	12.11	even	2
912.2.bo.d.385.1		6	228.119	even	18
2166.2.a.p.1.3		3	57.29	even	18
2166.2.a.r.1.3		3	57.47	odd	18
6498.2.a.bp.1.1		3	19.9	even	9
6498.2.a.bu.1.1		3	19.10	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.0923963 - 0.0775297i) q^{5} +(2.14543 - 3.71599i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.0923963 - 0.0775297i) q^{5} +(2.14543 - 3.71599i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.113341 - 0.0412527i) q^{10} +(1.28699 + 2.22913i) q^{11} +(0.141559 - 0.802823i) q^{13} +(3.28699 - 2.75811i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-0.439693 - 0.160035i) q^{17} +(3.16637 + 2.99568i) q^{19} +0.120615 q^{20} +(0.446967 + 2.53487i) q^{22} +(-4.25490 - 3.57029i) q^{23} +(-0.865715 + 4.90971i) q^{25} +(0.407604 - 0.705990i) q^{26} +(4.03209 - 1.46756i) q^{28} +(2.20574 - 0.802823i) q^{29} +(-2.67365 + 4.63089i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-0.358441 - 0.300767i) q^{34} +(-0.0898700 - 0.509678i) q^{35} -8.51754 q^{37} +(1.95084 + 3.89798i) q^{38} +(0.113341 + 0.0412527i) q^{40} +(-0.666374 - 3.77920i) q^{41} +(7.14930 - 5.99898i) q^{43} +(-0.446967 + 2.53487i) q^{44} +(-2.77719 - 4.81023i) q^{46} +(-8.90420 + 3.24086i) q^{47} +(-5.70574 - 9.88263i) q^{49} +(-2.49273 + 4.31753i) q^{50} +(0.624485 - 0.524005i) q^{52} +(-9.77379 - 8.20118i) q^{53} +(0.291737 + 0.106183i) q^{55} +4.29086 q^{56} +2.34730 q^{58} +(14.1420 + 5.14728i) q^{59} +(-1.31521 - 1.10359i) q^{61} +(-4.09627 + 3.43718i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-0.0491630 - 0.0851529i) q^{65} +(-10.7652 + 3.91820i) q^{67} +(-0.233956 - 0.405223i) q^{68} +(0.0898700 - 0.509678i) q^{70} +(-10.2135 + 8.57013i) q^{71} +(0.396459 + 2.24843i) q^{73} +(-8.00387 - 2.91317i) q^{74} +(0.500000 + 4.33013i) q^{76} +11.0446 q^{77} +(0.843426 + 4.78331i) q^{79} +(0.0923963 + 0.0775297i) q^{80} +(0.666374 - 3.77920i) q^{82} +(1.62449 - 2.81369i) q^{83} +(-0.0530334 + 0.0193026i) q^{85} +(8.76991 - 3.19199i) q^{86} +(-1.28699 + 2.22913i) q^{88} +(-0.595800 + 3.37895i) q^{89} +(-2.67958 - 2.24843i) q^{91} +(-0.964508 - 5.46999i) q^{92} -9.47565 q^{94} +(0.524815 + 0.0313013i) q^{95} +(-2.91400 - 1.06061i) q^{97} +(-1.98158 - 11.2381i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 3 * q^5 - 3 * q^7 + 3 * q^8	\( 6 q - 3 q^{5} - 3 q^{7} + 3 q^{8} - 6 q^{10} + 9 q^{13} + 12 q^{14} + 3 q^{17} + 12 q^{20} + 15 q^{22} - 27 q^{23} - 15 q^{25} + 6 q^{26} + 15 q^{28} + 3 q^{29} - 15 q^{31} + 6 q^{34} - 12 q^{35} - 6 q^{37} - 6 q^{40} + 15 q^{41} + 3 q^{43} - 15 q^{44} - 6 q^{46} - 15 q^{47} - 24 q^{49} + 3 q^{50} - 9 q^{52} - 6 q^{53} + 27 q^{55} - 6 q^{56} + 12 q^{58} + 27 q^{59} - 15 q^{61} + 3 q^{62} - 3 q^{64} - 12 q^{65} - 3 q^{67} - 6 q^{68} + 12 q^{70} - 3 q^{71} + 12 q^{73} - 24 q^{74} + 3 q^{76} + 42 q^{77} + 27 q^{79} - 3 q^{80} - 15 q^{82} - 3 q^{83} + 12 q^{85} + 24 q^{86} - 42 q^{89} - 42 q^{91} + 27 q^{92} - 18 q^{94} - 24 q^{95} + 18 q^{97}+O(q^{100}) \) 6 * q - 3 * q^5 - 3 * q^7 + 3 * q^8 - 6 * q^10 + 9 * q^13 + 12 * q^14 + 3 * q^17 + 12 * q^20 + 15 * q^22 - 27 * q^23 - 15 * q^25 + 6 * q^26 + 15 * q^28 + 3 * q^29 - 15 * q^31 + 6 * q^34 - 12 * q^35 - 6 * q^37 - 6 * q^40 + 15 * q^41 + 3 * q^43 - 15 * q^44 - 6 * q^46 - 15 * q^47 - 24 * q^49 + 3 * q^50 - 9 * q^52 - 6 * q^53 + 27 * q^55 - 6 * q^56 + 12 * q^58 + 27 * q^59 - 15 * q^61 + 3 * q^62 - 3 * q^64 - 12 * q^65 - 3 * q^67 - 6 * q^68 + 12 * q^70 - 3 * q^71 + 12 * q^73 - 24 * q^74 + 3 * q^76 + 42 * q^77 + 27 * q^79 - 3 * q^80 - 15 * q^82 - 3 * q^83 + 12 * q^85 + 24 * q^86 - 42 * q^89 - 42 * q^91 + 27 * q^92 - 18 * q^94 - 24 * q^95 + 18 * q^97

Introduction

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