LMFDB - Embedded newform 325.2.e.e.276.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(126,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("325.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.e (of order $3$, degree $2$, 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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 8x^{10} + 54x^{8} + 78x^{6} + 92x^{4} + 10x^{2} + 1 $ x^12 + 8x^10 + 54x^8 + 78x^6 + 92x^4 + 10*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			276.5
Root			$0.593667 - 1.02826i$ of defining polynomial
Character	$\chi$	$=$	325.276
Dual form			325.2.e.e.126.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.593667 + 1.02826i) q^{2} +(0.172555 + 0.298874i) q^{3} +(0.295120 - 0.511162i) q^{4} +(-0.204880 + 0.354863i) q^{6} +(1.01478 - 1.75765i) q^{7} +3.07548 q^{8} +(1.44045 - 2.49493i) q^{9} +O(q^{10})$	\(q+(0.593667 + 1.02826i) q^{2} +(0.172555 + 0.298874i) q^{3} +(0.295120 - 0.511162i) q^{4} +(-0.204880 + 0.354863i) q^{6} +(1.01478 - 1.75765i) q^{7} +3.07548 q^{8} +(1.44045 - 2.49493i) q^{9} +(-1.94045 - 3.36096i) q^{11} +0.203698 q^{12} +(2.05540 + 2.96232i) q^{13} +2.40976 q^{14} +(1.23557 + 2.14007i) q^{16} +(-2.72507 + 4.71996i) q^{17} +3.42059 q^{18} +(-2.94045 + 5.09301i) q^{19} +0.700420 q^{21} +(2.30396 - 3.99058i) q^{22} +(-0.172555 - 0.298874i) q^{23} +(0.530689 + 0.919180i) q^{24} +(-1.82581 + 3.87212i) q^{26} +2.02956 q^{27} +(-0.598962 - 1.03743i) q^{28} +(-1.50000 - 2.59808i) q^{29} +1.18048 q^{31} +(1.60845 - 2.78591i) q^{32} +(0.669668 - 1.15990i) q^{33} -6.47114 q^{34} +(-0.850210 - 1.47261i) q^{36} +(2.72507 + 4.71996i) q^{37} -6.98259 q^{38} +(-0.530689 + 1.12547i) q^{39} +(-0.0902394 - 0.156299i) q^{41} +(0.415816 + 0.720215i) q^{42} +(-0.669668 + 1.15990i) q^{43} -2.29066 q^{44} +(0.204880 - 0.354863i) q^{46} -12.2807 q^{47} +(-0.426407 + 0.738559i) q^{48} +(1.44045 + 2.49493i) q^{49} -1.88090 q^{51} +(2.12081 - 0.176407i) q^{52} -2.42636 q^{53} +(1.20488 + 2.08691i) q^{54} +(3.12093 - 5.40561i) q^{56} -2.02956 q^{57} +(1.78100 - 3.08478i) q^{58} +(3.53069 - 6.11533i) q^{59} +(-3.38090 + 5.85589i) q^{61} +(0.700811 + 1.21384i) q^{62} +(-2.92347 - 5.06361i) q^{63} +8.76180 q^{64} +1.59024 q^{66} +(-2.20211 - 3.81417i) q^{67} +(1.60845 + 2.78591i) q^{68} +(0.0595504 - 0.103144i) q^{69} +(0.940450 - 1.62891i) q^{71} +(4.43007 - 7.67311i) q^{72} -8.86014 q^{73} +(-3.23557 + 5.60417i) q^{74} +(1.73557 + 3.00609i) q^{76} -7.87651 q^{77} +(-1.47233 + 0.122467i) q^{78} +11.1805 q^{79} +(-3.97114 - 6.87821i) q^{81} +(0.107144 - 0.185579i) q^{82} -7.83540 q^{83} +(0.206708 - 0.358028i) q^{84} -1.59024 q^{86} +(0.517665 - 0.896622i) q^{87} +(-5.96781 - 10.3365i) q^{88} +(-6.12093 - 10.6018i) q^{89} +(7.29249 - 0.606582i) q^{91} -0.203698 q^{92} +(0.203698 + 0.352814i) q^{93} +(-7.29066 - 12.6278i) q^{94} +1.11018 q^{96} +(-2.90292 + 5.02801i) q^{97} +(-1.71029 + 2.96232i) q^{98} -11.1805 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q - 4 * q^4 - 10 * q^6 - 6 * q^9	$ 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9} + 44 q^{14} - 16 q^{16} - 12 q^{19} - 8 q^{21} - 32 q^{24} + 24 q^{26} - 18 q^{29} - 16 q^{31} - 16 q^{34} - 2 q^{36} + 32 q^{39} + 14 q^{41} + 4 q^{44} + 10 q^{46} - 6 q^{49} + 24 q^{51} + 22 q^{54} - 16 q^{56} + 4 q^{59} + 6 q^{61} + 12 q^{64} + 4 q^{66} + 24 q^{69} - 12 q^{71} - 8 q^{74} - 10 q^{76} + 104 q^{79} + 14 q^{81} - 90 q^{84} - 4 q^{86} - 20 q^{89} - 44 q^{91} - 56 q^{94} + 12 q^{96} - 104 q^{99}+O(q^{100}) $ 12 * q - 4 * q^4 - 10 * q^6 - 6 * q^9 + 44 * q^14 - 16 * q^16 - 12 * q^19 - 8 * q^21 - 32 * q^24 + 24 * q^26 - 18 * q^29 - 16 * q^31 - 16 * q^34 - 2 * q^36 + 32 * q^39 + 14 * q^41 + 4 * q^44 + 10 * q^46 - 6 * q^49 + 24 * q^51 + 22 * q^54 - 16 * q^56 + 4 * q^59 + 6 * q^61 + 12 * q^64 + 4 * q^66 + 24 * q^69 - 12 * q^71 - 8 * q^74 - 10 * q^76 + 104 * q^79 + 14 * q^81 - 90 * q^84 - 4 * q^86 - 20 * q^89 - 44 * q^91 - 56 * q^94 + 12 * q^96 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.593667	+	1.02826i	0.419786	+	0.727090i	0.995918	−	0.0902665i	$-0.0287719\pi$
$2$	0.593667	+	1.02826i	0.419786	+	0.727090i	−0.576132	+	0.817357i	$0.695439\pi$
$3$	0.172555	+	0.298874i	0.0996247	+	0.172555i	0.911529	−	0.411235i	$-0.134902\pi$
$3$	0.172555	+	0.298874i	0.0996247	+	0.172555i	−0.811905	+	0.583790i	$0.801569\pi$
$4$	0.295120	−	0.511162i	0.147560	−	0.255581i
$5$		0			0
$5$		0			0
$6$	−0.204880	+	0.354863i	−0.0836420	+	0.144872i
$7$	1.01478	−	1.75765i	0.383550	−	0.664328i	−0.608017	−	0.793924i	$-0.708035\pi$
$7$	1.01478	−	1.75765i	0.383550	−	0.664328i	0.991567	+	0.129596i	$0.0413680\pi$
$8$	3.07548			1.08735
$9$	1.44045	−	2.49493i	0.480150	−	0.831644i
$10$		0			0
$11$	−1.94045	−	3.36096i	−0.585068	−	1.01337i	−0.994867	−	0.101191i	$-0.967735\pi$
$11$	−1.94045	−	3.36096i	−0.585068	−	1.01337i	0.409799	−	0.912176i	$-0.365599\pi$
$12$	0.203698			0.0588024
$13$	2.05540	+	2.96232i	0.570066	+	0.821599i
$13$	2.05540	+	2.96232i	0.570066	+	0.821599i
$14$	2.40976			0.644036
$15$		0			0
$16$	1.23557	+	2.14007i	0.308892	+	0.535017i
$17$	−2.72507	+	4.71996i	−0.660927	+	1.14476i	0.319445	+	0.947605i	$0.396503\pi$
$17$	−2.72507	+	4.71996i	−0.660927	+	1.14476i	−0.980372	+	0.197155i	$0.936830\pi$
$18$	3.42059			0.806240
$19$	−2.94045	+	5.09301i	−0.674585	+	1.16842i	0.302005	+	0.953306i	$0.402344\pi$
$19$	−2.94045	+	5.09301i	−0.674585	+	1.16842i	−0.976590	+	0.215110i	$0.930989\pi$
$20$		0			0
$21$	0.700420			0.152844
$22$	2.30396	−	3.99058i	0.491206	−	0.850794i
$23$	−0.172555	−	0.298874i	−0.0359802	−	0.0623195i	0.847475	−	0.530836i	$-0.178122\pi$
$23$	−0.172555	−	0.298874i	−0.0359802	−	0.0623195i	−0.883455	+	0.468516i	$0.844789\pi$
$24$	0.530689	+	0.919180i	0.108326	+	0.187627i
$25$		0			0
$26$	−1.82581	+	3.87212i	−0.358071	+	0.759385i
$27$	2.02956			0.390588
$28$	−0.598962	−	1.03743i	−0.113193	−	0.196056i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	1.18048			0.212020			0.106010	−	0.994365i	$-0.466192\pi$
$31$	1.18048			0.212020			0.106010	+	0.994365i	$0.466192\pi$
$32$	1.60845	−	2.78591i	0.284336	−	0.492484i
$33$	0.669668	−	1.15990i	0.116574	−	0.201913i
$34$	−6.47114			−1.10979
$35$		0			0
$36$	−0.850210	−	1.47261i	−0.141702	−	0.245435i
$37$	2.72507	+	4.71996i	0.447999	+	0.775957i	0.998256	−	0.0590384i	$-0.0188034\pi$
$37$	2.72507	+	4.71996i	0.447999	+	0.775957i	−0.550257	+	0.834996i	$0.685470\pi$
$38$	−6.98259			−1.13273
$39$	−0.530689	+	1.12547i	−0.0849782	+	0.180219i
$40$		0			0
$41$	−0.0902394	−	0.156299i	−0.0140930	−	0.0244098i	0.858893	−	0.512155i	$-0.171153\pi$
$41$	−0.0902394	−	0.156299i	−0.0140930	−	0.0244098i	−0.872986	+	0.487745i	$0.837819\pi$
$42$	0.415816	+	0.720215i	0.0641618	+	0.111132i
$43$	−0.669668	+	1.15990i	−0.102123	+	0.176883i	−0.912559	−	0.408944i	$-0.865897\pi$
$43$	−0.669668	+	1.15990i	−0.102123	+	0.176883i	0.810436	+	0.585827i	$0.199230\pi$
$44$	−2.29066			−0.345330
$45$		0			0
$46$	0.204880	−	0.354863i	0.0302079	−	0.0523217i
$47$	−12.2807			−1.79133			−0.895664	−	0.444731i	$-0.853299\pi$
$47$	−12.2807			−1.79133			−0.895664	+	0.444731i	$0.853299\pi$
$48$	−0.426407	+	0.738559i	−0.0615466	+	0.106602i
$49$	1.44045	+	2.49493i	0.205779	+	0.356419i
$50$		0			0
$51$	−1.88090			−0.263379
$52$	2.12081	−	0.176407i	0.294104	−	0.0244633i
$53$	−2.42636			−0.333286			−0.166643	−	0.986017i	$-0.553293\pi$
$53$	−2.42636			−0.333286			−0.166643	+	0.986017i	$0.553293\pi$
$54$	1.20488	+	2.08691i	0.163963	+	0.283993i
$55$		0			0
$56$	3.12093	−	5.40561i	0.417052	−	0.722355i
$57$	−2.02956			−0.268821
$58$	1.78100	−	3.08478i	0.233857	−	0.405052i
$59$	3.53069	−	6.11533i	0.459657	−	0.796149i	−0.539286	−	0.842123i	$-0.681306\pi$
$59$	3.53069	−	6.11533i	0.459657	−	0.796149i	0.998943	+	0.0459741i	$0.0146392\pi$
$60$		0			0
$61$	−3.38090	+	5.85589i	−0.432880	+	0.749770i	−0.997120	−	0.0758409i	$-0.975836\pi$
$61$	−3.38090	+	5.85589i	−0.432880	+	0.749770i	0.564240	+	0.825611i	$0.309169\pi$
$62$	0.700811	+	1.21384i	0.0890031	+	0.154158i
$63$	−2.92347	−	5.06361i	−0.368323	−	0.637954i
$64$	8.76180			1.09522
$65$		0			0
$66$	1.59024			0.195745
$67$	−2.20211	−	3.81417i	−0.269031	−	0.465975i	0.699581	−	0.714553i	$-0.253370\pi$
$67$	−2.20211	−	3.81417i	−0.269031	−	0.465975i	−0.968612	+	0.248578i	$0.920037\pi$
$68$	1.60845	+	2.78591i	0.195053	+	0.337841i
$69$	0.0595504	−	0.103144i	0.00716903	−	0.0124171i
$70$		0			0
$71$	0.940450	−	1.62891i	0.111611	−	0.193316i	−0.804809	−	0.593534i	$-0.797732\pi$
$71$	0.940450	−	1.62891i	0.111611	−	0.193316i	0.916420	+	0.400218i	$0.131066\pi$
$72$	4.43007	−	7.67311i	0.522089	−	0.904284i
$73$	−8.86014			−1.03700			−0.518501	−	0.855077i	$-0.673510\pi$
$73$	−8.86014			−1.03700			−0.518501	+	0.855077i	$0.673510\pi$
$74$	−3.23557	+	5.60417i	−0.376127	+	0.651472i
$75$		0			0
$76$	1.73557	+	3.00609i	0.199083	+	0.344823i
$77$	−7.87651			−0.897611
$78$	−1.47233	+	0.122467i	−0.166708	+	0.0138666i
$79$	11.1805			1.25790			0.628951	−	0.777445i	$-0.283485\pi$
$79$	11.1805			1.25790			0.628951	+	0.777445i	$0.283485\pi$
$80$		0			0
$81$	−3.97114	−	6.87821i	−0.441238	−	0.764246i
$82$	0.107144	−	0.185579i	0.0118321	−	0.0204938i
$83$	−7.83540			−0.860047			−0.430024	−	0.902818i	$-0.641495\pi$
$83$	−7.83540			−0.860047			−0.430024	+	0.902818i	$0.641495\pi$
$84$	0.206708	−	0.358028i	0.0225537	−	0.0390641i
$85$		0			0
$86$	−1.59024			−0.171480
$87$	0.517665	−	0.896622i	0.0554995	−	0.0961280i
$88$	−5.96781	−	10.3365i	−0.636171	−	1.10188i
$89$	−6.12093	−	10.6018i	−0.648817	−	1.12378i	−0.983406	−	0.181420i	$-0.941931\pi$
$89$	−6.12093	−	10.6018i	−0.648817	−	1.12378i	0.334589	−	0.942364i	$-0.391403\pi$
$90$		0			0
$91$	7.29249	−	0.606582i	0.764460	−	0.0635870i
$92$	−0.203698			−0.0212369
$93$	0.203698	+	0.352814i	0.0211224	+	0.0365852i
$94$	−7.29066	−	12.6278i	−0.751974	−	1.30246i
$95$		0			0
$96$	1.11018			0.113307
$97$	−2.90292	+	5.02801i	−0.294747	+	0.510517i	−0.974926	−	0.222529i	$-0.928569\pi$
$97$	−2.90292	+	5.02801i	−0.294747	+	0.510517i	0.680179	+	0.733046i	$0.261902\pi$
$98$	−1.71029	+	2.96232i	−0.172766	+	0.299239i
$99$	−11.1805			−1.12368
$100$		0			0
$101$	2.97114	+	5.14616i	0.295639	+	0.512062i	0.975133	−	0.221619i	$-0.0711340\pi$
$101$	2.97114	+	5.14616i	0.295639	+	0.512062i	−0.679494	+	0.733681i	$0.737801\pi$
$102$	−1.11663	−	1.93405i	−0.110563	−	0.191500i
$103$	6.43378			0.633939			0.316970	−	0.948436i	$-0.397335\pi$
$103$	6.43378			0.633939			0.316970	+	0.948436i	$0.397335\pi$
$104$	6.32135	+	9.11054i	0.619859	+	0.893362i
$105$		0			0
$106$	−1.44045	−	2.49493i	−0.139909	−	0.242329i
$107$	8.83959	+	15.3106i	0.854555	+	1.48013i	0.877057	+	0.480387i	$0.159504\pi$
$107$	8.83959	+	15.3106i	0.854555	+	1.48013i	−0.0225015	+	0.999747i	$0.507163\pi$
$108$	0.598962	−	1.03743i	0.0576352	−	0.0998270i
$109$	5.76180			0.551880			0.275940	−	0.961175i	$-0.411011\pi$
$109$	5.76180			0.551880			0.275940	+	0.961175i	$0.411011\pi$
$110$		0			0
$111$	−0.940450	+	1.62891i	−0.0892635	+	0.154609i
$112$	5.01532			0.473903
$113$	−2.37996	+	4.12222i	−0.223888	+	0.387785i	−0.955985	−	0.293415i	$-0.905208\pi$
$113$	−2.37996	+	4.12222i	−0.223888	+	0.387785i	0.732097	+	0.681200i	$0.238542\pi$
$114$	−1.20488	−	2.08691i	−0.112847	−	0.195457i
$115$		0			0
$116$	−1.77072			−0.164407
$117$	10.3515	−	0.861026i	0.956995	−	0.0796019i
$118$	8.38421			0.771829
$119$	5.53069	+	9.57943i	0.506997	+	0.878145i
$120$		0			0
$121$	−2.03069	+	3.51726i	−0.184608	+	0.319751i
$122$	−8.02851			−0.726867
$123$	0.0311425	−	0.0539404i	0.00280803	−	0.00486365i
$124$	0.348383	−	0.603416i	0.0312857	−	0.0541884i
$125$		0			0
$126$	3.47114	−	6.01219i	0.309234	−	0.535608i
$127$	−8.35307	−	14.4679i	−0.741215	−	1.28382i	−0.951942	−	0.306277i	$-0.900917\pi$
$127$	−8.35307	−	14.4679i	−0.741215	−	1.28382i	0.210728	−	0.977545i	$-0.432417\pi$
$128$	1.98470	+	3.43760i	0.175424	+	0.303844i
$129$	−0.462218			−0.0406961
$130$		0			0
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$	−0.395265	−	0.684619i	−0.0344034	−	0.0595884i
$133$	5.96781	+	10.3365i	0.517475	+	0.896292i
$134$	2.61464	−	4.52869i	0.225871	−	0.391219i
$135$		0			0
$136$	−8.38090	+	14.5161i	−0.718656	+	1.24475i
$137$	0.988931	−	1.71288i	0.0844901	−	0.146341i	−0.820684	−	0.571383i	$-0.806407\pi$
$137$	0.988931	−	1.71288i	0.0844901	−	0.146341i	0.905174	+	0.425042i	$0.139741\pi$
$138$	0.141412			0.0120378
$139$	−4.35021	+	7.53478i	−0.368980	+	0.639092i	−0.989406	−	0.145173i	$-0.953626\pi$
$139$	−4.35021	+	7.53478i	−0.368980	+	0.639092i	0.620426	+	0.784265i	$0.286960\pi$
$140$		0			0
$141$	−2.11910	−	3.67039i	−0.178460	−	0.309103i
$142$	2.23325			0.187411
$143$	5.96781	−	12.6563i	0.499053	−	1.05838i
$144$	7.11910			0.593258
$145$		0			0
$146$	−5.25997	−	9.11054i	−0.435318	−	0.753993i
$147$	−0.497113	+	0.861026i	−0.0410012	+	0.0710162i
$148$	3.21689			0.264427
$149$	−11.1516	+	19.3152i	−0.913576	+	1.58236i	−0.104603	+	0.994514i	$0.533357\pi$
$149$	−11.1516	+	19.3152i	−0.913576	+	1.58236i	−0.808973	+	0.587846i	$0.799976\pi$
$150$		0			0
$151$	−19.1626			−1.55943			−0.779717	−	0.626132i	$-0.784637\pi$
$151$	−19.1626			−1.55943			−0.779717	+	0.626132i	$0.784637\pi$
$152$	−9.04329	+	15.6634i	−0.733507	+	1.27047i
$153$	7.85066	+	13.5977i	0.634688	+	1.09931i
$154$	−4.67602	−	8.09910i	−0.376804	−	0.652644i
$155$		0			0
$156$	0.418681	+	0.603416i	0.0335213	+	0.0483120i
$157$	6.20265			0.495025			0.247513	−	0.968885i	$-0.420387\pi$
$157$	6.20265			0.495025			0.247513	+	0.968885i	$0.420387\pi$
$158$	6.63748	+	11.4964i	0.528049	+	0.914608i
$159$	−0.418681	−	0.725176i	−0.0332035	−	0.0575102i
$160$		0			0
$161$	−0.700420			−0.0552008
$162$	4.71507	−	8.16673i	0.370451	−	0.641639i
$163$	5.96781	−	10.3365i	0.467435	−	0.809621i	−0.531873	−	0.846824i	$-0.678512\pi$
$163$	5.96781	−	10.3365i	0.467435	−	0.809621i	0.999308	+	0.0372032i	$0.0118449\pi$
$164$	−0.106526			−0.00831826
$165$		0			0
$166$	−4.65162	−	8.05684i	−0.361036	−	0.625332i
$167$	−1.01478	−	1.75765i	−0.0785259	−	0.136011i	0.824088	−	0.566461i	$-0.191688\pi$
$167$	−1.01478	−	1.75765i	−0.0785259	−	0.136011i	−0.902614	+	0.430451i	$0.858355\pi$
$168$	2.15413			0.166195
$169$	−4.55063	+	12.1775i	−0.350048	+	0.936732i
$170$		0			0
$171$	8.47114	+	14.6724i	0.647804	+	1.12203i
$172$	0.395265	+	0.684619i	0.0301387	+	0.0522017i
$173$	0.669668	−	1.15990i	0.0509139	−	0.0881855i	−0.839445	−	0.543444i	$-0.817120\pi$
$173$	0.669668	−	1.15990i	0.0509139	−	0.0881855i	0.890359	+	0.455259i	$0.150453\pi$
$174$	1.22928			0.0931916
$175$		0			0
$176$	4.79512	−	8.30539i	0.361446	−	0.626042i
$177$	2.43695			0.183173
$178$	7.26758	−	12.5878i	0.544728	−	0.943497i
$179$	−10.1120	−	17.5145i	−0.755807	−	1.30910i	−0.944972	−	0.327151i	$-0.893911\pi$
$179$	−10.1120	−	17.5145i	−0.755807	−	1.30910i	0.189165	−	0.981945i	$-0.439422\pi$
$180$		0			0
$181$	19.8232			1.47345			0.736723	−	0.676195i	$-0.236372\pi$
$181$	19.8232			1.47345			0.736723	+	0.676195i	$0.236372\pi$
$182$	4.95303	+	7.13847i	0.367143	+	0.529139i
$183$	−2.33356			−0.172502
$184$	−0.530689	−	0.919180i	−0.0391229	−	0.0677629i
$185$		0			0
$186$	−0.241857	+	0.418908i	−0.0177338	+	0.0307159i
$187$	21.1515			1.54675
$188$	−3.62429	+	6.27745i	−0.264328	+	0.457830i
$189$	2.05955	−	3.56725i	0.149810	−	0.259479i
$190$		0			0
$191$	−0.768891	+	1.33176i	−0.0556350	+	0.0963626i	−0.892502	−	0.451044i	$-0.851052\pi$
$191$	−0.768891	+	1.33176i	−0.0556350	+	0.0963626i	0.836867	+	0.547407i	$0.184385\pi$
$192$	1.51189	+	2.61867i	0.109111	+	0.188986i
$193$	10.6016	+	18.3625i	0.763118	+	1.32176i	0.941236	+	0.337750i	$0.109666\pi$
$193$	10.6016	+	18.3625i	0.763118	+	1.32176i	−0.178117	+	0.984009i	$0.557001\pi$
$194$	−6.89347			−0.494923
$195$		0			0
$196$	1.70042			0.121459
$197$	−4.62847	−	8.01675i	−0.329765	−	0.571170i	0.652700	−	0.757616i	$-0.273636\pi$
$197$	−4.62847	−	8.01675i	−0.329765	−	0.571170i	−0.982465	+	0.186447i	$0.940303\pi$
$198$	−6.63748	−	11.4964i	−0.471705	−	0.817017i
$199$	8.70225	−	15.0727i	0.616886	−	1.06848i	−0.373164	−	0.927765i	$-0.621727\pi$
$199$	8.70225	−	15.0727i	0.616886	−	1.06848i	0.990050	−	0.140713i	$-0.0449394\pi$
$200$		0			0
$201$	0.759971	−	1.31631i	0.0536042	−	0.0928452i
$202$	−3.52773	+	6.11021i	−0.248210	+	0.429913i
$203$	−6.08867			−0.427341
$204$	−0.555090	+	0.961445i	−0.0388641	+	0.0673146i
$205$		0			0
$206$	3.81952	+	6.61560i	0.266119	+	0.460931i
$207$	−0.994227			−0.0691036
$208$	−3.79997	+	8.05885i	−0.263480	+	0.558781i
$209$	22.8232			1.57871
$210$		0			0
$211$	3.64087	+	6.30617i	0.250648	+	0.434135i	0.963704	−	0.266972i	$-0.0860231\pi$
$211$	3.64087	+	6.30617i	0.250648	+	0.434135i	−0.713057	+	0.701107i	$0.752690\pi$
$212$	−0.716067	+	1.24026i	−0.0491797	+	0.0851817i
$213$	0.649117			0.0444768
$214$	−10.4955	+	18.1788i	−0.717460	+	1.24268i
$215$		0			0
$216$	6.24186			0.424705
$217$	1.19792	−	2.07487i	0.0813204	−	0.140851i
$218$	3.42059	+	5.92463i	0.231671	+	0.401267i
$219$	−1.52886	−	2.64807i	−0.103311	−	0.178940i
$220$		0			0
$221$	−19.5831	+	1.62891i	−1.31731	+	0.109572i
$222$	−2.23325			−0.149886
$223$	−9.73351	−	16.8589i	−0.651804	−	1.12896i	−0.982685	−	0.185285i	$-0.940679\pi$
$223$	−9.73351	−	16.8589i	−0.651804	−	1.12896i	0.330881	−	0.943672i	$-0.392654\pi$
$224$	−3.26443	−	5.65416i	−0.218114	−	0.377784i
$225$		0			0
$226$	−5.65162			−0.375940
$227$	2.40581	−	4.16698i	0.159679	−	0.276572i	−0.775074	−	0.631871i	$-0.782287\pi$
$227$	2.40581	−	4.16698i	0.159679	−	0.276572i	0.934753	+	0.355298i	$0.115621\pi$
$228$	−0.598962	+	1.03743i	−0.0396672	+	0.0687057i
$229$	1.52360			0.100682			0.0503410	−	0.998732i	$-0.483969\pi$
$229$	1.52360			0.100682			0.0503410	+	0.998732i	$0.483969\pi$
$230$		0			0
$231$	−1.35913	−	2.35408i	−0.0894242	−	0.154887i
$232$	−4.61322	−	7.99033i	−0.302873	−	0.524591i
$233$	13.9652			0.914889			0.457445	−	0.889238i	$-0.348765\pi$
$233$	13.9652			0.914889			0.457445	+	0.889238i	$0.348765\pi$
$234$	7.03069	+	10.1329i	0.459611	+	0.662406i
$235$		0			0
$236$	−2.08395	−	3.60951i	−0.135654	−	0.234959i
$237$	1.92925	+	3.34155i	0.125318	+	0.217057i
$238$	−6.56677	+	11.3740i	−0.425661	+	0.737266i
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$		0			0
$241$	8.73294	−	15.1259i	0.562538	−	0.974344i	−0.434736	−	0.900558i	$-0.643158\pi$
$241$	8.73294	−	15.1259i	0.562538	−	0.974344i	0.997274	−	0.0737864i	$-0.0235083\pi$
$242$	−4.82221			−0.309983
$243$	4.41481	−	7.64668i	0.283210	−	0.490535i
$244$	1.99554	+	3.45638i	0.127751	+	0.221272i
$245$		0			0
$246$	0.0739531			0.00471508
$247$	−21.1309	+	1.75765i	−1.34453	+	0.111836i
$248$	3.63054			0.230539
$249$	−1.35204	−	2.34180i	−0.0856819	−	0.148405i
$250$		0			0
$251$	−4.64979	+	8.05367i	−0.293492	+	0.508343i	−0.974633	−	0.223809i	$-0.928151\pi$
$251$	−4.64979	+	8.05367i	−0.293492	+	0.508343i	0.681141	+	0.732152i	$0.261484\pi$
$252$	−3.45110			−0.217399
$253$	−0.669668	+	1.15990i	−0.0421017	+	0.0729223i
$254$	9.91788	−	17.1783i	0.622303	−	1.07786i
$255$		0			0
$256$	6.40530	−	11.0943i	0.400331	−	0.693394i
$257$	5.44485	+	9.43076i	0.339640	+	0.588274i	0.984365	−	0.176141i	$-0.0563613\pi$
$257$	5.44485	+	9.43076i	0.339640	+	0.588274i	−0.644725	+	0.764415i	$0.723028\pi$
$258$	−0.274404	−	0.475281i	−0.0170836	−	0.0295897i
$259$	11.0614			0.687321
$260$		0			0
$261$	−8.64270			−0.534970
$262$	5.93667	+	10.2826i	0.366769	+	0.635262i
$263$	−6.72031	−	11.6399i	−0.414392	−	0.717749i	0.580972	−	0.813923i	$-0.302673\pi$
$263$	−6.72031	−	11.6399i	−0.414392	−	0.717749i	−0.995364	+	0.0961749i	$0.969339\pi$
$264$	2.05955	−	3.56725i	0.126757	−	0.219549i
$265$		0			0
$266$	−7.08578	+	12.2729i	−0.434457	+	0.752502i
$267$	2.11239	−	3.65877i	0.129276	−	0.223913i
$268$	−2.59955			−0.158793
$269$	−1.83027	+	3.17012i	−0.111593	+	0.193286i	−0.916413	−	0.400234i	$-0.868929\pi$
$269$	−1.83027	+	3.17012i	−0.111593	+	0.193286i	0.804819	+	0.593520i	$0.202262\pi$
$270$		0			0
$271$	−11.0018	−	19.0557i	−0.668313	−	1.15755i	−0.978376	−	0.206837i	$-0.933683\pi$
$271$	−11.0018	−	19.0557i	−0.668313	−	1.15755i	0.310062	−	0.950716i	$-0.399650\pi$
$272$	−13.4681			−0.816621
$273$	1.43965	+	2.07487i	0.0871314	+	0.125577i
$274$	2.34838			0.141871
$275$		0			0
$276$	−0.0351490	−	0.0608799i	−0.00211572	−	0.00366454i
$277$	4.94774	−	8.56973i	0.297281	−	0.514905i	−0.678232	−	0.734848i	$-0.737254\pi$
$277$	4.94774	−	8.56973i	0.297281	−	0.514905i	0.975513	+	0.219943i	$0.0705870\pi$
$278$	−10.3303			−0.619570
$279$	1.70042	−	2.94521i	0.101801	−	0.176325i
$280$		0			0
$281$	4.06138			0.242281			0.121141	−	0.992635i	$-0.461345\pi$
$281$	4.06138			0.242281			0.121141	+	0.992635i	$0.461345\pi$
$282$	2.51608	−	4.35798i	0.149830	−	0.259514i
$283$	−3.04434	−	5.27294i	−0.180967	−	0.313444i	0.761243	−	0.648467i	$-0.224589\pi$
$283$	−3.04434	−	5.27294i	−0.180967	−	0.313444i	−0.942210	+	0.335023i	$0.891256\pi$
$284$	−0.555090	−	0.961445i	−0.0329386	−	0.0570513i
$285$		0			0
$286$	16.5569	−	1.37719i	0.979031	−	0.0814348i
$287$	−0.366292			−0.0216215
$288$	−4.63377	−	8.02592i	−0.273047	−	0.472932i
$289$	−6.35204	−	11.0021i	−0.373649	−	0.647180i
$290$		0			0
$291$	−2.00366			−0.117456
$292$	−2.61480	+	4.52897i	−0.153020	+	0.265038i
$293$	−4.89604	+	8.48019i	−0.286030	+	0.495418i	−0.972858	−	0.231401i	$-0.925669\pi$
$293$	−4.89604	+	8.48019i	−0.286030	+	0.495418i	0.686829	+	0.726819i	$0.259002\pi$
$294$	−1.18048			−0.0688469
$295$		0			0
$296$	8.38090	+	14.5161i	0.487130	+	0.843734i
$297$	−3.93825	−	6.82125i	−0.228521	−	0.395809i
$298$	−26.4814			−1.53402
$299$	0.530689	−	1.12547i	0.0306905	−	0.0650876i
$300$		0			0
$301$	1.35913	+	2.35408i	0.0783390	+	0.135687i
$302$	−11.3762	−	19.7042i	−0.654628	−	1.13385i
$303$	−1.02537	+	1.77599i	−0.0589059	+	0.102028i
$304$	−14.5325			−0.833497
$305$		0			0
$306$	−9.32135	+	16.1450i	−0.532866	+	0.922951i
$307$	22.1046			1.26158			0.630788	−	0.775955i	$-0.282732\pi$
$307$	22.1046			1.26158			0.630788	+	0.775955i	$0.282732\pi$
$308$	−2.32451	+	4.02617i	−0.132451	+	0.229412i
$309$	1.11018	+	1.92289i	0.0631560	+	0.109389i
$310$		0			0
$311$	7.63904			0.433170			0.216585	−	0.976264i	$-0.430508\pi$
$311$	7.63904			0.433170			0.216585	+	0.976264i	$0.430508\pi$
$312$	−1.63212	+	3.46136i	−0.0924007	+	0.195961i
$313$	−26.1425			−1.47766			−0.738831	−	0.673891i	$-0.764622\pi$
$313$	−26.1425			−1.47766			−0.738831	+	0.673891i	$0.764622\pi$
$314$	3.68231	+	6.37794i	0.207805	+	0.359928i
$315$		0			0
$316$	3.29958	−	5.71504i	0.185616	−	0.321496i
$317$	−11.8428			−0.665159			−0.332580	−	0.943075i	$-0.607919\pi$
$317$	−11.8428			−0.665159			−0.332580	+	0.943075i	$0.607919\pi$
$318$	0.497113	−	0.861026i	0.0278767	−	0.0482839i
$319$	−5.82135	+	10.0829i	−0.325933	+	0.564532i
$320$		0			0
$321$	−3.05063	+	5.28385i	−0.170270	+	0.294916i
$322$	−0.415816	−	0.720215i	−0.0231725	−	0.0401360i
$323$	−16.0259	−	27.7576i	−0.891704	−	1.54448i
$324$	−4.68785			−0.260436
$325$		0			0
$326$	14.1716			0.784890
$327$	0.994227	+	1.72205i	0.0549809	+	0.0952297i
$328$	−0.277529	−	0.480695i	−0.0153240	−	0.0265419i
$329$	−12.4622	+	21.5852i	−0.687064	+	1.19003i
$330$		0			0
$331$	6.35021	−	10.9989i	0.349039	−	0.604553i	−0.637040	−	0.770831i	$-0.719841\pi$
$331$	6.35021	−	10.9989i	0.349039	−	0.604553i	0.986079	+	0.166277i	$0.0531747\pi$
$332$	−2.31238	+	4.00516i	−0.126908	+	0.219812i
$333$	15.7013			0.860427
$334$	1.20488	−	2.08691i	0.0659281	−	0.114191i
$335$		0			0
$336$	0.865418	+	1.49895i	0.0472124	+	0.0817743i
$337$	15.2939			0.833113			0.416556	−	0.909110i	$-0.363237\pi$
$337$	15.2939			0.833113			0.416556	+	0.909110i	$0.363237\pi$
$338$	−15.2232	+	2.55015i	−0.828034	+	0.138710i
$339$	−1.64270			−0.0892191
$340$		0			0
$341$	−2.29066	−	3.96754i	−0.124046	−	0.214854i
$342$	−10.0581	+	17.4211i	−0.543878	+	0.942024i
$343$	20.0538			1.08281
$344$	−2.05955	+	3.56725i	−0.111044	+	0.192333i
$345$		0			0
$346$	1.59024			0.0854918
$347$	6.11981	−	10.5998i	0.328529	−	0.569029i	−0.653691	−	0.756761i	$-0.726781\pi$
$347$	6.11981	−	10.5998i	0.328529	−	0.569029i	0.982220	+	0.187733i	$0.0601139\pi$
$348$	−0.305546	−	0.529222i	−0.0163790	−	0.0283693i
$349$	−9.35021	−	16.1950i	−0.500505	−	0.866901i	−1.00000		0.000583538i	$-0.999814\pi$
$349$	−9.35021	−	16.1950i	−0.500505	−	0.866901i	0.499495	−	0.866317i	$-0.333519\pi$
$350$		0			0
$351$	4.17156	+	6.01219i	0.222661	+	0.320907i
$352$	−12.4844			−0.665422
$353$	0.654413	+	1.13348i	0.0348309	+	0.0603288i	0.882915	−	0.469532i	$-0.155577\pi$
$353$	0.654413	+	1.13348i	0.0348309	+	0.0603288i	−0.848084	+	0.529861i	$0.822244\pi$
$354$	1.44674	+	2.50582i	0.0768932	+	0.133183i
$355$		0			0
$356$	−7.22563			−0.382957
$357$	−1.90870	+	3.30596i	−0.101019	+	0.174970i
$358$	12.0063	−	20.7956i	0.634554	−	1.09908i
$359$	−29.4082			−1.55210			−0.776051	−	0.630670i	$-0.782780\pi$
$359$	−29.4082			−1.55210			−0.776051	+	0.630670i	$0.782780\pi$
$360$		0			0
$361$	−7.79249	−	13.4970i	−0.410131	−	0.710368i
$362$	11.7684	+	20.3834i	0.618531	+	1.07133i
$363$	−1.40162			−0.0735661
$364$	1.84210	−	3.90666i	0.0965520	−	0.204765i
$365$		0			0
$366$	−1.38536	−	2.39951i	−0.0724139	−	0.125425i
$367$	−16.7161	−	28.9531i	−0.872573	−	1.51134i	−0.859326	−	0.511429i	$-0.829116\pi$
$367$	−16.7161	−	28.9531i	−0.872573	−	1.51134i	−0.0132473	−	0.999912i	$-0.504217\pi$
$368$	0.426407	−	0.738559i	0.0222280	−	0.0385001i
$369$	−0.519941			−0.0270671
$370$		0			0
$371$	−2.46222	+	4.26469i	−0.127832	+	0.221412i
$372$	0.240461			0.0124673
$373$	−17.2391	+	29.8589i	−0.892604	+	1.54604i	−0.0558628	+	0.998438i	$0.517791\pi$
$373$	−17.2391	+	29.8589i	−0.892604	+	1.54604i	−0.836742	+	0.547598i	$0.815542\pi$
$374$	12.5569	+	21.7492i	0.649303	+	1.12463i
$375$		0			0
$376$	−37.7691			−1.94779
$377$	4.61322	−	9.78357i	0.237593	−	0.503879i
$378$	4.89075			0.251553
$379$	8.70225	+	15.0727i	0.447004	+	0.774234i	0.998189	−	0.0601487i	$-0.0191575\pi$
$379$	8.70225	+	15.0727i	0.447004	+	0.774234i	−0.551185	+	0.834383i	$0.685824\pi$
$380$		0			0
$381$	2.88273	−	4.99303i	0.147687	−	0.255801i
$382$	−1.82586			−0.0934191
$383$	0.873366	−	1.51271i	0.0446269	−	0.0772961i	−0.842849	−	0.538150i	$-0.819123\pi$
$383$	0.873366	−	1.51271i	0.0446269	−	0.0772961i	0.887476	+	0.460854i	$0.152457\pi$
$384$	−0.684939	+	1.18635i	−0.0349531	+	0.0605406i
$385$		0			0
$386$	−12.5876	+	21.8024i	−0.640692	+	1.10971i
$387$	1.92925	+	3.34155i	0.0980692	+	0.169861i
$388$	1.71342	+	2.96773i	0.0869857	+	0.150664i
$389$	22.0435			1.11765			0.558826	−	0.829285i	$-0.311252\pi$
$389$	22.0435			1.11765			0.558826	+	0.829285i	$0.311252\pi$
$390$		0			0
$391$	1.88090			0.0951212
$392$	4.43007	+	7.67311i	0.223752	+	0.387550i
$393$	1.72555	+	2.98874i	0.0870425	+	0.150762i
$394$	5.49554	−	9.51855i	0.276861	−	0.479538i
$395$		0			0
$396$	−3.29958	+	5.71504i	−0.165810	+	0.287192i
$397$	−11.2660	+	19.5132i	−0.565422	+	0.979339i	0.431588	+	0.902071i	$0.357953\pi$
$397$	−11.2660	+	19.5132i	−0.565422	+	0.979339i	−0.997010	+	0.0772687i	$0.975380\pi$
$398$	20.6649			1.03584
$399$	−2.05955	+	3.56725i	−0.103106	+	0.178586i
$400$		0			0
$401$	1.85204	+	3.20782i	0.0924863	+	0.160191i	0.908557	−	0.417761i	$-0.137185\pi$
$401$	1.85204	+	3.20782i	0.0924863	+	0.160191i	−0.816070	+	0.577953i	$0.803852\pi$
$402$	1.80468			0.0900091
$403$	2.42636	+	3.49695i	0.120866	+	0.174196i
$404$	3.50737			0.174498
$405$		0			0
$406$	−3.61464	−	6.26074i	−0.179392	−	0.310715i
$407$	10.5757	−	18.3177i	0.524220	−	0.907975i
$408$	−5.78466			−0.286384
$409$	6.74186	−	11.6772i	0.333363	−	0.577402i	−0.649806	−	0.760100i	$-0.725150\pi$
$409$	6.74186	−	11.6772i	0.333363	−	0.577402i	0.983169	+	0.182698i	$0.0584831\pi$
$410$		0			0
$411$	0.682580			0.0336692
$412$	1.89874	−	3.28871i	0.0935440	−	0.162023i
$413$	−7.16573	−	12.4114i	−0.352603	−	0.610726i
$414$	−0.590239	−	1.02232i	−0.0290087	−	0.0502445i
$415$		0			0
$416$	11.5587	−	0.961445i	0.566714	−	0.0471387i
$417$	−3.00260			−0.147038
$418$	13.5494	+	23.4682i	0.662721	+	1.14787i
$419$	−8.41159	−	14.5693i	−0.410933	−	0.711757i	0.584059	−	0.811711i	$-0.301464\pi$
$419$	−8.41159	−	14.5693i	−0.410933	−	0.711757i	−0.994992	+	0.0999544i	$0.968130\pi$
$420$		0			0
$421$	17.1013			0.833464			0.416732	−	0.909029i	$-0.363175\pi$
$421$	17.1013			0.833464			0.416732	+	0.909029i	$0.363175\pi$
$422$	−4.32293	+	7.48753i	−0.210437	+	0.364487i
$423$	−17.6898	+	30.6396i	−0.860106	+	1.48975i
$424$	−7.46222			−0.362397
$425$		0			0
$426$	0.385359	+	0.667462i	0.0186707	+	0.0323386i
$427$	6.86173	+	11.8849i	0.332062	+	0.575149i
$428$	10.4349			0.504392
$429$	4.81243	−	0.400293i	0.232346	−	0.0193263i
$430$		0			0
$431$	−4.83027	−	8.36627i	−0.232666	−	0.402989i	0.725926	−	0.687773i	$-0.241412\pi$
$431$	−4.83027	−	8.36627i	−0.232666	−	0.402989i	−0.958592	+	0.284784i	$0.908078\pi$
$432$	2.50766	+	4.34339i	0.120650	+	0.208972i
$433$	12.3863	−	21.4538i	0.595249	−	1.03100i	−0.398262	−	0.917272i	$-0.630387\pi$
$433$	12.3863	−	21.4538i	0.595249	−	1.03100i	0.993512	−	0.113730i	$-0.0362800\pi$
$434$	2.84467			0.136549
$435$		0			0
$436$	1.70042	−	2.94521i	0.0814354	−	0.141050i
$437$	2.02956			0.0970869
$438$	1.81527	−	3.14414i	0.0867369	−	0.150233i
$439$	−3.53069	−	6.11533i	−0.168511	−	0.291869i	0.769386	−	0.638784i	$-0.220562\pi$
$439$	−3.53069	−	6.11533i	−0.168511	−	0.291869i	−0.937896	+	0.346915i	$0.887229\pi$
$440$		0			0
$441$	8.29958			0.395218
$442$	−13.3008	−	19.1696i	−0.632655	−	0.911803i
$443$	38.2438			1.81702			0.908509	−	0.417865i	$-0.137222\pi$
$443$	38.2438			1.81702			0.908509	+	0.417865i	$0.137222\pi$
$444$	0.555090	+	0.961445i	0.0263434	+	0.0456282i
$445$		0			0
$446$	11.5569	−	20.0172i	0.547236	−	0.947840i
$447$	−7.69707			−0.364059
$448$	8.89128	−	15.4002i	0.420074	−	0.727589i
$449$	6.24003	−	10.8080i	0.294485	−	0.510063i	−0.680380	−	0.732860i	$-0.738185\pi$
$449$	6.24003	−	10.8080i	0.294485	−	0.510063i	0.974865	+	0.222796i	$0.0715185\pi$
$450$		0			0
$451$	−0.350210	+	0.606582i	−0.0164908	+	0.0285628i
$452$	1.40475	+	2.43309i	0.0660738	+	0.114443i
$453$	−3.30661	−	5.72721i	−0.155358	−	0.269088i
$454$	5.71300			0.268124
$455$		0			0
$456$	−6.24186			−0.292302
$457$	4.11610	+	7.12930i	0.192543	+	0.333495i	0.946092	−	0.323897i	$-0.104993\pi$
$457$	4.11610	+	7.12930i	0.192543	+	0.333495i	−0.753549	+	0.657392i	$0.771660\pi$
$458$	0.904508	+	1.56665i	0.0422649	+	0.0732050i
$459$	−5.53069	+	9.57943i	−0.258150	+	0.447130i
$460$		0			0
$461$	2.27072	−	3.93300i	0.105758	−	0.183178i	−0.808290	−	0.588785i	$-0.799606\pi$
$461$	2.27072	−	3.93300i	0.105758	−	0.183178i	0.914048	+	0.405607i	$0.132940\pi$
$462$	1.61374	−	2.79508i	0.0750780	−	0.130039i
$463$	1.98845			0.0924113			0.0462056	−	0.998932i	$-0.485287\pi$
$463$	1.98845			0.0924113			0.0462056	+	0.998932i	$0.485287\pi$
$464$	3.70671	−	6.42021i	0.172080	−	0.298051i
$465$		0			0
$466$	8.29066	+	14.3598i	0.384057	+	0.665207i
$467$	32.8043			1.51800			0.759000	−	0.651091i	$-0.225688\pi$
$467$	32.8043			1.51800			0.759000	+	0.651091i	$0.225688\pi$
$468$	2.61480	−	5.54539i	0.120869	−	0.256336i
$469$	−8.93862			−0.412747
$470$		0			0
$471$	1.07030	+	1.85381i	0.0493167	+	0.0854191i
$472$	10.8586	−	18.8076i	0.499806	−	0.865689i
$473$	5.19783			0.238997
$474$	−2.29066	+	3.96754i	−0.105213	+	0.182235i
$475$		0			0
$476$	6.52886			0.299250
$477$	−3.49505	+	6.05360i	−0.160027	+	0.277176i
$478$	2.37467	+	4.11304i	0.108615	+	0.188126i
$479$	15.4027	+	26.6782i	0.703766	+	1.21896i	0.967135	+	0.254263i	$0.0818329\pi$
$479$	15.4027	+	26.6782i	0.703766	+	1.21896i	−0.263369	+	0.964695i	$0.584834\pi$
$480$		0			0
$481$	−8.38090	+	17.7740i	−0.382136	+	0.810423i
$482$	20.7378			0.944582
$483$	−0.120861	−	0.209337i	−0.00549937	−	0.00952518i
$484$	1.19859	+	2.07602i	0.0544815	+	0.0943647i
$485$		0			0
$486$	10.4837			0.475551
$487$	−11.1626	+	19.3341i	−0.505824	+	0.876113i	0.494153	+	0.869375i	$0.335478\pi$
$487$	−11.1626	+	19.3341i	−0.505824	+	0.876113i	−0.999977	+	0.00673807i	$0.997855\pi$
$488$	−10.3979	+	18.0097i	−0.470690	+	0.815259i
$489$	4.11910			0.186272
$490$		0			0
$491$	−5.34129	−	9.25139i	−0.241049	−	0.417509i	0.719964	−	0.694011i	$-0.244158\pi$
$491$	−5.34129	−	9.25139i	−0.241049	−	0.417509i	−0.961013	+	0.276502i	$0.910825\pi$
$492$	−0.0183815	−	0.0318378i	−0.000828704	−	0.00143536i
$493$	16.3504			0.736386
$494$	−14.3520	−	20.6846i	−0.645729	−	0.930646i
$495$		0			0
$496$	1.45856	+	2.52631i	0.0654914	+	0.113434i
$497$	−1.90870	−	3.30596i	−0.0856167	−	0.148292i
$498$	1.60532	−	2.78049i	0.0719361	−	0.124597i
$499$	18.8195			0.842477			0.421239	−	0.906950i	$-0.361595\pi$
$499$	18.8195			0.842477			0.421239	+	0.906950i	$0.361595\pi$
$500$		0			0
$501$	0.350210	−	0.606582i	0.0156462	−	0.0271001i
$502$	−11.0417			−0.492815
$503$	−2.84064	+	4.92013i	−0.126658	+	0.219378i	−0.922380	−	0.386284i	$-0.873758\pi$
$503$	−2.84064	+	4.92013i	−0.126658	+	0.219378i	0.795722	+	0.605662i	$0.207092\pi$
$504$	−8.99108	−	15.5730i	−0.400495	−	0.693677i
$505$		0			0
$506$	−1.59024			−0.0706948
$507$	−4.42478	+	0.741225i	−0.196511	+	0.0329190i
$508$	−9.86062			−0.437494
$509$	−13.9622	−	24.1833i	−0.618864	−	1.07190i	−0.989693	−	0.143203i	$-0.954260\pi$
$509$	−13.9622	−	24.1833i	−0.618864	−	1.07190i	0.370829	−	0.928701i	$-0.379074\pi$
$510$		0			0
$511$	−8.99108	+	15.5730i	−0.397742	+	0.688909i
$512$	23.1492			1.02306
$513$	−5.96781	+	10.3365i	−0.263485	+	0.456370i
$514$	−6.46485	+	11.1975i	−0.285152	+	0.493898i
$515$		0			0
$516$	−0.136410	+	0.236269i	−0.00600511	+	0.0104011i
$517$	23.8301	+	41.2750i	1.04805	+	1.81527i
$518$	6.56677	+	11.3740i	0.288527	+	0.499744i
$519$	0.462218			0.0202891
$520$		0			0
$521$	6.29958			0.275990			0.137995	−	0.990433i	$-0.455934\pi$
$521$	6.29958			0.275990			0.137995	+	0.990433i	$0.455934\pi$
$522$	−5.13088	−	8.88695i	−0.224573	−	0.388971i
$523$	11.4285	+	19.7948i	0.499735	+	0.865567i	1.00000		0.000305526i	$-9.72520e-5\pi$
$523$	11.4285	+	19.7948i	0.499735	+	0.865567i	−0.500265	+	0.865873i	$0.666764\pi$
$524$	2.95120	−	5.11162i	0.128924	−	0.223302i
$525$		0			0
$526$	7.97925	−	13.8205i	0.347912	−	0.602601i
$527$	−3.21689	+	5.57182i	−0.140130	+	0.242712i
$528$	3.30969			0.144036
$529$	11.4404	−	19.8154i	0.497411	−	0.861541i
$530$		0			0
$531$	−10.1716	−	17.6177i	−0.441408	−	0.764541i
$532$	7.04487			0.305434
$533$	0.277529	−	0.588576i	0.0120211	−	0.0254940i
$534$	5.01623			0.217074
$535$		0			0
$536$	−6.77255	−	11.7304i	−0.292529	−	0.506676i
$537$	3.48975	−	6.04443i	0.150594	−	0.260837i
$538$	−4.34628			−0.187381
$539$	5.59024	−	9.68258i	0.240789	−	0.417058i
$540$		0			0
$541$	−9.48006			−0.407580			−0.203790	−	0.979015i	$-0.565326\pi$
$541$	−9.48006			−0.407580			−0.203790	+	0.979015i	$0.565326\pi$
$542$	13.0628	−	22.6255i	0.561097	−	0.971848i
$543$	3.42059	+	5.92463i	0.146791	+	0.254250i
$544$	8.76626	+	15.1836i	0.375850	+	0.650992i
$545$		0			0
$546$	−1.27883	+	2.71211i	−0.0547290	+	0.116068i
$547$	−33.3911			−1.42770			−0.713850	−	0.700299i	$-0.753050\pi$
$547$	−33.3911			−1.42770			−0.713850	+	0.700299i	$0.753050\pi$
$548$	−0.583706	−	1.01101i	−0.0249347	−	0.0431882i
$549$	9.74003	+	16.8702i	0.415694	+	0.720004i
$550$		0			0
$551$	17.6427			0.751604
$552$	0.183146	−	0.317218i	0.00779521	−	0.0135017i
$553$	11.3457	−	19.6513i	0.482469	−	0.835660i
$554$	11.7492			0.499177
$555$		0			0
$556$	2.56767	+	4.44733i	0.108893	+	0.188609i
$557$	−18.8824	−	32.7053i	−0.800073	−	1.38577i	−0.919567	−	0.392932i	$-0.871461\pi$
$557$	−18.8824	−	32.7053i	−0.800073	−	1.38577i	0.119495	−	0.992835i	$-0.461873\pi$
$558$	4.03793			0.170939
$559$	−4.81243	+	0.400293i	−0.203544	+	0.0169306i
$560$		0			0
$561$	3.64979	+	6.32162i	0.154094	+	0.266899i
$562$	2.41110	+	4.17616i	0.101706	+	0.176161i
$563$	12.9504	−	22.4307i	0.545794	−	0.945343i	−0.452762	−	0.891631i	$-0.649561\pi$
$563$	12.9504	−	22.4307i	0.545794	−	0.945343i	0.998556	−	0.0537120i	$-0.0171053\pi$
$564$	−2.50155			−0.105334
$565$		0			0
$566$	3.61464	−	6.26074i	0.151935	−	0.263159i
$567$	−16.1193			−0.676947
$568$	2.89233	−	5.00967i	0.121360	−	0.210201i
$569$	10.7725	+	18.6586i	0.451609	+	0.782209i	0.998486	−	0.0550035i	$-0.0175170\pi$
$569$	10.7725	+	18.6586i	0.451609	+	0.782209i	−0.546878	+	0.837213i	$0.684184\pi$
$570$		0			0
$571$	−2.22036			−0.0929192			−0.0464596	−	0.998920i	$-0.514794\pi$
$571$	−2.22036			−0.0929192			−0.0464596	+	0.998920i	$0.514794\pi$
$572$	−4.70823	−	6.78566i	−0.196861	−	0.283723i
$573$	−0.530704			−0.0221705
$574$	−0.217455	−	0.376644i	−0.00907641	−	0.0157208i
$575$		0			0
$576$	12.6209	−	21.8601i	0.525872	−	0.910837i
$577$	−6.20265			−0.258220			−0.129110	−	0.991630i	$-0.541212\pi$
$577$	−6.20265			−0.258220			−0.129110	+	0.991630i	$0.541212\pi$
$578$	7.54199	−	13.0631i	0.313705	−	0.543353i
$579$	−3.65871	+	6.33707i	−0.152051	+	0.263360i
$580$		0			0
$581$	−7.95120	+	13.7719i	−0.329871	+	0.571354i
$582$	−1.18950	−	2.06028i	−0.0493065	−	0.0854014i
$583$	4.70823	+	8.15489i	0.194995	+	0.337741i
$584$	−27.2492			−1.12758
$585$		0			0
$586$	−11.6265			−0.480285
$587$	0.914469	+	1.58391i	0.0377442	+	0.0653748i	0.884280	−	0.466956i	$-0.154649\pi$
$587$	0.914469	+	1.58391i	0.0377442	+	0.0653748i	−0.846536	+	0.532331i	$0.821316\pi$
$588$	0.293416	+	0.508211i	0.0121003	+	0.0209583i
$589$	−3.47114	+	6.01219i	−0.143026	+	0.247728i
$590$		0			0
$591$	1.59733	−	2.76666i	0.0657055	−	0.113805i
$592$	−6.73403	+	11.6637i	−0.276767	+	0.479374i
$593$	−0.0728761			−0.00299266			−0.00149633	−	0.999999i	$-0.500476\pi$
$593$	−0.0728761			−0.00299266			−0.00149633	+	0.999999i	$0.500476\pi$
$594$	4.67602	−	8.09910i	0.191859	−	0.332310i
$595$		0			0
$596$	6.58212	+	11.4006i	0.269614	+	0.466986i
$597$	6.00646			0.245828
$598$	1.47233	−	0.122467i	0.0602080	−	0.00500804i
$599$	−14.5813			−0.595777			−0.297888	−	0.954601i	$-0.596282\pi$
$599$	−14.5813			−0.595777			−0.297888	+	0.954601i	$0.596282\pi$
$600$		0			0
$601$	22.2041	+	38.4586i	0.905723	+	1.56876i	0.819944	+	0.572444i	$0.194005\pi$
$601$	22.2041	+	38.4586i	0.905723	+	1.56876i	0.0857795	+	0.996314i	$0.472662\pi$
$602$	−1.61374	+	2.79508i	−0.0657712	+	0.113919i
$603$	−12.6881			−0.516700
$604$	−5.65527	+	9.79522i	−0.230110	+	0.398562i
$605$		0			0
$606$	−2.43491			−0.0989115
$607$	−18.1177	+	31.3808i	−0.735375	+	1.27371i	0.219183	+	0.975684i	$0.429661\pi$
$607$	−18.1177	+	31.3808i	−0.735375	+	1.27371i	−0.954558	+	0.298024i	$0.903672\pi$
$608$	9.45910	+	16.3836i	0.383617	+	0.664445i
$609$	−1.05063	−	1.81975i	−0.0425737	−	0.0737398i
$610$		0			0
$611$	−25.2419	−	36.3794i	−1.02118	−	1.47175i
$612$	9.26754			0.374618
$613$	−1.67915	−	2.90838i	−0.0678203	−	0.117468i	0.830121	−	0.557583i	$-0.188271\pi$
$613$	−1.67915	−	2.90838i	−0.0678203	−	0.117468i	−0.897942	+	0.440115i	$0.854938\pi$
$614$	13.1228	+	22.7293i	0.529591	+	0.917279i
$615$		0			0
$616$	−24.2240			−0.976013
$617$	10.5910	−	18.3441i	0.426377	−	0.738507i	−0.570171	−	0.821526i	$-0.693123\pi$
$617$	10.5910	−	18.3441i	0.426377	−	0.738507i	0.996548	+	0.0830194i	$0.0264563\pi$
$618$	−1.31815	+	2.28311i	−0.0530240	+	0.0918402i
$619$	25.4082			1.02124			0.510620	−	0.859807i	$-0.329416\pi$
$619$	25.4082			1.02124			0.510620	+	0.859807i	$0.329416\pi$
$620$		0			0
$621$	−0.350210	−	0.606582i	−0.0140534	−	0.0243413i
$622$	4.53504	+	7.85493i	0.181839	+	0.314954i
$623$	−24.8455			−0.995416
$624$	−3.06428	+	0.254884i	−0.122670	+	0.0102035i
$625$		0			0
$626$	−15.5199	−	26.8813i	−0.620302	−	1.07439i
$627$	3.93825	+	6.82125i	0.157279	+	0.272415i
$628$	1.83052	−	3.17056i	0.0730459	−	0.126519i
$629$	−29.7041			−1.18438
$630$		0			0
$631$	−21.7725	+	37.7112i	−0.866751	+	1.50126i	−0.00145375	+	0.999999i	$0.500463\pi$
$631$	−21.7725	+	37.7112i	−0.866751	+	1.50126i	−0.865298	+	0.501258i	$0.832871\pi$
$632$	34.3853			1.36777
$633$	−1.25650	+	2.17632i	−0.0499414	+	0.0865011i
$634$	−7.03069	−	12.1775i	−0.279224	−	0.483631i
$635$		0			0
$636$	−0.494244			−0.0195980
$637$	−4.43007	+	9.39516i	−0.175526	+	0.372250i
$638$	−13.8238			−0.547288
$639$	−2.70934	−	4.69272i	−0.107180	−	0.185641i
$640$		0			0
$641$	−24.1427	+	41.8164i	−0.953579	+	1.65165i	−0.215993	+	0.976395i	$0.569299\pi$
$641$	−24.1427	+	41.8164i	−0.953579	+	1.65165i	−0.737586	+	0.675253i	$0.764035\pi$
$642$	−7.24423			−0.285907
$643$	−21.1720	+	36.6710i	−0.834943	+	1.44616i	0.0591344	+	0.998250i	$0.481166\pi$
$643$	−21.1720	+	36.6710i	−0.834943	+	1.44616i	−0.894077	+	0.447913i	$0.852167\pi$
$644$	−0.206708	+	0.358028i	−0.00814543	+	0.0141083i
$645$		0			0
$646$	19.0281	−	32.9576i	0.748649	−	1.29670i
$647$	−17.2026	−	29.7958i	−0.676305	−	1.17139i	−0.976086	−	0.217386i	$-0.930247\pi$
$647$	−17.2026	−	29.7958i	−0.676305	−	1.17139i	0.299781	−	0.954008i	$-0.403086\pi$
$648$	−12.2131	−	21.1538i	−0.479778	−	0.830999i
$649$	−27.4045			−1.07572
$650$		0			0
$651$	0.826831			0.0324061
$652$	−3.52244	−	6.10104i	−0.137949	−	0.238935i
$653$	−7.16573	−	12.4114i	−0.280417	−	0.485696i	0.691071	−	0.722787i	$-0.257139\pi$
$653$	−7.16573	−	12.4114i	−0.280417	−	0.485696i	−0.971487	+	0.237091i	$0.923806\pi$
$654$	−1.18048	+	2.04465i	−0.0461604	+	0.0799521i
$655$		0			0
$656$	0.222994	−	0.386237i	0.00870646	−	0.0150800i
$657$	−12.7626	+	22.1054i	−0.497916	+	0.862416i
$658$	−29.5936			−1.15368
$659$	−11.4116	+	19.7655i	−0.444532	+	0.769953i	−0.998020	−	0.0629051i	$-0.979963\pi$
$659$	−11.4116	+	19.7655i	−0.444532	+	0.769953i	0.553487	+	0.832858i	$0.313297\pi$
$660$		0			0
$661$	−7.20934	−	12.4869i	−0.280411	−	0.485686i	0.691075	−	0.722783i	$-0.257137\pi$
$661$	−7.20934	−	12.4869i	−0.280411	−	0.485686i	−0.971486	+	0.237097i	$0.923804\pi$
$662$	15.0796			0.586087
$663$	−3.86601	−	5.57182i	−0.150143	−	0.216391i
$664$	−24.0976			−0.935168
$665$		0			0
$666$	9.32135	+	16.1450i	0.361195	+	0.625608i
$667$	−0.517665	+	0.896622i	−0.0200441	+	0.0347173i
$668$	−1.19792			−0.0463491
$669$	3.35913	−	5.81818i	0.129871	−	0.224944i
$670$		0			0
$671$	26.2419			1.01306
$672$	1.12659	−	1.95131i	0.0434591	−	0.0752733i
$673$	−17.0871	−	29.5956i	−0.658657	−	1.14083i	−0.980963	−	0.194193i	$-0.937791\pi$
$673$	−17.0871	−	29.5956i	−0.658657	−	1.14083i	0.322306	−	0.946636i	$-0.395542\pi$
$674$	9.07949	+	15.7261i	0.349729	+	0.605748i
$675$		0			0
$676$	4.88170	+	5.91993i	0.187758	+	0.227690i
$677$	−5.84695			−0.224716			−0.112358	−	0.993668i	$-0.535840\pi$
$677$	−5.84695			−0.224716			−0.112358	+	0.993668i	$0.535840\pi$
$678$	−0.975215	−	1.68912i	−0.0374529	−	0.0648703i
$679$	5.89165	+	10.2046i	0.226101	+	0.391618i
$680$		0			0
$681$	1.66054			0.0636319
$682$	2.71978	−	4.71079i	0.104146	−	0.180386i
$683$	−5.67439	+	9.82834i	−0.217125	+	0.376071i	−0.953928	−	0.300036i	$-0.903001\pi$
$683$	−5.67439	+	9.82834i	−0.217125	+	0.376071i	0.736803	+	0.676107i	$0.236334\pi$
$684$	10.0000			0.382360
$685$		0			0
$686$	11.9053	+	20.6206i	0.454546	+	0.787298i
$687$	0.262904	+	0.455363i	0.0100304	+	0.0173732i
$688$	−3.30969			−0.126181
$689$	−4.98715	−	7.18765i	−0.189995	−	0.273828i
$690$		0			0
$691$	9.41159	+	16.3013i	0.358034	+	0.620133i	0.987632	−	0.156788i	$-0.0501140\pi$
$691$	9.41159	+	16.3013i	0.358034	+	0.620133i	−0.629599	+	0.776921i	$0.716781\pi$
$692$	−0.395265	−	0.684619i	−0.0150257	−	0.0260253i
$693$	−11.3457	+	19.6513i	−0.430988	+	0.746493i
$694$	14.5325			0.551647
$695$		0			0
$696$	1.59207	−	2.75754i	0.0603471	−	0.104524i
$697$	0.983636			0.0372579
$698$	11.1018	−	19.2289i	0.420210	−	0.727825i
$699$	2.40976	+	4.17383i	0.0911455	+	0.157869i
$700$		0			0
$701$	19.1626			0.723763			0.361881	−	0.932224i	$-0.382135\pi$
$701$	19.1626			0.723763			0.361881	+	0.932224i	$0.382135\pi$
$702$	−3.70558	+	7.85869i	−0.139858	+	0.296607i
$703$	−32.0518			−1.20885
$704$	−17.0018	−	29.4480i	−0.640780	−	1.10986i
$705$		0			0
$706$	−0.777006	+	1.34581i	−0.0292430	+	0.0506504i
$707$	12.0602			0.453570
$708$	0.719193	−	1.24568i	0.0270289	−	0.0468154i
$709$	−11.7419	+	20.3375i	−0.440975	+	0.763791i	−0.997762	−	0.0668645i	$-0.978700\pi$
$709$	−11.7419	+	20.3375i	−0.440975	+	0.763791i	0.556787	+	0.830655i	$0.312034\pi$
$710$		0			0
$711$	16.1049	−	27.8945i	0.603982	−	1.04613i
$712$	−18.8248	−	32.6055i	−0.705488	−	1.22194i
$713$	−0.203698	−	0.352814i	−0.00762853	−	0.0132130i
$714$	−4.53252			−0.169625
$715$		0			0
$716$	−11.9370			−0.446107
$717$	0.690220	+	1.19550i	0.0257767	+	0.0446466i
$718$	−17.4586	−	30.2393i	−0.651551	−	1.12852i
$719$	7.05429	−	12.2184i	0.263080	−	0.455669i	−0.703978	−	0.710221i	$-0.748595\pi$
$719$	7.05429	−	12.2184i	0.263080	−	0.455669i	0.967059	+	0.254553i	$0.0819282\pi$
$720$		0			0
$721$	6.52886	−	11.3083i	0.243148	−	0.421144i
$722$	9.25228	−	16.0254i	0.344334	−	0.596404i
$723$	6.02765			0.224171
$724$	5.85021	−	10.1329i	0.217421	−	0.376585i
$725$		0			0
$726$	−0.832096	−	1.44123i	−0.0308820	−	0.0534892i
$727$	−25.3762			−0.941153			−0.470576	−	0.882359i	$-0.655954\pi$
$727$	−25.3762			−0.941153			−0.470576	+	0.882359i	$0.655954\pi$
$728$	22.4279	−	1.86553i	0.831233	−	0.0691411i
$729$	−20.7796			−0.769616
$730$		0			0
$731$	−3.64979	−	6.32162i	−0.134992	−	0.233814i
$732$	−0.688681	+	1.19283i	−0.0254544	+	0.0440883i
$733$	10.6692			0.394074			0.197037	−	0.980396i	$-0.436868\pi$
$733$	10.6692			0.394074			0.197037	+	0.980396i	$0.436868\pi$
$734$	19.8476	−	34.3770i	0.732587	−	1.26888i
$735$		0			0
$736$	−1.11018			−0.0409218
$737$	−8.54617	+	14.8024i	−0.314802	+	0.545254i
$738$	−0.308672	−	0.534635i	−0.0113624	−	0.0196802i
$739$	0.707513	+	1.22545i	0.0260263	+	0.0450788i	0.878745	−	0.477291i	$-0.158381\pi$
$739$	0.707513	+	1.22545i	0.0260263	+	0.0450788i	−0.852719	+	0.522370i	$0.825048\pi$
$740$		0			0
$741$	−4.17156	−	6.01219i	−0.153246	−	0.220863i
$742$	−5.84695			−0.214648
$743$	−14.9389	−	25.8748i	−0.548053	−	0.949256i	−0.998408	−	0.0564064i	$-0.982036\pi$
$743$	−14.9389	−	25.8748i	−0.548053	−	0.949256i	0.450355	−	0.892850i	$-0.351298\pi$
$744$	0.626467	+	1.08507i	0.0229674	+	0.0397807i
$745$		0			0
$746$	−40.9370			−1.49881
$747$	−11.2865	+	19.5488i	−0.412952	+	0.715253i
$748$	6.24221	−	10.8118i	0.228238	−	0.395320i
$749$	35.8809			1.31106
$750$		0			0
$751$	9.99291	+	17.3082i	0.364646	+	0.631586i	0.988719	−	0.149780i	$-0.0478565\pi$
$751$	9.99291	+	17.3082i	0.364646	+	0.631586i	−0.624073	+	0.781366i	$0.714523\pi$
$752$	−15.1737	−	26.2816i	−0.553328	−	0.958391i
$753$	−3.20938			−0.116956
$754$	12.7988	−	1.06459i	0.466104	−	0.0387701i
$755$		0			0
$756$	−1.21563	−	2.10553i	−0.0442120	−	0.0765774i
$757$	−8.54617	−	14.8024i	−0.310616	−	0.538003i	0.667880	−	0.744269i	$-0.267202\pi$
$757$	−8.54617	−	14.8024i	−0.310616	−	0.538003i	−0.978496	+	0.206266i	$0.933869\pi$
$758$	−10.3325	+	17.8964i	−0.375292	+	0.650025i
$759$	−0.462218			−0.0167775
$760$		0			0
$761$	21.1120	−	36.5671i	0.765310	−	1.32556i	−0.174773	−	0.984609i	$-0.555919\pi$
$761$	21.1120	−	36.5671i	0.765310	−	1.32556i	0.940083	−	0.340947i	$-0.110748\pi$
$762$	6.84552			0.247987
$763$	5.84695	−	10.1272i	0.211674	−	0.366630i
$764$	0.453830	+	0.786056i	0.0164190	+	0.0284385i
$765$		0			0
$766$	2.07395			0.0749350
$767$	25.3725	−	2.11046i	0.916149	−	0.0762044i
$768$	4.42107			0.159531
$769$	11.8827	+	20.5815i	0.428502	+	0.742187i	0.996740	−	0.0806767i	$-0.0257081\pi$
$769$	11.8827	+	20.5815i	0.428502	+	0.742187i	−0.568238	+	0.822864i	$0.692375\pi$
$770$		0			0
$771$	−1.87907	+	3.25465i	−0.0676731	+	0.117213i
$772$	12.5149			0.450422
$773$	−0.142043	+	0.246026i	−0.00510894	+	0.00884894i	−0.868569	−	0.495569i	$-0.834960\pi$
$773$	−0.142043	+	0.246026i	−0.00510894	+	0.00884894i	0.863460	+	0.504418i	$0.168293\pi$
$774$	−2.29066	+	3.96754i	−0.0823361	+	0.142610i
$775$		0			0
$776$	−8.92787	+	15.4635i	−0.320492	+	0.555108i
$777$	1.90870	+	3.30596i	0.0684741	+	0.118601i
$778$	13.0865	+	22.6665i	0.469174	+	0.812634i
$779$	1.06138			0.0380278
$780$		0			0
$781$	−7.29958			−0.261199
$782$	1.11663	+	1.93405i	0.0399305	+	0.0691617i
$783$	−3.04434	−	5.27294i	−0.108796	−	0.188440i
$784$	−3.55955	+	6.16532i	−0.127127	+	0.220190i
$785$		0			0
$786$	−2.04880	+	3.54863i	−0.0730784	+	0.126575i
$787$	12.0671	−	20.9008i	0.430145	−	0.745032i	−0.566741	−	0.823896i	$-0.691796\pi$
$787$	12.0671	−	20.9008i	0.430145	−	0.745032i	0.996885	+	0.0788638i	$0.0251292\pi$
$788$	−5.46381			−0.194640
$789$	2.31925	−	4.01705i	0.0825674	−	0.143011i
$790$		0			0
$791$	4.83027	+	8.36627i	0.171745	+	0.297470i
$792$	−34.3853			−1.22183
$793$	−24.2961	+	2.02093i	−0.862780	+	0.0717652i
$794$	−26.7529			−0.949424
$795$		0			0
$796$	−5.13641	−	8.89652i	−0.182055	−	0.315329i
$797$	−17.1721	+	29.7430i	−0.608267	+	1.05355i	0.383259	+	0.923641i	$0.374802\pi$
$797$	−17.1721	+	29.7430i	−0.608267	+	1.05355i	−0.991526	+	0.129909i	$0.958532\pi$
$798$	−4.89075			−0.173131
$799$	33.4659	−	57.9646i	1.18394	−	2.05064i
$800$		0			0
$801$	−35.2676			−1.24612
$802$	−2.19899	+	3.80876i	−0.0776489	+	0.134492i
$803$	17.1927	+	29.7786i	0.606716	+	1.05086i
$804$	−0.448565	−	0.776937i	−0.0158197	−	0.0274004i
$805$		0			0
$806$	−2.15533	+	4.57096i	−0.0759182	+	0.161005i
$807$	−1.26329			−0.0444698
$808$	9.13767	+	15.8269i	0.321462	+	0.556789i
$809$	23.8431	+	41.2975i	0.838279	+	1.45194i	0.891332	+	0.453351i	$0.149771\pi$
$809$	23.8431	+	41.2975i	0.838279	+	1.45194i	−0.0530528	+	0.998592i	$0.516895\pi$
$810$		0			0
$811$	24.5992			0.863793			0.431897	−	0.901923i	$-0.357845\pi$
$811$	24.5992			0.863793			0.431897	+	0.901923i	$0.357845\pi$
$812$	−1.79689	+	3.11230i	−0.0630584	+	0.109220i
$813$	3.79684	−	6.57632i	0.133161	−	0.230642i
$814$	25.1138			0.880239
$815$		0			0
$816$	−2.32398	−	4.02525i	−0.0813556	−	0.140912i
$817$	−3.93825	−	6.82125i	−0.137782	−	0.238645i
$818$	16.0097			0.559765
$819$	8.99108	−	19.0680i	0.314174	−	0.666290i
$820$		0			0
$821$	−8.64979	−	14.9819i	−0.301880	−	0.522871i	0.674682	−	0.738109i	$-0.264281\pi$
$821$	−8.64979	−	14.9819i	−0.301880	−	0.522871i	−0.976562	+	0.215237i	$0.930947\pi$
$822$	0.405225	+	0.701870i	0.0141338	+	0.0244805i
$823$	−16.2813	+	28.2000i	−0.567529	+	0.982990i	0.429280	+	0.903171i	$0.358767\pi$
$823$	−16.2813	+	28.2000i	−0.567529	+	0.982990i	−0.996809	+	0.0798182i	$0.974566\pi$
$824$	19.7869			0.689311
$825$		0			0
$826$	8.50812	−	14.7365i	0.296035	−	0.512748i
$827$	15.4702			0.537951			0.268976	−	0.963147i	$-0.413315\pi$
$827$	15.4702			0.537951			0.268976	+	0.963147i	$0.413315\pi$
$828$	−0.293416	+	0.508211i	−0.0101969	+	0.0176616i
$829$	7.26180	+	12.5778i	0.252213	+	0.436845i	0.964135	−	0.265413i	$-0.0855084\pi$
$829$	7.26180	+	12.5778i	0.252213	+	0.436845i	−0.711922	+	0.702258i	$0.752175\pi$
$830$		0			0
$831$	3.41503			0.118466
$832$	18.0090	+	25.9552i	0.624351	+	0.899835i
$833$	−15.7013			−0.544018
$834$	−1.78254	−	3.08746i	−0.0617245	−	0.106910i
$835$		0			0
$836$	6.73557	−	11.6663i	0.232955	−	0.403489i
$837$	2.39585			0.0828127
$838$	9.98736	−	17.2986i	0.345008	−	0.597571i
$839$	−0.407933	+	0.706561i	−0.0140834	+	0.0243932i	−0.872981	−	0.487754i	$-0.837816\pi$
$839$	−0.407933	+	0.706561i	−0.0140834	+	0.0243932i	0.858898	+	0.512147i	$0.171150\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	10.1524	+	17.5846i	0.349876	+	0.606004i
$843$	0.700811	+	1.21384i	0.0241372	+	0.0418069i
$844$	4.29797			0.147942
$845$		0			0
$846$	−42.0073			−1.44424
$847$	4.12140	+	7.13847i	0.141613	+	0.245281i
$848$	−2.99794	−	5.19258i	−0.102950	−	0.178314i
$849$	1.05063	−	1.81975i	0.0360575	−	0.0624535i
$850$		0			0
$851$	0.940450	−	1.62891i	0.0322382	−	0.0558382i
$852$	0.191567	−	0.331804i	0.00656299	−	0.0113674i
$853$	−20.0856			−0.687719			−0.343859	−	0.939021i	$-0.611734\pi$
$853$	−20.0856			−0.687719			−0.343859	+	0.939021i	$0.611734\pi$
$854$	−8.14716	+	14.1113i	−0.278790	+	0.482878i
$855$		0			0
$856$	27.1860	+	47.0875i	0.929197	+	1.60942i
$857$	−40.7886			−1.39331			−0.696656	−	0.717406i	$-0.745329\pi$
$857$	−40.7886			−1.39331			−0.696656	+	0.717406i	$0.745329\pi$
$858$	3.26858	+	4.71079i	0.111588	+	0.160824i
$859$	−40.1301			−1.36922			−0.684610	−	0.728909i	$-0.740028\pi$
$859$	−40.1301			−1.36922			−0.684610	+	0.728909i	$0.740028\pi$
$860$		0			0
$861$	−0.0632055	−	0.109475i	−0.00215404	−	0.00373090i
$862$	5.73514	−	9.93355i	0.195340	−	0.338338i
$863$	20.8275			0.708977			0.354489	−	0.935060i	$-0.384655\pi$
$863$	20.8275			0.708977			0.354489	+	0.935060i	$0.384655\pi$
$864$	3.26443	−	5.65416i	0.111058	−	0.192358i
$865$		0			0
$866$	29.4134			0.999509
$867$	2.19215	−	3.79692i	0.0744494	−	0.128950i
$868$	−0.707062	−	1.22467i	−0.0239993	−	0.0415679i
$869$	−21.6952	−	37.5771i	−0.735958	−	1.27472i
$870$		0			0
$871$	6.77255	−	14.3630i	0.229479	−	0.486672i
$872$	17.7203			0.600084
$873$	8.36303	+	14.4852i	0.283046	+	0.490249i
$874$	1.20488	+	2.08691i	0.0407557	+	0.0705909i
$875$		0			0
$876$	−1.80479			−0.0609782
$877$	23.2972	−	40.3520i	0.786691	−	1.36259i	−0.141293	−	0.989968i	$-0.545126\pi$
$877$	23.2972	−	40.3520i	0.786691	−	1.36259i	0.927984	−	0.372621i	$-0.121541\pi$
$878$	4.19210	−	7.26094i	0.141477	−	0.245045i
$879$	−3.37935			−0.113982
$880$		0			0
$881$	−11.9223	−	20.6501i	−0.401674	−	0.695719i	0.592254	−	0.805751i	$-0.298238\pi$
$881$	−11.9223	−	20.6501i	−0.401674	−	0.695719i	−0.993928	+	0.110032i	$0.964905\pi$
$882$	4.92718	+	8.53413i	0.165907	+	0.287359i
$883$	37.2496			1.25355			0.626774	−	0.779201i	$-0.284375\pi$
$883$	37.2496			1.25355			0.626774	+	0.779201i	$0.284375\pi$
$884$	−4.94674	+	10.4909i	−0.166377	+	0.352847i
$885$		0			0
$886$	22.7041	+	39.3246i	0.762758	+	1.32114i
$887$	14.2897	+	24.7505i	0.479802	+	0.831042i	0.999732	−	0.0231673i	$-0.00737505\pi$
$887$	14.2897	+	24.7505i	0.479802	+	0.831042i	−0.519929	+	0.854209i	$0.674042\pi$
$888$	−2.89233	+	5.00967i	−0.0970603	+	0.168113i
$889$	−33.9060			−1.13717
$890$		0			0
$891$	−15.4116	+	26.6937i	−0.516308	+	0.894271i
$892$	−11.4902			−0.384720
$893$	36.1109	−	62.5459i	1.20840	−	2.09302i
$894$	−4.56949	−	7.91459i	−0.152827	−	0.264704i
$895$		0			0
$896$	8.05611			0.269136
$897$	0.427946	−	0.0355962i	0.0142887	−	0.00118852i
$898$	14.8180			0.494483
$899$	−1.77072	−	3.06697i	−0.0590568	−	0.102289i
$900$		0			0
$901$	6.61201	−	11.4523i	0.220278	−	0.381533i
$902$	−0.831632			−0.0276903
$903$	−0.469049	+	0.812417i	−0.0156090	+	0.0270356i
$904$	−7.31952	+	12.6778i	−0.243444	+	0.421657i
$905$		0			0
$906$	3.92605	−	6.80011i	0.130434	−	0.225919i
$907$	3.20693	+	5.55457i	0.106484	+	0.184436i	0.914344	−	0.404939i	$-0.132707\pi$
$907$	3.20693	+	5.55457i	0.106484	+	0.184436i	−0.807859	+	0.589375i	$0.799374\pi$
$908$	−1.42000	−	2.45952i	−0.0471245	−	0.0816220i
$909$	17.1191			0.567805
$910$		0			0
$911$	22.2204			0.736193			0.368097	−	0.929788i	$-0.380010\pi$
$911$	22.2204			0.736193			0.368097	+	0.929788i	$0.380010\pi$
$912$	−2.50766	−	4.34339i	−0.0830369	−	0.143824i
$913$	15.2042	+	26.3345i	0.503186	+	0.871543i
$914$	−4.88719	+	8.46486i	−0.161654	+	0.279993i
$915$		0			0
$916$	0.449643	−	0.778805i	0.0148566	−	0.0257324i
$917$	10.1478	−	17.5765i	0.335109	−	0.580426i
$918$	−13.1335			−0.433472
$919$	−13.0632	+	22.6261i	−0.430915	+	0.746367i	−0.996952	−	0.0780125i	$-0.975143\pi$
$919$	−13.0632	+	22.6261i	−0.430915	+	0.746367i	0.566037	+	0.824380i	$0.308476\pi$
$920$		0			0
$921$	3.81426	+	6.60649i	0.125684	+	0.217691i
$922$	5.39220			0.177583
$923$	6.75834	−	0.562152i	0.222453	−	0.0185035i
$924$	−1.60442			−0.0527817
$925$		0			0
$926$	1.18048	+	2.04465i	0.0387929	+	0.0671913i
$927$	9.26754	−	16.0518i	0.304386	−	0.527212i
$928$	−9.65067			−0.316799
$929$	11.9711	−	20.7346i	0.392760	−	0.680281i	−0.600052	−	0.799961i	$-0.704854\pi$
$929$	11.9711	−	20.7346i	0.392760	−	0.680281i	0.992813	+	0.119680i	$0.0381869\pi$
$930$		0			0
$931$	−16.9423			−0.555261
$932$	4.12140	−	7.13847i	0.135001	−	0.233828i
$933$	1.31815	+	2.28311i	0.0431544	+	0.0747457i
$934$	19.4748	+	33.7313i	0.637235	+	1.10372i
$935$		0			0
$936$	31.8358	−	2.64807i	1.04058	−	0.0865547i
$937$	18.5046			0.604518			0.302259	−	0.953226i	$-0.402259\pi$
$937$	18.5046			0.604518			0.302259	+	0.953226i	$0.402259\pi$
$938$	−5.30656	−	9.19124i	−0.173265	−	0.300104i
$939$	−4.51102	−	7.81332i	−0.147212	−	0.254978i
$940$		0			0
$941$	−14.3788			−0.468735			−0.234368	−	0.972148i	$-0.575302\pi$
$941$	−14.3788			−0.468735			−0.234368	+	0.972148i	$0.575302\pi$
$942$	−1.27080	+	2.20109i	−0.0414049	+	0.0717154i
$943$	−0.0311425	+	0.0539404i	−0.00101414	+	0.00175654i
$944$	17.4496			0.567938
$945$		0			0
$946$	3.08578	+	5.34473i	0.100327	+	0.173772i
$947$	29.1594	+	50.5056i	0.947554	+	1.64121i	0.750555	+	0.660807i	$0.229786\pi$
$947$	29.1594	+	50.5056i	0.947554	+	1.64121i	0.196998	+	0.980404i	$0.436881\pi$
$948$	2.27744			0.0739677
$949$	−18.2112	−	26.2465i	−0.591160	−	0.851999i
$950$		0			0
$951$	−2.04354	−	3.53951i	−0.0662663	−	0.114777i
$952$	17.0095	+	29.4613i	0.551281	+	0.954847i
$953$	−6.89975	+	11.9507i	−0.223505	+	0.387122i	−0.955870	−	0.293791i	$-0.905083\pi$
$953$	−6.89975	+	11.9507i	−0.223505	+	0.387122i	0.732365	+	0.680912i	$0.238417\pi$
$954$	−8.29958			−0.268709
$955$		0			0
$956$	1.18048	−	2.04465i	0.0381794	−	0.0661287i
$957$	−4.01801			−0.129884
$958$	−18.2881	+	31.6759i	−0.590862	+	1.02340i
$959$	−2.00709	−	3.47639i	−0.0648124	−	0.112258i
$960$		0			0
$961$	−29.6065			−0.955047
$962$	−23.2517	+	1.93405i	−0.749666	+	0.0623564i
$963$	50.9319			1.64126
$964$	−5.15452	−	8.92790i	−0.166016	−	0.287548i
$965$		0			0
$966$	0.143502	−	0.248553i	0.00461711	−	0.00799707i
$967$	−30.3474			−0.975906			−0.487953	−	0.872870i	$-0.662256\pi$
$967$	−30.3474			−0.975906			−0.487953	+	0.872870i	$0.662256\pi$
$968$	−6.24534	+	10.8172i	−0.200733	+	0.347679i
$969$	5.53069	−	9.57943i	0.177671	−	0.307736i
$970$		0			0
$971$	−22.0506	+	38.1928i	−0.707638	+	1.22567i	0.258092	+	0.966120i	$0.416906\pi$
$971$	−22.0506	+	38.1928i	−0.707638	+	1.22567i	−0.965731	+	0.259545i	$0.916427\pi$
$972$	−2.60580	−	4.51337i	−0.0835810	−	0.144767i
$973$	8.82900	+	15.2923i	0.283045	+	0.490248i
$974$	−26.5074			−0.849351
$975$		0			0
$976$	−16.7093			−0.534853
$977$	−11.1610	−	19.3314i	−0.357071	−	0.618466i	0.630399	−	0.776271i	$-0.282891\pi$
$977$	−11.1610	−	19.3314i	−0.357071	−	0.618466i	−0.987470	+	0.157806i	$0.949558\pi$
$978$	2.44537	+	4.23551i	0.0781944	+	0.135437i
$979$	−23.7547	+	41.1444i	−0.759204	+	1.31498i
$980$		0			0
$981$	8.29958	−	14.3753i	0.264985	−	0.458968i
$982$	6.34189	−	10.9845i	0.202378	−	0.350529i
$983$	−4.03793			−0.128790			−0.0643950	−	0.997924i	$-0.520512\pi$
$983$	−4.03793			−0.128790			−0.0643950	+	0.997924i	$0.520512\pi$
$984$	0.0957781	−	0.165893i	0.00305330	−	0.00528846i
$985$		0			0
$986$	9.70671	+	16.8125i	0.309125	+	0.535419i
$987$	−8.60167			−0.273794
$988$	−5.33770	+	11.3200i	−0.169815	+	0.360139i
$989$	0.462218			0.0146977
$990$		0			0
$991$	−14.8250	−	25.6777i	−0.470932	−	0.815678i	0.528515	−	0.848924i	$-0.322749\pi$
$991$	−14.8250	−	25.6777i	−0.470932	−	0.815678i	−0.999447	+	0.0332459i	$0.989416\pi$
$992$	1.89874	−	3.28871i	0.0602849	−	0.104417i
$993$	4.38304			0.139092
$994$	2.26626	−	3.92527i	0.0718813	−	0.124502i
$995$		0			0
$996$	−1.59605			−0.0505728
$997$	11.0881	−	19.2052i	0.351164	−	0.608233i	−0.635290	−	0.772274i	$-0.719119\pi$
$997$	11.0881	−	19.2052i	0.351164	−	0.608233i	0.986454	+	0.164040i	$0.0524527\pi$
$998$	11.1725	+	19.3514i	0.353660	+	0.612557i
$999$	5.53069	+	9.57943i	0.174983	+	0.303080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.e.e.276.5		12
5.2	odd	4		65.2.n.a.29.2	yes	12
5.3	odd	4		65.2.n.a.29.5	yes	12
5.4	even	2	inner	325.2.e.e.276.2		12
13.3	even	3		4225.2.a.br.1.2		6
13.9	even	3	inner	325.2.e.e.126.5		12
13.10	even	6		4225.2.a.bq.1.5		6
15.2	even	4		585.2.bs.a.289.5		12
15.8	even	4		585.2.bs.a.289.2		12
20.3	even	4		1040.2.dh.a.289.4		12
20.7	even	4		1040.2.dh.a.289.3		12
65.2	even	12		845.2.d.d.844.4		12
65.3	odd	12		845.2.b.d.339.5		6
65.7	even	12		845.2.l.f.654.3		24
65.8	even	4		845.2.l.f.699.9		24
65.9	even	6	inner	325.2.e.e.126.2		12
65.12	odd	4		845.2.n.e.484.5		12
65.17	odd	12		845.2.n.e.529.2		12
65.18	even	4		845.2.l.f.699.3		24
65.22	odd	12		65.2.n.a.9.5	yes	12
65.23	odd	12		845.2.b.e.339.2		6
65.28	even	12		845.2.d.d.844.9		12
65.29	even	6		4225.2.a.br.1.5		6
65.32	even	12		845.2.l.f.654.9		24
65.33	even	12		845.2.l.f.654.10		24
65.37	even	12		845.2.d.d.844.10		12
65.38	odd	4		845.2.n.e.484.2		12
65.42	odd	12		845.2.b.d.339.2		6
65.43	odd	12		845.2.n.e.529.5		12
65.47	even	4		845.2.l.f.699.4		24
65.48	odd	12		65.2.n.a.9.2	✓	12
65.49	even	6		4225.2.a.bq.1.2		6
65.57	even	4		845.2.l.f.699.10		24
65.58	even	12		845.2.l.f.654.4		24
65.62	odd	12		845.2.b.e.339.5		6
65.63	even	12		845.2.d.d.844.3		12
195.113	even	12		585.2.bs.a.334.5		12
195.152	even	12		585.2.bs.a.334.2		12
260.87	even	12		1040.2.dh.a.529.4		12
260.243	even	12		1040.2.dh.a.529.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.n.a.9.2	✓	12	65.48	odd	12
65.2.n.a.9.5	yes	12	65.22	odd	12
65.2.n.a.29.2	yes	12	5.2	odd	4
65.2.n.a.29.5	yes	12	5.3	odd	4
325.2.e.e.126.2		12	65.9	even	6	inner
325.2.e.e.126.5		12	13.9	even	3	inner
325.2.e.e.276.2		12	5.4	even	2	inner
325.2.e.e.276.5		12	1.1	even	1	trivial
585.2.bs.a.289.2		12	15.8	even	4
585.2.bs.a.289.5		12	15.2	even	4
585.2.bs.a.334.2		12	195.152	even	12
585.2.bs.a.334.5		12	195.113	even	12
845.2.b.d.339.2		6	65.42	odd	12
845.2.b.d.339.5		6	65.3	odd	12
845.2.b.e.339.2		6	65.23	odd	12
845.2.b.e.339.5		6	65.62	odd	12
845.2.d.d.844.3		12	65.63	even	12
845.2.d.d.844.4		12	65.2	even	12
845.2.d.d.844.9		12	65.28	even	12
845.2.d.d.844.10		12	65.37	even	12
845.2.l.f.654.3		24	65.7	even	12
845.2.l.f.654.4		24	65.58	even	12
845.2.l.f.654.9		24	65.32	even	12
845.2.l.f.654.10		24	65.33	even	12
845.2.l.f.699.3		24	65.18	even	4
845.2.l.f.699.4		24	65.47	even	4
845.2.l.f.699.9		24	65.8	even	4
845.2.l.f.699.10		24	65.57	even	4
845.2.n.e.484.2		12	65.38	odd	4
845.2.n.e.484.5		12	65.12	odd	4
845.2.n.e.529.2		12	65.17	odd	12
845.2.n.e.529.5		12	65.43	odd	12
1040.2.dh.a.289.3		12	20.7	even	4
1040.2.dh.a.289.4		12	20.3	even	4
1040.2.dh.a.529.3		12	260.243	even	12
1040.2.dh.a.529.4		12	260.87	even	12
4225.2.a.bq.1.2		6	65.49	even	6
4225.2.a.bq.1.5		6	13.10	even	6
4225.2.a.br.1.2		6	13.3	even	3
4225.2.a.br.1.5		6	65.29	even	6

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.593667 + 1.02826i) q^{2} +(0.172555 + 0.298874i) q^{3} +(0.295120 - 0.511162i) q^{4} +(-0.204880 + 0.354863i) q^{6} +(1.01478 - 1.75765i) q^{7} +3.07548 q^{8} +(1.44045 - 2.49493i) q^{9} +O(q^{10})\)	\(q+(0.593667 + 1.02826i) q^{2} +(0.172555 + 0.298874i) q^{3} +(0.295120 - 0.511162i) q^{4} +(-0.204880 + 0.354863i) q^{6} +(1.01478 - 1.75765i) q^{7} +3.07548 q^{8} +(1.44045 - 2.49493i) q^{9} +(-1.94045 - 3.36096i) q^{11} +0.203698 q^{12} +(2.05540 + 2.96232i) q^{13} +2.40976 q^{14} +(1.23557 + 2.14007i) q^{16} +(-2.72507 + 4.71996i) q^{17} +3.42059 q^{18} +(-2.94045 + 5.09301i) q^{19} +0.700420 q^{21} +(2.30396 - 3.99058i) q^{22} +(-0.172555 - 0.298874i) q^{23} +(0.530689 + 0.919180i) q^{24} +(-1.82581 + 3.87212i) q^{26} +2.02956 q^{27} +(-0.598962 - 1.03743i) q^{28} +(-1.50000 - 2.59808i) q^{29} +1.18048 q^{31} +(1.60845 - 2.78591i) q^{32} +(0.669668 - 1.15990i) q^{33} -6.47114 q^{34} +(-0.850210 - 1.47261i) q^{36} +(2.72507 + 4.71996i) q^{37} -6.98259 q^{38} +(-0.530689 + 1.12547i) q^{39} +(-0.0902394 - 0.156299i) q^{41} +(0.415816 + 0.720215i) q^{42} +(-0.669668 + 1.15990i) q^{43} -2.29066 q^{44} +(0.204880 - 0.354863i) q^{46} -12.2807 q^{47} +(-0.426407 + 0.738559i) q^{48} +(1.44045 + 2.49493i) q^{49} -1.88090 q^{51} +(2.12081 - 0.176407i) q^{52} -2.42636 q^{53} +(1.20488 + 2.08691i) q^{54} +(3.12093 - 5.40561i) q^{56} -2.02956 q^{57} +(1.78100 - 3.08478i) q^{58} +(3.53069 - 6.11533i) q^{59} +(-3.38090 + 5.85589i) q^{61} +(0.700811 + 1.21384i) q^{62} +(-2.92347 - 5.06361i) q^{63} +8.76180 q^{64} +1.59024 q^{66} +(-2.20211 - 3.81417i) q^{67} +(1.60845 + 2.78591i) q^{68} +(0.0595504 - 0.103144i) q^{69} +(0.940450 - 1.62891i) q^{71} +(4.43007 - 7.67311i) q^{72} -8.86014 q^{73} +(-3.23557 + 5.60417i) q^{74} +(1.73557 + 3.00609i) q^{76} -7.87651 q^{77} +(-1.47233 + 0.122467i) q^{78} +11.1805 q^{79} +(-3.97114 - 6.87821i) q^{81} +(0.107144 - 0.185579i) q^{82} -7.83540 q^{83} +(0.206708 - 0.358028i) q^{84} -1.59024 q^{86} +(0.517665 - 0.896622i) q^{87} +(-5.96781 - 10.3365i) q^{88} +(-6.12093 - 10.6018i) q^{89} +(7.29249 - 0.606582i) q^{91} -0.203698 q^{92} +(0.203698 + 0.352814i) q^{93} +(-7.29066 - 12.6278i) q^{94} +1.11018 q^{96} +(-2.90292 + 5.02801i) q^{97} +(-1.71029 + 2.96232i) q^{98} -11.1805 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q - 4 * q^4 - 10 * q^6 - 6 * q^9	\( 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9} + 44 q^{14} - 16 q^{16} - 12 q^{19} - 8 q^{21} - 32 q^{24} + 24 q^{26} - 18 q^{29} - 16 q^{31} - 16 q^{34} - 2 q^{36} + 32 q^{39} + 14 q^{41} + 4 q^{44} + 10 q^{46} - 6 q^{49} + 24 q^{51} + 22 q^{54} - 16 q^{56} + 4 q^{59} + 6 q^{61} + 12 q^{64} + 4 q^{66} + 24 q^{69} - 12 q^{71} - 8 q^{74} - 10 q^{76} + 104 q^{79} + 14 q^{81} - 90 q^{84} - 4 q^{86} - 20 q^{89} - 44 q^{91} - 56 q^{94} + 12 q^{96} - 104 q^{99}+O(q^{100}) \) 12 * q - 4 * q^4 - 10 * q^6 - 6 * q^9 + 44 * q^14 - 16 * q^16 - 12 * q^19 - 8 * q^21 - 32 * q^24 + 24 * q^26 - 18 * q^29 - 16 * q^31 - 16 * q^34 - 2 * q^36 + 32 * q^39 + 14 * q^41 + 4 * q^44 + 10 * q^46 - 6 * q^49 + 24 * q^51 + 22 * q^54 - 16 * q^56 + 4 * q^59 + 6 * q^61 + 12 * q^64 + 4 * q^66 + 24 * q^69 - 12 * q^71 - 8 * q^74 - 10 * q^76 + 104 * q^79 + 14 * q^81 - 90 * q^84 - 4 * q^86 - 20 * q^89 - 44 * q^91 - 56 * q^94 + 12 * q^96 - 104 * q^99

Introduction

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