LMFDB - Embedded newform 845.2.k.d.268.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(268,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("845.268");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.k (of order $4$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			268.9
Root			$1.51805i$ of defining polynomial
Character	$\chi$	$=$	845.268
Dual form			845.2.k.d.577.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.51805 q^{2} +(0.478298 + 0.478298i) q^{3} +0.304465 q^{4} +(-0.600231 + 2.15400i) q^{5} +(0.726078 + 0.726078i) q^{6} +2.59488i q^{7} -2.57390 q^{8} -2.54246i q^{9} +(-0.911178 + 3.26987i) q^{10} +(-3.53513 + 3.53513i) q^{11} +(0.145625 + 0.145625i) q^{12} +3.93915i q^{14} +(-1.31734 + 0.743165i) q^{15} -4.51623 q^{16} +(0.0578870 + 0.0578870i) q^{17} -3.85958i q^{18} +(1.98490 - 1.98490i) q^{19} +(-0.182749 + 0.655819i) q^{20} +(-1.24113 + 1.24113i) q^{21} +(-5.36650 + 5.36650i) q^{22} +(-2.86909 + 2.86909i) q^{23} +(-1.23109 - 1.23109i) q^{24} +(-4.27945 - 2.58580i) q^{25} +(2.65095 - 2.65095i) q^{27} +0.790051i q^{28} +4.98486i q^{29} +(-1.99979 + 1.12816i) q^{30} +(2.32124 + 2.32124i) q^{31} -1.70805 q^{32} -3.38169 q^{33} +(0.0878751 + 0.0878751i) q^{34} +(-5.58938 - 1.55753i) q^{35} -0.774091i q^{36} +0.571501i q^{37} +(3.01318 - 3.01318i) q^{38} +(1.54493 - 5.54419i) q^{40} +(7.36174 + 7.36174i) q^{41} +(-1.88409 + 1.88409i) q^{42} +(-0.0967193 + 0.0967193i) q^{43} +(-1.07633 + 1.07633i) q^{44} +(5.47647 + 1.52606i) q^{45} +(-4.35541 + 4.35541i) q^{46} -2.30053i q^{47} +(-2.16010 - 2.16010i) q^{48} +0.266585 q^{49} +(-6.49640 - 3.92536i) q^{50} +0.0553744i q^{51} +(6.70735 + 6.70735i) q^{53} +(4.02426 - 4.02426i) q^{54} +(-5.49279 - 9.73658i) q^{55} -6.67897i q^{56} +1.89875 q^{57} +7.56725i q^{58} +(-1.89634 - 1.89634i) q^{59} +(-0.401085 + 0.226268i) q^{60} +5.48474 q^{61} +(3.52374 + 3.52374i) q^{62} +6.59739 q^{63} +6.43957 q^{64} -5.13357 q^{66} -15.7868 q^{67} +(0.0176246 + 0.0176246i) q^{68} -2.74456 q^{69} +(-8.48494 - 2.36440i) q^{70} +(5.43544 + 5.43544i) q^{71} +6.54405i q^{72} +6.61894 q^{73} +0.867565i q^{74} +(-0.810069 - 3.28363i) q^{75} +(0.604334 - 0.604334i) q^{76} +(-9.17326 - 9.17326i) q^{77} -5.71054i q^{79} +(2.71078 - 9.72797i) q^{80} -5.09150 q^{81} +(11.1755 + 11.1755i) q^{82} -3.70736i q^{83} +(-0.377880 + 0.377880i) q^{84} +(-0.159434 + 0.0899431i) q^{85} +(-0.146824 + 0.146824i) q^{86} +(-2.38425 + 2.38425i) q^{87} +(9.09908 - 9.09908i) q^{88} +(12.6520 + 12.6520i) q^{89} +(8.31353 + 2.31664i) q^{90} +(-0.873538 + 0.873538i) q^{92} +2.22048i q^{93} -3.49231i q^{94} +(3.08409 + 5.46689i) q^{95} +(-0.816956 - 0.816956i) q^{96} -5.36986 q^{97} +0.404689 q^{98} +(8.98794 + 8.98794i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 8 q^{2} + 4 q^{3} + 12 q^{4} + 6 q^{5} - 4 q^{6} - 12 q^{8} + 8 q^{10} - 8 q^{11} + 24 q^{12} + 24 q^{15} + 4 q^{16} + 14 q^{17} + 4 q^{19} + 22 q^{20} - 4 q^{21} - 32 q^{22} - 8 q^{23} - 4 q^{24}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q - 8 * q^2 + 4 * q^3 + 12 * q^4 + 6 * q^5 - 4 * q^6 - 12 * q^8 + 8 * q^10 - 8 * q^11 + 24 * q^12 + 24 * q^15 + 4 * q^16 + 14 * q^17 + 4 * q^19 + 22 * q^20 - 4 * q^21 - 32 * q^22 - 8 * q^23 - 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 - 12 * q^32 - 36 * q^33 + 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 + 32 * q^43 - 36 * q^44 + 20 * q^45 - 4 * q^46 + 28 * q^48 + 36 * q^49 + 52 * q^50 - 10 * q^53 + 36 * q^54 - 16 * q^55 + 12 * q^57 + 8 * q^59 + 92 * q^60 + 32 * q^61 - 4 * q^62 - 64 * q^63 - 20 * q^64 - 32 * q^66 - 116 * q^67 - 50 * q^68 - 32 * q^69 - 32 * q^70 + 40 * q^71 - 72 * q^73 - 4 * q^75 + 16 * q^76 + 28 * q^77 + 34 * q^80 + 28 * q^81 + 34 * q^82 + 8 * q^84 - 60 * q^86 - 28 * q^87 + 32 * q^88 + 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 - 56 * q^96 - 44 * q^97 + 8 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.51805			1.07342			0.536710	−	0.843766i	$-0.319667\pi$
$2$	1.51805			1.07342			0.536710	+	0.843766i	$0.319667\pi$
$3$	0.478298	+	0.478298i	0.276145	+	0.276145i	0.831568	−	0.555423i	$-0.187444\pi$
$3$	0.478298	+	0.478298i	0.276145	+	0.276145i	−0.555423	+	0.831568i	$0.687444\pi$
$4$	0.304465			0.152233
$5$	−0.600231	+	2.15400i	−0.268431	+	0.963299i
$5$	−0.600231	+	2.15400i	−0.268431	+	0.963299i
$6$	0.726078	+	0.726078i	0.296420	+	0.296420i
$7$			2.59488i			0.980773i	0.871505	+	0.490387i	$0.163144\pi$
$7$			2.59488i			0.980773i	−0.871505	+	0.490387i	$0.836856\pi$
$8$	−2.57390			−0.910011
$9$		−	2.54246i		−	0.847487i
$10$	−0.911178	+	3.26987i	−0.288140	+	1.03403i
$11$	−3.53513	+	3.53513i	−1.06588	+	1.06588i	−0.0682120	+	0.997671i	$0.521729\pi$
$11$	−3.53513	+	3.53513i	−1.06588	+	1.06588i	−0.997671	+	0.0682120i	$0.978271\pi$
$12$	0.145625	+	0.145625i	0.0420383	+	0.0420383i
$13$		0			0
$13$		0			0
$14$			3.93915i			1.05278i
$15$	−1.31734	+	0.743165i	−0.340137	+	0.191884i
$16$	−4.51623			−1.12906
$17$	0.0578870	+	0.0578870i	0.0140397	+	0.0140397i	0.714092	−	0.700052i	$-0.246840\pi$
$17$	0.0578870	+	0.0578870i	0.0140397	+	0.0140397i	−0.700052	+	0.714092i	$0.746840\pi$
$18$		−	3.85958i		−	0.909711i
$19$	1.98490	−	1.98490i	0.455368	−	0.455368i	−0.441763	−	0.897132i	$-0.645647\pi$
$19$	1.98490	−	1.98490i	0.455368	−	0.455368i	0.897132	+	0.441763i	$0.145647\pi$
$20$	−0.182749	+	0.655819i	−0.0408640	+	0.146645i
$21$	−1.24113	+	1.24113i	−0.270836	+	0.270836i
$22$	−5.36650	+	5.36650i	−1.14414	+	1.14414i
$23$	−2.86909	+	2.86909i	−0.598247	+	0.598247i	−0.939846	−	0.341599i	$-0.889031\pi$
$23$	−2.86909	+	2.86909i	−0.598247	+	0.598247i	0.341599	+	0.939846i	$0.389031\pi$
$24$	−1.23109	−	1.23109i	−0.251295	−	0.251295i
$25$	−4.27945	−	2.58580i	−0.855889	−	0.517159i
$26$		0			0
$27$	2.65095	−	2.65095i	0.510175	−	0.510175i
$28$			0.790051i			0.149306i
$29$			4.98486i			0.925665i	0.886446	+	0.462833i	$0.153167\pi$
$29$			4.98486i			0.925665i	−0.886446	+	0.462833i	$0.846833\pi$
$30$	−1.99979	+	1.12816i	−0.365110	+	0.205973i
$31$	2.32124	+	2.32124i	0.416906	+	0.416906i	0.884136	−	0.467230i	$-0.154748\pi$
$31$	2.32124	+	2.32124i	0.416906	+	0.416906i	−0.467230	+	0.884136i	$0.654748\pi$
$32$	−1.70805			−0.301943
$33$	−3.38169			−0.588677
$34$	0.0878751	+	0.0878751i	0.0150705	+	0.0150705i
$35$	−5.58938	−	1.55753i	−0.944778	−	0.263270i
$36$		−	0.774091i		−	0.129015i
$37$			0.571501i			0.0939542i	0.998896	+	0.0469771i	$0.0149588\pi$
$37$			0.571501i			0.0939542i	−0.998896	+	0.0469771i	$0.985041\pi$
$38$	3.01318	−	3.01318i	0.488802	−	0.488802i
$39$		0			0
$40$	1.54493	−	5.54419i	0.244276	−	0.876613i
$41$	7.36174	+	7.36174i	1.14971	+	1.14971i	0.986609	+	0.163100i	$0.0521495\pi$
$41$	7.36174	+	7.36174i	1.14971	+	1.14971i	0.163100	+	0.986609i	$0.447851\pi$
$42$	−1.88409	+	1.88409i	−0.290721	+	0.290721i
$43$	−0.0967193	+	0.0967193i	−0.0147496	+	0.0147496i	−0.714443	−	0.699694i	$-0.753320\pi$
$43$	−0.0967193	+	0.0967193i	−0.0147496	+	0.0147496i	0.699694	+	0.714443i	$0.253320\pi$
$44$	−1.07633	+	1.07633i	−0.162262	+	0.162262i
$45$	5.47647	+	1.52606i	0.816384	+	0.227492i
$46$	−4.35541	+	4.35541i	−0.642170	+	0.642170i
$47$		−	2.30053i		−	0.335567i	−0.985824	−	0.167784i	$-0.946339\pi$
$47$		−	2.30053i		−	0.335567i	0.985824	−	0.167784i	$-0.0536610\pi$
$48$	−2.16010	−	2.16010i	−0.311784	−	0.311784i
$49$	0.266585			0.0380836
$50$	−6.49640	−	3.92536i	−0.918729	−	0.555130i
$51$			0.0553744i			0.00775397i
$52$		0			0
$53$	6.70735	+	6.70735i	0.921326	+	0.921326i	0.997123	−	0.0757974i	$-0.0241502\pi$
$53$	6.70735	+	6.70735i	0.921326	+	0.921326i	−0.0757974	+	0.997123i	$0.524150\pi$
$54$	4.02426	−	4.02426i	0.547633	−	0.547633i
$55$	−5.49279	−	9.73658i	−0.740647	−	1.31288i
$56$		−	6.67897i		−	0.892515i
$57$	1.89875			0.251496
$58$			7.56725i			0.993628i
$59$	−1.89634	−	1.89634i	−0.246883	−	0.246883i	0.572807	−	0.819690i	$-0.305854\pi$
$59$	−1.89634	−	1.89634i	−0.246883	−	0.246883i	−0.819690	+	0.572807i	$0.805854\pi$
$60$	−0.401085	+	0.226268i	−0.0517799	+	0.0292111i
$61$	5.48474			0.702249			0.351124	−	0.936329i	$-0.385799\pi$
$61$	5.48474			0.702249			0.351124	+	0.936329i	$0.385799\pi$
$62$	3.52374	+	3.52374i	0.447516	+	0.447516i
$63$	6.59739			0.831193
$64$	6.43957			0.804946
$65$		0			0
$66$	−5.13357			−0.631899
$67$	−15.7868			−1.92866			−0.964331	−	0.264699i	$-0.914728\pi$
$67$	−15.7868			−1.92866			−0.964331	+	0.264699i	$0.914728\pi$
$68$	0.0176246	+	0.0176246i	0.00213729	+	0.00213729i
$69$	−2.74456			−0.330406
$70$	−8.48494	−	2.36440i	−1.01414	−	0.282600i
$71$	5.43544	+	5.43544i	0.645068	+	0.645068i	0.951797	−	0.306729i	$-0.0992344\pi$
$71$	5.43544	+	5.43544i	0.645068	+	0.645068i	−0.306729	+	0.951797i	$0.599234\pi$
$72$			6.54405i			0.771223i
$73$	6.61894			0.774688			0.387344	−	0.921935i	$-0.373393\pi$
$73$	6.61894			0.774688			0.387344	+	0.921935i	$0.373393\pi$
$74$			0.867565i			0.100852i
$75$	−0.810069	−	3.28363i	−0.0935387	−	0.379161i
$76$	0.604334	−	0.604334i	0.0693219	−	0.0693219i
$77$	−9.17326	−	9.17326i	−1.04539	−	1.04539i
$78$		0			0
$79$		−	5.71054i		−	0.642486i	−0.946997	−	0.321243i	$-0.895899\pi$
$79$		−	5.71054i		−	0.642486i	0.946997	−	0.321243i	$-0.104101\pi$
$80$	2.71078	−	9.72797i	0.303075	−	1.08762i
$81$	−5.09150			−0.565722
$82$	11.1755	+	11.1755i	1.23412	+	1.23412i
$83$		−	3.70736i		−	0.406936i	−0.979082	−	0.203468i	$-0.934779\pi$
$83$		−	3.70736i		−	0.406936i	0.979082	−	0.203468i	$-0.0652213\pi$
$84$	−0.377880	+	0.377880i	−0.0412301	+	0.0412301i
$85$	−0.159434	+	0.0899431i	−0.0172931	+	0.00975570i
$86$	−0.146824	+	0.146824i	−0.0158325	+	0.0158325i
$87$	−2.38425	+	2.38425i	−0.255618	+	0.255618i
$88$	9.09908	−	9.09908i	0.969965	−	0.969965i
$89$	12.6520	+	12.6520i	1.34110	+	1.34110i	0.894962	+	0.446142i	$0.147202\pi$
$89$	12.6520	+	12.6520i	1.34110	+	1.34110i	0.446142	+	0.894962i	$0.352798\pi$
$90$	8.31353	+	2.31664i	0.876323	+	0.244195i
$91$		0			0
$92$	−0.873538	+	0.873538i	−0.0910726	+	0.0910726i
$93$			2.22048i			0.230253i
$94$		−	3.49231i		−	0.360205i
$95$	3.08409	+	5.46689i	0.316421	+	0.560891i
$96$	−0.816956	−	0.816956i	−0.0833802	−	0.0833802i
$97$	−5.36986			−0.545226			−0.272613	−	0.962124i	$-0.587888\pi$
$97$	−5.36986			−0.545226			−0.272613	+	0.962124i	$0.587888\pi$
$98$	0.404689			0.0408798
$99$	8.98794	+	8.98794i	0.903322	+	0.903322i
$100$	−1.30294	−	0.787285i	−0.130294	−	0.0787285i
$101$		−	2.51081i		−	0.249835i	−0.992167	−	0.124918i	$-0.960133\pi$
$101$		−	2.51081i		−	0.249835i	0.992167	−	0.124918i	$-0.0398666\pi$
$102$			0.0840609i			0.00832327i
$103$	−4.71738	+	4.71738i	−0.464817	+	0.464817i	−0.900230	−	0.435414i	$-0.856602\pi$
$103$	−4.71738	+	4.71738i	−0.464817	+	0.464817i	0.435414	+	0.900230i	$0.356602\pi$
$104$		0			0
$105$	−1.92843	−	3.41835i	−0.188195	−	0.333597i
$106$	10.1821	+	10.1821i	0.988971	+	0.988971i
$107$	2.56582	−	2.56582i	0.248047	−	0.248047i	−0.572122	−	0.820169i	$-0.693880\pi$
$107$	2.56582	−	2.56582i	0.248047	−	0.248047i	0.820169	+	0.572122i	$0.193880\pi$
$108$	0.807121	−	0.807121i	0.0776653	−	0.0776653i
$109$	1.58528	−	1.58528i	0.151843	−	0.151843i	−0.627098	−	0.778941i	$-0.715757\pi$
$109$	1.58528	−	1.58528i	0.151843	−	0.151843i	0.778941	+	0.627098i	$0.215757\pi$
$110$	−8.33831	−	14.7806i	−0.795026	−	1.40927i
$111$	−0.273348	+	0.273348i	−0.0259450	+	0.0259450i
$112$		−	11.7191i		−	1.10735i
$113$	4.04975	+	4.04975i	0.380968	+	0.380968i	0.871451	−	0.490483i	$-0.163179\pi$
$113$	4.04975	+	4.04975i	0.380968	+	0.380968i	−0.490483	+	0.871451i	$0.663179\pi$
$114$	2.88239			0.269961
$115$	−4.45791	−	7.90214i	−0.415702	−	0.736878i
$116$			1.51772i			0.140916i
$117$		0			0
$118$	−2.87873	−	2.87873i	−0.265009	−	0.265009i
$119$	−0.150210	+	0.150210i	−0.0137697	+	0.0137697i
$120$	3.39071	−	1.91283i	0.309528	−	0.174617i
$121$		−	13.9943i		−	1.27221i
$122$	8.32609			0.753809
$123$			7.04220i			0.634974i
$124$	0.706736	+	0.706736i	0.0634667	+	0.0634667i
$125$	8.13846	−	7.66586i	0.727926	−	0.685655i
$126$	10.0151			0.892220
$127$	−0.575918	−	0.575918i	−0.0511044	−	0.0511044i	0.681093	−	0.732197i	$-0.261505\pi$
$127$	−0.575918	−	0.575918i	−0.0511044	−	0.0511044i	−0.732197	+	0.681093i	$0.761505\pi$
$128$	13.1917			1.16599
$129$	−0.0925213			−0.00814605
$130$		0			0
$131$	−16.1062			−1.40721			−0.703604	−	0.710592i	$-0.748427\pi$
$131$	−16.1062			−1.40721			−0.703604	+	0.710592i	$0.748427\pi$
$132$	−1.02961			−0.0896159
$133$	5.15059	+	5.15059i	0.446613	+	0.446613i
$134$	−23.9651			−2.07027
$135$	4.11897	+	7.30133i	0.354504	+	0.628398i
$136$	−0.148995	−	0.148995i	−0.0127762	−	0.0127762i
$137$		−	19.2374i		−	1.64356i	−0.569802	−	0.821782i	$-0.692980\pi$
$137$		−	19.2374i		−	1.64356i	0.569802	−	0.821782i	$-0.307020\pi$
$138$	−4.16637			−0.354665
$139$		−	15.8490i		−	1.34430i	−0.740417	−	0.672148i	$-0.765372\pi$
$139$		−	15.8490i		−	1.34430i	0.740417	−	0.672148i	$-0.234628\pi$
$140$	−1.70177	−	0.474213i	−0.143826	−	0.0400783i
$141$	1.10034	−	1.10034i	0.0926653	−	0.0926653i
$142$	8.25125	+	8.25125i	0.692430	+	0.692430i
$143$		0			0
$144$			11.4823i			0.956862i
$145$	−10.7374	−	2.99207i	−0.891692	−	0.248478i
$146$	10.0479			0.831566
$147$	0.127507	+	0.127507i	0.0105166	+	0.0105166i
$148$			0.174002i			0.0143029i
$149$	1.01843	−	1.01843i	0.0834332	−	0.0834332i	−0.664159	−	0.747592i	$-0.731210\pi$
$149$	1.01843	−	1.01843i	0.0834332	−	0.0834332i	0.747592	+	0.664159i	$0.231210\pi$
$150$	−1.22972	−	4.98470i	−0.100406	−	0.406999i
$151$	−13.9253	+	13.9253i	−1.13322	+	1.13322i	−0.143585	+	0.989638i	$0.545863\pi$
$151$	−13.9253	+	13.9253i	−1.13322	+	1.13322i	−0.989638	+	0.143585i	$0.954137\pi$
$152$	−5.10895	+	5.10895i	−0.414390	+	0.414390i
$153$	0.147175	−	0.147175i	0.0118984	−	0.0118984i
$154$	−13.9254	−	13.9254i	−1.12214	−	1.12214i
$155$	−6.39322	+	3.60667i	−0.513516	+	0.289695i
$156$		0			0
$157$	4.54644	−	4.54644i	0.362845	−	0.362845i	−0.502014	−	0.864859i	$-0.667408\pi$
$157$	4.54644	−	4.54644i	0.362845	−	0.362845i	0.864859	+	0.502014i	$0.167408\pi$
$158$		−	8.66887i		−	0.689658i
$159$			6.41623i			0.508840i
$160$	1.02522	−	3.67914i	0.0810510	−	0.290861i
$161$	−7.44495	−	7.44495i	−0.586744	−	0.586744i
$162$	−7.72914			−0.607258
$163$	13.1358			1.02887			0.514437	−	0.857528i	$-0.328001\pi$
$163$	13.1358			1.02887			0.514437	+	0.857528i	$0.328001\pi$
$164$	2.24139	+	2.24139i	0.175023	+	0.175023i
$165$	2.02980	−	7.28417i	0.158019	−	0.567072i
$166$		−	5.62795i		−	0.436814i
$167$			3.28516i			0.254213i	0.991889	+	0.127107i	$0.0405691\pi$
$167$			3.28516i			0.254213i	−0.991889	+	0.127107i	$0.959431\pi$
$168$	3.19454	−	3.19454i	0.246464	−	0.246464i
$169$		0			0
$170$	−0.242028	+	0.136538i	−0.0185627	+	0.0104720i
$171$	−5.04654	−	5.04654i	−0.385919	−	0.385919i
$172$	−0.0294477	+	0.0294477i	−0.00224536	+	0.00224536i
$173$	2.99677	−	2.99677i	0.227840	−	0.227840i	−0.583950	−	0.811790i	$-0.698493\pi$
$173$	2.99677	−	2.99677i	0.227840	−	0.227840i	0.811790	+	0.583950i	$0.198493\pi$
$174$	−3.61940	+	3.61940i	−0.274386	+	0.274386i
$175$	6.70984	−	11.1047i	0.507216	−	0.839433i
$176$	15.9655	−	15.9655i	1.20344	−	1.20344i
$177$		−	1.81403i		−	0.136351i
$178$	19.2062	+	19.2062i	1.43957	+	1.43957i
$179$	−13.9617			−1.04354			−0.521772	−	0.853085i	$-0.674729\pi$
$179$	−13.9617			−1.04354			−0.521772	+	0.853085i	$0.674729\pi$
$180$	1.66739	+	0.464633i	0.124280	+	0.0346317i
$181$			8.64775i			0.642782i	0.946947	+	0.321391i	$0.104150\pi$
$181$			8.64775i			0.642782i	−0.946947	+	0.321391i	$0.895850\pi$
$182$		0			0
$183$	2.62334	+	2.62334i	0.193923	+	0.193923i
$184$	7.38475	−	7.38475i	0.544411	−	0.544411i
$185$	−1.23101	−	0.343032i	−0.0905060	−	0.0252202i
$186$			3.37080i			0.247159i
$187$	−0.409276			−0.0299292
$188$		−	0.700432i		−	0.0510842i
$189$	6.87890	+	6.87890i	0.500366	+	0.500366i
$190$	4.68179	+	8.29899i	0.339653	+	0.602072i
$191$	16.9129			1.22378			0.611889	−	0.790944i	$-0.290410\pi$
$191$	16.9129			1.22378			0.611889	+	0.790944i	$0.290410\pi$
$192$	3.08003	+	3.08003i	0.222282	+	0.222282i
$193$	−8.55560			−0.615845			−0.307923	−	0.951411i	$-0.599634\pi$
$193$	−8.55560			−0.615845			−0.307923	+	0.951411i	$0.599634\pi$
$194$	−8.15169			−0.585257
$195$		0			0
$196$	0.0811660			0.00579757
$197$	−7.65684			−0.545527			−0.272764	−	0.962081i	$-0.587938\pi$
$197$	−7.65684			−0.545527			−0.272764	+	0.962081i	$0.587938\pi$
$198$	13.6441	+	13.6441i	0.969645	+	0.969645i
$199$	15.3276			1.08654			0.543272	−	0.839557i	$-0.317185\pi$
$199$	15.3276			1.08654			0.543272	+	0.839557i	$0.317185\pi$
$200$	11.0149	+	6.65558i	0.778869	+	0.470621i
$201$	−7.55078	−	7.55078i	−0.532591	−	0.532591i
$202$		−	3.81153i		−	0.268178i
$203$	−12.9351			−0.907868
$204$			0.0168596i			0.00118041i
$205$	−20.2759	+	11.4385i	−1.41613	+	0.798896i
$206$	−7.16120	+	7.16120i	−0.498944	+	0.498944i
$207$	7.29455	+	7.29455i	0.507006	+	0.507006i
$208$		0			0
$209$			14.0338i			0.970739i
$210$	−2.92744	−	5.18922i	−0.202013	−	0.358090i
$211$	19.8358			1.36555			0.682775	−	0.730629i	$-0.260773\pi$
$211$	19.8358			1.36555			0.682775	+	0.730629i	$0.260773\pi$
$212$	2.04216	+	2.04216i	0.140256	+	0.140256i
$213$			5.19952i			0.356265i
$214$	3.89503	−	3.89503i	0.266259	−	0.266259i
$215$	−0.150280	−	0.266388i	−0.0102490	−	0.0181675i
$216$	−6.82328	+	6.82328i	−0.464265	+	0.464265i
$217$	−6.02333	+	6.02333i	−0.408891	+	0.408891i
$218$	2.40654	−	2.40654i	0.162991	−	0.162991i
$219$	3.16582	+	3.16582i	0.213927	+	0.213927i
$220$	−1.67236	−	2.96445i	−0.112751	−	0.199863i
$221$		0			0
$222$	−0.414955	+	0.414955i	−0.0278499	+	0.0278499i
$223$			18.9731i			1.27053i	0.772294	+	0.635265i	$0.219109\pi$
$223$			18.9731i			1.27053i	−0.772294	+	0.635265i	$0.780891\pi$
$224$		−	4.43218i		−	0.296138i
$225$	−6.57429	+	10.8803i	−0.438286	+	0.725355i
$226$	6.14771	+	6.14771i	0.408939	+	0.408939i
$227$	−26.9587			−1.78931			−0.894656	−	0.446755i	$-0.852579\pi$
$227$	−26.9587			−1.78931			−0.894656	+	0.446755i	$0.852579\pi$
$228$	0.578104			0.0382858
$229$	−11.1801	−	11.1801i	−0.738799	−	0.738799i	0.233547	−	0.972346i	$-0.424967\pi$
$229$	−11.1801	−	11.1801i	−0.738799	−	0.738799i	−0.972346	+	0.233547i	$0.924967\pi$
$230$	−6.76731	−	11.9958i	−0.446223	−	0.790981i
$231$		−	8.77510i		−	0.577359i
$232$		−	12.8305i		−	0.842366i
$233$	−6.75797	+	6.75797i	−0.442729	+	0.442729i	−0.892928	−	0.450199i	$-0.851353\pi$
$233$	−6.75797	+	6.75797i	−0.442729	+	0.442729i	0.450199	+	0.892928i	$0.351353\pi$
$234$		0			0
$235$	4.95535	+	1.38085i	0.323251	+	0.0900767i
$236$	−0.577370	−	0.577370i	−0.0375836	−	0.0375836i
$237$	2.73134	−	2.73134i	0.177420	−	0.177420i
$238$	−0.228026	+	0.228026i	−0.0147807	+	0.0147807i
$239$	1.98766	−	1.98766i	0.128571	−	0.128571i	−0.639893	−	0.768464i	$-0.721021\pi$
$239$	1.98766	−	1.98766i	0.128571	−	0.128571i	0.768464	+	0.639893i	$0.221021\pi$
$240$	5.94943	−	3.35631i	0.384034	−	0.216649i
$241$	−1.94097	+	1.94097i	−0.125029	+	0.125029i	−0.766852	−	0.641824i	$-0.778178\pi$
$241$	−1.94097	+	1.94097i	−0.125029	+	0.125029i	0.641824	+	0.766852i	$0.278178\pi$
$242$		−	21.2441i		−	1.36562i
$243$	−10.3881	−	10.3881i	−0.666397	−	0.666397i
$244$	1.66991			0.106905
$245$	−0.160013	+	0.574225i	−0.0102228	+	0.0366859i
$246$			10.6904i			0.681595i
$247$		0			0
$248$	−5.97463	−	5.97463i	−0.379389	−	0.379389i
$249$	1.77322	−	1.77322i	0.112374	−	0.112374i
$250$	12.3546	−	11.6371i	0.781371	−	0.735997i
$251$		−	2.83379i		−	0.178867i	−0.995993	−	0.0894337i	$-0.971494\pi$
$251$		−	2.83379i		−	0.178867i	0.995993	−	0.0894337i	$-0.0285057\pi$
$252$	2.00868			0.126535
$253$		−	20.2852i		−	1.27532i
$254$	−0.874270	−	0.874270i	−0.0548566	−	0.0548566i
$255$	−0.119277	−	0.0332374i	−0.00746939	−	0.00208141i
$256$	7.14642			0.446651
$257$	14.1859	+	14.1859i	0.884895	+	0.884895i	0.994027	−	0.109132i	$-0.0348072\pi$
$257$	14.1859	+	14.1859i	0.884895	+	0.884895i	−0.109132	+	0.994027i	$0.534807\pi$
$258$	−0.140452			−0.00874414
$259$	−1.48298			−0.0921478
$260$		0			0
$261$	12.6738			0.784490
$262$	−24.4500			−1.51053
$263$	6.66222	+	6.66222i	0.410810	+	0.410810i	0.882021	−	0.471210i	$-0.156183\pi$
$263$	6.66222	+	6.66222i	0.410810	+	0.410810i	−0.471210	+	0.882021i	$0.656183\pi$
$264$	8.70414			0.535703
$265$	−18.4736	+	10.4217i	−1.13482	+	0.640199i
$266$	7.81884	+	7.81884i	0.479404	+	0.479404i
$267$			12.1028i			0.740679i
$268$	−4.80653			−0.293605
$269$			3.21488i			0.196015i	0.995186	+	0.0980075i	$0.0312469\pi$
$269$			3.21488i			0.196015i	−0.995186	+	0.0980075i	$0.968753\pi$
$270$	6.25278	+	11.0838i	0.380532	+	0.674536i
$271$	10.7387	−	10.7387i	0.652332	−	0.652332i	−0.301222	−	0.953554i	$-0.597395\pi$
$271$	10.7387	−	10.7387i	0.652332	−	0.652332i	0.953554	+	0.301222i	$0.0973945\pi$
$272$	−0.261431	−	0.261431i	−0.0158516	−	0.0158516i
$273$		0			0
$274$		−	29.2033i		−	1.76424i
$275$	24.2695	−	5.98728i	1.46351	−	0.361047i
$276$	−0.835623			−0.0502986
$277$	7.54121	+	7.54121i	0.453107	+	0.453107i	0.896385	−	0.443277i	$-0.146184\pi$
$277$	7.54121	+	7.54121i	0.453107	+	0.453107i	−0.443277	+	0.896385i	$0.646184\pi$
$278$		−	24.0595i		−	1.44300i
$279$	5.90165	−	5.90165i	0.353323	−	0.353323i
$280$	14.3865	+	4.00892i	0.859759	+	0.239579i
$281$	12.7630	−	12.7630i	0.761379	−	0.761379i	−0.215193	−	0.976572i	$-0.569038\pi$
$281$	12.7630	−	12.7630i	0.761379	−	0.761379i	0.976572	+	0.215193i	$0.0690380\pi$
$282$	1.67037	−	1.67037i	0.0994689	−	0.0994689i
$283$	−4.07125	+	4.07125i	−0.242010	+	0.242010i	−0.817681	−	0.575671i	$-0.804741\pi$
$283$	−4.07125	+	4.07125i	−0.242010	+	0.242010i	0.575671	+	0.817681i	$0.304741\pi$
$284$	1.65490	+	1.65490i	0.0982004	+	0.0982004i
$285$	−1.13969	+	4.08991i	−0.0675093	+	0.242266i
$286$		0			0
$287$	−19.1028	+	19.1028i	−1.12760	+	1.12760i
$288$			4.34265i			0.255893i
$289$		−	16.9933i		−	0.999606i
$290$	−16.2999	−	4.54209i	−0.957161	−	0.266721i
$291$	−2.56839	−	2.56839i	−0.150562	−	0.150562i
$292$	2.01524			0.117933
$293$	3.19607			0.186717			0.0933583	−	0.995633i	$-0.470240\pi$
$293$	3.19607			0.186717			0.0933583	+	0.995633i	$0.470240\pi$
$294$	0.193562	+	0.193562i	0.0112888	+	0.0112888i
$295$	5.22297	−	2.94648i	0.304093	−	0.171551i
$296$		−	1.47099i		−	0.0854994i
$297$			18.7429i			1.08757i
$298$	1.54603	−	1.54603i	0.0895590	−	0.0895590i
$299$		0			0
$300$	−0.246638	−	0.999751i	−0.0142396	−	0.0577207i
$301$	−0.250975	−	0.250975i	−0.0144660	−	0.0144660i
$302$	−21.1392	+	21.1392i	−1.21643	+	1.21643i
$303$	1.20092	−	1.20092i	0.0689908	−	0.0689908i
$304$	−8.96429	+	8.96429i	−0.514137	+	0.514137i
$305$	−3.29211	+	11.8141i	−0.188506	+	0.676476i
$306$	0.223419	−	0.223419i	0.0127720	−	0.0127720i
$307$			24.2740i			1.38539i	0.721231	+	0.692695i	$0.243577\pi$
$307$			24.2740i			1.38539i	−0.721231	+	0.692695i	$0.756423\pi$
$308$	−2.79294	−	2.79294i	−0.159142	−	0.159142i
$309$	−4.51262			−0.256714
$310$	−9.70521	+	5.47509i	−0.551219	+	0.310964i
$311$		−	16.9053i		−	0.958614i	−0.877647	−	0.479307i	$-0.840888\pi$
$311$		−	16.9053i		−	0.958614i	0.877647	−	0.479307i	$-0.159112\pi$
$312$		0			0
$313$	−8.40997	−	8.40997i	−0.475359	−	0.475359i	0.428285	−	0.903644i	$-0.359118\pi$
$313$	−8.40997	−	8.40997i	−0.475359	−	0.475359i	−0.903644	+	0.428285i	$0.859118\pi$
$314$	6.90170	−	6.90170i	0.389486	−	0.389486i
$315$	−3.95996	+	14.2108i	−0.223118	+	0.800687i
$316$		−	1.73866i		−	0.0978074i
$317$	−11.9484			−0.671087			−0.335543	−	0.942025i	$-0.608920\pi$
$317$	−11.9484			−0.671087			−0.335543	+	0.942025i	$0.608920\pi$
$318$			9.74013i			0.546199i
$319$	−17.6221	−	17.6221i	−0.986651	−	0.986651i
$320$	−3.86523	+	13.8708i	−0.216073	+	0.775403i
$321$	2.45445			0.136994
$322$	−11.3018	−	11.3018i	−0.629824	−	0.629824i
$323$	0.229800			0.0127864
$324$	−1.55018			−0.0861214
$325$		0			0
$326$	19.9407			1.10442
$327$	1.51648			0.0838613
$328$	−18.9484	−	18.9484i	−1.04625	−	1.04625i
$329$	5.96961			0.329115
$330$	3.08133	−	11.0577i	0.169621	−	0.608707i
$331$	15.1666	+	15.1666i	0.833631	+	0.833631i	0.988011	−	0.154380i	$-0.0493381\pi$
$331$	15.1666	+	15.1666i	0.833631	+	0.833631i	−0.154380	+	0.988011i	$0.549338\pi$
$332$		−	1.12876i		−	0.0619489i
$333$	1.45302			0.0796250
$334$			4.98703i			0.272878i
$335$	9.47571	−	34.0048i	0.517713	−	1.85788i
$336$	5.60522	−	5.60522i	0.305790	−	0.305790i
$337$	−14.1264	−	14.1264i	−0.769514	−	0.769514i	0.208507	−	0.978021i	$-0.433140\pi$
$337$	−14.1264	−	14.1264i	−0.769514	−	0.769514i	−0.978021	+	0.208507i	$0.933140\pi$
$338$		0			0
$339$			3.87397i			0.210405i
$340$	−0.0485421	+	0.0273845i	−0.00263257	+	0.00148514i
$341$	−16.4118			−0.888746
$342$	−7.66089	−	7.66089i	−0.414253	−	0.414253i
$343$			18.8559i			1.01812i
$344$	0.248946	−	0.248946i	0.0134223	−	0.0134223i
$345$	1.64737	−	5.91179i	0.0886914	−	0.318280i
$346$	4.54924	−	4.54924i	0.244569	−	0.244569i
$347$	−17.4159	+	17.4159i	−0.934936	+	0.934936i	−0.998009	−	0.0630727i	$-0.979910\pi$
$347$	−17.4159	+	17.4159i	−0.934936	+	0.934936i	0.0630727	+	0.998009i	$0.479910\pi$
$348$	−0.725920	+	0.725920i	−0.0389134	+	0.0389134i
$349$	−19.2668	−	19.2668i	−1.03133	−	1.03133i	−0.999493	−	0.0318358i	$-0.989865\pi$
$349$	−19.2668	−	19.2668i	−1.03133	−	1.03133i	−0.0318358	−	0.999493i	$-0.510135\pi$
$350$	10.1858	−	16.8574i	0.544456	−	0.901065i
$351$		0			0
$352$	6.03818	−	6.03818i	0.321836	−	0.321836i
$353$			8.79926i			0.468337i	0.972196	+	0.234169i	$0.0752368\pi$
$353$			8.79926i			0.468337i	−0.972196	+	0.234169i	$0.924763\pi$
$354$		−	2.75379i		−	0.146362i
$355$	−14.9705	+	8.44543i	−0.794550	+	0.448237i
$356$	3.85208	+	3.85208i	0.204160	+	0.204160i
$357$	−0.143690			−0.00760489
$358$	−21.1945			−1.12016
$359$	11.1256	+	11.1256i	0.587186	+	0.587186i	0.936868	−	0.349683i	$-0.113711\pi$
$359$	11.1256	+	11.1256i	0.587186	+	0.587186i	−0.349683	+	0.936868i	$0.613711\pi$
$360$	−14.0959	−	3.92794i	−0.742918	−	0.207020i
$361$			11.1203i			0.585279i
$362$			13.1277i			0.689976i
$363$	6.69346	−	6.69346i	0.351316	−	0.351316i
$364$		0			0
$365$	−3.97289	+	14.2572i	−0.207951	+	0.746256i
$366$	3.98235	+	3.98235i	0.208161	+	0.208161i
$367$	7.76295	−	7.76295i	0.405223	−	0.405223i	−0.474846	−	0.880069i	$-0.657496\pi$
$367$	7.76295	−	7.76295i	0.405223	−	0.405223i	0.880069	+	0.474846i	$0.157496\pi$
$368$	12.9575	−	12.9575i	0.675455	−	0.675455i
$369$	18.7169	−	18.7169i	0.974365	−	0.974365i
$370$	−1.86874	−	0.520739i	−0.0971510	−	0.0270719i
$371$	−17.4048	+	17.4048i	−0.903612	+	0.903612i
$372$			0.676060i			0.0350521i
$373$	7.48104	+	7.48104i	0.387354	+	0.387354i	0.873742	−	0.486389i	$-0.161686\pi$
$373$	7.48104	+	7.48104i	0.387354	+	0.387354i	−0.486389	+	0.873742i	$0.661686\pi$
$374$	−0.621300			−0.0321267
$375$	7.55917	+	0.226045i	0.390354	+	0.0116729i
$376$			5.92134i			0.305370i
$377$		0			0
$378$	10.4425	+	10.4425i	0.537104	+	0.537104i
$379$	−6.93105	+	6.93105i	−0.356024	+	0.356024i	−0.862345	−	0.506321i	$-0.831005\pi$
$379$	−6.93105	+	6.93105i	−0.356024	+	0.356024i	0.506321	+	0.862345i	$0.331005\pi$
$380$	0.938997	+	1.66448i	0.0481695	+	0.0853859i
$381$		−	0.550921i		−	0.0282245i
$382$	25.6746			1.31363
$383$			26.0567i			1.33144i	0.746204	+	0.665718i	$0.231874\pi$
$383$			26.0567i			1.33144i	−0.746204	+	0.665718i	$0.768126\pi$
$384$	6.30954	+	6.30954i	0.321982	+	0.321982i
$385$	25.2653	−	14.2531i	1.28764	−	0.726407i
$386$	−12.9878			−0.661061
$387$	0.245905	+	0.245905i	0.0125001	+	0.0125001i
$388$	−1.63493			−0.0830012
$389$	32.4888			1.64725			0.823623	−	0.567138i	$-0.191950\pi$
$389$	32.4888			1.64725			0.823623	+	0.567138i	$0.191950\pi$
$390$		0			0
$391$	−0.332166			−0.0167983
$392$	−0.686164			−0.0346565
$393$	−7.70358	−	7.70358i	−0.388594	−	0.388594i
$394$	−11.6234			−0.585580
$395$	12.3005	+	3.42764i	0.618906	+	0.172463i
$396$	2.73652	+	2.73652i	0.137515	+	0.137515i
$397$			24.1854i			1.21383i	0.794767	+	0.606914i	$0.207593\pi$
$397$			24.1854i			1.21383i	−0.794767	+	0.606914i	$0.792407\pi$
$398$	23.2680			1.16632
$399$			4.92704i			0.246660i
$400$	19.3270	+	11.6781i	0.966348	+	0.583903i
$401$	23.2202	−	23.2202i	1.15956	−	1.15956i	0.174992	−	0.984570i	$-0.444010\pi$
$401$	23.2202	−	23.2202i	1.15956	−	1.15956i	0.984570	−	0.174992i	$-0.0559899\pi$
$402$	−11.4624	−	11.4624i	−0.571695	−	0.571695i
$403$		0			0
$404$		−	0.764454i		−	0.0380330i
$405$	3.05608	−	10.9671i	0.151858	−	0.544960i
$406$	−19.6361			−0.974524
$407$	−2.02033	−	2.02033i	−0.100144	−	0.100144i
$408$		−	0.142528i		−	0.00705620i
$409$	−9.87122	+	9.87122i	−0.488101	+	0.488101i	−0.907706	−	0.419606i	$-0.862168\pi$
$409$	−9.87122	+	9.87122i	−0.488101	+	0.488101i	0.419606	+	0.907706i	$0.362168\pi$
$410$	−30.7798	+	17.3641i	−1.52011	+	0.857552i
$411$	9.20122	−	9.20122i	0.453863	−	0.453863i
$412$	−1.43628	+	1.43628i	−0.0707603	+	0.0707603i
$413$	4.92078	−	4.92078i	0.242136	−	0.242136i
$414$	11.0735	+	11.0735i	0.544231	+	0.544231i
$415$	7.98567	+	2.22527i	0.392001	+	0.109234i
$416$		0			0
$417$	7.58055	−	7.58055i	0.371221	−	0.371221i
$418$			21.3040i			1.04201i
$419$		−	2.21980i		−	0.108444i	−0.998529	−	0.0542221i	$-0.982732\pi$
$419$		−	2.21980i		−	0.108444i	0.998529	−	0.0542221i	$-0.0172679\pi$
$420$	−0.587139	−	1.04077i	−0.0286494	−	0.0507843i
$421$	−24.4795	−	24.4795i	−1.19306	−	1.19306i	−0.976204	−	0.216853i	$-0.930421\pi$
$421$	−24.4795	−	24.4795i	−1.19306	−	1.19306i	−0.216853	−	0.976204i	$-0.569579\pi$
$422$	30.1116			1.46581
$423$	−5.84901			−0.284389
$424$	−17.2641	−	17.2641i	−0.838417	−	0.838417i
$425$	−0.0980403	−	0.397408i	−0.00475565	−	0.0192771i
$426$			7.89311i			0.382423i
$427$			14.2323i			0.688747i
$428$	0.781202	−	0.781202i	0.0377608	−	0.0377608i
$429$		0			0
$430$	−0.228132	−	0.404389i	−0.0110015	−	0.0195014i
$431$	1.16851	+	1.16851i	0.0562851	+	0.0562851i	0.734689	−	0.678404i	$-0.237328\pi$
$431$	1.16851	+	1.16851i	0.0562851	+	0.0562851i	−0.678404	+	0.734689i	$0.737328\pi$
$432$	−11.9723	+	11.9723i	−0.576017	+	0.576017i
$433$	10.4765	−	10.4765i	0.503466	−	0.503466i	−0.409047	−	0.912513i	$-0.634139\pi$
$433$	10.4765	−	10.4765i	0.503466	−	0.503466i	0.912513	+	0.409047i	$0.134139\pi$
$434$	−9.14370	+	9.14370i	−0.438912	+	0.438912i
$435$	−3.70457	−	6.56677i	−0.177621	−	0.314853i
$436$	0.482664	−	0.482664i	0.0231154	−	0.0231154i
$437$			11.3897i			0.544845i
$438$	4.80587	+	4.80587i	0.229633	+	0.229633i
$439$	21.8725			1.04392			0.521959	−	0.852970i	$-0.325201\pi$
$439$	21.8725			1.04392			0.521959	+	0.852970i	$0.325201\pi$
$440$	14.1379	+	25.0610i	0.673997	+	1.19474i
$441$		−	0.677783i		−	0.0322754i
$442$		0			0
$443$	−6.14972	−	6.14972i	−0.292182	−	0.292182i	0.545760	−	0.837942i	$-0.316241\pi$
$443$	−6.14972	−	6.14972i	−0.292182	−	0.292182i	−0.837942	+	0.545760i	$0.816241\pi$
$444$	−0.0832249	+	0.0832249i	−0.00394968	+	0.00394968i
$445$	−34.8464	+	19.6582i	−1.65188	+	0.931890i
$446$			28.8020i			1.36381i
$447$	0.974228			0.0460794
$448$			16.7099i			0.789469i
$449$	3.30563	+	3.30563i	0.156002	+	0.156002i	0.780793	−	0.624790i	$-0.214816\pi$
$449$	3.30563	+	3.30563i	0.156002	+	0.156002i	−0.624790	+	0.780793i	$0.714816\pi$
$450$	−9.98008	+	16.5168i	−0.470465	+	0.778612i
$451$	−52.0494			−2.45091
$452$	1.23301	+	1.23301i	0.0579958	+	0.0579958i
$453$	−13.3209			−0.625869
$454$	−40.9246			−1.92069
$455$		0			0
$456$	−4.88720			−0.228864
$457$	30.0361			1.40503			0.702514	−	0.711670i	$-0.252061\pi$
$457$	30.0361			1.40503			0.702514	+	0.711670i	$0.252061\pi$
$458$	−16.9718	−	16.9718i	−0.793042	−	0.793042i
$459$	0.306911			0.0143254
$460$	−1.35728	−	2.40593i	−0.0632834	−	0.112177i
$461$	−1.85792	−	1.85792i	−0.0865318	−	0.0865318i	0.662516	−	0.749048i	$-0.269489\pi$
$461$	−1.85792	−	1.85792i	−0.0865318	−	0.0865318i	−0.749048	+	0.662516i	$0.769489\pi$
$462$		−	13.3210i		−	0.619749i
$463$	−25.1475			−1.16870			−0.584352	−	0.811500i	$-0.698651\pi$
$463$	−25.1475			−1.16870			−0.584352	+	0.811500i	$0.698651\pi$
$464$		−	22.5128i		−	1.04513i
$465$	−4.78293	−	1.33280i	−0.221803	−	0.0618073i
$466$	−10.2589	+	10.2589i	−0.475235	+	0.475235i
$467$	14.9907	+	14.9907i	0.693688	+	0.693688i	0.963041	−	0.269354i	$-0.0868100\pi$
$467$	14.9907	+	14.9907i	0.693688	+	0.693688i	−0.269354	+	0.963041i	$0.586810\pi$
$468$		0			0
$469$		−	40.9648i		−	1.89158i
$470$	7.52245	+	2.09619i	0.346985	+	0.0966902i
$471$	4.34910			0.200396
$472$	4.88100	+	4.88100i	0.224666	+	0.224666i
$473$		−	0.683832i		−	0.0314426i
$474$	4.14630	−	4.14630i	0.190446	−	0.190446i
$475$	−13.6268	+	3.36173i	−0.625243	+	0.154247i
$476$	−0.0457337	+	0.0457337i	−0.00209620	+	0.00209620i
$477$	17.0532	−	17.0532i	0.780812	−	0.780812i
$478$	3.01736	−	3.01736i	0.138011	−	0.138011i
$479$	−1.61898	−	1.61898i	−0.0739730	−	0.0739730i	0.669152	−	0.743125i	$-0.266657\pi$
$479$	−1.61898	−	1.61898i	−0.0739730	−	0.0739730i	−0.743125	+	0.669152i	$0.766657\pi$
$480$	2.25009	−	1.26936i	0.102702	−	0.0579382i
$481$		0			0
$482$	−2.94648	+	2.94648i	−0.134208	+	0.134208i
$483$		−	7.12181i		−	0.324054i
$484$		−	4.26079i		−	0.193672i
$485$	3.22315	−	11.5667i	0.146356	−	0.525216i
$486$	−15.7696	−	15.7696i	−0.715324	−	0.715324i
$487$	5.56643			0.252239			0.126119	−	0.992015i	$-0.459748\pi$
$487$	5.56643			0.252239			0.126119	+	0.992015i	$0.459748\pi$
$488$	−14.1172			−0.639054
$489$	6.28282	+	6.28282i	0.284119	+	0.284119i
$490$	−0.242907	+	0.871701i	−0.0109734	+	0.0393794i
$491$		−	6.10997i		−	0.275739i	−0.990450	−	0.137869i	$-0.955975\pi$
$491$		−	6.10997i		−	0.275739i	0.990450	−	0.137869i	$-0.0440255\pi$
$492$			2.14411i			0.0966638i
$493$	−0.288558	+	0.288558i	−0.0129960	+	0.0129960i
$494$		0			0
$495$	−24.7549	+	13.9652i	−1.11265	+	0.627689i
$496$	−10.4832	−	10.4832i	−0.470711	−	0.470711i
$497$	−14.1043	+	14.1043i	−0.632666	+	0.632666i
$498$	2.69184	−	2.69184i	0.120624	−	0.120624i
$499$	−6.22738	+	6.22738i	−0.278776	+	0.278776i	−0.832620	−	0.553844i	$-0.813160\pi$
$499$	−6.22738	+	6.22738i	−0.278776	+	0.278776i	0.553844	+	0.832620i	$0.313160\pi$
$500$	2.47788	−	2.33399i	0.110814	−	0.104379i
$501$	−1.57129	+	1.57129i	−0.0701999	+	0.0701999i
$502$		−	4.30183i		−	0.192000i
$503$	2.59944	+	2.59944i	0.115903	+	0.115903i	0.762680	−	0.646776i	$-0.223883\pi$
$503$	2.59944	+	2.59944i	0.115903	+	0.115903i	−0.646776	+	0.762680i	$0.723883\pi$
$504$	−16.9810			−0.756395
$505$	5.40829	+	1.50707i	0.240666	+	0.0670635i
$506$		−	30.7939i		−	1.36896i
$507$		0			0
$508$	−0.175347	−	0.175347i	−0.00777976	−	0.00777976i
$509$	−7.92432	+	7.92432i	−0.351239	+	0.351239i	−0.860571	−	0.509331i	$-0.829893\pi$
$509$	−7.92432	+	7.92432i	−0.351239	+	0.351239i	0.509331	+	0.860571i	$0.329893\pi$
$510$	−0.181067	−	0.0504560i	−0.00801780	−	0.00223423i
$511$			17.1754i			0.759793i
$512$	−15.5347			−0.686544
$513$		−	10.5238i		−	0.464635i
$514$	21.5349	+	21.5349i	0.949865	+	0.949865i
$515$	−7.32972	−	12.9927i	−0.322986	−	0.572529i
$516$	−0.0281695			−0.00124009
$517$	8.13269	+	8.13269i	0.357675	+	0.357675i
$518$	−2.25123			−0.0989133
$519$	2.86670			0.125834
$520$		0			0
$521$	35.9604			1.57545			0.787726	−	0.616026i	$-0.211258\pi$
$521$	35.9604			1.57545			0.787726	+	0.616026i	$0.211258\pi$
$522$	19.2394			0.842088
$523$	−5.93427	−	5.93427i	−0.259487	−	0.259487i	0.565358	−	0.824846i	$-0.308738\pi$
$523$	−5.93427	−	5.93427i	−0.259487	−	0.259487i	−0.824846	+	0.565358i	$0.808738\pi$
$524$	−4.90379			−0.214223
$525$	8.52064	−	2.10203i	0.371871	−	0.0917403i
$526$	10.1136	+	10.1136i	0.440972	+	0.440972i
$527$			0.268739i			0.0117064i
$528$	15.2725			0.664651
$529$			6.53664i			0.284202i
$530$	−28.0438	+	15.8206i	−1.21814	+	0.687203i
$531$	−4.82138	+	4.82138i	−0.209230	+	0.209230i
$532$	1.56818	+	1.56818i	0.0679891	+	0.0679891i
$533$		0			0
$534$			18.3726i			0.795061i
$535$	3.98669	+	7.06686i	0.172360	+	0.305527i
$536$	40.6336			1.75510
$537$	−6.67783	−	6.67783i	−0.288170	−	0.288170i
$538$			4.88034i			0.210407i
$539$	−0.942415	+	0.942415i	−0.0405927	+	0.0405927i
$540$	1.25408	+	2.22300i	0.0539671	+	0.0956627i
$541$	−4.13066	+	4.13066i	−0.177591	+	0.177591i	−0.790305	−	0.612714i	$-0.790078\pi$
$541$	−4.13066	+	4.13066i	−0.177591	+	0.177591i	0.612714	+	0.790305i	$0.290078\pi$
$542$	16.3019	−	16.3019i	0.700227	−	0.700227i
$543$	−4.13620	+	4.13620i	−0.177501	+	0.177501i
$544$	−0.0988737	−	0.0988737i	−0.00423917	−	0.00423917i
$545$	2.46317	+	4.36624i	0.105511	+	0.187029i
$546$		0			0
$547$	−7.90229	+	7.90229i	−0.337877	+	0.337877i	−0.855568	−	0.517691i	$-0.826792\pi$
$547$	−7.90229	+	7.90229i	−0.337877	+	0.337877i	0.517691	+	0.855568i	$0.326792\pi$
$548$		−	5.85713i		−	0.250204i
$549$		−	13.9447i		−	0.595147i
$550$	36.8423	−	9.08897i	1.57096	−	0.387555i
$551$	9.89447	+	9.89447i	0.421519	+	0.421519i
$552$	7.06422			0.300673
$553$	14.8182			0.630133
$554$	11.4479	+	11.4479i	0.486375	+	0.486375i
$555$	−0.424720	−	0.752863i	−0.0180283	−	0.0319573i
$556$		−	4.82547i		−	0.204646i
$557$		−	11.7868i		−	0.499423i	−0.968320	−	0.249712i	$-0.919664\pi$
$557$		−	11.7868i		−	0.499423i	0.968320	−	0.249712i	$-0.0803358\pi$
$558$	8.95899	−	8.95899i	0.379264	−	0.379264i
$559$		0			0
$560$	25.2429	+	7.03416i	1.06671	+	0.297247i
$561$	−0.195756	−	0.195756i	−0.00826482	−	0.00826482i
$562$	19.3749	−	19.3749i	0.817280	−	0.817280i
$563$	−22.7376	+	22.7376i	−0.958277	+	0.958277i	−0.999164	−	0.0408873i	$-0.986982\pi$
$563$	−22.7376	+	22.7376i	−0.958277	+	0.958277i	0.0408873	+	0.999164i	$0.486982\pi$
$564$	0.335015	−	0.335015i	0.0141067	−	0.0141067i
$565$	−11.1540	+	6.29238i	−0.469250	+	0.264723i
$566$	−6.18034	+	6.18034i	−0.259779	+	0.259779i
$567$		−	13.2118i		−	0.554845i
$568$	−13.9903	−	13.9903i	−0.587019	−	0.587019i
$569$	9.28474			0.389237			0.194618	−	0.980879i	$-0.437653\pi$
$569$	9.28474			0.389237			0.194618	+	0.980879i	$0.437653\pi$
$570$	−1.73010	+	6.20868i	−0.0724659	+	0.260053i
$571$		−	31.1596i		−	1.30399i	−0.758223	−	0.651995i	$-0.773932\pi$
$571$		−	31.1596i		−	1.30399i	0.758223	−	0.651995i	$-0.226068\pi$
$572$		0			0
$573$	8.08942	+	8.08942i	0.337940	+	0.337940i
$574$	−28.9990	+	28.9990i	−1.21039	+	1.21039i
$575$	19.6970	−	4.85924i	0.821422	−	0.202644i
$576$		−	16.3724i		−	0.682181i
$577$	−4.57285			−0.190370			−0.0951852	−	0.995460i	$-0.530344\pi$
$577$	−4.57285			−0.190370			−0.0951852	+	0.995460i	$0.530344\pi$
$578$		−	25.7966i		−	1.07300i
$579$	−4.09212	−	4.09212i	−0.170063	−	0.170063i
$580$	−3.26916	−	0.910980i	−0.135745	−	0.0378264i
$581$	9.62018			0.399112
$582$	−3.89894	−	3.89894i	−0.161616	−	0.161616i
$583$	−47.4228			−1.96405
$584$	−17.0365			−0.704975
$585$		0			0
$586$	4.85179			0.200425
$587$	7.19181			0.296838			0.148419	−	0.988925i	$-0.452582\pi$
$587$	7.19181			0.296838			0.148419	+	0.988925i	$0.452582\pi$
$588$	0.0388215	+	0.0388215i	0.00160097	+	0.00160097i
$589$	9.21486			0.379692
$590$	7.92870	−	4.47289i	0.326420	−	0.184146i
$591$	−3.66225	−	3.66225i	−0.150645	−	0.150645i
$592$		−	2.58103i		−	0.106080i
$593$	−28.0561			−1.15212			−0.576062	−	0.817406i	$-0.695411\pi$
$593$	−28.0561			−1.15212			−0.576062	+	0.817406i	$0.695411\pi$
$594$			28.4526i			1.16742i
$595$	−0.233392	−	0.413713i	−0.00956813	−	0.0169606i
$596$	0.310077	−	0.310077i	0.0127013	−	0.0127013i
$597$	7.33116	+	7.33116i	0.300044	+	0.300044i
$598$		0			0
$599$		−	0.912959i		−	0.0373025i	−0.999826	−	0.0186513i	$-0.994063\pi$
$599$		−	0.912959i		−	0.0373025i	0.999826	−	0.0186513i	$-0.00593722\pi$
$600$	2.08504	+	8.45174i	0.0851213	+	0.345041i
$601$	12.4538			0.508002			0.254001	−	0.967204i	$-0.418253\pi$
$601$	12.4538			0.508002			0.254001	+	0.967204i	$0.418253\pi$
$602$	−0.380992	−	0.380992i	−0.0155281	−	0.0155281i
$603$			40.1373i			1.63452i
$604$	−4.23976	+	4.23976i	−0.172514	+	0.172514i
$605$	30.1438	+	8.39983i	1.22552	+	0.341502i
$606$	1.82305	−	1.82305i	0.0740562	−	0.0740562i
$607$	−27.4162	+	27.4162i	−1.11279	+	1.11279i	−0.120017	+	0.992772i	$0.538295\pi$
$607$	−27.4162	+	27.4162i	−1.11279	+	1.11279i	−0.992772	+	0.120017i	$0.961705\pi$
$608$	−3.39031	+	3.39031i	−0.137495	+	0.137495i
$609$	−6.18684	−	6.18684i	−0.250703	−	0.250703i
$610$	−4.99757	+	17.9344i	−0.202346	+	0.726143i
$611$		0			0
$612$	0.0448098	−	0.0448098i	0.00181133	−	0.00181133i
$613$		−	24.6113i		−	0.994042i	−0.867739	−	0.497021i	$-0.834427\pi$
$613$		−	24.6113i		−	0.994042i	0.867739	−	0.497021i	$-0.165573\pi$
$614$			36.8490i			1.48711i
$615$	−15.1689	−	4.22695i	−0.611670	−	0.170447i
$616$	23.6110	+	23.6110i	0.951316	+	0.951316i
$617$	15.4154			0.620600			0.310300	−	0.950639i	$-0.399571\pi$
$617$	15.4154			0.620600			0.310300	+	0.950639i	$0.399571\pi$
$618$	−6.85037			−0.275562
$619$	−20.7915	−	20.7915i	−0.835683	−	0.835683i	0.152604	−	0.988287i	$-0.451234\pi$
$619$	−20.7915	−	20.7915i	−0.835683	−	0.835683i	−0.988287	+	0.152604i	$0.951234\pi$
$620$	−1.94651	+	1.09811i	−0.0781739	+	0.0441010i
$621$			15.2116i			0.610421i
$622$		−	25.6631i		−	1.02900i
$623$	−32.8303	+	32.8303i	−1.31532	+	1.31532i
$624$		0			0
$625$	11.6273	+	22.1315i	0.465093	+	0.885262i
$626$	−12.7667	−	12.7667i	−0.510261	−	0.510261i
$627$	−6.71234	+	6.71234i	−0.268065	+	0.268065i
$628$	1.38423	−	1.38423i	0.0552369	−	0.0552369i
$629$	−0.0330825	+	0.0330825i	−0.00131908	+	0.00131908i
$630$	−6.01140	+	21.5726i	−0.239500	+	0.859475i
$631$	8.91183	−	8.91183i	0.354774	−	0.354774i	−0.507108	−	0.861882i	$-0.669286\pi$
$631$	8.91183	−	8.91183i	0.354774	−	0.354774i	0.861882	+	0.507108i	$0.169286\pi$
$632$			14.6984i			0.584670i
$633$	9.48740	+	9.48740i	0.377090	+	0.377090i
$634$	−18.1382			−0.720359
$635$	1.58621	−	0.894844i	0.0629469	−	0.0355108i
$636$			1.95352i			0.0774620i
$637$		0			0
$638$	−26.7512	−	26.7512i	−1.05909	−	1.05909i
$639$	13.8194	−	13.8194i	0.546687	−	0.546687i
$640$	−7.91804	+	28.4149i	−0.312988	+	1.12320i
$641$		−	9.76116i		−	0.385543i	−0.981244	−	0.192771i	$-0.938252\pi$
$641$		−	9.76116i		−	0.385543i	0.981244	−	0.192771i	$-0.0617476\pi$
$642$	3.72597			0.147052
$643$		−	27.8114i		−	1.09677i	−0.836225	−	0.548387i	$-0.815242\pi$
$643$		−	27.8114i		−	1.09677i	0.836225	−	0.548387i	$-0.184758\pi$
$644$	−2.26673	−	2.26673i	−0.0893216	−	0.0893216i
$645$	0.0555341	−	0.199291i	0.00218665	−	0.00784708i
$646$	0.348847			0.0137252
$647$	13.0281	+	13.0281i	0.512188	+	0.512188i	0.915196	−	0.403008i	$-0.132035\pi$
$647$	13.0281	+	13.0281i	0.512188	+	0.512188i	−0.403008	+	0.915196i	$0.632035\pi$
$648$	13.1050			0.514814
$649$	13.4076			0.526296
$650$		0			0
$651$	−5.76190			−0.225826
$652$	3.99939			0.156628
$653$	5.21579	+	5.21579i	0.204110	+	0.204110i	0.801758	−	0.597648i	$-0.203898\pi$
$653$	5.21579	+	5.21579i	0.204110	+	0.204110i	−0.597648	+	0.801758i	$0.703898\pi$
$654$	2.30208			0.0900185
$655$	9.66746	−	34.6929i	0.377739	−	1.35556i
$656$	−33.2473	−	33.2473i	−1.29809	−	1.29809i
$657$		−	16.8284i		−	0.656538i
$658$	9.06214			0.353279
$659$			13.9472i			0.543304i	0.962396	+	0.271652i	$0.0875700\pi$
$659$			13.9472i			0.543304i	−0.962396	+	0.271652i	$0.912430\pi$
$660$	0.618002	−	2.21778i	0.0240557	−	0.0863269i
$661$	−0.160275	+	0.160275i	−0.00623398	+	0.00623398i	−0.710217	−	0.703983i	$-0.751403\pi$
$661$	−0.160275	+	0.160275i	−0.00623398	+	0.00623398i	0.703983	+	0.710217i	$0.251403\pi$
$662$	23.0236	+	23.0236i	0.894837	+	0.894837i
$663$		0			0
$664$			9.54239i			0.370317i
$665$	−14.1859	+	8.00284i	−0.550107	+	0.310337i
$666$	2.20575			0.0854711
$667$	−14.3020	−	14.3020i	−0.553776	−	0.553776i
$668$			1.00022i			0.0386996i
$669$	−9.07477	+	9.07477i	−0.350851	+	0.350851i
$670$	14.3846	−	51.6208i	0.555724	−	1.99429i
$671$	−19.3893	+	19.3893i	−0.748515	+	0.748515i
$672$	2.11990	−	2.11990i	0.0817771	−	0.0817771i
$673$	−23.7719	+	23.7719i	−0.916340	+	0.916340i	−0.996761	−	0.0804210i	$-0.974374\pi$
$673$	−23.7719	+	23.7719i	−0.916340	+	0.916340i	0.0804210	+	0.996761i	$0.474374\pi$
$674$	−21.4445	−	21.4445i	−0.826012	−	0.826012i
$675$	−18.1994	+	4.48978i	−0.700495	+	0.172812i
$676$		0			0
$677$	25.1691	−	25.1691i	0.967326	−	0.967326i	−0.0321566	−	0.999483i	$-0.510238\pi$
$677$	25.1691	−	25.1691i	0.967326	−	0.967326i	0.999483	+	0.0321566i	$0.0102375\pi$
$678$			5.88087i			0.225854i
$679$		−	13.9341i		−	0.534743i
$680$	0.410368	−	0.231505i	0.0157369	−	0.00887779i
$681$	−12.8943	−	12.8943i	−0.494110	−	0.494110i
$682$	−24.9138			−0.953999
$683$	30.7567			1.17687			0.588437	−	0.808543i	$-0.299744\pi$
$683$	30.7567			1.17687			0.588437	+	0.808543i	$0.299744\pi$
$684$	−1.53650	−	1.53650i	−0.0587494	−	0.0587494i
$685$	41.4374	+	11.5469i	1.58324	+	0.441184i
$686$			28.6242i			1.09288i
$687$		−	10.6948i		−	0.408032i
$688$	0.436807	−	0.436807i	0.0166531	−	0.0166531i
$689$		0			0
$690$	2.50078	−	8.97436i	0.0952032	−	0.341648i
$691$	−27.3944	−	27.3944i	−1.04213	−	1.04213i	−0.999072	−	0.0430609i	$-0.986289\pi$
$691$	−27.3944	−	27.3944i	−1.04213	−	1.04213i	−0.0430609	−	0.999072i	$-0.513711\pi$
$692$	0.912413	−	0.912413i	0.0346847	−	0.0346847i
$693$	−23.3227	+	23.3227i	−0.885954	+	0.885954i
$694$	−26.4382	+	26.4382i	−1.00358	+	1.00358i
$695$	34.1388	+	9.51307i	1.29496	+	0.360851i
$696$	6.13682	−	6.13682i	0.232615	−	0.232615i
$697$			0.852297i			0.0322831i
$698$	−29.2479	−	29.2479i	−1.10705	−	1.10705i
$699$	−6.46464			−0.244515
$700$	2.04291	−	3.38098i	0.0772148	−	0.127789i
$701$			19.8876i			0.751143i	0.926793	+	0.375571i	$0.122553\pi$
$701$			19.8876i			0.751143i	−0.926793	+	0.375571i	$0.877447\pi$
$702$		0			0
$703$	1.13437	+	1.13437i	0.0427838	+	0.0427838i
$704$	−22.7647	+	22.7647i	−0.857978	+	0.857978i
$705$	1.70968	+	3.03059i	0.0643901	+	0.114139i
$706$			13.3577i			0.502723i
$707$	6.51526			0.245032
$708$		−	0.552310i		−	0.0207571i
$709$	−22.5347	−	22.5347i	−0.846309	−	0.846309i	0.143362	−	0.989670i	$-0.454209\pi$
$709$	−22.5347	−	22.5347i	−0.846309	−	0.846309i	−0.989670	+	0.143362i	$0.954209\pi$
$710$	−22.7259	+	12.8206i	−0.852887	+	0.481147i
$711$	−14.5188			−0.544499
$712$	−32.5649	−	32.5649i	−1.22042	−	1.22042i
$713$	−13.3197			−0.498826
$714$	−0.218128			−0.00816325
$715$		0			0
$716$	−4.25084			−0.158861
$717$	1.90138			0.0710085
$718$	16.8892	+	16.8892i	0.630298	+	0.630298i
$719$	30.9635			1.15474			0.577372	−	0.816481i	$-0.304078\pi$
$719$	30.9635			1.15474			0.577372	+	0.816481i	$0.304078\pi$
$720$	−24.7330	−	6.89206i	−0.921744	−	0.256852i
$721$	−12.2410	−	12.2410i	−0.455880	−	0.455880i
$722$			16.8811i			0.628251i
$723$	−1.85672			−0.0690522
$724$			2.63294i			0.0978524i
$725$	12.8898	−	21.3324i	0.478716	−	0.792267i
$726$	10.1610	−	10.1610i	0.377110	−	0.377110i
$727$	−16.2588	−	16.2588i	−0.603007	−	0.603007i	0.338103	−	0.941109i	$-0.390215\pi$
$727$	−16.2588	−	16.2588i	−0.603007	−	0.603007i	−0.941109	+	0.338103i	$0.890215\pi$
$728$		0			0
$729$			5.33729i			0.197678i
$730$	−6.03103	+	21.6431i	−0.223218	+	0.801047i
$731$	−0.0111976			−0.000414157
$732$	0.798715	+	0.798715i	0.0295214	+	0.0295214i
$733$		−	31.2515i		−	1.15430i	−0.816638	−	0.577150i	$-0.804165\pi$
$733$		−	31.2515i		−	1.15430i	0.816638	−	0.577150i	$-0.195835\pi$
$734$	11.7845	−	11.7845i	0.434975	−	0.434975i
$735$	−0.351185	+	0.198117i	−0.0129536	+	0.00730766i
$736$	4.90054	−	4.90054i	0.180636	−	0.180636i
$737$	55.8084	−	55.8084i	2.05573	−	2.05573i
$738$	28.4132	−	28.4132i	1.04590	−	1.04590i
$739$	19.3018	+	19.3018i	0.710029	+	0.710029i	0.966541	−	0.256512i	$-0.0825733\pi$
$739$	19.3018	+	19.3018i	0.710029	+	0.710029i	−0.256512	+	0.966541i	$0.582573\pi$
$740$	−0.374801	−	0.104441i	−0.0137780	−	0.00383934i
$741$		0			0
$742$	−26.4213	+	26.4213i	−0.969956	+	0.969956i
$743$		−	32.9660i		−	1.20941i	−0.796451	−	0.604703i	$-0.793292\pi$
$743$		−	32.9660i		−	1.20941i	0.796451	−	0.604703i	$-0.206708\pi$
$744$		−	5.71531i		−	0.209533i
$745$	1.58241	+	2.80500i	0.0579750	+	0.102767i
$746$	11.3566	+	11.3566i	0.415794	+	0.415794i
$747$	−9.42584			−0.344873
$748$	−0.124610			−0.00455621
$749$	6.65800	+	6.65800i	0.243278	+	0.243278i
$750$	11.4752	+	0.343147i	0.419014	+	0.0125300i
$751$		−	30.9738i		−	1.13025i	−0.825005	−	0.565125i	$-0.808828\pi$
$751$		−	30.9738i		−	1.13025i	0.825005	−	0.565125i	$-0.191172\pi$
$752$			10.3897i			0.378875i
$753$	1.35540	−	1.35540i	0.0493934	−	0.0493934i
$754$		0			0
$755$	−21.6367	−	38.3535i	−0.787440	−	1.39583i
$756$	2.09439	+	2.09439i	0.0761720	+	0.0761720i
$757$	36.1312	−	36.1312i	1.31321	−	1.31321i	0.394173	−	0.919036i	$-0.371031\pi$
$757$	36.1312	−	36.1312i	1.31321	−	1.31321i	0.919036	−	0.394173i	$-0.128969\pi$
$758$	−10.5217	+	10.5217i	−0.382164	+	0.382164i
$759$	9.70238	−	9.70238i	0.352174	−	0.352174i
$760$	−7.93813	−	14.0712i	−0.287946	−	0.510417i
$761$	0.818500	−	0.818500i	0.0296706	−	0.0296706i	−0.692116	−	0.721786i	$-0.743321\pi$
$761$	0.818500	−	0.818500i	0.0296706	−	0.0296706i	0.721786	+	0.692116i	$0.243321\pi$
$762$		−	0.836323i		−	0.0302968i
$763$	4.11363	+	4.11363i	0.148923	+	0.148923i
$764$	5.14940			0.186299
$765$	0.228677	+	0.405355i	0.00826783	+	0.0146557i
$766$			39.5553i			1.42919i
$767$		0			0
$768$	3.41812	+	3.41812i	0.123341	+	0.123341i
$769$	21.3762	−	21.3762i	0.770844	−	0.770844i	−0.207410	−	0.978254i	$-0.566503\pi$
$769$	21.3762	−	21.3762i	0.770844	−	0.770844i	0.978254	+	0.207410i	$0.0665035\pi$
$770$	38.3539	−	21.6369i	1.38218	−	0.779741i
$771$			13.5702i			0.488719i
$772$	−2.60488			−0.0937517
$773$		−	7.19282i		−	0.258708i	−0.991598	−	0.129354i	$-0.958710\pi$
$773$		−	7.19282i		−	0.258708i	0.991598	−	0.129354i	$-0.0412903\pi$
$774$	0.373296	+	0.373296i	0.0134178	+	0.0134178i
$775$	−3.93136	−	15.9358i	−0.141219	−	0.572432i
$776$	13.8215			0.496162
$777$	−0.709305	−	0.709305i	−0.0254462	−	0.0254462i
$778$	49.3194			1.76819
$779$	29.2247			1.04708
$780$		0			0
$781$	−38.4300			−1.37513
$782$	−0.504243			−0.0180317
$783$	13.2146	+	13.2146i	0.472251	+	0.472251i
$784$	−1.20396			−0.0429986
$785$	7.06412	+	12.5219i	0.252129	+	0.446927i
$786$	−11.6944	−	11.6944i	−0.417125	−	0.417125i
$787$			7.17886i			0.255899i	0.991781	+	0.127949i	$0.0408395\pi$
$787$			7.17886i			0.255899i	−0.991781	+	0.127949i	$0.959160\pi$
$788$	−2.33124			−0.0830470
$789$			6.37306i			0.226887i
$790$	18.6728	+	5.20332i	0.664347	+	0.185126i
$791$	−10.5086	+	10.5086i	−0.373644	+	0.373644i
$792$	−23.1341	−	23.1341i	−0.822034	−	0.822034i
$793$		0			0
$794$			36.7145i			1.30295i
$795$	−13.8206	−	3.85122i	−0.490165	−	0.136589i
$796$	4.66672			0.165407
$797$	−27.8584	−	27.8584i	−0.986795	−	0.986795i	0.0131190	−	0.999914i	$-0.495824\pi$
$797$	−27.8584	−	27.8584i	−0.986795	−	0.986795i	−0.999914	+	0.0131190i	$0.995824\pi$
$798$			7.47947i			0.264770i
$799$	0.133171	−	0.133171i	0.00471124	−	0.00471124i
$800$	7.30950	+	4.41666i	0.258430	+	0.156153i
$801$	32.1671	−	32.1671i	1.13657	−	1.13657i
$802$	35.2493	−	35.2493i	1.24470	−	1.24470i
$803$	−23.3988	+	23.3988i	−0.825727	+	0.825727i
$804$	−2.29895	−	2.29895i	−0.0810778	−	0.0810778i
$805$	20.5051	−	11.5677i	0.722711	−	0.407710i
$806$		0			0
$807$	−1.53767	+	1.53767i	−0.0541286	+	0.0541286i
$808$			6.46258i			0.227353i
$809$			27.9509i			0.982700i	0.870962	+	0.491350i	$0.163496\pi$
$809$			27.9509i			0.982700i	−0.870962	+	0.491350i	$0.836504\pi$
$810$	4.63926	−	16.6486i	0.163007	−	0.584971i
$811$	23.2784	+	23.2784i	0.817415	+	0.817415i	0.985733	−	0.168317i	$-0.0538334\pi$
$811$	23.2784	+	23.2784i	0.817415	+	0.817415i	−0.168317	+	0.985733i	$0.553833\pi$
$812$	−3.93829			−0.138207
$813$	10.2726			0.360277
$814$	−3.06696	−	3.06696i	−0.107497	−	0.107497i
$815$	−7.88450	+	28.2945i	−0.276182	+	0.991113i
$816$		−	0.250084i		−	0.00875468i
$817$			0.383957i			0.0134330i
$818$	−14.9850	+	14.9850i	−0.523937	+	0.523937i
$819$		0			0
$820$	−6.17331	+	3.48261i	−0.215582	+	0.121618i
$821$	13.8264	+	13.8264i	0.482545	+	0.482545i	0.905944	−	0.423398i	$-0.139163\pi$
$821$	13.8264	+	13.8264i	0.482545	+	0.482545i	−0.423398	+	0.905944i	$0.639163\pi$
$822$	13.9679	−	13.9679i	0.487186	−	0.487186i
$823$	28.8649	−	28.8649i	1.00617	−	1.00617i	0.00618675	−	0.999981i	$-0.498031\pi$
$823$	28.8649	−	28.8649i	1.00617	−	1.00617i	0.999981	−	0.00618675i	$-0.00196932\pi$
$824$	12.1421	−	12.1421i	0.422989	−	0.422989i
$825$	14.4718	+	8.74437i	0.503843	+	0.304440i
$826$	7.46998	−	7.46998i	0.259914	−	0.259914i
$827$			31.8649i			1.10805i	0.832499	+	0.554026i	$0.186909\pi$
$827$			31.8649i			1.10805i	−0.832499	+	0.554026i	$0.813091\pi$
$828$	2.22094	+	2.22094i	0.0771829	+	0.0771829i
$829$	55.2782			1.91989			0.959946	−	0.280184i	$-0.0903956\pi$
$829$	55.2782			1.91989			0.959946	+	0.280184i	$0.0903956\pi$
$830$	12.1226	+	3.37807i	0.420782	+	0.117255i
$831$			7.21389i			0.250247i
$832$		0			0
$833$	0.0154318	+	0.0154318i	0.000534681	+	0.000534681i
$834$	11.5076	−	11.5076i	0.398477	−	0.398477i
$835$	−7.07624	−	1.97185i	−0.244883	−	0.0682388i
$836$			4.27281i			0.147778i
$837$	12.3070			0.425390
$838$		−	3.36976i		−	0.116406i
$839$	2.75809	+	2.75809i	0.0952197	+	0.0952197i	0.753112	−	0.657892i	$-0.228552\pi$
$839$	2.75809	+	2.75809i	0.0952197	+	0.0952197i	−0.657892	+	0.753112i	$0.728552\pi$
$840$	4.96358	+	8.79850i	0.171260	+	0.303577i
$841$	4.15118			0.143144
$842$	−37.1610	−	37.1610i	−1.28065	−	1.28065i
$843$	12.2091			0.420503
$844$	6.03930			0.207881
$845$		0			0
$846$	−8.87908			−0.305269
$847$	36.3137			1.24775
$848$	−30.2920	−	30.2920i	−1.04023	−	1.04023i
$849$	−3.89454			−0.133660
$850$	−0.148830	−	0.603284i	−0.00510482	−	0.0206925i
$851$	−1.63969	−	1.63969i	−0.0562078	−	0.0562078i
$852$			1.58307i			0.0542352i
$853$	53.5726			1.83429			0.917145	−	0.398554i	$-0.130488\pi$
$853$	53.5726			1.83429			0.917145	+	0.398554i	$0.130488\pi$
$854$			21.6052i			0.739315i
$855$	13.8994	−	7.84117i	0.475348	−	0.268163i
$856$	−6.60416	+	6.60416i	−0.225726	+	0.225726i
$857$	18.9164	+	18.9164i	0.646171	+	0.646171i	0.952066	−	0.305894i	$-0.0989554\pi$
$857$	18.9164	+	18.9164i	0.646171	+	0.646171i	−0.305894	+	0.952066i	$0.598955\pi$
$858$		0			0
$859$		−	18.1203i		−	0.618258i	−0.951020	−	0.309129i	$-0.899963\pi$
$859$		−	18.1203i		−	0.618258i	0.951020	−	0.309129i	$-0.100037\pi$
$860$	−0.0457549	−	0.0811057i	−0.00156023	−	0.00276568i
$861$	−18.2737			−0.622766
$862$	1.77385	+	1.77385i	0.0604176	+	0.0604176i
$863$		−	21.4967i		−	0.731757i	−0.930663	−	0.365879i	$-0.880768\pi$
$863$		−	21.4967i		−	0.731757i	0.930663	−	0.365879i	$-0.119232\pi$
$864$	−4.52795	+	4.52795i	−0.154044	+	0.154044i
$865$	4.65630	+	8.25380i	0.158319	+	0.280638i
$866$	15.9037	−	15.9037i	0.540431	−	0.540431i
$867$	8.12786	−	8.12786i	0.276037	−	0.276037i
$868$	−1.83390	+	1.83390i	−0.0622465	+	0.0622465i
$869$	20.1875	+	20.1875i	0.684815	+	0.684815i
$870$	−5.62372	−	9.96866i	−0.190662	−	0.337969i
$871$		0			0
$872$	−4.08036	+	4.08036i	−0.138179	+	0.138179i
$873$			13.6527i			0.462072i
$874$			17.2902i			0.584848i
$875$	19.8920	+	21.1184i	0.672473	+	0.713931i
$876$	0.963883	+	0.963883i	0.0325666	+	0.0325666i
$877$	21.3491			0.720907			0.360454	−	0.932777i	$-0.382622\pi$
$877$	21.3491			0.720907			0.360454	+	0.932777i	$0.382622\pi$
$878$	33.2035			1.12056
$879$	1.52867	+	1.52867i	0.0515609	+	0.0515609i
$880$	24.8067	+	43.9726i	0.836234	+	1.48232i
$881$		−	13.2448i		−	0.446227i	−0.974792	−	0.223114i	$-0.928378\pi$
$881$		−	13.2448i		−	0.446227i	0.974792	−	0.223114i	$-0.0716221\pi$
$882$		−	1.02891i		−	0.0346451i
$883$	32.5668	−	32.5668i	1.09596	−	1.09596i	0.101082	−	0.994878i	$-0.467770\pi$
$883$	32.5668	−	32.5668i	1.09596	−	1.09596i	0.994878	−	0.101082i	$-0.0322304\pi$
$884$		0			0
$885$	3.90743	+	1.08884i	0.131347	+	0.0366009i
$886$	−9.33555	−	9.33555i	−0.313634	−	0.313634i
$887$	11.2998	−	11.2998i	0.379409	−	0.379409i	−0.491480	−	0.870889i	$-0.663544\pi$
$887$	11.2998	−	11.2998i	0.379409	−	0.379409i	0.870889	+	0.491480i	$0.163544\pi$
$888$	0.703570	−	0.703570i	0.0236103	−	0.0236103i
$889$	1.49444	−	1.49444i	0.0501219	−	0.0501219i
$890$	−52.8985	+	29.8421i	−1.77316	+	1.00031i
$891$	17.9991	−	17.9991i	0.602994	−	0.602994i
$892$			5.77663i			0.193416i
$893$	−4.56634	−	4.56634i	−0.152807	−	0.152807i
$894$	1.47892			0.0494626
$895$	8.38022	−	30.0734i	0.280120	−	1.00524i
$896$			34.2308i			1.14357i
$897$		0			0
$898$	5.01810	+	5.01810i	0.167456	+	0.167456i
$899$	−11.5710	+	11.5710i	−0.385916	+	0.385916i
$900$	−2.00164	+	3.31268i	−0.0667214	+	0.110423i
$901$			0.776537i			0.0258702i
$902$	−79.0135			−2.63086
$903$		−	0.240082i		−	0.00798943i
$904$	−10.4237	−	10.4237i	−0.346686	−	0.346686i
$905$	−18.6273	−	5.19065i	−0.619192	−	0.172543i
$906$	−20.2217			−0.671821
$907$	−3.71485	−	3.71485i	−0.123350	−	0.123350i	0.642737	−	0.766087i	$-0.277799\pi$
$907$	−3.71485	−	3.71485i	−0.123350	−	0.123350i	−0.766087	+	0.642737i	$0.777799\pi$
$908$	−8.20799			−0.272392
$909$	−6.38364			−0.211732
$910$		0			0
$911$	9.49722			0.314657			0.157328	−	0.987546i	$-0.449712\pi$
$911$	9.49722			0.314657			0.157328	+	0.987546i	$0.449712\pi$
$912$	−8.57520			−0.283953
$913$	13.1060	+	13.1060i	0.433746	+	0.433746i
$914$	45.5961			1.50819
$915$	−7.22529	+	4.07607i	−0.238861	+	0.134751i
$916$	−3.40394	−	3.40394i	−0.112469	−	0.112469i
$917$		−	41.7938i		−	1.38015i
$918$	0.465905			0.0153771
$919$		−	52.6782i		−	1.73769i	−0.495081	−	0.868847i	$-0.664862\pi$
$919$		−	52.6782i		−	1.73769i	0.495081	−	0.868847i	$-0.335138\pi$
$920$	11.4742	+	20.3393i	0.378294	+	0.670568i
$921$	−11.6102	+	11.6102i	−0.382569	+	0.382569i
$922$	−2.82041	−	2.82041i	−0.0928851	−	0.0928851i
$923$		0			0
$924$		−	2.67171i		−	0.0878929i
$925$	1.47778	−	2.44571i	0.0485893	−	0.0804144i
$926$	−38.1751			−1.25451
$927$	11.9937	+	11.9937i	0.393926	+	0.393926i
$928$		−	8.51438i		−	0.279498i
$929$	5.89185	−	5.89185i	0.193305	−	0.193305i	−0.603817	−	0.797123i	$-0.706354\pi$
$929$	5.89185	−	5.89185i	0.193305	−	0.193305i	0.797123	+	0.603817i	$0.206354\pi$
$930$	−7.26071	−	2.02326i	−0.238088	−	0.0663452i
$931$	0.529147	−	0.529147i	0.0173421	−	0.0173421i
$932$	−2.05757	+	2.05757i	−0.0673978	+	0.0673978i
$933$	8.08579	−	8.08579i	0.264717	−	0.264717i
$934$	22.7566	+	22.7566i	0.744619	+	0.744619i
$935$	0.245660	−	0.881582i	0.00803395	−	0.0288308i
$936$		0			0
$937$	16.3814	−	16.3814i	0.535156	−	0.535156i	−0.386947	−	0.922102i	$-0.626470\pi$
$937$	16.3814	−	16.3814i	0.535156	−	0.535156i	0.922102	+	0.386947i	$0.126470\pi$
$938$		−	62.1865i		−	2.03046i
$939$		−	8.04494i		−	0.262537i
$940$	1.50873	+	0.420421i	0.0492094	+	0.0137126i
$941$	24.2325	+	24.2325i	0.789956	+	0.789956i	0.981487	−	0.191530i	$-0.0613451\pi$
$941$	24.2325	+	24.2325i	0.789956	+	0.789956i	−0.191530	+	0.981487i	$0.561345\pi$
$942$	6.60214			0.215109
$943$	−42.2430			−1.37562
$944$	8.56432	+	8.56432i	0.278745	+	0.278745i
$945$	−18.9461	+	10.6882i	−0.616316	+	0.347688i
$946$		−	1.03809i		−	0.0337512i
$947$		−	33.4416i		−	1.08671i	−0.839505	−	0.543353i	$-0.817155\pi$
$947$		−	33.4416i		−	1.08671i	0.839505	−	0.543353i	$-0.182845\pi$
$948$	0.831598	−	0.831598i	0.0270091	−	0.0270091i
$949$		0			0
$950$	−20.6862	+	5.10327i	−0.671149	+	0.165572i
$951$	−5.71487	−	5.71487i	−0.185318	−	0.185318i
$952$	0.386625	−	0.386625i	0.0125306	−	0.0125306i
$953$	−10.6248	+	10.6248i	−0.344171	+	0.344171i	−0.857933	−	0.513762i	$-0.828252\pi$
$953$	−10.6248	+	10.6248i	−0.344171	+	0.344171i	0.513762	+	0.857933i	$0.328252\pi$
$954$	25.8875	−	25.8875i	0.838140	−	0.838140i
$955$	−10.1517	+	36.4305i	−0.328500	+	1.17886i
$956$	0.605172	−	0.605172i	0.0195727	−	0.0195727i
$957$		−	16.8573i		−	0.544918i
$958$	−2.45769	−	2.45769i	−0.0794042	−	0.0794042i
$959$	49.9188			1.61196
$960$	−8.48312	+	4.78566i	−0.273792	+	0.154457i
$961$		−	20.2237i		−	0.652378i
$962$		0			0
$963$	−6.52350	−	6.52350i	−0.210217	−	0.210217i
$964$	−0.590957	+	0.590957i	−0.0190334	+	0.0190334i
$965$	5.13533	−	18.4288i	0.165312	−	0.593243i
$966$		−	10.8112i		−	0.347846i
$967$	−7.49252			−0.240943			−0.120472	−	0.992717i	$-0.538441\pi$
$967$	−7.49252			−0.240943			−0.120472	+	0.992717i	$0.538441\pi$
$968$			36.0200i			1.15773i
$969$	0.109913	+	0.109913i	0.00353091	+	0.00353091i
$970$	4.89290	−	17.5588i	0.157101	−	0.563778i
$971$	27.8606			0.894090			0.447045	−	0.894512i	$-0.352476\pi$
$971$	27.8606			0.894090			0.447045	+	0.894512i	$0.352476\pi$
$972$	−3.16281	−	3.16281i	−0.101447	−	0.101447i
$973$	41.1263			1.31845
$974$	8.45010			0.270759
$975$		0			0
$976$	−24.7704			−0.792880
$977$	−38.8764			−1.24377			−0.621883	−	0.783110i	$-0.713632\pi$
$977$	−38.8764			−1.24377			−0.621883	+	0.783110i	$0.713632\pi$
$978$	9.53761	+	9.53761i	0.304979	+	0.304979i
$979$	−89.4527			−2.85892
$980$	−0.0487183	+	0.174832i	−0.00155625	+	0.00558479i
$981$	−4.03053	−	4.03053i	−0.128685	−	0.128685i
$982$		−	9.27522i		−	0.295984i
$983$	−0.207440			−0.00661630			−0.00330815	−	0.999995i	$-0.501053\pi$
$983$	−0.207440			−0.00661630			−0.00330815	+	0.999995i	$0.501053\pi$
$984$		−	18.1259i		−	0.577834i
$985$	4.59587	−	16.4928i	0.146437	−	0.525506i
$986$	−0.438045	+	0.438045i	−0.0139502	+	0.0139502i
$987$	2.85525	+	2.85525i	0.0908836	+	0.0908836i
$988$		0			0
$989$		−	0.554993i		−	0.0176477i
$990$	−37.5791	+	21.1998i	−1.19434	+	0.673775i
$991$	−25.4961			−0.809910			−0.404955	−	0.914337i	$-0.632713\pi$
$991$	−25.4961			−0.809910			−0.404955	+	0.914337i	$0.632713\pi$
$992$	−3.96478	−	3.96478i	−0.125882	−	0.125882i
$993$			14.5083i			0.460407i
$994$	−21.4110	+	21.4110i	−0.679117	+	0.679117i
$995$	−9.20009	+	33.0157i	−0.291663	+	1.04667i
$996$	0.539885	−	0.539885i	0.0171069	−	0.0171069i
$997$	−24.5049	+	24.5049i	−0.776078	+	0.776078i	−0.979162	−	0.203083i	$-0.934904\pi$
$997$	−24.5049	+	24.5049i	−0.776078	+	0.776078i	0.203083	+	0.979162i	$0.434904\pi$
$998$	−9.45345	+	9.45345i	−0.299244	+	0.299244i
$999$	1.51502	+	1.51502i	0.0479331	+	0.0479331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.k.d.268.9		20
5.2	odd	4		845.2.f.d.437.9		20
13.2	odd	12		845.2.t.e.188.5		20
13.3	even	3		845.2.o.g.488.1		20
13.4	even	6		845.2.o.e.258.5		20
13.5	odd	4		845.2.f.d.408.2		20
13.6	odd	12		845.2.t.g.418.1		20
13.7	odd	12		65.2.t.a.28.5	yes	20
13.8	odd	4		845.2.f.e.408.9		20
13.9	even	3		845.2.o.f.258.1		20
13.10	even	6		65.2.o.a.33.5	yes	20
13.11	odd	12		845.2.t.f.188.1		20
13.12	even	2		845.2.k.e.268.2		20
39.20	even	12		585.2.dp.a.28.1		20
39.23	odd	6		585.2.cf.a.163.1		20
65.2	even	12		845.2.o.f.357.1		20
65.7	even	12		65.2.o.a.2.5	✓	20
65.12	odd	4		845.2.f.e.437.2		20
65.17	odd	12		845.2.t.f.427.1		20
65.22	odd	12		845.2.t.e.427.5		20
65.23	odd	12		325.2.x.b.7.1		20
65.32	even	12		845.2.o.g.587.1		20
65.33	even	12		325.2.s.b.132.1		20
65.37	even	12		845.2.o.e.357.5		20
65.42	odd	12		845.2.t.g.657.1		20
65.47	even	4		845.2.k.e.577.2		20
65.49	even	6		325.2.s.b.293.1		20
65.57	even	4	inner	845.2.k.d.577.9		20
65.59	odd	12		325.2.x.b.93.1		20
65.62	odd	12		65.2.t.a.7.5	yes	20
195.62	even	12		585.2.dp.a.397.1		20
195.137	odd	12		585.2.cf.a.262.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.5	✓	20	65.7	even	12
65.2.o.a.33.5	yes	20	13.10	even	6
65.2.t.a.7.5	yes	20	65.62	odd	12
65.2.t.a.28.5	yes	20	13.7	odd	12
325.2.s.b.132.1		20	65.33	even	12
325.2.s.b.293.1		20	65.49	even	6
325.2.x.b.7.1		20	65.23	odd	12
325.2.x.b.93.1		20	65.59	odd	12
585.2.cf.a.163.1		20	39.23	odd	6
585.2.cf.a.262.1		20	195.137	odd	12
585.2.dp.a.28.1		20	39.20	even	12
585.2.dp.a.397.1		20	195.62	even	12
845.2.f.d.408.2		20	13.5	odd	4
845.2.f.d.437.9		20	5.2	odd	4
845.2.f.e.408.9		20	13.8	odd	4
845.2.f.e.437.2		20	65.12	odd	4
845.2.k.d.268.9		20	1.1	even	1	trivial
845.2.k.d.577.9		20	65.57	even	4	inner
845.2.k.e.268.2		20	13.12	even	2
845.2.k.e.577.2		20	65.47	even	4
845.2.o.e.258.5		20	13.4	even	6
845.2.o.e.357.5		20	65.37	even	12
845.2.o.f.258.1		20	13.9	even	3
845.2.o.f.357.1		20	65.2	even	12
845.2.o.g.488.1		20	13.3	even	3
845.2.o.g.587.1		20	65.32	even	12
845.2.t.e.188.5		20	13.2	odd	12
845.2.t.e.427.5		20	65.22	odd	12
845.2.t.f.188.1		20	13.11	odd	12
845.2.t.f.427.1		20	65.17	odd	12
845.2.t.g.418.1		20	13.6	odd	12
845.2.t.g.657.1		20	65.42	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.51805 q^{2} +(0.478298 + 0.478298i) q^{3} +0.304465 q^{4} +(-0.600231 + 2.15400i) q^{5} +(0.726078 + 0.726078i) q^{6} +2.59488i q^{7} -2.57390 q^{8} -2.54246i q^{9} +(-0.911178 + 3.26987i) q^{10} +(-3.53513 + 3.53513i) q^{11} +(0.145625 + 0.145625i) q^{12} +3.93915i q^{14} +(-1.31734 + 0.743165i) q^{15} -4.51623 q^{16} +(0.0578870 + 0.0578870i) q^{17} -3.85958i q^{18} +(1.98490 - 1.98490i) q^{19} +(-0.182749 + 0.655819i) q^{20} +(-1.24113 + 1.24113i) q^{21} +(-5.36650 + 5.36650i) q^{22} +(-2.86909 + 2.86909i) q^{23} +(-1.23109 - 1.23109i) q^{24} +(-4.27945 - 2.58580i) q^{25} +(2.65095 - 2.65095i) q^{27} +0.790051i q^{28} +4.98486i q^{29} +(-1.99979 + 1.12816i) q^{30} +(2.32124 + 2.32124i) q^{31} -1.70805 q^{32} -3.38169 q^{33} +(0.0878751 + 0.0878751i) q^{34} +(-5.58938 - 1.55753i) q^{35} -0.774091i q^{36} +0.571501i q^{37} +(3.01318 - 3.01318i) q^{38} +(1.54493 - 5.54419i) q^{40} +(7.36174 + 7.36174i) q^{41} +(-1.88409 + 1.88409i) q^{42} +(-0.0967193 + 0.0967193i) q^{43} +(-1.07633 + 1.07633i) q^{44} +(5.47647 + 1.52606i) q^{45} +(-4.35541 + 4.35541i) q^{46} -2.30053i q^{47} +(-2.16010 - 2.16010i) q^{48} +0.266585 q^{49} +(-6.49640 - 3.92536i) q^{50} +0.0553744i q^{51} +(6.70735 + 6.70735i) q^{53} +(4.02426 - 4.02426i) q^{54} +(-5.49279 - 9.73658i) q^{55} -6.67897i q^{56} +1.89875 q^{57} +7.56725i q^{58} +(-1.89634 - 1.89634i) q^{59} +(-0.401085 + 0.226268i) q^{60} +5.48474 q^{61} +(3.52374 + 3.52374i) q^{62} +6.59739 q^{63} +6.43957 q^{64} -5.13357 q^{66} -15.7868 q^{67} +(0.0176246 + 0.0176246i) q^{68} -2.74456 q^{69} +(-8.48494 - 2.36440i) q^{70} +(5.43544 + 5.43544i) q^{71} +6.54405i q^{72} +6.61894 q^{73} +0.867565i q^{74} +(-0.810069 - 3.28363i) q^{75} +(0.604334 - 0.604334i) q^{76} +(-9.17326 - 9.17326i) q^{77} -5.71054i q^{79} +(2.71078 - 9.72797i) q^{80} -5.09150 q^{81} +(11.1755 + 11.1755i) q^{82} -3.70736i q^{83} +(-0.377880 + 0.377880i) q^{84} +(-0.159434 + 0.0899431i) q^{85} +(-0.146824 + 0.146824i) q^{86} +(-2.38425 + 2.38425i) q^{87} +(9.09908 - 9.09908i) q^{88} +(12.6520 + 12.6520i) q^{89} +(8.31353 + 2.31664i) q^{90} +(-0.873538 + 0.873538i) q^{92} +2.22048i q^{93} -3.49231i q^{94} +(3.08409 + 5.46689i) q^{95} +(-0.816956 - 0.816956i) q^{96} -5.36986 q^{97} +0.404689 q^{98} +(8.98794 + 8.98794i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 8 q^{2} + 4 q^{3} + 12 q^{4} + 6 q^{5} - 4 q^{6} - 12 q^{8} + 8 q^{10} - 8 q^{11} + 24 q^{12} + 24 q^{15} + 4 q^{16} + 14 q^{17} + 4 q^{19} + 22 q^{20} - 4 q^{21} - 32 q^{22} - 8 q^{23} - 4 q^{24}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q - 8 * q^2 + 4 * q^3 + 12 * q^4 + 6 * q^5 - 4 * q^6 - 12 * q^8 + 8 * q^10 - 8 * q^11 + 24 * q^12 + 24 * q^15 + 4 * q^16 + 14 * q^17 + 4 * q^19 + 22 * q^20 - 4 * q^21 - 32 * q^22 - 8 * q^23 - 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 - 12 * q^32 - 36 * q^33 + 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 + 32 * q^43 - 36 * q^44 + 20 * q^45 - 4 * q^46 + 28 * q^48 + 36 * q^49 + 52 * q^50 - 10 * q^53 + 36 * q^54 - 16 * q^55 + 12 * q^57 + 8 * q^59 + 92 * q^60 + 32 * q^61 - 4 * q^62 - 64 * q^63 - 20 * q^64 - 32 * q^66 - 116 * q^67 - 50 * q^68 - 32 * q^69 - 32 * q^70 + 40 * q^71 - 72 * q^73 - 4 * q^75 + 16 * q^76 + 28 * q^77 + 34 * q^80 + 28 * q^81 + 34 * q^82 + 8 * q^84 - 60 * q^86 - 28 * q^87 + 32 * q^88 + 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 - 56 * q^96 - 44 * q^97 + 8 * q^98 + 60 * q^99

Introduction

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