LMFDB - Embedded newform 845.2.f.e.437.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(408,845)]

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, 3]))

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

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

chi := DirichletCharacter("845.408");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.f (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			437.2
Root			$-1.51805i$ of defining polynomial
Character	$\chi$	$=$	845.437
Dual form			845.2.f.e.408.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.51805i q^{2} +(0.478298 - 0.478298i) q^{3} -0.304465 q^{4} +(-2.15400 + 0.600231i) q^{5} +(-0.726078 - 0.726078i) q^{6} +2.59488 q^{7} -2.57390i 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} +(-0.743165 + 1.31734i) q^{15} -4.51623 q^{16} +(-0.0578870 + 0.0578870i) q^{17} +3.85958 q^{18} +(1.98490 - 1.98490i) q^{19} +(0.655819 - 0.182749i) 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} -0.790051 q^{28} -4.98486i q^{29} +(1.99979 + 1.12816i) q^{30} +(-2.32124 - 2.32124i) q^{31} +1.70805i q^{32} -3.38169i q^{33} +(0.0878751 + 0.0878751i) q^{34} +(-5.58938 + 1.55753i) q^{35} -0.774091i q^{36} +0.571501 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} +(-1.52606 - 5.47647i) q^{45} +(4.35541 - 4.35541i) q^{46} -2.30053 q^{47} +(-2.16010 + 2.16010i) q^{48} -0.266585 q^{49} +(-3.92536 - 6.49640i) 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} -1.89875i q^{57} -7.56725 q^{58} +(-1.89634 - 1.89634i) q^{59} +(0.226268 - 0.401085i) q^{60} +5.48474 q^{61} +(-3.52374 + 3.52374i) q^{62} +6.59739i q^{63} -6.43957 q^{64} -5.13357 q^{66} +15.7868i q^{67} +(0.0176246 - 0.0176246i) q^{68} +2.74456 q^{69} +(2.36440 + 8.48494i) q^{70} +(-5.43544 - 5.43544i) q^{71} +6.54405 q^{72} +6.61894i 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} +(9.72797 - 2.71078i) q^{80} -5.09150 q^{81} +(-11.1755 + 11.1755i) q^{82} +3.70736 q^{83} +(-0.377880 + 0.377880i) q^{84} +(0.0899431 - 0.159434i) 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} -2.22048 q^{93} +3.49231i q^{94} +(-3.08409 + 5.46689i) q^{95} +(0.816956 + 0.816956i) q^{96} +5.36986i q^{97} +0.404689i q^{98} +(8.98794 + 8.98794i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7} - 8 q^{10} + 8 q^{11} - 24 q^{12} + 28 q^{15} + 4 q^{16} - 14 q^{17} + 4 q^{19} - 12 q^{20} + 4 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{24} + 18 q^{25} + 4 q^{27}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7 - 8 * q^10 + 8 * q^11 - 24 * q^12 + 28 * q^15 + 4 * q^16 - 14 * q^17 + 4 * q^19 - 12 * q^20 + 4 * q^21 - 32 * q^22 + 8 * q^23 - 4 * q^24 + 18 * q^25 + 4 * q^27 - 36 * q^28 + 40 * q^30 + 2 * q^34 - 20 * q^35 + 8 * q^37 - 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 - 32 * q^43 - 36 * q^44 - 6 * q^45 + 4 * q^46 - 40 * q^47 + 28 * q^48 - 36 * q^49 + 42 * q^50 - 10 * q^53 + 36 * q^54 - 16 * q^55 + 8 * q^59 + 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 - 12 * q^70 - 40 * q^71 - 8 * q^72 + 4 * q^75 - 16 * q^76 - 28 * q^77 + 112 * q^80 + 28 * q^81 - 34 * q^82 + 48 * q^83 + 8 * q^84 - 2 * q^85 + 60 * q^86 - 28 * q^87 - 32 * q^88 + 12 * q^89 + 46 * q^90 - 8 * q^92 - 64 * q^93 + 40 * q^95 + 56 * q^96 + 60 * q^99

Character values

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

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

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 $

$2$		−	1.51805i		−	1.07342i	−0.843766	−	0.536710i	$-0.819667\pi$
$2$		−	1.51805i		−	1.07342i	0.843766	−	0.536710i	$-0.180333\pi$
$3$	0.478298	−	0.478298i	0.276145	−	0.276145i	−0.555423	−	0.831568i	$-0.687444\pi$
$3$	0.478298	−	0.478298i	0.276145	−	0.276145i	0.831568	+	0.555423i	$0.187444\pi$
$4$	−0.304465			−0.152233
$5$	−2.15400	+	0.600231i	−0.963299	+	0.268431i
$5$	−2.15400	+	0.600231i	−0.963299	+	0.268431i
$6$	−0.726078	−	0.726078i	−0.296420	−	0.296420i
$7$	2.59488			0.980773			0.490387	−	0.871505i	$-0.336856\pi$
$7$	2.59488			0.980773			0.490387	+	0.871505i	$0.336856\pi$
$8$		−	2.57390i		−	0.910011i
$9$			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	$-0.478271\pi$
$11$	3.53513	−	3.53513i	1.06588	−	1.06588i	0.997671	−	0.0682120i	$-0.0217294\pi$
$12$	−0.145625	+	0.145625i	−0.0420383	+	0.0420383i
$13$		0			0
$13$		0			0
$14$		−	3.93915i		−	1.05278i
$15$	−0.743165	+	1.31734i	−0.191884	+	0.340137i
$16$	−4.51623			−1.12906
$17$	−0.0578870	+	0.0578870i	−0.0140397	+	0.0140397i	−0.714092	−	0.700052i	$-0.753160\pi$
$17$	−0.0578870	+	0.0578870i	−0.0140397	+	0.0140397i	0.700052	+	0.714092i	$0.253160\pi$
$18$	3.85958			0.909711
$19$	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	$0.145647\pi$
$20$	0.655819	−	0.182749i	0.146645	−	0.0408640i
$21$	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	$-0.110969\pi$
$23$	2.86909	+	2.86909i	0.598247	+	0.598247i	−0.341599	+	0.939846i	$0.610969\pi$
$24$	−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
$28$	−0.790051			−0.149306
$29$		−	4.98486i		−	0.925665i	−0.886446	−	0.462833i	$-0.846833\pi$
$29$		−	4.98486i		−	0.925665i	0.886446	−	0.462833i	$-0.153167\pi$
$30$	1.99979	+	1.12816i	0.365110	+	0.205973i
$31$	−2.32124	−	2.32124i	−0.416906	−	0.416906i	0.467230	−	0.884136i	$-0.345252\pi$
$31$	−2.32124	−	2.32124i	−0.416906	−	0.416906i	−0.884136	+	0.467230i	$0.845252\pi$
$32$			1.70805i			0.301943i
$33$		−	3.38169i		−	0.588677i
$34$	0.0878751	+	0.0878751i	0.0150705	+	0.0150705i
$35$	−5.58938	+	1.55753i	−0.944778	+	0.263270i
$36$		−	0.774091i		−	0.129015i
$37$	0.571501			0.0939542			0.0469771	−	0.998896i	$-0.485041\pi$
$37$	0.571501			0.0939542			0.0469771	+	0.998896i	$0.485041\pi$
$38$	−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	$-0.947851\pi$
$41$	−7.36174	−	7.36174i	−1.14971	−	1.14971i	−0.163100	−	0.986609i	$-0.552149\pi$
$42$	−1.88409	−	1.88409i	−0.290721	−	0.290721i
$43$	0.0967193	+	0.0967193i	0.0147496	+	0.0147496i	0.714443	−	0.699694i	$-0.246680\pi$
$43$	0.0967193	+	0.0967193i	0.0147496	+	0.0147496i	−0.699694	+	0.714443i	$0.746680\pi$
$44$	−1.07633	+	1.07633i	−0.162262	+	0.162262i
$45$	−1.52606	−	5.47647i	−0.227492	−	0.816384i
$46$	4.35541	−	4.35541i	0.642170	−	0.642170i
$47$	−2.30053			−0.335567			−0.167784	−	0.985824i	$-0.553661\pi$
$47$	−2.30053			−0.335567			−0.167784	+	0.985824i	$0.553661\pi$
$48$	−2.16010	+	2.16010i	−0.311784	+	0.311784i
$49$	−0.266585			−0.0380836
$50$	−3.92536	−	6.49640i	−0.555130	−	0.918729i
$51$			0.0553744i			0.00775397i
$52$		0			0
$53$	6.70735	−	6.70735i	0.921326	−	0.921326i	−0.0757974	−	0.997123i	$-0.524150\pi$
$53$	6.70735	−	6.70735i	0.921326	−	0.921326i	0.997123	+	0.0757974i	$0.0241502\pi$
$54$	4.02426	−	4.02426i	0.547633	−	0.547633i
$55$	−5.49279	+	9.73658i	−0.740647	+	1.31288i
$56$		−	6.67897i		−	0.892515i
$57$		−	1.89875i		−	0.251496i
$58$	−7.56725			−0.993628
$59$	−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	$0.805854\pi$
$60$	0.226268	−	0.401085i	0.0292111	−	0.0517799i
$61$	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
$63$			6.59739i			0.831193i
$64$	−6.43957			−0.804946
$65$		0			0
$66$	−5.13357			−0.631899
$67$			15.7868i			1.92866i	0.264699	+	0.964331i	$0.414728\pi$
$67$			15.7868i			1.92866i	−0.264699	+	0.964331i	$0.585272\pi$
$68$	0.0176246	−	0.0176246i	0.00213729	−	0.00213729i
$69$	2.74456			0.330406
$70$	2.36440	+	8.48494i	0.282600	+	1.01414i
$71$	−5.43544	−	5.43544i	−0.645068	−	0.645068i	0.306729	−	0.951797i	$-0.400766\pi$
$71$	−5.43544	−	5.43544i	−0.645068	−	0.645068i	−0.951797	+	0.306729i	$0.900766\pi$
$72$	6.54405			0.771223
$73$			6.61894i			0.774688i	0.921935	+	0.387344i	$0.126607\pi$
$73$			6.61894i			0.774688i	−0.921935	+	0.387344i	$0.873393\pi$
$74$		−	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	$0.104101\pi$
$79$			5.71054i			0.642486i	−0.946997	+	0.321243i	$0.895899\pi$
$80$	9.72797	−	2.71078i	1.08762	−	0.303075i
$81$	−5.09150			−0.565722
$82$	−11.1755	+	11.1755i	−1.23412	+	1.23412i
$83$	3.70736			0.406936			0.203468	−	0.979082i	$-0.434779\pi$
$83$	3.70736			0.406936			0.203468	+	0.979082i	$0.434779\pi$
$84$	−0.377880	+	0.377880i	−0.0412301	+	0.0412301i
$85$	0.0899431	−	0.159434i	0.00975570	−	0.0172931i
$86$	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
$93$	−2.22048			−0.230253
$94$			3.49231i			0.360205i
$95$	−3.08409	+	5.46689i	−0.316421	+	0.560891i
$96$	0.816956	+	0.816956i	0.0833802	+	0.0833802i
$97$			5.36986i			0.545226i	0.962124	+	0.272613i	$0.0878879\pi$
$97$			5.36986i			0.545226i	−0.962124	+	0.272613i	$0.912112\pi$
$98$			0.404689i			0.0408798i
$99$	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	$-0.0398666\pi$
$102$	0.0840609			0.00832327
$103$	4.71738	+	4.71738i	0.464817	+	0.464817i	0.900230	−	0.435414i	$-0.143398\pi$
$103$	4.71738	+	4.71738i	0.464817	+	0.464817i	−0.435414	+	0.900230i	$0.643398\pi$
$104$		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	0.820169	−	0.572122i	$-0.193880\pi$
$107$	2.56582	+	2.56582i	0.248047	+	0.248047i	−0.572122	+	0.820169i	$0.693880\pi$
$108$	−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	$0.215757\pi$
$110$	14.7806	+	8.33831i	1.40927	+	0.795026i
$111$	0.273348	−	0.273348i	0.0259450	−	0.0259450i
$112$	−11.7191			−1.10735
$113$	4.04975	−	4.04975i	0.380968	−	0.380968i	−0.490483	−	0.871451i	$-0.663179\pi$
$113$	4.04975	−	4.04975i	0.380968	−	0.380968i	0.871451	+	0.490483i	$0.163179\pi$
$114$	−2.88239			−0.269961
$115$	−7.90214	−	4.45791i	−0.736878	−	0.415702i
$116$			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
$122$		−	8.32609i		−	0.753809i
$123$	−7.04220			−0.634974
$124$	0.706736	+	0.706736i	0.0634667	+	0.0634667i
$125$	−7.66586	+	8.13846i	−0.685655	+	0.727926i
$126$	10.0151			0.892220
$127$	0.575918	−	0.575918i	0.0511044	−	0.0511044i	−0.681093	−	0.732197i	$-0.738495\pi$
$127$	0.575918	−	0.575918i	0.0511044	−	0.0511044i	0.732197	+	0.681093i	$0.238495\pi$
$128$			13.1917i			1.16599i
$129$	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	$0.748427\pi$
$132$			1.02961i			0.0896159i
$133$	5.15059	−	5.15059i	0.446613	−	0.446613i
$134$	23.9651			2.07027
$135$	−7.30133	−	4.11897i	−0.628398	−	0.354504i
$136$	0.148995	+	0.148995i	0.0127762	+	0.0127762i
$137$	−19.2374			−1.64356			−0.821782	−	0.569802i	$-0.807020\pi$
$137$	−19.2374			−1.64356			−0.821782	+	0.569802i	$0.807020\pi$
$138$		−	4.16637i		−	0.354665i
$139$			15.8490i			1.34430i	0.740417	+	0.672148i	$0.234628\pi$
$139$			15.8490i			1.34430i	−0.740417	+	0.672148i	$0.765372\pi$
$140$	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
$145$	2.99207	+	10.7374i	0.248478	+	0.891692i
$146$	10.0479			0.831566
$147$	−0.127507	+	0.127507i	−0.0105166	+	0.0105166i
$148$	−0.174002			−0.0143029
$149$	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	$0.231210\pi$
$150$	−4.98470	−	1.22972i	−0.406999	−	0.100406i
$151$	13.9253	−	13.9253i	1.13322	−	1.13322i	0.143585	−	0.989638i	$-0.454137\pi$
$151$	13.9253	−	13.9253i	1.13322	−	1.13322i	0.989638	−	0.143585i	$-0.0458631\pi$
$152$	−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	0.864859	−	0.502014i	$-0.167408\pi$
$157$	4.54644	+	4.54644i	0.362845	+	0.362845i	−0.502014	+	0.864859i	$0.667408\pi$
$158$	8.66887			0.689658
$159$		−	6.41623i		−	0.508840i
$160$	−1.02522	−	3.67914i	−0.0810510	−	0.290861i
$161$	7.44495	+	7.44495i	0.586744	+	0.586744i
$162$			7.72914i			0.607258i
$163$			13.1358i			1.02887i	0.857528	+	0.514437i	$0.171999\pi$
$163$			13.1358i			1.02887i	−0.857528	+	0.514437i	$0.828001\pi$
$164$	2.24139	+	2.24139i	0.175023	+	0.175023i
$165$	2.02980	+	7.28417i	0.158019	+	0.567072i
$166$		−	5.62795i		−	0.436814i
$167$	3.28516			0.254213			0.127107	−	0.991889i	$-0.459431\pi$
$167$	3.28516			0.254213			0.127107	+	0.991889i	$0.459431\pi$
$168$	−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	$-0.301507\pi$
$173$	−2.99677	−	2.99677i	−0.227840	−	0.227840i	−0.811790	+	0.583950i	$0.801507\pi$
$174$	−3.61940	+	3.61940i	−0.274386	+	0.274386i
$175$	11.1047	−	6.70984i	0.839433	−	0.507216i
$176$	−15.9655	+	15.9655i	−1.20344	+	1.20344i
$177$	−1.81403			−0.136351
$178$	19.2062	−	19.2062i	1.43957	−	1.43957i
$179$	13.9617			1.04354			0.521772	−	0.853085i	$-0.325271\pi$
$179$	13.9617			1.04354			0.521772	+	0.853085i	$0.325271\pi$
$180$	0.464633	+	1.66739i	0.0346317	+	0.124280i
$181$			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
$187$			0.409276i			0.0299292i
$188$	0.700432			0.0510842
$189$	6.87890	+	6.87890i	0.500366	+	0.500366i
$190$	8.29899	+	4.68179i	0.602072	+	0.339653i
$191$	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
$193$		−	8.55560i		−	0.615845i	−0.951411	−	0.307923i	$-0.900366\pi$
$193$		−	8.55560i		−	0.615845i	0.951411	−	0.307923i	$-0.0996338\pi$
$194$	8.15169			0.585257
$195$		0			0
$196$	0.0811660			0.00579757
$197$			7.65684i			0.545527i	0.962081	+	0.272764i	$0.0879377\pi$
$197$			7.65684i			0.545527i	−0.962081	+	0.272764i	$0.912062\pi$
$198$	13.6441	−	13.6441i	0.969645	−	0.969645i
$199$	−15.3276			−1.08654			−0.543272	−	0.839557i	$-0.682815\pi$
$199$	−15.3276			−1.08654			−0.543272	+	0.839557i	$0.682815\pi$
$200$	−6.65558	−	11.0149i	−0.470621	−	0.778869i
$201$	7.55078	+	7.55078i	0.532591	+	0.532591i
$202$	−3.81153			−0.268178
$203$		−	12.9351i		−	0.907868i
$204$		−	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
$210$	5.18922	+	2.92744i	0.358090	+	0.202013i
$211$	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
$213$	−5.19952			−0.356265
$214$	3.89503	−	3.89503i	0.266259	−	0.266259i
$215$	−0.266388	−	0.150280i	−0.0181675	−	0.0102490i
$216$	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
$223$	−18.9731			−1.27053			−0.635265	−	0.772294i	$-0.719109\pi$
$223$	−18.9731			−1.27053			−0.635265	+	0.772294i	$0.719109\pi$
$224$			4.43218i			0.296138i
$225$	6.57429	+	10.8803i	0.438286	+	0.725355i
$226$	−6.14771	−	6.14771i	−0.408939	−	0.408939i
$227$			26.9587i			1.78931i	0.446755	+	0.894656i	$0.352579\pi$
$227$			26.9587i			1.78931i	−0.446755	+	0.894656i	$0.647421\pi$
$228$			0.578104i			0.0382858i
$229$	−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
$232$	−12.8305			−0.842366
$233$	6.75797	+	6.75797i	0.442729	+	0.442729i	0.892928	−	0.450199i	$-0.148647\pi$
$233$	6.75797	+	6.75797i	0.442729	+	0.442729i	−0.450199	+	0.892928i	$0.648647\pi$
$234$		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	$0.221021\pi$
$240$	3.35631	−	5.94943i	0.216649	−	0.384034i
$241$	1.94097	−	1.94097i	0.125029	−	0.125029i	−0.641824	−	0.766852i	$-0.721822\pi$
$241$	1.94097	−	1.94097i	0.125029	−	0.125029i	0.766852	+	0.641824i	$0.221822\pi$
$242$	−21.2441			−1.36562
$243$	−10.3881	+	10.3881i	−0.666397	+	0.666397i
$244$	−1.66991			−0.106905
$245$	0.574225	−	0.160013i	0.0366859	−	0.0102228i
$246$			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	$-0.0285057\pi$
$252$		−	2.00868i		−	0.126535i
$253$	20.2852			1.27532
$254$	−0.874270	−	0.874270i	−0.0548566	−	0.0548566i
$255$	−0.0332374	−	0.119277i	−0.00208141	−	0.00746939i
$256$	7.14642			0.446651
$257$	−14.1859	+	14.1859i	−0.884895	+	0.884895i	−0.994027	−	0.109132i	$-0.965193\pi$
$257$	−14.1859	+	14.1859i	−0.884895	+	0.884895i	0.109132	+	0.994027i	$0.465193\pi$
$258$		−	0.140452i		−	0.00874414i
$259$	1.48298			0.0921478
$260$		0			0
$261$	12.6738			0.784490
$262$			24.4500i			1.51053i
$263$	6.66222	−	6.66222i	0.410810	−	0.410810i	−0.471210	−	0.882021i	$-0.656183\pi$
$263$	6.66222	−	6.66222i	0.410810	−	0.410810i	0.882021	+	0.471210i	$0.156183\pi$
$264$	−8.70414			−0.535703
$265$	−10.4217	+	18.4736i	−0.640199	+	1.13482i
$266$	−7.81884	−	7.81884i	−0.479404	−	0.479404i
$267$	12.1028			0.740679
$268$		−	4.80653i		−	0.293605i
$269$		−	3.21488i		−	0.196015i	−0.995186	−	0.0980075i	$-0.968753\pi$
$269$		−	3.21488i		−	0.196015i	0.995186	−	0.0980075i	$-0.0312469\pi$
$270$	−6.25278	+	11.0838i	−0.380532	+	0.674536i
$271$	−10.7387	+	10.7387i	−0.652332	+	0.652332i	−0.953554	−	0.301222i	$-0.902605\pi$
$271$	−10.7387	+	10.7387i	−0.652332	+	0.652332i	0.301222	+	0.953554i	$0.402605\pi$
$272$	0.261431	−	0.261431i	0.0158516	−	0.0158516i
$273$		0			0
$274$			29.2033i			1.76424i
$275$	5.98728	−	24.2695i	0.361047	−	1.46351i
$276$	−0.835623			−0.0502986
$277$	−7.54121	+	7.54121i	−0.453107	+	0.453107i	−0.896385	−	0.443277i	$-0.853816\pi$
$277$	−7.54121	+	7.54121i	−0.453107	+	0.453107i	0.443277	+	0.896385i	$0.353816\pi$
$278$	24.0595			1.44300
$279$	5.90165	−	5.90165i	0.353323	−	0.353323i
$280$	4.00892	+	14.3865i	0.239579	+	0.859759i
$281$	−12.7630	+	12.7630i	−0.761379	+	0.761379i	−0.976572	−	0.215193i	$-0.930962\pi$
$281$	−12.7630	+	12.7630i	−0.761379	+	0.761379i	0.215193	+	0.976572i	$0.430962\pi$
$282$	1.67037	+	1.67037i	0.0994689	+	0.0994689i
$283$	4.07125	+	4.07125i	0.242010	+	0.242010i	0.817681	−	0.575671i	$-0.195259\pi$
$283$	4.07125	+	4.07125i	0.242010	+	0.242010i	−0.575671	+	0.817681i	$0.695259\pi$
$284$	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
$288$	−4.34265			−0.255893
$289$			16.9933i			0.999606i
$290$	16.2999	−	4.54209i	0.957161	−	0.266721i
$291$	2.56839	+	2.56839i	0.150562	+	0.150562i
$292$		−	2.01524i		−	0.117933i
$293$			3.19607i			0.186717i	0.995633	+	0.0933583i	$0.0297602\pi$
$293$			3.19607i			0.186717i	−0.995633	+	0.0933583i	$0.970240\pi$
$294$	0.193562	+	0.193562i	0.0112888	+	0.0112888i
$295$	5.22297	+	2.94648i	0.304093	+	0.171551i
$296$		−	1.47099i		−	0.0854994i
$297$	18.7429			1.08757
$298$	−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
$305$	−11.8141	+	3.29211i	−0.676476	+	0.188506i
$306$	−0.223419	+	0.223419i	−0.0127720	+	0.0127720i
$307$	24.2740			1.38539			0.692695	−	0.721231i	$-0.256423\pi$
$307$	24.2740			1.38539			0.692695	+	0.721231i	$0.256423\pi$
$308$	−2.79294	+	2.79294i	−0.159142	+	0.159142i
$309$	4.51262			0.256714
$310$	5.47509	−	9.70521i	0.310964	−	0.551219i
$311$		−	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	−0.903644	−	0.428285i	$-0.859118\pi$
$313$	−8.40997	+	8.40997i	−0.475359	+	0.475359i	0.428285	+	0.903644i	$0.359118\pi$
$314$	6.90170	−	6.90170i	0.389486	−	0.389486i
$315$	−3.95996	−	14.2108i	−0.223118	−	0.800687i
$316$		−	1.73866i		−	0.0978074i
$317$			11.9484i			0.671087i	0.942025	+	0.335543i	$0.108920\pi$
$317$			11.9484i			0.671087i	−0.942025	+	0.335543i	$0.891080\pi$
$318$	−9.74013			−0.546199
$319$	−17.6221	−	17.6221i	−0.986651	−	0.986651i
$320$	13.8708	−	3.86523i	0.775403	−	0.216073i
$321$	2.45445			0.136994
$322$	11.3018	−	11.3018i	0.629824	−	0.629824i
$323$			0.229800i			0.0127864i
$324$	1.55018			0.0861214
$325$		0			0
$326$	19.9407			1.10442
$327$		−	1.51648i		−	0.0838613i
$328$	−18.9484	+	18.9484i	−1.04625	+	1.04625i
$329$	−5.96961			−0.329115
$330$	11.0577	−	3.08133i	0.608707	−	0.169621i
$331$	−15.1666	−	15.1666i	−0.833631	−	0.833631i	0.154380	−	0.988011i	$-0.450662\pi$
$331$	−15.1666	−	15.1666i	−0.833631	−	0.833631i	−0.988011	+	0.154380i	$0.950662\pi$
$332$	−1.12876			−0.0619489
$333$			1.45302i			0.0796250i
$334$		−	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	$-0.566860\pi$
$337$	14.1264	−	14.1264i	0.769514	−	0.769514i	0.978021	+	0.208507i	$0.0668604\pi$
$338$		0			0
$339$		−	3.87397i		−	0.210405i
$340$	−0.0273845	+	0.0485421i	−0.00148514	+	0.00263257i
$341$	−16.4118			−0.888746
$342$	7.66089	−	7.66089i	0.414253	−	0.414253i
$343$	−18.8559			−1.01812
$344$	0.248946	−	0.248946i	0.0134223	−	0.0134223i
$345$	−5.91179	+	1.64737i	−0.318280	+	0.0886914i
$346$	−4.54924	+	4.54924i	−0.244569	+	0.244569i
$347$	−17.4159	−	17.4159i	−0.934936	−	0.934936i	0.0630727	−	0.998009i	$-0.479910\pi$
$347$	−17.4159	−	17.4159i	−0.934936	−	0.934936i	−0.998009	+	0.0630727i	$0.979910\pi$
$348$	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
$353$	−8.79926			−0.468337			−0.234169	−	0.972196i	$-0.575237\pi$
$353$	−8.79926			−0.468337			−0.234169	+	0.972196i	$0.575237\pi$
$354$			2.75379i			0.146362i
$355$	14.9705	+	8.44543i	0.794550	+	0.448237i
$356$	−3.85208	−	3.85208i	−0.204160	−	0.204160i
$357$			0.143690i			0.00760489i
$358$		−	21.1945i		−	1.12016i
$359$	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
$362$	13.1277			0.689976
$363$	−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	0.880069	−	0.474846i	$-0.157496\pi$
$367$	7.76295	+	7.76295i	0.405223	+	0.405223i	−0.474846	+	0.880069i	$0.657496\pi$
$368$	−12.9575	−	12.9575i	−0.675455	−	0.675455i
$369$	18.7169	−	18.7169i	0.974365	−	0.974365i
$370$	0.520739	+	1.86874i	0.0270719	+	0.0971510i
$371$	17.4048	−	17.4048i	0.903612	−	0.903612i
$372$	0.676060			0.0350521
$373$	7.48104	−	7.48104i	0.387354	−	0.387354i	−0.486389	−	0.873742i	$-0.661686\pi$
$373$	7.48104	−	7.48104i	0.387354	−	0.387354i	0.873742	+	0.486389i	$0.161686\pi$
$374$	0.621300			0.0321267
$375$	0.226045	+	7.55917i	0.0116729	+	0.390354i
$376$			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
$382$		−	25.6746i		−	1.31363i
$383$	−26.0567			−1.33144			−0.665718	−	0.746204i	$-0.731874\pi$
$383$	−26.0567			−1.33144			−0.665718	+	0.746204i	$0.731874\pi$
$384$	6.30954	+	6.30954i	0.321982	+	0.321982i
$385$	−14.2531	+	25.2653i	−0.726407	+	1.28764i
$386$	−12.9878			−0.661061
$387$	−0.245905	+	0.245905i	−0.0125001	+	0.0125001i
$388$		−	1.63493i		−	0.0830012i
$389$	−32.4888			−1.64725			−0.823623	−	0.567138i	$-0.808050\pi$
$389$	−32.4888			−1.64725			−0.823623	+	0.567138i	$0.808050\pi$
$390$		0			0
$391$	−0.332166			−0.0167983
$392$			0.686164i			0.0346565i
$393$	−7.70358	+	7.70358i	−0.388594	+	0.388594i
$394$	11.6234			0.585580
$395$	−3.42764	−	12.3005i	−0.172463	−	0.618906i
$396$	−2.73652	−	2.73652i	−0.137515	−	0.137515i
$397$	24.1854			1.21383			0.606914	−	0.794767i	$-0.292407\pi$
$397$	24.1854			1.21383			0.606914	+	0.794767i	$0.292407\pi$
$398$			23.2680i			1.16632i
$399$		−	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	$0.555990\pi$
$401$	−23.2202	+	23.2202i	−1.15956	+	1.15956i	−0.984570	+	0.174992i	$0.944010\pi$
$402$	11.4624	−	11.4624i	0.571695	−	0.571695i
$403$		0			0
$404$			0.764454i			0.0380330i
$405$	10.9671	−	3.05608i	0.544960	−	0.151858i
$406$	−19.6361			−0.974524
$407$	2.02033	−	2.02033i	0.100144	−	0.100144i
$408$	0.142528			0.00705620
$409$	−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	$0.362168\pi$
$410$	17.3641	−	30.7798i	0.857552	−	1.52011i
$411$	−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
$418$	−21.3040			−1.04201
$419$			2.21980i			0.108444i	0.998529	+	0.0542221i	$0.0172679\pi$
$419$			2.21980i			0.108444i	−0.998529	+	0.0542221i	$0.982732\pi$
$420$	0.587139	−	1.04077i	0.0286494	−	0.0507843i
$421$	24.4795	+	24.4795i	1.19306	+	1.19306i	0.976204	+	0.216853i	$0.0695792\pi$
$421$	24.4795	+	24.4795i	1.19306	+	1.19306i	0.216853	+	0.976204i	$0.430421\pi$
$422$		−	30.1116i		−	1.46581i
$423$		−	5.84901i		−	0.284389i
$424$	−17.2641	−	17.2641i	−0.838417	−	0.838417i
$425$	−0.0980403	+	0.397408i	−0.00475565	+	0.0192771i
$426$			7.89311i			0.382423i
$427$	14.2323			0.688747
$428$	−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	0.678404	−	0.734689i	$-0.262672\pi$
$431$	−1.16851	−	1.16851i	−0.0562851	−	0.0562851i	−0.734689	+	0.678404i	$0.762672\pi$
$432$	−11.9723	−	11.9723i	−0.576017	−	0.576017i
$433$	−10.4765	−	10.4765i	−0.503466	−	0.503466i	0.409047	−	0.912513i	$-0.365861\pi$
$433$	−10.4765	−	10.4765i	−0.503466	−	0.503466i	−0.912513	+	0.409047i	$0.865861\pi$
$434$	−9.14370	+	9.14370i	−0.438912	+	0.438912i
$435$	6.56677	+	3.70457i	0.314853	+	0.177621i
$436$	−0.482664	+	0.482664i	−0.0231154	+	0.0231154i
$437$	11.3897			0.544845
$438$	4.80587	−	4.80587i	0.229633	−	0.229633i
$439$	−21.8725			−1.04392			−0.521959	−	0.852970i	$-0.674799\pi$
$439$	−21.8725			−1.04392			−0.521959	+	0.852970i	$0.674799\pi$
$440$	25.0610	+	14.1379i	1.19474	+	0.673997i
$441$		−	0.677783i		−	0.0322754i
$442$		0			0
$443$	−6.14972	+	6.14972i	−0.292182	+	0.292182i	−0.837942	−	0.545760i	$-0.816241\pi$
$443$	−6.14972	+	6.14972i	−0.292182	+	0.292182i	0.545760	+	0.837942i	$0.316241\pi$
$444$	−0.0832249	+	0.0832249i	−0.00394968	+	0.00394968i
$445$	−34.8464	−	19.6582i	−1.65188	−	0.931890i
$446$			28.8020i			1.36381i
$447$		−	0.974228i		−	0.0460794i
$448$	−16.7099			−0.789469
$449$	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	$0.714816\pi$
$450$	16.5168	−	9.98008i	0.778612	−	0.470465i
$451$	−52.0494			−2.45091
$452$	−1.23301	+	1.23301i	−0.0579958	+	0.0579958i
$453$		−	13.3209i		−	0.625869i
$454$	40.9246			1.92069
$455$		0			0
$456$	−4.88720			−0.228864
$457$		−	30.0361i		−	1.40503i	−0.711670	−	0.702514i	$-0.752061\pi$
$457$		−	30.0361i		−	1.40503i	0.711670	−	0.702514i	$-0.247939\pi$
$458$	−16.9718	+	16.9718i	−0.793042	+	0.793042i
$459$	−0.306911			−0.0143254
$460$	2.40593	+	1.35728i	0.112177	+	0.0632834i
$461$	1.85792	+	1.85792i	0.0865318	+	0.0865318i	0.749048	−	0.662516i	$-0.230511\pi$
$461$	1.85792	+	1.85792i	0.0865318	+	0.0865318i	−0.662516	+	0.749048i	$0.730511\pi$
$462$	−13.3210			−0.619749
$463$		−	25.1475i		−	1.16870i	−0.811500	−	0.584352i	$-0.801349\pi$
$463$		−	25.1475i		−	1.16870i	0.811500	−	0.584352i	$-0.198651\pi$
$464$			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	$-0.913190\pi$
$467$	−14.9907	+	14.9907i	−0.693688	+	0.693688i	0.269354	+	0.963041i	$0.413190\pi$
$468$		0			0
$469$			40.9648i			1.89158i
$470$	−2.09619	−	7.52245i	−0.0966902	−	0.346985i
$471$	4.34910			0.200396
$472$	−4.88100	+	4.88100i	−0.224666	+	0.224666i
$473$	0.683832			0.0314426
$474$	4.14630	−	4.14630i	0.190446	−	0.190446i
$475$	3.36173	−	13.6268i	0.154247	−	0.625243i
$476$	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
$483$	7.12181			0.324054
$484$			4.26079i			0.193672i
$485$	−3.22315	−	11.5667i	−0.146356	−	0.525216i
$486$	15.7696	+	15.7696i	0.715324	+	0.715324i
$487$		−	5.56643i		−	0.252239i	−0.992015	−	0.126119i	$-0.959748\pi$
$487$		−	5.56643i		−	0.252239i	0.992015	−	0.126119i	$-0.0402523\pi$
$488$		−	14.1172i		−	0.639054i
$489$	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	$-0.0440255\pi$
$492$	2.14411			0.0966638
$493$	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	$0.313160\pi$
$500$	2.33399	−	2.47788i	0.104379	−	0.110814i
$501$	1.57129	−	1.57129i	0.0701999	−	0.0701999i
$502$	−4.30183			−0.192000
$503$	2.59944	−	2.59944i	0.115903	−	0.115903i	−0.646776	−	0.762680i	$-0.723883\pi$
$503$	2.59944	−	2.59944i	0.115903	−	0.115903i	0.762680	+	0.646776i	$0.223883\pi$
$504$	16.9810			0.756395
$505$	1.50707	+	5.40829i	0.0670635	+	0.240666i
$506$		−	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
$512$			15.5347i			0.686544i
$513$	10.5238			0.464635
$514$	21.5349	+	21.5349i	0.949865	+	0.949865i
$515$	−12.9927	−	7.32972i	−0.572529	−	0.322986i
$516$	−0.0281695			−0.00124009
$517$	−8.13269	+	8.13269i	−0.357675	+	0.357675i
$518$		−	2.25123i		−	0.0989133i
$519$	−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	$0.211258\pi$
$522$		−	19.2394i		−	0.842088i
$523$	−5.93427	+	5.93427i	−0.259487	+	0.259487i	−0.824846	−	0.565358i	$-0.808738\pi$
$523$	−5.93427	+	5.93427i	−0.259487	+	0.259487i	0.565358	+	0.824846i	$0.308738\pi$
$524$	4.90379			0.214223
$525$	2.10203	−	8.52064i	0.0917403	−	0.371871i
$526$	−10.1136	−	10.1136i	−0.440972	−	0.440972i
$527$	0.268739			0.0117064
$528$			15.2725i			0.664651i
$529$		−	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
$535$	−7.06686	−	3.98669i	−0.305527	−	0.172360i
$536$	40.6336			1.75510
$537$	6.67783	−	6.67783i	0.288170	−	0.288170i
$538$	−4.88034			−0.210407
$539$	−0.942415	+	0.942415i	−0.0405927	+	0.0405927i
$540$	2.22300	+	1.25408i	0.0956627	+	0.0539671i
$541$	4.13066	−	4.13066i	0.177591	−	0.177591i	−0.612714	−	0.790305i	$-0.709922\pi$
$541$	4.13066	−	4.13066i	0.177591	−	0.177591i	0.790305	+	0.612714i	$0.209922\pi$
$542$	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	0.517691	−	0.855568i	$-0.326792\pi$
$547$	−7.90229	−	7.90229i	−0.337877	−	0.337877i	−0.855568	+	0.517691i	$0.826792\pi$
$548$	5.85713			0.250204
$549$			13.9447i			0.595147i
$550$	−36.8423	−	9.08897i	−1.57096	−	0.387555i
$551$	−9.89447	−	9.89447i	−0.421519	−	0.421519i
$552$		−	7.06422i		−	0.300673i
$553$			14.8182i			0.630133i
$554$	11.4479	+	11.4479i	0.486375	+	0.486375i
$555$	−0.424720	+	0.752863i	−0.0180283	+	0.0319573i
$556$		−	4.82547i		−	0.204646i
$557$	−11.7868			−0.499423			−0.249712	−	0.968320i	$-0.580336\pi$
$557$	−11.7868			−0.499423			−0.249712	+	0.968320i	$0.580336\pi$
$558$	−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	$-0.0130184\pi$
$563$	22.7376	+	22.7376i	0.958277	+	0.958277i	−0.0408873	+	0.999164i	$0.513018\pi$
$564$	0.335015	−	0.335015i	0.0141067	−	0.0141067i
$565$	−6.29238	+	11.1540i	−0.264723	+	0.469250i
$566$	6.18034	−	6.18034i	0.259779	−	0.259779i
$567$	−13.2118			−0.554845
$568$	−13.9903	+	13.9903i	−0.587019	+	0.587019i
$569$	−9.28474			−0.389237			−0.194618	−	0.980879i	$-0.562347\pi$
$569$	−9.28474			−0.389237			−0.194618	+	0.980879i	$0.562347\pi$
$570$	6.20868	−	1.73010i	0.260053	−	0.0724659i
$571$		−	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
$577$			4.57285i			0.190370i	0.995460	+	0.0951852i	$0.0303443\pi$
$577$			4.57285i			0.190370i	−0.995460	+	0.0951852i	$0.969656\pi$
$578$	25.7966			1.07300
$579$	−4.09212	−	4.09212i	−0.170063	−	0.170063i
$580$	−0.910980	−	3.26916i	−0.0378264	−	0.135745i
$581$	9.62018			0.399112
$582$	3.89894	−	3.89894i	0.161616	−	0.161616i
$583$		−	47.4228i		−	1.96405i
$584$	17.0365			0.704975
$585$		0			0
$586$	4.85179			0.200425
$587$		−	7.19181i		−	0.296838i	−0.988925	−	0.148419i	$-0.952582\pi$
$587$		−	7.19181i		−	0.296838i	0.988925	−	0.148419i	$-0.0474184\pi$
$588$	0.0388215	−	0.0388215i	0.00160097	−	0.00160097i
$589$	−9.21486			−0.379692
$590$	4.47289	−	7.92870i	0.184146	−	0.326420i
$591$	3.66225	+	3.66225i	0.150645	+	0.150645i
$592$	−2.58103			−0.106080
$593$		−	28.0561i		−	1.15212i	−0.817406	−	0.576062i	$-0.804589\pi$
$593$		−	28.0561i		−	1.15212i	0.817406	−	0.576062i	$-0.195411\pi$
$594$		−	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	$0.00593722\pi$
$599$			0.912959i			0.0373025i	−0.999826	+	0.0186513i	$0.994063\pi$
$600$	−8.45174	−	2.08504i	−0.345041	−	0.0851213i
$601$	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
$603$	−40.1373			−1.63452
$604$	−4.23976	+	4.23976i	−0.172514	+	0.172514i
$605$	8.39983	+	30.1438i	0.341502	+	1.22552i
$606$	−1.82305	+	1.82305i	−0.0740562	+	0.0740562i
$607$	−27.4162	−	27.4162i	−1.11279	−	1.11279i	−0.992772	−	0.120017i	$-0.961705\pi$
$607$	−27.4162	−	27.4162i	−1.11279	−	1.11279i	−0.120017	−	0.992772i	$-0.538295\pi$
$608$	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
$613$	24.6113			0.994042			0.497021	−	0.867739i	$-0.334427\pi$
$613$	24.6113			0.994042			0.497021	+	0.867739i	$0.334427\pi$
$614$		−	36.8490i		−	1.48711i
$615$	15.1689	−	4.22695i	0.611670	−	0.170447i
$616$	−23.6110	−	23.6110i	−0.951316	−	0.951316i
$617$		−	15.4154i		−	0.620600i	−0.950639	−	0.310300i	$-0.899571\pi$
$617$		−	15.4154i		−	0.620600i	0.950639	−	0.310300i	$-0.100429\pi$
$618$		−	6.85037i		−	0.275562i
$619$	−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
$622$	−25.6631			−1.02900
$623$	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
$630$	−21.5726	+	6.01140i	−0.859475	+	0.239500i
$631$	−8.91183	+	8.91183i	−0.354774	+	0.354774i	−0.861882	−	0.507108i	$-0.830714\pi$
$631$	−8.91183	+	8.91183i	−0.354774	+	0.354774i	0.507108	+	0.861882i	$0.330714\pi$
$632$	14.6984			0.584670
$633$	9.48740	−	9.48740i	0.377090	−	0.377090i
$634$	18.1382			0.720359
$635$	−0.894844	+	1.58621i	−0.0355108	+	0.0629469i
$636$			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	$-0.0617476\pi$
$642$		−	3.72597i		−	0.147052i
$643$	27.8114			1.09677			0.548387	−	0.836225i	$-0.315242\pi$
$643$	27.8114			1.09677			0.548387	+	0.836225i	$0.315242\pi$
$644$	−2.26673	−	2.26673i	−0.0893216	−	0.0893216i
$645$	−0.199291	+	0.0555341i	−0.00784708	+	0.00218665i
$646$	0.348847			0.0137252
$647$	−13.0281	+	13.0281i	−0.512188	+	0.512188i	−0.915196	−	0.403008i	$-0.867965\pi$
$647$	−13.0281	+	13.0281i	−0.512188	+	0.512188i	0.403008	+	0.915196i	$0.367965\pi$
$648$			13.1050i			0.514814i
$649$	−13.4076			−0.526296
$650$		0			0
$651$	−5.76190			−0.225826
$652$		−	3.99939i		−	0.156628i
$653$	5.21579	−	5.21579i	0.204110	−	0.204110i	−0.597648	−	0.801758i	$-0.703898\pi$
$653$	5.21579	−	5.21579i	0.204110	−	0.204110i	0.801758	+	0.597648i	$0.203898\pi$
$654$	−2.30208			−0.0900185
$655$	34.6929	−	9.66746i	1.35556	−	0.377739i
$656$	33.2473	+	33.2473i	1.29809	+	1.29809i
$657$	−16.8284			−0.656538
$658$			9.06214i			0.353279i
$659$		−	13.9472i		−	0.543304i	−0.962396	−	0.271652i	$-0.912430\pi$
$659$		−	13.9472i		−	0.543304i	0.962396	−	0.271652i	$-0.0875700\pi$
$660$	−0.618002	−	2.21778i	−0.0240557	−	0.0863269i
$661$	0.160275	−	0.160275i	0.00623398	−	0.00623398i	−0.703983	−	0.710217i	$-0.748597\pi$
$661$	0.160275	−	0.160275i	0.00623398	−	0.00623398i	0.710217	+	0.703983i	$0.248597\pi$
$662$	−23.0236	+	23.0236i	−0.894837	+	0.894837i
$663$		0			0
$664$		−	9.54239i		−	0.370317i
$665$	−8.00284	+	14.1859i	−0.310337	+	0.550107i
$666$	2.20575			0.0854711
$667$	14.3020	−	14.3020i	0.553776	−	0.553776i
$668$	−1.00022			−0.0386996
$669$	−9.07477	+	9.07477i	−0.350851	+	0.350851i
$670$	−51.6208	+	14.3846i	−1.99429	+	0.555724i
$671$	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	$-0.0256265\pi$
$673$	23.7719	+	23.7719i	0.916340	+	0.916340i	−0.0804210	+	0.996761i	$0.525626\pi$
$674$	−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	0.999483	−	0.0321566i	$-0.0102375\pi$
$677$	25.1691	+	25.1691i	0.967326	+	0.967326i	−0.0321566	+	0.999483i	$0.510238\pi$
$678$	−5.88087			−0.225854
$679$			13.9341i			0.534743i
$680$	−0.410368	−	0.231505i	−0.0157369	−	0.00887779i
$681$	12.8943	+	12.8943i	0.494110	+	0.494110i
$682$			24.9138i			0.953999i
$683$			30.7567i			1.17687i	0.808543	+	0.588437i	$0.200256\pi$
$683$			30.7567i			1.17687i	−0.808543	+	0.588437i	$0.799744\pi$
$684$	−1.53650	−	1.53650i	−0.0587494	−	0.0587494i
$685$	41.4374	−	11.5469i	1.58324	−	0.441184i
$686$			28.6242i			1.09288i
$687$	−10.6948			−0.408032
$688$	−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	$0.0137109\pi$
$691$	27.3944	+	27.3944i	1.04213	+	1.04213i	0.0430609	+	0.999072i	$0.486289\pi$
$692$	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
$695$	−9.51307	−	34.1388i	−0.360851	−	1.29496i
$696$	−6.13682	+	6.13682i	−0.232615	+	0.232615i
$697$	0.852297			0.0322831
$698$	−29.2479	+	29.2479i	−1.10705	+	1.10705i
$699$	6.46464			0.244515
$700$	−3.38098	+	2.04291i	−0.127789	+	0.0772148i
$701$			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
$707$		−	6.51526i		−	0.245032i
$708$	0.552310			0.0207571
$709$	−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	$0.954209\pi$
$710$	12.8206	−	22.7259i	0.481147	−	0.852887i
$711$	−14.5188			−0.544499
$712$	32.5649	−	32.5649i	1.22042	−	1.22042i
$713$		−	13.3197i		−	0.498826i
$714$	0.218128			0.00816325
$715$		0			0
$716$	−4.25084			−0.158861
$717$		−	1.90138i		−	0.0710085i
$718$	16.8892	−	16.8892i	0.630298	−	0.630298i
$719$	−30.9635			−1.15474			−0.577372	−	0.816481i	$-0.695922\pi$
$719$	−30.9635			−1.15474			−0.577372	+	0.816481i	$0.695922\pi$
$720$	6.89206	+	24.7330i	0.256852	+	0.921744i
$721$	12.2410	+	12.2410i	0.455880	+	0.455880i
$722$	16.8811			0.628251
$723$		−	1.85672i		−	0.0690522i
$724$		−	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	$-0.609785\pi$
$727$	16.2588	−	16.2588i	0.603007	−	0.603007i	0.941109	+	0.338103i	$0.109785\pi$
$728$		0			0
$729$		−	5.33729i		−	0.197678i
$730$	−21.6431	+	6.03103i	−0.801047	+	0.223218i
$731$	−0.0111976			−0.000414157
$732$	−0.798715	+	0.798715i	−0.0295214	+	0.0295214i
$733$	31.2515			1.15430			0.577150	−	0.816638i	$-0.304165\pi$
$733$	31.2515			1.15430			0.577150	+	0.816638i	$0.304165\pi$
$734$	11.7845	−	11.7845i	0.434975	−	0.434975i
$735$	0.198117	−	0.351185i	0.00730766	−	0.0129536i
$736$	−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
$743$	32.9660			1.20941			0.604703	−	0.796451i	$-0.293292\pi$
$743$	32.9660			1.20941			0.604703	+	0.796451i	$0.293292\pi$
$744$			5.71531i			0.209533i
$745$	−1.58241	+	2.80500i	−0.0579750	+	0.102767i
$746$	−11.3566	−	11.3566i	−0.415794	−	0.415794i
$747$			9.42584i			0.344873i
$748$		−	0.124610i		−	0.00455621i
$749$	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	$-0.191172\pi$
$752$	10.3897			0.378875
$753$	−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	0.919036	+	0.394173i	$0.128969\pi$
$757$	36.1312	+	36.1312i	1.31321	+	1.31321i	0.394173	+	0.919036i	$0.371031\pi$
$758$	10.5217	+	10.5217i	0.382164	+	0.382164i
$759$	9.70238	−	9.70238i	0.352174	−	0.352174i
$760$	14.0712	+	7.93813i	0.510417	+	0.287946i
$761$	−0.818500	+	0.818500i	−0.0296706	+	0.0296706i	−0.721786	−	0.692116i	$-0.756679\pi$
$761$	−0.818500	+	0.818500i	−0.0296706	+	0.0296706i	0.692116	+	0.721786i	$0.256679\pi$
$762$	−0.836323			−0.0302968
$763$	4.11363	−	4.11363i	0.148923	−	0.148923i
$764$	−5.14940			−0.186299
$765$	0.405355	+	0.228677i	0.0146557	+	0.00826783i
$766$			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
$772$			2.60488i			0.0937517i
$773$	7.19282			0.258708			0.129354	−	0.991598i	$-0.458710\pi$
$773$	7.19282			0.258708			0.129354	+	0.991598i	$0.458710\pi$
$774$	0.373296	+	0.373296i	0.0134178	+	0.0134178i
$775$	−15.9358	−	3.93136i	−0.572432	−	0.141219i
$776$	13.8215			0.496162
$777$	0.709305	−	0.709305i	0.0254462	−	0.0254462i
$778$			49.3194i			1.76819i
$779$	−29.2247			−1.04708
$780$		0			0
$781$	−38.4300			−1.37513
$782$			0.504243i			0.0180317i
$783$	13.2146	−	13.2146i	0.472251	−	0.472251i
$784$	1.20396			0.0429986
$785$	−12.5219	−	7.06412i	−0.446927	−	0.252129i
$786$	11.6944	+	11.6944i	0.417125	+	0.417125i
$787$	7.17886			0.255899			0.127949	−	0.991781i	$-0.459160\pi$
$787$	7.17886			0.255899			0.127949	+	0.991781i	$0.459160\pi$
$788$		−	2.33124i		−	0.0830470i
$789$		−	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
$795$	3.85122	+	13.8206i	0.136589	+	0.490165i
$796$	4.66672			0.165407
$797$	27.8584	−	27.8584i	0.986795	−	0.986795i	−0.0131190	−	0.999914i	$-0.504176\pi$
$797$	27.8584	−	27.8584i	0.986795	−	0.986795i	0.999914	+	0.0131190i	$0.00417602\pi$
$798$	−7.47947			−0.264770
$799$	0.133171	−	0.133171i	0.00471124	−	0.00471124i
$800$	4.41666	+	7.30950i	0.156153	+	0.258430i
$801$	−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
$808$	−6.46258			−0.227353
$809$		−	27.9509i		−	0.982700i	−0.870962	−	0.491350i	$-0.836504\pi$
$809$		−	27.9509i		−	0.982700i	0.870962	−	0.491350i	$-0.163496\pi$
$810$	−4.63926	−	16.6486i	−0.163007	−	0.584971i
$811$	−23.2784	−	23.2784i	−0.817415	−	0.817415i	0.168317	−	0.985733i	$-0.446167\pi$
$811$	−23.2784	−	23.2784i	−0.817415	−	0.817415i	−0.985733	+	0.168317i	$0.946167\pi$
$812$			3.93829i			0.138207i
$813$			10.2726i			0.360277i
$814$	−3.06696	−	3.06696i	−0.107497	−	0.107497i
$815$	−7.88450	−	28.2945i	−0.276182	−	0.991113i
$816$		−	0.250084i		−	0.00875468i
$817$	0.383957			0.0134330
$818$	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	0.423398	−	0.905944i	$-0.360837\pi$
$821$	−13.8264	−	13.8264i	−0.482545	−	0.482545i	−0.905944	+	0.423398i	$0.860837\pi$
$822$	13.9679	+	13.9679i	0.487186	+	0.487186i
$823$	−28.8649	−	28.8649i	−1.00617	−	1.00617i	−0.999981	−	0.00618675i	$-0.998031\pi$
$823$	−28.8649	−	28.8649i	−1.00617	−	1.00617i	−0.00618675	−	0.999981i	$-0.501969\pi$
$824$	12.1421	−	12.1421i	0.422989	−	0.422989i
$825$	−8.74437	−	14.4718i	−0.304440	−	0.503843i
$826$	−7.46998	+	7.46998i	−0.259914	+	0.259914i
$827$	31.8649			1.10805			0.554026	−	0.832499i	$-0.313091\pi$
$827$	31.8649			1.10805			0.554026	+	0.832499i	$0.313091\pi$
$828$	2.22094	−	2.22094i	0.0771829	−	0.0771829i
$829$	−55.2782			−1.91989			−0.959946	−	0.280184i	$-0.909604\pi$
$829$	−55.2782			−1.91989			−0.959946	+	0.280184i	$0.909604\pi$
$830$	3.37807	+	12.1226i	0.117255	+	0.420782i
$831$			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
$837$		−	12.3070i		−	0.425390i
$838$	3.36976			0.116406
$839$	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	$0.728552\pi$
$840$	8.79850	+	4.96358i	0.303577	+	0.171260i
$841$	4.15118			0.143144
$842$	37.1610	−	37.1610i	1.28065	−	1.28065i
$843$			12.2091i			0.420503i
$844$	−6.03930			−0.207881
$845$		0			0
$846$	−8.87908			−0.305269
$847$		−	36.3137i		−	1.24775i
$848$	−30.2920	+	30.2920i	−1.04023	+	1.04023i
$849$	3.89454			0.133660
$850$	0.603284	+	0.148830i	0.0206925	+	0.00510482i
$851$	1.63969	+	1.63969i	0.0562078	+	0.0562078i
$852$	1.58307			0.0542352
$853$			53.5726i			1.83429i	0.398554	+	0.917145i	$0.369512\pi$
$853$			53.5726i			1.83429i	−0.398554	+	0.917145i	$0.630488\pi$
$854$		−	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	$-0.901045\pi$
$857$	−18.9164	+	18.9164i	−0.646171	+	0.646171i	0.305894	+	0.952066i	$0.401045\pi$
$858$		0			0
$859$			18.1203i			0.618258i	0.951020	+	0.309129i	$0.100037\pi$
$859$			18.1203i			0.618258i	−0.951020	+	0.309129i	$0.899963\pi$
$860$	0.0811057	+	0.0457549i	0.00276568	+	0.00156023i
$861$	−18.2737			−0.622766
$862$	−1.77385	+	1.77385i	−0.0604176	+	0.0604176i
$863$	21.4967			0.731757			0.365879	−	0.930663i	$-0.380768\pi$
$863$	21.4967			0.731757			0.365879	+	0.930663i	$0.380768\pi$
$864$	−4.52795	+	4.52795i	−0.154044	+	0.154044i
$865$	8.25380	+	4.65630i	0.280638	+	0.158319i
$866$	−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
$873$	−13.6527			−0.462072
$874$		−	17.2902i		−	0.584848i
$875$	−19.8920	+	21.1184i	−0.672473	+	0.713931i
$876$	−0.963883	−	0.963883i	−0.0325666	−	0.0325666i
$877$		−	21.3491i		−	0.720907i	−0.932777	−	0.360454i	$-0.882622\pi$
$877$		−	21.3491i		−	0.720907i	0.932777	−	0.360454i	$-0.117378\pi$
$878$			33.2035i			1.12056i
$879$	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	$-0.0716221\pi$
$882$	−1.02891			−0.0346451
$883$	−32.5668	−	32.5668i	−1.09596	−	1.09596i	−0.994878	−	0.101082i	$-0.967770\pi$
$883$	−32.5668	−	32.5668i	−1.09596	−	1.09596i	−0.101082	−	0.994878i	$-0.532230\pi$
$884$		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	0.870889	−	0.491480i	$-0.163544\pi$
$887$	11.2998	+	11.2998i	0.379409	+	0.379409i	−0.491480	+	0.870889i	$0.663544\pi$
$888$	−0.703570	−	0.703570i	−0.0236103	−	0.0236103i
$889$	1.49444	−	1.49444i	0.0501219	−	0.0501219i
$890$	−29.8421	+	52.8985i	−1.00031	+	1.77316i
$891$	−17.9991	+	17.9991i	−0.602994	+	0.602994i
$892$	5.77663			0.193416
$893$	−4.56634	+	4.56634i	−0.152807	+	0.152807i
$894$	−1.47892			−0.0494626
$895$	−30.0734	+	8.38022i	−1.00524	+	0.280120i
$896$			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
$902$			79.0135i			2.63086i
$903$	0.240082			0.00798943
$904$	−10.4237	−	10.4237i	−0.346686	−	0.346686i
$905$	−5.19065	−	18.6273i	−0.172543	−	0.619192i
$906$	−20.2217			−0.671821
$907$	3.71485	−	3.71485i	0.123350	−	0.123350i	−0.642737	−	0.766087i	$-0.722201\pi$
$907$	3.71485	−	3.71485i	0.123350	−	0.123350i	0.766087	+	0.642737i	$0.222201\pi$
$908$		−	8.20799i		−	0.272392i
$909$	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	$0.449712\pi$
$912$			8.57520i			0.283953i
$913$	13.1060	−	13.1060i	0.433746	−	0.433746i
$914$	−45.5961			−1.50819
$915$	−4.07607	+	7.22529i	−0.134751	+	0.238861i
$916$	3.40394	+	3.40394i	0.112469	+	0.112469i
$917$	−41.7938			−1.38015
$918$			0.465905i			0.0153771i
$919$			52.6782i			1.73769i	0.495081	+	0.868847i	$0.335138\pi$
$919$			52.6782i			1.73769i	−0.495081	+	0.868847i	$0.664862\pi$
$920$	−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
$925$	2.44571	−	1.47778i	0.0804144	−	0.0485893i
$926$	−38.1751			−1.25451
$927$	−11.9937	+	11.9937i	−0.393926	+	0.393926i
$928$	8.51438			0.279498
$929$	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	$0.206354\pi$
$930$	−2.02326	−	7.26071i	−0.0663452	−	0.238088i
$931$	−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	0.922102	−	0.386947i	$-0.126470\pi$
$937$	16.3814	+	16.3814i	0.535156	+	0.535156i	−0.386947	+	0.922102i	$0.626470\pi$
$938$	62.1865			2.03046
$939$			8.04494i			0.262537i
$940$	−1.50873	+	0.420421i	−0.0492094	+	0.0137126i
$941$	−24.2325	−	24.2325i	−0.789956	−	0.789956i	0.191530	−	0.981487i	$-0.438655\pi$
$941$	−24.2325	−	24.2325i	−0.789956	−	0.789956i	−0.981487	+	0.191530i	$0.938655\pi$
$942$		−	6.60214i		−	0.215109i
$943$		−	42.2430i		−	1.37562i
$944$	8.56432	+	8.56432i	0.278745	+	0.278745i
$945$	−18.9461	−	10.6882i	−0.616316	−	0.347688i
$946$		−	1.03809i		−	0.0337512i
$947$	−33.4416			−1.08671			−0.543353	−	0.839505i	$-0.682845\pi$
$947$	−33.4416			−1.08671			−0.543353	+	0.839505i	$0.682845\pi$
$948$	−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	$-0.171748\pi$
$953$	10.6248	+	10.6248i	0.344171	+	0.344171i	−0.513762	+	0.857933i	$0.671748\pi$
$954$	25.8875	−	25.8875i	0.838140	−	0.838140i
$955$	−36.4305	+	10.1517i	−1.17886	+	0.328500i
$956$	−0.605172	+	0.605172i	−0.0195727	+	0.0195727i
$957$	−16.8573			−0.544918
$958$	−2.45769	+	2.45769i	−0.0794042	+	0.0794042i
$959$	−49.9188			−1.61196
$960$	4.78566	−	8.48312i	0.154457	−	0.273792i
$961$		−	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
$967$			7.49252i			0.240943i	0.992717	+	0.120472i	$0.0384407\pi$
$967$			7.49252i			0.240943i	−0.992717	+	0.120472i	$0.961559\pi$
$968$	−36.0200			−1.15773
$969$	0.109913	+	0.109913i	0.00353091	+	0.00353091i
$970$	−17.5588	+	4.89290i	−0.563778	+	0.157101i
$971$	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
$973$			41.1263i			1.31845i
$974$	−8.45010			−0.270759
$975$		0			0
$976$	−24.7704			−0.792880
$977$			38.8764i			1.24377i	0.783110	+	0.621883i	$0.213632\pi$
$977$			38.8764i			1.24377i	−0.783110	+	0.621883i	$0.786368\pi$
$978$	9.53761	−	9.53761i	0.304979	−	0.304979i
$979$	89.4527			2.85892
$980$	−0.174832	+	0.0487183i	−0.00558479	+	0.00155625i
$981$	4.03053	+	4.03053i	0.128685	+	0.128685i
$982$	−9.27522			−0.295984
$983$		−	0.207440i		−	0.00661630i	−0.999995	−	0.00330815i	$-0.998947\pi$
$983$		−	0.207440i		−	0.00661630i	0.999995	−	0.00330815i	$-0.00105302\pi$
$984$			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
$990$	−21.1998	+	37.5791i	−0.673775	+	1.19434i
$991$	−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
$993$	−14.5083			−0.460407
$994$	−21.4110	+	21.4110i	−0.679117	+	0.679117i
$995$	33.0157	−	9.20009i	1.04667	−	0.291663i
$996$	−0.539885	+	0.539885i	−0.0171069	+	0.0171069i
$997$	−24.5049	−	24.5049i	−0.776078	−	0.776078i	0.203083	−	0.979162i	$-0.434904\pi$
$997$	−24.5049	−	24.5049i	−0.776078	−	0.776078i	−0.979162	+	0.203083i	$0.934904\pi$
$998$	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.f.e.437.2		20
5.3	odd	4		845.2.k.e.268.2		20
13.2	odd	12		845.2.o.e.357.5		20
13.3	even	3		65.2.t.a.7.5	yes	20
13.4	even	6		845.2.t.e.427.5		20
13.5	odd	4		845.2.k.e.577.2		20
13.6	odd	12		65.2.o.a.2.5	✓	20
13.7	odd	12		845.2.o.g.587.1		20
13.8	odd	4		845.2.k.d.577.9		20
13.9	even	3		845.2.t.f.427.1		20
13.10	even	6		845.2.t.g.657.1		20
13.11	odd	12		845.2.o.f.357.1		20
13.12	even	2		845.2.f.d.437.9		20
39.29	odd	6		585.2.dp.a.397.1		20
39.32	even	12		585.2.cf.a.262.1		20
65.3	odd	12		65.2.o.a.33.5	yes	20
65.8	even	4		845.2.f.d.408.2		20
65.18	even	4	inner	845.2.f.e.408.9		20
65.19	odd	12		325.2.s.b.132.1		20
65.23	odd	12		845.2.o.g.488.1		20
65.28	even	12		845.2.t.f.188.1		20
65.29	even	6		325.2.x.b.7.1		20
65.32	even	12		325.2.x.b.93.1		20
65.33	even	12		845.2.t.g.418.1		20
65.38	odd	4		845.2.k.d.268.9		20
65.42	odd	12		325.2.s.b.293.1		20
65.43	odd	12		845.2.o.f.258.1		20
65.48	odd	12		845.2.o.e.258.5		20
65.58	even	12		65.2.t.a.28.5	yes	20
65.63	even	12		845.2.t.e.188.5		20
195.68	even	12		585.2.cf.a.163.1		20
195.188	odd	12		585.2.dp.a.28.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.5	✓	20	13.6	odd	12
65.2.o.a.33.5	yes	20	65.3	odd	12
65.2.t.a.7.5	yes	20	13.3	even	3
65.2.t.a.28.5	yes	20	65.58	even	12
325.2.s.b.132.1		20	65.19	odd	12
325.2.s.b.293.1		20	65.42	odd	12
325.2.x.b.7.1		20	65.29	even	6
325.2.x.b.93.1		20	65.32	even	12
585.2.cf.a.163.1		20	195.68	even	12
585.2.cf.a.262.1		20	39.32	even	12
585.2.dp.a.28.1		20	195.188	odd	12
585.2.dp.a.397.1		20	39.29	odd	6
845.2.f.d.408.2		20	65.8	even	4
845.2.f.d.437.9		20	13.12	even	2
845.2.f.e.408.9		20	65.18	even	4	inner
845.2.f.e.437.2		20	1.1	even	1	trivial
845.2.k.d.268.9		20	65.38	odd	4
845.2.k.d.577.9		20	13.8	odd	4
845.2.k.e.268.2		20	5.3	odd	4
845.2.k.e.577.2		20	13.5	odd	4
845.2.o.e.258.5		20	65.48	odd	12
845.2.o.e.357.5		20	13.2	odd	12
845.2.o.f.258.1		20	65.43	odd	12
845.2.o.f.357.1		20	13.11	odd	12
845.2.o.g.488.1		20	65.23	odd	12
845.2.o.g.587.1		20	13.7	odd	12
845.2.t.e.188.5		20	65.63	even	12
845.2.t.e.427.5		20	13.4	even	6
845.2.t.f.188.1		20	65.28	even	12
845.2.t.f.427.1		20	13.9	even	3
845.2.t.g.418.1		20	65.33	even	12
845.2.t.g.657.1		20	13.10	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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.51805i q^{2} +(0.478298 - 0.478298i) q^{3} -0.304465 q^{4} +(-2.15400 + 0.600231i) q^{5} +(-0.726078 - 0.726078i) q^{6} +2.59488 q^{7} -2.57390i 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} +(-0.743165 + 1.31734i) q^{15} -4.51623 q^{16} +(-0.0578870 + 0.0578870i) q^{17} +3.85958 q^{18} +(1.98490 - 1.98490i) q^{19} +(0.655819 - 0.182749i) 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} -0.790051 q^{28} -4.98486i q^{29} +(1.99979 + 1.12816i) q^{30} +(-2.32124 - 2.32124i) q^{31} +1.70805i q^{32} -3.38169i q^{33} +(0.0878751 + 0.0878751i) q^{34} +(-5.58938 + 1.55753i) q^{35} -0.774091i q^{36} +0.571501 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} +(-1.52606 - 5.47647i) q^{45} +(4.35541 - 4.35541i) q^{46} -2.30053 q^{47} +(-2.16010 + 2.16010i) q^{48} -0.266585 q^{49} +(-3.92536 - 6.49640i) 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} -1.89875i q^{57} -7.56725 q^{58} +(-1.89634 - 1.89634i) q^{59} +(0.226268 - 0.401085i) q^{60} +5.48474 q^{61} +(-3.52374 + 3.52374i) q^{62} +6.59739i q^{63} -6.43957 q^{64} -5.13357 q^{66} +15.7868i q^{67} +(0.0176246 - 0.0176246i) q^{68} +2.74456 q^{69} +(2.36440 + 8.48494i) q^{70} +(-5.43544 - 5.43544i) q^{71} +6.54405 q^{72} +6.61894i 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} +(9.72797 - 2.71078i) q^{80} -5.09150 q^{81} +(-11.1755 + 11.1755i) q^{82} +3.70736 q^{83} +(-0.377880 + 0.377880i) q^{84} +(0.0899431 - 0.159434i) 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} -2.22048 q^{93} +3.49231i q^{94} +(-3.08409 + 5.46689i) q^{95} +(0.816956 + 0.816956i) q^{96} +5.36986i q^{97} +0.404689i q^{98} +(8.98794 + 8.98794i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7} - 8 q^{10} + 8 q^{11} - 24 q^{12} + 28 q^{15} + 4 q^{16} - 14 q^{17} + 4 q^{19} - 12 q^{20} + 4 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{24} + 18 q^{25} + 4 q^{27}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7 - 8 * q^10 + 8 * q^11 - 24 * q^12 + 28 * q^15 + 4 * q^16 - 14 * q^17 + 4 * q^19 - 12 * q^20 + 4 * q^21 - 32 * q^22 + 8 * q^23 - 4 * q^24 + 18 * q^25 + 4 * q^27 - 36 * q^28 + 40 * q^30 + 2 * q^34 - 20 * q^35 + 8 * q^37 - 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 - 32 * q^43 - 36 * q^44 - 6 * q^45 + 4 * q^46 - 40 * q^47 + 28 * q^48 - 36 * q^49 + 42 * q^50 - 10 * q^53 + 36 * q^54 - 16 * q^55 + 8 * q^59 + 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 - 12 * q^70 - 40 * q^71 - 8 * q^72 + 4 * q^75 - 16 * q^76 - 28 * q^77 + 112 * q^80 + 28 * q^81 - 34 * q^82 + 48 * q^83 + 8 * q^84 - 2 * q^85 + 60 * q^86 - 28 * q^87 - 32 * q^88 + 12 * q^89 + 46 * q^90 - 8 * q^92 - 64 * q^93 + 40 * q^95 + 56 * q^96 + 60 * q^99

Introduction

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