LMFDB - Embedded newform 845.2.f.e.408.9

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			408.9
Root			$1.51805i$ of defining polynomial
Character	$\chi$	$=$	845.408
Dual form			845.2.f.e.437.2

$q$-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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

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

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 $

$2$			1.51805i			1.07342i	0.843766	+	0.536710i	$0.180333\pi$
$2$			1.51805i			1.07342i	−0.843766	+	0.536710i	$0.819667\pi$
$3$	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
$5$	−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	0.997671	+	0.0682120i	$0.0217294\pi$
$11$	3.53513	+	3.53513i	1.06588	+	1.06588i	0.0682120	+	0.997671i	$0.478271\pi$
$12$	−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	0.700052	−	0.714092i	$-0.253160\pi$
$17$	−0.0578870	−	0.0578870i	−0.0140397	−	0.0140397i	−0.714092	+	0.700052i	$0.753160\pi$
$18$	3.85958			0.909711
$19$	1.98490	+	1.98490i	0.455368	+	0.455368i	0.897132	−	0.441763i	$-0.145647\pi$
$19$	1.98490	+	1.98490i	0.455368	+	0.455368i	−0.441763	+	0.897132i	$0.645647\pi$
$20$	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	−0.341599	−	0.939846i	$-0.610969\pi$
$23$	2.86909	−	2.86909i	0.598247	−	0.598247i	0.939846	+	0.341599i	$0.110969\pi$
$24$	−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	$0.153167\pi$
$29$			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	$-0.845252\pi$
$31$	−2.32124	+	2.32124i	−0.416906	+	0.416906i	0.467230	+	0.884136i	$0.345252\pi$
$32$		−	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	−0.163100	+	0.986609i	$0.552149\pi$
$41$	−7.36174	+	7.36174i	−1.14971	+	1.14971i	−0.986609	+	0.163100i	$0.947851\pi$
$42$	−1.88409	+	1.88409i	−0.290721	+	0.290721i
$43$	0.0967193	−	0.0967193i	0.0147496	−	0.0147496i	−0.699694	−	0.714443i	$-0.746680\pi$
$43$	0.0967193	−	0.0967193i	0.0147496	−	0.0147496i	0.714443	+	0.699694i	$0.246680\pi$
$44$	−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	0.997123	−	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
$57$			1.89875i			0.251496i
$58$	−7.56725			−0.993628
$59$	−1.89634	+	1.89634i	−0.246883	+	0.246883i	−0.819690	−	0.572807i	$-0.805854\pi$
$59$	−1.89634	+	1.89634i	−0.246883	+	0.246883i	0.572807	+	0.819690i	$0.305854\pi$
$60$	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	$-0.585272\pi$
$67$		−	15.7868i		−	1.92866i	0.264699	−	0.964331i	$-0.414728\pi$
$68$	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	−0.951797	−	0.306729i	$-0.900766\pi$
$71$	−5.43544	+	5.43544i	−0.645068	+	0.645068i	0.306729	+	0.951797i	$0.400766\pi$
$72$	6.54405			0.771223
$73$		−	6.61894i		−	0.774688i	−0.921935	−	0.387344i	$-0.873393\pi$
$73$		−	6.61894i		−	0.774688i	0.921935	−	0.387344i	$-0.126607\pi$
$74$			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	$-0.104101\pi$
$80$	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	0.446142	−	0.894962i	$-0.352798\pi$
$89$	12.6520	−	12.6520i	1.34110	−	1.34110i	0.894962	−	0.446142i	$-0.147202\pi$
$90$	−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	$-0.912112\pi$
$97$		−	5.36986i		−	0.545226i	0.962124	−	0.272613i	$-0.0878879\pi$
$98$		−	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	$0.0398666\pi$
$101$			2.51081i			0.249835i	−0.992167	+	0.124918i	$0.960133\pi$
$102$	0.0840609			0.00832327
$103$	4.71738	−	4.71738i	0.464817	−	0.464817i	−0.435414	−	0.900230i	$-0.643398\pi$
$103$	4.71738	−	4.71738i	0.464817	−	0.464817i	0.900230	+	0.435414i	$0.143398\pi$
$104$		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	0.778941	−	0.627098i	$-0.215757\pi$
$109$	1.58528	+	1.58528i	0.151843	+	0.151843i	−0.627098	+	0.778941i	$0.715757\pi$
$110$	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	0.871451	−	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
$115$	−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	0.732197	−	0.681093i	$-0.238495\pi$
$127$	0.575918	+	0.575918i	0.0511044	+	0.0511044i	−0.681093	+	0.732197i	$0.738495\pi$
$128$		−	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	$-0.765372\pi$
$139$		−	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
$145$	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	0.747592	−	0.664159i	$-0.231210\pi$
$149$	1.01843	+	1.01843i	0.0834332	+	0.0834332i	−0.664159	+	0.747592i	$0.731210\pi$
$150$	−4.98470	+	1.22972i	−0.406999	+	0.100406i
$151$	13.9253	+	13.9253i	1.13322	+	1.13322i	0.989638	+	0.143585i	$0.0458631\pi$
$151$	13.9253	+	13.9253i	1.13322	+	1.13322i	0.143585	+	0.989638i	$0.454137\pi$
$152$	−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	$0.167408\pi$
$158$	8.66887			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	$-0.828001\pi$
$163$		−	13.1358i		−	1.02887i	0.857528	−	0.514437i	$-0.171999\pi$
$164$	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	−0.811790	−	0.583950i	$-0.801507\pi$
$173$	−2.99677	+	2.99677i	−0.227840	+	0.227840i	0.583950	+	0.811790i	$0.301507\pi$
$174$	−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	$-0.895850\pi$
$181$		−	8.64775i		−	0.642782i	0.946947	−	0.321391i	$-0.104150\pi$
$182$		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	$0.0996338\pi$
$193$			8.55560i			0.615845i	−0.951411	+	0.307923i	$0.900366\pi$
$194$	8.15169			0.585257
$195$		0			0
$196$	0.0811660			0.00579757
$197$		−	7.65684i		−	0.545527i	−0.962081	−	0.272764i	$-0.912062\pi$
$197$		−	7.65684i		−	0.545527i	0.962081	−	0.272764i	$-0.0879377\pi$
$198$	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	$-0.647421\pi$
$227$		−	26.9587i		−	1.78931i	0.446755	−	0.894656i	$-0.352579\pi$
$228$		−	0.578104i		−	0.0382858i
$229$	−11.1801	+	11.1801i	−0.738799	+	0.738799i	−0.972346	−	0.233547i	$-0.924967\pi$
$229$	−11.1801	+	11.1801i	−0.738799	+	0.738799i	0.233547	+	0.972346i	$0.424967\pi$
$230$	−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	−0.450199	−	0.892928i	$-0.648647\pi$
$233$	6.75797	−	6.75797i	0.442729	−	0.442729i	0.892928	+	0.450199i	$0.148647\pi$
$234$		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	0.768464	−	0.639893i	$-0.221021\pi$
$239$	1.98766	+	1.98766i	0.128571	+	0.128571i	−0.639893	+	0.768464i	$0.721021\pi$
$240$	3.35631	+	5.94943i	0.216649	+	0.384034i
$241$	1.94097	+	1.94097i	0.125029	+	0.125029i	0.766852	−	0.641824i	$-0.221822\pi$
$241$	1.94097	+	1.94097i	0.125029	+	0.125029i	−0.641824	+	0.766852i	$0.721822\pi$
$242$	−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	$0.0285057\pi$
$251$			2.83379i			0.178867i	−0.995993	+	0.0894337i	$0.971494\pi$
$252$			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	0.109132	−	0.994027i	$-0.465193\pi$
$257$	−14.1859	−	14.1859i	−0.884895	−	0.884895i	−0.994027	+	0.109132i	$0.965193\pi$
$258$			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	0.882021	−	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
$265$	−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	$0.0312469\pi$
$269$			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	$-0.402605\pi$
$271$	−10.7387	−	10.7387i	−0.652332	−	0.652332i	−0.953554	+	0.301222i	$0.902605\pi$
$272$	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	0.443277	−	0.896385i	$-0.353816\pi$
$277$	−7.54121	−	7.54121i	−0.453107	−	0.453107i	−0.896385	+	0.443277i	$0.853816\pi$
$278$	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	0.215193	−	0.976572i	$-0.430962\pi$
$281$	−12.7630	−	12.7630i	−0.761379	−	0.761379i	−0.976572	+	0.215193i	$0.930962\pi$
$282$	1.67037	−	1.67037i	0.0994689	−	0.0994689i
$283$	4.07125	−	4.07125i	0.242010	−	0.242010i	−0.575671	−	0.817681i	$-0.695259\pi$
$283$	4.07125	−	4.07125i	0.242010	−	0.242010i	0.817681	+	0.575671i	$0.195259\pi$
$284$	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	$-0.970240\pi$
$293$		−	3.19607i		−	0.186717i	0.995633	−	0.0933583i	$-0.0297602\pi$
$294$	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	$0.159112\pi$
$311$			16.9053i			0.958614i	−0.877647	+	0.479307i	$0.840888\pi$
$312$		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
$317$		−	11.9484i		−	0.671087i	−0.942025	−	0.335543i	$-0.891080\pi$
$317$		−	11.9484i		−	0.671087i	0.942025	−	0.335543i	$-0.108920\pi$
$318$	−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	−0.988011	−	0.154380i	$-0.950662\pi$
$331$	−15.1666	+	15.1666i	−0.833631	+	0.833631i	0.154380	+	0.988011i	$0.450662\pi$
$332$	−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	0.978021	−	0.208507i	$-0.0668604\pi$
$337$	14.1264	+	14.1264i	0.769514	+	0.769514i	−0.208507	+	0.978021i	$0.566860\pi$
$338$		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	−0.998009	−	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	−0.0318358	+	0.999493i	$0.510135\pi$
$349$	−19.2668	+	19.2668i	−1.03133	+	1.03133i	−0.999493	+	0.0318358i	$0.989865\pi$
$350$	−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	−0.349683	−	0.936868i	$-0.613711\pi$
$359$	11.1256	−	11.1256i	0.587186	−	0.587186i	0.936868	+	0.349683i	$0.113711\pi$
$360$	−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	−0.474846	−	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
$370$	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	0.873742	−	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
$375$	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	0.506321	−	0.862345i	$-0.331005\pi$
$379$	−6.93105	−	6.93105i	−0.356024	−	0.356024i	−0.862345	+	0.506321i	$0.831005\pi$
$380$	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	−0.984570	−	0.174992i	$-0.944010\pi$
$401$	−23.2202	−	23.2202i	−1.15956	−	1.15956i	−0.174992	−	0.984570i	$-0.555990\pi$
$402$	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	0.419606	−	0.907706i	$-0.362168\pi$
$409$	−9.87122	−	9.87122i	−0.488101	−	0.488101i	−0.907706	+	0.419606i	$0.862168\pi$
$410$	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	$-0.982732\pi$
$419$		−	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	0.216853	−	0.976204i	$-0.430421\pi$
$421$	24.4795	−	24.4795i	1.19306	−	1.19306i	0.976204	−	0.216853i	$-0.0695792\pi$
$422$			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	−0.734689	−	0.678404i	$-0.762672\pi$
$431$	−1.16851	+	1.16851i	−0.0562851	+	0.0562851i	0.678404	+	0.734689i	$0.262672\pi$
$432$	−11.9723	+	11.9723i	−0.576017	+	0.576017i
$433$	−10.4765	+	10.4765i	−0.503466	+	0.503466i	−0.912513	−	0.409047i	$-0.865861\pi$
$433$	−10.4765	+	10.4765i	−0.503466	+	0.503466i	0.409047	+	0.912513i	$0.365861\pi$
$434$	−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	0.545760	−	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
$447$			0.974228i			0.0460794i
$448$	−16.7099			−0.789469
$449$	3.30563	−	3.30563i	0.156002	−	0.156002i	−0.624790	−	0.780793i	$-0.714816\pi$
$449$	3.30563	−	3.30563i	0.156002	−	0.156002i	0.780793	+	0.624790i	$0.214816\pi$
$450$	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	$0.247939\pi$
$457$			30.0361i			1.40503i	−0.711670	+	0.702514i	$0.752061\pi$
$458$	−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	−0.662516	−	0.749048i	$-0.730511\pi$
$461$	1.85792	−	1.85792i	0.0865318	−	0.0865318i	0.749048	+	0.662516i	$0.230511\pi$
$462$	−13.3210			−0.619749
$463$			25.1475i			1.16870i	0.811500	+	0.584352i	$0.198651\pi$
$463$			25.1475i			1.16870i	−0.811500	+	0.584352i	$0.801349\pi$
$464$		−	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	0.269354	−	0.963041i	$-0.413190\pi$
$467$	−14.9907	−	14.9907i	−0.693688	−	0.693688i	−0.963041	+	0.269354i	$0.913190\pi$
$468$		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	−0.743125	−	0.669152i	$-0.766657\pi$
$479$	−1.61898	+	1.61898i	−0.0739730	+	0.0739730i	0.669152	+	0.743125i	$0.266657\pi$
$480$	−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	$0.0402523\pi$
$487$			5.56643i			0.252239i	−0.992015	+	0.126119i	$0.959748\pi$
$488$			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	$0.0440255\pi$
$491$			6.10997i			0.275739i	−0.990450	+	0.137869i	$0.955975\pi$
$492$	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	0.553844	−	0.832620i	$-0.313160\pi$
$499$	−6.22738	−	6.22738i	−0.278776	−	0.278776i	−0.832620	+	0.553844i	$0.813160\pi$
$500$	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	0.762680	−	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
$505$	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	0.509331	−	0.860571i	$-0.329893\pi$
$509$	−7.92432	−	7.92432i	−0.351239	−	0.351239i	−0.860571	+	0.509331i	$0.829893\pi$
$510$	−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	0.565358	−	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
$525$	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	0.790305	−	0.612714i	$-0.209922\pi$
$541$	4.13066	+	4.13066i	0.177591	+	0.177591i	−0.612714	+	0.790305i	$0.709922\pi$
$542$	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	$0.326792\pi$
$548$	5.85713			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	−0.0408873	−	0.999164i	$-0.513018\pi$
$563$	22.7376	−	22.7376i	0.958277	−	0.958277i	0.999164	+	0.0408873i	$0.0130184\pi$
$564$	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	$0.226068\pi$
$571$			31.1596i			1.30399i	−0.758223	+	0.651995i	$0.773932\pi$
$572$		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	$-0.969656\pi$
$577$		−	4.57285i		−	0.190370i	0.995460	−	0.0951852i	$-0.0303443\pi$
$578$	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	$0.0474184\pi$
$587$			7.19181i			0.296838i	−0.988925	+	0.148419i	$0.952582\pi$
$588$	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	$0.195411\pi$
$593$			28.0561i			1.15212i	−0.817406	+	0.576062i	$0.804589\pi$
$594$			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	$-0.00593722\pi$
$600$	−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	−0.120017	+	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
$613$	24.6113			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	$0.100429\pi$
$617$			15.4154i			0.620600i	−0.950639	+	0.310300i	$0.899571\pi$
$618$			6.85037i			0.275562i
$619$	−20.7915	+	20.7915i	−0.835683	+	0.835683i	−0.988287	−	0.152604i	$-0.951234\pi$
$619$	−20.7915	+	20.7915i	−0.835683	+	0.835683i	0.152604	+	0.988287i	$0.451234\pi$
$620$	−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	0.507108	−	0.861882i	$-0.330714\pi$
$631$	−8.91183	−	8.91183i	−0.354774	−	0.354774i	−0.861882	+	0.507108i	$0.830714\pi$
$632$	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	$0.0617476\pi$
$641$			9.76116i			0.385543i	−0.981244	+	0.192771i	$0.938252\pi$
$642$			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	0.403008	−	0.915196i	$-0.367965\pi$
$647$	−13.0281	−	13.0281i	−0.512188	−	0.512188i	−0.915196	+	0.403008i	$0.867965\pi$
$648$		−	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	0.801758	−	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
$655$	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	$0.0875700\pi$
$659$			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	$-0.248597\pi$
$661$	0.160275	+	0.160275i	0.00623398	+	0.00623398i	−0.703983	+	0.710217i	$0.748597\pi$
$662$	−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	−0.0804210	−	0.996761i	$-0.525626\pi$
$673$	23.7719	−	23.7719i	0.916340	−	0.916340i	0.996761	+	0.0804210i	$0.0256265\pi$
$674$	−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	$0.0102375\pi$
$678$	−5.88087			−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	$-0.799744\pi$
$683$		−	30.7567i		−	1.17687i	0.808543	−	0.588437i	$-0.200256\pi$
$684$	−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	0.0430609	−	0.999072i	$-0.486289\pi$
$691$	27.3944	−	27.3944i	1.04213	−	1.04213i	0.999072	−	0.0430609i	$-0.0137109\pi$
$692$	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	$-0.877447\pi$
$701$		−	19.8876i		−	0.751143i	0.926793	−	0.375571i	$-0.122553\pi$
$702$		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	−0.989670	−	0.143362i	$-0.954209\pi$
$709$	−22.5347	+	22.5347i	−0.846309	+	0.846309i	0.143362	+	0.989670i	$0.454209\pi$
$710$	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	0.941109	−	0.338103i	$-0.109785\pi$
$727$	16.2588	+	16.2588i	0.603007	+	0.603007i	−0.338103	+	0.941109i	$0.609785\pi$
$728$		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	−0.256512	−	0.966541i	$-0.582573\pi$
$739$	19.3018	−	19.3018i	0.710029	−	0.710029i	0.966541	+	0.256512i	$0.0825733\pi$
$740$	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	$0.191172\pi$
$751$			30.9738i			1.13025i	−0.825005	+	0.565125i	$0.808828\pi$
$752$	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	0.394173	−	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
$760$	14.0712	−	7.93813i	0.510417	−	0.287946i
$761$	−0.818500	−	0.818500i	−0.0296706	−	0.0296706i	0.692116	−	0.721786i	$-0.256679\pi$
$761$	−0.818500	−	0.818500i	−0.0296706	−	0.0296706i	−0.721786	+	0.692116i	$0.756679\pi$
$762$	−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	0.978254	−	0.207410i	$-0.0665035\pi$
$769$	21.3762	+	21.3762i	0.770844	+	0.770844i	−0.207410	+	0.978254i	$0.566503\pi$
$770$	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	0.999914	−	0.0131190i	$-0.00417602\pi$
$797$	27.8584	+	27.8584i	0.986795	+	0.986795i	−0.0131190	+	0.999914i	$0.504176\pi$
$798$	−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	$0.163496\pi$
$809$			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	$-0.946167\pi$
$811$	−23.2784	+	23.2784i	−0.817415	+	0.817415i	0.168317	+	0.985733i	$0.446167\pi$
$812$		−	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	−0.905944	−	0.423398i	$-0.860837\pi$
$821$	−13.8264	+	13.8264i	−0.482545	+	0.482545i	0.423398	+	0.905944i	$0.360837\pi$
$822$	13.9679	−	13.9679i	0.487186	−	0.487186i
$823$	−28.8649	+	28.8649i	−1.00617	+	1.00617i	−0.00618675	+	0.999981i	$0.501969\pi$
$823$	−28.8649	+	28.8649i	−1.00617	+	1.00617i	−0.999981	+	0.00618675i	$0.998031\pi$
$824$	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	−0.657892	−	0.753112i	$-0.728552\pi$
$839$	2.75809	−	2.75809i	0.0952197	−	0.0952197i	0.753112	+	0.657892i	$0.228552\pi$
$840$	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	$-0.630488\pi$
$853$		−	53.5726i		−	1.83429i	0.398554	−	0.917145i	$-0.369512\pi$
$854$			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	0.305894	−	0.952066i	$-0.401045\pi$
$857$	−18.9164	−	18.9164i	−0.646171	−	0.646171i	−0.952066	+	0.305894i	$0.901045\pi$
$858$		0			0
$859$		−	18.1203i		−	0.618258i	−0.951020	−	0.309129i	$-0.899963\pi$
$859$		−	18.1203i		−	0.618258i	0.951020	−	0.309129i	$-0.100037\pi$
$860$	0.0811057	−	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	$0.117378\pi$
$877$			21.3491i			0.720907i	−0.932777	+	0.360454i	$0.882622\pi$
$878$		−	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	$0.0716221\pi$
$881$			13.2448i			0.446227i	−0.974792	+	0.223114i	$0.928378\pi$
$882$	−1.02891			−0.0346451
$883$	−32.5668	+	32.5668i	−1.09596	+	1.09596i	−0.101082	+	0.994878i	$0.532230\pi$
$883$	−32.5668	+	32.5668i	−1.09596	+	1.09596i	−0.994878	+	0.101082i	$0.967770\pi$
$884$		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
$890$	−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	0.766087	−	0.642737i	$-0.222201\pi$
$907$	3.71485	+	3.71485i	0.123350	+	0.123350i	−0.642737	+	0.766087i	$0.722201\pi$
$908$			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	$-0.664862\pi$
$919$		−	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
$925$	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	0.797123	−	0.603817i	$-0.206354\pi$
$929$	5.89185	+	5.89185i	0.193305	+	0.193305i	−0.603817	+	0.797123i	$0.706354\pi$
$930$	−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	−0.386947	−	0.922102i	$-0.626470\pi$
$937$	16.3814	−	16.3814i	0.535156	−	0.535156i	0.922102	+	0.386947i	$0.126470\pi$
$938$	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	−0.981487	−	0.191530i	$-0.938655\pi$
$941$	−24.2325	+	24.2325i	−0.789956	+	0.789956i	0.191530	+	0.981487i	$0.438655\pi$
$942$			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	−0.513762	−	0.857933i	$-0.671748\pi$
$953$	10.6248	−	10.6248i	0.344171	−	0.344171i	0.857933	+	0.513762i	$0.171748\pi$
$954$	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	$-0.961559\pi$
$967$		−	7.49252i		−	0.240943i	0.992717	−	0.120472i	$-0.0384407\pi$
$968$	−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	$-0.786368\pi$
$977$		−	38.8764i		−	1.24377i	0.783110	−	0.621883i	$-0.213632\pi$
$978$	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	$0.00105302\pi$
$983$			0.207440i			0.00661630i	−0.999995	+	0.00330815i	$0.998947\pi$
$984$		−	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	−0.979162	−	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.f.e.408.9		20
5.2	odd	4		845.2.k.e.577.2		20
13.2	odd	12		845.2.o.g.488.1		20
13.3	even	3		845.2.t.f.188.1		20
13.4	even	6		845.2.t.g.418.1		20
13.5	odd	4		845.2.k.d.268.9		20
13.6	odd	12		845.2.o.f.258.1		20
13.7	odd	12		845.2.o.e.258.5		20
13.8	odd	4		845.2.k.e.268.2		20
13.9	even	3		65.2.t.a.28.5	yes	20
13.10	even	6		845.2.t.e.188.5		20
13.11	odd	12		65.2.o.a.33.5	yes	20
13.12	even	2		845.2.f.d.408.2		20
39.11	even	12		585.2.cf.a.163.1		20
39.35	odd	6		585.2.dp.a.28.1		20
65.2	even	12		845.2.t.g.657.1		20
65.7	even	12		845.2.t.f.427.1		20
65.9	even	6		325.2.x.b.93.1		20
65.12	odd	4		845.2.k.d.577.9		20
65.17	odd	12		845.2.o.g.587.1		20
65.22	odd	12		65.2.o.a.2.5	✓	20
65.24	odd	12		325.2.s.b.293.1		20
65.32	even	12		845.2.t.e.427.5		20
65.37	even	12		65.2.t.a.7.5	yes	20
65.42	odd	12		845.2.o.e.357.5		20
65.47	even	4	inner	845.2.f.e.437.2		20
65.48	odd	12		325.2.s.b.132.1		20
65.57	even	4		845.2.f.d.437.9		20
65.62	odd	12		845.2.o.f.357.1		20
65.63	even	12		325.2.x.b.7.1		20
195.152	even	12		585.2.cf.a.262.1		20
195.167	odd	12		585.2.dp.a.397.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.5	✓	20	65.22	odd	12
65.2.o.a.33.5	yes	20	13.11	odd	12
65.2.t.a.7.5	yes	20	65.37	even	12
65.2.t.a.28.5	yes	20	13.9	even	3
325.2.s.b.132.1		20	65.48	odd	12
325.2.s.b.293.1		20	65.24	odd	12
325.2.x.b.7.1		20	65.63	even	12
325.2.x.b.93.1		20	65.9	even	6
585.2.cf.a.163.1		20	39.11	even	12
585.2.cf.a.262.1		20	195.152	even	12
585.2.dp.a.28.1		20	39.35	odd	6
585.2.dp.a.397.1		20	195.167	odd	12
845.2.f.d.408.2		20	13.12	even	2
845.2.f.d.437.9		20	65.57	even	4
845.2.f.e.408.9		20	1.1	even	1	trivial
845.2.f.e.437.2		20	65.47	even	4	inner
845.2.k.d.268.9		20	13.5	odd	4
845.2.k.d.577.9		20	65.12	odd	4
845.2.k.e.268.2		20	13.8	odd	4
845.2.k.e.577.2		20	5.2	odd	4
845.2.o.e.258.5		20	13.7	odd	12
845.2.o.e.357.5		20	65.42	odd	12
845.2.o.f.258.1		20	13.6	odd	12
845.2.o.f.357.1		20	65.62	odd	12
845.2.o.g.488.1		20	13.2	odd	12
845.2.o.g.587.1		20	65.17	odd	12
845.2.t.e.188.5		20	13.10	even	6
845.2.t.e.427.5		20	65.32	even	12
845.2.t.f.188.1		20	13.3	even	3
845.2.t.f.427.1		20	65.7	even	12
845.2.t.g.418.1		20	13.4	even	6
845.2.t.g.657.1		20	65.2	even	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.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

L-functions

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