LMFDB - Embedded newform 845.2.k.d.577.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("845.268");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			577.9
Root			$-1.51805i$ of defining polynomial
Character	$\chi$	$=$	845.577
Dual form			845.2.k.d.268.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.51805			1.07342			0.536710	−	0.843766i	$-0.319667\pi$
$2$	1.51805			1.07342			0.536710	+	0.843766i	$0.319667\pi$
$3$	0.478298	−	0.478298i	0.276145	−	0.276145i	−0.555423	−	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
$5$	−0.600231	−	2.15400i	−0.268431	−	0.963299i
$5$	−0.600231	−	2.15400i	−0.268431	−	0.963299i
$6$	0.726078	−	0.726078i	0.296420	−	0.296420i
$7$		−	2.59488i		−	0.980773i	−0.871505	−	0.490387i	$-0.836856\pi$
$7$		−	2.59488i		−	0.980773i	0.871505	−	0.490387i	$-0.163144\pi$
$8$	−2.57390			−0.910011
$9$			2.54246i			0.847487i
$10$	−0.911178	−	3.26987i	−0.288140	−	1.03403i
$11$	−3.53513	−	3.53513i	−1.06588	−	1.06588i	−0.997671	−	0.0682120i	$-0.978271\pi$
$11$	−3.53513	−	3.53513i	−1.06588	−	1.06588i	−0.0682120	−	0.997671i	$-0.521729\pi$
$12$	0.145625	−	0.145625i	0.0420383	−	0.0420383i
$13$		0			0
$13$		0			0
$14$		−	3.93915i		−	1.05278i
$15$	−1.31734	−	0.743165i	−0.340137	−	0.191884i
$16$	−4.51623			−1.12906
$17$	0.0578870	−	0.0578870i	0.0140397	−	0.0140397i	−0.700052	−	0.714092i	$-0.746840\pi$
$17$	0.0578870	−	0.0578870i	0.0140397	−	0.0140397i	0.714092	+	0.700052i	$0.246840\pi$
$18$			3.85958i			0.909711i
$19$	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	$0.645647\pi$
$20$	−0.182749	−	0.655819i	−0.0408640	−	0.146645i
$21$	−1.24113	−	1.24113i	−0.270836	−	0.270836i
$22$	−5.36650	−	5.36650i	−1.14414	−	1.14414i
$23$	−2.86909	−	2.86909i	−0.598247	−	0.598247i	0.341599	−	0.939846i	$-0.389031\pi$
$23$	−2.86909	−	2.86909i	−0.598247	−	0.598247i	−0.939846	+	0.341599i	$0.889031\pi$
$24$	−1.23109	+	1.23109i	−0.251295	+	0.251295i
$25$	−4.27945	+	2.58580i	−0.855889	+	0.517159i
$26$		0			0
$27$	2.65095	+	2.65095i	0.510175	+	0.510175i
$28$		−	0.790051i		−	0.149306i
$29$		−	4.98486i		−	0.925665i	−0.886446	−	0.462833i	$-0.846833\pi$
$29$		−	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	$-0.654748\pi$
$31$	2.32124	−	2.32124i	0.416906	−	0.416906i	0.884136	+	0.467230i	$0.154748\pi$
$32$	−1.70805			−0.301943
$33$	−3.38169			−0.588677
$34$	0.0878751	−	0.0878751i	0.0150705	−	0.0150705i
$35$	−5.58938	+	1.55753i	−0.944778	+	0.263270i
$36$			0.774091i			0.129015i
$37$		−	0.571501i		−	0.0939542i	−0.998896	−	0.0469771i	$-0.985041\pi$
$37$		−	0.571501i		−	0.0939542i	0.998896	−	0.0469771i	$-0.0149588\pi$
$38$	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	$-0.447851\pi$
$41$	7.36174	−	7.36174i	1.14971	−	1.14971i	0.986609	−	0.163100i	$-0.0521495\pi$
$42$	−1.88409	−	1.88409i	−0.290721	−	0.290721i
$43$	−0.0967193	−	0.0967193i	−0.0147496	−	0.0147496i	0.699694	−	0.714443i	$-0.253320\pi$
$43$	−0.0967193	−	0.0967193i	−0.0147496	−	0.0147496i	−0.714443	+	0.699694i	$0.753320\pi$
$44$	−1.07633	−	1.07633i	−0.162262	−	0.162262i
$45$	5.47647	−	1.52606i	0.816384	−	0.227492i
$46$	−4.35541	−	4.35541i	−0.642170	−	0.642170i
$47$			2.30053i			0.335567i	0.985824	+	0.167784i	$0.0536610\pi$
$47$			2.30053i			0.335567i	−0.985824	+	0.167784i	$0.946339\pi$
$48$	−2.16010	+	2.16010i	−0.311784	+	0.311784i
$49$	0.266585			0.0380836
$50$	−6.49640	+	3.92536i	−0.918729	+	0.555130i
$51$		−	0.0553744i		−	0.00775397i
$52$		0			0
$53$	6.70735	−	6.70735i	0.921326	−	0.921326i	−0.0757974	−	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
$57$	1.89875			0.251496
$58$		−	7.56725i		−	0.993628i
$59$	−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	$0.305854\pi$
$60$	−0.401085	−	0.226268i	−0.0517799	−	0.0292111i
$61$	5.48474			0.702249			0.351124	−	0.936329i	$-0.385799\pi$
$61$	5.48474			0.702249			0.351124	+	0.936329i	$0.385799\pi$
$62$	3.52374	−	3.52374i	0.447516	−	0.447516i
$63$	6.59739			0.831193
$64$	6.43957			0.804946
$65$		0			0
$66$	−5.13357			−0.631899
$67$	−15.7868			−1.92866			−0.964331	−	0.264699i	$-0.914728\pi$
$67$	−15.7868			−1.92866			−0.964331	+	0.264699i	$0.914728\pi$
$68$	0.0176246	−	0.0176246i	0.00213729	−	0.00213729i
$69$	−2.74456			−0.330406
$70$	−8.48494	+	2.36440i	−1.01414	+	0.282600i
$71$	5.43544	−	5.43544i	0.645068	−	0.645068i	−0.306729	−	0.951797i	$-0.599234\pi$
$71$	5.43544	−	5.43544i	0.645068	−	0.645068i	0.951797	+	0.306729i	$0.0992344\pi$
$72$		−	6.54405i		−	0.771223i
$73$	6.61894			0.774688			0.387344	−	0.921935i	$-0.373393\pi$
$73$	6.61894			0.774688			0.387344	+	0.921935i	$0.373393\pi$
$74$		−	0.867565i		−	0.100852i
$75$	−0.810069	+	3.28363i	−0.0935387	+	0.379161i
$76$	0.604334	+	0.604334i	0.0693219	+	0.0693219i
$77$	−9.17326	+	9.17326i	−1.04539	+	1.04539i
$78$		0			0
$79$			5.71054i			0.642486i	0.946997	+	0.321243i	$0.104101\pi$
$79$			5.71054i			0.642486i	−0.946997	+	0.321243i	$0.895899\pi$
$80$	2.71078	+	9.72797i	0.303075	+	1.08762i
$81$	−5.09150			−0.565722
$82$	11.1755	−	11.1755i	1.23412	−	1.23412i
$83$			3.70736i			0.406936i	0.979082	+	0.203468i	$0.0652213\pi$
$83$			3.70736i			0.406936i	−0.979082	+	0.203468i	$0.934779\pi$
$84$	−0.377880	−	0.377880i	−0.0412301	−	0.0412301i
$85$	−0.159434	−	0.0899431i	−0.0172931	−	0.00975570i
$86$	−0.146824	−	0.146824i	−0.0158325	−	0.0158325i
$87$	−2.38425	−	2.38425i	−0.255618	−	0.255618i
$88$	9.09908	+	9.09908i	0.969965	+	0.969965i
$89$	12.6520	−	12.6520i	1.34110	−	1.34110i	0.446142	−	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
$93$		−	2.22048i		−	0.230253i
$94$			3.49231i			0.360205i
$95$	3.08409	−	5.46689i	0.316421	−	0.560891i
$96$	−0.816956	+	0.816956i	−0.0833802	+	0.0833802i
$97$	−5.36986			−0.545226			−0.272613	−	0.962124i	$-0.587888\pi$
$97$	−5.36986			−0.545226			−0.272613	+	0.962124i	$0.587888\pi$
$98$	0.404689			0.0408798
$99$	8.98794	−	8.98794i	0.903322	−	0.903322i
$100$	−1.30294	+	0.787285i	−0.130294	+	0.0787285i
$101$			2.51081i			0.249835i	0.992167	+	0.124918i	$0.0398666\pi$
$101$			2.51081i			0.249835i	−0.992167	+	0.124918i	$0.960133\pi$
$102$		−	0.0840609i		−	0.00832327i
$103$	−4.71738	−	4.71738i	−0.464817	−	0.464817i	0.435414	−	0.900230i	$-0.356602\pi$
$103$	−4.71738	−	4.71738i	−0.464817	−	0.464817i	−0.900230	+	0.435414i	$0.856602\pi$
$104$		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	0.778941	−	0.627098i	$-0.215757\pi$
$109$	1.58528	+	1.58528i	0.151843	+	0.151843i	−0.627098	+	0.778941i	$0.715757\pi$
$110$	−8.33831	+	14.7806i	−0.795026	+	1.40927i
$111$	−0.273348	−	0.273348i	−0.0259450	−	0.0259450i
$112$			11.7191i			1.10735i
$113$	4.04975	−	4.04975i	0.380968	−	0.380968i	−0.490483	−	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
$115$	−4.45791	+	7.90214i	−0.415702	+	0.736878i
$116$		−	1.51772i		−	0.140916i
$117$		0			0
$118$	−2.87873	+	2.87873i	−0.265009	+	0.265009i
$119$	−0.150210	−	0.150210i	−0.0137697	−	0.0137697i
$120$	3.39071	+	1.91283i	0.309528	+	0.174617i
$121$			13.9943i			1.27221i
$122$	8.32609			0.753809
$123$		−	7.04220i		−	0.634974i
$124$	0.706736	−	0.706736i	0.0634667	−	0.0634667i
$125$	8.13846	+	7.66586i	0.727926	+	0.685655i
$126$	10.0151			0.892220
$127$	−0.575918	+	0.575918i	−0.0511044	+	0.0511044i	−0.732197	−	0.681093i	$-0.761505\pi$
$127$	−0.575918	+	0.575918i	−0.0511044	+	0.0511044i	0.681093	+	0.732197i	$0.261505\pi$
$128$	13.1917			1.16599
$129$	−0.0925213			−0.00814605
$130$		0			0
$131$	−16.1062			−1.40721			−0.703604	−	0.710592i	$-0.748427\pi$
$131$	−16.1062			−1.40721			−0.703604	+	0.710592i	$0.748427\pi$
$132$	−1.02961			−0.0896159
$133$	5.15059	−	5.15059i	0.446613	−	0.446613i
$134$	−23.9651			−2.07027
$135$	4.11897	−	7.30133i	0.354504	−	0.628398i
$136$	−0.148995	+	0.148995i	−0.0127762	+	0.0127762i
$137$			19.2374i			1.64356i	0.569802	+	0.821782i	$0.307020\pi$
$137$			19.2374i			1.64356i	−0.569802	+	0.821782i	$0.692980\pi$
$138$	−4.16637			−0.354665
$139$			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
$145$	−10.7374	+	2.99207i	−0.891692	+	0.248478i
$146$	10.0479			0.831566
$147$	0.127507	−	0.127507i	0.0105166	−	0.0105166i
$148$		−	0.174002i		−	0.0143029i
$149$	1.01843	+	1.01843i	0.0834332	+	0.0834332i	0.747592	−	0.664159i	$-0.231210\pi$
$149$	1.01843	+	1.01843i	0.0834332	+	0.0834332i	−0.664159	+	0.747592i	$0.731210\pi$
$150$	−1.22972	+	4.98470i	−0.100406	+	0.406999i
$151$	−13.9253	−	13.9253i	−1.13322	−	1.13322i	−0.989638	−	0.143585i	$-0.954137\pi$
$151$	−13.9253	−	13.9253i	−1.13322	−	1.13322i	−0.143585	−	0.989638i	$-0.545863\pi$
$152$	−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	$0.667408\pi$
$158$			8.66887i			0.689658i
$159$		−	6.41623i		−	0.508840i
$160$	1.02522	+	3.67914i	0.0810510	+	0.290861i
$161$	−7.44495	+	7.44495i	−0.586744	+	0.586744i
$162$	−7.72914			−0.607258
$163$	13.1358			1.02887			0.514437	−	0.857528i	$-0.328001\pi$
$163$	13.1358			1.02887			0.514437	+	0.857528i	$0.328001\pi$
$164$	2.24139	−	2.24139i	0.175023	−	0.175023i
$165$	2.02980	+	7.28417i	0.158019	+	0.567072i
$166$			5.62795i			0.436814i
$167$		−	3.28516i		−	0.254213i	−0.991889	−	0.127107i	$-0.959431\pi$
$167$		−	3.28516i		−	0.254213i	0.991889	−	0.127107i	$-0.0405691\pi$
$168$	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	$-0.198493\pi$
$173$	2.99677	+	2.99677i	0.227840	+	0.227840i	−0.583950	+	0.811790i	$0.698493\pi$
$174$	−3.61940	−	3.61940i	−0.274386	−	0.274386i
$175$	6.70984	+	11.1047i	0.507216	+	0.839433i
$176$	15.9655	+	15.9655i	1.20344	+	1.20344i
$177$			1.81403i			0.136351i
$178$	19.2062	−	19.2062i	1.43957	−	1.43957i
$179$	−13.9617			−1.04354			−0.521772	−	0.853085i	$-0.674729\pi$
$179$	−13.9617			−1.04354			−0.521772	+	0.853085i	$0.674729\pi$
$180$	1.66739	−	0.464633i	0.124280	−	0.0346317i
$181$		−	8.64775i		−	0.642782i	−0.946947	−	0.321391i	$-0.895850\pi$
$181$		−	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
$187$	−0.409276			−0.0299292
$188$			0.700432i			0.0510842i
$189$	6.87890	−	6.87890i	0.500366	−	0.500366i
$190$	4.68179	−	8.29899i	0.339653	−	0.602072i
$191$	16.9129			1.22378			0.611889	−	0.790944i	$-0.290410\pi$
$191$	16.9129			1.22378			0.611889	+	0.790944i	$0.290410\pi$
$192$	3.08003	−	3.08003i	0.222282	−	0.222282i
$193$	−8.55560			−0.615845			−0.307923	−	0.951411i	$-0.599634\pi$
$193$	−8.55560			−0.615845			−0.307923	+	0.951411i	$0.599634\pi$
$194$	−8.15169			−0.585257
$195$		0			0
$196$	0.0811660			0.00579757
$197$	−7.65684			−0.545527			−0.272764	−	0.962081i	$-0.587938\pi$
$197$	−7.65684			−0.545527			−0.272764	+	0.962081i	$0.587938\pi$
$198$	13.6441	−	13.6441i	0.969645	−	0.969645i
$199$	15.3276			1.08654			0.543272	−	0.839557i	$-0.317185\pi$
$199$	15.3276			1.08654			0.543272	+	0.839557i	$0.317185\pi$
$200$	11.0149	−	6.65558i	0.778869	−	0.470621i
$201$	−7.55078	+	7.55078i	−0.532591	+	0.532591i
$202$			3.81153i			0.268178i
$203$	−12.9351			−0.907868
$204$		−	0.0168596i		−	0.00118041i
$205$	−20.2759	−	11.4385i	−1.41613	−	0.798896i
$206$	−7.16120	−	7.16120i	−0.498944	−	0.498944i
$207$	7.29455	−	7.29455i	0.507006	−	0.507006i
$208$		0			0
$209$		−	14.0338i		−	0.970739i
$210$	−2.92744	+	5.18922i	−0.202013	+	0.358090i
$211$	19.8358			1.36555			0.682775	−	0.730629i	$-0.260773\pi$
$211$	19.8358			1.36555			0.682775	+	0.730629i	$0.260773\pi$
$212$	2.04216	−	2.04216i	0.140256	−	0.140256i
$213$		−	5.19952i		−	0.356265i
$214$	3.89503	+	3.89503i	0.266259	+	0.266259i
$215$	−0.150280	+	0.266388i	−0.0102490	+	0.0181675i
$216$	−6.82328	−	6.82328i	−0.464265	−	0.464265i
$217$	−6.02333	−	6.02333i	−0.408891	−	0.408891i
$218$	2.40654	+	2.40654i	0.162991	+	0.162991i
$219$	3.16582	−	3.16582i	0.213927	−	0.213927i
$220$	−1.67236	+	2.96445i	−0.112751	+	0.199863i
$221$		0			0
$222$	−0.414955	−	0.414955i	−0.0278499	−	0.0278499i
$223$		−	18.9731i		−	1.27053i	−0.772294	−	0.635265i	$-0.780891\pi$
$223$		−	18.9731i		−	1.27053i	0.772294	−	0.635265i	$-0.219109\pi$
$224$			4.43218i			0.296138i
$225$	−6.57429	−	10.8803i	−0.438286	−	0.725355i
$226$	6.14771	−	6.14771i	0.408939	−	0.408939i
$227$	−26.9587			−1.78931			−0.894656	−	0.446755i	$-0.852579\pi$
$227$	−26.9587			−1.78931			−0.894656	+	0.446755i	$0.852579\pi$
$228$	0.578104			0.0382858
$229$	−11.1801	+	11.1801i	−0.738799	+	0.738799i	−0.972346	−	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
$232$			12.8305i			0.842366i
$233$	−6.75797	−	6.75797i	−0.442729	−	0.442729i	0.450199	−	0.892928i	$-0.351353\pi$
$233$	−6.75797	−	6.75797i	−0.442729	−	0.442729i	−0.892928	+	0.450199i	$0.851353\pi$
$234$		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	$0.721021\pi$
$240$	5.94943	+	3.35631i	0.384034	+	0.216649i
$241$	−1.94097	−	1.94097i	−0.125029	−	0.125029i	0.641824	−	0.766852i	$-0.278178\pi$
$241$	−1.94097	−	1.94097i	−0.125029	−	0.125029i	−0.766852	+	0.641824i	$0.778178\pi$
$242$			21.2441i			1.36562i
$243$	−10.3881	+	10.3881i	−0.666397	+	0.666397i
$244$	1.66991			0.106905
$245$	−0.160013	−	0.574225i	−0.0102228	−	0.0366859i
$246$		−	10.6904i		−	0.681595i
$247$		0			0
$248$	−5.97463	+	5.97463i	−0.379389	+	0.379389i
$249$	1.77322	+	1.77322i	0.112374	+	0.112374i
$250$	12.3546	+	11.6371i	0.781371	+	0.735997i
$251$			2.83379i			0.178867i	0.995993	+	0.0894337i	$0.0285057\pi$
$251$			2.83379i			0.178867i	−0.995993	+	0.0894337i	$0.971494\pi$
$252$	2.00868			0.126535
$253$			20.2852i			1.27532i
$254$	−0.874270	+	0.874270i	−0.0548566	+	0.0548566i
$255$	−0.119277	+	0.0332374i	−0.00746939	+	0.00208141i
$256$	7.14642			0.446651
$257$	14.1859	−	14.1859i	0.884895	−	0.884895i	−0.109132	−	0.994027i	$-0.534807\pi$
$257$	14.1859	−	14.1859i	0.884895	−	0.884895i	0.994027	+	0.109132i	$0.0348072\pi$
$258$	−0.140452			−0.00874414
$259$	−1.48298			−0.0921478
$260$		0			0
$261$	12.6738			0.784490
$262$	−24.4500			−1.51053
$263$	6.66222	−	6.66222i	0.410810	−	0.410810i	−0.471210	−	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
$265$	−18.4736	−	10.4217i	−1.13482	−	0.640199i
$266$	7.81884	−	7.81884i	0.479404	−	0.479404i
$267$		−	12.1028i		−	0.740679i
$268$	−4.80653			−0.293605
$269$		−	3.21488i		−	0.196015i	−0.995186	−	0.0980075i	$-0.968753\pi$
$269$		−	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	$-0.0973945\pi$
$271$	10.7387	+	10.7387i	0.652332	+	0.652332i	−0.301222	+	0.953554i	$0.597395\pi$
$272$	−0.261431	+	0.261431i	−0.0158516	+	0.0158516i
$273$		0			0
$274$			29.2033i			1.76424i
$275$	24.2695	+	5.98728i	1.46351	+	0.361047i
$276$	−0.835623			−0.0502986
$277$	7.54121	−	7.54121i	0.453107	−	0.453107i	−0.443277	−	0.896385i	$-0.646184\pi$
$277$	7.54121	−	7.54121i	0.453107	−	0.453107i	0.896385	+	0.443277i	$0.146184\pi$
$278$			24.0595i			1.44300i
$279$	5.90165	+	5.90165i	0.353323	+	0.353323i
$280$	14.3865	−	4.00892i	0.859759	−	0.239579i
$281$	12.7630	+	12.7630i	0.761379	+	0.761379i	0.976572	−	0.215193i	$-0.0690380\pi$
$281$	12.7630	+	12.7630i	0.761379	+	0.761379i	−0.215193	+	0.976572i	$0.569038\pi$
$282$	1.67037	+	1.67037i	0.0994689	+	0.0994689i
$283$	−4.07125	−	4.07125i	−0.242010	−	0.242010i	0.575671	−	0.817681i	$-0.304741\pi$
$283$	−4.07125	−	4.07125i	−0.242010	−	0.242010i	−0.817681	+	0.575671i	$0.804741\pi$
$284$	1.65490	−	1.65490i	0.0982004	−	0.0982004i
$285$	−1.13969	−	4.08991i	−0.0675093	−	0.242266i
$286$		0			0
$287$	−19.1028	−	19.1028i	−1.12760	−	1.12760i
$288$		−	4.34265i		−	0.255893i
$289$			16.9933i			0.999606i
$290$	−16.2999	+	4.54209i	−0.957161	+	0.266721i
$291$	−2.56839	+	2.56839i	−0.150562	+	0.150562i
$292$	2.01524			0.117933
$293$	3.19607			0.186717			0.0933583	−	0.995633i	$-0.470240\pi$
$293$	3.19607			0.186717			0.0933583	+	0.995633i	$0.470240\pi$
$294$	0.193562	−	0.193562i	0.0112888	−	0.0112888i
$295$	5.22297	+	2.94648i	0.304093	+	0.171551i
$296$			1.47099i			0.0854994i
$297$		−	18.7429i		−	1.08757i
$298$	1.54603	+	1.54603i	0.0895590	+	0.0895590i
$299$		0			0
$300$	−0.246638	+	0.999751i	−0.0142396	+	0.0577207i
$301$	−0.250975	+	0.250975i	−0.0144660	+	0.0144660i
$302$	−21.1392	−	21.1392i	−1.21643	−	1.21643i
$303$	1.20092	+	1.20092i	0.0689908	+	0.0689908i
$304$	−8.96429	−	8.96429i	−0.514137	−	0.514137i
$305$	−3.29211	−	11.8141i	−0.188506	−	0.676476i
$306$	0.223419	+	0.223419i	0.0127720	+	0.0127720i
$307$		−	24.2740i		−	1.38539i	−0.721231	−	0.692695i	$-0.756423\pi$
$307$		−	24.2740i		−	1.38539i	0.721231	−	0.692695i	$-0.243577\pi$
$308$	−2.79294	+	2.79294i	−0.159142	+	0.159142i
$309$	−4.51262			−0.256714
$310$	−9.70521	−	5.47509i	−0.551219	−	0.310964i
$311$			16.9053i			0.958614i	0.877647	+	0.479307i	$0.159112\pi$
$311$			16.9053i			0.958614i	−0.877647	+	0.479307i	$0.840888\pi$
$312$		0			0
$313$	−8.40997	+	8.40997i	−0.475359	+	0.475359i	−0.903644	−	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
$317$	−11.9484			−0.671087			−0.335543	−	0.942025i	$-0.608920\pi$
$317$	−11.9484			−0.671087			−0.335543	+	0.942025i	$0.608920\pi$
$318$		−	9.74013i		−	0.546199i
$319$	−17.6221	+	17.6221i	−0.986651	+	0.986651i
$320$	−3.86523	−	13.8708i	−0.216073	−	0.775403i
$321$	2.45445			0.136994
$322$	−11.3018	+	11.3018i	−0.629824	+	0.629824i
$323$	0.229800			0.0127864
$324$	−1.55018			−0.0861214
$325$		0			0
$326$	19.9407			1.10442
$327$	1.51648			0.0838613
$328$	−18.9484	+	18.9484i	−1.04625	+	1.04625i
$329$	5.96961			0.329115
$330$	3.08133	+	11.0577i	0.169621	+	0.608707i
$331$	15.1666	−	15.1666i	0.833631	−	0.833631i	−0.154380	−	0.988011i	$-0.549338\pi$
$331$	15.1666	−	15.1666i	0.833631	−	0.833631i	0.988011	+	0.154380i	$0.0493381\pi$
$332$			1.12876i			0.0619489i
$333$	1.45302			0.0796250
$334$		−	4.98703i		−	0.272878i
$335$	9.47571	+	34.0048i	0.517713	+	1.85788i
$336$	5.60522	+	5.60522i	0.305790	+	0.305790i
$337$	−14.1264	+	14.1264i	−0.769514	+	0.769514i	−0.978021	−	0.208507i	$-0.933140\pi$
$337$	−14.1264	+	14.1264i	−0.769514	+	0.769514i	0.208507	+	0.978021i	$0.433140\pi$
$338$		0			0
$339$		−	3.87397i		−	0.210405i
$340$	−0.0485421	−	0.0273845i	−0.00263257	−	0.00148514i
$341$	−16.4118			−0.888746
$342$	−7.66089	+	7.66089i	−0.414253	+	0.414253i
$343$		−	18.8559i		−	1.01812i
$344$	0.248946	+	0.248946i	0.0134223	+	0.0134223i
$345$	1.64737	+	5.91179i	0.0886914	+	0.318280i
$346$	4.54924	+	4.54924i	0.244569	+	0.244569i
$347$	−17.4159	−	17.4159i	−0.934936	−	0.934936i	0.0630727	−	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	−0.0318358	+	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
$353$		−	8.79926i		−	0.468337i	−0.972196	−	0.234169i	$-0.924763\pi$
$353$		−	8.79926i		−	0.468337i	0.972196	−	0.234169i	$-0.0752368\pi$
$354$			2.75379i			0.146362i
$355$	−14.9705	−	8.44543i	−0.794550	−	0.448237i
$356$	3.85208	−	3.85208i	0.204160	−	0.204160i
$357$	−0.143690			−0.00760489
$358$	−21.1945			−1.12016
$359$	11.1256	−	11.1256i	0.587186	−	0.587186i	−0.349683	−	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
$362$		−	13.1277i		−	0.689976i
$363$	6.69346	+	6.69346i	0.351316	+	0.351316i
$364$		0			0
$365$	−3.97289	−	14.2572i	−0.207951	−	0.746256i
$366$	3.98235	−	3.98235i	0.208161	−	0.208161i
$367$	7.76295	+	7.76295i	0.405223	+	0.405223i	0.880069	−	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
$370$	−1.86874	+	0.520739i	−0.0971510	+	0.0270719i
$371$	−17.4048	−	17.4048i	−0.903612	−	0.903612i
$372$		−	0.676060i		−	0.0350521i
$373$	7.48104	−	7.48104i	0.387354	−	0.387354i	−0.486389	−	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
$375$	7.55917	−	0.226045i	0.390354	−	0.0116729i
$376$		−	5.92134i		−	0.305370i
$377$		0			0
$378$	10.4425	−	10.4425i	0.537104	−	0.537104i
$379$	−6.93105	−	6.93105i	−0.356024	−	0.356024i	0.506321	−	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
$382$	25.6746			1.31363
$383$		−	26.0567i		−	1.33144i	−0.746204	−	0.665718i	$-0.768126\pi$
$383$		−	26.0567i		−	1.33144i	0.746204	−	0.665718i	$-0.231874\pi$
$384$	6.30954	−	6.30954i	0.321982	−	0.321982i
$385$	25.2653	+	14.2531i	1.28764	+	0.726407i
$386$	−12.9878			−0.661061
$387$	0.245905	−	0.245905i	0.0125001	−	0.0125001i
$388$	−1.63493			−0.0830012
$389$	32.4888			1.64725			0.823623	−	0.567138i	$-0.191950\pi$
$389$	32.4888			1.64725			0.823623	+	0.567138i	$0.191950\pi$
$390$		0			0
$391$	−0.332166			−0.0167983
$392$	−0.686164			−0.0346565
$393$	−7.70358	+	7.70358i	−0.388594	+	0.388594i
$394$	−11.6234			−0.585580
$395$	12.3005	−	3.42764i	0.618906	−	0.172463i
$396$	2.73652	−	2.73652i	0.137515	−	0.137515i
$397$		−	24.1854i		−	1.21383i	−0.794767	−	0.606914i	$-0.792407\pi$
$397$		−	24.1854i		−	1.21383i	0.794767	−	0.606914i	$-0.207593\pi$
$398$	23.2680			1.16632
$399$		−	4.92704i		−	0.246660i
$400$	19.3270	−	11.6781i	0.966348	−	0.583903i
$401$	23.2202	+	23.2202i	1.15956	+	1.15956i	0.984570	+	0.174992i	$0.0559899\pi$
$401$	23.2202	+	23.2202i	1.15956	+	1.15956i	0.174992	+	0.984570i	$0.444010\pi$
$402$	−11.4624	+	11.4624i	−0.571695	+	0.571695i
$403$		0			0
$404$			0.764454i			0.0380330i
$405$	3.05608	+	10.9671i	0.151858	+	0.544960i
$406$	−19.6361			−0.974524
$407$	−2.02033	+	2.02033i	−0.100144	+	0.100144i
$408$			0.142528i			0.00705620i
$409$	−9.87122	−	9.87122i	−0.488101	−	0.488101i	0.419606	−	0.907706i	$-0.362168\pi$
$409$	−9.87122	−	9.87122i	−0.488101	−	0.488101i	−0.907706	+	0.419606i	$0.862168\pi$
$410$	−30.7798	−	17.3641i	−1.52011	−	0.857552i
$411$	9.20122	+	9.20122i	0.453863	+	0.453863i
$412$	−1.43628	−	1.43628i	−0.0707603	−	0.0707603i
$413$	4.92078	+	4.92078i	0.242136	+	0.242136i
$414$	11.0735	−	11.0735i	0.544231	−	0.544231i
$415$	7.98567	−	2.22527i	0.392001	−	0.109234i
$416$		0			0
$417$	7.58055	+	7.58055i	0.371221	+	0.371221i
$418$		−	21.3040i		−	1.04201i
$419$			2.21980i			0.108444i	0.998529	+	0.0542221i	$0.0172679\pi$
$419$			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	−0.216853	+	0.976204i	$0.569579\pi$
$421$	−24.4795	+	24.4795i	−1.19306	+	1.19306i	−0.976204	+	0.216853i	$0.930421\pi$
$422$	30.1116			1.46581
$423$	−5.84901			−0.284389
$424$	−17.2641	+	17.2641i	−0.838417	+	0.838417i
$425$	−0.0980403	+	0.397408i	−0.00475565	+	0.0192771i
$426$		−	7.89311i		−	0.382423i
$427$		−	14.2323i		−	0.688747i
$428$	0.781202	+	0.781202i	0.0377608	+	0.0377608i
$429$		0			0
$430$	−0.228132	+	0.404389i	−0.0110015	+	0.0195014i
$431$	1.16851	−	1.16851i	0.0562851	−	0.0562851i	−0.678404	−	0.734689i	$-0.737328\pi$
$431$	1.16851	−	1.16851i	0.0562851	−	0.0562851i	0.734689	+	0.678404i	$0.237328\pi$
$432$	−11.9723	−	11.9723i	−0.576017	−	0.576017i
$433$	10.4765	+	10.4765i	0.503466	+	0.503466i	0.912513	−	0.409047i	$-0.134139\pi$
$433$	10.4765	+	10.4765i	0.503466	+	0.503466i	−0.409047	+	0.912513i	$0.634139\pi$
$434$	−9.14370	−	9.14370i	−0.438912	−	0.438912i
$435$	−3.70457	+	6.56677i	−0.177621	+	0.314853i
$436$	0.482664	+	0.482664i	0.0231154	+	0.0231154i
$437$		−	11.3897i		−	0.544845i
$438$	4.80587	−	4.80587i	0.229633	−	0.229633i
$439$	21.8725			1.04392			0.521959	−	0.852970i	$-0.325201\pi$
$439$	21.8725			1.04392			0.521959	+	0.852970i	$0.325201\pi$
$440$	14.1379	−	25.0610i	0.673997	−	1.19474i
$441$			0.677783i			0.0322754i
$442$		0			0
$443$	−6.14972	+	6.14972i	−0.292182	+	0.292182i	−0.837942	−	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
$447$	0.974228			0.0460794
$448$		−	16.7099i		−	0.789469i
$449$	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	$0.214816\pi$
$450$	−9.98008	−	16.5168i	−0.470465	−	0.778612i
$451$	−52.0494			−2.45091
$452$	1.23301	−	1.23301i	0.0579958	−	0.0579958i
$453$	−13.3209			−0.625869
$454$	−40.9246			−1.92069
$455$		0			0
$456$	−4.88720			−0.228864
$457$	30.0361			1.40503			0.702514	−	0.711670i	$-0.252061\pi$
$457$	30.0361			1.40503			0.702514	+	0.711670i	$0.252061\pi$
$458$	−16.9718	+	16.9718i	−0.793042	+	0.793042i
$459$	0.306911			0.0143254
$460$	−1.35728	+	2.40593i	−0.0632834	+	0.112177i
$461$	−1.85792	+	1.85792i	−0.0865318	+	0.0865318i	−0.749048	−	0.662516i	$-0.769489\pi$
$461$	−1.85792	+	1.85792i	−0.0865318	+	0.0865318i	0.662516	+	0.749048i	$0.269489\pi$
$462$			13.3210i			0.619749i
$463$	−25.1475			−1.16870			−0.584352	−	0.811500i	$-0.698651\pi$
$463$	−25.1475			−1.16870			−0.584352	+	0.811500i	$0.698651\pi$
$464$			22.5128i			1.04513i
$465$	−4.78293	+	1.33280i	−0.221803	+	0.0618073i
$466$	−10.2589	−	10.2589i	−0.475235	−	0.475235i
$467$	14.9907	−	14.9907i	0.693688	−	0.693688i	−0.269354	−	0.963041i	$-0.586810\pi$
$467$	14.9907	−	14.9907i	0.693688	−	0.693688i	0.963041	+	0.269354i	$0.0868100\pi$
$468$		0			0
$469$			40.9648i			1.89158i
$470$	7.52245	−	2.09619i	0.346985	−	0.0966902i
$471$	4.34910			0.200396
$472$	4.88100	−	4.88100i	0.224666	−	0.224666i
$473$			0.683832i			0.0314426i
$474$	4.14630	+	4.14630i	0.190446	+	0.190446i
$475$	−13.6268	−	3.36173i	−0.625243	−	0.154247i
$476$	−0.0457337	−	0.0457337i	−0.00209620	−	0.00209620i
$477$	17.0532	+	17.0532i	0.780812	+	0.780812i
$478$	3.01736	+	3.01736i	0.138011	+	0.138011i
$479$	−1.61898	+	1.61898i	−0.0739730	+	0.0739730i	−0.743125	−	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
$483$			7.12181i			0.324054i
$484$			4.26079i			0.193672i
$485$	3.22315	+	11.5667i	0.146356	+	0.525216i
$486$	−15.7696	+	15.7696i	−0.715324	+	0.715324i
$487$	5.56643			0.252239			0.126119	−	0.992015i	$-0.459748\pi$
$487$	5.56643			0.252239			0.126119	+	0.992015i	$0.459748\pi$
$488$	−14.1172			−0.639054
$489$	6.28282	−	6.28282i	0.284119	−	0.284119i
$490$	−0.242907	−	0.871701i	−0.0109734	−	0.0393794i
$491$			6.10997i			0.275739i	0.990450	+	0.137869i	$0.0440255\pi$
$491$			6.10997i			0.275739i	−0.990450	+	0.137869i	$0.955975\pi$
$492$		−	2.14411i		−	0.0966638i
$493$	−0.288558	−	0.288558i	−0.0129960	−	0.0129960i
$494$		0			0
$495$	−24.7549	−	13.9652i	−1.11265	−	0.627689i
$496$	−10.4832	+	10.4832i	−0.470711	+	0.470711i
$497$	−14.1043	−	14.1043i	−0.632666	−	0.632666i
$498$	2.69184	+	2.69184i	0.120624	+	0.120624i
$499$	−6.22738	−	6.22738i	−0.278776	−	0.278776i	0.553844	−	0.832620i	$-0.313160\pi$
$499$	−6.22738	−	6.22738i	−0.278776	−	0.278776i	−0.832620	+	0.553844i	$0.813160\pi$
$500$	2.47788	+	2.33399i	0.110814	+	0.104379i
$501$	−1.57129	−	1.57129i	−0.0701999	−	0.0701999i
$502$			4.30183i			0.192000i
$503$	2.59944	−	2.59944i	0.115903	−	0.115903i	−0.646776	−	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
$505$	5.40829	−	1.50707i	0.240666	−	0.0670635i
$506$			30.7939i			1.36896i
$507$		0			0
$508$	−0.175347	+	0.175347i	−0.00777976	+	0.00777976i
$509$	−7.92432	−	7.92432i	−0.351239	−	0.351239i	0.509331	−	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
$512$	−15.5347			−0.686544
$513$			10.5238i			0.464635i
$514$	21.5349	−	21.5349i	0.949865	−	0.949865i
$515$	−7.32972	+	12.9927i	−0.322986	+	0.572529i
$516$	−0.0281695			−0.00124009
$517$	8.13269	−	8.13269i	0.357675	−	0.357675i
$518$	−2.25123			−0.0989133
$519$	2.86670			0.125834
$520$		0			0
$521$	35.9604			1.57545			0.787726	−	0.616026i	$-0.211258\pi$
$521$	35.9604			1.57545			0.787726	+	0.616026i	$0.211258\pi$
$522$	19.2394			0.842088
$523$	−5.93427	+	5.93427i	−0.259487	+	0.259487i	−0.824846	−	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
$525$	8.52064	+	2.10203i	0.371871	+	0.0917403i
$526$	10.1136	−	10.1136i	0.440972	−	0.440972i
$527$		−	0.268739i		−	0.0117064i
$528$	15.2725			0.664651
$529$		−	6.53664i		−	0.284202i
$530$	−28.0438	−	15.8206i	−1.21814	−	0.687203i
$531$	−4.82138	−	4.82138i	−0.209230	−	0.209230i
$532$	1.56818	−	1.56818i	0.0679891	−	0.0679891i
$533$		0			0
$534$		−	18.3726i		−	0.795061i
$535$	3.98669	−	7.06686i	0.172360	−	0.305527i
$536$	40.6336			1.75510
$537$	−6.67783	+	6.67783i	−0.288170	+	0.288170i
$538$		−	4.88034i		−	0.210407i
$539$	−0.942415	−	0.942415i	−0.0405927	−	0.0405927i
$540$	1.25408	−	2.22300i	0.0539671	−	0.0956627i
$541$	−4.13066	−	4.13066i	−0.177591	−	0.177591i	0.612714	−	0.790305i	$-0.290078\pi$
$541$	−4.13066	−	4.13066i	−0.177591	−	0.177591i	−0.790305	+	0.612714i	$0.790078\pi$
$542$	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	$0.826792\pi$
$548$			5.85713i			0.250204i
$549$			13.9447i			0.595147i
$550$	36.8423	+	9.08897i	1.57096	+	0.387555i
$551$	9.89447	−	9.89447i	0.421519	−	0.421519i
$552$	7.06422			0.300673
$553$	14.8182			0.630133
$554$	11.4479	−	11.4479i	0.486375	−	0.486375i
$555$	−0.424720	+	0.752863i	−0.0180283	+	0.0319573i
$556$			4.82547i			0.204646i
$557$			11.7868i			0.499423i	0.968320	+	0.249712i	$0.0803358\pi$
$557$			11.7868i			0.499423i	−0.968320	+	0.249712i	$0.919664\pi$
$558$	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	$-0.486982\pi$
$563$	−22.7376	−	22.7376i	−0.958277	−	0.958277i	−0.999164	+	0.0408873i	$0.986982\pi$
$564$	0.335015	+	0.335015i	0.0141067	+	0.0141067i
$565$	−11.1540	−	6.29238i	−0.469250	−	0.264723i
$566$	−6.18034	−	6.18034i	−0.259779	−	0.259779i
$567$			13.2118i			0.554845i
$568$	−13.9903	+	13.9903i	−0.587019	+	0.587019i
$569$	9.28474			0.389237			0.194618	−	0.980879i	$-0.437653\pi$
$569$	9.28474			0.389237			0.194618	+	0.980879i	$0.437653\pi$
$570$	−1.73010	−	6.20868i	−0.0724659	−	0.260053i
$571$			31.1596i			1.30399i	0.758223	+	0.651995i	$0.226068\pi$
$571$			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
$577$	−4.57285			−0.190370			−0.0951852	−	0.995460i	$-0.530344\pi$
$577$	−4.57285			−0.190370			−0.0951852	+	0.995460i	$0.530344\pi$
$578$			25.7966i			1.07300i
$579$	−4.09212	+	4.09212i	−0.170063	+	0.170063i
$580$	−3.26916	+	0.910980i	−0.135745	+	0.0378264i
$581$	9.62018			0.399112
$582$	−3.89894	+	3.89894i	−0.161616	+	0.161616i
$583$	−47.4228			−1.96405
$584$	−17.0365			−0.704975
$585$		0			0
$586$	4.85179			0.200425
$587$	7.19181			0.296838			0.148419	−	0.988925i	$-0.452582\pi$
$587$	7.19181			0.296838			0.148419	+	0.988925i	$0.452582\pi$
$588$	0.0388215	−	0.0388215i	0.00160097	−	0.00160097i
$589$	9.21486			0.379692
$590$	7.92870	+	4.47289i	0.326420	+	0.184146i
$591$	−3.66225	+	3.66225i	−0.150645	+	0.150645i
$592$			2.58103i			0.106080i
$593$	−28.0561			−1.15212			−0.576062	−	0.817406i	$-0.695411\pi$
$593$	−28.0561			−1.15212			−0.576062	+	0.817406i	$0.695411\pi$
$594$		−	28.4526i		−	1.16742i
$595$	−0.233392	+	0.413713i	−0.00956813	+	0.0169606i
$596$	0.310077	+	0.310077i	0.0127013	+	0.0127013i
$597$	7.33116	−	7.33116i	0.300044	−	0.300044i
$598$		0			0
$599$			0.912959i			0.0373025i	0.999826	+	0.0186513i	$0.00593722\pi$
$599$			0.912959i			0.0373025i	−0.999826	+	0.0186513i	$0.994063\pi$
$600$	2.08504	−	8.45174i	0.0851213	−	0.345041i
$601$	12.4538			0.508002			0.254001	−	0.967204i	$-0.418253\pi$
$601$	12.4538			0.508002			0.254001	+	0.967204i	$0.418253\pi$
$602$	−0.380992	+	0.380992i	−0.0155281	+	0.0155281i
$603$		−	40.1373i		−	1.63452i
$604$	−4.23976	−	4.23976i	−0.172514	−	0.172514i
$605$	30.1438	−	8.39983i	1.22552	−	0.341502i
$606$	1.82305	+	1.82305i	0.0740562	+	0.0740562i
$607$	−27.4162	−	27.4162i	−1.11279	−	1.11279i	−0.992772	−	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
$613$			24.6113i			0.994042i	0.867739	+	0.497021i	$0.165573\pi$
$613$			24.6113i			0.994042i	−0.867739	+	0.497021i	$0.834427\pi$
$614$		−	36.8490i		−	1.48711i
$615$	−15.1689	+	4.22695i	−0.611670	+	0.170447i
$616$	23.6110	−	23.6110i	0.951316	−	0.951316i
$617$	15.4154			0.620600			0.310300	−	0.950639i	$-0.399571\pi$
$617$	15.4154			0.620600			0.310300	+	0.950639i	$0.399571\pi$
$618$	−6.85037			−0.275562
$619$	−20.7915	+	20.7915i	−0.835683	+	0.835683i	−0.988287	−	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
$622$			25.6631i			1.02900i
$623$	−32.8303	−	32.8303i	−1.31532	−	1.31532i
$624$		0			0
$625$	11.6273	−	22.1315i	0.465093	−	0.885262i
$626$	−12.7667	+	12.7667i	−0.510261	+	0.510261i
$627$	−6.71234	−	6.71234i	−0.268065	−	0.268065i
$628$	1.38423	+	1.38423i	0.0552369	+	0.0552369i
$629$	−0.0330825	−	0.0330825i	−0.00131908	−	0.00131908i
$630$	−6.01140	−	21.5726i	−0.239500	−	0.859475i
$631$	8.91183	+	8.91183i	0.354774	+	0.354774i	0.861882	−	0.507108i	$-0.169286\pi$
$631$	8.91183	+	8.91183i	0.354774	+	0.354774i	−0.507108	+	0.861882i	$0.669286\pi$
$632$		−	14.6984i		−	0.584670i
$633$	9.48740	−	9.48740i	0.377090	−	0.377090i
$634$	−18.1382			−0.720359
$635$	1.58621	+	0.894844i	0.0629469	+	0.0355108i
$636$		−	1.95352i		−	0.0774620i
$637$		0			0
$638$	−26.7512	+	26.7512i	−1.05909	+	1.05909i
$639$	13.8194	+	13.8194i	0.546687	+	0.546687i
$640$	−7.91804	−	28.4149i	−0.312988	−	1.12320i
$641$			9.76116i			0.385543i	0.981244	+	0.192771i	$0.0617476\pi$
$641$			9.76116i			0.385543i	−0.981244	+	0.192771i	$0.938252\pi$
$642$	3.72597			0.147052
$643$			27.8114i			1.09677i	0.836225	+	0.548387i	$0.184758\pi$
$643$			27.8114i			1.09677i	−0.836225	+	0.548387i	$0.815242\pi$
$644$	−2.26673	+	2.26673i	−0.0893216	+	0.0893216i
$645$	0.0555341	+	0.199291i	0.00218665	+	0.00784708i
$646$	0.348847			0.0137252
$647$	13.0281	−	13.0281i	0.512188	−	0.512188i	−0.403008	−	0.915196i	$-0.632035\pi$
$647$	13.0281	−	13.0281i	0.512188	−	0.512188i	0.915196	+	0.403008i	$0.132035\pi$
$648$	13.1050			0.514814
$649$	13.4076			0.526296
$650$		0			0
$651$	−5.76190			−0.225826
$652$	3.99939			0.156628
$653$	5.21579	−	5.21579i	0.204110	−	0.204110i	−0.597648	−	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
$655$	9.66746	+	34.6929i	0.377739	+	1.35556i
$656$	−33.2473	+	33.2473i	−1.29809	+	1.29809i
$657$			16.8284i			0.656538i
$658$	9.06214			0.353279
$659$		−	13.9472i		−	0.543304i	−0.962396	−	0.271652i	$-0.912430\pi$
$659$		−	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	$-0.251403\pi$
$661$	−0.160275	−	0.160275i	−0.00623398	−	0.00623398i	−0.710217	+	0.703983i	$0.751403\pi$
$662$	23.0236	−	23.0236i	0.894837	−	0.894837i
$663$		0			0
$664$		−	9.54239i		−	0.370317i
$665$	−14.1859	−	8.00284i	−0.550107	−	0.310337i
$666$	2.20575			0.0854711
$667$	−14.3020	+	14.3020i	−0.553776	+	0.553776i
$668$		−	1.00022i		−	0.0386996i
$669$	−9.07477	−	9.07477i	−0.350851	−	0.350851i
$670$	14.3846	+	51.6208i	0.555724	+	1.99429i
$671$	−19.3893	−	19.3893i	−0.748515	−	0.748515i
$672$	2.11990	+	2.11990i	0.0817771	+	0.0817771i
$673$	−23.7719	−	23.7719i	−0.916340	−	0.916340i	0.0804210	−	0.996761i	$-0.474374\pi$
$673$	−23.7719	−	23.7719i	−0.916340	−	0.916340i	−0.996761	+	0.0804210i	$0.974374\pi$
$674$	−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	$0.510238\pi$
$678$		−	5.88087i		−	0.225854i
$679$			13.9341i			0.534743i
$680$	0.410368	+	0.231505i	0.0157369	+	0.00887779i
$681$	−12.8943	+	12.8943i	−0.494110	+	0.494110i
$682$	−24.9138			−0.953999
$683$	30.7567			1.17687			0.588437	−	0.808543i	$-0.299744\pi$
$683$	30.7567			1.17687			0.588437	+	0.808543i	$0.299744\pi$
$684$	−1.53650	+	1.53650i	−0.0587494	+	0.0587494i
$685$	41.4374	−	11.5469i	1.58324	−	0.441184i
$686$		−	28.6242i		−	1.09288i
$687$			10.6948i			0.408032i
$688$	0.436807	+	0.436807i	0.0166531	+	0.0166531i
$689$		0			0
$690$	2.50078	+	8.97436i	0.0952032	+	0.341648i
$691$	−27.3944	+	27.3944i	−1.04213	+	1.04213i	−0.0430609	+	0.999072i	$0.513711\pi$
$691$	−27.3944	+	27.3944i	−1.04213	+	1.04213i	−0.999072	+	0.0430609i	$0.986289\pi$
$692$	0.912413	+	0.912413i	0.0346847	+	0.0346847i
$693$	−23.3227	−	23.3227i	−0.885954	−	0.885954i
$694$	−26.4382	−	26.4382i	−1.00358	−	1.00358i
$695$	34.1388	−	9.51307i	1.29496	−	0.360851i
$696$	6.13682	+	6.13682i	0.232615	+	0.232615i
$697$		−	0.852297i		−	0.0322831i
$698$	−29.2479	+	29.2479i	−1.10705	+	1.10705i
$699$	−6.46464			−0.244515
$700$	2.04291	+	3.38098i	0.0772148	+	0.127789i
$701$		−	19.8876i		−	0.751143i	−0.926793	−	0.375571i	$-0.877447\pi$
$701$		−	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
$707$	6.51526			0.245032
$708$			0.552310i			0.0207571i
$709$	−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	$0.454209\pi$
$710$	−22.7259	−	12.8206i	−0.852887	−	0.481147i
$711$	−14.5188			−0.544499
$712$	−32.5649	+	32.5649i	−1.22042	+	1.22042i
$713$	−13.3197			−0.498826
$714$	−0.218128			−0.00816325
$715$		0			0
$716$	−4.25084			−0.158861
$717$	1.90138			0.0710085
$718$	16.8892	−	16.8892i	0.630298	−	0.630298i
$719$	30.9635			1.15474			0.577372	−	0.816481i	$-0.304078\pi$
$719$	30.9635			1.15474			0.577372	+	0.816481i	$0.304078\pi$
$720$	−24.7330	+	6.89206i	−0.921744	+	0.256852i
$721$	−12.2410	+	12.2410i	−0.455880	+	0.455880i
$722$		−	16.8811i		−	0.628251i
$723$	−1.85672			−0.0690522
$724$		−	2.63294i		−	0.0978524i
$725$	12.8898	+	21.3324i	0.478716	+	0.792267i
$726$	10.1610	+	10.1610i	0.377110	+	0.377110i
$727$	−16.2588	+	16.2588i	−0.603007	+	0.603007i	−0.941109	−	0.338103i	$-0.890215\pi$
$727$	−16.2588	+	16.2588i	−0.603007	+	0.603007i	0.338103	+	0.941109i	$0.390215\pi$
$728$		0			0
$729$		−	5.33729i		−	0.197678i
$730$	−6.03103	−	21.6431i	−0.223218	−	0.801047i
$731$	−0.0111976			−0.000414157
$732$	0.798715	−	0.798715i	0.0295214	−	0.0295214i
$733$			31.2515i			1.15430i	0.816638	+	0.577150i	$0.195835\pi$
$733$			31.2515i			1.15430i	−0.816638	+	0.577150i	$0.804165\pi$
$734$	11.7845	+	11.7845i	0.434975	+	0.434975i
$735$	−0.351185	−	0.198117i	−0.0129536	−	0.00730766i
$736$	4.90054	+	4.90054i	0.180636	+	0.180636i
$737$	55.8084	+	55.8084i	2.05573	+	2.05573i
$738$	28.4132	+	28.4132i	1.04590	+	1.04590i
$739$	19.3018	−	19.3018i	0.710029	−	0.710029i	−0.256512	−	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
$743$			32.9660i			1.20941i	0.796451	+	0.604703i	$0.206708\pi$
$743$			32.9660i			1.20941i	−0.796451	+	0.604703i	$0.793292\pi$
$744$			5.71531i			0.209533i
$745$	1.58241	−	2.80500i	0.0579750	−	0.102767i
$746$	11.3566	−	11.3566i	0.415794	−	0.415794i
$747$	−9.42584			−0.344873
$748$	−0.124610			−0.00455621
$749$	6.65800	−	6.65800i	0.243278	−	0.243278i
$750$	11.4752	−	0.343147i	0.419014	−	0.0125300i
$751$			30.9738i			1.13025i	0.825005	+	0.565125i	$0.191172\pi$
$751$			30.9738i			1.13025i	−0.825005	+	0.565125i	$0.808828\pi$
$752$		−	10.3897i		−	0.378875i
$753$	1.35540	+	1.35540i	0.0493934	+	0.0493934i
$754$		0			0
$755$	−21.6367	+	38.3535i	−0.787440	+	1.39583i
$756$	2.09439	−	2.09439i	0.0761720	−	0.0761720i
$757$	36.1312	+	36.1312i	1.31321	+	1.31321i	0.919036	+	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
$760$	−7.93813	+	14.0712i	−0.287946	+	0.510417i
$761$	0.818500	+	0.818500i	0.0296706	+	0.0296706i	0.721786	−	0.692116i	$-0.243321\pi$
$761$	0.818500	+	0.818500i	0.0296706	+	0.0296706i	−0.692116	+	0.721786i	$0.743321\pi$
$762$			0.836323i			0.0302968i
$763$	4.11363	−	4.11363i	0.148923	−	0.148923i
$764$	5.14940			0.186299
$765$	0.228677	−	0.405355i	0.00826783	−	0.0146557i
$766$		−	39.5553i		−	1.42919i
$767$		0			0
$768$	3.41812	−	3.41812i	0.123341	−	0.123341i
$769$	21.3762	+	21.3762i	0.770844	+	0.770844i	0.978254	−	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
$772$	−2.60488			−0.0937517
$773$			7.19282i			0.258708i	0.991598	+	0.129354i	$0.0412903\pi$
$773$			7.19282i			0.258708i	−0.991598	+	0.129354i	$0.958710\pi$
$774$	0.373296	−	0.373296i	0.0134178	−	0.0134178i
$775$	−3.93136	+	15.9358i	−0.141219	+	0.572432i
$776$	13.8215			0.496162
$777$	−0.709305	+	0.709305i	−0.0254462	+	0.0254462i
$778$	49.3194			1.76819
$779$	29.2247			1.04708
$780$		0			0
$781$	−38.4300			−1.37513
$782$	−0.504243			−0.0180317
$783$	13.2146	−	13.2146i	0.472251	−	0.472251i
$784$	−1.20396			−0.0429986
$785$	7.06412	−	12.5219i	0.252129	−	0.446927i
$786$	−11.6944	+	11.6944i	−0.417125	+	0.417125i
$787$		−	7.17886i		−	0.255899i	−0.991781	−	0.127949i	$-0.959160\pi$
$787$		−	7.17886i		−	0.255899i	0.991781	−	0.127949i	$-0.0408395\pi$
$788$	−2.33124			−0.0830470
$789$		−	6.37306i		−	0.226887i
$790$	18.6728	−	5.20332i	0.664347	−	0.185126i
$791$	−10.5086	−	10.5086i	−0.373644	−	0.373644i
$792$	−23.1341	+	23.1341i	−0.822034	+	0.822034i
$793$		0			0
$794$		−	36.7145i		−	1.30295i
$795$	−13.8206	+	3.85122i	−0.490165	+	0.136589i
$796$	4.66672			0.165407
$797$	−27.8584	+	27.8584i	−0.986795	+	0.986795i	−0.999914	−	0.0131190i	$-0.995824\pi$
$797$	−27.8584	+	27.8584i	−0.986795	+	0.986795i	0.0131190	+	0.999914i	$0.495824\pi$
$798$		−	7.47947i		−	0.264770i
$799$	0.133171	+	0.133171i	0.00471124	+	0.00471124i
$800$	7.30950	−	4.41666i	0.258430	−	0.156153i
$801$	32.1671	+	32.1671i	1.13657	+	1.13657i
$802$	35.2493	+	35.2493i	1.24470	+	1.24470i
$803$	−23.3988	−	23.3988i	−0.825727	−	0.825727i
$804$	−2.29895	+	2.29895i	−0.0810778	+	0.0810778i
$805$	20.5051	+	11.5677i	0.722711	+	0.407710i
$806$		0			0
$807$	−1.53767	−	1.53767i	−0.0541286	−	0.0541286i
$808$		−	6.46258i		−	0.227353i
$809$		−	27.9509i		−	0.982700i	−0.870962	−	0.491350i	$-0.836504\pi$
$809$		−	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	$-0.553833\pi$
$811$	23.2784	−	23.2784i	0.817415	−	0.817415i	0.985733	+	0.168317i	$0.0538334\pi$
$812$	−3.93829			−0.138207
$813$	10.2726			0.360277
$814$	−3.06696	+	3.06696i	−0.107497	+	0.107497i
$815$	−7.88450	−	28.2945i	−0.276182	−	0.991113i
$816$			0.250084i			0.00875468i
$817$		−	0.383957i		−	0.0134330i
$818$	−14.9850	−	14.9850i	−0.523937	−	0.523937i
$819$		0			0
$820$	−6.17331	−	3.48261i	−0.215582	−	0.121618i
$821$	13.8264	−	13.8264i	0.482545	−	0.482545i	−0.423398	−	0.905944i	$-0.639163\pi$
$821$	13.8264	−	13.8264i	0.482545	−	0.482545i	0.905944	+	0.423398i	$0.139163\pi$
$822$	13.9679	+	13.9679i	0.487186	+	0.487186i
$823$	28.8649	+	28.8649i	1.00617	+	1.00617i	0.999981	+	0.00618675i	$0.00196932\pi$
$823$	28.8649	+	28.8649i	1.00617	+	1.00617i	0.00618675	+	0.999981i	$0.498031\pi$
$824$	12.1421	+	12.1421i	0.422989	+	0.422989i
$825$	14.4718	−	8.74437i	0.503843	−	0.304440i
$826$	7.46998	+	7.46998i	0.259914	+	0.259914i
$827$		−	31.8649i		−	1.10805i	−0.832499	−	0.554026i	$-0.813091\pi$
$827$		−	31.8649i		−	1.10805i	0.832499	−	0.554026i	$-0.186909\pi$
$828$	2.22094	−	2.22094i	0.0771829	−	0.0771829i
$829$	55.2782			1.91989			0.959946	−	0.280184i	$-0.0903956\pi$
$829$	55.2782			1.91989			0.959946	+	0.280184i	$0.0903956\pi$
$830$	12.1226	−	3.37807i	0.420782	−	0.117255i
$831$		−	7.21389i		−	0.250247i
$832$		0			0
$833$	0.0154318	−	0.0154318i	0.000534681	−	0.000534681i
$834$	11.5076	+	11.5076i	0.398477	+	0.398477i
$835$	−7.07624	+	1.97185i	−0.244883	+	0.0682388i
$836$		−	4.27281i		−	0.147778i
$837$	12.3070			0.425390
$838$			3.36976i			0.116406i
$839$	2.75809	−	2.75809i	0.0952197	−	0.0952197i	−0.657892	−	0.753112i	$-0.728552\pi$
$839$	2.75809	−	2.75809i	0.0952197	−	0.0952197i	0.753112	+	0.657892i	$0.228552\pi$
$840$	4.96358	−	8.79850i	0.171260	−	0.303577i
$841$	4.15118			0.143144
$842$	−37.1610	+	37.1610i	−1.28065	+	1.28065i
$843$	12.2091			0.420503
$844$	6.03930			0.207881
$845$		0			0
$846$	−8.87908			−0.305269
$847$	36.3137			1.24775
$848$	−30.2920	+	30.2920i	−1.04023	+	1.04023i
$849$	−3.89454			−0.133660
$850$	−0.148830	+	0.603284i	−0.00510482	+	0.0206925i
$851$	−1.63969	+	1.63969i	−0.0562078	+	0.0562078i
$852$		−	1.58307i		−	0.0542352i
$853$	53.5726			1.83429			0.917145	−	0.398554i	$-0.130488\pi$
$853$	53.5726			1.83429			0.917145	+	0.398554i	$0.130488\pi$
$854$		−	21.6052i		−	0.739315i
$855$	13.8994	+	7.84117i	0.475348	+	0.268163i
$856$	−6.60416	−	6.60416i	−0.225726	−	0.225726i
$857$	18.9164	−	18.9164i	0.646171	−	0.646171i	−0.305894	−	0.952066i	$-0.598955\pi$
$857$	18.9164	−	18.9164i	0.646171	−	0.646171i	0.952066	+	0.305894i	$0.0989554\pi$
$858$		0			0
$859$			18.1203i			0.618258i	0.951020	+	0.309129i	$0.100037\pi$
$859$			18.1203i			0.618258i	−0.951020	+	0.309129i	$0.899963\pi$
$860$	−0.0457549	+	0.0811057i	−0.00156023	+	0.00276568i
$861$	−18.2737			−0.622766
$862$	1.77385	−	1.77385i	0.0604176	−	0.0604176i
$863$			21.4967i			0.731757i	0.930663	+	0.365879i	$0.119232\pi$
$863$			21.4967i			0.731757i	−0.930663	+	0.365879i	$0.880768\pi$
$864$	−4.52795	−	4.52795i	−0.154044	−	0.154044i
$865$	4.65630	−	8.25380i	0.158319	−	0.280638i
$866$	15.9037	+	15.9037i	0.540431	+	0.540431i
$867$	8.12786	+	8.12786i	0.276037	+	0.276037i
$868$	−1.83390	−	1.83390i	−0.0622465	−	0.0622465i
$869$	20.1875	−	20.1875i	0.684815	−	0.684815i
$870$	−5.62372	+	9.96866i	−0.190662	+	0.337969i
$871$		0			0
$872$	−4.08036	−	4.08036i	−0.138179	−	0.138179i
$873$		−	13.6527i		−	0.462072i
$874$		−	17.2902i		−	0.584848i
$875$	19.8920	−	21.1184i	0.672473	−	0.713931i
$876$	0.963883	−	0.963883i	0.0325666	−	0.0325666i
$877$	21.3491			0.720907			0.360454	−	0.932777i	$-0.382622\pi$
$877$	21.3491			0.720907			0.360454	+	0.932777i	$0.382622\pi$
$878$	33.2035			1.12056
$879$	1.52867	−	1.52867i	0.0515609	−	0.0515609i
$880$	24.8067	−	43.9726i	0.836234	−	1.48232i
$881$			13.2448i			0.446227i	0.974792	+	0.223114i	$0.0716221\pi$
$881$			13.2448i			0.446227i	−0.974792	+	0.223114i	$0.928378\pi$
$882$			1.02891i			0.0346451i
$883$	32.5668	+	32.5668i	1.09596	+	1.09596i	0.994878	+	0.101082i	$0.0322304\pi$
$883$	32.5668	+	32.5668i	1.09596	+	1.09596i	0.101082	+	0.994878i	$0.467770\pi$
$884$		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
$890$	−52.8985	−	29.8421i	−1.77316	−	1.00031i
$891$	17.9991	+	17.9991i	0.602994	+	0.602994i
$892$		−	5.77663i		−	0.193416i
$893$	−4.56634	+	4.56634i	−0.152807	+	0.152807i
$894$	1.47892			0.0494626
$895$	8.38022	+	30.0734i	0.280120	+	1.00524i
$896$		−	34.2308i		−	1.14357i
$897$		0			0
$898$	5.01810	−	5.01810i	0.167456	−	0.167456i
$899$	−11.5710	−	11.5710i	−0.385916	−	0.385916i
$900$	−2.00164	−	3.31268i	−0.0667214	−	0.110423i
$901$		−	0.776537i		−	0.0258702i
$902$	−79.0135			−2.63086
$903$			0.240082i			0.00798943i
$904$	−10.4237	+	10.4237i	−0.346686	+	0.346686i
$905$	−18.6273	+	5.19065i	−0.619192	+	0.172543i
$906$	−20.2217			−0.671821
$907$	−3.71485	+	3.71485i	−0.123350	+	0.123350i	−0.766087	−	0.642737i	$-0.777799\pi$
$907$	−3.71485	+	3.71485i	−0.123350	+	0.123350i	0.642737	+	0.766087i	$0.277799\pi$
$908$	−8.20799			−0.272392
$909$	−6.38364			−0.211732
$910$		0			0
$911$	9.49722			0.314657			0.157328	−	0.987546i	$-0.449712\pi$
$911$	9.49722			0.314657			0.157328	+	0.987546i	$0.449712\pi$
$912$	−8.57520			−0.283953
$913$	13.1060	−	13.1060i	0.433746	−	0.433746i
$914$	45.5961			1.50819
$915$	−7.22529	−	4.07607i	−0.238861	−	0.134751i
$916$	−3.40394	+	3.40394i	−0.112469	+	0.112469i
$917$			41.7938i			1.38015i
$918$	0.465905			0.0153771
$919$			52.6782i			1.73769i	0.495081	+	0.868847i	$0.335138\pi$
$919$			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
$925$	1.47778	+	2.44571i	0.0485893	+	0.0804144i
$926$	−38.1751			−1.25451
$927$	11.9937	−	11.9937i	0.393926	−	0.393926i
$928$			8.51438i			0.279498i
$929$	5.89185	+	5.89185i	0.193305	+	0.193305i	0.797123	−	0.603817i	$-0.206354\pi$
$929$	5.89185	+	5.89185i	0.193305	+	0.193305i	−0.603817	+	0.797123i	$0.706354\pi$
$930$	−7.26071	+	2.02326i	−0.238088	+	0.0663452i
$931$	0.529147	+	0.529147i	0.0173421	+	0.0173421i
$932$	−2.05757	−	2.05757i	−0.0673978	−	0.0673978i
$933$	8.08579	+	8.08579i	0.264717	+	0.264717i
$934$	22.7566	−	22.7566i	0.744619	−	0.744619i
$935$	0.245660	+	0.881582i	0.00803395	+	0.0288308i
$936$		0			0
$937$	16.3814	+	16.3814i	0.535156	+	0.535156i	0.922102	−	0.386947i	$-0.126470\pi$
$937$	16.3814	+	16.3814i	0.535156	+	0.535156i	−0.386947	+	0.922102i	$0.626470\pi$
$938$			62.1865i			2.03046i
$939$			8.04494i			0.262537i
$940$	1.50873	−	0.420421i	0.0492094	−	0.0137126i
$941$	24.2325	−	24.2325i	0.789956	−	0.789956i	−0.191530	−	0.981487i	$-0.561345\pi$
$941$	24.2325	−	24.2325i	0.789956	−	0.789956i	0.981487	+	0.191530i	$0.0613451\pi$
$942$	6.60214			0.215109
$943$	−42.2430			−1.37562
$944$	8.56432	−	8.56432i	0.278745	−	0.278745i
$945$	−18.9461	−	10.6882i	−0.616316	−	0.347688i
$946$			1.03809i			0.0337512i
$947$			33.4416i			1.08671i	0.839505	+	0.543353i	$0.182845\pi$
$947$			33.4416i			1.08671i	−0.839505	+	0.543353i	$0.817155\pi$
$948$	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	$-0.328252\pi$
$953$	−10.6248	−	10.6248i	−0.344171	−	0.344171i	−0.857933	+	0.513762i	$0.828252\pi$
$954$	25.8875	+	25.8875i	0.838140	+	0.838140i
$955$	−10.1517	−	36.4305i	−0.328500	−	1.17886i
$956$	0.605172	+	0.605172i	0.0195727	+	0.0195727i
$957$			16.8573i			0.544918i
$958$	−2.45769	+	2.45769i	−0.0794042	+	0.0794042i
$959$	49.9188			1.61196
$960$	−8.48312	−	4.78566i	−0.273792	−	0.154457i
$961$			20.2237i			0.652378i
$962$		0			0
$963$	−6.52350	+	6.52350i	−0.210217	+	0.210217i
$964$	−0.590957	−	0.590957i	−0.0190334	−	0.0190334i
$965$	5.13533	+	18.4288i	0.165312	+	0.593243i
$966$			10.8112i			0.347846i
$967$	−7.49252			−0.240943			−0.120472	−	0.992717i	$-0.538441\pi$
$967$	−7.49252			−0.240943			−0.120472	+	0.992717i	$0.538441\pi$
$968$		−	36.0200i		−	1.15773i
$969$	0.109913	−	0.109913i	0.00353091	−	0.00353091i
$970$	4.89290	+	17.5588i	0.157101	+	0.563778i
$971$	27.8606			0.894090			0.447045	−	0.894512i	$-0.352476\pi$
$971$	27.8606			0.894090			0.447045	+	0.894512i	$0.352476\pi$
$972$	−3.16281	+	3.16281i	−0.101447	+	0.101447i
$973$	41.1263			1.31845
$974$	8.45010			0.270759
$975$		0			0
$976$	−24.7704			−0.792880
$977$	−38.8764			−1.24377			−0.621883	−	0.783110i	$-0.713632\pi$
$977$	−38.8764			−1.24377			−0.621883	+	0.783110i	$0.713632\pi$
$978$	9.53761	−	9.53761i	0.304979	−	0.304979i
$979$	−89.4527			−2.85892
$980$	−0.0487183	−	0.174832i	−0.00155625	−	0.00558479i
$981$	−4.03053	+	4.03053i	−0.128685	+	0.128685i
$982$			9.27522i			0.295984i
$983$	−0.207440			−0.00661630			−0.00330815	−	0.999995i	$-0.501053\pi$
$983$	−0.207440			−0.00661630			−0.00330815	+	0.999995i	$0.501053\pi$
$984$			18.1259i			0.577834i
$985$	4.59587	+	16.4928i	0.146437	+	0.525506i
$986$	−0.438045	−	0.438045i	−0.0139502	−	0.0139502i
$987$	2.85525	−	2.85525i	0.0908836	−	0.0908836i
$988$		0			0
$989$			0.554993i			0.0176477i
$990$	−37.5791	−	21.1998i	−1.19434	−	0.673775i
$991$	−25.4961			−0.809910			−0.404955	−	0.914337i	$-0.632713\pi$
$991$	−25.4961			−0.809910			−0.404955	+	0.914337i	$0.632713\pi$
$992$	−3.96478	+	3.96478i	−0.125882	+	0.125882i
$993$		−	14.5083i		−	0.460407i
$994$	−21.4110	−	21.4110i	−0.679117	−	0.679117i
$995$	−9.20009	−	33.0157i	−0.291663	−	1.04667i
$996$	0.539885	+	0.539885i	0.0171069	+	0.0171069i
$997$	−24.5049	−	24.5049i	−0.776078	−	0.776078i	0.203083	−	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.k.d.577.9		20
5.3	odd	4		845.2.f.d.408.2		20
13.2	odd	12		65.2.t.a.7.5	yes	20
13.3	even	3		845.2.o.f.357.1		20
13.4	even	6		65.2.o.a.2.5	✓	20
13.5	odd	4		845.2.f.e.437.2		20
13.6	odd	12		845.2.t.f.427.1		20
13.7	odd	12		845.2.t.e.427.5		20
13.8	odd	4		845.2.f.d.437.9		20
13.9	even	3		845.2.o.g.587.1		20
13.10	even	6		845.2.o.e.357.5		20
13.11	odd	12		845.2.t.g.657.1		20
13.12	even	2		845.2.k.e.577.2		20
39.2	even	12		585.2.dp.a.397.1		20
39.17	odd	6		585.2.cf.a.262.1		20
65.2	even	12		325.2.s.b.293.1		20
65.3	odd	12		845.2.t.e.188.5		20
65.4	even	6		325.2.s.b.132.1		20
65.8	even	4	inner	845.2.k.d.268.9		20
65.17	odd	12		325.2.x.b.93.1		20
65.18	even	4		845.2.k.e.268.2		20
65.23	odd	12		845.2.t.f.188.1		20
65.28	even	12		65.2.o.a.33.5	yes	20
65.33	even	12		845.2.o.f.258.1		20
65.38	odd	4		845.2.f.e.408.9		20
65.43	odd	12		65.2.t.a.28.5	yes	20
65.48	odd	12		845.2.t.g.418.1		20
65.54	odd	12		325.2.x.b.7.1		20
65.58	even	12		845.2.o.e.258.5		20
65.63	even	12		845.2.o.g.488.1		20
195.158	odd	12		585.2.cf.a.163.1		20
195.173	even	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	13.4	even	6
65.2.o.a.33.5	yes	20	65.28	even	12
65.2.t.a.7.5	yes	20	13.2	odd	12
65.2.t.a.28.5	yes	20	65.43	odd	12
325.2.s.b.132.1		20	65.4	even	6
325.2.s.b.293.1		20	65.2	even	12
325.2.x.b.7.1		20	65.54	odd	12
325.2.x.b.93.1		20	65.17	odd	12
585.2.cf.a.163.1		20	195.158	odd	12
585.2.cf.a.262.1		20	39.17	odd	6
585.2.dp.a.28.1		20	195.173	even	12
585.2.dp.a.397.1		20	39.2	even	12
845.2.f.d.408.2		20	5.3	odd	4
845.2.f.d.437.9		20	13.8	odd	4
845.2.f.e.408.9		20	65.38	odd	4
845.2.f.e.437.2		20	13.5	odd	4
845.2.k.d.268.9		20	65.8	even	4	inner
845.2.k.d.577.9		20	1.1	even	1	trivial
845.2.k.e.268.2		20	65.18	even	4
845.2.k.e.577.2		20	13.12	even	2
845.2.o.e.258.5		20	65.58	even	12
845.2.o.e.357.5		20	13.10	even	6
845.2.o.f.258.1		20	65.33	even	12
845.2.o.f.357.1		20	13.3	even	3
845.2.o.g.488.1		20	65.63	even	12
845.2.o.g.587.1		20	13.9	even	3
845.2.t.e.188.5		20	65.3	odd	12
845.2.t.e.427.5		20	13.7	odd	12
845.2.t.f.188.1		20	65.23	odd	12
845.2.t.f.427.1		20	13.6	odd	12
845.2.t.g.418.1		20	65.48	odd	12
845.2.t.g.657.1		20	13.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more