LMFDB - Embedded newform 1045.2.b.c.419.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(419,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("1045.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.b (of order $2$, degree $1$, 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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$20$
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} + 281 x^{16} + 1640 x^{14} + 5623 x^{12} + 11551 x^{10} + 13894 x^{8} + 9095 x^{6} + \cdots + 4 $ x^20 + 26x^18 + 281x^16 + 1640x^14 + 5623x^12 + 11551x^10 + 13894x^8 + 9095x^6 + 2753x^4 + 276*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.10
Root			$-0.131596i$ of defining polynomial
Character	$\chi$	$=$	1045.419
Dual form			1045.2.b.c.419.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.131596i q^{2} +1.44045i q^{3} +1.98268 q^{4} +(-2.22416 - 0.230433i) q^{5} +0.189557 q^{6} -0.456875i q^{7} -0.524103i q^{8} +0.925103 q^{9} +O(q^{10})$	\(q-0.131596i q^{2} +1.44045i q^{3} +1.98268 q^{4} +(-2.22416 - 0.230433i) q^{5} +0.189557 q^{6} -0.456875i q^{7} -0.524103i q^{8} +0.925103 q^{9} +(-0.0303239 + 0.292690i) q^{10} +1.00000 q^{11} +2.85596i q^{12} -5.24500i q^{13} -0.0601227 q^{14} +(0.331927 - 3.20380i) q^{15} +3.89640 q^{16} -6.95508i q^{17} -0.121739i q^{18} +1.00000 q^{19} +(-4.40981 - 0.456875i) q^{20} +0.658106 q^{21} -0.131596i q^{22} +3.13721i q^{23} +0.754945 q^{24} +(4.89380 + 1.02504i) q^{25} -0.690219 q^{26} +5.65392i q^{27} -0.905838i q^{28} +4.35289 q^{29} +(-0.421605 - 0.0436801i) q^{30} +2.59338 q^{31} -1.56096i q^{32} +1.44045i q^{33} -0.915258 q^{34} +(-0.105279 + 1.01616i) q^{35} +1.83419 q^{36} -0.922846i q^{37} -0.131596i q^{38} +7.55516 q^{39} +(-0.120771 + 1.16569i) q^{40} -3.30790 q^{41} -0.0866038i q^{42} +0.870374i q^{43} +1.98268 q^{44} +(-2.05758 - 0.213174i) q^{45} +0.412843 q^{46} +10.3842i q^{47} +5.61256i q^{48} +6.79127 q^{49} +(0.134891 - 0.644003i) q^{50} +10.0184 q^{51} -10.3992i q^{52} -8.75191i q^{53} +0.744030 q^{54} +(-2.22416 - 0.230433i) q^{55} -0.239450 q^{56} +1.44045i q^{57} -0.572821i q^{58} -13.2528 q^{59} +(0.658106 - 6.35211i) q^{60} +3.21550 q^{61} -0.341277i q^{62} -0.422657i q^{63} +7.58738 q^{64} +(-1.20862 + 11.6657i) q^{65} +0.189557 q^{66} +1.23632i q^{67} -13.7897i q^{68} -4.51900 q^{69} +(0.133723 + 0.0138543i) q^{70} +8.08829 q^{71} -0.484850i q^{72} -2.75185i q^{73} -0.121442 q^{74} +(-1.47652 + 7.04928i) q^{75} +1.98268 q^{76} -0.456875i q^{77} -0.994226i q^{78} -3.24490 q^{79} +(-8.66622 - 0.897857i) q^{80} -5.36888 q^{81} +0.435305i q^{82} +4.84685i q^{83} +1.30482 q^{84} +(-1.60268 + 15.4692i) q^{85} +0.114537 q^{86} +6.27012i q^{87} -0.524103i q^{88} +5.97606 q^{89} +(-0.0280528 + 0.270768i) q^{90} -2.39631 q^{91} +6.22010i q^{92} +3.73564i q^{93} +1.36652 q^{94} +(-2.22416 - 0.230433i) q^{95} +2.24848 q^{96} +9.50533i q^{97} -0.893700i q^{98} +0.925103 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 12 q^{4} - 8 q^{6} - 10 q^{9}+O(q^{10}) $ 20 * q - 12 * q^4 - 8 * q^6 - 10 * q^9	$ 20 q - 12 q^{4} - 8 q^{6} - 10 q^{9} - 6 q^{10} + 20 q^{11} + 24 q^{14} - 6 q^{15} - 4 q^{16} + 20 q^{19} - 6 q^{20} - 30 q^{21} + 38 q^{24} + 2 q^{25} + 8 q^{26} + 50 q^{29} - 20 q^{30} - 50 q^{31} + 28 q^{34} + 6 q^{35} - 12 q^{36} + 48 q^{39} + 12 q^{40} - 34 q^{41} - 12 q^{44} - 18 q^{45} - 36 q^{46} - 6 q^{49} + 26 q^{50} - 40 q^{51} - 6 q^{54} - 40 q^{56} + 30 q^{59} - 30 q^{60} - 14 q^{61} + 36 q^{64} + 30 q^{65} - 8 q^{66} - 12 q^{69} - 54 q^{70} - 40 q^{71} + 50 q^{74} - 8 q^{75} - 12 q^{76} + 106 q^{79} + 8 q^{80} - 30 q^{84} - 22 q^{85} + 56 q^{86} + 36 q^{89} - 64 q^{90} - 56 q^{91} + 28 q^{94} + 66 q^{96} - 10 q^{99}+O(q^{100}) $ 20 * q - 12 * q^4 - 8 * q^6 - 10 * q^9 - 6 * q^10 + 20 * q^11 + 24 * q^14 - 6 * q^15 - 4 * q^16 + 20 * q^19 - 6 * q^20 - 30 * q^21 + 38 * q^24 + 2 * q^25 + 8 * q^26 + 50 * q^29 - 20 * q^30 - 50 * q^31 + 28 * q^34 + 6 * q^35 - 12 * q^36 + 48 * q^39 + 12 * q^40 - 34 * q^41 - 12 * q^44 - 18 * q^45 - 36 * q^46 - 6 * q^49 + 26 * q^50 - 40 * q^51 - 6 * q^54 - 40 * q^56 + 30 * q^59 - 30 * q^60 - 14 * q^61 + 36 * q^64 + 30 * q^65 - 8 * q^66 - 12 * q^69 - 54 * q^70 - 40 * q^71 + 50 * q^74 - 8 * q^75 - 12 * q^76 + 106 * q^79 + 8 * q^80 - 30 * q^84 - 22 * q^85 + 56 * q^86 + 36 * q^89 - 64 * q^90 - 56 * q^91 + 28 * q^94 + 66 * q^96 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times$.

$n$	$496$	$761$	$837$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	0.131596i		−	0.0930521i	−0.998917	−	0.0465261i	$-0.985185\pi$
$2$		−	0.131596i		−	0.0930521i	0.998917	−	0.0465261i	$-0.0148151\pi$
$3$			1.44045i			0.831644i	0.909446	+	0.415822i	$0.136506\pi$
$3$			1.44045i			0.831644i	−0.909446	+	0.415822i	$0.863494\pi$
$4$	1.98268			0.991341
$5$	−2.22416	−	0.230433i	−0.994676	−	0.103053i
$5$	−2.22416	−	0.230433i	−0.994676	−	0.103053i
$6$	0.189557			0.0773863
$7$		−	0.456875i		−	0.172683i	−0.996266	−	0.0863413i	$-0.972482\pi$
$7$		−	0.456875i		−	0.172683i	0.996266	−	0.0863413i	$-0.0275175\pi$
$8$		−	0.524103i		−	0.185299i
$9$	0.925103			0.308368
$10$	−0.0303239	+	0.292690i	−0.00958927	+	0.0925567i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$			2.85596i			0.824443i
$13$		−	5.24500i		−	1.45470i	−0.686266	−	0.727351i	$-0.740751\pi$
$13$		−	5.24500i		−	1.45470i	0.686266	−	0.727351i	$-0.259249\pi$
$14$	−0.0601227			−0.0160685
$15$	0.331927	−	3.20380i	0.0857032	−	0.827217i
$16$	3.89640			0.974099
$17$		−	6.95508i		−	1.68685i	−0.537243	−	0.843427i	$-0.680534\pi$
$17$		−	6.95508i		−	1.68685i	0.537243	−	0.843427i	$-0.319466\pi$
$18$		−	0.121739i		−	0.0286943i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−4.40981	−	0.456875i	−0.986063	−	0.102160i
$21$	0.658106			0.143610
$22$		−	0.131596i		−	0.0280563i
$23$			3.13721i			0.654154i	0.944998	+	0.327077i	$0.106064\pi$
$23$			3.13721i			0.654154i	−0.944998	+	0.327077i	$0.893936\pi$
$24$	0.754945			0.154102
$25$	4.89380	+	1.02504i	0.978760	+	0.205008i
$26$	−0.690219			−0.135363
$27$			5.65392i			1.08810i
$28$		−	0.905838i		−	0.171187i
$29$	4.35289			0.808312			0.404156	−	0.914690i	$-0.367565\pi$
$29$	4.35289			0.808312			0.404156	+	0.914690i	$0.367565\pi$
$30$	−0.421605	−	0.0436801i	−0.0769743	−	0.00797486i
$31$	2.59338			0.465785			0.232892	−	0.972502i	$-0.425181\pi$
$31$	2.59338			0.465785			0.232892	+	0.972502i	$0.425181\pi$
$32$		−	1.56096i		−	0.275941i
$33$			1.44045i			0.250750i
$34$	−0.915258			−0.156965
$35$	−0.105279	+	1.01616i	−0.0177954	+	0.171763i
$36$	1.83419			0.305698
$37$		−	0.922846i		−	0.151715i	−0.997119	−	0.0758575i	$-0.975831\pi$
$37$		−	0.922846i		−	0.151715i	0.997119	−	0.0758575i	$-0.0241694\pi$
$38$		−	0.131596i		−	0.0213476i
$39$	7.55516			1.20979
$40$	−0.120771	+	1.16569i	−0.0190955	+	0.184312i
$41$	−3.30790			−0.516607			−0.258304	−	0.966064i	$-0.583164\pi$
$41$	−3.30790			−0.516607			−0.258304	+	0.966064i	$0.583164\pi$
$42$		−	0.0866038i		−	0.0133633i
$43$			0.870374i			0.132731i	0.997795	+	0.0663654i	$0.0211403\pi$
$43$			0.870374i			0.132731i	−0.997795	+	0.0663654i	$0.978860\pi$
$44$	1.98268			0.298901
$45$	−2.05758	−	0.213174i	−0.306726	−	0.0317781i
$46$	0.412843			0.0608704
$47$			10.3842i			1.51469i	0.653014	+	0.757346i	$0.273504\pi$
$47$			10.3842i			1.51469i	−0.653014	+	0.757346i	$0.726496\pi$
$48$			5.61256i			0.810104i
$49$	6.79127			0.970181
$50$	0.134891	−	0.644003i	0.0190764	−	0.0910757i
$51$	10.0184			1.40286
$52$		−	10.3992i		−	1.44211i
$53$		−	8.75191i		−	1.20217i	−0.799186	−	0.601084i	$-0.794736\pi$
$53$		−	8.75191i		−	1.20217i	0.799186	−	0.601084i	$-0.205264\pi$
$54$	0.744030			0.101250
$55$	−2.22416	−	0.230433i	−0.299906	−	0.0310716i
$56$	−0.239450			−0.0319978
$57$			1.44045i			0.190792i
$58$		−	0.572821i		−	0.0752151i
$59$	−13.2528			−1.72537			−0.862686	−	0.505739i	$-0.831220\pi$
$59$	−13.2528			−1.72537			−0.862686	+	0.505739i	$0.831220\pi$
$60$	0.658106	−	6.35211i	0.0849611	−	0.820054i
$61$	3.21550			0.411702			0.205851	−	0.978583i	$-0.434004\pi$
$61$	3.21550			0.411702			0.205851	+	0.978583i	$0.434004\pi$
$62$		−	0.341277i		−	0.0433423i
$63$		−	0.422657i		−	0.0532497i
$64$	7.58738			0.948422
$65$	−1.20862	+	11.6657i	−0.149911	+	1.44696i
$66$	0.189557			0.0233328
$67$			1.23632i			0.151040i	0.997144	+	0.0755202i	$0.0240617\pi$
$67$			1.23632i			0.151040i	−0.997144	+	0.0755202i	$0.975938\pi$
$68$		−	13.7897i		−	1.67225i
$69$	−4.51900			−0.544024
$70$	0.133723	+	0.0138543i	0.0159829	+	0.00165590i
$71$	8.08829			0.959903			0.479951	−	0.877295i	$-0.340654\pi$
$71$	8.08829			0.959903			0.479951	+	0.877295i	$0.340654\pi$
$72$		−	0.484850i		−	0.0571401i
$73$		−	2.75185i		−	0.322079i	−0.986948	−	0.161040i	$-0.948515\pi$
$73$		−	2.75185i		−	0.322079i	0.986948	−	0.161040i	$-0.0514847\pi$
$74$	−0.121442			−0.0141174
$75$	−1.47652	+	7.04928i	−0.170494	+	0.813980i
$76$	1.98268			0.227429
$77$		−	0.456875i		−	0.0520658i
$78$		−	0.994226i		−	0.112574i
$79$	−3.24490			−0.365080			−0.182540	−	0.983198i	$-0.558432\pi$
$79$	−3.24490			−0.365080			−0.182540	+	0.983198i	$0.558432\pi$
$80$	−8.66622	−	0.897857i	−0.968913	−	0.100384i
$81$	−5.36888			−0.596542
$82$			0.435305i			0.0480714i
$83$			4.84685i			0.532011i	0.963972	+	0.266005i	$0.0857039\pi$
$83$			4.84685i			0.532011i	−0.963972	+	0.266005i	$0.914296\pi$
$84$	1.30482			0.142367
$85$	−1.60268	+	15.4692i	−0.173835	+	1.67787i
$86$	0.114537			0.0123509
$87$			6.27012i			0.672228i
$88$		−	0.524103i		−	0.0558696i
$89$	5.97606			0.633461			0.316731	−	0.948516i	$-0.397415\pi$
$89$	5.97606			0.633461			0.316731	+	0.948516i	$0.397415\pi$
$90$	−0.0280528	+	0.270768i	−0.00295702	+	0.0285415i
$91$	−2.39631			−0.251202
$92$			6.22010i			0.648490i
$93$			3.73564i			0.387367i
$94$	1.36652			0.140945
$95$	−2.22416	−	0.230433i	−0.228194	−	0.0236419i
$96$	2.24848			0.229484
$97$			9.50533i			0.965120i	0.875863	+	0.482560i	$0.160293\pi$
$97$			9.50533i			0.965120i	−0.875863	+	0.482560i	$0.839707\pi$
$98$		−	0.893700i		−	0.0902774i
$99$	0.925103			0.0929763
$100$	9.70285	+	2.03233i	0.970285	+	0.203233i
$101$	−4.04218			−0.402212			−0.201106	−	0.979570i	$-0.564453\pi$
$101$	−4.04218			−0.402212			−0.201106	+	0.979570i	$0.564453\pi$
$102$		−	1.31838i		−	0.130539i
$103$		−	5.05269i		−	0.497856i	−0.968522	−	0.248928i	$-0.919922\pi$
$103$		−	5.05269i		−	0.497856i	0.968522	−	0.248928i	$-0.0800783\pi$
$104$	−2.74892			−0.269554
$105$	−1.46373	−	0.151649i	−0.142846	−	0.0147994i
$106$	−1.15171			−0.111864
$107$			5.66293i			0.547456i	0.961807	+	0.273728i	$0.0882568\pi$
$107$			5.66293i			0.547456i	−0.961807	+	0.273728i	$0.911743\pi$
$108$			11.2099i			1.07868i
$109$	8.25596			0.790778			0.395389	−	0.918514i	$-0.370610\pi$
$109$	8.25596			0.790778			0.395389	+	0.918514i	$0.370610\pi$
$110$	−0.0303239	+	0.292690i	−0.00289127	+	0.0279069i
$111$	1.32931			0.126173
$112$		−	1.78017i		−	0.168210i
$113$		−	16.4508i		−	1.54757i	−0.633451	−	0.773783i	$-0.718362\pi$
$113$		−	16.4508i		−	1.54757i	0.633451	−	0.773783i	$-0.281638\pi$
$114$	0.189557			0.0177536
$115$	0.722917	−	6.97767i	0.0674124	−	0.650672i
$116$	8.63040			0.801313
$117$		−	4.85217i		−	0.448583i
$118$			1.74402i			0.160550i
$119$	−3.17760			−0.291290
$120$	−1.67912	−	0.173964i	−0.153282	−	0.0158807i
$121$	1.00000			0.0909091
$122$		−	0.423145i		−	0.0383098i
$123$		−	4.76487i		−	0.429634i
$124$	5.14185			0.461752
$125$	−10.6484	−	3.40755i	−0.952423	−	0.304780i
$126$	−0.0556197			−0.00495500
$127$		−	9.13274i		−	0.810399i	−0.914228	−	0.405200i	$-0.867202\pi$
$127$		−	9.13274i		−	0.810399i	0.914228	−	0.405200i	$-0.132798\pi$
$128$		−	4.12038i		−	0.364193i
$129$	−1.25373			−0.110385
$130$	1.53516	+	0.159049i	0.134642	+	0.0139495i
$131$	−22.0116			−1.92316			−0.961580	−	0.274525i	$-0.911480\pi$
$131$	−22.0116			−1.92316			−0.961580	+	0.274525i	$0.911480\pi$
$132$			2.85596i			0.248579i
$133$		−	0.456875i		−	0.0396161i
$134$	0.162694			0.0140546
$135$	1.30285	−	12.5752i	0.112131	−	1.08230i
$136$	−3.64518			−0.312572
$137$			10.1936i			0.870897i	0.900214	+	0.435448i	$0.143410\pi$
$137$			10.1936i			0.870897i	−0.900214	+	0.435448i	$0.856590\pi$
$138$			0.594680i			0.0506226i
$139$	14.7543			1.25144			0.625720	−	0.780048i	$-0.284805\pi$
$139$	14.7543			1.25144			0.625720	+	0.780048i	$0.284805\pi$
$140$	−0.208735	+	2.01473i	−0.0176413	+	0.170276i
$141$	−14.9579			−1.25968
$142$		−	1.06438i		−	0.0893210i
$143$		−	5.24500i		−	0.438609i
$144$	3.60457			0.300381
$145$	−9.68154	−	1.00305i	−0.804008	−	0.0832987i
$146$	−0.362131			−0.0299702
$147$			9.78248i			0.806845i
$148$		−	1.82971i		−	0.150401i
$149$	16.9982			1.39255			0.696275	−	0.717775i	$-0.254839\pi$
$149$	16.9982			1.39255			0.696275	+	0.717775i	$0.254839\pi$
$150$	0.927654	+	0.194303i	0.0757426	+	0.0158648i
$151$	−16.2869			−1.32541			−0.662703	−	0.748882i	$-0.730591\pi$
$151$	−16.2869			−1.32541			−0.662703	+	0.748882i	$0.730591\pi$
$152$		−	0.524103i		−	0.0425104i
$153$		−	6.43417i		−	0.520171i
$154$	−0.0601227			−0.00484483
$155$	−5.76810	−	0.597600i	−0.463305	−	0.0480004i
$156$	14.9795			1.19932
$157$		−	18.8960i		−	1.50807i	−0.656835	−	0.754034i	$-0.728105\pi$
$157$		−	18.8960i		−	1.50807i	0.656835	−	0.754034i	$-0.271895\pi$
$158$			0.427015i			0.0339715i
$159$	12.6067			0.999776
$160$	−0.359695	+	3.47182i	−0.0284364	+	0.274471i
$161$	1.43331			0.112961
$162$			0.706520i			0.0555095i
$163$			0.640614i			0.0501768i	0.999685	+	0.0250884i	$0.00798672\pi$
$163$			0.640614i			0.0501768i	−0.999685	+	0.0250884i	$0.992013\pi$
$164$	−6.55852			−0.512134
$165$	0.331927	−	3.20380i	0.0258405	−	0.249415i
$166$	0.637824			0.0495047
$167$			8.05621i			0.623408i	0.950179	+	0.311704i	$0.100900\pi$
$167$			8.05621i			0.623408i	−0.950179	+	0.311704i	$0.899100\pi$
$168$		−	0.344916i		−	0.0266108i
$169$	−14.5100			−1.11616
$170$	2.03568	+	0.210905i	0.156130	+	0.0161757i
$171$	0.925103			0.0707444
$172$			1.72567i			0.131581i
$173$		−	16.5942i		−	1.26163i	−0.775933	−	0.630815i	$-0.782721\pi$
$173$		−	16.5942i		−	1.26163i	0.775933	−	0.630815i	$-0.217279\pi$
$174$	0.825121			0.0625522
$175$	0.468315	−	2.23586i	0.0354013	−	0.169015i
$176$	3.89640			0.293702
$177$		−	19.0901i		−	1.43490i
$178$		−	0.786423i		−	0.0589449i
$179$	−17.6845			−1.32180			−0.660902	−	0.750472i	$-0.729826\pi$
$179$	−17.6845			−1.32180			−0.660902	+	0.750472i	$0.729826\pi$
$180$	−4.07953	−	0.422657i	−0.304070	−	0.0315030i
$181$	0.536073			0.0398460			0.0199230	−	0.999802i	$-0.493658\pi$
$181$	0.536073			0.0398460			0.0199230	+	0.999802i	$0.493658\pi$
$182$			0.315344i			0.0233748i
$183$			4.63176i			0.342390i
$184$	1.64422			0.121214
$185$	−0.212654	+	2.05256i	−0.0156346	+	0.150907i
$186$	0.491593			0.0360454
$187$		−	6.95508i		−	0.508606i
$188$			20.5886i			1.50158i
$189$	2.58313			0.187895
$190$	−0.0303239	+	0.292690i	−0.00219993	+	0.0212340i
$191$	−11.5909			−0.838686			−0.419343	−	0.907828i	$-0.637739\pi$
$191$	−11.5909			−0.838686			−0.419343	+	0.907828i	$0.637739\pi$
$192$			10.9292i			0.788750i
$193$			16.7746i			1.20746i	0.797189	+	0.603730i	$0.206319\pi$
$193$			16.7746i			1.20746i	−0.797189	+	0.603730i	$0.793681\pi$
$194$	1.25086			0.0898065
$195$	−16.8039	−	1.74096i	−1.20335	−	0.124673i
$196$	13.4649			0.961780
$197$			19.4422i			1.38520i	0.721323	+	0.692599i	$0.243535\pi$
$197$			19.4422i			1.38520i	−0.721323	+	0.692599i	$0.756465\pi$
$198$		−	0.121739i		−	0.00865165i
$199$	16.5303			1.17180			0.585901	−	0.810383i	$-0.300741\pi$
$199$	16.5303			1.17180			0.585901	+	0.810383i	$0.300741\pi$
$200$	0.537227	−	2.56486i	0.0379877	−	0.181363i
$201$	−1.78086			−0.125612
$202$			0.531933i			0.0374266i
$203$		−	1.98873i		−	0.139581i
$204$	19.8634			1.39072
$205$	7.35731	+	0.762249i	0.513857	+	0.0532378i
$206$	−0.664911			−0.0463266
$207$			2.90225i			0.201720i
$208$		−	20.4366i		−	1.41702i
$209$	1.00000			0.0691714
$210$	−0.0199564	+	0.192621i	−0.00137712	+	0.0132921i
$211$	−10.7883			−0.742695			−0.371348	−	0.928494i	$-0.621104\pi$
$211$	−10.7883			−0.742695			−0.371348	+	0.928494i	$0.621104\pi$
$212$		−	17.3523i		−	1.19176i
$213$			11.6508i			0.798298i
$214$	0.745217			0.0509420
$215$	0.200563	−	1.93585i	0.0136783	−	0.132024i
$216$	2.96324			0.201623
$217$		−	1.18485i		−	0.0804329i
$218$		−	1.08645i		−	0.0735836i
$219$	3.96390			0.267855
$220$	−4.40981	−	0.456875i	−0.297309	−	0.0308025i
$221$	−36.4794			−2.45387
$222$		−	0.174932i		−	0.0117407i
$223$			17.3295i			1.16047i	0.814450	+	0.580233i	$0.197039\pi$
$223$			17.3295i			1.16047i	−0.814450	+	0.580233i	$0.802961\pi$
$224$	−0.713162			−0.0476501
$225$	4.52727	+	0.948268i	0.301818	+	0.0632178i
$226$	−2.16486			−0.144004
$227$		−	8.11839i		−	0.538836i	−0.963023	−	0.269418i	$-0.913169\pi$
$227$		−	8.11839i		−	0.538836i	0.963023	−	0.269418i	$-0.0868314\pi$
$228$			2.85596i			0.189140i
$229$	0.532942			0.0352178			0.0176089	−	0.999845i	$-0.494395\pi$
$229$	0.532942			0.0352178			0.0176089	+	0.999845i	$0.494395\pi$
$230$	−0.918231	−	0.0951327i	−0.0605464	−	0.00627286i
$231$	0.658106			0.0433002
$232$		−	2.28137i		−	0.149779i
$233$			14.4041i			0.943646i	0.881693	+	0.471823i	$0.156404\pi$
$233$			14.4041i			0.943646i	−0.881693	+	0.471823i	$0.843596\pi$
$234$	−0.638524			−0.0417416
$235$	2.39286	−	23.0962i	0.156093	−	1.50663i
$236$	−26.2762			−1.71043
$237$		−	4.67412i		−	0.303617i
$238$			0.418159i			0.0271052i
$239$	−15.5773			−1.00761			−0.503804	−	0.863818i	$-0.668067\pi$
$239$	−15.5773			−1.00761			−0.503804	+	0.863818i	$0.668067\pi$
$240$	1.29332	−	12.4833i	0.0834834	−	0.805791i
$241$	−19.4978			−1.25596			−0.627980	−	0.778229i	$-0.716118\pi$
$241$	−19.4978			−1.25596			−0.627980	+	0.778229i	$0.716118\pi$
$242$		−	0.131596i		−	0.00845928i
$243$			9.22815i			0.591986i
$244$	6.37531			0.408137
$245$	−15.1049	−	1.56493i	−0.965015	−	0.0999797i
$246$	−0.627035			−0.0399783
$247$		−	5.24500i		−	0.333731i
$248$		−	1.35920i		−	0.0863093i
$249$	−6.98165			−0.442444
$250$	−0.448418	+	1.40128i	−0.0283605	+	0.0886250i
$251$	−17.8989			−1.12977			−0.564883	−	0.825171i	$-0.691079\pi$
$251$	−17.8989			−1.12977			−0.564883	+	0.825171i	$0.691079\pi$
$252$		−	0.837994i		−	0.0527886i
$253$			3.13721i			0.197235i
$254$	−1.20183			−0.0754094
$255$	−22.2827	−	2.30858i	−1.39539	−	0.144569i
$256$	14.6325			0.914533
$257$			7.87295i			0.491101i	0.969384	+	0.245551i	$0.0789688\pi$
$257$			7.87295i			0.491101i	−0.969384	+	0.245551i	$0.921031\pi$
$258$			0.164985i			0.0102715i
$259$	−0.421625			−0.0261985
$260$	−2.39631	+	23.1295i	−0.148613	+	1.43443i
$261$	4.02687			0.249257
$262$			2.89663i			0.178954i
$263$			10.0759i			0.621308i	0.950523	+	0.310654i	$0.100548\pi$
$263$			10.0759i			0.621308i	−0.950523	+	0.310654i	$0.899452\pi$
$264$	0.754945			0.0464636
$265$	−2.01673	+	19.4657i	−0.123887	+	1.19577i
$266$	−0.0601227			−0.00368636
$267$			8.60822i			0.526814i
$268$			2.45123i			0.149733i
$269$	−12.7561			−0.777751			−0.388876	−	0.921290i	$-0.627136\pi$
$269$	−12.7561			−0.777751			−0.388876	+	0.921290i	$0.627136\pi$
$270$	−1.65484	−	0.171449i	−0.100711	−	0.0104341i
$271$	−7.76932			−0.471953			−0.235976	−	0.971759i	$-0.575829\pi$
$271$	−7.76932			−0.471953			−0.235976	+	0.971759i	$0.575829\pi$
$272$		−	27.0997i		−	1.64316i
$273$		−	3.45177i		−	0.208910i
$274$	1.34143			0.0810388
$275$	4.89380	+	1.02504i	0.295107	+	0.0618123i
$276$	−8.95974			−0.539313
$277$		−	25.3910i		−	1.52559i	−0.646638	−	0.762797i	$-0.723825\pi$
$277$		−	25.3910i		−	1.52559i	0.646638	−	0.762797i	$-0.276175\pi$
$278$		−	1.94159i		−	0.116449i
$279$	2.39914			0.143633
$280$	0.532575	+	0.0551771i	0.0318275	+	0.00329746i
$281$	10.4799			0.625181			0.312590	−	0.949888i	$-0.398803\pi$
$281$	10.4799			0.625181			0.312590	+	0.949888i	$0.398803\pi$
$282$			1.96840i			0.117216i
$283$			31.6855i			1.88350i	0.336307	+	0.941752i	$0.390822\pi$
$283$			31.6855i			1.88350i	−0.336307	+	0.941752i	$0.609178\pi$
$284$	16.0365			0.951591
$285$	0.331927	−	3.20380i	0.0196617	−	0.189777i
$286$	−0.690219			−0.0408135
$287$			1.51130i			0.0892091i
$288$		−	1.44404i		−	0.0850911i
$289$	−31.3731			−1.84548
$290$	−0.131997	+	1.27405i	−0.00775112	+	0.0748147i
$291$	−13.6920			−0.802636
$292$		−	5.45604i		−	0.319291i
$293$		−	15.0863i		−	0.881352i	−0.897666	−	0.440676i	$-0.854739\pi$
$293$		−	15.0863i		−	0.881352i	0.897666	−	0.440676i	$-0.145261\pi$
$294$	1.28733			0.0750787
$295$	29.4765	+	3.05389i	1.71619	+	0.177804i
$296$	−0.483667			−0.0281126
$297$			5.65392i			0.328073i
$298$		−	2.23689i		−	0.129580i
$299$	16.4547			0.951599
$300$	−2.92747	+	13.9765i	−0.169018	+	0.806932i
$301$	0.397652			0.0229203
$302$			2.14328i			0.123332i
$303$		−	5.82255i		−	0.334497i
$304$	3.89640			0.223474
$305$	−7.15179	−	0.740956i	−0.409510	−	0.0424270i
$306$	−0.846708			−0.0484031
$307$		−	8.63283i		−	0.492702i	−0.969181	−	0.246351i	$-0.920768\pi$
$307$		−	8.63283i		−	0.492702i	0.969181	−	0.246351i	$-0.0792315\pi$
$308$		−	0.905838i		−	0.0516149i
$309$	7.27814			0.414039
$310$	−0.0786415	+	0.759057i	−0.00446654	+	0.0431115i
$311$	−0.0886279			−0.00502562			−0.00251281	−	0.999997i	$-0.500800\pi$
$311$	−0.0886279			−0.00502562			−0.00251281	+	0.999997i	$0.500800\pi$
$312$		−	3.95969i		−	0.224173i
$313$			4.80502i			0.271596i	0.990737	+	0.135798i	$0.0433598\pi$
$313$			4.80502i			0.271596i	−0.990737	+	0.135798i	$0.956640\pi$
$314$	−2.48664			−0.140329
$315$	−0.0973939	+	0.940057i	−0.00548753	+	0.0529662i
$316$	−6.43361			−0.361919
$317$			11.4320i			0.642083i	0.947065	+	0.321042i	$0.104033\pi$
$317$			11.4320i			0.642083i	−0.947065	+	0.321042i	$0.895967\pi$
$318$		−	1.65899i		−	0.0930313i
$319$	4.35289			0.243715
$320$	−16.8756	−	1.74838i	−0.943373	−	0.0977374i
$321$	−8.15717			−0.455289
$322$		−	0.188618i		−	0.0105113i
$323$		−	6.95508i		−	0.386991i
$324$	−10.6448			−0.591376
$325$	5.37634	−	25.6680i	0.298226	−	1.42380i
$326$	0.0843020			0.00466906
$327$			11.8923i			0.657646i
$328$			1.73368i			0.0957266i
$329$	4.74428			0.261561
$330$	−0.421605	−	0.0436801i	−0.0232086	−	0.00240451i
$331$	−14.2878			−0.785331			−0.392665	−	0.919681i	$-0.628447\pi$
$331$	−14.2878			−0.785331			−0.392665	+	0.919681i	$0.628447\pi$
$332$			9.60976i			0.527404i
$333$		−	0.853728i		−	0.0467840i
$334$	1.06016			0.0580095
$335$	0.284888	−	2.74977i	0.0155651	−	0.150236i
$336$	2.56424			0.139891
$337$			20.8355i			1.13498i	0.823380	+	0.567490i	$0.192085\pi$
$337$			20.8355i			1.13498i	−0.823380	+	0.567490i	$0.807915\pi$
$338$			1.90946i			0.103861i
$339$	23.6966			1.28702
$340$	−3.17760	+	30.6706i	−0.172330	+	1.66335i
$341$	2.59338			0.140439
$342$		−	0.121739i		−	0.00658292i
$343$		−	6.30089i		−	0.340216i
$344$	0.456166			0.0245948
$345$	10.0510	+	1.04133i	0.541127	+	0.0560631i
$346$	−2.18372			−0.117397
$347$		−	4.98017i		−	0.267350i	−0.991025	−	0.133675i	$-0.957322\pi$
$347$		−	4.98017i		−	0.267350i	0.991025	−	0.133675i	$-0.0426778\pi$
$348$			12.4317i			0.666407i
$349$	−8.50465			−0.455244			−0.227622	−	0.973750i	$-0.573095\pi$
$349$	−8.50465			−0.455244			−0.227622	+	0.973750i	$0.573095\pi$
$350$	−0.294229	−	0.0616282i	−0.0157272	−	0.00329417i
$351$	29.6548			1.58286
$352$		−	1.56096i		−	0.0831992i
$353$			34.6465i			1.84405i	0.387135	+	0.922023i	$0.373465\pi$
$353$			34.6465i			1.84405i	−0.387135	+	0.922023i	$0.626535\pi$
$354$	−2.51217			−0.133520
$355$	−17.9897	−	1.86381i	−0.954792	−	0.0989206i
$356$	11.8486			0.627976
$357$		−	4.57718i		−	0.242250i
$358$			2.32721i			0.122997i
$359$	22.4347			1.18406			0.592030	−	0.805916i	$-0.298327\pi$
$359$	22.4347			1.18406			0.592030	+	0.805916i	$0.298327\pi$
$360$	−0.111725	+	1.07838i	−0.00588844	+	0.0568359i
$361$	1.00000			0.0526316
$362$		−	0.0705448i		−	0.00370775i
$363$			1.44045i			0.0756040i
$364$	−4.75112			−0.249027
$365$	−0.634116	+	6.12056i	−0.0331911	+	0.320365i
$366$	0.609520			0.0318601
$367$			5.40720i			0.282253i	0.989992	+	0.141127i	$0.0450725\pi$
$367$			5.40720i			0.282253i	−0.989992	+	0.141127i	$0.954927\pi$
$368$			12.2238i			0.637211i
$369$	−3.06015			−0.159305
$370$	0.270108	+	0.0279843i	0.0140422	+	0.00145484i
$371$	−3.99853			−0.207593
$372$			7.40658i			0.384013i
$373$		−	21.4126i		−	1.10870i	−0.832283	−	0.554351i	$-0.812966\pi$
$373$		−	21.4126i		−	1.10870i	0.832283	−	0.554351i	$-0.187034\pi$
$374$	−0.915258			−0.0473269
$375$	4.90840	−	15.3385i	0.253469	−	0.792077i
$376$	5.44240			0.280670
$377$		−	22.8309i		−	1.17585i
$378$		−	0.339929i		−	0.0174841i
$379$	−3.74465			−0.192350			−0.0961749	−	0.995364i	$-0.530661\pi$
$379$	−3.74465			−0.192350			−0.0961749	+	0.995364i	$0.530661\pi$
$380$	−4.40981	−	0.456875i	−0.226218	−	0.0234372i
$381$	13.1553			0.673964
$382$			1.52531i			0.0780415i
$383$		−	18.2790i		−	0.934014i	−0.884254	−	0.467007i	$-0.845332\pi$
$383$		−	18.2790i		−	0.934014i	0.884254	−	0.467007i	$-0.154668\pi$
$384$	5.93520			0.302879
$385$	−0.105279	+	1.01616i	−0.00536552	+	0.0517885i
$386$	2.20746			0.112357
$387$			0.805185i			0.0409299i
$388$			18.8460i			0.956763i
$389$	6.32254			0.320565			0.160283	−	0.987071i	$-0.448759\pi$
$389$	6.32254			0.320565			0.160283	+	0.987071i	$0.448759\pi$
$390$	−0.229102	+	2.21132i	−0.0116010	+	0.111975i
$391$	21.8196			1.10346
$392$		−	3.55933i		−	0.179773i
$393$		−	31.7066i		−	1.59939i
$394$	2.55851			0.128896
$395$	7.21719	+	0.747732i	0.363136	+	0.0376225i
$396$	1.83419			0.0921713
$397$			27.6346i			1.38694i	0.720485	+	0.693470i	$0.243919\pi$
$397$			27.6346i			1.38694i	−0.720485	+	0.693470i	$0.756081\pi$
$398$		−	2.17531i		−	0.109039i
$399$	0.658106			0.0329465
$400$	19.0682	+	3.99396i	0.953409	+	0.199698i
$401$	−27.5885			−1.37770			−0.688851	−	0.724903i	$-0.741885\pi$
$401$	−27.5885			−1.37770			−0.688851	+	0.724903i	$0.741885\pi$
$402$			0.234353i			0.0116885i
$403$		−	13.6023i		−	0.677578i
$404$	−8.01435			−0.398729
$405$	11.9413	+	1.23717i	0.593366	+	0.0614752i
$406$	−0.261708			−0.0129883
$407$		−	0.922846i		−	0.0457438i
$408$		−	5.25070i		−	0.259949i
$409$	−22.5074			−1.11292			−0.556459	−	0.830875i	$-0.687840\pi$
$409$	−22.5074			−1.11292			−0.556459	+	0.830875i	$0.687840\pi$
$410$	0.100309	−	0.968190i	0.00495389	−	0.0478155i
$411$	−14.6834			−0.724277
$412$		−	10.0179i		−	0.493545i
$413$			6.05489i			0.297942i
$414$	0.381923			0.0187705
$415$	1.11687	−	10.7802i	0.0548251	−	0.529178i
$416$	−8.18721			−0.401411
$417$			21.2528i			1.04075i
$418$		−	0.131596i		−	0.00643655i
$419$	25.6597			1.25356			0.626779	−	0.779197i	$-0.284373\pi$
$419$	25.6597			1.25356			0.626779	+	0.779197i	$0.284373\pi$
$420$	−2.90212	−	0.300672i	−0.141609	−	0.0146713i
$421$	−24.6504			−1.20139			−0.600693	−	0.799480i	$-0.705108\pi$
$421$	−24.6504			−1.20139			−0.600693	+	0.799480i	$0.705108\pi$
$422$			1.41969i			0.0691094i
$423$			9.60646i			0.467082i
$424$	−4.58691			−0.222760
$425$	7.12924	−	34.0368i	0.345819	−	1.65103i
$426$	1.53319			0.0742833
$427$		−	1.46908i		−	0.0710938i
$428$			11.2278i			0.542716i
$429$	7.55516			0.364767
$430$	−0.254750	−	0.0263932i	−0.0122851	−	0.00127279i
$431$	24.6399			1.18686			0.593431	−	0.804885i	$-0.297773\pi$
$431$	24.6399			1.18686			0.593431	+	0.804885i	$0.297773\pi$
$432$			22.0299i			1.05991i
$433$		−	27.2031i		−	1.30730i	−0.756798	−	0.653649i	$-0.773237\pi$
$433$		−	27.2031i		−	1.30730i	0.756798	−	0.653649i	$-0.226763\pi$
$434$	−0.155921			−0.00748446
$435$	1.44484	−	13.9458i	0.0692749	−	0.668649i
$436$	16.3690			0.783931
$437$			3.13721i			0.150073i
$438$		−	0.521632i		−	0.0249245i
$439$	22.7258			1.08464			0.542321	−	0.840172i	$-0.317546\pi$
$439$	22.7258			1.08464			0.542321	+	0.840172i	$0.317546\pi$
$440$	−0.120771	+	1.16569i	−0.00575751	+	0.0555722i
$441$	6.28262			0.299172
$442$			4.80053i			0.228338i
$443$			32.9667i			1.56629i	0.621837	+	0.783146i	$0.286386\pi$
$443$			32.9667i			1.56629i	−0.621837	+	0.783146i	$0.713614\pi$
$444$	2.63561			0.125080
$445$	−13.2917	−	1.37708i	−0.630089	−	0.0652799i
$446$	2.28048			0.107984
$447$			24.4851i			1.15811i
$448$		−	3.46648i		−	0.163776i
$449$	30.3903			1.43421			0.717103	−	0.696967i	$-0.245468\pi$
$449$	30.3903			1.43421			0.717103	+	0.696967i	$0.245468\pi$
$450$	0.124788	−	0.595769i	0.00588256	−	0.0280848i
$451$	−3.30790			−0.155763
$452$		−	32.6168i		−	1.53417i
$453$		−	23.4604i		−	1.10227i
$454$	−1.06834			−0.0501399
$455$	5.32978	+	0.552189i	0.249864	+	0.0258870i
$456$	0.754945			0.0353535
$457$			18.0322i			0.843509i	0.906710	+	0.421755i	$0.138586\pi$
$457$			18.0322i			0.843509i	−0.906710	+	0.421755i	$0.861414\pi$
$458$		−	0.0701328i		−	0.00327709i
$459$	39.3234			1.83546
$460$	1.43331	−	13.8345i	0.0668287	−	0.645038i
$461$	14.1522			0.659135			0.329568	−	0.944132i	$-0.393097\pi$
$461$	14.1522			0.659135			0.329568	+	0.944132i	$0.393097\pi$
$462$		−	0.0866038i		−	0.00402917i
$463$			7.97479i			0.370620i	0.982680	+	0.185310i	$0.0593289\pi$
$463$			7.97479i			0.370620i	−0.982680	+	0.185310i	$0.940671\pi$
$464$	16.9606			0.787375
$465$	0.860813	−	8.30866i	0.0399193	−	0.385305i
$466$	1.89552			0.0878083
$467$		−	18.6954i		−	0.865121i	−0.901605	−	0.432561i	$-0.857610\pi$
$467$		−	18.6954i		−	0.865121i	0.901605	−	0.432561i	$-0.142390\pi$
$468$		−	9.62030i		−	0.444699i
$469$	0.564843			0.0260820
$470$	−3.03935	−	0.314890i	−0.140195	−	0.0145248i
$471$	27.2188			1.25418
$472$			6.94586i			0.319709i
$473$			0.870374i			0.0400198i
$474$	−0.615094			−0.0282522
$475$	4.89380	+	1.02504i	0.224543	+	0.0470321i
$476$	−6.30018			−0.288768
$477$		−	8.09642i		−	0.370710i
$478$			2.04990i			0.0937601i
$479$	19.3936			0.886115			0.443057	−	0.896493i	$-0.353894\pi$
$479$	19.3936			0.886115			0.443057	+	0.896493i	$0.353894\pi$
$480$	−5.00098	−	0.518123i	−0.228263	−	0.0236490i
$481$	−4.84033			−0.220700
$482$			2.56582i			0.116870i
$483$			2.06462i			0.0939434i
$484$	1.98268			0.0901219
$485$	2.19034	−	21.1414i	0.0994582	−	0.959981i
$486$	1.21438			0.0550856
$487$			24.0327i			1.08903i	0.838753	+	0.544513i	$0.183285\pi$
$487$			24.0327i			1.08903i	−0.838753	+	0.544513i	$0.816715\pi$
$488$		−	1.68525i		−	0.0762878i
$489$	−0.922773			−0.0417292
$490$	−0.205938	+	1.98774i	−0.00930333	+	0.0897967i
$491$	12.2443			0.552579			0.276290	−	0.961074i	$-0.410895\pi$
$491$	12.2443			0.552579			0.276290	+	0.961074i	$0.410895\pi$
$492$		−	9.44722i		−	0.425914i
$493$		−	30.2747i		−	1.36350i
$494$	−0.690219			−0.0310544
$495$	−2.05758	−	0.213174i	−0.0924813	−	0.00958146i
$496$	10.1048			0.453721
$497$		−	3.69534i		−	0.165759i
$498$			0.918754i			0.0411703i
$499$	−15.9356			−0.713373			−0.356687	−	0.934224i	$-0.616094\pi$
$499$	−15.9356			−0.713373			−0.356687	+	0.934224i	$0.616094\pi$
$500$	−21.1124	−	6.75609i	−0.944176	−	0.302141i
$501$	−11.6046			−0.518454
$502$			2.35541i			0.105127i
$503$		−	15.2623i		−	0.680514i	−0.940332	−	0.340257i	$-0.889486\pi$
$503$		−	15.2623i		−	0.680514i	0.940332	−	0.340257i	$-0.110514\pi$
$504$	−0.221516			−0.00986709
$505$	8.99046	+	0.931450i	0.400070	+	0.0414490i
$506$	0.412843			0.0183531
$507$		−	20.9010i		−	0.928245i
$508$		−	18.1073i		−	0.803382i
$509$	−6.35745			−0.281789			−0.140894	−	0.990025i	$-0.544998\pi$
$509$	−6.35745			−0.281789			−0.140894	+	0.990025i	$0.544998\pi$
$510$	−0.303799	+	2.93230i	−0.0134524	+	0.129844i
$511$	−1.25725			−0.0556175
$512$		−	10.1663i		−	0.449292i
$513$			5.65392i			0.249626i
$514$	1.03605			0.0456980
$515$	−1.16430	+	11.2380i	−0.0513054	+	0.495205i
$516$	−2.48575			−0.109429
$517$			10.3842i			0.456697i
$518$			0.0554840i			0.00243783i
$519$	23.9031			1.04923
$520$	6.11405	+	0.633442i	0.268119	+	0.0277783i
$521$	−9.47236			−0.414992			−0.207496	−	0.978236i	$-0.566531\pi$
$521$	−9.47236			−0.414992			−0.207496	+	0.978236i	$0.566531\pi$
$522$		−	0.529919i		−	0.0231939i
$523$			23.8569i			1.04319i	0.853193	+	0.521595i	$0.174663\pi$
$523$			23.8569i			1.04319i	−0.853193	+	0.521595i	$0.825337\pi$
$524$	−43.6420			−1.90651
$525$	3.22064	+	0.674585i	0.140560	+	0.0294413i
$526$	1.32595			0.0578140
$527$		−	18.0372i		−	0.785712i
$528$			5.61256i			0.244255i
$529$	13.1579			0.572082
$530$	2.56160	+	0.265392i	0.111269	+	0.0115279i
$531$	−12.2602			−0.532049
$532$		−	0.905838i		−	0.0392731i
$533$			17.3499i			0.751509i
$534$	1.13280			0.0490212
$535$	1.30493	−	12.5953i	0.0564168	−	0.544541i
$536$	0.647959			0.0279876
$537$		−	25.4737i		−	1.09927i
$538$			1.67864i			0.0723714i
$539$	6.79127			0.292520
$540$	2.58313	−	24.9327i	0.111160	−	1.07293i
$541$	−1.20982			−0.0520142			−0.0260071	−	0.999662i	$-0.508279\pi$
$541$	−1.20982			−0.0520142			−0.0260071	+	0.999662i	$0.508279\pi$
$542$			1.02241i			0.0439162i
$543$			0.772186i			0.0331377i
$544$	−10.8566			−0.465472
$545$	−18.3626	−	1.90244i	−0.786568	−	0.0814918i
$546$	−0.454237			−0.0194396
$547$			9.94790i			0.425341i	0.977124	+	0.212671i	$0.0682162\pi$
$547$			9.94790i			0.425341i	−0.977124	+	0.212671i	$0.931784\pi$
$548$			20.2106i			0.863356i
$549$	2.97467			0.126956
$550$	0.134891	−	0.644003i	0.00575176	−	0.0274604i
$551$	4.35289			0.185439
$552$			2.36842i			0.100807i
$553$			1.48252i			0.0630430i
$554$	−3.34134			−0.141960
$555$	−2.95661	−	0.306318i	−0.125501	−	0.0130025i
$556$	29.2530			1.24060
$557$		−	31.0507i		−	1.31566i	−0.753166	−	0.657831i	$-0.771474\pi$
$557$		−	31.0507i		−	1.31566i	0.753166	−	0.657831i	$-0.228526\pi$
$558$		−	0.315717i		−	0.0133654i
$559$	4.56511			0.193084
$560$	−0.410209	+	3.95938i	−0.0173345	+	0.167314i
$561$	10.0184			0.422979
$562$		−	1.37911i		−	0.0581744i
$563$			44.8070i			1.88839i	0.329390	+	0.944194i	$0.393157\pi$
$563$			44.8070i			1.88839i	−0.329390	+	0.944194i	$0.606843\pi$
$564$	−29.6568			−1.24878
$565$	−3.79081	+	36.5894i	−0.159481	+	1.53933i
$566$	4.16967			0.175264
$567$			2.45291i			0.103012i
$568$		−	4.23910i		−	0.177869i
$569$	35.6674			1.49526			0.747628	−	0.664118i	$-0.231193\pi$
$569$	35.6674			1.49526			0.747628	+	0.664118i	$0.231193\pi$
$570$	−0.421605	−	0.0436801i	−0.0176591	−	0.00182956i
$571$	−21.6619			−0.906524			−0.453262	−	0.891377i	$-0.649740\pi$
$571$	−21.6619			−0.906524			−0.453262	+	0.891377i	$0.649740\pi$
$572$		−	10.3992i		−	0.434811i
$573$		−	16.6961i		−	0.697488i
$574$	0.198880			0.00830109
$575$	−3.21577	+	15.3529i	−0.134107	+	0.640260i
$576$	7.01910			0.292463
$577$		−	21.2075i		−	0.882879i	−0.897291	−	0.441440i	$-0.854468\pi$
$577$		−	21.2075i		−	0.882879i	0.897291	−	0.441440i	$-0.145532\pi$
$578$			4.12857i			0.171726i
$579$	−24.1629			−1.00418
$580$	−19.1954	−	1.98873i	−0.797046	−	0.0825774i
$581$	2.21441			0.0918690
$582$			1.80180i			0.0746870i
$583$		−	8.75191i		−	0.362467i
$584$	−1.44225			−0.0596808
$585$	−1.11810	+	10.7920i	−0.0462277	+	0.446195i
$586$	−1.98529			−0.0820117
$587$		−	47.6238i		−	1.96565i	−0.184552	−	0.982823i	$-0.559084\pi$
$587$		−	47.6238i		−	1.96565i	0.184552	−	0.982823i	$-0.440916\pi$
$588$			19.3956i			0.799859i
$589$	2.59338			0.106858
$590$	0.401878	−	3.87897i	0.0165451	−	0.159695i
$591$	−28.0055			−1.15199
$592$		−	3.59577i		−	0.147785i
$593$		−	14.7406i		−	0.605323i	−0.953098	−	0.302661i	$-0.902125\pi$
$593$		−	14.7406i		−	0.605323i	0.953098	−	0.302661i	$-0.0978751\pi$
$594$	0.744030			0.0305279
$595$	7.06751	+	0.732224i	0.289740	+	0.0300183i
$596$	33.7021			1.38049
$597$			23.8111i			0.974522i
$598$		−	2.16536i		−	0.0885483i
$599$	−29.8502			−1.21965			−0.609823	−	0.792538i	$-0.708759\pi$
$599$	−29.8502			−1.21965			−0.609823	+	0.792538i	$0.708759\pi$
$600$	3.69455	+	0.773849i	0.150829	+	0.0315923i
$601$	−9.23160			−0.376565			−0.188282	−	0.982115i	$-0.560292\pi$
$601$	−9.23160			−0.376565			−0.188282	+	0.982115i	$0.560292\pi$
$602$		−	0.0523292i		−	0.00213278i
$603$			1.14372i			0.0465760i
$604$	−32.2917			−1.31393
$605$	−2.22416	−	0.230433i	−0.0904251	−	0.00936843i
$606$	−0.766222			−0.0311257
$607$		−	27.9086i		−	1.13278i	−0.824138	−	0.566389i	$-0.808340\pi$
$607$		−	27.9086i		−	1.13278i	0.824138	−	0.566389i	$-0.191660\pi$
$608$		−	1.56096i		−	0.0633051i
$609$	2.86466			0.116082
$610$	−0.0975065	+	0.941144i	−0.00394792	+	0.0381058i
$611$	54.4652			2.20342
$612$		−	12.7569i		−	0.515667i
$613$			44.6257i			1.80241i	0.433390	+	0.901207i	$0.357317\pi$
$613$			44.6257i			1.80241i	−0.433390	+	0.901207i	$0.642683\pi$
$614$	−1.13604			−0.0458469
$615$	−1.09798	+	10.5978i	−0.0442749	+	0.427346i
$616$	−0.239450			−0.00964771
$617$			46.6619i			1.87854i	0.343184	+	0.939268i	$0.388495\pi$
$617$			46.6619i			1.87854i	−0.343184	+	0.939268i	$0.611505\pi$
$618$		−	0.957772i		−	0.0385272i
$619$	−16.6735			−0.670165			−0.335083	−	0.942189i	$-0.608764\pi$
$619$	−16.6735			−0.670165			−0.335083	+	0.942189i	$0.608764\pi$
$620$	−11.4363	−	1.18485i	−0.459293	−	0.0475848i
$621$	−17.7375			−0.711783
$622$			0.0116630i			0.000467645i
$623$		−	2.73031i		−	0.109388i
$624$	29.4379			1.17846
$625$	22.8986	+	10.0327i	0.915943	+	0.401307i
$626$	0.632320			0.0252726
$627$			1.44045i			0.0575260i
$628$		−	37.4649i		−	1.49501i
$629$	−6.41847			−0.255921
$630$	0.123707	+	0.0128166i	0.00492862	+	0.000510626i
$631$	18.2634			0.727053			0.363527	−	0.931584i	$-0.381573\pi$
$631$	18.2634			0.727053			0.363527	+	0.931584i	$0.381573\pi$
$632$			1.70067i			0.0676488i
$633$		−	15.5400i		−	0.617658i
$634$	1.50440			0.0597472
$635$	−2.10448	+	20.3127i	−0.0835138	+	0.806085i
$636$	24.9951			0.991119
$637$		−	35.6202i		−	1.41132i
$638$		−	0.572821i		−	0.0226782i
$639$	7.48250			0.296003
$640$	−0.949470	+	9.16439i	−0.0375311	+	0.362254i
$641$	2.90244			0.114639			0.0573197	−	0.998356i	$-0.481745\pi$
$641$	2.90244			0.114639			0.0573197	+	0.998356i	$0.481745\pi$
$642$			1.07345i			0.0423656i
$643$			37.5112i			1.47930i	0.672993	+	0.739648i	$0.265008\pi$
$643$			37.5112i			1.47930i	−0.672993	+	0.739648i	$0.734992\pi$
$644$	2.84181			0.111983
$645$	2.78850	+	0.288900i	0.109797	+	0.0113754i
$646$	−0.915258			−0.0360103
$647$		−	2.87727i		−	0.113117i	−0.998399	−	0.0565585i	$-0.981987\pi$
$647$		−	2.87727i		−	0.113117i	0.998399	−	0.0565585i	$-0.0180127\pi$
$648$			2.81385i			0.110538i
$649$	−13.2528			−0.520219
$650$	−3.37779	−	0.707502i	−0.132488	−	0.0277505i
$651$	1.70672			0.0668916
$652$			1.27014i			0.0497423i
$653$		−	7.45085i		−	0.291574i	−0.989316	−	0.145787i	$-0.953429\pi$
$653$		−	7.45085i		−	0.291574i	0.989316	−	0.145787i	$-0.0465715\pi$
$654$	1.56497			0.0611953
$655$	48.9573	+	5.07219i	1.91292	+	0.198187i
$656$	−12.8889			−0.503227
$657$		−	2.54574i		−	0.0993189i
$658$		−	0.624327i		−	0.0243388i
$659$	−24.9272			−0.971025			−0.485512	−	0.874230i	$-0.661367\pi$
$659$	−24.9272			−0.971025			−0.485512	+	0.874230i	$0.661367\pi$
$660$	0.658106	−	6.35211i	0.0256167	−	0.247256i
$661$	−6.76983			−0.263316			−0.131658	−	0.991295i	$-0.542030\pi$
$661$	−6.76983			−0.263316			−0.131658	+	0.991295i	$0.542030\pi$
$662$			1.88022i			0.0730767i
$663$		−	52.5468i		−	2.04075i
$664$	2.54025			0.0985808
$665$	−0.105279	+	1.01616i	−0.00408255	+	0.0394052i
$666$	−0.112347			−0.00435335
$667$			13.6560i			0.528761i
$668$			15.9729i			0.618010i
$669$	−24.9622			−0.965095
$670$	−0.361858	−	0.0374901i	−0.0139798	−	0.00144837i
$671$	3.21550			0.124133
$672$		−	1.02727i		−	0.0396280i
$673$			47.8457i			1.84432i	0.386812	+	0.922159i	$0.373576\pi$
$673$			47.8457i			1.84432i	−0.386812	+	0.922159i	$0.626424\pi$
$674$	2.74185			0.105612
$675$	−5.79549	+	27.6691i	−0.223069	+	1.06499i
$676$	−28.7688			−1.10649
$677$			29.3775i			1.12907i	0.825410	+	0.564534i	$0.190944\pi$
$677$			29.3775i			1.12907i	−0.825410	+	0.564534i	$0.809056\pi$
$678$		−	3.11837i		−	0.119760i
$679$	4.34275			0.166659
$680$	8.10748	+	0.839969i	0.310908	+	0.0322114i
$681$	11.6941			0.448120
$682$		−	0.341277i		−	0.0130682i
$683$			35.4637i			1.35698i	0.734610	+	0.678490i	$0.237365\pi$
$683$			35.4637i			1.35698i	−0.734610	+	0.678490i	$0.762635\pi$
$684$	1.83419			0.0701318
$685$	2.34894	−	22.6722i	0.0897483	−	0.866260i
$686$	−0.829169			−0.0316578
$687$			0.767677i			0.0292887i
$688$			3.39132i			0.129293i
$689$	−45.9038			−1.74880
$690$	0.137034	−	1.32267i	0.00521679	−	0.0503530i
$691$	37.1831			1.41451			0.707256	−	0.706957i	$-0.249933\pi$
$691$	37.1831			1.41451			0.707256	+	0.706957i	$0.249933\pi$
$692$		−	32.9009i		−	1.25071i
$693$		−	0.422657i		−	0.0160554i
$694$	−0.655369			−0.0248775
$695$	−32.8159	−	3.39986i	−1.24478	−	0.128964i
$696$	3.28619			0.124563
$697$			23.0067i			0.871442i
$698$			1.11917i			0.0423614i
$699$	−20.7484			−0.784778
$700$	0.928521	−	4.43299i	0.0350948	−	0.167551i
$701$	7.78088			0.293880			0.146940	−	0.989145i	$-0.453058\pi$
$701$	7.78088			0.293880			0.146940	+	0.989145i	$0.453058\pi$
$702$		−	3.90244i		−	0.147288i
$703$		−	0.922846i		−	0.0348058i
$704$	7.58738			0.285960
$705$	33.2689	+	3.44680i	1.25298	+	0.129814i
$706$	4.55932			0.171592
$707$			1.84677i			0.0694549i
$708$		−	37.8495i		−	1.42247i
$709$	43.5495			1.63554			0.817769	−	0.575547i	$-0.195211\pi$
$709$	43.5495			1.63554			0.817769	+	0.575547i	$0.195211\pi$
$710$	−0.245269	+	2.36736i	−0.00920477	+	0.0888455i
$711$	−3.00187			−0.112579
$712$		−	3.13207i		−	0.117379i
$713$			8.13599i			0.304695i
$714$	−0.602337			−0.0225419
$715$	−1.20862	+	11.6657i	−0.0451998	+	0.436274i
$716$	−35.0628			−1.31036
$717$		−	22.4383i		−	0.837972i
$718$		−	2.95231i		−	0.110179i
$719$	19.1645			0.714716			0.357358	−	0.933967i	$-0.383678\pi$
$719$	19.1645			0.714716			0.357358	+	0.933967i	$0.383678\pi$
$720$	−8.01714	−	0.830610i	−0.298781	−	0.0309550i
$721$	−2.30845			−0.0859711
$722$		−	0.131596i		−	0.00489748i
$723$		−	28.0856i		−	1.04451i
$724$	1.06286			0.0395010
$725$	21.3022	+	4.46189i	0.791143	+	0.165710i
$726$	0.189557			0.00703512
$727$		−	38.1779i		−	1.41594i	−0.706243	−	0.707970i	$-0.749611\pi$
$727$		−	38.1779i		−	1.41594i	0.706243	−	0.707970i	$-0.250389\pi$
$728$			1.25591i			0.0465473i
$729$	−29.3993			−1.08886
$730$	0.805438	+	0.0834468i	0.0298106	+	0.00308851i
$731$	6.05352			0.223897
$732$			9.18332i			0.339425i
$733$		−	29.5379i		−	1.09101i	−0.838109	−	0.545503i	$-0.816338\pi$
$733$		−	29.5379i		−	1.09101i	0.838109	−	0.545503i	$-0.183662\pi$
$734$	0.711563			0.0262643
$735$	2.25420	−	21.7578i	0.0831476	−	0.802550i
$736$	4.89705			0.180508
$737$			1.23632i			0.0455404i
$738$			0.402702i			0.0148237i
$739$	24.9966			0.919516			0.459758	−	0.888044i	$-0.347936\pi$
$739$	24.9966			0.919516			0.459758	+	0.888044i	$0.347936\pi$
$740$	−0.421625	+	4.06957i	−0.0154993	+	0.149601i
$741$	7.55516			0.277546
$742$			0.526189i			0.0193170i
$743$		−	23.9140i		−	0.877318i	−0.898653	−	0.438659i	$-0.855454\pi$
$743$		−	23.9140i		−	0.877318i	0.898653	−	0.438659i	$-0.144546\pi$
$744$	1.95786			0.0717786
$745$	−37.8069	−	3.91695i	−1.38514	−	0.143506i
$746$	−2.81780			−0.103167
$747$			4.48383i			0.164055i
$748$		−	13.7897i		−	0.504202i
$749$	2.58725			0.0945361
$750$	−2.01848	−	0.645924i	−0.0737044	−	0.0235858i
$751$	32.9159			1.20112			0.600560	−	0.799580i	$-0.294944\pi$
$751$	32.9159			1.20112			0.600560	+	0.799580i	$0.294944\pi$
$752$			40.4610i			1.47546i
$753$		−	25.7824i		−	0.939564i
$754$	−3.00445			−0.109416
$755$	36.2246	+	3.75303i	1.31835	+	0.136587i
$756$	5.12153			0.186268
$757$			19.8968i			0.723161i	0.932341	+	0.361580i	$0.117763\pi$
$757$			19.8968i			0.723161i	−0.932341	+	0.361580i	$0.882237\pi$
$758$			0.492780i			0.0178986i
$759$	−4.51900			−0.164029
$760$	−0.120771	+	1.16569i	−0.00438081	+	0.0422841i
$761$	28.8803			1.04691			0.523456	−	0.852053i	$-0.324642\pi$
$761$	28.8803			1.04691			0.523456	+	0.852053i	$0.324642\pi$
$762$		−	1.73117i		−	0.0627138i
$763$		−	3.77194i		−	0.136554i
$764$	−22.9810			−0.831424
$765$	−1.48264	+	14.3106i	−0.0536051	+	0.517402i
$766$	−2.40544			−0.0869120
$767$			69.5112i			2.50990i
$768$			21.0774i			0.760566i
$769$	17.5385			0.632455			0.316228	−	0.948683i	$-0.397584\pi$
$769$	17.5385			0.632455			0.316228	+	0.948683i	$0.397584\pi$
$770$	0.133723	+	0.0138543i	0.00481903	+	0.000499273i
$771$	−11.3406			−0.408422
$772$			33.2586i			1.19700i
$773$			45.4884i			1.63611i	0.575143	+	0.818053i	$0.304946\pi$
$773$			45.4884i			1.63611i	−0.575143	+	0.818053i	$0.695054\pi$
$774$	0.105959			0.00380861
$775$	12.6915	+	2.65832i	0.455892	+	0.0954897i
$776$	4.98177			0.178835
$777$		−	0.607330i		−	0.0217879i
$778$		−	0.832018i		−	0.0298293i
$779$	−3.30790			−0.118518
$780$	−33.3168	−	3.45177i	−1.19293	−	0.123593i
$781$	8.08829			0.289422
$782$		−	2.87136i		−	0.102680i
$783$			24.6109i			0.879521i
$784$	26.4615			0.945052
$785$	−4.35427	+	42.0279i	−0.155411	+	1.50004i
$786$	−4.17245			−0.148826
$787$			14.4706i			0.515820i	0.966169	+	0.257910i	$0.0830337\pi$
$787$			14.4706i			0.515820i	−0.966169	+	0.257910i	$0.916966\pi$
$788$			38.5477i			1.37320i
$789$	−14.5139			−0.516707
$790$	0.0983983	−	0.949751i	0.00350085	−	0.0337906i
$791$	−7.51598			−0.267238
$792$		−	0.484850i		−	0.0172284i
$793$		−	16.8653i		−	0.598904i
$794$	3.63659			0.129058
$795$	−28.0393	−	2.90500i	−0.994453	−	0.103030i
$796$	32.7743			1.16165
$797$		−	16.3564i		−	0.579374i	−0.957121	−	0.289687i	$-0.906449\pi$
$797$		−	16.3564i		−	0.579374i	0.957121	−	0.289687i	$-0.0935513\pi$
$798$		−	0.0866038i		−	0.00306574i
$799$	72.2230			2.55507
$800$	1.60004	−	7.63901i	0.0565700	−	0.270080i
$801$	5.52847			0.195339
$802$			3.63052i			0.128198i
$803$		−	2.75185i		−	0.0971106i
$804$	−3.53087			−0.124524
$805$	−3.18793	−	0.330283i	−0.112360	−	0.0116409i
$806$	−1.79000			−0.0630501
$807$		−	18.3745i		−	0.646812i
$808$			2.11852i			0.0745292i
$809$	−33.2546			−1.16917			−0.584585	−	0.811332i	$-0.698743\pi$
$809$	−33.2546			−1.16917			−0.584585	+	0.811332i	$0.698743\pi$
$810$	0.162805	−	1.57142i	0.00572040	−	0.0552139i
$811$	−35.9446			−1.26219			−0.631094	−	0.775707i	$-0.717394\pi$
$811$	−35.9446			−1.26219			−0.631094	+	0.775707i	$0.717394\pi$
$812$		−	3.94302i		−	0.138373i
$813$		−	11.1913i		−	0.392497i
$814$	−0.121442			−0.00425656
$815$	0.147619	−	1.42483i	0.00517085	−	0.0499096i
$816$	39.0358			1.36653
$817$			0.870374i			0.0304505i
$818$			2.96187i			0.103559i
$819$	−2.21683			−0.0774624
$820$	14.5872	+	1.51130i	0.509408	+	0.0527768i
$821$	−13.7687			−0.480531			−0.240266	−	0.970707i	$-0.577235\pi$
$821$	−13.7687			−0.480531			−0.240266	+	0.970707i	$0.577235\pi$
$822$			1.93226i			0.0673955i
$823$		−	4.39908i		−	0.153342i	−0.997056	−	0.0766712i	$-0.975571\pi$
$823$		−	4.39908i		−	0.153342i	0.997056	−	0.0766712i	$-0.0244292\pi$
$824$	−2.64813			−0.0922520
$825$	−1.47652	+	7.04928i	−0.0514058	+	0.245424i
$826$	0.796797			0.0277241
$827$		−	12.4264i		−	0.432108i	−0.976381	−	0.216054i	$-0.930681\pi$
$827$		−	12.4264i		−	0.432108i	0.976381	−	0.216054i	$-0.0693187\pi$
$828$			5.75423i			0.199973i
$829$	−56.5829			−1.96521			−0.982603	−	0.185718i	$-0.940539\pi$
$829$	−56.5829			−1.96521			−0.982603	+	0.185718i	$0.940539\pi$
$830$	−1.41862	−	0.146976i	−0.0492412	−	0.00510160i
$831$	36.5744			1.26875
$832$		−	39.7958i		−	1.37967i
$833$		−	47.2338i		−	1.63655i
$834$	2.79677			0.0968443
$835$	1.85641	−	17.9183i	0.0642439	−	0.620089i
$836$	1.98268			0.0685725
$837$			14.6628i			0.506819i
$838$		−	3.37670i		−	0.116646i
$839$	−3.17520			−0.109620			−0.0548100	−	0.998497i	$-0.517455\pi$
$839$	−3.17520			−0.109620			−0.0548100	+	0.998497i	$0.517455\pi$
$840$	−0.0794799	+	0.767148i	−0.00274232	+	0.0264691i
$841$	−10.0523			−0.346632
$842$			3.24388i			0.111791i
$843$			15.0958i			0.519928i
$844$	−21.3897			−0.736265
$845$	32.2727	+	3.34359i	1.11021	+	0.115023i
$846$	1.26417			0.0434630
$847$		−	0.456875i		−	0.0156984i
$848$		−	34.1009i		−	1.17103i
$849$	−45.6413			−1.56641
$850$	−4.47909	−	0.938176i	−0.153632	−	0.0321792i
$851$	2.89517			0.0992450
$852$			23.0998i			0.791386i
$853$		−	5.63265i		−	0.192858i	−0.995340	−	0.0964291i	$-0.969258\pi$
$853$		−	5.63265i		−	0.192858i	0.995340	−	0.0964291i	$-0.0307421\pi$
$854$	−0.193324			−0.00661543
$855$	−2.05758	−	0.213174i	−0.0703677	−	0.00729040i
$856$	2.96796			0.101443
$857$			18.1582i			0.620271i	0.950692	+	0.310135i	$0.100374\pi$
$857$			18.1582i			0.620271i	−0.950692	+	0.310135i	$0.899626\pi$
$858$		−	0.994226i		−	0.0339423i
$859$	9.75939			0.332986			0.166493	−	0.986043i	$-0.446756\pi$
$859$	9.75939			0.332986			0.166493	+	0.986043i	$0.446756\pi$
$860$	0.397652	−	3.83818i	0.0135598	−	0.130881i
$861$	−2.17695			−0.0741902
$862$		−	3.24250i		−	0.110440i
$863$		−	44.8518i		−	1.52677i	−0.645942	−	0.763386i	$-0.723535\pi$
$863$		−	44.8518i		−	1.52677i	0.645942	−	0.763386i	$-0.276465\pi$
$864$	8.82551			0.300250
$865$	−3.82384	+	36.9081i	−0.130014	+	1.25491i
$866$	−3.57981			−0.121647
$867$		−	45.1915i		−	1.53478i
$868$		−	2.34918i		−	0.0797365i
$869$	−3.24490			−0.110076
$870$	−1.83520	−	0.190135i	−0.0622192	−	0.00644618i
$871$	6.48449			0.219719
$872$		−	4.32698i		−	0.146530i
$873$			8.79341i			0.297612i
$874$	0.412843			0.0139646
$875$	−1.55682	+	4.86499i	−0.0526303	+	0.164467i
$876$	7.85915			0.265536
$877$			30.7975i			1.03996i	0.854179	+	0.519978i	$0.174060\pi$
$877$			30.7975i			1.03996i	−0.854179	+	0.519978i	$0.825940\pi$
$878$		−	2.99061i		−	0.100928i
$879$	21.7311			0.732972
$880$	−8.66622	−	0.897857i	−0.292138	−	0.0302668i
$881$	15.9941			0.538856			0.269428	−	0.963021i	$-0.413165\pi$
$881$	15.9941			0.538856			0.269428	+	0.963021i	$0.413165\pi$
$882$		−	0.826765i		−	0.0278386i
$883$		−	6.19800i		−	0.208579i	−0.994547	−	0.104290i	$-0.966743\pi$
$883$		−	6.19800i		−	0.208579i	0.994547	−	0.104290i	$-0.0332569\pi$
$884$	−72.3271			−2.43262
$885$	−4.39898	+	42.4594i	−0.147870	+	1.42726i
$886$	4.33827			0.145747
$887$			57.1613i			1.91929i	0.281218	+	0.959644i	$0.409262\pi$
$887$			57.1613i			1.91929i	−0.281218	+	0.959644i	$0.590738\pi$
$888$		−	0.696698i		−	0.0233797i
$889$	−4.17252			−0.139942
$890$	−0.181218	+	1.74913i	−0.00607443	+	0.0586311i
$891$	−5.36888			−0.179864
$892$			34.3588i			1.15042i
$893$			10.3842i			0.347494i
$894$	3.22213			0.107764
$895$	39.3333	+	4.07510i	1.31477	+	0.136216i
$896$	−1.88250			−0.0628898
$897$			23.7022i			0.791392i
$898$		−	3.99923i		−	0.133456i
$899$	11.2887			0.376499
$900$	8.97614	+	1.88011i	0.299205	+	0.0626705i
$901$	−60.8703			−2.02788
$902$			0.435305i			0.0144941i
$903$			0.572798i			0.0190615i
$904$	−8.62194			−0.286762
$905$	−1.19231	−	0.123529i	−0.0396338	−	0.00410623i
$906$	−3.08729			−0.102568
$907$		−	58.6428i		−	1.94720i	−0.228258	−	0.973601i	$-0.573303\pi$
$907$		−	58.6428i		−	1.94720i	0.228258	−	0.973601i	$-0.426697\pi$
$908$		−	16.0962i		−	0.534171i
$909$	−3.73943			−0.124029
$910$	0.0726656	−	0.701376i	0.00240884	−	0.0232504i
$911$	29.8092			0.987623			0.493811	−	0.869569i	$-0.335603\pi$
$911$	29.8092			0.987623			0.493811	+	0.869569i	$0.335603\pi$
$912$			5.61256i			0.185851i
$913$			4.84685i			0.160407i
$914$	2.37295			0.0784903
$915$	1.06731	−	10.3018i	0.0352842	−	0.340567i
$916$	1.05665			0.0349129
$917$			10.0565i			0.332096i
$918$		−	5.17479i		−	0.170794i
$919$	−12.6160			−0.416163			−0.208082	−	0.978111i	$-0.566722\pi$
$919$	−12.6160			−0.416163			−0.208082	+	0.978111i	$0.566722\pi$
$920$	−3.65702	−	0.378883i	−0.120568	−	0.0124914i
$921$	12.4352			0.409753
$922$		−	1.86237i		−	0.0613339i
$923$		−	42.4231i		−	1.39637i
$924$	1.30482			0.0429253
$925$	0.945954	−	4.51623i	0.0311028	−	0.148493i
$926$	1.04945			0.0344870
$927$		−	4.67426i		−	0.153523i
$928$		−	6.79467i		−	0.223046i
$929$	−15.4757			−0.507740			−0.253870	−	0.967238i	$-0.581704\pi$
$929$	−15.4757			−0.507740			−0.253870	+	0.967238i	$0.581704\pi$
$930$	−1.09338	−	0.113279i	−0.0358535	−	0.00371457i
$931$	6.79127			0.222575
$932$			28.5588i			0.935476i
$933$		−	0.127664i		−	0.00417953i
$934$	−2.46024			−0.0805014
$935$	−1.60268	+	15.4692i	−0.0524132	+	0.505898i
$936$	−2.54304			−0.0831218
$937$			33.1867i			1.08416i	0.840326	+	0.542081i	$0.182363\pi$
$937$			33.1867i			1.08416i	−0.840326	+	0.542081i	$0.817637\pi$
$938$		−	0.0743309i		−	0.00242699i
$939$	−6.92140			−0.225871
$940$	4.74428	−	45.7924i	0.154741	−	1.49358i
$941$	−53.3449			−1.73899			−0.869497	−	0.493937i	$-0.835557\pi$
$941$	−53.3449			−1.73899			−0.869497	+	0.493937i	$0.835557\pi$
$942$		−	3.58188i		−	0.116704i
$943$		−	10.3776i		−	0.337941i
$944$	−51.6383			−1.68068
$945$	−5.74531	−	0.595239i	−0.186895	−	0.0193631i
$946$	0.114537			0.00372393
$947$		−	27.4898i		−	0.893300i	−0.894709	−	0.446650i	$-0.852617\pi$
$947$		−	27.4898i		−	0.893300i	0.894709	−	0.446650i	$-0.147383\pi$
$948$		−	9.26730i		−	0.300988i
$949$	−14.4334			−0.468529
$950$	0.134891	−	0.644003i	0.00437643	−	0.0208942i
$951$	−16.4672			−0.533985
$952$			1.66539i			0.0539757i
$953$			14.7424i			0.477553i	0.971075	+	0.238776i	$0.0767463\pi$
$953$			14.7424i			0.477553i	−0.971075	+	0.238776i	$0.923254\pi$
$954$	−1.06545			−0.0344953
$955$	25.7800	+	2.67092i	0.834220	+	0.0864288i
$956$	−30.8847			−0.998884
$957$			6.27012i			0.202684i
$958$		−	2.55211i		−	0.0824548i
$959$	4.65720			0.150389
$960$	2.51846	−	24.3084i	0.0812828	−	0.784550i
$961$	−24.2744			−0.783044
$962$			0.636966i			0.0205366i
$963$			5.23879i			0.168818i
$964$	−38.6579			−1.24509
$965$	3.86541	−	37.3094i	0.124432	−	1.20103i
$966$	0.271695			0.00874163
$967$		−	14.1757i		−	0.455860i	−0.973678	−	0.227930i	$-0.926804\pi$
$967$		−	14.1757i		−	0.455860i	0.973678	−	0.227930i	$-0.0731957\pi$
$968$		−	0.524103i		−	0.0168453i
$969$	10.0184			0.321839
$970$	−2.78211	−	0.288239i	−0.0893283	−	0.00925480i
$971$	30.6648			0.984079			0.492040	−	0.870573i	$-0.336252\pi$
$971$	30.6648			0.984079			0.492040	+	0.870573i	$0.336252\pi$
$972$			18.2965i			0.586860i
$973$		−	6.74085i		−	0.216102i
$974$	3.16260			0.101336
$975$	36.9735	+	7.74435i	1.18410	+	0.248018i
$976$	12.5288			0.401039
$977$		−	36.7937i		−	1.17713i	−0.808448	−	0.588567i	$-0.799692\pi$
$977$		−	36.7937i		−	1.17713i	0.808448	−	0.588567i	$-0.200308\pi$
$978$			0.121433i			0.00388300i
$979$	5.97606			0.190996
$980$	−29.9482	−	3.10276i	−0.956660	−	0.0991140i
$981$	7.63761			0.243850
$982$		−	1.61130i		−	0.0514187i
$983$		−	41.0129i		−	1.30811i	−0.756448	−	0.654054i	$-0.773067\pi$
$983$		−	41.0129i		−	1.30811i	0.756448	−	0.654054i	$-0.226933\pi$
$984$	−2.49728			−0.0796105
$985$	4.48012	−	43.2426i	0.142748	−	1.37782i
$986$	−3.98402			−0.126877
$987$			6.83391i			0.217526i
$988$		−	10.3992i		−	0.330842i
$989$	−2.73055			−0.0868264
$990$	−0.0280528	+	0.270768i	−0.000891575	+	0.00860558i
$991$	−36.2674			−1.15207			−0.576035	−	0.817425i	$-0.695401\pi$
$991$	−36.2674			−1.15207			−0.576035	+	0.817425i	$0.695401\pi$
$992$		−	4.04815i		−	0.128529i
$993$		−	20.5809i		−	0.653116i
$994$	−0.486290			−0.0154242
$995$	−36.7661	−	3.80912i	−1.16556	−	0.120757i
$996$	−13.8424			−0.438613
$997$		−	7.41034i		−	0.234688i	−0.993091	−	0.117344i	$-0.962562\pi$
$997$		−	7.41034i		−	0.234688i	0.993091	−	0.117344i	$-0.0374380\pi$
$998$			2.09705i			0.0663809i
$999$	5.21769			0.165081

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.b.c.419.10	✓	20
5.2	odd	4		5225.2.a.ba.1.11		20
5.3	odd	4		5225.2.a.ba.1.10		20
5.4	even	2	inner	1045.2.b.c.419.11	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.b.c.419.10	✓	20	1.1	even	1	trivial
1045.2.b.c.419.11	yes	20	5.4	even	2	inner
5225.2.a.ba.1.10		20	5.3	odd	4
5225.2.a.ba.1.11		20	5.2	odd	4

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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.131596i q^{2} +1.44045i q^{3} +1.98268 q^{4} +(-2.22416 - 0.230433i) q^{5} +0.189557 q^{6} -0.456875i q^{7} -0.524103i q^{8} +0.925103 q^{9} +O(q^{10})\)	\(q-0.131596i q^{2} +1.44045i q^{3} +1.98268 q^{4} +(-2.22416 - 0.230433i) q^{5} +0.189557 q^{6} -0.456875i q^{7} -0.524103i q^{8} +0.925103 q^{9} +(-0.0303239 + 0.292690i) q^{10} +1.00000 q^{11} +2.85596i q^{12} -5.24500i q^{13} -0.0601227 q^{14} +(0.331927 - 3.20380i) q^{15} +3.89640 q^{16} -6.95508i q^{17} -0.121739i q^{18} +1.00000 q^{19} +(-4.40981 - 0.456875i) q^{20} +0.658106 q^{21} -0.131596i q^{22} +3.13721i q^{23} +0.754945 q^{24} +(4.89380 + 1.02504i) q^{25} -0.690219 q^{26} +5.65392i q^{27} -0.905838i q^{28} +4.35289 q^{29} +(-0.421605 - 0.0436801i) q^{30} +2.59338 q^{31} -1.56096i q^{32} +1.44045i q^{33} -0.915258 q^{34} +(-0.105279 + 1.01616i) q^{35} +1.83419 q^{36} -0.922846i q^{37} -0.131596i q^{38} +7.55516 q^{39} +(-0.120771 + 1.16569i) q^{40} -3.30790 q^{41} -0.0866038i q^{42} +0.870374i q^{43} +1.98268 q^{44} +(-2.05758 - 0.213174i) q^{45} +0.412843 q^{46} +10.3842i q^{47} +5.61256i q^{48} +6.79127 q^{49} +(0.134891 - 0.644003i) q^{50} +10.0184 q^{51} -10.3992i q^{52} -8.75191i q^{53} +0.744030 q^{54} +(-2.22416 - 0.230433i) q^{55} -0.239450 q^{56} +1.44045i q^{57} -0.572821i q^{58} -13.2528 q^{59} +(0.658106 - 6.35211i) q^{60} +3.21550 q^{61} -0.341277i q^{62} -0.422657i q^{63} +7.58738 q^{64} +(-1.20862 + 11.6657i) q^{65} +0.189557 q^{66} +1.23632i q^{67} -13.7897i q^{68} -4.51900 q^{69} +(0.133723 + 0.0138543i) q^{70} +8.08829 q^{71} -0.484850i q^{72} -2.75185i q^{73} -0.121442 q^{74} +(-1.47652 + 7.04928i) q^{75} +1.98268 q^{76} -0.456875i q^{77} -0.994226i q^{78} -3.24490 q^{79} +(-8.66622 - 0.897857i) q^{80} -5.36888 q^{81} +0.435305i q^{82} +4.84685i q^{83} +1.30482 q^{84} +(-1.60268 + 15.4692i) q^{85} +0.114537 q^{86} +6.27012i q^{87} -0.524103i q^{88} +5.97606 q^{89} +(-0.0280528 + 0.270768i) q^{90} -2.39631 q^{91} +6.22010i q^{92} +3.73564i q^{93} +1.36652 q^{94} +(-2.22416 - 0.230433i) q^{95} +2.24848 q^{96} +9.50533i q^{97} -0.893700i q^{98} +0.925103 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 12 q^{4} - 8 q^{6} - 10 q^{9}+O(q^{10}) \) 20 * q - 12 * q^4 - 8 * q^6 - 10 * q^9	\( 20 q - 12 q^{4} - 8 q^{6} - 10 q^{9} - 6 q^{10} + 20 q^{11} + 24 q^{14} - 6 q^{15} - 4 q^{16} + 20 q^{19} - 6 q^{20} - 30 q^{21} + 38 q^{24} + 2 q^{25} + 8 q^{26} + 50 q^{29} - 20 q^{30} - 50 q^{31} + 28 q^{34} + 6 q^{35} - 12 q^{36} + 48 q^{39} + 12 q^{40} - 34 q^{41} - 12 q^{44} - 18 q^{45} - 36 q^{46} - 6 q^{49} + 26 q^{50} - 40 q^{51} - 6 q^{54} - 40 q^{56} + 30 q^{59} - 30 q^{60} - 14 q^{61} + 36 q^{64} + 30 q^{65} - 8 q^{66} - 12 q^{69} - 54 q^{70} - 40 q^{71} + 50 q^{74} - 8 q^{75} - 12 q^{76} + 106 q^{79} + 8 q^{80} - 30 q^{84} - 22 q^{85} + 56 q^{86} + 36 q^{89} - 64 q^{90} - 56 q^{91} + 28 q^{94} + 66 q^{96} - 10 q^{99}+O(q^{100}) \) 20 * q - 12 * q^4 - 8 * q^6 - 10 * q^9 - 6 * q^10 + 20 * q^11 + 24 * q^14 - 6 * q^15 - 4 * q^16 + 20 * q^19 - 6 * q^20 - 30 * q^21 + 38 * q^24 + 2 * q^25 + 8 * q^26 + 50 * q^29 - 20 * q^30 - 50 * q^31 + 28 * q^34 + 6 * q^35 - 12 * q^36 + 48 * q^39 + 12 * q^40 - 34 * q^41 - 12 * q^44 - 18 * q^45 - 36 * q^46 - 6 * q^49 + 26 * q^50 - 40 * q^51 - 6 * q^54 - 40 * q^56 + 30 * q^59 - 30 * q^60 - 14 * q^61 + 36 * q^64 + 30 * q^65 - 8 * q^66 - 12 * q^69 - 54 * q^70 - 40 * q^71 + 50 * q^74 - 8 * q^75 - 12 * q^76 + 106 * q^79 + 8 * q^80 - 30 * q^84 - 22 * q^85 + 56 * q^86 + 36 * q^89 - 64 * q^90 - 56 * q^91 + 28 * q^94 + 66 * q^96 - 10 * q^99

Introduction

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Modular forms

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Database

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