LMFDB - Embedded newform 220.2.r.a.171.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(51,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 7]))

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

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

chi := DirichletCharacter("220.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.r (of order $10$, degree $4$, 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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			171.2
Root			$-0.104528 - 0.994522i$ of defining polynomial
Character	$\chi$	$=$	220.171
Dual form			220.2.r.a.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.16913 - 0.795697i) q^{2} +(0.722562 - 0.994522i) q^{3} +(0.733733 - 1.86055i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.0534318 - 1.73767i) q^{6} +(0.948903 - 0.689419i) q^{7} +(-0.622602 - 2.75905i) q^{8} +(0.460074 + 1.41596i) q^{9} +(0.395472 + 1.35779i) q^{10} +(-3.11426 + 1.14079i) q^{11} +(-1.32019 - 2.07407i) q^{12} +(1.03536 - 0.336408i) q^{13} +(0.560824 - 1.56106i) q^{14} +(0.722562 + 0.994522i) q^{15} +(-2.92327 - 2.73029i) q^{16} +(-4.70810 - 1.52976i) q^{17} +(1.66456 + 1.28936i) q^{18} +(4.36984 + 3.17488i) q^{19} +(1.54275 + 1.27276i) q^{20} -1.44185i q^{21} +(-2.73324 + 3.81174i) q^{22} +3.28095i q^{23} +(-3.19381 - 1.37440i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(0.942790 - 1.21714i) q^{26} +(5.24803 + 1.70519i) q^{27} +(-0.586455 - 2.27133i) q^{28} +(0.622602 + 0.856939i) q^{29} +(1.63611 + 0.587785i) q^{30} +(-6.07715 + 1.97459i) q^{31} +(-5.59017 - 0.866025i) q^{32} +(-1.11570 + 3.92149i) q^{33} +(-6.72161 + 1.95774i) q^{34} +(0.362449 + 1.11550i) q^{35} +(2.97203 + 0.182948i) q^{36} +(1.19710 - 0.869742i) q^{37} +(7.63515 + 0.234775i) q^{38} +(0.413545 - 1.27276i) q^{39} +(2.81641 + 0.260464i) q^{40} +(3.01196 - 4.14561i) q^{41} +(-1.14728 - 1.68571i) q^{42} +9.12165 q^{43} +(-0.162529 + 6.63126i) q^{44} -1.48883 q^{45} +(2.61064 + 3.83586i) q^{46} +(-0.973579 + 1.34002i) q^{47} +(-4.82758 + 0.934454i) q^{48} +(-1.73800 + 5.34901i) q^{49} +(-1.41355 - 0.0434654i) q^{50} +(-4.92327 + 3.57697i) q^{51} +(0.133773 - 2.17317i) q^{52} +(-1.39344 - 4.28856i) q^{53} +(7.49244 - 2.18225i) q^{54} +(-0.122602 - 3.31436i) q^{55} +(-2.49293 - 2.18884i) q^{56} +(6.31497 - 2.05186i) q^{57} +(1.40977 + 0.506470i) q^{58} +(2.36799 + 3.25926i) q^{59} +(2.38052 - 0.614648i) q^{60} +(-13.2591 - 4.30815i) q^{61} +(-5.53381 + 7.14412i) q^{62} +(1.41276 + 1.02643i) q^{63} +(-7.22473 + 3.43558i) q^{64} +1.08864i q^{65} +(1.81592 + 5.47249i) q^{66} -10.3928i q^{67} +(-6.30067 + 7.63721i) q^{68} +(3.26298 + 2.37069i) q^{69} +(1.31135 + 1.01577i) q^{70} +(-14.9187 - 4.84738i) q^{71} +(3.62027 - 2.15095i) q^{72} +(8.53598 + 11.7488i) q^{73} +(0.707512 - 1.96937i) q^{74} +(-1.16913 + 0.379874i) q^{75} +(9.11330 - 5.80079i) q^{76} +(-2.16864 + 3.22953i) q^{77} +(-0.529244 - 1.81708i) q^{78} +(-2.99070 - 9.20442i) q^{79} +(3.50000 - 1.93649i) q^{80} +(1.87441 - 1.36184i) q^{81} +(0.222728 - 7.24336i) q^{82} +(0.989908 - 3.04662i) q^{83} +(-2.68264 - 1.05793i) q^{84} +(2.90977 - 4.00495i) q^{85} +(10.6644 - 7.25807i) q^{86} +1.30211 q^{87} +(5.08645 + 7.88213i) q^{88} -0.254342 q^{89} +(-1.74064 + 1.18466i) q^{90} +(0.750529 - 1.03301i) q^{91} +(6.10436 + 2.40734i) q^{92} +(-2.42735 + 7.47062i) q^{93} +(-0.0719940 + 2.34133i) q^{94} +(-4.36984 + 3.17488i) q^{95} +(-4.90053 + 4.93379i) q^{96} +(-0.00979012 - 0.0301309i) q^{97} +(2.22424 + 7.63661i) q^{98} +(-3.04811 - 3.88482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} - 5 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} + 3 q^{7} + 5 q^{8} + 3 q^{9} + 5 q^{10} + q^{11} - 10 q^{12} + 10 q^{13} - 15 q^{14} - 5 q^{15} + 7 q^{16} - 5 q^{17} + 10 q^{18} + 11 q^{19} + q^{20}+ \cdots + 6 q^{99}+O(q^{100}) $ 8 * q + 5 * q^2 - 5 * q^3 - q^4 + 2 * q^5 - 6 * q^6 + 3 * q^7 + 5 * q^8 + 3 * q^9 + 5 * q^10 + q^11 - 10 * q^12 + 10 * q^13 - 15 * q^14 - 5 * q^15 + 7 * q^16 - 5 * q^17 + 10 * q^18 + 11 * q^19 + q^20 - 16 * q^22 - 18 * q^24 - 2 * q^25 - 3 * q^26 + 10 * q^27 - 11 * q^28 - 5 * q^29 - 4 * q^30 - 10 * q^31 - 11 * q^33 - 14 * q^34 - 8 * q^35 + 9 * q^36 + 20 * q^37 + 15 * q^38 - 3 * q^39 + 5 * q^40 + 10 * q^41 + 4 * q^42 + 34 * q^43 + 8 * q^44 - 8 * q^45 + 25 * q^46 - 25 * q^48 - 23 * q^49 - 5 * q^50 - 9 * q^51 - 5 * q^52 - 7 * q^53 + 26 * q^54 + 9 * q^55 + 15 * q^56 + 5 * q^57 - 12 * q^58 + 5 * q^59 - 10 * q^61 - 39 * q^62 + 23 * q^63 + 11 * q^64 - 2 * q^66 - 30 * q^68 + 15 * q^69 - 5 * q^70 - 90 * q^71 + 30 * q^72 + 5 * q^73 - 5 * q^74 - 5 * q^75 + 18 * q^76 - 14 * q^77 + 21 * q^79 + 28 * q^80 - 10 * q^81 + 38 * q^82 - 19 * q^83 - 10 * q^84 + 35 * q^86 + 18 * q^87 + 47 * q^88 + 20 * q^89 + 5 * q^90 + 10 * q^91 + 11 * q^93 + 15 * q^94 - 11 * q^95 - 39 * q^96 - 44 * q^97 - 50 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$1$

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 $

$2$	1.16913	−	0.795697i	0.826700	−	0.562643i
$2$	1.16913	−	0.795697i	0.826700	−	0.562643i
$3$	0.722562	−	0.994522i	0.417172	−	0.574187i	−0.547778	−	0.836624i	$-0.684526\pi$
$3$	0.722562	−	0.994522i	0.417172	−	0.574187i	0.964949	+	0.262436i	$0.0845260\pi$
$4$	0.733733	−	1.86055i	0.366866	−	0.930274i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$	0.0534318	−	1.73767i	0.0218135	−	0.709399i
$7$	0.948903	−	0.689419i	0.358652	−	0.260576i	−0.393838	−	0.919180i	$-0.628853\pi$
$7$	0.948903	−	0.689419i	0.358652	−	0.260576i	0.752490	+	0.658604i	$0.228853\pi$
$8$	−0.622602	−	2.75905i	−0.220123	−	0.975472i
$9$	0.460074	+	1.41596i	0.153358	+	0.471987i
$10$	0.395472	+	1.35779i	0.125059	+	0.429372i
$11$	−3.11426	+	1.14079i	−0.938983	+	0.343963i
$11$	−3.11426	+	1.14079i	−0.938983	+	0.343963i
$12$	−1.32019	−	2.07407i	−0.381105	−	0.598734i
$13$	1.03536	−	0.336408i	0.287157	−	0.0933028i	−0.161897	−	0.986808i	$-0.551761\pi$
$13$	1.03536	−	0.336408i	0.287157	−	0.0933028i	0.449054	+	0.893505i	$0.351761\pi$
$14$	0.560824	−	1.56106i	0.149886	−	0.417211i
$15$	0.722562	+	0.994522i	0.186565	+	0.256784i
$16$	−2.92327	−	2.73029i	−0.730818	−	0.682572i
$17$	−4.70810	−	1.52976i	−1.14188	−	0.371020i	−0.323803	−	0.946125i	$-0.604961\pi$
$17$	−4.70810	−	1.52976i	−1.14188	−	0.371020i	−0.818080	+	0.575105i	$0.804961\pi$
$18$	1.66456	+	1.28936i	0.392341	+	0.303906i
$19$	4.36984	+	3.17488i	1.00251	+	0.728366i	0.962625	−	0.270838i	$-0.0873008\pi$
$19$	4.36984	+	3.17488i	1.00251	+	0.728366i	0.0398853	+	0.999204i	$0.487301\pi$
$20$	1.54275	+	1.27276i	0.344969	+	0.284598i
$21$		−	1.44185i		−	0.314638i
$22$	−2.73324	+	3.81174i	−0.582730	+	0.812666i
$23$			3.28095i			0.684125i	0.939677	+	0.342063i	$0.111126\pi$
$23$			3.28095i			0.684125i	−0.939677	+	0.342063i	$0.888874\pi$
$24$	−3.19381	−	1.37440i	−0.651933	−	0.280547i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	0.942790	−	1.21714i	0.184896	−	0.238700i
$27$	5.24803	+	1.70519i	1.00998	+	0.328164i
$28$	−0.586455	−	2.27133i	−0.110829	−	0.429241i
$29$	0.622602	+	0.856939i	0.115614	+	0.159130i	0.862902	−	0.505371i	$-0.168644\pi$
$29$	0.622602	+	0.856939i	0.115614	+	0.159130i	−0.747288	+	0.664501i	$0.768644\pi$
$30$	1.63611	+	0.587785i	0.298711	+	0.107314i
$31$	−6.07715	+	1.97459i	−1.09149	+	0.354646i	−0.798822	−	0.601568i	$-0.794543\pi$
$31$	−6.07715	+	1.97459i	−1.09149	+	0.354646i	−0.292667	+	0.956214i	$0.594543\pi$
$32$	−5.59017	−	0.866025i	−0.988212	−	0.153093i
$33$	−1.11570	+	3.92149i	−0.194218	+	0.682644i
$34$	−6.72161	+	1.95774i	−1.15275	+	0.335749i
$35$	0.362449	+	1.11550i	0.0612650	+	0.188554i
$36$	2.97203	+	0.182948i	0.495339	+	0.0304914i
$37$	1.19710	−	0.869742i	0.196801	−	0.142985i	−0.485021	−	0.874503i	$-0.661188\pi$
$37$	1.19710	−	0.869742i	0.196801	−	0.142985i	0.681822	+	0.731518i	$0.261188\pi$
$38$	7.63515	+	0.234775i	1.23859	+	0.0380855i
$39$	0.413545	−	1.27276i	0.0662203	−	0.203805i
$40$	2.81641	+	0.260464i	0.445313	+	0.0411829i
$41$	3.01196	−	4.14561i	0.470389	−	0.647435i	−0.506233	−	0.862397i	$-0.668963\pi$
$41$	3.01196	−	4.14561i	0.470389	−	0.647435i	0.976623	+	0.214961i	$0.0689626\pi$
$42$	−1.14728	−	1.68571i	−0.177029	−	0.260111i
$43$	9.12165			1.39104			0.695519	−	0.718508i	$-0.255174\pi$
$43$	9.12165			1.39104			0.695519	+	0.718508i	$0.255174\pi$
$44$	−0.162529	+	6.63126i	−0.0245021	+	0.999700i
$45$	−1.48883			−0.221942
$46$	2.61064	+	3.83586i	0.384918	+	0.565567i
$47$	−0.973579	+	1.34002i	−0.142011	+	0.195462i	−0.874098	−	0.485750i	$-0.838547\pi$
$47$	−0.973579	+	1.34002i	−0.142011	+	0.195462i	0.732087	+	0.681211i	$0.238547\pi$
$48$	−4.82758	+	0.934454i	−0.696801	+	0.134877i
$49$	−1.73800	+	5.34901i	−0.248286	+	0.764145i
$50$	−1.41355	−	0.0434654i	−0.199906	−	0.00614693i
$51$	−4.92327	+	3.57697i	−0.689396	+	0.500876i
$52$	0.133773	−	2.17317i	0.0185509	−	0.301364i
$53$	−1.39344	−	4.28856i	−0.191403	−	0.589079i	−1.00000		0.000715358i	$-0.999772\pi$
$53$	−1.39344	−	4.28856i	−0.191403	−	0.589079i	0.808596	−	0.588364i	$-0.200228\pi$
$54$	7.49244	−	2.18225i	1.01959	−	0.296967i
$55$	−0.122602	−	3.31436i	−0.0165317	−	0.446908i
$56$	−2.49293	−	2.18884i	−0.333132	−	0.292496i
$57$	6.31497	−	2.05186i	0.836438	−	0.271775i
$58$	1.40977	+	0.506470i	0.185111	+	0.0665028i
$59$	2.36799	+	3.25926i	0.308287	+	0.424320i	0.934846	−	0.355054i	$-0.115537\pi$
$59$	2.36799	+	3.25926i	0.308287	+	0.424320i	−0.626559	+	0.779374i	$0.715537\pi$
$60$	2.38052	−	0.614648i	0.307324	−	0.0793508i
$61$	−13.2591	−	4.30815i	−1.69766	−	0.551603i	−0.709455	−	0.704751i	$-0.751059\pi$
$61$	−13.2591	−	4.30815i	−1.69766	−	0.551603i	−0.988203	+	0.153148i	$0.951059\pi$
$62$	−5.53381	+	7.14412i	−0.702795	+	0.907304i
$63$	1.41276	+	1.02643i	0.177990	+	0.129318i
$64$	−7.22473	+	3.43558i	−0.903092	+	0.429448i
$65$			1.08864i			0.135029i
$66$	1.81592	+	5.47249i	0.223524	+	0.673617i
$67$		−	10.3928i		−	1.26968i	−0.772643	−	0.634841i	$-0.781066\pi$
$67$		−	10.3928i		−	1.26968i	0.772643	−	0.634841i	$-0.218934\pi$
$68$	−6.30067	+	7.63721i	−0.764068	+	0.926148i
$69$	3.26298	+	2.37069i	0.392816	+	0.285398i
$70$	1.31135	+	1.01577i	0.156737	+	0.121408i
$71$	−14.9187	−	4.84738i	−1.77052	−	0.575278i	−0.772323	−	0.635230i	$-0.780905\pi$
$71$	−14.9187	−	4.84738i	−1.77052	−	0.575278i	−0.998201	+	0.0599516i	$0.980905\pi$
$72$	3.62027	−	2.15095i	0.426653	−	0.253492i
$73$	8.53598	+	11.7488i	0.999061	+	1.37509i	0.925900	+	0.377770i	$0.123309\pi$
$73$	8.53598	+	11.7488i	0.999061	+	1.37509i	0.0731616	+	0.997320i	$0.476691\pi$
$74$	0.707512	−	1.96937i	0.0822466	−	0.228934i
$75$	−1.16913	+	0.379874i	−0.135000	+	0.0438640i
$76$	9.11330	−	5.80079i	1.04537	−	0.665396i
$77$	−2.16864	+	3.22953i	−0.247140	+	0.368039i
$78$	−0.529244	−	1.81708i	−0.0599251	−	0.205744i
$79$	−2.99070	−	9.20442i	−0.336480	−	1.03558i	−0.965989	−	0.258585i	$-0.916744\pi$
$79$	−2.99070	−	9.20442i	−0.336480	−	1.03558i	0.629509	−	0.776993i	$-0.283256\pi$
$80$	3.50000	−	1.93649i	0.391312	−	0.216506i
$81$	1.87441	−	1.36184i	0.208268	−	0.151315i
$82$	0.222728	−	7.24336i	0.0245961	−	0.799896i
$83$	0.989908	−	3.04662i	0.108657	−	0.334410i	−0.881915	−	0.471409i	$-0.843746\pi$
$83$	0.989908	−	3.04662i	0.108657	−	0.334410i	0.990571	+	0.136999i	$0.0437456\pi$
$84$	−2.68264	−	1.05793i	−0.292700	−	0.115430i
$85$	2.90977	−	4.00495i	0.315609	−	0.434398i
$86$	10.6644	−	7.25807i	1.14997	−	0.782657i
$87$	1.30211			0.139601
$88$	5.08645	+	7.88213i	0.542218	+	0.840238i
$89$	−0.254342			−0.0269602			−0.0134801	−	0.999909i	$-0.504291\pi$
$89$	−0.254342			−0.0269602			−0.0134801	+	0.999909i	$0.504291\pi$
$90$	−1.74064	+	1.18466i	−0.183479	+	0.124874i
$91$	0.750529	−	1.03301i	0.0786768	−	0.108289i
$92$	6.10436	+	2.40734i	0.636424	+	0.250983i
$93$	−2.42735	+	7.47062i	−0.251705	+	0.774668i
$94$	−0.0719940	+	2.34133i	−0.00742561	+	0.241490i
$95$	−4.36984	+	3.17488i	−0.448336	+	0.325735i
$96$	−4.90053	+	4.93379i	−0.500158	+	0.503553i
$97$	−0.00979012	−	0.0301309i	−0.000994036	−	0.00305933i	0.950558	−	0.310546i	$-0.100512\pi$
$97$	−0.00979012	−	0.0301309i	−0.000994036	−	0.00305933i	−0.951552	+	0.307487i	$0.900512\pi$
$98$	2.22424	+	7.63661i	0.224683	+	0.771415i
$99$	−3.04811	−	3.88482i	−0.306346	−	0.390439i
$100$	−1.68720	+	1.07394i	−0.168720	+	0.107394i
$101$	4.37365	−	1.42109i	0.435195	−	0.141403i	−0.0832228	−	0.996531i	$-0.526521\pi$
$101$	4.37365	−	1.42109i	0.435195	−	0.141403i	0.518418	+	0.855128i	$0.326521\pi$
$102$	−2.90977	+	8.09937i	−0.288110	+	0.801958i
$103$	−2.37868	−	3.27397i	−0.234378	−	0.322593i	0.675586	−	0.737281i	$-0.263891\pi$
$103$	−2.37868	−	3.27397i	−0.234378	−	0.322593i	−0.909964	+	0.414688i	$0.863891\pi$
$104$	−1.57278	−	2.64716i	−0.154224	−	0.259575i
$105$	1.37128	+	0.445557i	0.133824	+	0.0434819i
$106$	−5.04151	−	3.90513i	−0.489674	−	0.379300i
$107$	4.44417	+	3.22888i	0.429634	+	0.312147i	0.781503	−	0.623902i	$-0.214454\pi$
$107$	4.44417	+	3.22888i	0.429634	+	0.312147i	−0.351868	+	0.936049i	$0.614454\pi$
$108$	7.02323	−	8.51305i	0.675811	−	0.819169i
$109$		−	15.2250i		−	1.45829i	−0.684359	−	0.729145i	$-0.739918\pi$
$109$		−	15.2250i		−	1.45829i	0.684359	−	0.729145i	$-0.260082\pi$
$110$	−2.78056	−	3.77736i	−0.265116	−	0.360157i
$111$		−	1.81898i		−	0.172650i
$112$	−4.65622	−	0.575422i	−0.439971	−	0.0543723i
$113$	−11.2728	−	8.19017i	−1.06046	−	0.770467i	−0.0862836	−	0.996271i	$-0.527499\pi$
$113$	−11.2728	−	8.19017i	−1.06046	−	0.770467i	−0.974173	+	0.225804i	$0.927499\pi$
$114$	5.75036	−	7.42369i	0.538571	−	0.695292i
$115$	−3.12037	−	1.01387i	−0.290976	−	0.0945438i
$116$	2.05120	−	0.529617i	0.190449	−	0.0491737i
$117$	0.952682	+	1.31125i	0.0880755	+	0.121225i
$118$	5.36188	+	1.92630i	0.493601	+	0.177330i
$119$	−5.52218	+	1.79426i	−0.506217	+	0.164480i
$120$	2.29407	−	2.61278i	0.209419	−	0.238513i
$121$	8.39717	−	7.10545i	0.763380	−	0.645950i
$122$	−18.9296	+	5.51346i	−1.71381	+	0.499165i
$123$	−1.94657	−	5.99092i	−0.175516	−	0.540183i
$124$	−0.785194	+	12.7556i	−0.0705125	+	1.14549i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	2.46842	+	0.0759019i	0.219904	+	0.00676188i
$127$	5.16913	−	15.9089i	0.458686	−	1.41169i	−0.408066	−	0.912952i	$-0.633797\pi$
$127$	5.16913	−	15.9089i	0.458686	−	1.41169i	0.866752	−	0.498739i	$-0.166203\pi$
$128$	−5.71297	+	9.76534i	−0.504960	+	0.863143i
$129$	6.59096	−	9.07168i	0.580302	−	0.798717i
$130$	0.866227	+	1.27276i	0.0759732	+	0.111629i
$131$	−5.02294			−0.438857			−0.219428	−	0.975629i	$-0.570419\pi$
$131$	−5.02294			−0.438857			−0.219428	+	0.975629i	$0.570419\pi$
$132$	6.47749	+	4.95314i	0.563794	+	0.431115i
$133$	6.33537			0.549347
$134$	−8.26952	−	12.1505i	−0.714377	−	1.04965i
$135$	−3.24346	+	4.46424i	−0.279153	+	0.384221i
$136$	−1.28940	+	13.9423i	−0.110565	+	1.19554i
$137$	−4.37723	+	13.4717i	−0.373972	+	1.15097i	0.570197	+	0.821508i	$0.306867\pi$
$137$	−4.37723	+	13.4717i	−0.373972	+	1.15097i	−0.944169	+	0.329460i	$0.893133\pi$
$138$	5.70120	+	0.175307i	0.485318	+	0.0149231i
$139$	13.5531	−	9.84690i	1.14956	−	0.835204i	0.161137	−	0.986932i	$-0.448484\pi$
$139$	13.5531	−	9.84690i	1.14956	−	0.835204i	0.988422	+	0.151729i	$0.0484839\pi$
$140$	2.34139	+	0.144128i	0.197883	+	0.0121810i
$141$	0.629204	+	1.93649i	0.0529886	+	0.163082i
$142$	−21.2990	+	6.20355i	−1.78737	+	0.520590i
$143$	−2.84060	+	2.22879i	−0.237543	+	0.186381i
$144$	2.52106	−	5.39537i	0.210089	−	0.449615i
$145$	−1.00739	+	0.327321i	−0.0836593	+	0.0271826i
$146$	19.3281	+	6.94379i	1.59961	+	0.574672i
$147$	4.06390	+	5.59347i	0.335185	+	0.461342i
$148$	−0.739846	−	2.86541i	−0.0608150	−	0.235535i
$149$	−2.09086	−	0.679361i	−0.171290	−	0.0556554i	0.222117	−	0.975020i	$-0.428703\pi$
$149$	−2.09086	−	0.679361i	−0.171290	−	0.0556554i	−0.393406	+	0.919365i	$0.628703\pi$
$150$	−1.06460	+	1.37440i	−0.0869244	+	0.112219i
$151$	−2.43950	−	1.77240i	−0.198524	−	0.144236i	0.484082	−	0.875022i	$-0.339153\pi$
$151$	−2.43950	−	1.77240i	−0.198524	−	0.144236i	−0.682606	+	0.730787i	$0.739153\pi$
$152$	6.03897	−	14.0333i	0.489825	−	1.13825i
$153$		−	7.37029i		−	0.595853i
$154$	0.0343008	+	5.50132i	0.00276404	+	0.443309i
$155$		−	6.38990i		−	0.513249i
$156$	−2.06460	−	1.70329i	−0.165300	−	0.136372i
$157$	12.6955	+	9.22381i	1.01321	+	0.736140i	0.964880	−	0.262691i	$-0.0846100\pi$
$157$	12.6955	+	9.22381i	1.01321	+	0.736140i	0.0483303	+	0.998831i	$0.484610\pi$
$158$	−10.8204	−	8.38148i	−0.860829	−	0.666795i
$159$	−5.27191	−	1.71295i	−0.418090	−	0.135846i
$160$	2.55110	−	5.04895i	0.201682	−	0.399155i
$161$	2.26195	+	3.11330i	0.178267	+	0.245363i
$162$	1.10782	−	3.08363i	0.0870385	−	0.242273i
$163$	15.1523	−	4.92328i	1.18682	−	0.385621i	0.351924	−	0.936029i	$-0.385528\pi$
$163$	15.1523	−	4.92328i	1.18682	−	0.385621i	0.834896	+	0.550407i	$0.185528\pi$
$164$	−5.50313	−	8.64566i	−0.429722	−	0.675113i
$165$	−3.38479	−	2.27290i	−0.263506	−	0.176945i
$166$	−1.26686	−	4.34957i	−0.0983272	−	0.337592i
$167$	4.60542	+	14.1740i	0.356378	+	1.09682i	0.955206	+	0.295941i	$0.0956333\pi$
$167$	4.60542	+	14.1740i	0.356378	+	1.09682i	−0.598828	+	0.800878i	$0.704367\pi$
$168$	−3.97815	+	0.897701i	−0.306921	+	0.0692592i
$169$	−9.55843	+	6.94460i	−0.735263	+	0.534200i
$170$	0.215171	−	6.99760i	0.0165028	−	0.536692i
$171$	−2.48505	+	7.64820i	−0.190037	+	0.584873i
$172$	6.69285	−	16.9713i	0.510325	−	1.29405i
$173$	7.07542	−	9.73848i	0.537934	−	0.740403i	−0.450379	−	0.892837i	$-0.648711\pi$
$173$	7.07542	−	9.73848i	0.537934	−	0.740403i	0.988314	+	0.152434i	$0.0487112\pi$
$174$	1.52234	−	1.03609i	0.115408	−	0.0785456i
$175$	−1.17291			−0.0886636
$176$	12.2185	+	5.16796i	0.921005	+	0.389550i
$177$	4.95243			0.372248
$178$	−0.297359	+	0.202379i	−0.0222880	+	0.0151689i
$179$	−4.24947	+	5.84890i	−0.317620	+	0.437167i	−0.937739	−	0.347341i	$-0.887085\pi$
$179$	−4.24947	+	5.84890i	−0.317620	+	0.437167i	0.620118	+	0.784508i	$0.287085\pi$
$180$	−1.09240	+	2.77004i	−0.0814229	+	0.206466i
$181$	−7.81407	+	24.0492i	−0.580816	+	1.78757i	0.0346463	+	0.999400i	$0.488970\pi$
$181$	−7.81407	+	24.0492i	−0.580816	+	1.78757i	−0.615462	+	0.788167i	$0.711030\pi$
$182$	0.0554999	−	1.80492i	0.00411392	−	0.133790i
$183$	−13.8651	+	10.0736i	−1.02494	+	0.744661i
$184$	9.05231	−	2.04273i	0.667345	−	0.150592i
$185$	0.457250	+	1.40727i	0.0336177	+	0.103465i
$186$	3.10646	+	10.6656i	0.227777	+	0.782038i
$187$	16.4074	−	0.606930i	1.19983	−	0.0443831i
$188$	1.77882	+	2.79460i	0.129734	+	0.203817i
$189$	6.15546	−	2.00003i	0.447744	−	0.145481i
$190$	−2.58268	+	7.18891i	−0.187367	+	0.521539i
$191$	1.02514	+	1.41099i	0.0741767	+	0.102095i	0.844493	−	0.535566i	$-0.179902\pi$
$191$	1.02514	+	1.41099i	0.0741767	+	0.102095i	−0.770317	+	0.637662i	$0.779902\pi$
$192$	−1.80356	+	9.66758i	−0.130160	+	0.697697i
$193$	−10.9311	−	3.55173i	−0.786837	−	0.255659i	−0.112080	−	0.993699i	$-0.535751\pi$
$193$	−10.9311	−	3.55173i	−0.786837	−	0.255659i	−0.674757	+	0.738040i	$0.735751\pi$
$194$	−0.0354210	−	0.0274370i	−0.00254308	−	0.00196986i
$195$	1.08268	+	0.786610i	0.0775320	+	0.0563303i
$196$	8.67686	+	7.15838i	0.619776	+	0.511313i
$197$		−	11.4119i		−	0.813063i	−0.913637	−	0.406532i	$-0.866738\pi$
$197$		−	11.4119i		−	0.813063i	0.913637	−	0.406532i	$-0.133262\pi$
$198$	−6.65477	−	2.11649i	−0.472934	−	0.150412i
$199$			11.5940i			0.821875i	0.911664	+	0.410937i	$0.134799\pi$
$199$			11.5940i			0.821875i	−0.911664	+	0.410937i	$0.865201\pi$
$200$	−1.11803	+	2.59808i	−0.0790569	+	0.183712i
$201$	−10.3359	−	7.50944i	−0.729036	−	0.529675i
$202$	3.98262	−	5.14154i	0.280216	−	0.361757i
$203$	1.18158	+	0.383918i	0.0829306	+	0.0269458i
$204$	3.04275	+	11.7845i	0.213035	+	0.825081i
$205$	3.01196	+	4.14561i	0.210364	+	0.289542i
$206$	−5.38607	−	1.93499i	−0.375265	−	0.134817i
$207$	−4.64570	+	1.50948i	−0.322898	+	0.104916i
$208$	−3.94512	−	1.84341i	−0.273545	−	0.127818i
$209$	−17.2307	−	4.90228i	−1.19187	−	0.339098i
$210$	1.95774	−	0.570212i	0.135097	−	0.0393484i
$211$	7.35063	+	22.6229i	0.506038	+	1.55742i	0.799019	+	0.601306i	$0.205353\pi$
$211$	7.35063	+	22.6229i	0.506038	+	1.55742i	−0.292981	+	0.956118i	$0.594647\pi$
$212$	−9.00148	−	0.554100i	−0.618224	−	0.0380558i
$213$	−15.6005	+	11.3344i	−1.06893	+	0.776623i
$214$	7.76502	+	0.238768i	0.530806	+	0.0163219i
$215$	−2.81874	+	8.67520i	−0.192237	+	0.591644i
$216$	1.43727	−	15.5412i	0.0977936	−	1.05745i
$217$	−4.40531	+	6.06339i	−0.299052	+	0.411610i
$218$	−12.1145	−	17.8000i	−0.820496	−	1.20557i
$219$	17.8522			1.20634
$220$	−6.25648	−	2.20375i	−0.421812	−	0.148576i
$221$	−5.38919			−0.362516
$222$	−1.44736	−	2.12663i	−0.0971403	−	0.142730i
$223$	−3.65167	+	5.02609i	−0.244534	+	0.336572i	−0.913588	−	0.406642i	$-0.866700\pi$
$223$	−3.65167	+	5.02609i	−0.244534	+	0.336572i	0.669054	+	0.743214i	$0.266700\pi$
$224$	−5.90159	+	3.03219i	−0.394316	+	0.202597i
$225$	0.460074	−	1.41596i	0.0306716	−	0.0943974i
$226$	−19.6963	−	0.605645i	−1.31018	−	0.0402869i
$227$	−9.21277	+	6.69347i	−0.611473	+	0.444261i	−0.849933	−	0.526891i	$-0.823358\pi$
$227$	−9.21277	+	6.69347i	−0.611473	+	0.444261i	0.238460	+	0.971152i	$0.423358\pi$
$228$	0.815921	−	13.2548i	0.0540357	−	0.877821i
$229$	6.37812	+	19.6298i	0.421478	+	1.29718i	0.906326	+	0.422578i	$0.138875\pi$
$229$	6.37812	+	19.6298i	0.421478	+	1.29718i	−0.484848	+	0.874598i	$0.661125\pi$
$230$	−4.45485	+	1.29752i	−0.293744	+	0.0855561i
$231$	1.64486	+	4.49030i	0.108224	+	0.295440i
$232$	1.97670	−	2.25132i	0.129777	−	0.147807i
$233$	11.2344	−	3.65029i	0.735992	−	0.239138i	0.0830489	−	0.996545i	$-0.473534\pi$
$233$	11.2344	−	3.65029i	0.735992	−	0.239138i	0.652943	+	0.757407i	$0.273534\pi$
$234$	2.15717	+	0.774981i	0.141019	+	0.0506621i
$235$	−0.973579	−	1.34002i	−0.0635093	−	0.0874131i
$236$	7.80149	−	2.01434i	0.507834	−	0.131122i
$237$	−11.3150	−	3.67646i	−0.734986	−	0.238811i
$238$	−5.02845	+	6.49171i	−0.325946	+	0.420795i
$239$	17.0935	+	12.4192i	1.10569	+	0.803329i	0.981979	−	0.188990i	$-0.0605212\pi$
$239$	17.0935	+	12.4192i	1.10569	+	0.803329i	0.123709	+	0.992319i	$0.460521\pi$
$240$	0.603085	−	4.88006i	0.0389290	−	0.315007i
$241$			5.64518i			0.363638i	0.983332	+	0.181819i	$0.0581985\pi$
$241$			5.64518i			0.363638i	−0.983332	+	0.181819i	$0.941801\pi$
$242$	4.16361	−	14.9888i	0.267647	−	0.963517i
$243$			13.7062i			0.879250i
$244$	−17.7442	+	21.5082i	−1.13596	+	1.37692i
$245$	−4.55014	−	3.30587i	−0.290698	−	0.211204i
$246$	−7.04275	−	5.45529i	−0.449029	−	0.347817i
$247$	5.59240	+	1.81708i	0.355836	+	0.115618i
$248$	9.23164	+	15.5378i	0.586209	+	0.986651i
$249$	−2.31466	−	3.18586i	−0.146686	−	0.201896i
$250$	0.478148	−	1.33093i	0.0302407	−	0.0841754i
$251$	18.9217	−	6.14803i	1.19433	−	0.388060i	0.356656	−	0.934236i	$-0.383917\pi$
$251$	18.9217	−	6.14803i	1.19433	−	0.388060i	0.837671	+	0.546176i	$0.183917\pi$
$252$	2.94630	−	1.87538i	0.185600	−	0.118138i
$253$	−3.74289	−	10.2177i	−0.235314	−	0.642382i
$254$	−6.61531	−	22.7127i	−0.415082	−	1.42512i
$255$	−1.88052	−	5.78765i	−0.117763	−	0.362437i
$256$	1.09104	+	15.9628i	0.0681903	+	0.997672i
$257$	−2.53312	+	1.84042i	−0.158012	+	0.114802i	−0.663982	−	0.747749i	$-0.731135\pi$
$257$	−2.53312	+	1.84042i	−0.158012	+	0.114802i	0.505970	+	0.862551i	$0.331135\pi$
$258$	0.487386	−	15.8504i	0.0303434	−	0.986802i
$259$	0.536313	−	1.65060i	0.0333249	−	0.102563i
$260$	2.02547	+	0.798771i	0.125614	+	0.0495377i
$261$	−0.926949	+	1.27584i	−0.0573767	+	0.0789722i
$262$	−5.87248	+	3.99674i	−0.362803	+	0.246919i
$263$	−27.6248			−1.70342			−0.851709	−	0.524015i	$-0.824434\pi$
$263$	−27.6248			−1.70342			−0.851709	+	0.524015i	$0.824434\pi$
$264$	11.5142	+	0.636741i	0.708652	+	0.0391887i
$265$	4.50926			0.277002
$266$	7.40688	−	5.04104i	0.454145	−	0.309086i
$267$	−0.183778	+	0.252948i	−0.0112470	+	0.0154802i
$268$	−19.3363	−	7.62553i	−1.18115	−	0.465804i
$269$	−4.34312	+	13.3667i	−0.264805	+	0.814985i	0.726934	+	0.686708i	$0.240945\pi$
$269$	−4.34312	+	13.3667i	−0.264805	+	0.814985i	−0.991738	+	0.128277i	$0.959055\pi$
$270$	−0.239846	+	7.80009i	−0.0145966	+	0.474698i
$271$	16.7063	−	12.1379i	1.01484	−	0.737322i	0.0496190	−	0.998768i	$-0.484199\pi$
$271$	16.7063	−	12.1379i	1.01484	−	0.737322i	0.965218	+	0.261446i	$0.0841993\pi$
$272$	9.58639	+	17.3264i	0.581260	+	1.05057i
$273$	−0.485051	−	1.49283i	−0.0293566	−	0.0903504i
$274$	5.60186	+	19.2332i	0.338421	+	1.16192i
$275$	3.19003	+	0.907591i	0.192366	+	0.0547298i
$276$	6.80494	−	4.33147i	0.409609	−	0.260724i
$277$	22.3792	−	7.27144i	1.34464	−	0.436899i	0.453751	−	0.891128i	$-0.350085\pi$
$277$	22.3792	−	7.27144i	1.34464	−	0.436899i	0.890885	+	0.454230i	$0.150085\pi$
$278$	8.01019	−	22.2965i	0.480420	−	1.33725i
$279$	−5.59188	−	7.69656i	−0.334777	−	0.460781i
$280$	2.85207	−	1.69453i	0.170444	−	0.101268i
$281$	7.16953	+	2.32952i	0.427699	+	0.138968i	0.514953	−	0.857218i	$-0.327809\pi$
$281$	7.16953	+	2.32952i	0.427699	+	0.138968i	−0.0872545	+	0.996186i	$0.527809\pi$
$282$	2.27648	+	1.76336i	0.135563	+	0.105006i
$283$	−4.57587	−	3.32457i	−0.272008	−	0.197625i	0.443416	−	0.896316i	$-0.353766\pi$
$283$	−4.57587	−	3.32457i	−0.272008	−	0.197625i	−0.715424	+	0.698691i	$0.753766\pi$
$284$	−19.9651	+	24.2003i	−1.18471	+	1.43602i
$285$			6.63995i			0.393317i
$286$	−1.54759	+	4.86600i	−0.0915106	+	0.287733i
$287$		−	6.01028i		−	0.354776i
$288$	−1.34563	−	8.31390i	−0.0792921	−	0.489901i
$289$	6.07278	+	4.41214i	0.357223	+	0.259537i
$290$	−0.917324	+	1.18426i	−0.0538671	+	0.0695421i
$291$	−0.0370398	−	0.0120350i	−0.00217131	−	0.000705502i
$292$	28.1223	−	7.26114i	1.64573	−	0.424926i
$293$	7.13351	+	9.81843i	0.416744	+	0.573599i	0.964847	−	0.262812i	$-0.0846499\pi$
$293$	7.13351	+	9.81843i	0.416744	+	0.573599i	−0.548103	+	0.836411i	$0.684650\pi$
$294$	9.20194	+	3.30587i	0.536668	+	0.192802i
$295$	−3.83149	+	1.24493i	−0.223078	+	0.0724825i
$296$	−3.14498	−	2.76135i	−0.182798	−	0.160500i
$297$	−18.2890	+	0.676533i	−1.06123	+	0.0392564i
$298$	−2.98505	+	0.869428i	−0.172919	+	0.0503646i
$299$	1.10374	+	3.39696i	0.0638308	+	0.196451i
$300$	−0.151057	+	2.45395i	−0.00872126	+	0.141679i
$301$	8.65556	−	6.28863i	0.498898	−	0.362471i
$302$	−4.26239	−	0.131065i	−0.245273	−	0.00754194i
$303$	1.74694	−	5.37652i	0.100359	−	0.308873i
$304$	−4.10591	−	21.2120i	−0.235490	−	1.21659i
$305$	8.19460	−	11.2789i	0.469221	−	0.645828i
$306$	−5.86452	−	8.61683i	−0.335252	−	0.492591i
$307$	0.470760			0.0268677			0.0134339	−	0.999910i	$-0.495724\pi$
$307$	0.470760			0.0268677			0.0134339	+	0.999910i	$0.495724\pi$
$308$	4.41749	+	6.40447i	0.251710	+	0.364929i
$309$	−4.97477			−0.283005
$310$	−5.08442	−	7.47062i	−0.288776	−	0.424303i
$311$	8.08609	−	11.1295i	0.458520	−	0.631099i	−0.515681	−	0.856781i	$-0.672461\pi$
$311$	8.08609	−	11.1295i	0.458520	−	0.631099i	0.974201	+	0.225682i	$0.0724610\pi$
$312$	−3.76909	−	0.348569i	−0.213383	−	0.0197338i
$313$	8.37201	−	25.7664i	0.473214	−	1.45640i	−0.375137	−	0.926969i	$-0.622404\pi$
$313$	8.37201	−	25.7664i	0.473214	−	1.45640i	0.848351	−	0.529434i	$-0.177596\pi$
$314$	22.1820	+	0.682080i	1.25181	+	0.0384920i
$315$	−1.41276	+	1.02643i	−0.0795998	+	0.0578326i
$316$	−19.3196	−	1.18925i	−1.08681	−	0.0669006i
$317$	−1.53670	−	4.72947i	−0.0863096	−	0.265634i	0.898582	−	0.438806i	$-0.144598\pi$
$317$	−1.53670	−	4.72947i	−0.0863096	−	0.265634i	−0.984892	+	0.173172i	$0.944598\pi$
$318$	−7.52654	+	2.19219i	−0.422068	+	0.122932i
$319$	−2.91653	−	1.95846i	−0.163295	−	0.109653i
$320$	−1.03487	−	7.93278i	−0.0578510	−	0.443456i
$321$	6.42238	−	2.08676i	0.358462	−	0.116471i
$322$	5.12176	+	1.84003i	0.285425	+	0.102541i
$323$	−15.7169	−	21.6324i	−0.874510	−	1.20366i
$324$	−1.15845	−	4.48665i	−0.0643583	−	0.249258i
$325$	−1.03536	−	0.336408i	−0.0574313	−	0.0186606i
$326$	13.7976	−	17.8126i	0.764177	−	0.986549i
$327$	−15.1416	−	11.0010i	−0.837332	−	0.608357i
$328$	−13.3132	−	5.72909i	−0.735098	−	0.316336i
$329$			1.94275i			0.107107i
$330$	−5.76580	+	0.0359498i	−0.317397	+	0.00197897i
$331$		−	8.10096i		−	0.445269i	−0.974902	−	0.222634i	$-0.928534\pi$
$331$		−	8.10096i		−	0.445269i	0.974902	−	0.222634i	$-0.0714656\pi$
$332$	−4.94206	−	4.07718i	−0.271231	−	0.223764i
$333$	1.78227	+	1.29490i	0.0976680	+	0.0709599i
$334$	16.6626	+	12.9068i	0.911735	+	0.706227i
$335$	9.88414	+	3.21155i	0.540028	+	0.175466i
$336$	−3.93668	+	4.21493i	−0.214763	+	0.229943i
$337$	−7.07709	−	9.74078i	−0.385514	−	0.530614i	0.571521	−	0.820587i	$-0.306354\pi$
$337$	−7.07709	−	9.74078i	−0.385514	−	0.530614i	−0.957035	+	0.289973i	$0.906354\pi$
$338$	−5.64925	+	15.7248i	−0.307279	+	0.855314i
$339$	−16.2906	+	5.29314i	−0.884785	+	0.287484i
$340$	−5.31641	−	8.35232i	−0.288323	−	0.452968i
$341$	16.6732	−	13.0822i	0.902905	−	0.708438i
$342$	3.18030	+	10.9191i	0.171971	+	0.590437i
$343$	4.57566	+	14.0824i	0.247062	+	0.760379i
$344$	−5.67916	−	25.1671i	−0.306200	−	1.35692i
$345$	−3.26298	+	2.37069i	−0.175673	+	0.127634i
$346$	0.523211	−	17.0154i	0.0281280	−	0.914756i
$347$	−4.19742	+	12.9183i	−0.225329	+	0.693492i	0.772929	+	0.634493i	$0.218791\pi$
$347$	−4.19742	+	12.9183i	−0.225329	+	0.693492i	−0.998258	+	0.0589994i	$0.981209\pi$
$348$	0.955403	−	2.42264i	0.0512150	−	0.129867i
$349$	−2.59967	+	3.57814i	−0.139157	+	0.191533i	−0.872907	−	0.487886i	$-0.837768\pi$
$349$	−2.59967	+	3.57814i	−0.139157	+	0.191533i	0.733750	+	0.679419i	$0.237768\pi$
$350$	−1.37128	+	0.933280i	−0.0732982	+	0.0498859i
$351$	6.00723			0.320642
$352$	18.3972	−	3.68021i	0.980573	−	0.196156i
$353$	27.1653			1.44586			0.722931	−	0.690921i	$-0.242795\pi$
$353$	27.1653			1.44586			0.722931	+	0.690921i	$0.242795\pi$
$354$	5.79004	−	3.94064i	0.307737	−	0.209442i
$355$	9.22027	−	12.6906i	0.489361	−	0.673548i
$356$	−0.186619	+	0.473215i	−0.00989077	+	0.0250803i
$357$	−2.20568	+	6.78839i	−0.116737	+	0.359280i
$358$	−0.314239	+	10.2194i	−0.0166080	+	0.540113i
$359$	4.54147	−	3.29957i	0.239690	−	0.174145i	−0.461455	−	0.887163i	$-0.652673\pi$
$359$	4.54147	−	3.29957i	0.239690	−	0.174145i	0.701145	+	0.713019i	$0.252673\pi$
$360$	0.926949	+	4.10776i	0.0488545	+	0.216498i
$361$	3.14435	+	9.67732i	0.165492	+	0.509333i
$362$	10.0002	+	34.3343i	0.525601	+	1.80457i
$363$	−0.999045	−	13.4853i	−0.0524363	−	0.707795i
$364$	−1.37128	−	2.15435i	−0.0718748	−	0.112919i
$365$	−13.8115	+	4.48763i	−0.722927	+	0.234893i
$366$	−8.19460	+	22.8098i	−0.428338	+	1.19229i
$367$	−20.6644	−	28.4421i	−1.07867	−	1.48467i	−0.860974	−	0.508650i	$-0.830145\pi$
$367$	−20.6644	−	28.4421i	−1.07867	−	1.48467i	−0.217699	−	0.976016i	$-0.569855\pi$
$368$	8.95794	−	9.59111i	0.466965	−	0.499971i
$369$	7.25574	+	2.35753i	0.377719	+	0.122728i
$370$	1.65435	+	1.28145i	0.0860054	+	0.0666195i
$371$	−4.27885	−	3.10877i	−0.222147	−	0.161399i
$372$	12.1184	+	9.99765i	0.628311	+	0.518354i
$373$		−	0.260135i		−	0.0134693i	−0.999977	−	0.00673465i	$-0.997856\pi$
$373$		−	0.260135i		−	0.0134693i	0.999977	−	0.00673465i	$-0.00214372\pi$
$374$	18.6994	−	13.7649i	0.966924	−	0.711765i
$375$		−	1.22930i		−	0.0634806i
$376$	4.30333	+	1.85186i	0.221927	+	0.0955023i
$377$	0.932897	+	0.677790i	0.0480467	+	0.0349079i
$378$	5.60512	−	7.23618i	0.288296	−	0.372189i
$379$	−18.0893	−	5.87758i	−0.929186	−	0.301911i	−0.194956	−	0.980812i	$-0.562456\pi$
$379$	−18.0893	−	5.87758i	−0.929186	−	0.301911i	−0.734230	+	0.678901i	$0.762456\pi$
$380$	2.70071	+	10.4598i	0.138544	+	0.536577i
$381$	−12.0868	−	16.6360i	−0.619224	−	0.852289i
$382$	2.32124	+	0.833926i	0.118765	+	0.0426674i
$383$	7.47256	−	2.42798i	0.381830	−	0.124064i	−0.111812	−	0.993729i	$-0.535665\pi$
$383$	7.47256	−	2.42798i	0.381830	−	0.124064i	0.493642	+	0.869665i	$0.335665\pi$
$384$	5.58387	+	12.7377i	0.284951	+	0.650020i
$385$	−2.40132	−	3.06048i	−0.122382	−	0.155977i
$386$	−15.6060	+	4.54540i	−0.794323	+	0.231355i
$387$	4.19663	+	12.9159i	0.213327	+	0.656552i
$388$	−0.0632433	−	0.00389304i	−0.00321069	−	0.000197639i
$389$	25.3393	−	18.4101i	1.28475	−	0.933428i	0.285069	−	0.958507i	$-0.407984\pi$
$389$	25.3393	−	18.4101i	1.28475	−	0.933428i	0.999685	+	0.0250786i	$0.00798362\pi$
$390$	1.89169	+	0.0581680i	0.0957896	+	0.00294545i
$391$	5.01905	−	15.4470i	0.253824	−	0.781191i
$392$	15.8403	+	1.46492i	0.800055	+	0.0739898i
$393$	−3.62939	+	4.99543i	−0.183079	+	0.251986i
$394$	−9.08040	−	13.3420i	−0.457464	−	0.672159i
$395$	9.67810			0.486958
$396$	−9.46438	+	2.82073i	−0.475603	+	0.141747i
$397$	11.4928			0.576805			0.288403	−	0.957509i	$-0.406876\pi$
$397$	11.4928			0.576805			0.288403	+	0.957509i	$0.406876\pi$
$398$	9.22529	+	13.5549i	0.462422	+	0.679444i
$399$	4.57770	−	6.30067i	0.229172	−	0.315428i
$400$	0.760154	+	3.92711i	0.0380077	+	0.196355i
$401$	−10.2784	+	31.6336i	−0.513277	+	1.57970i	0.273118	+	0.961980i	$0.411945\pi$
$401$	−10.2784	+	31.6336i	−0.513277	+	1.57970i	−0.786395	+	0.617724i	$0.788055\pi$
$402$	−18.0592	−	0.555306i	−0.900712	−	0.0276962i
$403$	−5.62776	+	4.08881i	−0.280339	+	0.203678i
$404$	0.565095	−	9.18009i	0.0281145	−	0.456726i
$405$	0.715961	+	2.20350i	0.0355764	+	0.109493i
$406$	1.68690	−	0.491328i	0.0837196	−	0.0243842i
$407$	−2.73587	+	4.07424i	−0.135612	+	0.201953i
$408$	12.9343	+	11.3565i	0.640342	+	0.562232i
$409$	6.59049	−	2.14138i	0.325879	−	0.105884i	−0.141509	−	0.989937i	$-0.545195\pi$
$409$	6.59049	−	2.14138i	0.325879	−	0.105884i	0.467388	+	0.884053i	$0.345195\pi$
$410$	6.82002	+	2.45015i	0.336817	+	0.121004i
$411$	10.2351	+	14.0874i	0.504861	+	0.694881i
$412$	−7.83668	+	2.02342i	−0.386086	+	0.0996869i
$413$	4.49399	+	1.46019i	0.221135	+	0.0718511i
$414$	−4.23034	+	5.46135i	−0.207910	+	0.268411i
$415$	2.59161	+	1.88292i	0.127217	+	0.0924288i
$416$	−6.07916	+	0.983933i	−0.298056	+	0.0482413i
$417$		−	20.5939i		−	1.00849i
$418$	−24.0456	+	7.97899i	−1.17611	+	0.390265i
$419$			14.0522i			0.686493i	0.939245	+	0.343246i	$0.111527\pi$
$419$			14.0522i			0.686493i	−0.939245	+	0.343246i	$0.888473\pi$
$420$	1.83514	−	2.22442i	0.0895455	−	0.108541i
$421$	−20.5969	−	14.9645i	−1.00383	−	0.729327i	−0.0409255	−	0.999162i	$-0.513031\pi$
$421$	−20.5969	−	14.9645i	−1.00383	−	0.729327i	−0.962906	+	0.269836i	$0.913031\pi$
$422$	26.5948	+	20.6003i	1.29462	+	1.00280i
$423$	−2.34533	−	0.762044i	−0.114034	−	0.0370518i
$424$	−10.9648	+	6.51464i	−0.532498	+	0.316379i
$425$	2.90977	+	4.00495i	0.141144	+	0.194269i
$426$	−9.22027	+	25.6647i	−0.446723	+	1.24346i
$427$	−15.5518	+	5.05307i	−0.752602	+	0.244535i
$428$	9.26831	−	5.89945i	0.448001	−	0.285161i
$429$	0.164074	+	4.43548i	0.00792157	+	0.214147i
$430$	3.60735	+	12.3853i	0.173962	+	0.597273i
$431$	−7.68857	−	23.6630i	−0.370345	−	1.13981i	−0.946566	−	0.322512i	$-0.895473\pi$
$431$	−7.68857	−	23.6630i	−0.370345	−	1.13981i	0.576220	−	0.817295i	$-0.304527\pi$
$432$	−10.6858	−	19.3134i	−0.514119	−	0.929215i
$433$	−21.8035	+	15.8411i	−1.04781	+	0.761277i	−0.971794	−	0.235830i	$-0.924219\pi$
$433$	−21.8035	+	15.8411i	−1.04781	+	0.761277i	−0.0760133	+	0.997107i	$0.524219\pi$
$434$	−0.325763	+	10.5942i	−0.0156371	+	0.508538i
$435$	−0.402375	+	1.23838i	−0.0192924	+	0.0593759i
$436$	−28.3268	−	11.1711i	−1.35661	−	0.534998i
$437$	−10.4166	+	14.3372i	−0.498294	+	0.685843i
$438$	20.8715	−	14.2049i	0.997281	−	0.678738i
$439$	−31.9624			−1.52548			−0.762742	−	0.646703i	$-0.776147\pi$
$439$	−31.9624			−1.52548			−0.762742	+	0.646703i	$0.776147\pi$
$440$	−9.06815	+	2.40179i	−0.432307	+	0.114501i
$441$	−8.37360			−0.398743
$442$	−6.30067	+	4.28816i	−0.299692	+	0.203967i
$443$	24.5259	−	33.7570i	1.16526	−	1.60384i	0.475710	−	0.879602i	$-0.342191\pi$
$443$	24.5259	−	33.7570i	1.16526	−	1.60384i	0.689549	−	0.724239i	$-0.257809\pi$
$444$	−3.38430	−	1.33465i	−0.160612	−	0.0633395i
$445$	0.0785959	−	0.241893i	0.00372580	−	0.0114668i
$446$	−0.270033	+	8.78178i	−0.0127864	+	0.415829i
$447$	−2.18641	+	1.58852i	−0.103414	+	0.0751346i
$448$	−4.48702	+	8.24090i	−0.211992	+	0.389346i
$449$	0.860114	+	2.64716i	0.0405913	+	0.124927i	0.969299	−	0.245886i	$-0.0790790\pi$
$449$	0.860114	+	2.64716i	0.0405913	+	0.124927i	−0.928707	+	0.370813i	$0.879079\pi$
$450$	−0.588790	−	2.02152i	−0.0277558	−	0.0952955i
$451$	−4.65073	+	16.3465i	−0.218994	+	0.769727i
$452$	−23.5094	+	14.9642i	−1.10579	+	0.703856i
$453$	−3.52538	+	1.14547i	−0.165637	+	0.0538187i
$454$	−5.44496	+	15.1561i	−0.255545	+	0.711312i
$455$	0.750529	+	1.03301i	0.0351853	+	0.0484284i
$456$	−9.59289	−	16.1458i	−0.449228	−	0.756098i
$457$	−5.57551	−	1.81159i	−0.260811	−	0.0847427i	0.175693	−	0.984445i	$-0.443783\pi$
$457$	−5.57551	−	1.81159i	−0.260811	−	0.0847427i	−0.436504	+	0.899702i	$0.643783\pi$
$458$	23.0763	+	17.8748i	1.07828	+	0.835235i
$459$	−22.0997	−	16.0564i	−1.03153	−	0.749448i
$460$	−4.17587	+	5.06169i	−0.194701	+	0.236002i
$461$			37.8294i			1.76189i	0.473219	+	0.880945i	$0.343092\pi$
$461$			37.8294i			1.76189i	−0.473219	+	0.880945i	$0.656908\pi$
$462$	5.49597	+	3.94094i	0.255696	+	0.183349i
$463$			34.9685i			1.62513i	0.582873	+	0.812563i	$0.301928\pi$
$463$			34.9685i			1.62513i	−0.582873	+	0.812563i	$0.698072\pi$
$464$	0.519654	−	4.20495i	0.0241243	−	0.195210i
$465$	−6.35489	−	4.61710i	−0.294701	−	0.214113i
$466$	10.2300	−	13.2069i	0.473895	−	0.611796i
$467$	−24.6769	−	8.01802i	−1.14191	−	0.371030i	−0.323821	−	0.946118i	$-0.604967\pi$
$467$	−24.6769	−	8.01802i	−1.14191	−	0.371030i	−0.818091	+	0.575089i	$0.804967\pi$
$468$	3.13866	−	0.810400i	0.145085	−	0.0374607i
$469$	−7.16499	−	9.86176i	−0.330848	−	0.455374i
$470$	−2.20449	−	0.791981i	−0.101685	−	0.0365313i
$471$	18.3466	−	5.96116i	0.845365	−	0.274676i
$472$	7.51816	−	8.56264i	0.346051	−	0.394128i
$473$	−28.4071	+	10.4059i	−1.30616	+	0.478465i
$474$	−16.1540	+	4.70503i	−0.741979	+	0.216109i
$475$	−1.66913	−	5.13706i	−0.0765850	−	0.235704i
$476$	−0.713489	+	11.5908i	−0.0327027	+	0.531262i
$477$	5.43135	−	3.94611i	0.248685	−	0.180680i
$478$	29.8664	+	0.918369i	1.36606	+	0.0420052i
$479$	−1.60201	+	4.93049i	−0.0731979	+	0.225280i	−0.980962	−	0.194202i	$-0.937788\pi$
$479$	−1.60201	+	4.93049i	−0.0731979	+	0.225280i	0.907764	+	0.419482i	$0.137788\pi$
$480$	−3.17797	−	6.18530i	−0.145054	−	0.282319i
$481$	0.946835	−	1.30321i	0.0431720	−	0.0594211i
$482$	4.49185	+	6.59995i	0.204598	+	0.300620i
$483$	4.73065			0.215252
$484$	−7.05875	−	20.8368i	−0.320852	−	0.947129i
$485$	0.0316815			0.00143858
$486$	10.9059	+	16.0243i	0.494704	+	0.726876i
$487$	−13.4505	+	18.5131i	−0.609502	+	0.838908i	−0.996536	−	0.0831573i	$-0.973500\pi$
$487$	−13.4505	+	18.5131i	−0.609502	+	0.838908i	0.387034	+	0.922065i	$0.373500\pi$
$488$	−3.63125	+	39.2649i	−0.164379	+	1.77744i
$489$	6.05218	−	18.6267i	0.273689	−	0.842328i
$490$	−7.95018	−	0.244462i	−0.359153	−	0.0110437i
$491$	8.56332	−	6.22162i	0.386457	−	0.280778i	−0.377545	−	0.925991i	$-0.623232\pi$
$491$	8.56332	−	6.22162i	0.386457	−	0.280778i	0.764002	+	0.645214i	$0.223232\pi$
$492$	−12.5747	−	0.774053i	−0.566909	−	0.0348970i
$493$	−1.62037	−	4.98698i	−0.0729778	−	0.224602i
$494$	7.98410	−	2.32545i	0.359221	−	0.104627i
$495$	4.63660	−	1.69845i	0.208399	−	0.0763396i
$496$	23.1564	+	10.8201i	1.03975	+	0.485838i
$497$	−17.4983	+	5.68554i	−0.784905	+	0.255031i
$498$	−5.24112	−	1.88292i	−0.234860	−	0.0843755i
$499$	13.6423	+	18.7770i	0.610713	+	0.840575i	0.996636	−	0.0819562i	$-0.0261168\pi$
$499$	13.6423	+	18.7770i	0.610713	+	0.840575i	−0.385922	+	0.922531i	$0.626117\pi$
$500$	−0.500000	−	1.93649i	−0.0223607	−	0.0866025i
$501$	17.4241	+	5.66143i	0.778451	+	0.252934i
$502$	17.2300	−	22.2438i	0.769010	−	0.992788i
$503$	10.6983	+	7.77275i	0.477013	+	0.346570i	0.800168	−	0.599776i	$-0.204744\pi$
$503$	10.6983	+	7.77275i	0.477013	+	0.346570i	−0.323155	+	0.946346i	$0.604744\pi$
$504$	1.95238	−	4.53692i	0.0869659	−	0.202091i
$505$			4.59873i			0.204641i
$506$	−12.5061	−	8.96764i	−0.555966	−	0.398660i
$507$			14.5240i			0.645032i
$508$	−25.8066	−	21.2903i	−1.14498	−	0.944606i
$509$	−1.56969	−	1.14045i	−0.0695754	−	0.0505495i	0.552454	−	0.833543i	$-0.313692\pi$
$509$	−1.56969	−	1.14045i	−0.0695754	−	0.0505495i	−0.622029	+	0.782994i	$0.713692\pi$
$510$	−6.80380	−	5.27020i	−0.301277	−	0.233368i
$511$	16.1996	+	5.26358i	0.716630	+	0.232847i
$512$	13.9771	+	17.7944i	0.617706	+	0.786409i
$513$	17.5193	+	24.1132i	0.773496	+	1.06463i
$514$	−1.49713	+	4.16729i	−0.0660358	+	0.183811i
$515$	3.84878	−	1.25054i	0.169597	−	0.0551055i
$516$	−12.0423	−	18.9190i	−0.530132	−	0.832862i
$517$	1.50329	−	5.28381i	0.0661146	−	0.232382i
$518$	−0.686359	−	2.35651i	−0.0301569	−	0.103539i
$519$	−4.57270	−	14.0733i	−0.200719	−	0.617750i
$520$	3.00361	−	0.677790i	0.131717	−	0.0297230i
$521$	33.4080	−	24.2723i	1.46363	−	1.06339i	0.481230	−	0.876594i	$-0.340190\pi$
$521$	33.4080	−	24.2723i	1.46363	−	1.06339i	0.982399	−	0.186794i	$-0.0598098\pi$
$522$	−0.0685458	+	2.22919i	−0.00300017	+	0.0975690i
$523$	−1.72381	+	5.30533i	−0.0753768	+	0.231986i	−0.981645	−	0.190717i	$-0.938919\pi$
$523$	−1.72381	+	5.30533i	−0.0753768	+	0.231986i	0.906268	+	0.422703i	$0.138919\pi$
$524$	−3.68550	+	9.34542i	−0.161002	+	0.408257i
$525$	−0.847500	+	1.16648i	−0.0369879	+	0.0509095i
$526$	−32.2970	+	21.9810i	−1.40822	+	0.958416i
$527$	31.6325			1.37793
$528$	13.9683	−	8.41741i	0.607892	−	0.366321i
$529$	12.2354			0.531972
$530$	5.27191	−	3.58800i	0.228997	−	0.155853i
$531$	−3.52554	+	4.85249i	−0.152995	+	0.210580i
$532$	4.64847	−	11.7873i	0.201537	−	0.511043i
$533$	1.72384	−	5.30544i	0.0746678	−	0.229804i
$534$	−0.0135899	+	0.441961i	−0.000588094	+	0.0191255i
$535$	−4.44417	+	3.22888i	−0.192138	+	0.139597i
$536$	−28.6743	+	6.47058i	−1.23854	+	0.279486i
$537$	2.74635	+	8.45238i	0.118514	+	0.364747i
$538$	5.55820	+	19.0833i	0.239631	+	0.822738i
$539$	−0.689551	−	18.6409i	−0.0297010	−	0.802920i
$540$	5.92610	+	9.31017i	0.255019	+	0.400646i
$541$	−1.33241	+	0.432925i	−0.0572847	+	0.0186129i	−0.337519	−	0.941319i	$-0.609588\pi$
$541$	−1.33241	+	0.432925i	−0.0572847	+	0.0186129i	0.280234	+	0.959932i	$0.409588\pi$
$542$	9.87382	−	27.4839i	0.424117	−	1.18054i
$543$	18.2713	+	25.1483i	0.784098	+	1.07922i
$544$	24.9943	+	12.6289i	1.07162	+	0.541461i
$545$	14.4798	+	4.70478i	0.620248	+	0.201531i
$546$	−1.75493	−	1.35936i	−0.0751041	−	0.0581754i
$547$	−32.1360	−	23.3482i	−1.37404	−	0.998296i	−0.997410	−	0.0719306i	$-0.977084\pi$
$547$	−32.1360	−	23.3482i	−1.37404	−	0.998296i	−0.376627	−	0.926365i	$-0.622916\pi$
$548$	21.8531	+	18.0287i	0.933517	+	0.770148i
$549$		−	20.7565i		−	0.885865i
$550$	4.45173	−	1.47720i	0.189822	−	0.0629881i
$551$			5.72137i			0.243739i
$552$	4.50932	−	10.4787i	0.191930	−	0.446004i
$553$	−9.18358	−	6.67226i	−0.390526	−	0.283734i
$554$	20.3783	−	26.3083i	0.865793	−	1.11773i
$555$	1.72995	+	0.562096i	0.0734325	+	0.0238597i
$556$	−8.37628	−	32.4412i	−0.355233	−	1.37581i
$557$	−21.9168	−	30.1659i	−0.928646	−	1.27817i	−0.960385	−	0.278675i	$-0.910105\pi$
$557$	−21.9168	−	30.1659i	−0.928646	−	1.27817i	0.0317396	−	0.999496i	$-0.489895\pi$
$558$	−12.6618	−	4.54884i	−0.536015	−	0.192568i
$559$	9.44417	−	3.06860i	0.399446	−	0.129788i
$560$	1.98611	−	4.25051i	0.0839284	−	0.179617i
$561$	11.2517	−	16.7560i	0.475049	−	0.707440i
$562$	10.2357	−	2.98126i	0.431768	−	0.125757i
$563$	−5.64739	−	17.3809i	−0.238009	−	0.732517i	−0.996708	−	0.0810755i	$-0.974165\pi$
$563$	−5.64739	−	17.3809i	−0.238009	−	0.732517i	0.758699	−	0.651442i	$-0.225835\pi$
$564$	4.06460	+	0.250203i	0.171151	+	0.0105354i
$565$	11.2728	−	8.19017i	0.474251	−	0.344563i
$566$	−7.99514	−	0.245844i	−0.336061	−	0.0103336i
$567$	0.839757	−	2.58451i	0.0352665	−	0.108539i
$568$	−4.08575	+	44.1795i	−0.171434	+	1.85373i
$569$	−16.4429	+	22.6317i	−0.689321	+	0.948769i	−0.999998	−	0.00174640i	$-0.999444\pi$
$569$	−16.4429	+	22.6317i	−0.689321	+	0.948769i	0.310677	+	0.950515i	$0.399444\pi$
$570$	5.28339	+	7.76297i	0.221297	+	0.325155i
$571$	−2.95106			−0.123498			−0.0617489	−	0.998092i	$-0.519668\pi$
$571$	−2.95106			−0.123498			−0.0617489	+	0.998092i	$0.519668\pi$
$572$	2.06253	+	6.92040i	0.0862389	+	0.289357i
$573$	2.14399			0.0895664
$574$	−4.78236	−	7.02681i	−0.199612	−	0.293293i
$575$	1.92849	−	2.65434i	0.0804238	−	0.110694i
$576$	−8.18856	−	8.64932i	−0.341190	−	0.360388i
$577$	13.2912	−	40.9060i	0.553318	−	1.70294i	−0.147025	−	0.989133i	$-0.546970\pi$
$577$	13.2912	−	40.9060i	0.553318	−	1.70294i	0.700343	−	0.713806i	$-0.253030\pi$
$578$	10.6106	+	0.326267i	0.441343	+	0.0135709i
$579$	−11.4307	+	8.30486i	−0.475042	+	0.345138i
$580$	−0.130159	+	2.11447i	−0.00540457	+	0.0877984i
$581$	−1.16107	−	3.57341i	−0.0481694	−	0.148250i
$582$	−0.0528806	+	0.0154020i	−0.00219197	+	0.000638434i
$583$	9.23189	+	11.7660i	0.382346	+	0.487300i
$584$	27.1009	−	30.8660i	1.12145	−	1.27725i
$585$	−1.54147	+	0.500854i	−0.0637320	+	0.0207078i
$586$	16.1525	+	5.80292i	0.667253	+	0.239716i
$587$	5.66886	+	7.80252i	0.233979	+	0.322045i	0.909820	−	0.415003i	$-0.136219\pi$
$587$	5.66886	+	7.80252i	0.233979	+	0.322045i	−0.675841	+	0.737047i	$0.736219\pi$
$588$	13.3887	−	3.45696i	0.552142	−	0.142563i
$589$	−32.8253	−	10.6656i	−1.35254	−	0.439467i
$590$	−3.48893	+	4.50419i	−0.143637	+	0.185435i
$591$	−11.3494	−	8.24580i	−0.466851	−	0.339187i
$592$	−5.87409	−	0.725928i	−0.241423	−	0.0298355i
$593$			21.0743i			0.865419i	0.901533	+	0.432710i	$0.142442\pi$
$593$			21.0743i			0.865419i	−0.901533	+	0.432710i	$0.857558\pi$
$594$	−20.8439	+	15.3434i	−0.855235	+	0.629549i
$595$		−	5.80636i		−	0.238038i
$596$	−2.79811	+	3.39167i	−0.114615	+	0.138928i
$597$	11.5305	+	8.37737i	0.471910	+	0.342863i
$598$	3.99336	+	3.09325i	0.163301	+	0.126492i
$599$	26.9630	+	8.76080i	1.10168	+	0.357957i	0.802748	−	0.596319i	$-0.203370\pi$
$599$	26.9630	+	8.76080i	1.10168	+	0.357957i	0.298929	+	0.954275i	$0.403370\pi$
$600$	1.77599	+	2.98918i	0.0725047	+	0.122033i
$601$	12.0497	+	16.5849i	0.491516	+	0.676514i	0.980667	−	0.195685i	$-0.0626931\pi$
$601$	12.0497	+	16.5849i	0.491516	+	0.676514i	−0.489150	+	0.872199i	$0.662693\pi$
$602$	5.11564	−	14.2394i	0.208498	−	0.580356i
$603$	14.7158	−	4.78145i	0.599274	−	0.194716i
$604$	−5.08757	+	3.23834i	−0.207010	+	0.131766i
$605$	4.16282	+	10.1819i	0.169243	+	0.413953i
$606$	−2.23568	−	7.67588i	−0.0908184	−	0.311811i
$607$	−3.85789	−	11.8734i	−0.156587	−	0.481925i	0.841731	−	0.539897i	$-0.181537\pi$
$607$	−3.85789	−	11.8734i	−0.156587	−	0.481925i	−0.998318	+	0.0579714i	$0.981537\pi$
$608$	−21.6786	−	21.5325i	−0.879185	−	0.873258i
$609$	1.23558	−	0.897701i	0.0500682	−	0.0363767i
$610$	0.605972	−	19.7069i	0.0245351	−	0.797910i
$611$	−0.557210	+	1.71492i	−0.0225423	+	0.0693781i
$612$	−13.7128	−	5.40782i	−0.554306	−	0.218598i
$613$	−9.79969	+	13.4881i	−0.395806	+	0.544780i	−0.959685	−	0.281077i	$-0.909308\pi$
$613$	−9.79969	+	13.4881i	−0.395806	+	0.544780i	0.563879	+	0.825857i	$0.309308\pi$
$614$	0.550380	−	0.374582i	0.0222115	−	0.0151169i
$615$	6.29923			0.254009
$616$	10.2606	+	3.97268i	0.413413	+	0.160064i
$617$	41.3214			1.66354			0.831769	−	0.555121i	$-0.187328\pi$
$617$	41.3214			1.66354			0.831769	+	0.555121i	$0.187328\pi$
$618$	−5.81616	+	3.95841i	−0.233960	+	0.159231i
$619$	−18.0636	+	24.8624i	−0.726037	+	0.999304i	0.273265	+	0.961939i	$0.411896\pi$
$619$	−18.0636	+	24.8624i	−0.726037	+	0.999304i	−0.999302	+	0.0373650i	$0.988104\pi$
$620$	−11.8887	−	4.68848i	−0.477462	−	0.188294i
$621$	−5.59464	+	17.2185i	−0.224505	+	0.690955i
$622$	0.597948	−	19.4460i	0.0239755	−	0.779712i
$623$	−0.241346	+	0.175348i	−0.00966931	+	0.00702516i
$624$	−4.68391	+	2.59153i	−0.187507	+	0.103744i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−10.7143	−	36.7859i	−0.428228	−	1.47026i
$627$	−17.3257	+	13.5941i	−0.691921	+	0.542895i
$628$	26.4764	−	16.8527i	1.05652	−	0.672498i
$629$	−6.96654	+	2.26357i	−0.277774	+	0.0902544i
$630$	−0.834971	+	2.32415i	−0.0332660	+	0.0925965i
$631$	6.22294	+	8.56514i	0.247731	+	0.340973i	0.914715	−	0.404099i	$-0.132415\pi$
$631$	6.22294	+	8.56514i	0.247731	+	0.340973i	−0.666984	+	0.745072i	$0.732415\pi$
$632$	−23.5335	+	13.9822i	−0.936111	+	0.556181i
$633$	27.8103	+	9.03610i	1.10536	+	0.359153i
$634$	−5.55983	−	4.30663i	−0.220809	−	0.171038i
$635$	13.5330	+	9.83227i	0.537039	+	0.390182i
$636$	−7.05520	+	8.55180i	−0.279757	+	0.339101i
$637$			6.12282i			0.242595i
$638$	−4.96815	+	0.0309765i	−0.196691	+	0.00122637i
$639$		−	23.3545i		−	0.923888i
$640$	−7.52199	−	8.45102i	−0.297333	−	0.334056i
$641$	−25.8134	−	18.7545i	−1.01957	−	0.740758i	−0.0533724	−	0.998575i	$-0.516997\pi$
$641$	−25.8134	−	18.7545i	−1.01957	−	0.740758i	−0.966194	+	0.257816i	$0.916997\pi$
$642$	5.84817	−	7.54996i	0.230809	−	0.297973i
$643$	31.0930	+	10.1027i	1.22619	+	0.398412i	0.849332	−	0.527860i	$-0.177005\pi$
$643$	31.0930	+	10.1027i	1.22619	+	0.398412i	0.376855	+	0.926272i	$0.377005\pi$
$644$	7.45212	−	1.92413i	0.293655	−	0.0758213i
$645$	6.59096	+	9.07168i	0.259519	+	0.357197i
$646$	−35.5879	−	12.7853i	−1.40019	−	0.503029i
$647$	−25.7250	+	8.35856i	−1.01135	+	0.328609i	−0.767394	−	0.641176i	$-0.778447\pi$
$647$	−25.7250	+	8.35856i	−1.01135	+	0.328609i	−0.243961	+	0.969785i	$0.578447\pi$
$648$	−4.92439	−	4.32371i	−0.193448	−	0.169851i
$649$	−11.0927	−	7.44879i	−0.435426	−	0.292390i
$650$	−1.47815	+	0.430526i	−0.0579777	+	0.0168866i
$651$	2.84706	+	8.76236i	0.111585	+	0.343424i
$652$	1.95774	−	31.8040i	0.0766711	−	1.24554i
$653$	8.43560	−	6.12882i	0.330111	−	0.239839i	−0.410367	−	0.911920i	$-0.634599\pi$
$653$	8.43560	−	6.12882i	0.330111	−	0.239839i	0.740478	+	0.672081i	$0.234599\pi$
$654$	−26.4560	−	0.813500i	−1.03451	−	0.0318103i
$655$	1.55218	−	4.77710i	0.0606485	−	0.186657i
$656$	−20.1235	+	3.89522i	−0.785690	+	0.152083i
$657$	−12.7086	+	17.4919i	−0.495811	+	0.682425i
$658$	1.54584	+	2.27133i	0.0602631	+	0.0885456i
$659$	−21.1112			−0.822377			−0.411189	−	0.911550i	$-0.634886\pi$
$659$	−21.1112			−0.822377			−0.411189	+	0.911550i	$0.634886\pi$
$660$	−6.71237	+	4.62986i	−0.261279	+	0.180217i
$661$	−29.6003			−1.15132			−0.575659	−	0.817690i	$-0.695254\pi$
$661$	−29.6003			−1.15132			−0.575659	+	0.817690i	$0.695254\pi$
$662$	−6.44591	−	9.47108i	−0.250527	−	0.368104i
$663$	−3.89403	+	5.35967i	−0.151232	+	0.208152i
$664$	−9.02211	−	0.834372i	−0.350126	−	0.0323799i
$665$	−1.95774	+	6.02530i	−0.0759178	+	0.233651i
$666$	3.11406	+	0.0957547i	0.120667	+	0.00371042i
$667$	−2.81157	+	2.04273i	−0.108865	+	0.0790947i
$668$	29.7506	+	1.83134i	1.15109	+	0.0708569i
$669$	2.36000	+	7.26333i	0.0912428	+	0.280816i
$670$	14.1113	−	4.11005i	0.545166	−	0.158785i
$671$	46.2071	−	1.70926i	1.78380	−	0.0659852i
$672$	−1.24868	+	8.06020i	−0.0481689	+	0.310929i
$673$	−24.4137	+	7.93249i	−0.941078	+	0.305775i	−0.739085	−	0.673612i	$-0.764742\pi$
$673$	−24.4137	+	7.93249i	−0.941078	+	0.305775i	−0.201993	+	0.979387i	$0.564742\pi$
$674$	−16.0247	−	5.75702i	−0.617250	−	0.221752i
$675$	−3.24346	−	4.46424i	−0.124841	−	0.171829i
$676$	5.90743	+	22.8794i	0.227209	+	0.879976i
$677$	−13.0270	−	4.23272i	−0.500667	−	0.162677i	0.0477867	−	0.998858i	$-0.484783\pi$
$677$	−13.0270	−	4.23272i	−0.500667	−	0.162677i	−0.548453	+	0.836181i	$0.684783\pi$
$678$	−14.8341	+	19.1508i	−0.569701	+	0.735481i
$679$	−0.0300627	−	0.0218418i	−0.00115370	−	0.000838212i
$680$	−12.8615	−	5.53471i	−0.493216	−	0.212246i
$681$			13.9988i			0.536433i
$682$	9.08373	−	28.5616i	0.347834	−	1.09368i
$683$		−	33.6874i		−	1.28901i	−0.764599	−	0.644506i	$-0.777063\pi$
$683$		−	33.6874i		−	1.28901i	0.764599	−	0.644506i	$-0.222937\pi$
$684$	12.4065	+	10.2353i	0.474373	+	0.391356i
$685$	−11.4597	−	8.32599i	−0.437854	−	0.318120i
$686$	16.5549	+	12.8234i	0.632068	+	0.489598i
$687$	24.1309	+	7.84061i	0.920652	+	0.299138i
$688$	−26.6651	−	24.9047i	−1.01660	−	0.949484i
$689$	−2.88541	−	3.97143i	−0.109926	−	0.151300i
$690$	−1.92849	+	5.36799i	−0.0734165	+	0.204356i
$691$	−47.4696	+	15.4238i	−1.80583	+	0.586749i	−0.999986	−	0.00537974i	$-0.998288\pi$
$691$	−47.4696	+	15.4238i	−1.80583	+	0.586749i	−0.805843	+	0.592129i	$0.798288\pi$
$692$	−12.9274	−	20.3096i	−0.491427	−	0.772055i
$693$	−5.57062	−	1.58489i	−0.211611	−	0.0602051i
$694$	5.37174	+	18.4431i	0.203909	+	0.700090i
$695$	5.17682	+	15.9326i	0.196368	+	0.604359i
$696$	−0.810699	−	3.59260i	−0.0307295	−	0.136177i
$697$	−20.5224	+	14.9104i	−0.777341	+	0.564771i
$698$	−0.192240	+	6.25186i	−0.00727638	+	0.236637i
$699$	4.48728	−	13.8104i	0.169725	−	0.522359i
$700$	−0.860602	+	2.18225i	−0.0325277	+	0.0824814i
$701$	9.05876	−	12.4683i	0.342144	−	0.470921i	−0.602922	−	0.797800i	$-0.705997\pi$
$701$	9.05876	−	12.4683i	0.342144	−	0.470921i	0.945066	+	0.326879i	$0.105997\pi$
$702$	7.02323	−	4.77993i	0.265075	−	0.180407i
$703$	7.99244			0.301441
$704$	18.5804	−	18.9412i	0.700274	−	0.713874i
$705$	−2.03615			−0.0766858
$706$	31.7597	−	21.6153i	1.19529	−	0.813503i
$707$	3.17045	−	4.36375i	0.119237	−	0.164116i
$708$	3.63376	−	9.21423i	0.136565	−	0.346292i
$709$	7.62254	−	23.4598i	0.286270	−	0.881050i	−0.699745	−	0.714393i	$-0.746703\pi$
$709$	7.62254	−	23.4598i	0.286270	−	0.881050i	0.986015	−	0.166657i	$-0.0532972\pi$
$710$	0.681818	−	22.1735i	0.0255882	−	0.832157i
$711$	11.6572	−	8.46942i	0.437178	−	0.317628i
$712$	0.158354	+	0.701742i	0.00593455	+	0.0262989i
$713$	−6.47852	−	19.9388i	−0.242623	−	0.746715i
$714$	2.82277	+	9.69157i	0.105640	+	0.362698i
$715$	−1.24191	−	3.39030i	−0.0464450	−	0.126790i
$716$	7.76417	+	12.1979i	0.290161	+	0.455856i
$717$	24.7023	−	8.02625i	0.922523	−	0.299746i
$718$	2.68411	−	7.47127i	0.100170	−	0.278825i
$719$	28.5063	+	39.2355i	1.06310	+	1.46324i	0.876867	+	0.480732i	$0.159629\pi$
$719$	28.5063	+	39.2355i	1.06310	+	1.46324i	0.186237	+	0.982505i	$0.440371\pi$
$720$	4.35225	+	4.06494i	0.162199	+	0.151491i
$721$	−4.51427	−	1.46677i	−0.168120	−	0.0546255i
$722$	11.3764	+	8.81210i	0.423385	+	0.327952i
$723$	5.61426	+	4.07900i	0.208796	+	0.151699i
$724$	39.0113	+	32.1842i	1.44984	+	1.19612i
$725$		−	1.05923i		−	0.0393390i
$726$	−11.8982	−	14.9711i	−0.441585	−	0.555631i
$727$		−	3.60653i		−	0.133759i	−0.997761	−	0.0668795i	$-0.978696\pi$
$727$		−	3.60653i		−	0.133759i	0.997761	−	0.0668795i	$-0.0213043\pi$
$728$	−3.31742	−	1.42759i	−0.122952	−	0.0529100i
$729$	19.2543	+	13.9891i	0.713122	+	0.518114i
$730$	−12.5767	+	16.2364i	−0.465483	+	0.600936i
$731$	−42.9456	−	13.9539i	−1.58840	−	0.516103i
$732$	8.56911	+	33.1880i	0.316723	+	1.22666i
$733$	−0.0867563	−	0.119410i	−0.00320442	−	0.00441050i	0.807412	−	0.589988i	$-0.200868\pi$
$733$	−0.0867563	−	0.119410i	−0.00320442	−	0.00441050i	−0.810616	+	0.585578i	$0.800868\pi$
$734$	−46.7907	−	16.8099i	−1.72708	−	0.620466i
$735$	−6.57552	+	2.13652i	−0.242542	+	0.0788066i
$736$	2.84139	−	18.3411i	0.104735	−	0.676061i
$737$	11.8560	+	32.3658i	0.436723	+	1.19221i
$738$	10.3588	−	3.01711i	0.381312	−	0.111061i
$739$	5.49675	+	16.9173i	0.202201	+	0.622311i	0.999817	+	0.0191450i	$0.00609443\pi$
$739$	5.49675	+	16.9173i	0.202201	+	0.622311i	−0.797616	+	0.603166i	$0.793906\pi$
$740$	2.95379	+	0.181826i	0.108584	+	0.00668404i
$741$	5.84799	−	4.24881i	0.214831	−	0.156084i
$742$	−7.47617	−	0.229886i	−0.274459	−	0.00843939i
$743$	−6.92700	+	21.3191i	−0.254127	+	0.782123i	0.739873	+	0.672746i	$0.234885\pi$
$743$	−6.92700	+	21.3191i	−0.254127	+	0.782123i	−0.994000	+	0.109376i	$0.965115\pi$
$744$	22.1231	+	2.04596i	0.811073	+	0.0750087i
$745$	1.29222	−	1.77859i	0.0473433	−	0.0651625i
$746$	−0.206989	−	0.304132i	−0.00757840	−	0.0111351i
$747$	4.76933			0.174501
$748$	10.9094	−	30.9720i	0.398887	−	1.13245i
$749$	6.44314			0.235427
$750$	−0.978148	−	1.43721i	−0.0357169	−	0.0524794i
$751$	15.1954	−	20.9146i	0.554487	−	0.763186i	−0.436125	−	0.899886i	$-0.643650\pi$
$751$	15.1954	−	20.9146i	0.554487	−	0.763186i	0.990613	+	0.136700i	$0.0436496\pi$
$752$	6.50467	−	1.25908i	0.237201	−	0.0459140i
$753$	7.55775	−	23.2604i	0.275420	−	0.847655i
$754$	1.62999	+	0.0501210i	0.0593609	+	0.00182530i
$755$	2.43950	−	1.77240i	0.0887825	−	0.0645042i
$756$	0.795312	−	12.9200i	0.0289252	−	0.469896i
$757$	7.50828	+	23.1081i	0.272893	+	0.839879i	0.989769	+	0.142678i	$0.0455714\pi$
$757$	7.50828	+	23.1081i	0.272893	+	0.839879i	−0.716876	+	0.697201i	$0.754429\pi$
$758$	−25.8255	+	7.52196i	−0.938026	+	0.273210i
$759$	−12.8662	−	3.66055i	−0.467014	−	0.132870i
$760$	11.4803	+	10.0799i	0.416435	+	0.365638i
$761$	−39.2239	+	12.7446i	−1.42187	+	0.461992i	−0.916195	−	0.400733i	$-0.868755\pi$
$761$	−39.2239	+	12.7446i	−1.42187	+	0.461992i	−0.505672	+	0.862726i	$0.668755\pi$
$762$	−27.3683	−	9.83227i	−0.991447	−	0.356186i
$763$	−10.4964	−	14.4470i	−0.379995	−	0.523018i
$764$	3.37739	−	0.872038i	0.122190	−	0.0315492i
$765$	7.00956	+	2.27754i	0.253431	+	0.0823448i

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16913 - 0.795697i) q^{2} +(0.722562 - 0.994522i) q^{3} +(0.733733 - 1.86055i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.0534318 - 1.73767i) q^{6} +(0.948903 - 0.689419i) q^{7} +(-0.622602 - 2.75905i) q^{8} +(0.460074 + 1.41596i) q^{9} +(0.395472 + 1.35779i) q^{10} +(-3.11426 + 1.14079i) q^{11} +(-1.32019 - 2.07407i) q^{12} +(1.03536 - 0.336408i) q^{13} +(0.560824 - 1.56106i) q^{14} +(0.722562 + 0.994522i) q^{15} +(-2.92327 - 2.73029i) q^{16} +(-4.70810 - 1.52976i) q^{17} +(1.66456 + 1.28936i) q^{18} +(4.36984 + 3.17488i) q^{19} +(1.54275 + 1.27276i) q^{20} -1.44185i q^{21} +(-2.73324 + 3.81174i) q^{22} +3.28095i q^{23} +(-3.19381 - 1.37440i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(0.942790 - 1.21714i) q^{26} +(5.24803 + 1.70519i) q^{27} +(-0.586455 - 2.27133i) q^{28} +(0.622602 + 0.856939i) q^{29} +(1.63611 + 0.587785i) q^{30} +(-6.07715 + 1.97459i) q^{31} +(-5.59017 - 0.866025i) q^{32} +(-1.11570 + 3.92149i) q^{33} +(-6.72161 + 1.95774i) q^{34} +(0.362449 + 1.11550i) q^{35} +(2.97203 + 0.182948i) q^{36} +(1.19710 - 0.869742i) q^{37} +(7.63515 + 0.234775i) q^{38} +(0.413545 - 1.27276i) q^{39} +(2.81641 + 0.260464i) q^{40} +(3.01196 - 4.14561i) q^{41} +(-1.14728 - 1.68571i) q^{42} +9.12165 q^{43} +(-0.162529 + 6.63126i) q^{44} -1.48883 q^{45} +(2.61064 + 3.83586i) q^{46} +(-0.973579 + 1.34002i) q^{47} +(-4.82758 + 0.934454i) q^{48} +(-1.73800 + 5.34901i) q^{49} +(-1.41355 - 0.0434654i) q^{50} +(-4.92327 + 3.57697i) q^{51} +(0.133773 - 2.17317i) q^{52} +(-1.39344 - 4.28856i) q^{53} +(7.49244 - 2.18225i) q^{54} +(-0.122602 - 3.31436i) q^{55} +(-2.49293 - 2.18884i) q^{56} +(6.31497 - 2.05186i) q^{57} +(1.40977 + 0.506470i) q^{58} +(2.36799 + 3.25926i) q^{59} +(2.38052 - 0.614648i) q^{60} +(-13.2591 - 4.30815i) q^{61} +(-5.53381 + 7.14412i) q^{62} +(1.41276 + 1.02643i) q^{63} +(-7.22473 + 3.43558i) q^{64} +1.08864i q^{65} +(1.81592 + 5.47249i) q^{66} -10.3928i q^{67} +(-6.30067 + 7.63721i) q^{68} +(3.26298 + 2.37069i) q^{69} +(1.31135 + 1.01577i) q^{70} +(-14.9187 - 4.84738i) q^{71} +(3.62027 - 2.15095i) q^{72} +(8.53598 + 11.7488i) q^{73} +(0.707512 - 1.96937i) q^{74} +(-1.16913 + 0.379874i) q^{75} +(9.11330 - 5.80079i) q^{76} +(-2.16864 + 3.22953i) q^{77} +(-0.529244 - 1.81708i) q^{78} +(-2.99070 - 9.20442i) q^{79} +(3.50000 - 1.93649i) q^{80} +(1.87441 - 1.36184i) q^{81} +(0.222728 - 7.24336i) q^{82} +(0.989908 - 3.04662i) q^{83} +(-2.68264 - 1.05793i) q^{84} +(2.90977 - 4.00495i) q^{85} +(10.6644 - 7.25807i) q^{86} +1.30211 q^{87} +(5.08645 + 7.88213i) q^{88} -0.254342 q^{89} +(-1.74064 + 1.18466i) q^{90} +(0.750529 - 1.03301i) q^{91} +(6.10436 + 2.40734i) q^{92} +(-2.42735 + 7.47062i) q^{93} +(-0.0719940 + 2.34133i) q^{94} +(-4.36984 + 3.17488i) q^{95} +(-4.90053 + 4.93379i) q^{96} +(-0.00979012 - 0.0301309i) q^{97} +(2.22424 + 7.63661i) q^{98} +(-3.04811 - 3.88482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} - 5 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} + 3 q^{7} + 5 q^{8} + 3 q^{9} + 5 q^{10} + q^{11} - 10 q^{12} + 10 q^{13} - 15 q^{14} - 5 q^{15} + 7 q^{16} - 5 q^{17} + 10 q^{18} + 11 q^{19} + q^{20}+ \cdots + 6 q^{99}+O(q^{100}) \) 8 * q + 5 * q^2 - 5 * q^3 - q^4 + 2 * q^5 - 6 * q^6 + 3 * q^7 + 5 * q^8 + 3 * q^9 + 5 * q^10 + q^11 - 10 * q^12 + 10 * q^13 - 15 * q^14 - 5 * q^15 + 7 * q^16 - 5 * q^17 + 10 * q^18 + 11 * q^19 + q^20 - 16 * q^22 - 18 * q^24 - 2 * q^25 - 3 * q^26 + 10 * q^27 - 11 * q^28 - 5 * q^29 - 4 * q^30 - 10 * q^31 - 11 * q^33 - 14 * q^34 - 8 * q^35 + 9 * q^36 + 20 * q^37 + 15 * q^38 - 3 * q^39 + 5 * q^40 + 10 * q^41 + 4 * q^42 + 34 * q^43 + 8 * q^44 - 8 * q^45 + 25 * q^46 - 25 * q^48 - 23 * q^49 - 5 * q^50 - 9 * q^51 - 5 * q^52 - 7 * q^53 + 26 * q^54 + 9 * q^55 + 15 * q^56 + 5 * q^57 - 12 * q^58 + 5 * q^59 - 10 * q^61 - 39 * q^62 + 23 * q^63 + 11 * q^64 - 2 * q^66 - 30 * q^68 + 15 * q^69 - 5 * q^70 - 90 * q^71 + 30 * q^72 + 5 * q^73 - 5 * q^74 - 5 * q^75 + 18 * q^76 - 14 * q^77 + 21 * q^79 + 28 * q^80 - 10 * q^81 + 38 * q^82 - 19 * q^83 - 10 * q^84 + 35 * q^86 + 18 * q^87 + 47 * q^88 + 20 * q^89 + 5 * q^90 + 10 * q^91 + 11 * q^93 + 15 * q^94 - 11 * q^95 - 39 * q^96 - 44 * q^97 - 50 * q^98 + 6 * q^99

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