LMFDB - Embedded newform 370.2.o.b.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (of order $9$, degree $6$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 18 x^{16} - 25 x^{15} + 132 x^{14} - 135 x^{13} + 666 x^{12} - 297 x^{11} + 1845 x^{10} + \cdots + 9 $ x^18 - 3x^17 + 18x^16 - 25x^15 + 132x^14 - 135x^13 + 666x^12 - 297x^11 + 1845x^10 - 382x^9 + 3810x^8 - 63x^7 + 3325x^6 - 1329x^5 + 1332x^4 - 192x^3 + 117x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			71.1
Root			$1.28031 - 2.21756i$ of defining polynomial
Character	$\chi$	$=$	370.71
Dual form			370.2.o.b.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(-1.96154 + 1.64593i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{5} +2.56061 q^{6} +(1.15931 + 0.421953i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.617622 - 3.50271i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.96154 + 1.64593i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{5} +2.56061 q^{6} +(1.15931 + 0.421953i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.617622 - 3.50271i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.59351 - 4.49209i) q^{11} +(-1.96154 - 1.64593i) q^{12} +(0.922896 + 5.23400i) q^{13} +(-0.616854 - 1.06842i) q^{14} +(-2.40619 + 0.875782i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.821891 + 4.66118i) q^{17} +(-2.72463 + 2.28623i) q^{18} +(-4.80522 + 4.03206i) q^{19} +(-0.173648 + 0.984808i) q^{20} +(-2.96854 + 1.08046i) q^{21} +(-4.87420 + 1.77406i) q^{22} +(0.104526 + 0.181044i) q^{23} +(0.444646 + 2.52171i) q^{24} +(0.766044 + 0.642788i) q^{25} +(2.65737 - 4.60270i) q^{26} +(0.712805 + 1.23461i) q^{27} +(-0.214231 + 1.21497i) q^{28} +(-2.63740 + 4.56812i) q^{29} +(2.40619 + 0.875782i) q^{30} +3.14695 q^{31} +(0.939693 + 0.342020i) q^{32} +(2.30639 + 13.0802i) q^{33} +(3.62575 - 3.04237i) q^{34} +(0.945076 + 0.793013i) q^{35} +3.55675 q^{36} +(5.88885 + 1.52364i) q^{37} +6.27277 q^{38} +(-10.4251 - 8.74770i) q^{39} +(0.766044 - 0.642788i) q^{40} +(0.775606 + 4.39868i) q^{41} +(2.96854 + 1.08046i) q^{42} -11.6019 q^{43} +(4.87420 + 1.77406i) q^{44} +(1.77837 - 3.08023i) q^{45} +(0.0363015 - 0.205876i) q^{46} +(4.63640 + 8.03048i) q^{47} +(1.28031 - 2.21756i) q^{48} +(-4.19636 - 3.52117i) q^{49} +(-0.173648 - 0.984808i) q^{50} +(-6.05980 - 10.4959i) q^{51} +(-4.99423 + 1.81775i) q^{52} +(-0.676178 + 0.246109i) q^{53} +(0.247555 - 1.40395i) q^{54} +(3.97348 - 3.33415i) q^{55} +(0.945076 - 0.793013i) q^{56} +(2.78916 - 15.8181i) q^{57} +(4.95670 - 1.80409i) q^{58} +(7.79670 - 2.83777i) q^{59} +(-1.28031 - 2.21756i) q^{60} +(1.46096 + 8.28554i) q^{61} +(-2.41071 - 2.02282i) q^{62} +(2.19399 - 3.80011i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.922896 + 5.23400i) q^{65} +(6.64097 - 11.5025i) q^{66} +(-11.9309 - 4.34250i) q^{67} -4.73308 q^{68} +(-0.503019 - 0.183084i) q^{69} +(-0.214231 - 1.21497i) q^{70} +(6.25749 - 5.25066i) q^{71} +(-2.72463 - 2.28623i) q^{72} +0.148554 q^{73} +(-3.53175 - 4.95245i) q^{74} -2.56061 q^{75} +(-4.80522 - 4.03206i) q^{76} +(4.90212 - 4.11337i) q^{77} +(2.36318 + 13.4023i) q^{78} +(3.02805 + 1.10212i) q^{79} -1.00000 q^{80} +(6.59645 + 2.40091i) q^{81} +(2.23327 - 3.86813i) q^{82} +(0.665479 - 3.77412i) q^{83} +(-1.57953 - 2.73582i) q^{84} +(-2.36654 + 4.09897i) q^{85} +(8.88756 + 7.45755i) q^{86} +(-2.34542 - 13.3016i) q^{87} +(-2.59351 - 4.49209i) q^{88} +(9.40327 - 3.42251i) q^{89} +(-3.34225 + 1.21648i) q^{90} +(-1.13858 + 6.45723i) q^{91} +(-0.160143 + 0.134376i) q^{92} +(-6.17289 + 5.17967i) q^{93} +(1.61021 - 9.13193i) q^{94} +(-5.89448 + 2.14541i) q^{95} +(-2.40619 + 0.875782i) q^{96} +(-1.83095 - 3.17129i) q^{97} +(0.951238 + 5.39474i) q^{98} +(-14.1327 - 11.8587i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9}+O(q^{10}) $ 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9	$ 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9} - 9 q^{10} + 15 q^{11} + 3 q^{13} - 6 q^{14} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 12 q^{21} - 12 q^{22} + 15 q^{23} + 6 q^{26} + 12 q^{27} + 9 q^{28} - 12 q^{29} + 54 q^{31} + 9 q^{33} + 3 q^{34} - 12 q^{37} - 24 q^{38} - 30 q^{39} + 15 q^{41} + 12 q^{42} - 60 q^{43} + 12 q^{44} - 6 q^{46} + 6 q^{47} + 3 q^{48} - 27 q^{49} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} + 45 q^{57} + 3 q^{58} - 27 q^{59} - 3 q^{60} - 9 q^{62} + 18 q^{63} - 9 q^{64} - 3 q^{65} - 9 q^{66} - 54 q^{67} + 12 q^{68} - 6 q^{69} + 9 q^{70} + 36 q^{71} - 6 q^{72} - 6 q^{73} + 18 q^{74} - 6 q^{75} - 3 q^{76} - 24 q^{77} + 12 q^{78} + 12 q^{79} - 18 q^{80} - 6 q^{81} + 3 q^{82} - 15 q^{83} - 6 q^{84} + 6 q^{85} + 30 q^{87} - 15 q^{88} + 84 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 18 q^{93} + 36 q^{94} - 24 q^{95} - 9 q^{97} - 30 q^{99}+O(q^{100}) $ 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9 - 9 * q^10 + 15 * q^11 + 3 * q^13 - 6 * q^14 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 12 * q^21 - 12 * q^22 + 15 * q^23 + 6 * q^26 + 12 * q^27 + 9 * q^28 - 12 * q^29 + 54 * q^31 + 9 * q^33 + 3 * q^34 - 12 * q^37 - 24 * q^38 - 30 * q^39 + 15 * q^41 + 12 * q^42 - 60 * q^43 + 12 * q^44 - 6 * q^46 + 6 * q^47 + 3 * q^48 - 27 * q^49 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 + 45 * q^57 + 3 * q^58 - 27 * q^59 - 3 * q^60 - 9 * q^62 + 18 * q^63 - 9 * q^64 - 3 * q^65 - 9 * q^66 - 54 * q^67 + 12 * q^68 - 6 * q^69 + 9 * q^70 + 36 * q^71 - 6 * q^72 - 6 * q^73 + 18 * q^74 - 6 * q^75 - 3 * q^76 - 24 * q^77 + 12 * q^78 + 12 * q^79 - 18 * q^80 - 6 * q^81 + 3 * q^82 - 15 * q^83 - 6 * q^84 + 6 * q^85 + 30 * q^87 - 15 * q^88 + 84 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 18 * q^93 + 36 * q^94 - 24 * q^95 - 9 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

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 $

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	−1.96154	+	1.64593i	−1.13250	+	0.950279i	−0.999168	−	0.0407929i	$-0.987012\pi$
$3$	−1.96154	+	1.64593i	−1.13250	+	0.950279i	−0.133331	+	0.991072i	$0.542567\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$5$	0.939693	+	0.342020i	0.420243	+	0.152956i
$6$	2.56061			1.04537
$7$	1.15931	+	0.421953i	0.438177	+	0.159483i	0.551683	−	0.834054i	$-0.313986\pi$
$7$	1.15931	+	0.421953i	0.438177	+	0.159483i	−0.113506	+	0.993537i	$0.536208\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.617622	−	3.50271i	0.205874	−	1.16757i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	2.59351	−	4.49209i	0.781972	−	1.35442i	−0.148819	−	0.988864i	$-0.547547\pi$
$11$	2.59351	−	4.49209i	0.781972	−	1.35442i	0.930791	−	0.365551i	$-0.119119\pi$
$12$	−1.96154	−	1.64593i	−0.566249	−	0.475139i
$13$	0.922896	+	5.23400i	0.255965	+	1.45165i	0.793583	+	0.608462i	$0.208213\pi$
$13$	0.922896	+	5.23400i	0.255965	+	1.45165i	−0.537618	+	0.843189i	$0.680676\pi$
$14$	−0.616854	−	1.06842i	−0.164861	−	0.285548i
$15$	−2.40619	+	0.875782i	−0.621276	+	0.226126i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.821891	+	4.66118i	−0.199338	+	1.13050i	0.706766	+	0.707447i	$0.250153\pi$
$17$	−0.821891	+	4.66118i	−0.199338	+	1.13050i	−0.906104	+	0.423054i	$0.860958\pi$
$18$	−2.72463	+	2.28623i	−0.642200	+	0.538870i
$19$	−4.80522	+	4.03206i	−1.10239	+	0.925018i	−0.997584	−	0.0694745i	$-0.977868\pi$
$19$	−4.80522	+	4.03206i	−1.10239	+	0.925018i	−0.104810	+	0.994492i	$0.533423\pi$
$20$	−0.173648	+	0.984808i	−0.0388289	+	0.220210i
$21$	−2.96854	+	1.08046i	−0.647788	+	0.235776i
$22$	−4.87420	+	1.77406i	−1.03918	+	0.378232i
$23$	0.104526	+	0.181044i	0.0217952	+	0.0377504i	0.876717	−	0.481006i	$-0.159728\pi$
$23$	0.104526	+	0.181044i	0.0217952	+	0.0377504i	−0.854922	+	0.518756i	$0.826395\pi$
$24$	0.444646	+	2.52171i	0.0907630	+	0.514742i
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$	2.65737	−	4.60270i	0.521154	−	0.902664i
$27$	0.712805	+	1.23461i	0.137179	+	0.237602i
$28$	−0.214231	+	1.21497i	−0.0404859	+	0.229607i
$29$	−2.63740	+	4.56812i	−0.489754	+	0.848278i	−0.999930	−	0.0117913i	$-0.996247\pi$
$29$	−2.63740	+	4.56812i	−0.489754	+	0.848278i	0.510177	+	0.860070i	$0.329580\pi$
$30$	2.40619	+	0.875782i	0.439308	+	0.159895i
$31$	3.14695			0.565210			0.282605	−	0.959236i	$-0.408802\pi$
$31$	3.14695			0.565210			0.282605	+	0.959236i	$0.408802\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	2.30639	+	13.0802i	0.401490	+	2.27696i
$34$	3.62575	−	3.04237i	0.621811	−	0.521762i
$35$	0.945076	+	0.793013i	0.159747	+	0.134044i
$36$	3.55675			0.592791
$37$	5.88885	+	1.52364i	0.968121	+	0.250484i
$37$	5.88885	+	1.52364i	0.968121	+	0.250484i
$38$	6.27277			1.01758
$39$	−10.4251	−	8.74770i	−1.66935	−	1.40075i
$40$	0.766044	−	0.642788i	0.121122	−	0.101634i
$41$	0.775606	+	4.39868i	0.121129	+	0.686958i	0.983532	+	0.180735i	$0.0578477\pi$
$41$	0.775606	+	4.39868i	0.121129	+	0.686958i	−0.862402	+	0.506223i	$0.831041\pi$
$42$	2.96854	+	1.08046i	0.458055	+	0.166718i
$43$	−11.6019			−1.76927			−0.884635	−	0.466284i	$-0.845593\pi$
$43$	−11.6019			−1.76927			−0.884635	+	0.466284i	$0.845593\pi$
$44$	4.87420	+	1.77406i	0.734813	+	0.267450i
$45$	1.77837	−	3.08023i	0.265104	−	0.459174i
$46$	0.0363015	−	0.205876i	0.00535236	−	0.0303548i
$47$	4.63640	+	8.03048i	0.676289	+	1.17137i	0.976090	+	0.217365i	$0.0697461\pi$
$47$	4.63640	+	8.03048i	0.676289	+	1.17137i	−0.299802	+	0.954002i	$0.596921\pi$
$48$	1.28031	−	2.21756i	0.184796	−	0.320077i
$49$	−4.19636	−	3.52117i	−0.599480	−	0.503024i
$50$	−0.173648	−	0.984808i	−0.0245576	−	0.139273i
$51$	−6.05980	−	10.4959i	−0.848542	−	1.46972i
$52$	−4.99423	+	1.81775i	−0.692575	+	0.252077i
$53$	−0.676178	+	0.246109i	−0.0928802	+	0.0338056i	−0.388042	−	0.921642i	$-0.626849\pi$
$53$	−0.676178	+	0.246109i	−0.0928802	+	0.0338056i	0.295162	+	0.955447i	$0.404626\pi$
$54$	0.247555	−	1.40395i	0.0336879	−	0.191054i
$55$	3.97348	−	3.33415i	0.535785	−	0.449577i
$56$	0.945076	−	0.793013i	0.126291	−	0.105971i
$57$	2.78916	−	15.8181i	0.369434	−	2.09516i
$58$	4.95670	−	1.80409i	0.650846	−	0.236889i
$59$	7.79670	−	2.83777i	1.01504	−	0.369446i	0.219676	−	0.975573i	$-0.429500\pi$
$59$	7.79670	−	2.83777i	1.01504	−	0.369446i	0.795368	+	0.606127i	$0.207278\pi$
$60$	−1.28031	−	2.21756i	−0.165287	−	0.286285i
$61$	1.46096	+	8.28554i	0.187057	+	1.06086i	0.923283	+	0.384119i	$0.125495\pi$
$61$	1.46096	+	8.28554i	0.187057	+	1.06086i	−0.736226	+	0.676736i	$0.763394\pi$
$62$	−2.41071	−	2.02282i	−0.306160	−	0.256899i
$63$	2.19399	−	3.80011i	0.276417	−	0.478769i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.922896	+	5.23400i	−0.114471	+	0.649198i
$66$	6.64097	−	11.5025i	0.817447	−	1.41586i
$67$	−11.9309	−	4.34250i	−1.45759	−	0.530520i	−0.512892	−	0.858453i	$-0.671426\pi$
$67$	−11.9309	−	4.34250i	−1.45759	−	0.530520i	−0.944701	+	0.327933i	$0.893648\pi$
$68$	−4.73308			−0.573971
$69$	−0.503019	−	0.183084i	−0.0605564	−	0.0220407i
$70$	−0.214231	−	1.21497i	−0.0256055	−	0.145216i
$71$	6.25749	−	5.25066i	0.742627	−	0.623138i	−0.190915	−	0.981607i	$-0.561145\pi$
$71$	6.25749	−	5.25066i	0.742627	−	0.623138i	0.933542	+	0.358468i	$0.116701\pi$
$72$	−2.72463	−	2.28623i	−0.321100	−	0.269435i
$73$	0.148554			0.0173870			0.00869349	−	0.999962i	$-0.497233\pi$
$73$	0.148554			0.0173870			0.00869349	+	0.999962i	$0.497233\pi$
$74$	−3.53175	−	4.95245i	−0.410557	−	0.575711i
$75$	−2.56061			−0.295674
$76$	−4.80522	−	4.03206i	−0.551197	−	0.462509i
$77$	4.90212	−	4.11337i	0.558649	−	0.468762i
$78$	2.36318	+	13.4023i	0.267577	+	1.51751i
$79$	3.02805	+	1.10212i	0.340682	+	0.123998i	0.506695	−	0.862125i	$-0.330867\pi$
$79$	3.02805	+	1.10212i	0.340682	+	0.123998i	−0.166013	+	0.986124i	$0.553089\pi$
$80$	−1.00000			−0.111803
$81$	6.59645	+	2.40091i	0.732939	+	0.266768i
$82$	2.23327	−	3.86813i	0.246623	−	0.427164i
$83$	0.665479	−	3.77412i	0.0730458	−	0.414263i	−0.926256	−	0.376895i	$-0.876992\pi$
$83$	0.665479	−	3.77412i	0.0730458	−	0.414263i	0.999302	−	0.0373677i	$-0.0118973\pi$
$84$	−1.57953	−	2.73582i	−0.172340	−	0.298502i
$85$	−2.36654	+	4.09897i	−0.256687	+	0.444596i
$86$	8.88756	+	7.45755i	0.958370	+	0.804168i
$87$	−2.34542	−	13.3016i	−0.251456	−	1.42608i
$88$	−2.59351	−	4.49209i	−0.276469	−	0.478858i
$89$	9.40327	−	3.42251i	0.996745	−	0.362786i	0.208417	−	0.978040i	$-0.433169\pi$
$89$	9.40327	−	3.42251i	0.996745	−	0.362786i	0.788328	+	0.615255i	$0.210947\pi$
$90$	−3.34225	+	1.21648i	−0.352304	+	0.128228i
$91$	−1.13858	+	6.45723i	−0.119356	+	0.676902i
$92$	−0.160143	+	0.134376i	−0.0166961	+	0.0140097i
$93$	−6.17289	+	5.17967i	−0.640099	+	0.537107i
$94$	1.61021	−	9.13193i	0.166080	−	0.941886i
$95$	−5.89448	+	2.14541i	−0.604761	+	0.220115i
$96$	−2.40619	+	0.875782i	−0.245581	+	0.0893841i
$97$	−1.83095	−	3.17129i	−0.185904	−	0.321996i	0.757977	−	0.652282i	$-0.226188\pi$
$97$	−1.83095	−	3.17129i	−0.185904	−	0.321996i	−0.943881	+	0.330286i	$0.892855\pi$
$98$	0.951238	+	5.39474i	0.0960896	+	0.544951i
$99$	−14.1327	−	11.8587i	−1.42039	−	1.19185i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−7.72107	−	13.3733i	−0.768276	−	1.33069i	−0.938497	−	0.345287i	$-0.887782\pi$
$101$	−7.72107	−	13.3733i	−0.768276	−	1.33069i	0.170222	−	0.985406i	$-0.445552\pi$
$102$	−2.10455	+	11.9355i	−0.208381	+	1.18179i
$103$	−1.23107	+	2.13228i	−0.121301	+	0.210100i	−0.920281	−	0.391258i	$-0.872040\pi$
$103$	−1.23107	+	2.13228i	−0.121301	+	0.210100i	0.798980	+	0.601358i	$0.205373\pi$
$104$	4.99423	+	1.81775i	0.489724	+	0.178245i
$105$	−3.15905			−0.308292
$106$	0.676178	+	0.246109i	0.0656762	+	0.0239042i
$107$	0.483855	+	2.74408i	0.0467761	+	0.265280i	0.999222	−	0.0394258i	$-0.0125529\pi$
$107$	0.483855	+	2.74408i	0.0467761	+	0.265280i	−0.952446	+	0.304706i	$0.901442\pi$
$108$	−1.09208	+	0.916365i	−0.105086	+	0.0881772i
$109$	15.4292	+	12.9466i	1.47785	+	1.24006i	0.908445	+	0.418005i	$0.137270\pi$
$109$	15.4292	+	12.9466i	1.47785	+	1.24006i	0.569404	+	0.822058i	$0.307174\pi$
$110$	−5.18702			−0.494563
$111$	−14.0590	+	6.70396i	−1.33442	+	0.636312i
$112$	−1.23371			−0.116574
$113$	3.26550	+	2.74008i	0.307193	+	0.257765i	0.783331	−	0.621605i	$-0.213519\pi$
$113$	3.26550	+	2.74008i	0.307193	+	0.257765i	−0.476138	+	0.879371i	$0.657964\pi$
$114$	−12.3043	+	10.3245i	−1.15240	+	0.966983i
$115$	0.0363015	+	0.205876i	0.00338513	+	0.0191980i
$116$	−4.95670	−	1.80409i	−0.460218	−	0.167506i
$117$	18.9032			1.74760
$118$	−7.79670	−	2.83777i	−0.717745	−	0.261238i
$119$	−2.91962	+	5.05693i	−0.267641	+	0.463568i
$120$	−0.444646	+	2.52171i	−0.0405904	+	0.230200i
$121$	−7.95257	−	13.7743i	−0.722961	−	1.25220i
$122$	4.20668	−	7.28618i	0.380855	−	0.659660i
$123$	−8.76131	−	7.35161i	−0.789981	−	0.662873i
$124$	0.546463	+	3.09914i	0.0490738	+	0.278311i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	−4.12336	+	1.50078i	−0.367338	+	0.133700i
$127$	6.02529	−	2.19303i	0.534658	−	0.194600i	−0.0605588	−	0.998165i	$-0.519288\pi$
$127$	6.02529	−	2.19303i	0.534658	−	0.194600i	0.595217	+	0.803565i	$0.297066\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	22.7576	−	19.0959i	2.00370	−	1.68130i
$130$	4.07133	−	3.41625i	0.357079	−	0.299625i
$131$	−0.285928	+	1.62158i	−0.0249816	+	0.141678i	−0.994747	−	0.102359i	$-0.967361\pi$
$131$	−0.285928	+	1.62158i	−0.0249816	+	0.141678i	0.969766	+	0.244037i	$0.0784719\pi$
$132$	−12.4809	+	4.54269i	−1.08633	+	0.395391i
$133$	−7.27207	+	2.64682i	−0.630568	+	0.229508i
$134$	6.34831	+	10.9956i	0.548410	+	0.949874i
$135$	0.247555	+	1.40395i	0.0213061	+	0.120833i
$136$	3.62575	+	3.04237i	0.310906	+	0.260881i
$137$	7.35786	−	12.7442i	0.628624	−	1.08881i	−0.359204	−	0.933259i	$-0.616952\pi$
$137$	7.35786	−	12.7442i	0.628624	−	1.08881i	0.987828	−	0.155550i	$-0.0497149\pi$
$138$	0.267651	+	0.463585i	0.0227839	+	0.0394630i
$139$	−2.77406	+	15.7325i	−0.235293	+	1.33441i	0.606703	+	0.794929i	$0.292492\pi$
$139$	−2.77406	+	15.7325i	−0.235293	+	1.33441i	−0.841996	+	0.539484i	$0.818619\pi$
$140$	−0.616854	+	1.06842i	−0.0521337	+	0.0902982i
$141$	−22.3121	−	8.12095i	−1.87902	−	0.683907i
$142$	−8.16857			−0.685491
$143$	25.9051	+	9.42870i	2.16630	+	0.788467i
$144$	0.617622	+	3.50271i	0.0514685	+	0.291893i
$145$	−4.04074	+	3.39058i	−0.335565	+	0.281572i
$146$	−0.113799	−	0.0954890i	−0.00941810	−	0.00790272i
$147$	14.0270			1.15692
$148$	−0.477900	+	6.06396i	−0.0392832	+	0.498454i
$149$	13.1694			1.07888			0.539438	−	0.842025i	$-0.318637\pi$
$149$	13.1694			1.07888			0.539438	+	0.842025i	$0.318637\pi$
$150$	1.96154	+	1.64593i	0.160159	+	0.134390i
$151$	−5.51716	+	4.62945i	−0.448980	+	0.376739i	−0.839057	−	0.544043i	$-0.816893\pi$
$151$	−5.51716	+	4.62945i	−0.448980	+	0.376739i	0.390077	+	0.920782i	$0.372448\pi$
$152$	1.08926	+	6.17747i	0.0883503	+	0.501059i
$153$	15.8191	+	5.75769i	1.27890	+	0.465482i
$154$	−6.39927			−0.515668
$155$	2.95717	+	1.07632i	0.237526	+	0.0864522i
$156$	6.80451	−	11.7857i	0.544796	−	0.943615i
$157$	−0.127352	+	0.722248i	−0.0101638	+	0.0576417i	−0.989468	−	0.144753i	$-0.953761\pi$
$157$	−0.127352	+	0.722248i	−0.0101638	+	0.0576417i	0.979304	+	0.202395i	$0.0648724\pi$
$158$	−1.61119	−	2.79066i	−0.128179	−	0.222013i
$159$	0.921275	−	1.59569i	0.0730618	−	0.126547i
$160$	0.766044	+	0.642788i	0.0605611	+	0.0508168i
$161$	0.0447855	+	0.253991i	0.00352959	+	0.0200173i
$162$	−3.50990	−	6.07932i	−0.275764	−	0.477637i
$163$	10.5919	−	3.85515i	0.829624	−	0.301958i	0.107919	−	0.994160i	$-0.465581\pi$
$163$	10.5919	−	3.85515i	0.829624	−	0.301958i	0.721705	+	0.692201i	$0.243359\pi$
$164$	−4.19717	+	1.52765i	−0.327744	+	0.119289i
$165$	−2.30639	+	13.0802i	−0.179552	+	1.01829i
$166$	−2.93574	+	2.46338i	−0.227858	+	0.191195i
$167$	11.7362	−	9.84787i	0.908177	−	0.762051i	−0.0635941	−	0.997976i	$-0.520256\pi$
$167$	11.7362	−	9.84787i	0.908177	−	0.762051i	0.971771	+	0.235925i	$0.0758119\pi$
$168$	−0.548564	+	3.11106i	−0.0423226	+	0.240023i
$169$	−14.3270	+	5.21461i	−1.10208	+	0.401124i
$170$	4.44764	−	1.61881i	0.341119	−	0.124157i
$171$	11.1553	+	19.3216i	0.853069	+	1.47756i
$172$	−2.01465	−	11.4256i	−0.153615	−	0.871196i
$173$	−10.3013	−	8.64382i	−0.783193	−	0.657177i	0.160857	−	0.986978i	$-0.448574\pi$
$173$	−10.3013	−	8.64382i	−0.783193	−	0.657177i	−0.944051	+	0.329800i	$0.893019\pi$
$174$	−6.75337	+	11.6972i	−0.511972	+	0.886762i
$175$	0.616854	+	1.06842i	0.0466298	+	0.0807652i
$176$	−0.900716	+	5.10821i	−0.0678940	+	0.385046i
$177$	−10.6228	+	18.3992i	−0.798459	+	1.38297i
$178$	−9.40327	−	3.42251i	−0.704805	−	0.256528i
$179$	17.9949			1.34500			0.672502	−	0.740096i	$-0.265220\pi$
$179$	17.9949			1.34500			0.672502	+	0.740096i	$0.265220\pi$
$180$	3.34225	+	1.21648i	0.249116	+	0.0906710i
$181$	−0.0543893	−	0.308457i	−0.00404273	−	0.0229274i	0.982720	−	0.185100i	$-0.0592609\pi$
$181$	−0.0543893	−	0.308457i	−0.00404273	−	0.0229274i	−0.986762	+	0.162173i	$0.948150\pi$
$182$	5.02284	−	4.21466i	0.372317	−	0.312411i
$183$	−16.5032	−	13.8478i	−1.21995	−	1.02366i
$184$	0.209052			0.0154115
$185$	5.01259	+	3.44585i	0.368533	+	0.253344i
$186$	8.05813			0.590851
$187$	18.8068	+	15.7808i	1.37529	+	1.15401i
$188$	−7.10338	+	5.96044i	−0.518067	+	0.434710i
$189$	0.305410	+	1.73207i	0.0222153	+	0.125989i
$190$	5.89448	+	2.14541i	0.427630	+	0.155645i
$191$	−13.3311			−0.964606			−0.482303	−	0.876005i	$-0.660200\pi$
$191$	−13.3311			−0.964606			−0.482303	+	0.876005i	$0.660200\pi$
$192$	2.40619	+	0.875782i	0.173652	+	0.0632041i
$193$	2.83112	−	4.90364i	0.203788	−	0.352972i	−0.745958	−	0.665993i	$-0.768008\pi$
$193$	2.83112	−	4.90364i	0.203788	−	0.352972i	0.949746	+	0.313022i	$0.101341\pi$
$194$	−0.635881	+	3.60626i	−0.0456536	+	0.258914i
$195$	−6.80451	−	11.7857i	−0.487281	−	0.843995i
$196$	2.73898	−	4.74406i	0.195642	−	0.338861i
$197$	−9.49637	−	7.96840i	−0.676588	−	0.567725i	0.238419	−	0.971162i	$-0.423371\pi$
$197$	−9.49637	−	7.96840i	−0.676588	−	0.567725i	−0.915007	+	0.403437i	$0.867815\pi$
$198$	3.20362	+	18.1686i	0.227671	+	1.29119i
$199$	−10.7998	−	18.7058i	−0.765575	−	1.32602i	−0.939942	−	0.341335i	$-0.889121\pi$
$199$	−10.7998	−	18.7058i	−0.765575	−	1.32602i	0.174366	−	0.984681i	$-0.444212\pi$
$200$	0.939693	−	0.342020i	0.0664463	−	0.0241845i
$201$	30.5505	−	11.1195i	2.15486	−	0.784306i
$202$	−2.68150	+	15.2075i	−0.188670	+	1.07000i
$203$	−4.98509	+	4.18299i	−0.349885	+	0.293588i
$204$	9.28415	−	7.79033i	0.650021	−	0.545432i
$205$	−0.775606	+	4.39868i	−0.0541707	+	0.307217i
$206$	2.31366	−	0.842103i	0.161200	−	0.0586721i
$207$	0.698704	−	0.254307i	0.0485633	−	0.0176756i
$208$	−2.65737	−	4.60270i	−0.184256	−	0.319140i
$209$	5.64998	+	32.0427i	0.390818	+	2.21644i
$210$	2.41997	+	2.03060i	0.166994	+	0.140125i
$211$	−0.296574	+	0.513681i	−0.0204170	+	0.0353633i	−0.876053	−	0.482214i	$-0.839833\pi$
$211$	−0.296574	+	0.513681i	−0.0204170	+	0.0353633i	0.855636	+	0.517577i	$0.173166\pi$
$212$	−0.359787	−	0.623169i	−0.0247102	−	0.0427994i
$213$	−3.63212	+	20.5988i	−0.248869	+	1.41141i
$214$	1.39321	−	2.41310i	0.0952376	−	0.164956i
$215$	−10.9022	−	3.96808i	−0.743524	−	0.270621i
$216$	1.42561			0.0970005
$217$	3.64828	+	1.32787i	0.247662	+	0.0901415i
$218$	−3.49751	−	19.8354i	−0.236882	−	1.34342i
$219$	−0.291396	+	0.244510i	−0.0196907	+	0.0165225i
$220$	3.97348	+	3.33415i	0.267892	+	0.224788i
$221$	−25.1551			−1.69212
$222$	15.0791	+	3.90144i	1.01204	+	0.261848i
$223$	15.8884			1.06397			0.531983	−	0.846755i	$-0.321447\pi$
$223$	15.8884			1.06397			0.531983	+	0.846755i	$0.321447\pi$
$224$	0.945076	+	0.793013i	0.0631455	+	0.0529854i
$225$	2.72463	−	2.28623i	0.181642	−	0.152415i
$226$	−0.740230	−	4.19805i	−0.0492393	−	0.279250i
$227$	0.182449	+	0.0664061i	0.0121096	+	0.00440753i	0.348068	−	0.937469i	$-0.386838\pi$
$227$	0.182449	+	0.0664061i	0.0121096	+	0.00440753i	−0.335958	+	0.941877i	$0.609060\pi$
$228$	16.0621			1.06374
$229$	−26.3821	−	9.60230i	−1.74338	−	0.634538i	−0.743946	−	0.668240i	$-0.767048\pi$
$229$	−26.3821	−	9.60230i	−1.74338	−	0.634538i	−0.999432	+	0.0337020i	$0.989270\pi$
$230$	0.104526	−	0.181044i	0.00689224	−	0.0119377i
$231$	−2.84541	+	16.1371i	−0.187214	+	1.06174i
$232$	2.63740	+	4.56812i	0.173154	+	0.299912i
$233$	5.31591	−	9.20742i	0.348257	−	0.603198i	−0.637683	−	0.770299i	$-0.720107\pi$
$233$	5.31591	−	9.20742i	0.348257	−	0.603198i	0.985940	+	0.167101i	$0.0534405\pi$
$234$	−14.4807	−	12.1507i	−0.946632	−	0.794319i
$235$	1.61021	+	9.13193i	0.105038	+	0.595701i
$236$	4.14854	+	7.18548i	0.270047	+	0.467735i
$237$	−7.75366	+	2.82210i	−0.503655	+	0.183315i
$238$	5.48710	−	1.99714i	0.355676	−	0.129455i
$239$	2.33920	−	13.2663i	0.151310	−	0.858124i	−0.810771	−	0.585363i	$-0.800952\pi$
$239$	2.33920	−	13.2663i	0.151310	−	0.858124i	0.962082	−	0.272761i	$-0.0879369\pi$
$240$	1.96154	−	1.64593i	0.126617	−	0.106244i
$241$	21.8597	−	18.3425i	1.40811	−	1.18154i	0.450748	−	0.892651i	$-0.351157\pi$
$241$	21.8597	−	18.3425i	1.40811	−	1.18154i	0.957361	−	0.288893i	$-0.0932871\pi$
$242$	−2.76190	+	15.6635i	−0.177542	+	1.00689i
$243$	−20.9099	+	7.61057i	−1.34137	+	0.488218i
$244$	−7.90597	+	2.87754i	−0.506128	+	0.184216i
$245$	−2.73898	−	4.74406i	−0.174987	−	0.303087i
$246$	1.98603	+	11.2633i	0.126624	+	0.718123i
$247$	−25.5385	−	21.4294i	−1.62498	−	1.36352i
$248$	1.57348	−	2.72534i	0.0999159	−	0.173059i
$249$	4.90657	+	8.49843i	0.310941	+	0.538566i
$250$	0.173648	−	0.984808i	0.0109825	−	0.0622847i
$251$	−14.6985	+	25.4586i	−0.927764	+	1.60693i	−0.140709	+	0.990051i	$0.544938\pi$
$251$	−14.6985	+	25.4586i	−0.927764	+	1.60693i	−0.787055	+	0.616883i	$0.788395\pi$
$252$	4.12336	+	1.50078i	0.259747	+	0.0945402i
$253$	1.08436			0.0681729
$254$	−6.02529	−	2.19303i	−0.378061	−	0.137603i
$255$	−2.10455	−	11.9355i	−0.131792	−	0.747429i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−17.1169	−	14.3628i	−1.06772	−	0.895924i	−0.0728768	−	0.997341i	$-0.523218\pi$
$257$	−17.1169	−	14.3628i	−1.06772	−	0.895924i	−0.994844	+	0.101417i	$0.967662\pi$
$258$	−29.7079			−1.84954
$259$	6.18408	+	4.25118i	0.384260	+	0.264155i
$260$	−5.31474			−0.329606
$261$	14.3719	+	12.0594i	0.889597	+	0.746460i
$262$	1.26136	−	1.05841i	0.0779273	−	0.0653887i
$263$	0.300098	+	1.70194i	0.0185048	+	0.104946i	0.992661	−	0.120928i	$-0.0385872\pi$
$263$	0.300098	+	1.70194i	0.0185048	+	0.104946i	−0.974156	+	0.225875i	$0.927476\pi$
$264$	12.4809	+	4.54269i	0.768149	+	0.279583i
$265$	−0.719573			−0.0442030
$266$	7.27207	+	2.64682i	0.445879	+	0.162287i
$267$	−12.8117	+	22.1905i	−0.784064	+	1.35804i
$268$	2.20474	−	12.5037i	0.134676	−	0.763786i
$269$	7.47806	+	12.9524i	0.455945	+	0.789720i	0.998742	−	0.0501438i	$-0.0159679\pi$
$269$	7.47806	+	12.9524i	0.455945	+	0.789720i	−0.542797	+	0.839864i	$0.682635\pi$
$270$	0.712805	−	1.23461i	0.0433799	−	0.0751362i
$271$	7.99367	+	6.70749i	0.485581	+	0.407451i	0.852439	−	0.522826i	$-0.175122\pi$
$271$	7.99367	+	6.70749i	0.485581	+	0.407451i	−0.366859	+	0.930277i	$0.619567\pi$
$272$	−0.821891	−	4.66118i	−0.0498345	−	0.282625i
$273$	−8.39478	−	14.5402i	−0.508075	−	0.880012i
$274$	−13.8282	+	5.03307i	−0.835395	+	0.304059i
$275$	4.87420	−	1.77406i	0.293925	−	0.106980i
$276$	0.0929541	−	0.527169i	0.00559518	−	0.0317319i
$277$	−2.30168	+	1.93134i	−0.138294	+	0.116043i	−0.709311	−	0.704896i	$-0.750994\pi$
$277$	−2.30168	+	1.93134i	−0.138294	+	0.116043i	0.571016	+	0.820939i	$0.306549\pi$
$278$	12.2377	−	10.2687i	0.733969	−	0.615873i
$279$	1.94363	−	11.0229i	0.116362	−	0.659922i
$280$	1.15931	−	0.421953i	0.0692818	−	0.0252165i
$281$	3.33230	−	1.21286i	0.198788	−	0.0723530i	−0.240707	−	0.970598i	$-0.577379\pi$
$281$	3.33230	−	1.21286i	0.198788	−	0.0723530i	0.439496	+	0.898245i	$0.355157\pi$
$282$	11.8720	+	20.5630i	0.706969	+	1.22451i
$283$	−2.40182	−	13.6214i	−0.142774	−	0.809709i	−0.969128	−	0.246558i	$-0.920700\pi$
$283$	−2.40182	−	13.6214i	−0.142774	−	0.809709i	0.826354	−	0.563150i	$-0.190411\pi$
$284$	6.25749	+	5.25066i	0.371314	+	0.311569i
$285$	8.03107	−	13.9102i	0.475720	−	0.823971i
$286$	−13.7838	−	23.8743i	−0.815055	−	1.41172i
$287$	−0.956872	+	5.42669i	−0.0564823	+	0.320327i
$288$	1.77837	−	3.08023i	0.104792	−	0.181504i
$289$	−5.07629	−	1.84762i	−0.298606	−	0.108684i
$290$	5.27481			0.309747
$291$	8.81121	+	3.20702i	0.516522	+	0.187999i
$292$	0.0257962	+	0.146298i	0.00150961	+	0.00856142i
$293$	−16.4592	+	13.8109i	−0.961554	+	0.806840i	−0.981205	−	0.192967i	$-0.938189\pi$
$293$	−16.4592	+	13.8109i	−0.961554	+	0.806840i	0.0196511	+	0.999807i	$0.493744\pi$
$294$	−10.7453	−	9.01635i	−0.626677	−	0.525844i
$295$	8.29708			0.483075
$296$	4.26393	−	4.33807i	0.247836	−	0.252145i
$297$	7.39466			0.429082
$298$	−10.0883	−	8.46510i	−0.584400	−	0.490370i
$299$	−0.851120	+	0.714174i	−0.0492215	+	0.0413018i
$300$	−0.444646	−	2.52171i	−0.0256716	−	0.145591i
$301$	−13.4501	−	4.89545i	−0.775253	−	0.282169i
$302$	7.20215			0.414437
$303$	37.1567	+	13.5240i	2.13460	+	0.776931i
$304$	3.13639	−	5.43238i	0.179884	−	0.311568i
$305$	−1.46096	+	8.28554i	−0.0836546	+	0.474429i
$306$	−8.41719	−	14.5790i	−0.481179	−	0.833426i
$307$	−6.54385	+	11.3343i	−0.373477	+	0.646881i	−0.990098	−	0.140379i	$-0.955168\pi$
$307$	−6.54385	+	11.3343i	−0.373477	+	0.646881i	0.616621	+	0.787260i	$0.288501\pi$
$308$	4.90212	+	4.11337i	0.279324	+	0.234381i
$309$	−1.09478	−	6.20882i	−0.0622800	−	0.353207i
$310$	−1.57348	−	2.72534i	−0.0893675	−	0.154789i
$311$	1.41780	−	0.516038i	0.0803962	−	0.0292618i	−0.301509	−	0.953463i	$-0.597490\pi$
$311$	1.41780	−	0.516038i	0.0803962	−	0.0292618i	0.381905	+	0.924202i	$0.375268\pi$
$312$	−12.7883	+	4.65456i	−0.723994	+	0.263512i
$313$	5.38544	−	30.5423i	0.304403	−	1.72635i	−0.321899	−	0.946774i	$-0.604321\pi$
$313$	5.38544	−	30.5423i	0.304403	−	1.72635i	0.626302	−	0.779581i	$-0.284568\pi$
$314$	0.561810	−	0.471414i	0.0317047	−	0.0266034i
$315$	3.36139	−	2.82054i	0.189393	−	0.158920i
$316$	−0.559561	+	3.17343i	−0.0314777	+	0.178519i
$317$	4.88872	−	1.77935i	0.274578	−	0.0999382i	−0.201061	−	0.979579i	$-0.564439\pi$
$317$	4.88872	−	1.77935i	0.274578	−	0.0999382i	0.475639	+	0.879640i	$0.342217\pi$
$318$	−1.73143	+	0.630189i	−0.0970938	+	0.0353392i
$319$	13.6803	+	23.6949i	0.765947	+	1.32666i
$320$	−0.173648	−	0.984808i	−0.00970723	−	0.0550524i
$321$	−5.46567	−	4.58624i	−0.305064	−	0.255979i
$322$	0.128955	−	0.223356i	0.00718636	−	0.0124471i
$323$	−14.8448	−	25.7119i	−0.825985	−	1.43065i
$324$	−1.21898	+	6.91315i	−0.0677208	+	0.384064i
$325$	−2.65737	+	4.60270i	−0.147404	+	0.255312i
$326$	−10.5919	−	3.85515i	−0.586633	−	0.213517i
$327$	−51.5743			−2.85207
$328$	4.19717	+	1.52765i	0.231750	+	0.0843501i
$329$	1.98652	+	11.2661i	0.109521	+	0.621122i
$330$	10.1746	−	8.53747i	0.560091	−	0.469972i
$331$	−7.65843	−	6.42619i	−0.420945	−	0.353215i	0.407577	−	0.913171i	$-0.366374\pi$
$331$	−7.65843	−	6.42619i	−0.420945	−	0.353215i	−0.828523	+	0.559956i	$0.810818\pi$
$332$	3.83234			0.210327
$333$	8.97394	−	19.6859i	0.491769	−	1.07878i
$334$	−15.3206			−0.838304
$335$	−9.72617	−	8.16122i	−0.531397	−	0.445895i
$336$	2.41997	−	2.03060i	0.132020	−	0.110778i
$337$	4.15151	+	23.5444i	0.226147	+	1.28255i	0.860479	+	0.509485i	$0.170164\pi$
$337$	4.15151	+	23.5444i	0.226147	+	1.28255i	−0.634332	+	0.773061i	$0.718725\pi$
$338$	14.3270	+	5.21461i	0.779288	+	0.283638i
$339$	−10.9154			−0.592844
$340$	−4.44764	−	1.61881i	−0.241207	−	0.0877923i
$341$	8.16165	−	14.1364i	0.441978	−	0.765529i
$342$	3.87420	−	21.9717i	0.209493	−	1.18809i
$343$	−7.69708	−	13.3317i	−0.415604	−	0.719846i
$344$	−5.80094	+	10.0475i	−0.312766	+	0.541726i
$345$	−0.410065	−	0.344085i	−0.0220771	−	0.0185249i
$346$	2.33512	+	13.2431i	0.125537	+	0.711953i
$347$	−3.96705	−	6.87113i	−0.212962	−	0.368861i	0.739678	−	0.672961i	$-0.234978\pi$
$347$	−3.96705	−	6.87113i	−0.212962	−	0.368861i	−0.952640	+	0.304100i	$0.901644\pi$
$348$	12.6922	−	4.61958i	0.680373	−	0.247636i
$349$	14.4718	−	5.26731i	0.774658	−	0.281952i	0.0757146	−	0.997130i	$-0.475876\pi$
$349$	14.4718	−	5.26731i	0.774658	−	0.281952i	0.698943	+	0.715177i	$0.253654\pi$
$350$	0.214231	−	1.21497i	0.0114511	−	0.0649426i
$351$	−5.80413	+	4.87024i	−0.309802	+	0.259954i
$352$	3.97348	−	3.33415i	0.211787	−	0.177711i
$353$	1.46385	−	8.30193i	0.0779131	−	0.441867i	−0.920749	−	0.390155i	$-0.872421\pi$
$353$	1.46385	−	8.30193i	0.0779131	−	0.441867i	0.998662	−	0.0517115i	$-0.0164676\pi$
$354$	19.9643	−	7.26643i	1.06109	−	0.386206i
$355$	7.67595	−	2.79382i	0.407397	−	0.148280i
$356$	5.00338	+	8.66610i	0.265178	+	0.459303i
$357$	−2.59640	−	14.7249i	−0.137416	−	0.779324i
$358$	−13.7849	−	11.5669i	−0.728555	−	0.611330i
$359$	−5.98883	+	10.3730i	−0.316079	+	0.547464i	−0.979666	−	0.200634i	$-0.935700\pi$
$359$	−5.98883	+	10.3730i	−0.316079	+	0.547464i	0.663588	+	0.748099i	$0.269033\pi$
$360$	−1.77837	−	3.08023i	−0.0937285	−	0.162342i
$361$	3.53333	−	20.0385i	0.185965	−	1.05466i
$362$	−0.156608	+	0.271253i	−0.00823112	+	0.0142567i
$363$	38.2708	+	13.9294i	2.00870	+	0.731105i
$364$	−6.55685			−0.343672
$365$	0.139596	+	0.0508086i	0.00730676	+	0.00265944i
$366$	3.74097	+	21.2161i	0.195543	+	1.10898i
$367$	27.3321	−	22.9343i	1.42672	−	1.19716i	0.479106	−	0.877757i	$-0.340961\pi$
$367$	27.3321	−	22.9343i	1.42672	−	1.19716i	0.947618	−	0.319406i	$-0.103483\pi$
$368$	−0.160143	−	0.134376i	−0.00834804	−	0.00700484i
$369$	15.8863			0.827009
$370$	−1.62492	−	5.86171i	−0.0844754	−	0.304736i
$371$	−0.887744			−0.0460894
$372$	−6.17289	−	5.17967i	−0.320049	−	0.268553i
$373$	4.75384	−	3.98894i	0.246144	−	0.206540i	−0.511366	−	0.859363i	$-0.670860\pi$
$373$	4.75384	−	3.98894i	0.246144	−	0.206540i	0.757510	+	0.652824i	$0.226416\pi$
$374$	−4.26316	−	24.1776i	−0.220443	−	1.25019i
$375$	−2.40619	−	0.875782i	−0.124255	−	0.0452252i
$376$	9.27280			0.478208
$377$	−26.3436	−	9.58828i	−1.35676	−	0.493822i
$378$	0.879394	−	1.52315i	0.0452311	−	0.0783426i
$379$	2.51631	−	14.2707i	0.129254	−	0.733036i	−0.849436	−	0.527692i	$-0.823057\pi$
$379$	2.51631	−	14.2707i	0.129254	−	0.733036i	0.978690	−	0.205344i	$-0.0658314\pi$
$380$	−3.13639	−	5.43238i	−0.160893	−	0.278675i
$381$	−8.20931	+	14.2189i	−0.420576	+	0.728458i
$382$	10.2122	+	8.56908i	0.522503	+	0.438432i
$383$	−3.65503	−	20.7287i	−0.186763	−	1.05919i	−0.923669	−	0.383192i	$-0.874825\pi$
$383$	−3.65503	−	20.7287i	−0.186763	−	1.05919i	0.736905	−	0.675996i	$-0.236286\pi$
$384$	−1.28031	−	2.21756i	−0.0653354	−	0.113164i
$385$	6.01334	−	2.18868i	0.306468	−	0.111545i
$386$	−5.32076	+	1.93660i	−0.270820	+	0.0985703i
$387$	−7.16558	+	40.6380i	−0.364247	+	2.06575i
$388$	2.80517	−	2.35382i	0.142411	−	0.119497i
$389$	19.8340	−	16.6427i	1.00562	−	0.843817i	0.0178685	−	0.999840i	$-0.494312\pi$
$389$	19.8340	−	16.6427i	1.00562	−	0.843817i	0.987753	+	0.156023i	$0.0498675\pi$
$390$	−2.36318	+	13.4023i	−0.119664	+	0.678650i
$391$	−0.929789	+	0.338415i	−0.0470214	+	0.0171144i
$392$	−5.14760	+	1.87357i	−0.259993	+	0.0946298i
$393$	−2.10814	−	3.65141i	−0.106342	−	0.184189i
$394$	2.15265	+	12.2083i	0.108449	+	0.615045i
$395$	2.46849	+	2.07131i	0.124203	+	0.104219i
$396$	9.22445	−	15.9772i	0.463546	−	0.802885i
$397$	18.5033	+	32.0486i	0.928653	+	1.60847i	0.785578	+	0.618763i	$0.212366\pi$
$397$	18.5033	+	32.0486i	0.928653	+	1.60847i	0.143075	+	0.989712i	$0.454301\pi$
$398$	−3.75072	+	21.2714i	−0.188007	+	1.06624i
$399$	9.90800	−	17.1612i	0.496021	−	0.859133i
$400$	−0.939693	−	0.342020i	−0.0469846	−	0.0171010i
$401$	14.4053			0.719368			0.359684	−	0.933074i	$-0.382884\pi$
$401$	14.4053			0.719368			0.359684	+	0.933074i	$0.382884\pi$
$402$	−30.5505	−	11.1195i	−1.52372	−	0.554588i
$403$	2.90431	+	16.4712i	0.144674	+	0.820487i
$404$	11.8294	−	9.92602i	0.588533	−	0.493838i
$405$	5.37748	+	4.51224i	0.267209	+	0.224215i
$406$	6.50758			0.322966
$407$	22.1171	−	22.5017i	1.09630	−	1.11537i
$408$	−12.1196			−0.600010
$409$	25.8435	+	21.6853i	1.27788	+	1.07227i	0.993533	+	0.113546i	$0.0362209\pi$
$409$	25.8435	+	21.6853i	1.27788	+	1.07227i	0.284346	+	0.958722i	$0.408223\pi$
$410$	3.42157	−	2.87103i	0.168979	−	0.141790i
$411$	6.54328	+	37.1088i	0.322756	+	1.83044i
$412$	−2.31366	−	0.842103i	−0.113986	−	0.0414874i
$413$	10.2362			0.503689
$414$	−0.698704	−	0.254307i	−0.0343394	−	0.0124985i
$415$	1.91617	−	3.31890i	0.0940610	−	0.162919i
$416$	−0.922896	+	5.23400i	−0.0452487	+	0.256618i
$417$	−20.4532	−	35.4259i	−1.00160	−	1.73481i
$418$	16.2685	−	28.1778i	0.795717	−	1.37822i
$419$	−30.2096	−	25.3489i	−1.47584	−	1.23837i	−0.910498	−	0.413513i	$-0.864302\pi$
$419$	−30.2096	−	25.3489i	−1.47584	−	1.23837i	−0.565337	−	0.824860i	$-0.691254\pi$
$420$	−0.548564	−	3.11106i	−0.0267672	−	0.151804i
$421$	1.02550	+	1.77622i	0.0499798	+	0.0865675i	0.889933	−	0.456091i	$-0.150751\pi$
$421$	1.02550	+	1.77622i	0.0499798	+	0.0865675i	−0.839953	+	0.542659i	$0.817418\pi$
$422$	0.557377	−	0.202868i	0.0271327	−	0.00987548i
$423$	30.9920	−	11.2802i	1.50688	−	0.548460i
$424$	−0.124953	+	0.708641i	−0.00606823	+	0.0344147i
$425$	−3.62575	+	3.04237i	−0.175875	+	0.147576i
$426$	16.0230	−	13.4449i	0.776318	−	0.651408i
$427$	−1.80240	+	10.2219i	−0.0872245	+	0.494675i
$428$	−2.61837	+	0.953009i	−0.126564	+	0.0460654i
$429$	−66.3331	+	24.1433i	−3.20259	+	1.16565i
$430$	5.80094	+	10.0475i	0.279746	+	0.484535i
$431$	2.35103	+	13.3334i	0.113245	+	0.642246i	0.987604	+	0.156966i	$0.0501713\pi$
$431$	2.35103	+	13.3334i	0.113245	+	0.642246i	−0.874359	+	0.485280i	$0.838718\pi$
$432$	−1.09208	−	0.916365i	−0.0525428	−	0.0440886i
$433$	−13.5422	+	23.4558i	−0.650796	+	1.12721i	0.332134	+	0.943232i	$0.392231\pi$
$433$	−13.5422	+	23.4558i	−0.650796	+	1.12721i	−0.982930	+	0.183980i	$0.941102\pi$
$434$	−1.94121	−	3.36228i	−0.0931811	−	0.161394i
$435$	2.34542	−	13.3016i	0.112454	−	0.637761i
$436$	−10.0707	+	17.4430i	−0.482299	+	0.835366i
$437$	−1.23225	−	0.448503i	−0.0589466	−	0.0214548i
$438$	0.380391			0.0181758
$439$	−21.0506	−	7.66180i	−1.00469	−	0.365678i	−0.213299	−	0.976987i	$-0.568421\pi$
$439$	−21.0506	−	7.66180i	−1.00469	−	0.365678i	−0.791392	+	0.611309i	$0.790643\pi$
$440$	−0.900716	−	5.10821i	−0.0429399	−	0.243525i
$441$	−14.9254	+	12.5239i	−0.710733	+	0.596376i
$442$	19.2699	+	16.1694i	0.916578	+	0.769100i
$443$	8.87936			0.421871			0.210936	−	0.977500i	$-0.432349\pi$
$443$	8.87936			0.421871			0.210936	+	0.977500i	$0.432349\pi$
$444$	−9.04344	−	12.6813i	−0.429183	−	0.601829i
$445$	10.0068			0.474366
$446$	−12.1712	−	10.2129i	−0.576324	−	0.483593i
$447$	−25.8323	+	21.6759i	−1.22182	+	1.02523i
$448$	−0.214231	−	1.21497i	−0.0101215	−	0.0574017i
$449$	1.91474	+	0.696910i	0.0903624	+	0.0328892i	0.386806	−	0.922161i	$-0.373578\pi$
$449$	1.91474	+	0.696910i	0.0903624	+	0.0328892i	−0.296443	+	0.955050i	$0.595801\pi$
$450$	−3.55675			−0.167667
$451$	21.7708	+	7.92392i	1.02515	+	0.373123i
$452$	−2.13141	+	3.69170i	−0.100253	+	0.173643i
$453$	3.20241	−	18.1617i	0.150462	−	0.853313i
$454$	−0.0970793	−	0.168146i	−0.00455616	−	0.00789149i
$455$	−3.27842	+	5.67839i	−0.153695	+	0.266207i
$456$	−12.3043	−	10.3245i	−0.576202	−	0.483491i
$457$	2.63244	+	14.9293i	0.123140	+	0.698364i	0.982395	+	0.186816i	$0.0598167\pi$
$457$	2.63244	+	14.9293i	0.123140	+	0.698364i	−0.859255	+	0.511548i	$0.829072\pi$
$458$	14.0376	+	24.3139i	0.655935	+	1.13611i
$459$	−6.34061	+	2.30779i	−0.295954	+	0.107718i
$460$	−0.196445	+	0.0715000i	−0.00915928	+	0.00333370i
$461$	2.73767	−	15.5261i	0.127506	−	0.723122i	−0.852282	−	0.523083i	$-0.824782\pi$
$461$	2.73767	−	15.5261i	0.127506	−	0.723122i	0.979788	−	0.200039i	$-0.0641070\pi$
$462$	12.5524	−	10.5328i	0.583993	−	0.490028i
$463$	−23.1635	+	19.4365i	−1.07650	+	0.903289i	−0.995625	−	0.0934355i	$-0.970215\pi$
$463$	−23.1635	+	19.4365i	−1.07650	+	0.903289i	−0.0808725	+	0.996724i	$0.525771\pi$
$464$	0.915961	−	5.19467i	0.0425224	−	0.241157i
$465$	−7.57217	+	2.75604i	−0.351151	+	0.127808i
$466$	−9.99063	+	3.63629i	−0.462807	+	0.168448i
$467$	12.7541	+	22.0907i	0.590187	+	1.02223i	0.994207	+	0.107484i	$0.0342795\pi$
$467$	12.7541	+	22.0907i	0.590187	+	1.02223i	−0.404019	+	0.914750i	$0.632387\pi$
$468$	3.28251	+	18.6160i	0.151734	+	0.860525i
$469$	−11.9993	−	10.0686i	−0.554074	−	0.464923i
$470$	4.63640	−	8.03048i	0.213861	−	0.370419i
$471$	−0.938965	−	1.62633i	−0.0432652	−	0.0749376i
$472$	1.44077	−	8.17103i	0.0663169	−	0.376102i
$473$	−30.0896	+	52.1167i	−1.38352	+	2.39633i
$474$	7.75366	+	2.82210i	0.356138	+	0.129623i
$475$	−6.27277			−0.287814
$476$	−5.48710	−	1.99714i	−0.251501	−	0.0915387i
$477$	0.444425	+	2.52046i	0.0203488	+	0.115404i
$478$	−10.3193	+	8.65895i	−0.471995	+	0.396051i
$479$	0.539694	+	0.452857i	0.0246592	+	0.0206916i	0.655034	−	0.755599i	$-0.272654\pi$
$479$	0.539694	+	0.452857i	0.0246592	+	0.0206916i	−0.630375	+	0.776291i	$0.717099\pi$
$480$	−2.56061			−0.116876
$481$	−2.53992	+	32.2284i	−0.115810	+	1.46949i
$482$	−28.5359			−1.29977
$483$	−0.505900	−	0.424501i	−0.0230193	−	0.0193155i
$484$	12.1840	−	10.2236i	0.553820	−	0.464710i
$485$	−0.635881	−	3.60626i	−0.0288739	−	0.163752i
$486$	20.9099	+	7.61057i	0.948491	+	0.345223i
$487$	38.2000			1.73101			0.865503	−	0.500904i	$-0.166999\pi$
$487$	38.2000			1.73101			0.865503	+	0.500904i	$0.166999\pi$
$488$	7.90597	+	2.87754i	0.357887	+	0.130260i
$489$	−14.4312	+	24.9956i	−0.652603	+	1.13034i
$490$	−0.951238	+	5.39474i	−0.0429726	+	0.243710i
$491$	−8.22378	−	14.2440i	−0.371134	−	0.642823i	0.618606	−	0.785701i	$-0.287698\pi$
$491$	−8.22378	−	14.2440i	−0.371134	−	0.642823i	−0.989740	+	0.142878i	$0.954364\pi$
$492$	5.71854	−	9.90480i	0.257812	−	0.446543i
$493$	−19.1251	−	16.0479i	−0.861353	−	0.722761i
$494$	5.78911	+	32.8317i	0.260465	+	1.47717i
$495$	−9.22445	−	15.9772i	−0.414608	−	0.718122i
$496$	−2.95717	+	1.07632i	−0.132781	+	0.0483283i
$497$	9.46988	−	3.44675i	0.424782	−	0.154608i
$498$	1.70403	−	9.66406i	0.0763596	−	0.433057i
$499$	−0.191593	+	0.160766i	−0.00857689	+	0.00719687i	−0.647066	−	0.762434i	$-0.724004\pi$
$499$	−0.191593	+	0.160766i	−0.00857689	+	0.00719687i	0.638489	+	0.769631i	$0.279560\pi$
$500$	−0.766044	+	0.642788i	−0.0342585	+	0.0287463i
$501$	−6.81223	+	38.6341i	−0.304348	+	1.72604i
$502$	27.6242	−	10.0544i	1.23293	−	0.448750i
$503$	−19.6548	+	7.15377i	−0.876365	+	0.318971i	−0.740742	−	0.671790i	$-0.765526\pi$
$503$	−19.6548	+	7.15377i	−0.876365	+	0.318971i	−0.135623	+	0.990760i	$0.543304\pi$
$504$	−2.19399	−	3.80011i	−0.0977282	−	0.169270i
$505$	−2.68150	−	15.2075i	−0.119325	−	0.676727i
$506$	−0.830665	−	0.697011i	−0.0369276	−	0.0309859i
$507$	19.5202	−	33.8100i	0.866923	−	1.50156i
$508$	3.20599	+	5.55294i	0.142243	+	0.246372i
$509$	−2.31984	+	13.1565i	−0.102825	+	0.583150i	0.889242	+	0.457438i	$0.151233\pi$
$509$	−2.31984	+	13.1565i	−0.102825	+	0.583150i	−0.992067	+	0.125712i	$0.959878\pi$
$510$	−6.05980	+	10.4959i	−0.268332	+	0.464765i
$511$	0.172220	+	0.0626830i	0.00761857	+	0.00277293i
$512$	−1.00000			−0.0441942
$513$	−8.40322	−	3.05852i	−0.371011	−	0.135037i
$514$	3.88008	+	22.0050i	0.171143	+	0.970600i
$515$	−1.88611	+	1.58264i	−0.0831120	+	0.0697393i
$516$	22.7576	+	19.0959i	1.00185	+	0.840650i
$517$	48.0982			2.11536
$518$	−2.00467	−	7.23164i	−0.0880803	−	0.317740i
$519$	34.4336			1.51147
$520$	4.07133	+	3.41625i	0.178540	+	0.149813i
$521$	−7.60639	+	6.38252i	−0.333242	+	0.279623i	−0.794019	−	0.607893i	$-0.792015\pi$
$521$	−7.60639	+	6.38252i	−0.333242	+	0.279623i	0.460777	+	0.887516i	$0.347571\pi$
$522$	−3.25784	−	18.4761i	−0.142592	−	0.808678i
$523$	6.70570	+	2.44067i	0.293220	+	0.106723i	0.484442	−	0.874824i	$-0.339023\pi$
$523$	6.70570	+	2.44067i	0.293220	+	0.106723i	−0.191222	+	0.981547i	$0.561245\pi$
$524$	−1.64659			−0.0719317
$525$	−2.96854	−	1.08046i	−0.129558	−	0.0471551i
$526$	0.864097	−	1.49666i	0.0376764	−	0.0652575i
$527$	−2.58645	+	14.6685i	−0.112668	+	0.638970i
$528$	−6.64097	−	11.5025i	−0.289011	−	0.500582i
$529$	11.4781	−	19.8807i	0.499050	−	0.864380i
$530$	0.551225	+	0.462533i	0.0239437	+	0.0200911i
$531$	−5.12446	−	29.0623i	−0.222383	−	1.26119i
$532$	−3.86939	−	6.70197i	−0.167759	−	0.290567i
$533$	−22.3069	+	8.11905i	−0.966219	+	0.351675i
$534$	24.0782	−	8.76373i	1.04196	−	0.379244i
$535$	−0.483855	+	2.74408i	−0.0209189	+	0.118637i
$536$	−9.72617	+	8.16122i	−0.420107	+	0.352511i
$537$	−35.2978	+	29.6184i	−1.52321	+	1.27813i
$538$	2.59710	−	14.7289i	0.111969	−	0.635008i
$539$	−26.7007	+	9.71826i	−1.15008	+	0.418595i
$540$	−1.33964	+	0.487587i	−0.0576487	+	0.0209824i
$541$	−0.0854817	−	0.148059i	−0.00367515	−	0.00636554i	0.864182	−	0.503179i	$-0.167837\pi$
$541$	−0.0854817	−	0.148059i	−0.00367515	−	0.00636554i	−0.867857	+	0.496814i	$0.834503\pi$
$542$	−1.81202	−	10.2765i	−0.0778328	−	0.441412i
$543$	0.614386	+	0.515531i	0.0263658	+	0.0221236i
$544$	−2.36654	+	4.09897i	−0.101465	+	0.175742i
$545$	10.0707	+	17.4430i	0.431381	+	0.747174i
$546$	−2.91548	+	16.5345i	−0.124771	+	0.707610i
$547$	−15.1096	+	26.1705i	−0.646038	+	1.11897i	0.338023	+	0.941138i	$0.390242\pi$
$547$	−15.1096	+	26.1705i	−0.646038	+	1.11897i	−0.984061	+	0.177832i	$0.943091\pi$
$548$	13.8282	+	5.03307i	0.590713	+	0.215002i
$549$	29.9242			1.27713
$550$	−4.87420	−	1.77406i	−0.207837	−	0.0756463i
$551$	−5.74561	−	32.5850i	−0.244771	−	1.38817i
$552$	−0.410065	+	0.344085i	−0.0174535	+	0.0146452i
$553$	3.04539	+	2.55539i	0.129503	+	0.108666i
$554$	3.00463			0.127654
$555$	−15.5041	+	1.49119i	−0.658111	+	0.0632974i
$556$	−15.9752			−0.677499
$557$	−21.8629	−	18.3452i	−0.926363	−	0.777311i	0.0487981	−	0.998809i	$-0.484461\pi$
$557$	−21.8629	−	18.3452i	−0.926363	−	0.777311i	−0.975161	+	0.221498i	$0.928905\pi$
$558$	−8.57427	+	7.19467i	−0.362978	+	0.304574i
$559$	−10.7073	−	60.7243i	−0.452872	−	2.56836i
$560$	−1.15931	−	0.421953i	−0.0489897	−	0.0178308i
$561$	−62.8646			−2.65414
$562$	−3.33230	−	1.21286i	−0.140564	−	0.0511613i
$563$	20.8304	−	36.0792i	0.877895	−	1.52056i	0.0242485	−	0.999706i	$-0.492281\pi$
$563$	20.8304	−	36.0792i	0.877895	−	1.52056i	0.853646	−	0.520853i	$-0.174386\pi$
$564$	4.12311	−	23.3833i	0.173614	−	0.984616i
$565$	2.13141	+	3.69170i	0.0896689	+	0.155311i
$566$	−6.91577	+	11.9785i	−0.290692	+	0.503493i
$567$	6.63424	+	5.56679i	0.278612	+	0.233783i
$568$	−1.41846	−	8.04447i	−0.0595172	−	0.337539i
$569$	−7.22157	−	12.5081i	−0.302744	−	0.524368i	0.674013	−	0.738720i	$-0.264569\pi$
$569$	−7.22157	−	12.5081i	−0.302744	−	0.524368i	−0.976756	+	0.214352i	$0.931236\pi$
$570$	−15.0935	+	5.49358i	−0.632196	+	0.230101i
$571$	1.18862	−	0.432622i	0.0497422	−	0.0181047i	−0.317029	−	0.948416i	$-0.602685\pi$
$571$	1.18862	−	0.432622i	0.0497422	−	0.0181047i	0.366771	+	0.930311i	$0.380463\pi$
$572$	−4.78708	+	27.1489i	−0.200158	+	1.13515i
$573$	26.1496	−	21.9421i	1.09241	−	0.916644i
$574$	4.22121	−	3.54202i	0.176190	−	0.147841i
$575$	−0.0363015	+	0.205876i	−0.00151388	+	0.00858562i
$576$	−3.34225	+	1.21648i	−0.139260	+	0.0506866i
$577$	−29.1827	+	10.6216i	−1.21489	+	0.442185i	−0.868399	−	0.495867i	$-0.834850\pi$
$577$	−29.1827	+	10.6216i	−1.21489	+	0.442185i	−0.346495	+	0.938052i	$0.612628\pi$
$578$	2.70104	+	4.67834i	0.112348	+	0.194593i
$579$	2.51769	+	14.2785i	0.104632	+	0.593396i
$580$	−4.04074	−	3.39058i	−0.167782	−	0.140786i
$581$	2.36399	−	4.09456i	0.0980750	−	0.169871i
$582$	−4.68835	−	8.12045i	−0.194338	−	0.336604i
$583$	−0.648131	+	3.67573i	−0.0268428	+	0.152233i
$584$	0.0742772	−	0.128652i	0.00307361	−	0.00532365i
$585$	17.7632	+	6.46527i	0.734418	+	0.267306i
$586$	21.4859			0.887574
$587$	21.1947	+	7.71425i	0.874800	+	0.318401i	0.740109	−	0.672487i	$-0.234774\pi$
$587$	21.1947	+	7.71425i	0.874800	+	0.318401i	0.134690	+	0.990888i	$0.456996\pi$
$588$	2.43575	+	13.8139i	0.100449	+	0.569674i
$589$	−15.1218	+	12.6887i	−0.623083	+	0.522829i
$590$	−6.35593	−	5.33326i	−0.261669	−	0.219567i
$591$	31.7430			1.30573
$592$	−6.05482	+	0.582356i	−0.248852	+	0.0239347i
$593$	8.95667			0.367807			0.183903	−	0.982944i	$-0.441127\pi$
$593$	8.95667			0.367807			0.183903	+	0.982944i	$0.441127\pi$
$594$	−5.66464	−	4.75320i	−0.232423	−	0.195026i
$595$	−4.47312	+	3.75339i	−0.183380	+	0.153874i
$596$	2.28683	+	12.9693i	0.0936724	+	0.531243i
$597$	51.9726	+	18.9165i	2.12710	+	0.774200i
$598$	1.11106			0.0454345
$599$	36.5749	+	13.3122i	1.49441	+	0.543921i	0.954607	−	0.297869i	$-0.0962757\pi$
$599$	36.5749	+	13.3122i	1.49441	+	0.543921i	0.539805	+	0.841790i	$0.318498\pi$
$600$	−1.28031	+	2.21756i	−0.0522683	+	0.0905314i
$601$	−3.44190	+	19.5200i	−0.140398	+	0.796237i	0.830549	+	0.556945i	$0.188027\pi$
$601$	−3.44190	+	19.5200i	−0.140398	+	0.796237i	−0.970948	+	0.239292i	$0.923085\pi$
$602$	7.15667	+	12.3957i	0.291684	+	0.505212i
$603$	−22.5793	+	39.1085i	−0.919500	+	1.59262i
$604$	−5.51716	−	4.62945i	−0.224490	−	0.188370i
$605$	−2.76190	−	15.6635i	−0.112287	−	0.636812i
$606$	−19.7707	−	34.2438i	−0.803129	−	1.39106i
$607$	4.73454	−	1.72323i	0.192169	−	0.0699438i	−0.244143	−	0.969739i	$-0.578507\pi$
$607$	4.73454	−	1.72323i	0.192169	−	0.0699438i	0.436312	+	0.899795i	$0.356284\pi$
$608$	−5.89448	+	2.14541i	−0.239053	+	0.0870080i
$609$	2.89357	−	16.4102i	0.117253	−	0.664976i
$610$	6.44501	−	5.40800i	0.260951	−	0.218964i
$611$	−37.7526	+	31.6782i	−1.52731	+	1.28156i
$612$	−2.92326	+	16.5786i	−0.118166	+	0.670151i
$613$	31.5968	−	11.5003i	1.27618	−	0.464493i	0.387016	−	0.922073i	$-0.373506\pi$
$613$	31.5968	−	11.5003i	1.27618	−	0.464493i	0.889168	+	0.457580i	$0.151284\pi$
$614$	12.2984	−	4.47625i	0.496323	−	0.180647i
$615$	−5.71854	−	9.90480i	−0.230594	−	0.399400i
$616$	−1.11122	−	6.30205i	−0.0447724	−	0.253917i
$617$	−2.44482	−	2.05145i	−0.0984248	−	0.0825882i	0.592247	−	0.805756i	$-0.298241\pi$
$617$	−2.44482	−	2.05145i	−0.0984248	−	0.0825882i	−0.690672	+	0.723168i	$0.742685\pi$
$618$	−3.15230	+	5.45994i	−0.126804	+	0.219631i
$619$	3.73169	+	6.46348i	0.149989	+	0.259789i	0.931223	−	0.364449i	$-0.118743\pi$
$619$	3.73169	+	6.46348i	0.149989	+	0.259789i	−0.781234	+	0.624238i	$0.785409\pi$
$620$	−0.546463	+	3.09914i	−0.0219465	+	0.124465i
$621$	−0.149013	+	0.258099i	−0.00597970	+	0.0103571i
$622$	−1.41780	−	0.516038i	−0.0568487	−	0.0206912i
$623$	12.3454			0.494609
$624$	12.7883	+	4.65456i	0.511941	+	0.186331i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	−23.7577	+	19.9351i	−0.949549	+	0.796767i
$627$	−63.8227	−	53.5536i	−2.54883	−	2.13872i
$628$	−0.733390			−0.0292655
$629$	−11.9419	+	26.1967i	−0.476156	+	1.04453i
$630$	−4.38799			−0.174822
$631$	34.1017	+	28.6147i	1.35757	+	1.13913i	0.976725	+	0.214493i	$0.0688101\pi$
$631$	34.1017	+	28.6147i	1.35757	+	1.13913i	0.380841	+	0.924640i	$0.375634\pi$
$632$	2.46849	−	2.07131i	0.0981912	−	0.0823922i
$633$	−0.263741	−	1.49575i	−0.0104828	−	0.0594507i
$634$	−4.88872	−	1.77935i	−0.194156	−	0.0706670i
$635$	6.41198			0.254452
$636$	1.73143	+	0.630189i	0.0686557	+	0.0249886i
$637$	14.5570	−	25.2134i	0.576769	−	0.998993i
$638$	4.75110	−	26.9448i	0.188098	−	1.06676i
$639$	−14.5268	−	25.1611i	−0.574670	−	0.995357i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−14.1068	−	11.8370i	−0.557185	−	0.467534i	0.320180	−	0.947357i	$-0.396256\pi$
$641$	−14.1068	−	11.8370i	−0.557185	−	0.467534i	−0.877365	+	0.479823i	$0.840701\pi$
$642$	1.23897	+	7.02653i	0.0488981	+	0.277315i
$643$	20.6846	+	35.8269i	0.815723	+	1.41287i	0.908808	+	0.417215i	$0.136994\pi$
$643$	20.6846	+	35.8269i	0.815723	+	1.41287i	−0.0930847	+	0.995658i	$0.529673\pi$
$644$	−0.242355	+	0.0882102i	−0.00955014	+	0.00347597i
$645$	27.9163	−	10.1607i	1.09920	−	0.400078i
$646$	−5.15554	+	29.2385i	−0.202842	+	1.15037i
$647$	28.2040	−	23.6660i	1.10881	−	0.930405i	0.110828	−	0.993840i	$-0.464650\pi$
$647$	28.2040	−	23.6660i	1.10881	−	0.930405i	0.997986	+	0.0634343i	$0.0202053\pi$
$648$	5.37748	−	4.51224i	0.211247	−	0.177258i
$649$	7.47331	−	42.3832i	0.293353	−	1.66369i
$650$	4.99423	−	1.81775i	0.195890	−	0.0712980i
$651$	−9.34185	+	3.40016i	−0.366136	+	0.133263i
$652$	5.63585	+	9.76157i	0.220717	+	0.382293i
$653$	−5.41184	−	30.6921i	−0.211782	−	1.20107i	−0.886404	−	0.462912i	$-0.846805\pi$
$653$	−5.41184	−	30.6921i	−0.211782	−	1.20107i	0.674623	−	0.738163i	$-0.264306\pi$
$654$	39.5082	+	33.1513i	1.54489	+	1.29632i
$655$	−0.823296	+	1.42599i	−0.0321688	+	0.0557181i
$656$	−2.23327	−	3.86813i	−0.0871945	−	0.151025i
$657$	0.0917505	−	0.520343i	0.00357953	−	0.0203005i
$658$	5.71997	−	9.90727i	0.222988	−	0.386226i
$659$	31.8800	+	11.6034i	1.24187	+	0.452003i	0.877646	−	0.479309i	$-0.159113\pi$
$659$	31.8800	+	11.6034i	1.24187	+	0.452003i	0.364222	+	0.931312i	$0.381335\pi$
$660$	−13.2819			−0.516999
$661$	−32.3769	−	11.7842i	−1.25931	−	0.458353i	−0.375775	−	0.926711i	$-0.622624\pi$
$661$	−32.3769	−	11.7842i	−1.25931	−	0.458353i	−0.883539	+	0.468358i	$0.844846\pi$
$662$	1.73603	+	9.84549i	0.0674726	+	0.382656i
$663$	49.3429	−	41.4036i	1.91632	−	1.60798i
$664$	−2.93574	−	2.46338i	−0.113929	−	0.0955977i
$665$	−7.73877			−0.300097
$666$	−19.5283	+	9.31194i	−0.756706	+	0.360830i
$667$	−1.10271			−0.0426971
$668$	11.7362	+	9.84787i	0.454089	+	0.381026i
$669$	−31.1658	+	26.1512i	−1.20494	+	1.01106i
$670$	2.20474	+	12.5037i	0.0851767	+	0.483061i
$671$	41.0084	+	14.9258i	1.58311	+	0.576206i
$672$	−3.15905			−0.121863
$673$	8.42098	+	3.06498i	0.324605	+	0.118146i	0.499182	−	0.866497i	$-0.333634\pi$
$673$	8.42098	+	3.06498i	0.324605	+	0.118146i	−0.174578	+	0.984643i	$0.555856\pi$
$674$	11.9538	−	20.7046i	0.460444	−	0.797512i
$675$	−0.247555	+	1.40395i	−0.00952838	+	0.0540381i
$676$	−7.62326	−	13.2039i	−0.293202	−	0.507841i
$677$	14.5075	−	25.1277i	0.557568	−	0.965737i	−0.440130	−	0.897934i	$-0.645068\pi$
$677$	14.5075	−	25.1277i	0.557568	−	0.965737i	0.997699	−	0.0678028i	$-0.0215989\pi$
$678$	8.36170	+	7.01630i	0.321129	+	0.269459i
$679$	−0.784492	−	4.44907i	−0.0301060	−	0.170740i
$680$	2.36654	+	4.09897i	0.0907527	+	0.157188i
$681$	−0.467182	+	0.170040i	−0.0179025	+	0.00651597i
$682$	−15.3389	+	5.58290i	−0.587356	+	0.213780i
$683$	0.703610	−	3.99037i	0.0269229	−	0.152687i	−0.968383	−	0.249469i	$-0.919744\pi$
$683$	0.703610	−	3.99037i	0.0269229	−	0.152687i	0.995306	+	0.0967819i	$0.0308549\pi$
$684$	−17.0909	+	14.3410i	−0.653489	+	0.548342i
$685$	11.2729	−	9.45908i	0.430715	−	0.361413i
$686$	−2.67317	+	15.1603i	−0.102062	+	0.578823i
$687$	67.5544	−	24.5878i	2.57736	−	0.938082i
$688$	10.9022	−	3.96808i	0.415643	−	0.151282i
$689$	−1.91217	−	3.31198i	−0.0728480	−	0.126176i
$690$	0.0929541	+	0.527169i	0.00353870	+	0.0200690i
$691$	−8.61951	−	7.23263i	−0.327902	−	0.275142i	0.463942	−	0.885865i	$-0.346434\pi$
$691$	−8.61951	−	7.23263i	−0.327902	−	0.275142i	−0.791844	+	0.610723i	$0.790879\pi$
$692$	6.72370	−	11.6458i	0.255597	−	0.442706i
$693$	−11.3803	−	19.7112i	−0.432301	−	0.748767i
$694$	−1.37774	+	7.81356i	−0.0522983	+	0.296599i
$695$	−7.98760	+	13.8349i	−0.302987	+	0.524789i
$696$	−12.6922	−	4.61958i	−0.481096	−	0.175105i
$697$	−21.1405			−0.800753
$698$	−14.4718	−	5.26731i	−0.547766	−	0.199370i
$699$	4.72739	+	26.8104i	0.178806	+	1.01406i
$700$	−0.945076	+	0.793013i	−0.0357205	+	0.0299731i
$701$	11.8712	+	9.96111i	0.448369	+	0.376226i	0.838830	−	0.544393i	$-0.183240\pi$
$701$	11.8712	+	9.96111i	0.448369	+	0.376226i	−0.390461	+	0.920619i	$0.627685\pi$
$702$	7.57675			0.285966
$703$	−34.4406	+	16.4228i	−1.29895	+	0.619397i
$704$	−5.18702			−0.195493
$705$	−18.1890	−	15.2624i	−0.685038	−	0.574815i
$706$	−6.45775	+	5.41870i	−0.243041	+	0.203935i
$707$	−3.30819	−	18.7617i	−0.124417	−	0.705606i
$708$	−19.9643	−	7.26643i	−0.750306	−	0.273089i
$709$	−13.1354			−0.493311			−0.246656	−	0.969103i	$-0.579332\pi$
$709$	−13.1354			−0.493311			−0.246656	+	0.969103i	$0.579332\pi$
$710$	−7.67595	−	2.79382i	−0.288073	−	0.104850i
$711$	5.73060	−	9.92568i	0.214914	−	0.372242i
$712$	1.73765	−	9.85473i	0.0651214	−	0.369322i
$713$	0.328939	+	0.569738i	0.0123188	+	0.0213369i
$714$	−7.47603	+	12.9489i	−0.279783	+	0.484599i
$715$	21.1181	+	17.7202i	0.789771	+	0.662696i
$716$	3.12479	+	17.7215i	0.116779	+	0.662285i
$717$	17.2469	+	29.8726i	0.644098	+	1.11561i
$718$	11.2553	−	4.09660i	0.420045	−	0.152884i
$719$	−33.9503	+	12.3569i	−1.26613	+	0.460834i	−0.885822	−	0.464026i	$-0.846405\pi$
$719$	−33.9503	+	12.3569i	−1.26613	+	0.460834i	−0.380309	+	0.924859i	$0.624182\pi$
$720$	−0.617622	+	3.50271i	−0.0230174	+	0.130538i
$721$	−2.32691	+	1.95251i	−0.0866587	+	0.0727153i
$722$	−15.5872	+	13.0792i	−0.580096	+	0.486758i
$723$	−12.6884	+	71.9592i	−0.471885	+	2.67619i
$724$	0.294326	−	0.107126i	0.0109386	−	0.00398131i
$725$	−4.95670	+	1.80409i	−0.184087	+	0.0670022i
$726$	−20.3635	−	35.2705i	−0.755759	−	1.30901i
$727$	2.17248	+	12.3207i	0.0805728	+	0.456951i	0.998224	+	0.0595652i	$0.0189714\pi$
$727$	2.17248	+	12.3207i	0.0805728	+	0.456951i	−0.917652	+	0.397386i	$0.869917\pi$
$728$	5.02284	+	4.21466i	0.186159	+	0.156206i
$729$	17.9595	−	31.1067i	0.665166	−	1.15210i
$730$	−0.0742772	−	0.128652i	−0.00274912	−	0.00476162i
$731$	9.53549	−	54.0784i	0.352683	−	2.00016i
$732$	10.7717	−	18.6571i	0.398133	−	0.689587i
$733$	−4.10097	−	1.49263i	−0.151473	−	0.0551316i	0.265171	−	0.964201i	$-0.414572\pi$
$733$	−4.10097	−	1.49263i	−0.151473	−	0.0551316i	−0.416644	+	0.909070i	$0.636794\pi$
$734$	−35.6795			−1.31695
$735$	13.1810	+	4.79750i	0.486189	+	0.176958i
$736$	0.0363015	+	0.205876i	0.00133809	+	0.00758869i
$737$	−50.4498	+	42.3324i	−1.85834	+	1.55933i
$738$	−12.1696	−	10.2115i	−0.447971	−	0.375892i
$739$	−46.2494			−1.70131			−0.850655	−	0.525724i	$-0.823794\pi$
$739$	−46.2494			−1.70131			−0.850655	+	0.525724i	$0.823794\pi$
$740$	−2.52308	+	5.53481i	−0.0927501	+	0.203464i
$741$	85.3662			3.13601
$742$	0.680051	+	0.570631i	0.0249655	+	0.0209485i
$743$	−3.63320	+	3.04862i	−0.133289	+	0.111843i	−0.706995	−	0.707218i	$-0.749950\pi$
$743$	−3.63320	+	3.04862i	−0.133289	+	0.111843i	0.573706	+	0.819061i	$0.305505\pi$
$744$	1.39928	+	7.93571i	0.0513001	+	0.290937i
$745$	12.3751	+	4.50418i	0.453390	+	0.165021i
$746$	−6.20569			−0.227207
$747$	−12.8086	−	4.66196i	−0.468643	−	0.170572i
$748$	−12.2753	+	21.2614i	−0.448829	+	0.777395i
$749$	−0.596936	+	3.38539i	−0.0218116	+	0.123700i
$750$	1.28031	+	2.21756i	0.0467502	+	0.0809737i
$751$	−3.83809	+	6.64777i	−0.140054	+	0.242581i	−0.927517	−	0.373782i	$-0.878061\pi$
$751$	−3.83809	+	6.64777i	−0.140054	+	0.242581i	0.787463	+	0.616362i	$0.211394\pi$
$752$	−7.10338	−	5.96044i	−0.259034	−	0.217355i
$753$	−13.0713	−	74.1310i	−0.476345	−	2.70148i
$754$	14.0171	+	24.2784i	0.510474	+	0.884166i
$755$	−6.76780	+	2.46328i	−0.246306	+	0.0896479i
$756$	−1.65272	+	0.601541i	−0.0601088	+	0.0218778i
$757$	0.290832	−	1.64939i	0.0105705	−	0.0599481i	−0.979066	−	0.203542i	$-0.934755\pi$
$757$	0.290832	−	1.64939i	0.0105705	−	0.0599481i	0.989637	+	0.143594i	$0.0458658\pi$
$758$	−11.1006	+	9.31454i	−0.403193	+	0.338319i
$759$	−2.12701	+	1.78478i	−0.0772057	+	0.0647832i
$760$	−1.08926	+	6.17747i	−0.0395114	+	0.224081i
$761$	36.7864	−	13.3892i	1.33351	−	0.485357i	0.425745	−	0.904843i	$-0.360012\pi$
$761$	36.7864	−	13.3892i	1.33351	−	0.485357i	0.907761	+	0.419487i	$0.137790\pi$
$762$	15.4285	−	5.61550i	0.558914	−	0.203428i
$763$	12.4243	+	21.5195i	0.449790	+	0.779059i
$764$	−2.31492	−	13.1286i	−0.0837510	−	0.474976i
$765$	12.8959	+	10.8209i	0.466251	+	0.391231i
$766$	−10.5242	+	18.2285i	−0.380256	+	0.658623i
$767$	22.0484	+	38.1890i	0.796122	+	1.37892i
$768$	−0.444646	+	2.52171i	−0.0160448	+	0.0909945i
$769$	4.54244	−	7.86774i	0.163805	−	0.283718i	−0.772426	−	0.635105i	$-0.780957\pi$
$769$	4.54244	−	7.86774i	0.163805	−	0.283718i	0.936230	+	0.351387i	$0.114290\pi$
$770$	−6.01334	−	2.18868i	−0.216706	−	0.0788745i
$771$	57.2156			2.06057
$772$	5.32076	+	1.93660i	0.191498	+	0.0696997i
$773$	0.491724	+	2.78870i	0.0176861	+	0.100303i	0.992373	−	0.123272i	$-0.0393386\pi$
$773$	0.491724	+	2.78870i	0.0176861	+	0.100303i	−0.974687	+	0.223574i	$0.928227\pi$
$774$	31.6108	−	26.5246i	1.13623	−	0.953407i
$775$	2.41071	+	2.02282i	0.0865951	+	0.0726619i
$776$	−3.66189			−0.131454
$777$	−19.1275	+	1.83969i	−0.686195	+	0.0659986i
$778$	−25.8914			−0.928252
$779$	−21.4627	−	18.0093i	−0.768981	−	0.645252i
$780$	10.4251	−	8.74770i	0.373279	−	0.313218i
$781$	−7.35756	−	41.7268i	−0.263274	−	1.49310i
$782$	0.929789	+	0.338415i	0.0332492	+	0.0121017i
$783$	−7.51982			−0.268736
$784$	5.14760	+	1.87357i	0.183843	+	0.0669134i
$785$	−0.366695	+	0.635135i	−0.0130879	+	0.0226689i
$786$	−0.732151	+	4.15223i	−0.0261149	+	0.148105i
$787$	22.9098	+	39.6809i	0.816646	+	1.41447i	0.908140	+	0.418667i	$0.137502\pi$
$787$	22.9098	+	39.6809i	0.816646	+	1.41447i	−0.0914941	+	0.995806i	$0.529164\pi$
$788$	6.19832	−	10.7358i	0.220806	−	0.382447i
$789$	−3.38993	−	2.84449i	−0.120685	−	0.101267i
$790$	−0.559561	−	3.17343i	−0.0199083	−	0.112905i
$791$	2.62953	+	4.55449i	0.0934955	+	0.161939i
$792$	−17.3363	+	6.30989i	−0.616018	+	0.224212i
$793$	−42.0182	+	15.2934i	−1.49211	+	0.543084i
$794$	6.42612	−	36.4444i	0.228055	−	1.29336i
$795$	1.41147	−	1.18437i	0.0500599	−	0.0420052i
$796$	16.5462	−	13.8839i	0.586465	−	0.492102i
$797$	−2.33609	+	13.2486i	−0.0827485	+	0.469290i	0.915071	+	0.403292i	$0.132134\pi$
$797$	−2.33609	+	13.2486i	−0.0827485	+	0.469290i	−0.997820	+	0.0659980i	$0.978977\pi$
$798$	−18.6210	+	6.77747i	−0.659175	+	0.239920i
$799$	−41.2421	+	15.0109i	−1.45904	+	0.531048i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−6.18040	−	35.0508i	−0.218374	−	1.23846i
$802$	−11.0351	−	9.25958i	−0.389664	−	0.326967i
$803$	0.385277	−	0.667320i	0.0135961	−	0.0235492i
$804$	16.2556	+	28.1555i	0.573289	+	0.992967i
$805$	−0.0447855	+	0.253991i	−0.00157848	+	0.00895201i
$806$	8.36263	−	14.4845i	0.294561	−	0.510195i
$807$	−35.9873	−	13.0983i	−1.26681	−	0.461082i
$808$	−15.4421			−0.543253
$809$	23.5189	+	8.56020i	0.826882	+	0.300961i	0.720579	−	0.693373i	$-0.243876\pi$
$809$	23.5189	+	8.56020i	0.826882	+	0.300961i	0.106304	+	0.994334i	$0.466098\pi$
$810$	−1.21898	−	6.91315i	−0.0428304	−	0.242903i
$811$	42.5977	−	35.7437i	1.49581	−	1.25513i	0.608848	−	0.793287i	$-0.291632\pi$
$811$	42.5977	−	35.7437i	1.49581	−	1.25513i	0.886961	−	0.461845i	$-0.152812\pi$
$812$	−4.98509	−	4.18299i	−0.174942	−	0.146794i
$813$	−26.7200			−0.937111
$814$	−31.4065	+	3.02069i	−1.10080	+	0.105875i
$815$	11.2717			0.394830
$816$	9.28415	+	7.79033i	0.325010	+	0.272716i
$817$	55.7496	−	46.7795i	1.95043	−	1.63661i
$818$	−5.85825	−	33.2238i	−0.204829	−	1.16164i
$819$	21.9146	+	7.97626i	0.765758	+	0.278713i
$820$	−4.46654			−0.155978
$821$	−37.0045	−	13.4685i	−1.29147	−	0.470055i	−0.397258	−	0.917707i	$-0.630038\pi$
$821$	−37.0045	−	13.4685i	−1.29147	−	0.470055i	−0.894208	+	0.447652i	$0.852260\pi$
$822$	18.8406	−	32.6329i	0.657143	−	1.13820i
$823$	−6.02623	+	34.1765i	−0.210061	+	1.19132i	0.679213	+	0.733941i	$0.262321\pi$
$823$	−6.02623	+	34.1765i	−0.210061	+	1.19132i	−0.889274	+	0.457375i	$0.848790\pi$
$824$	1.23107	+	2.13228i	0.0428864	+	0.0742815i
$825$	−6.64097	+	11.5025i	−0.231209	+	0.400466i
$826$	−7.84136	−	6.57969i	−0.272836	−	0.228937i
$827$	−1.74495	−	9.89608i	−0.0606777	−	0.344120i	−0.999999	−	0.00108292i	$-0.999655\pi$
$827$	−1.74495	−	9.89608i	−0.0606777	−	0.344120i	0.939322	−	0.343038i	$-0.111456\pi$
$828$	0.371772	+	0.643929i	0.0129200	+	0.0223781i
$829$	36.3909	−	13.2452i	1.26391	−	0.460025i	0.378830	−	0.925466i	$-0.376327\pi$
$829$	36.3909	−	13.2452i	1.26391	−	0.460025i	0.885079	+	0.465441i	$0.154104\pi$
$830$	−3.60122	+	1.31074i	−0.125000	+	0.0454963i
$831$	1.33599	−	7.57680i	0.0463451	−	0.262836i
$832$	4.07133	−	3.41625i	0.141148	−	0.118437i
$833$	19.8617	−	16.6660i	0.688168	−	0.577442i
$834$	−7.10331	+	40.2848i	−0.245967	+	1.39495i
$835$	14.3966	−	5.23994i	0.498216	−	0.181336i
$836$	−30.5747	+	11.1283i	−1.05745	+	0.384880i
$837$	2.24316	+	3.88527i	0.0775351	+	0.134295i
$838$	6.84796	+	38.8367i	0.236559	+	1.34159i
$839$	−13.9997	−	11.7471i	−0.483322	−	0.405556i	0.368304	−	0.929706i	$-0.379939\pi$
$839$	−13.9997	−	11.7471i	−0.483322	−	0.405556i	−0.851626	+	0.524150i	$0.824383\pi$
$840$	−1.57953	+	2.73582i	−0.0544988	+	0.0943947i
$841$	0.588198	+	1.01879i	0.0202827	+	0.0351307i
$842$	0.356152	−	2.01984i	0.0122738	−	0.0696083i
$843$	−4.54017	+	7.86380i	−0.156372	+	0.270844i
$844$	−0.557377	−	0.202868i	−0.0191857	−	0.00698302i
$845$	−15.2465			−0.524496
$846$	−30.9920	−	11.2802i	−1.06553	−	0.387820i
$847$	−3.40738	−	19.3242i	−0.117079	−	0.663987i
$848$	0.551225	−	0.462533i	0.0189291	−	0.0158834i
$849$	27.1312	+	22.7658i	0.931140	+	0.781319i
$850$	4.73308			0.162343
$851$	0.339692	+	1.22540i	0.0116445	+	0.0420062i
$852$	−20.9166			−0.716590
$853$	−8.50644	−	7.13775i	−0.291255	−	0.244392i	0.485438	−	0.874271i	$-0.338660\pi$
$853$	−8.50644	−	7.13775i	−0.291255	−	0.244392i	−0.776693	+	0.629879i	$0.783104\pi$
$854$	7.95126	−	6.67190i	0.272087	−	0.228308i
$855$	3.87420	+	21.9717i	0.132495	+	0.751416i
$856$	2.61837	+	0.953009i	0.0894941	+	0.0325732i
$857$	−45.3422			−1.54886			−0.774430	−	0.632660i	$-0.781963\pi$
$857$	−45.3422			−1.54886			−0.774430	+	0.632660i	$0.781963\pi$
$858$	66.3331	+	24.1433i	2.26457	+	0.824237i
$859$	−14.8977	+	25.8036i	−0.508304	+	0.880409i	0.491649	+	0.870793i	$0.336394\pi$
$859$	−14.8977	+	25.8036i	−0.508304	+	0.880409i	−0.999954	+	0.00961583i	$0.996939\pi$
$860$	2.01465	−	11.4256i	0.0686988	−	0.389610i
$861$	−7.05501	−	12.2196i	−0.240434	−	0.416444i
$862$	6.76953	−	11.7252i	0.230571	−	0.399361i
$863$	−30.4195	−	25.5250i	−1.03549	−	0.868879i	−0.0439961	−	0.999032i	$-0.514009\pi$
$863$	−30.4195	−	25.5250i	−1.03549	−	0.868879i	−0.991494	+	0.130152i	$0.958453\pi$
$864$	0.247555	+	1.40395i	0.00842198	+	0.0477634i
$865$	−6.72370	−	11.6458i	−0.228613	−	0.395969i
$866$	25.4510	−	9.26340i	0.864860	−	0.314783i
$867$	12.9984	−	4.73104i	0.441450	−	0.160675i
$868$	−0.674176	+	3.82344i	−0.0228830	+	0.129776i
$869$	12.8041	−	10.7439i	0.434349	−	0.364462i
$870$	−10.3468	+	8.68197i	−0.350788	+	0.294346i
$871$	11.7176	−	66.4541i	0.397037	−	2.25171i
$872$	18.9267	−	6.88876i	0.640939	−	0.233283i
$873$	−12.2389	+	4.45461i	−0.414226	+	0.150766i
$874$	0.655668	+	1.13565i	0.0221783	+	0.0384139i
$875$	0.214231	+	1.21497i	0.00724234	+	0.0410733i
$876$	−0.291396	−	0.244510i	−0.00984536	−	0.00826124i
$877$	18.9319	−	32.7909i	0.639284	−	1.10727i	−0.346307	−	0.938121i	$-0.612564\pi$
$877$	18.9319	−	32.7909i	0.639284	−	1.10727i	0.985590	−	0.169150i	$-0.0541023\pi$
$878$	11.2008	+	19.4004i	0.378009	+	0.654730i
$879$	9.55362	−	54.1813i	0.322236	−	1.82749i
$880$	−2.59351	+	4.49209i	−0.0874271	+	0.151428i
$881$	−14.7854	−	5.38146i	−0.498134	−	0.181306i	0.0807207	−	0.996737i	$-0.474278\pi$
$881$	−14.7854	−	5.38146i	−0.498134	−	0.181306i	−0.578854	+	0.815431i	$0.696500\pi$
$882$	19.4837			0.656051
$883$	−40.2869	−	14.6632i	−1.35576	−	0.493457i	−0.441020	−	0.897497i	$-0.645383\pi$
$883$	−40.2869	−	14.6632i	−1.35576	−	0.493457i	−0.914741	+	0.404040i	$0.867605\pi$
$884$	−4.36814	−	24.7730i	−0.146917	−	0.833205i
$885$	−16.2751	+	13.6564i	−0.547081	+	0.459055i
$886$	−6.80198	−	5.70754i	−0.228517	−	0.191749i
$887$	−16.8325			−0.565181			−0.282590	−	0.959241i	$-0.591194\pi$
$887$	−16.8325			−0.565181			−0.282590	+	0.959241i	$0.591194\pi$
$888$	−1.22372	+	15.5275i	−0.0410653	+	0.521068i
$889$	7.91052			0.265310
$890$	−7.66562	−	6.43222i	−0.256952	−	0.215608i
$891$	27.8931	−	23.4051i	0.934453	−	0.784099i
$892$	2.75899	+	15.6470i	0.0923779	+	0.523901i
$893$	−54.6583	−	19.8940i	−1.82907	−	0.665727i
$894$	33.7216			1.12782
$895$	16.9097	+	6.15463i	0.565229	+	0.205726i
$896$	−0.616854	+	1.06842i	−0.0206077	+	0.0356935i
$897$	0.494028	−	2.80177i	0.0164951	−	0.0935484i
$898$	−1.01881	−	1.76464i	−0.0339983	−	0.0588867i
$899$	−8.29979	+	14.3757i	−0.276813	+	0.479455i
$900$	2.72463	+	2.28623i	0.0908208	+	0.0762077i
$901$	−0.591411	−	3.35406i	−0.0197028	−	0.111740i
$902$	−11.5840	−	20.0641i	−0.385705	−	0.668061i
$903$	34.4406	−	12.5354i	1.14611	−	0.417151i
$904$	4.00573	−	1.45797i	0.133229	−	0.0484913i
$905$	0.0543893	−	0.308457i	0.00180796	−	0.0102535i
$906$	−14.1273	+	11.8542i	−0.469349	+	0.393831i
$907$	−25.6138	+	21.4925i	−0.850493	+	0.713648i	−0.959898	−	0.280349i	$-0.909550\pi$
$907$	−25.6138	+	21.4925i	−0.850493	+	0.713648i	0.109406	+	0.993997i	$0.465105\pi$
$908$	−0.0337153	+	0.191209i	−0.00111888	+	0.00634549i
$909$	−51.6115	+	18.7850i	−1.71184	+	0.623061i
$910$	6.16142	−	2.24257i	0.204249	−	0.0743406i
$911$	−12.0817	−	20.9260i	−0.400283	−	0.693311i	0.593477	−	0.804851i	$-0.297755\pi$
$911$	−12.0817	−	20.9260i	−0.400283	−	0.693311i	−0.993760	+	0.111540i	$0.964422\pi$
$912$	2.78916	+	15.8181i	0.0923584	+	0.523790i
$913$	−15.2277	−	12.7776i	−0.503965	−	0.422877i
$914$	7.57981	−	13.1286i	0.250718	−	0.434256i
$915$	−10.7717	−	18.6571i	−0.356101	−	0.616785i
$916$	4.87521	−	27.6487i	0.161082	−	0.913539i
$917$	−1.01571	+	1.75926i	−0.0335416	+	0.0580958i
$918$	6.34061	+	2.30779i	0.209271	+	0.0761685i
$919$	−34.5483			−1.13964			−0.569822	−	0.821768i	$-0.692988\pi$
$919$	−34.5483			−1.13964			−0.569822	+	0.821768i	$0.692988\pi$
$920$	0.196445	+	0.0715000i	0.00647659	+	0.00235729i
$921$	−5.81939	−	33.0034i	−0.191755	−	1.08750i
$922$	−12.0771	+	10.1339i	−0.397740	+	0.333743i
$923$	33.2570	+	27.9059i	1.09467	+	0.918534i
$924$	−16.3861			−0.539062
$925$	3.53175	+	4.95245i	0.116123	+	0.162836i
$926$	30.2378			0.993675
$927$	6.70842	+	5.62903i	0.220333	+	0.184882i
$928$	−4.04074	+	3.39058i	−0.132644	+	0.111301i
$929$	2.28817	+	12.9768i	0.0750723	+	0.425756i	0.999061	+	0.0433355i	$0.0137984\pi$
$929$	2.28817	+	12.9768i	0.0750723	+	0.425756i	−0.923988	+	0.382421i	$0.875090\pi$
$930$	7.57217	+	2.75604i	0.248301	+	0.0903743i
$931$	34.3620			1.12617
$932$	9.99063	+	3.63629i	0.327254	+	0.119111i
$933$	−1.93172	+	3.34584i	−0.0632417	+	0.109538i
$934$	4.42944	−	25.1206i	0.144936	−	0.821971i
$935$	12.2753	+	21.2614i	0.401445	+	0.695323i
$936$	9.45160	−	16.3706i	0.308935	−	0.535091i
$937$	40.3012	+	33.8168i	1.31658	+	1.10475i	0.987017	+	0.160613i	$0.0513471\pi$
$937$	40.3012	+	33.8168i	1.31658	+	1.10475i	0.329567	+	0.944132i	$0.393097\pi$
$938$	2.72001	+	15.4259i	0.0888115	+	0.503675i
$939$	39.7068	+	68.7742i	1.29578	+	2.24436i
$940$	−8.71358	+	3.17149i	−0.284206	+	0.103442i
$941$	10.9998	−	4.00360i	0.358584	−	0.130514i	−0.156445	−	0.987687i	$-0.550003\pi$
$941$	10.9998	−	4.00360i	0.358584	−	0.130514i	0.515029	+	0.857173i	$0.327781\pi$
$942$	−0.326099	+	1.84940i	−0.0106249	+	0.0602567i
$943$	−0.715285	+	0.600196i	−0.0232929	+	0.0195451i
$944$	−6.35593	+	5.33326i	−0.206868	+	0.173583i
$945$	−0.305410	+	1.73207i	−0.00993499	+	0.0563442i
$946$	56.5499	−	20.5825i	1.83860	−	0.669194i
$947$	−30.1448	+	10.9718i	−0.979573	+	0.356535i	−0.781674	−	0.623687i	$-0.785634\pi$
$947$	−30.1448	+	10.9718i	−0.979573	+	0.356535i	−0.197899	+	0.980222i	$0.563412\pi$
$948$	−4.12564	−	7.14581i	−0.133994	−	0.232085i
$949$	0.137100	+	0.777534i	0.00445046	+	0.0252398i
$950$	4.80522	+	4.03206i	0.155902	+	0.130817i
$951$	−6.66076	+	11.5368i	−0.215990	+	0.374105i
$952$	2.91962	+	5.05693i	0.0946255	+	0.163896i
$953$	−1.93939	+	10.9989i	−0.0628232	+	0.356288i	0.937150	+	0.348927i	$0.113454\pi$
$953$	−1.93939	+	10.9989i	−0.0628232	+	0.356288i	−0.999973	+	0.00736044i	$0.997657\pi$
$954$	1.27967	−	2.21645i	0.0414308	−	0.0717603i
$955$	−12.5272	−	4.55951i	−0.405369	−	0.147542i
$956$	13.4709			0.435681
$957$	−65.8346	−	23.9618i	−2.12813	−	0.774576i
$958$	−0.122339	−	0.693817i	−0.00395258	−	0.0224162i
$959$	13.9075	−	11.6697i	0.449095	−	0.376836i
$960$	1.96154	+	1.64593i	0.0633086	+	0.0531222i
$961$	−21.0967			−0.680538
$962$	22.6617	−	23.0558i	0.730643	−	0.743347i
$963$	9.91056			0.319363
$964$	21.8597	+	18.3425i	0.704055	+	0.590772i
$965$	4.33752	−	3.63962i	0.139630	−	0.117163i
$966$	0.114678	+	0.650373i	0.00368971	+	0.0209254i
$967$	−15.6131	−	5.68271i	−0.502084	−	0.182744i	0.0785470	−	0.996910i	$-0.474972\pi$
$967$	−15.6131	−	5.68271i	−0.502084	−	0.182744i	−0.580631	+	0.814167i	$0.697194\pi$
$968$	−15.9051			−0.511210
$969$	71.4387	+	26.0016i	2.29494	+	0.835290i
$970$	−1.83095	+	3.17129i	−0.0587881	+	0.101824i
$971$	2.77993	−	15.7658i	0.0892122	−	0.505948i	−0.907156	−	0.420795i	$-0.861751\pi$
$971$	2.77993	−	15.7658i	0.0892122	−	0.505948i	0.996368	−	0.0851526i	$-0.0271378\pi$
$972$	−11.1259	−	19.2706i	−0.356864	−	0.618106i
$973$	−9.85436	+	17.0683i	−0.315916	+	0.547183i
$974$	−29.2629	−	24.5545i	−0.937643	−	0.786776i
$975$	−2.36318	−	13.4023i	−0.0756823	−	0.429216i
$976$	−4.20668	−	7.28618i	−0.134653	−	0.233225i
$977$	−46.8808	+	17.0632i	−1.49985	+	0.545900i	−0.956021	−	0.293297i	$-0.905247\pi$
$977$	−46.8808	+	17.0632i	−1.49985	+	0.545900i	−0.543827	+	0.839197i	$0.683025\pi$
$978$	27.1218	−	9.87154i	0.867261	−	0.315657i
$979$	9.01324	−	51.1166i	0.288065	−	1.63369i
$980$	4.19636	−	3.52117i	0.134048	−	0.112480i
$981$	54.8777	−	46.0479i	1.75211	−	1.47020i
$982$	−2.85609	+	16.1977i	−0.0911415	+	0.516889i
$983$	−13.4957	+	4.91202i	−0.430444	+	0.156669i	−0.548151	−	0.836379i	$-0.684668\pi$
$983$	−13.4957	+	4.91202i	−0.430444	+	0.156669i	0.117706	+	0.993048i	$0.462446\pi$
$984$	−10.7473	+	3.91171i	−0.342613	+	0.124701i
$985$	−6.19832	−	10.7358i	−0.197495	−	0.342071i
$986$	4.33532	+	24.5868i	0.138065	+	0.783004i
$987$	−22.4399	−	18.8293i	−0.714271	−	0.599345i
$988$	16.6691	−	28.8717i	0.530314	−	0.918531i
$989$	−1.21270	−	2.10046i	−0.0385616	−	0.0667906i
$990$	−3.20362	+	18.1686i	−0.101818	+	0.577437i
$991$	−15.2243	+	26.3692i	−0.483615	+	0.837646i	−0.999823	−	0.0188171i	$-0.994010\pi$
$991$	−15.2243	+	26.3692i	−0.483615	+	0.837646i	0.516208	+	0.856464i	$0.327343\pi$
$992$	2.95717	+	1.07632i	0.0938902	+	0.0341732i
$993$	25.5994			0.812373
$994$	−9.46988	−	3.44675i	−0.300366	−	0.109324i
$995$	−3.75072	−	21.2714i	−0.118906	−	0.674349i
$996$	−7.51730	+	6.30776i	−0.238195	+	0.199869i
$997$	−37.5042	−	31.4698i	−1.18777	−	0.996658i	−0.999895	−	0.0144648i	$-0.995396\pi$
$997$	−37.5042	−	31.4698i	−1.18777	−	0.996658i	−0.187875	−	0.982193i	$-0.560160\pi$
$998$	0.250107			0.00791701
$999$	2.31650	+	8.35651i	0.0732908	+	0.264388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.b.71.1	✓	18
37.12	even	9	inner	370.2.o.b.271.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.b.71.1	✓	18	1.1	even	1	trivial
370.2.o.b.271.1	yes	18	37.12	even	9	inner

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.96154 + 1.64593i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{5} +2.56061 q^{6} +(1.15931 + 0.421953i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.617622 - 3.50271i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-1.96154 + 1.64593i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{5} +2.56061 q^{6} +(1.15931 + 0.421953i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.617622 - 3.50271i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.59351 - 4.49209i) q^{11} +(-1.96154 - 1.64593i) q^{12} +(0.922896 + 5.23400i) q^{13} +(-0.616854 - 1.06842i) q^{14} +(-2.40619 + 0.875782i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.821891 + 4.66118i) q^{17} +(-2.72463 + 2.28623i) q^{18} +(-4.80522 + 4.03206i) q^{19} +(-0.173648 + 0.984808i) q^{20} +(-2.96854 + 1.08046i) q^{21} +(-4.87420 + 1.77406i) q^{22} +(0.104526 + 0.181044i) q^{23} +(0.444646 + 2.52171i) q^{24} +(0.766044 + 0.642788i) q^{25} +(2.65737 - 4.60270i) q^{26} +(0.712805 + 1.23461i) q^{27} +(-0.214231 + 1.21497i) q^{28} +(-2.63740 + 4.56812i) q^{29} +(2.40619 + 0.875782i) q^{30} +3.14695 q^{31} +(0.939693 + 0.342020i) q^{32} +(2.30639 + 13.0802i) q^{33} +(3.62575 - 3.04237i) q^{34} +(0.945076 + 0.793013i) q^{35} +3.55675 q^{36} +(5.88885 + 1.52364i) q^{37} +6.27277 q^{38} +(-10.4251 - 8.74770i) q^{39} +(0.766044 - 0.642788i) q^{40} +(0.775606 + 4.39868i) q^{41} +(2.96854 + 1.08046i) q^{42} -11.6019 q^{43} +(4.87420 + 1.77406i) q^{44} +(1.77837 - 3.08023i) q^{45} +(0.0363015 - 0.205876i) q^{46} +(4.63640 + 8.03048i) q^{47} +(1.28031 - 2.21756i) q^{48} +(-4.19636 - 3.52117i) q^{49} +(-0.173648 - 0.984808i) q^{50} +(-6.05980 - 10.4959i) q^{51} +(-4.99423 + 1.81775i) q^{52} +(-0.676178 + 0.246109i) q^{53} +(0.247555 - 1.40395i) q^{54} +(3.97348 - 3.33415i) q^{55} +(0.945076 - 0.793013i) q^{56} +(2.78916 - 15.8181i) q^{57} +(4.95670 - 1.80409i) q^{58} +(7.79670 - 2.83777i) q^{59} +(-1.28031 - 2.21756i) q^{60} +(1.46096 + 8.28554i) q^{61} +(-2.41071 - 2.02282i) q^{62} +(2.19399 - 3.80011i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.922896 + 5.23400i) q^{65} +(6.64097 - 11.5025i) q^{66} +(-11.9309 - 4.34250i) q^{67} -4.73308 q^{68} +(-0.503019 - 0.183084i) q^{69} +(-0.214231 - 1.21497i) q^{70} +(6.25749 - 5.25066i) q^{71} +(-2.72463 - 2.28623i) q^{72} +0.148554 q^{73} +(-3.53175 - 4.95245i) q^{74} -2.56061 q^{75} +(-4.80522 - 4.03206i) q^{76} +(4.90212 - 4.11337i) q^{77} +(2.36318 + 13.4023i) q^{78} +(3.02805 + 1.10212i) q^{79} -1.00000 q^{80} +(6.59645 + 2.40091i) q^{81} +(2.23327 - 3.86813i) q^{82} +(0.665479 - 3.77412i) q^{83} +(-1.57953 - 2.73582i) q^{84} +(-2.36654 + 4.09897i) q^{85} +(8.88756 + 7.45755i) q^{86} +(-2.34542 - 13.3016i) q^{87} +(-2.59351 - 4.49209i) q^{88} +(9.40327 - 3.42251i) q^{89} +(-3.34225 + 1.21648i) q^{90} +(-1.13858 + 6.45723i) q^{91} +(-0.160143 + 0.134376i) q^{92} +(-6.17289 + 5.17967i) q^{93} +(1.61021 - 9.13193i) q^{94} +(-5.89448 + 2.14541i) q^{95} +(-2.40619 + 0.875782i) q^{96} +(-1.83095 - 3.17129i) q^{97} +(0.951238 + 5.39474i) q^{98} +(-14.1327 - 11.8587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9}+O(q^{10}) \) 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9	\( 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9} - 9 q^{10} + 15 q^{11} + 3 q^{13} - 6 q^{14} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 12 q^{21} - 12 q^{22} + 15 q^{23} + 6 q^{26} + 12 q^{27} + 9 q^{28} - 12 q^{29} + 54 q^{31} + 9 q^{33} + 3 q^{34} - 12 q^{37} - 24 q^{38} - 30 q^{39} + 15 q^{41} + 12 q^{42} - 60 q^{43} + 12 q^{44} - 6 q^{46} + 6 q^{47} + 3 q^{48} - 27 q^{49} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} + 45 q^{57} + 3 q^{58} - 27 q^{59} - 3 q^{60} - 9 q^{62} + 18 q^{63} - 9 q^{64} - 3 q^{65} - 9 q^{66} - 54 q^{67} + 12 q^{68} - 6 q^{69} + 9 q^{70} + 36 q^{71} - 6 q^{72} - 6 q^{73} + 18 q^{74} - 6 q^{75} - 3 q^{76} - 24 q^{77} + 12 q^{78} + 12 q^{79} - 18 q^{80} - 6 q^{81} + 3 q^{82} - 15 q^{83} - 6 q^{84} + 6 q^{85} + 30 q^{87} - 15 q^{88} + 84 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 18 q^{93} + 36 q^{94} - 24 q^{95} - 9 q^{97} - 30 q^{99}+O(q^{100}) \) 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9 - 9 * q^10 + 15 * q^11 + 3 * q^13 - 6 * q^14 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 12 * q^21 - 12 * q^22 + 15 * q^23 + 6 * q^26 + 12 * q^27 + 9 * q^28 - 12 * q^29 + 54 * q^31 + 9 * q^33 + 3 * q^34 - 12 * q^37 - 24 * q^38 - 30 * q^39 + 15 * q^41 + 12 * q^42 - 60 * q^43 + 12 * q^44 - 6 * q^46 + 6 * q^47 + 3 * q^48 - 27 * q^49 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 + 45 * q^57 + 3 * q^58 - 27 * q^59 - 3 * q^60 - 9 * q^62 + 18 * q^63 - 9 * q^64 - 3 * q^65 - 9 * q^66 - 54 * q^67 + 12 * q^68 - 6 * q^69 + 9 * q^70 + 36 * q^71 - 6 * q^72 - 6 * q^73 + 18 * q^74 - 6 * q^75 - 3 * q^76 - 24 * q^77 + 12 * q^78 + 12 * q^79 - 18 * q^80 - 6 * q^81 + 3 * q^82 - 15 * q^83 - 6 * q^84 + 6 * q^85 + 30 * q^87 - 15 * q^88 + 84 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 18 * q^93 + 36 * q^94 - 24 * q^95 - 9 * q^97 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more