LMFDB - Embedded newform 310.2.q.b.231.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(41,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("310.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.q (of order $15$, degree $8$, 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:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$8$
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:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			231.1
Root			$-0.104528 + 0.994522i$ of defining polynomial
Character	$\chi$	$=$	310.231
Dual form			310.2.q.b.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.413545 + 0.459289i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.309017 + 0.535233i) q^{6} +(-0.309017 + 2.94010i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.273659 + 2.60369i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.413545 + 0.459289i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.309017 + 0.535233i) q^{6} +(-0.309017 + 2.94010i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.273659 + 2.60369i) q^{9} +(0.669131 + 0.743145i) q^{10} +(-0.340596 + 0.151643i) q^{11} +(0.604528 - 0.128496i) q^{12} +(5.79232 + 1.23120i) q^{13} +(2.70071 + 1.20243i) q^{14} +(-0.190983 - 0.587785i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.506904 - 0.225688i) q^{17} +(2.56082 + 0.544320i) q^{18} +(-4.43901 + 0.943541i) q^{19} +(0.913545 - 0.406737i) q^{20} +(-1.22256 - 1.35779i) q^{21} +(0.0389713 + 0.370787i) q^{22} +(4.09240 - 2.97330i) q^{23} +(0.0646021 - 0.614648i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.96086 - 5.12837i) q^{26} +(-2.80902 - 2.04087i) q^{27} +(1.97815 - 2.19696i) q^{28} +(-1.50516 + 4.63240i) q^{29} -0.618034 q^{30} +(2.69236 + 4.87352i) q^{31} +1.00000 q^{32} +(0.0712040 - 0.219144i) q^{33} +(-0.371284 + 0.412353i) q^{34} +(-2.39169 - 1.73767i) q^{35} +(1.30902 - 2.26728i) q^{36} +(-0.0938464 - 0.162547i) q^{37} +(-0.474369 + 4.51332i) q^{38} +(-2.96086 + 2.15119i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(-0.0111703 - 0.0124059i) q^{41} +(-1.66913 + 0.743145i) q^{42} +(-0.456295 + 0.0969885i) q^{43} +(0.364682 + 0.0775156i) q^{44} +(-2.39169 - 1.06485i) q^{45} +(-1.56316 - 4.81091i) q^{46} +(-2.96320 - 9.11979i) q^{47} +(-0.564602 - 0.251377i) q^{48} +(-1.70167 - 0.361700i) q^{49} +(-0.978148 + 0.207912i) q^{50} +(0.313284 - 0.139483i) q^{51} +(-3.96241 - 4.40070i) q^{52} +(-0.381766 - 3.63226i) q^{53} +(-2.80902 + 2.04087i) q^{54} +(0.0389713 - 0.370787i) q^{55} +(-1.47815 - 2.56023i) q^{56} +(1.40238 - 2.42899i) q^{57} +(3.94056 + 2.86298i) q^{58} +(-0.0584884 + 0.0649580i) q^{59} +(-0.190983 + 0.587785i) q^{60} +0.553899 q^{61} +(5.46698 - 1.05459i) q^{62} -7.73968 q^{63} +(0.309017 - 0.951057i) q^{64} +(-3.96241 + 4.40070i) q^{65} +(-0.186415 - 0.135438i) q^{66} +(-0.408977 + 0.708369i) q^{67} +(0.277438 + 0.480536i) q^{68} +(-0.326789 + 3.10919i) q^{69} +(-2.39169 + 1.73767i) q^{70} +(0.428006 + 4.07221i) q^{71} +(-1.75181 - 1.94558i) q^{72} +(15.0903 - 6.71864i) q^{73} +(-0.183591 + 0.0390235i) q^{74} +(0.604528 + 0.128496i) q^{75} +(4.14583 + 1.84584i) q^{76} +(-0.340596 - 1.04825i) q^{77} +(1.13095 + 3.48070i) q^{78} +(-11.5492 - 5.14203i) q^{79} +(-0.978148 - 0.207912i) q^{80} +(-5.58347 + 1.18680i) q^{81} +(-0.0152505 + 0.00678996i) q^{82} +(-5.35930 - 5.95210i) q^{83} +(0.190983 + 1.81708i) q^{84} +(0.448903 - 0.326147i) q^{85} +(-0.0487614 + 0.463934i) q^{86} +(-1.50516 - 2.60701i) q^{87} +(0.186415 - 0.322880i) q^{88} +(1.00585 + 0.730790i) q^{89} +(-1.75181 + 1.94558i) q^{90} +(-5.40977 + 16.6496i) q^{91} -5.05849 q^{92} +(-3.35177 - 0.778849i) q^{93} -9.58911 q^{94} +(1.40238 - 4.31607i) q^{95} +(-0.413545 + 0.459289i) q^{96} +(13.7202 + 9.96828i) q^{97} +(-0.869841 + 1.50661i) q^{98} +(-0.488040 - 0.845310i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9} + q^{10} + 17 q^{11} + 3 q^{12} + 10 q^{13} + 2 q^{14} - 6 q^{15} - 2 q^{16} + 8 q^{17} + q^{18} - 8 q^{19} + q^{20} + q^{21} - 28 q^{22} - 2 q^{23} - 2 q^{24} - 4 q^{25} + 5 q^{26} - 18 q^{27} + 7 q^{28} + 11 q^{29} + 4 q^{30} - 14 q^{31} + 8 q^{32} + 3 q^{33} - 7 q^{34} - 4 q^{35} + 6 q^{36} + 6 q^{37} + 22 q^{38} - 5 q^{39} + q^{40} - 4 q^{41} - 9 q^{42} + 14 q^{43} + 2 q^{44} - 4 q^{45} + 18 q^{46} + 6 q^{47} - 2 q^{48} - 23 q^{49} + q^{50} + 14 q^{51} - 20 q^{52} - 8 q^{53} - 18 q^{54} - 28 q^{55} - 3 q^{56} + q^{57} + 11 q^{58} + 8 q^{59} - 6 q^{60} + 28 q^{61} + 31 q^{62} - 14 q^{63} - 2 q^{64} - 20 q^{65} - 7 q^{66} + 2 q^{67} + 13 q^{68} - 7 q^{69} - 4 q^{70} + 19 q^{71} + q^{72} + 12 q^{73} - 19 q^{74} + 3 q^{75} - 8 q^{76} + 17 q^{77} + 15 q^{78} - 39 q^{79} + q^{80} - 16 q^{81} - 4 q^{82} + 50 q^{83} + 6 q^{84} - q^{85} - 16 q^{86} + 11 q^{87} + 7 q^{88} - 12 q^{89} + q^{90} - 20 q^{91} - 32 q^{92} - 11 q^{93} - 24 q^{94} + q^{95} + 3 q^{96} + 42 q^{97} + 17 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9 + q^10 + 17 * q^11 + 3 * q^12 + 10 * q^13 + 2 * q^14 - 6 * q^15 - 2 * q^16 + 8 * q^17 + q^18 - 8 * q^19 + q^20 + q^21 - 28 * q^22 - 2 * q^23 - 2 * q^24 - 4 * q^25 + 5 * q^26 - 18 * q^27 + 7 * q^28 + 11 * q^29 + 4 * q^30 - 14 * q^31 + 8 * q^32 + 3 * q^33 - 7 * q^34 - 4 * q^35 + 6 * q^36 + 6 * q^37 + 22 * q^38 - 5 * q^39 + q^40 - 4 * q^41 - 9 * q^42 + 14 * q^43 + 2 * q^44 - 4 * q^45 + 18 * q^46 + 6 * q^47 - 2 * q^48 - 23 * q^49 + q^50 + 14 * q^51 - 20 * q^52 - 8 * q^53 - 18 * q^54 - 28 * q^55 - 3 * q^56 + q^57 + 11 * q^58 + 8 * q^59 - 6 * q^60 + 28 * q^61 + 31 * q^62 - 14 * q^63 - 2 * q^64 - 20 * q^65 - 7 * q^66 + 2 * q^67 + 13 * q^68 - 7 * q^69 - 4 * q^70 + 19 * q^71 + q^72 + 12 * q^73 - 19 * q^74 + 3 * q^75 - 8 * q^76 + 17 * q^77 + 15 * q^78 - 39 * q^79 + q^80 - 16 * q^81 - 4 * q^82 + 50 * q^83 + 6 * q^84 - q^85 - 16 * q^86 + 11 * q^87 + 7 * q^88 - 12 * q^89 + q^90 - 20 * q^91 - 32 * q^92 - 11 * q^93 - 24 * q^94 + q^95 + 3 * q^96 + 42 * q^97 + 17 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$1$	$e\left(\frac{11}{15}\right)$

Coefficient data

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

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

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−0.413545	+	0.459289i	−0.238761	+	0.265170i	−0.850602	−	0.525810i	$-0.823762\pi$
$3$	−0.413545	+	0.459289i	−0.238761	+	0.265170i	0.611842	+	0.790980i	$0.290429\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.309017	+	0.535233i	0.126156	+	0.218508i
$7$	−0.309017	+	2.94010i	−0.116797	+	1.11125i	0.766436	+	0.642320i	$0.222028\pi$
$7$	−0.309017	+	2.94010i	−0.116797	+	1.11125i	−0.883234	+	0.468933i	$0.844639\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.273659	+	2.60369i	0.0912197	+	0.867897i
$10$	0.669131	+	0.743145i	0.211598	+	0.235003i
$11$	−0.340596	+	0.151643i	−0.102694	+	0.0457222i	−0.457441	−	0.889240i	$-0.651234\pi$
$11$	−0.340596	+	0.151643i	−0.102694	+	0.0457222i	0.354747	+	0.934962i	$0.384567\pi$
$12$	0.604528	−	0.128496i	0.174512	−	0.0370937i
$13$	5.79232	+	1.23120i	1.60650	+	0.341472i	0.921895	−	0.387440i	$-0.126641\pi$
$13$	5.79232	+	1.23120i	1.60650	+	0.341472i	0.684607	+	0.728913i	$0.259974\pi$
$14$	2.70071	+	1.20243i	0.721795	+	0.321364i
$15$	−0.190983	−	0.587785i	−0.0493116	−	0.151765i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.506904	−	0.225688i	−0.122942	−	0.0547374i	0.344344	−	0.938844i	$-0.388101\pi$
$17$	−0.506904	−	0.225688i	−0.122942	−	0.0547374i	−0.467286	+	0.884106i	$0.654768\pi$
$18$	2.56082	+	0.544320i	0.603592	+	0.128297i
$19$	−4.43901	+	0.943541i	−1.01838	+	0.216463i	−0.686709	−	0.726932i	$-0.740945\pi$
$19$	−4.43901	+	0.943541i	−1.01838	+	0.216463i	−0.331670	+	0.943395i	$0.607612\pi$
$20$	0.913545	−	0.406737i	0.204275	−	0.0909491i
$21$	−1.22256	−	1.35779i	−0.266785	−	0.296295i
$22$	0.0389713	+	0.370787i	0.00830870	+	0.0790520i
$23$	4.09240	−	2.97330i	0.853325	−	0.619977i	−0.0727358	−	0.997351i	$-0.523173\pi$
$23$	4.09240	−	2.97330i	0.853325	−	0.619977i	0.926061	+	0.377374i	$0.123173\pi$
$24$	0.0646021	−	0.614648i	0.0131869	−	0.125465i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.96086	−	5.12837i	0.580673	−	1.00576i
$27$	−2.80902	−	2.04087i	−0.540596	−	0.392766i
$28$	1.97815	−	2.19696i	0.373835	−	0.415186i
$29$	−1.50516	+	4.63240i	−0.279501	+	0.860215i	0.708492	+	0.705719i	$0.249376\pi$
$29$	−1.50516	+	4.63240i	−0.279501	+	0.860215i	−0.987993	+	0.154497i	$0.950624\pi$
$30$	−0.618034			−0.112837
$31$	2.69236	+	4.87352i	0.483563	+	0.875310i
$31$	2.69236	+	4.87352i	0.483563	+	0.875310i
$32$	1.00000			0.176777
$33$	0.0712040	−	0.219144i	0.0123950	−	0.0381480i
$34$	−0.371284	+	0.412353i	−0.0636747	+	0.0707179i
$35$	−2.39169	−	1.73767i	−0.404270	−	0.293719i
$36$	1.30902	−	2.26728i	0.218169	−	0.377881i
$37$	−0.0938464	−	0.162547i	−0.0154282	−	0.0267225i	0.858208	−	0.513302i	$-0.171578\pi$
$37$	−0.0938464	−	0.162547i	−0.0154282	−	0.0267225i	−0.873636	+	0.486579i	$0.838244\pi$
$38$	−0.474369	+	4.51332i	−0.0769528	+	0.732157i
$39$	−2.96086	+	2.15119i	−0.474118	+	0.344467i
$40$	−0.104528	−	0.994522i	−0.0165274	−	0.157248i
$41$	−0.0111703	−	0.0124059i	−0.00174451	−	0.00193747i	0.742272	−	0.670099i	$-0.233748\pi$
$41$	−0.0111703	−	0.0124059i	−0.00174451	−	0.00193747i	−0.744016	+	0.668161i	$0.767082\pi$
$42$	−1.66913	+	0.743145i	−0.257552	+	0.114670i
$43$	−0.456295	+	0.0969885i	−0.0695844	+	0.0147906i	−0.242572	−	0.970133i	$-0.577991\pi$
$43$	−0.456295	+	0.0969885i	−0.0695844	+	0.0147906i	0.172988	+	0.984924i	$0.444658\pi$
$44$	0.364682	+	0.0775156i	0.0549779	+	0.0116859i
$45$	−2.39169	−	1.06485i	−0.356533	−	0.158739i
$46$	−1.56316	−	4.81091i	−0.230475	−	0.709330i
$47$	−2.96320	−	9.11979i	−0.432227	−	1.33026i	−0.895902	−	0.444252i	$-0.853469\pi$
$47$	−2.96320	−	9.11979i	−0.432227	−	1.33026i	0.463675	−	0.886005i	$-0.346531\pi$
$48$	−0.564602	−	0.251377i	−0.0814933	−	0.0362832i
$49$	−1.70167	−	0.361700i	−0.243095	−	0.0516714i
$50$	−0.978148	+	0.207912i	−0.138331	+	0.0294032i
$51$	0.313284	−	0.139483i	0.0438685	−	0.0195315i
$52$	−3.96241	−	4.40070i	−0.549487	−	0.610267i
$53$	−0.381766	−	3.63226i	−0.0524396	−	0.498930i	−0.988946	−	0.148278i	$-0.952627\pi$
$53$	−0.381766	−	3.63226i	−0.0524396	−	0.498930i	0.936506	−	0.350651i	$-0.114040\pi$
$54$	−2.80902	+	2.04087i	−0.382259	+	0.277727i
$55$	0.0389713	−	0.370787i	0.00525488	−	0.0499969i
$56$	−1.47815	−	2.56023i	−0.197526	−	0.342125i
$57$	1.40238	−	2.42899i	0.185749	−	0.321727i
$58$	3.94056	+	2.86298i	0.517420	+	0.375928i
$59$	−0.0584884	+	0.0649580i	−0.00761455	+	0.00845681i	−0.746940	−	0.664891i	$-0.768478\pi$
$59$	−0.0584884	+	0.0649580i	−0.00761455	+	0.00845681i	0.739326	+	0.673348i	$0.235144\pi$
$60$	−0.190983	+	0.587785i	−0.0246558	+	0.0758827i
$61$	0.553899			0.0709195			0.0354597	−	0.999371i	$-0.488710\pi$
$61$	0.553899			0.0709195			0.0354597	+	0.999371i	$0.488710\pi$
$62$	5.46698	−	1.05459i	0.694307	−	0.133933i
$63$	−7.73968			−0.975108
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−3.96241	+	4.40070i	−0.491476	+	0.545840i
$66$	−0.186415	−	0.135438i	−0.0229461	−	0.0166713i
$67$	−0.408977	+	0.708369i	−0.0499645	+	0.0865411i	−0.889926	−	0.456105i	$-0.849244\pi$
$67$	−0.408977	+	0.708369i	−0.0499645	+	0.0865411i	0.839961	+	0.542646i	$0.182577\pi$
$68$	0.277438	+	0.480536i	0.0336442	+	0.0582735i
$69$	−0.326789	+	3.10919i	−0.0393408	+	0.374303i
$70$	−2.39169	+	1.73767i	−0.285862	+	0.207691i
$71$	0.428006	+	4.07221i	0.0507950	+	0.483282i	0.990117	+	0.140245i	$0.0447890\pi$
$71$	0.428006	+	4.07221i	0.0507950	+	0.483282i	−0.939322	+	0.343037i	$0.888544\pi$
$72$	−1.75181	−	1.94558i	−0.206452	−	0.229289i
$73$	15.0903	−	6.71864i	1.76619	−	0.786357i	0.778952	−	0.627083i	$-0.215751\pi$
$73$	15.0903	−	6.71864i	1.76619	−	0.786357i	0.987234	−	0.159274i	$-0.0509153\pi$
$74$	−0.183591	+	0.0390235i	−0.0213420	+	0.00453639i
$75$	0.604528	+	0.128496i	0.0698049	+	0.0148375i
$76$	4.14583	+	1.84584i	0.475560	+	0.211733i
$77$	−0.340596	−	1.04825i	−0.0388146	−	0.119459i
$78$	1.13095	+	3.48070i	0.128055	+	0.394112i
$79$	−11.5492	−	5.14203i	−1.29939	−	0.578523i	−0.363751	−	0.931496i	$-0.618504\pi$
$79$	−11.5492	−	5.14203i	−1.29939	−	0.578523i	−0.935634	+	0.352973i	$0.885171\pi$
$80$	−0.978148	−	0.207912i	−0.109360	−	0.0232452i
$81$	−5.58347	+	1.18680i	−0.620385	+	0.131867i
$82$	−0.0152505	+	0.00678996i	−0.00168414	+	0.000749826i
$83$	−5.35930	−	5.95210i	−0.588259	−	0.653328i	0.373369	−	0.927683i	$-0.378202\pi$
$83$	−5.35930	−	5.95210i	−0.588259	−	0.653328i	−0.961629	+	0.274355i	$0.911536\pi$
$84$	0.190983	+	1.81708i	0.0208380	+	0.198260i
$85$	0.448903	−	0.326147i	0.0486904	−	0.0353757i
$86$	−0.0487614	+	0.463934i	−0.00525808	+	0.0500273i
$87$	−1.50516	−	2.60701i	−0.161370	−	0.279501i
$88$	0.186415	−	0.322880i	0.0198719	−	0.0344191i
$89$	1.00585	+	0.730790i	0.106620	+	0.0774636i	0.639818	−	0.768527i	$-0.279010\pi$
$89$	1.00585	+	0.730790i	0.106620	+	0.0774636i	−0.533198	+	0.845990i	$0.679010\pi$
$90$	−1.75181	+	1.94558i	−0.184657	+	0.205082i
$91$	−5.40977	+	16.6496i	−0.567098	+	1.74535i
$92$	−5.05849			−0.527384
$93$	−3.35177	−	0.778849i	−0.347562	−	0.0807629i
$94$	−9.58911			−0.989041
$95$	1.40238	−	4.31607i	0.143881	−	0.442819i
$96$	−0.413545	+	0.459289i	−0.0422073	+	0.0468760i
$97$	13.7202	+	9.96828i	1.39307	+	1.01213i	0.995521	+	0.0945457i	$0.0301399\pi$
$97$	13.7202	+	9.96828i	1.39307	+	1.01213i	0.397551	+	0.917580i	$0.369860\pi$
$98$	−0.869841	+	1.50661i	−0.0878672	+	0.152190i
$99$	−0.488040	−	0.845310i	−0.0490498	−	0.0849568i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	14.1457	−	10.2774i	1.40755	−	1.02264i	0.413873	−	0.910334i	$-0.364176\pi$
$101$	14.1457	−	10.2774i	1.40755	−	1.02264i	0.993673	−	0.112308i	$-0.0358244\pi$
$102$	−0.0358461	−	0.341053i	−0.00354929	−	0.0337693i
$103$	−2.62999	−	2.92090i	−0.259141	−	0.287805i	0.599509	−	0.800368i	$-0.295363\pi$
$103$	−2.62999	−	2.92090i	−0.259141	−	0.287805i	−0.858650	+	0.512563i	$0.828696\pi$
$104$	−5.40977	+	2.40858i	−0.530471	+	0.236181i
$105$	1.78716	−	0.379874i	0.174409	−	0.0370719i
$106$	−3.57246	−	0.759350i	−0.346988	−	0.0737546i
$107$	1.95203	+	0.869099i	0.188710	+	0.0840190i	0.498916	−	0.866650i	$-0.333732\pi$
$107$	1.95203	+	0.869099i	0.188710	+	0.0840190i	−0.310207	+	0.950669i	$0.600398\pi$
$108$	1.07295	+	3.30220i	0.103245	+	0.317754i
$109$	−2.85495	−	8.78665i	−0.273455	−	0.841608i	−0.989624	−	0.143681i	$-0.954106\pi$
$109$	−2.85495	−	8.78665i	−0.273455	−	0.841608i	0.716169	−	0.697927i	$-0.245894\pi$
$110$	−0.340596	−	0.151643i	−0.0324746	−	0.0144586i
$111$	0.113466	+	0.0241179i	0.0107697	+	0.00228917i
$112$	−2.89169	+	0.614648i	−0.273239	+	0.0580788i
$113$	15.4984	−	6.90033i	1.45797	−	0.649128i	0.483845	−	0.875154i	$-0.339240\pi$
$113$	15.4984	−	6.90033i	1.45797	−	0.649128i	0.974121	+	0.226026i	$0.0725733\pi$
$114$	−1.87674	−	2.08434i	−0.175773	−	0.195216i
$115$	0.528756	+	5.03078i	0.0493068	+	0.469122i
$116$	3.94056	−	2.86298i	0.365871	−	0.265821i
$117$	−1.62053	+	15.4184i	−0.149818	+	1.42543i
$118$	0.0437048	+	0.0756989i	0.00402335	+	0.00696865i
$119$	0.820187	−	1.42061i	0.0751864	−	0.130227i
$120$	0.500000	+	0.363271i	0.0456435	+	0.0331620i
$121$	−7.26743	+	8.07129i	−0.660675	+	0.733754i
$122$	0.171164	−	0.526789i	0.0154965	−	0.0476932i
$123$	0.0103173			0.000930280
$124$	0.686415	−	5.52529i	0.0616419	−	0.496186i
$125$	1.00000			0.0894427
$126$	−2.39169	+	7.36087i	−0.213069	+	0.655759i
$127$	−3.58564	+	3.98225i	−0.318174	+	0.353368i	−0.880923	−	0.473260i	$-0.843077\pi$
$127$	−3.58564	+	3.98225i	−0.318174	+	0.353368i	0.562749	+	0.826628i	$0.309744\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	0.144153	−	0.249680i	0.0126920	−	0.0219831i
$130$	2.96086	+	5.12837i	0.259685	+	0.449787i
$131$	2.26015	−	21.5039i	0.197471	−	1.87881i	−0.227754	−	0.973719i	$-0.573138\pi$
$131$	2.26015	−	21.5039i	0.197471	−	1.87881i	0.425225	−	0.905088i	$-0.360195\pi$
$132$	−0.186415	+	0.135438i	−0.0162253	+	0.0117884i
$133$	−1.40238	−	13.3427i	−0.121601	−	1.15696i
$134$	0.547318	+	0.607858i	0.0472811	+	0.0525110i
$135$	3.17195	−	1.41224i	0.272998	−	0.121547i
$136$	0.542750	−	0.115365i	0.0465404	−	0.00989247i
$137$	13.4056	+	2.84945i	1.14532	+	0.243445i	0.741215	−	0.671268i	$-0.234250\pi$
$137$	13.4056	+	2.84945i	1.14532	+	0.243445i	0.404105	+	0.914713i	$0.367583\pi$
$138$	2.85603	+	1.27159i	0.243122	+	0.108245i
$139$	6.61793	+	20.3679i	0.561326	+	1.72758i	0.678624	+	0.734486i	$0.262577\pi$
$139$	6.61793	+	20.3679i	0.561326	+	1.72758i	−0.117298	+	0.993097i	$0.537423\pi$
$140$	0.913545	+	2.81160i	0.0772087	+	0.237624i
$141$	5.41403	+	2.41048i	0.455944	+	0.202999i
$142$	4.00516	+	0.851323i	0.336105	+	0.0714414i
$143$	−2.15955	+	0.459026i	−0.180590	+	0.0383857i
$144$	−2.39169	+	1.06485i	−0.199308	+	0.0887375i
$145$	−3.25920	−	3.61971i	−0.270662	−	0.300600i
$146$	−1.72664	−	16.4279i	−0.142898	−	1.35958i
$147$	0.869841	−	0.631976i	0.0717432	−	0.0521245i
$148$	−0.0196192	+	0.186665i	−0.00161269	+	0.0153437i
$149$	−8.03296	−	13.9135i	−0.658086	−	1.13984i	−0.981111	−	0.193447i	$-0.938033\pi$
$149$	−8.03296	−	13.9135i	−0.658086	−	1.13984i	0.323025	−	0.946390i	$-0.395300\pi$
$150$	0.309017	−	0.535233i	0.0252311	−	0.0437016i
$151$	12.3519	+	8.97416i	1.00518	+	0.730307i	0.963193	−	0.268811i	$-0.0866309\pi$
$151$	12.3519	+	8.97416i	1.00518	+	0.730307i	0.0419880	+	0.999118i	$0.486631\pi$
$152$	3.03664	−	3.37253i	0.246304	−	0.273548i
$153$	0.448903	−	1.38158i	0.0362917	−	0.111694i
$154$	−1.10219			−0.0888173
$155$	−5.56677	−	0.105104i	−0.447134	−	0.00844218i
$156$	3.65983			0.293021
$157$	0.479528	−	1.47583i	0.0382705	−	0.117784i	−0.930096	−	0.367316i	$-0.880277\pi$
$157$	0.479528	−	1.47583i	0.0382705	−	0.117784i	0.968367	+	0.249532i	$0.0802767\pi$
$158$	−8.45926	+	9.39495i	−0.672982	+	0.747422i
$159$	1.82614	+	1.32677i	0.144822	+	0.105219i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	7.47719	+	12.9509i	0.589285	+	1.02067i
$162$	−0.596670	+	5.67693i	−0.0468788	+	0.446022i
$163$	6.75999	−	4.91142i	0.529483	−	0.384692i	−0.290681	−	0.956820i	$-0.593882\pi$
$163$	6.75999	−	4.91142i	0.529483	−	0.384692i	0.820164	+	0.572128i	$0.193882\pi$
$164$	0.00174497	+	0.0166023i	0.000136259	+	0.00129642i
$165$	0.154182	+	0.171236i	0.0120030	+	0.0133307i
$166$	−7.31690	+	3.25769i	−0.567901	+	0.252846i
$167$	19.6846	−	4.18410i	1.52324	−	0.323775i	0.631162	−	0.775651i	$-0.282578\pi$
$167$	19.6846	−	4.18410i	1.52324	−	0.323775i	0.892081	+	0.451875i	$0.149245\pi$
$168$	1.78716	+	0.379874i	0.137883	+	0.0293079i
$169$	20.1591	+	8.97540i	1.55070	+	0.690415i
$170$	−0.171466	−	0.527718i	−0.0131508	−	0.0404741i
$171$	−3.67147	−	11.2996i	−0.280764	−	0.864103i
$172$	0.426159	+	0.189738i	0.0324943	+	0.0144674i
$173$	−1.32689	−	0.282039i	−0.100882	−	0.0214431i	0.157194	−	0.987568i	$-0.449755\pi$
$173$	−1.32689	−	0.282039i	−0.100882	−	0.0214431i	−0.258076	+	0.966125i	$0.583088\pi$
$174$	−2.94453	+	0.625880i	−0.223225	+	0.0474479i
$175$	2.70071	−	1.20243i	0.204154	−	0.0908954i
$176$	−0.249471	−	0.277066i	−0.0188046	−	0.0208846i
$177$	−0.00564685	−	0.0537262i	−0.000424443	−	0.00403831i
$178$	1.00585	−	0.730790i	0.0753914	−	0.0547750i
$179$	0.0988399	−	0.940399i	0.00738764	−	0.0702887i	−0.990207	−	0.139608i	$-0.955416\pi$
$179$	0.0988399	−	0.940399i	0.00738764	−	0.0702887i	0.997595	+	0.0693188i	$0.0220826\pi$
$180$	1.30902	+	2.26728i	0.0975684	+	0.168993i
$181$	4.98272	−	8.63032i	0.370362	−	0.641486i	−0.619259	−	0.785187i	$-0.712567\pi$
$181$	4.98272	−	8.63032i	0.370362	−	0.641486i	0.989621	+	0.143700i	$0.0459002\pi$
$182$	14.1630	+	10.2900i	1.04983	+	0.762745i
$183$	−0.229062	+	0.254399i	−0.0169328	+	0.0188057i
$184$	−1.56316	+	4.81091i	−0.115238	+	0.354665i
$185$	0.187693			0.0137994
$186$	−1.77648	+	2.94704i	−0.130258	+	0.216088i
$187$	0.206874			0.0151281
$188$	−2.96320	+	9.11979i	−0.216113	+	0.665129i
$189$	6.86840	−	7.62813i	0.499602	−	0.554865i
$190$	−3.67147	−	2.66748i	−0.266356	−	0.193519i
$191$	−1.21878	+	2.11100i	−0.0881881	+	0.152746i	−0.906745	−	0.421679i	$-0.861441\pi$
$191$	−1.21878	+	2.11100i	−0.0881881	+	0.152746i	0.818557	+	0.574425i	$0.194774\pi$
$192$	0.309017	+	0.535233i	0.0223014	+	0.0386271i
$193$	−2.00522	+	19.0784i	−0.144339	+	1.37329i	0.647268	+	0.762263i	$0.275912\pi$
$193$	−2.00522	+	19.0784i	−0.144339	+	1.37329i	−0.791607	+	0.611031i	$0.790755\pi$
$194$	13.7202	−	9.96828i	0.985050	−	0.715681i
$195$	−0.382556	−	3.63978i	−0.0273954	−	0.260650i
$196$	1.16407	+	1.29284i	0.0831481	+	0.0923454i
$197$	−24.1639	+	10.7584i	−1.72160	+	0.766508i	−0.724599	+	0.689170i	$0.757975\pi$
$197$	−24.1639	+	10.7584i	−1.72160	+	0.766508i	−0.997005	+	0.0773371i	$0.975358\pi$
$198$	−0.954750	+	0.202938i	−0.0678511	+	0.0144222i
$199$	−15.7875	−	3.35573i	−1.11914	−	0.237881i	−0.389042	−	0.921220i	$-0.627194\pi$
$199$	−15.7875	−	3.35573i	−1.11914	−	0.237881i	−0.730102	+	0.683339i	$0.760527\pi$
$200$	0.913545	+	0.406737i	0.0645974	+	0.0287606i
$201$	−0.156215	−	0.480781i	−0.0110186	−	0.0339117i
$202$	−5.40317	−	16.6292i	−0.380165	−	1.17003i
$203$	−13.1546	−	5.85681i	−0.923272	−	0.411067i
$204$	−0.335438	−	0.0712995i	−0.0234853	−	0.00499196i
$205$	0.0163289	−	0.00347083i	0.00114046	−	0.000242413i
$206$	−3.59066	+	1.59866i	−0.250173	+	0.111384i
$207$	8.86149	+	9.84169i	0.615916	+	0.684044i
$208$	0.618989	+	5.88929i	0.0429192	+	0.408349i
$209$	1.36883	−	0.994513i	0.0946839	−	0.0687919i
$210$	0.190983	−	1.81708i	0.0131791	−	0.125391i
$211$	1.48127	+	2.56564i	0.101975	+	0.176626i	0.912498	−	0.409081i	$-0.134150\pi$
$211$	1.48127	+	2.56564i	0.101975	+	0.176626i	−0.810523	+	0.585706i	$0.800817\pi$
$212$	−1.82614	+	3.16296i	−0.125420	+	0.217233i
$213$	−2.04732	−	1.48746i	−0.140280	−	0.101919i
$214$	1.42977	−	1.58792i	0.0977372	−	0.108548i
$215$	0.144153	−	0.443658i	0.00983116	−	0.0302572i
$216$	3.47214			0.236249
$217$	−15.1606	+	6.40982i	−1.02917	+	0.435127i
$218$	−9.23883			−0.625732
$219$	−3.15473	+	9.70927i	−0.213177	+	0.656092i
$220$	−0.249471	+	0.277066i	−0.0168194	+	0.0186798i
$221$	−2.65828	−	1.93136i	−0.178815	−	0.129917i
$222$	0.0580002	−	0.100459i	0.00389272	−	0.00674239i
$223$	1.84624	+	3.19779i	0.123634	+	0.214140i	0.921198	−	0.389094i	$-0.127212\pi$
$223$	1.84624	+	3.19779i	0.123634	+	0.214140i	−0.797564	+	0.603234i	$0.793879\pi$
$224$	−0.309017	+	2.94010i	−0.0206471	+	0.196444i
$225$	2.11803	−	1.53884i	0.141202	−	0.102589i
$226$	−1.77334	−	16.8722i	−0.117961	−	1.12232i
$227$	−6.10423	−	6.77943i	−0.405152	−	0.449967i	0.505694	−	0.862713i	$-0.331236\pi$
$227$	−6.10423	−	6.77943i	−0.405152	−	0.449967i	−0.910846	+	0.412746i	$0.864570\pi$
$228$	−2.56227	+	1.14079i	−0.169690	+	0.0755510i
$229$	4.03062	−	0.856736i	0.266351	−	0.0566147i	−0.0728001	−	0.997347i	$-0.523193\pi$
$229$	4.03062	−	0.856736i	0.266351	−	0.0566147i	0.339151	+	0.940732i	$0.389860\pi$
$230$	4.94795	+	1.05172i	0.326258	+	0.0693483i
$231$	0.622301	+	0.277066i	0.0409444	+	0.0182296i
$232$	−1.50516	−	4.63240i	−0.0988185	−	0.304132i
$233$	1.14320	+	3.51840i	0.0748934	+	0.230498i	0.981494	−	0.191491i	$-0.0613322\pi$
$233$	1.14320	+	3.51840i	0.0748934	+	0.230498i	−0.906601	+	0.421989i	$0.861332\pi$
$234$	14.1630	+	6.30575i	0.925861	+	0.412220i
$235$	9.37957	+	1.99369i	0.611856	+	0.130054i
$236$	0.0854995	−	0.0181735i	0.00556554	−	0.00118299i
$237$	7.13779	−	3.17795i	0.463649	−	0.206430i
$238$	−1.09762	−	1.21904i	−0.0711485	−	0.0790184i
$239$	−0.0828625	−	0.788384i	−0.00535993	−	0.0509963i	0.991515	−	0.129992i	$-0.0414953\pi$
$239$	−0.0828625	−	0.788384i	−0.00535993	−	0.0509963i	−0.996875	+	0.0789959i	$0.974829\pi$
$240$	0.500000	−	0.363271i	0.0322749	−	0.0234491i
$241$	−3.07616	+	29.2677i	−0.198153	+	1.88530i	0.217916	+	0.975968i	$0.430074\pi$
$241$	−3.07616	+	29.2677i	−0.198153	+	1.88530i	−0.416069	+	0.909333i	$0.636593\pi$
$242$	5.43050	+	9.40590i	0.349086	+	0.604634i
$243$	6.97214	−	12.0761i	0.447263	−	0.774682i
$244$	−0.448113	−	0.325573i	−0.0286875	−	0.0208427i
$245$	1.16407	−	1.29284i	0.0743700	−	0.0825962i
$246$	0.00318822	−	0.00981234i	0.000203274	−	0.000625612i
$247$	−26.8739			−1.70994
$248$	−5.04275	−	2.36023i	−0.320215	−	0.149875i
$249$	4.95004			0.313696
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	−7.17869	+	7.97275i	−0.453115	+	0.503235i	−0.925809	−	0.377991i	$-0.876615\pi$
$251$	−7.17869	+	7.97275i	−0.453115	+	0.503235i	0.472694	+	0.881227i	$0.343282\pi$
$252$	6.26153	+	4.54927i	0.394440	+	0.286577i
$253$	−0.942976	+	1.63328i	−0.0592844	+	0.102684i
$254$	2.67932	+	4.64073i	0.168116	+	0.291185i
$255$	−0.0358461	+	0.341053i	−0.00224477	+	0.0213576i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−1.19815	−	11.3997i	−0.0747388	−	0.711092i	−0.966165	−	0.257926i	$-0.916961\pi$
$257$	−1.19815	−	11.3997i	−0.0747388	−	0.711092i	0.891426	−	0.453166i	$-0.149706\pi$
$258$	−0.192914	−	0.214253i	−0.0120103	−	0.0133388i
$259$	0.506904	−	0.225688i	0.0314975	−	0.0140236i
$260$	5.79232	−	1.23120i	0.359225	−	0.0763556i
$261$	−12.4732	−	2.65127i	−0.772075	−	0.164110i
$262$	−19.7530	−	8.79461i	−1.22035	−	0.543333i
$263$	7.88743	+	24.2750i	0.486360	+	1.49686i	0.830002	+	0.557760i	$0.188339\pi$
$263$	7.88743	+	24.2750i	0.486360	+	1.49686i	−0.343643	+	0.939101i	$0.611661\pi$
$264$	0.0712040	+	0.219144i	0.00438231	+	0.0134874i
$265$	3.33652	+	1.48551i	0.204961	+	0.0912543i
$266$	−13.1230	−	2.78939i	−0.804624	−	0.171028i
$267$	−0.751607	+	0.159759i	−0.0459976	+	0.00977709i
$268$	0.747238	−	0.332692i	0.0456448	−	0.0203224i
$269$	−15.1752	−	16.8537i	−0.925245	−	1.02759i	−0.999539	−	0.0303527i	$-0.990337\pi$
$269$	−15.1752	−	16.8537i	−0.925245	−	1.02759i	0.0742939	−	0.997236i	$-0.476330\pi$
$270$	−0.362937	−	3.45312i	−0.0220876	−	0.210150i
$271$	−4.04557	+	2.93928i	−0.245751	+	0.178549i	−0.703842	−	0.710357i	$-0.748534\pi$
$271$	−4.04557	+	2.93928i	−0.245751	+	0.178549i	0.458091	+	0.888906i	$0.348534\pi$
$272$	0.0580002	−	0.551835i	0.00351678	−	0.0334599i
$273$	−5.40977	−	9.36999i	−0.327414	−	0.567098i
$274$	6.85256	−	11.8690i	0.413978	−	0.717031i
$275$	0.301625	+	0.219144i	0.0181887	+	0.0132149i
$276$	2.09191	−	2.32331i	0.125918	−	0.139847i
$277$	−2.07246	+	6.37838i	−0.124522	+	0.383240i	−0.993814	−	0.111060i	$-0.964575\pi$
$277$	−2.07246	+	6.37838i	−0.124522	+	0.383240i	0.869292	+	0.494300i	$0.164575\pi$
$278$	21.4161			1.28445
$279$	−11.9524	+	8.34377i	−0.715569	+	0.499528i
$280$	2.95630			0.176672
$281$	4.85285	−	14.9355i	0.289496	−	0.890979i	−0.695518	−	0.718508i	$-0.744825\pi$
$281$	4.85285	−	14.9355i	0.289496	−	0.890979i	0.985015	−	0.172470i	$-0.0551748\pi$
$282$	3.96553	−	4.40417i	0.236144	−	0.262265i
$283$	−20.5455	−	14.9272i	−1.22130	−	0.887329i	−0.225096	−	0.974337i	$-0.572270\pi$
$283$	−20.5455	−	14.9272i	−1.22130	−	0.887329i	−0.996208	+	0.0870074i	$0.972270\pi$
$284$	2.04732	−	3.54606i	0.121486	−	0.210420i
$285$	1.40238	+	2.42899i	0.0830695	+	0.143881i
$286$	−0.230777	+	2.19570i	−0.0136461	+	0.129834i
$287$	0.0399263	−	0.0290082i	0.00235678	−	0.00171230i
$288$	0.273659	+	2.60369i	0.0161255	+	0.153424i
$289$	−11.1692	−	12.4047i	−0.657012	−	0.729686i
$290$	−4.44969	+	1.98113i	−0.261295	+	0.116336i
$291$	−10.2522	+	2.17918i	−0.600996	+	0.127746i
$292$	−16.1574	−	3.43437i	−0.945542	−	0.200981i
$293$	−17.8406	−	7.94313i	−1.04226	−	0.464042i	−0.187061	−	0.982348i	$-0.559896\pi$
$293$	−17.8406	−	7.94313i	−1.04226	−	0.464042i	−0.855195	+	0.518306i	$0.826563\pi$
$294$	−0.332250	−	1.02256i	−0.0193772	−	0.0596369i
$295$	−0.0270111	−	0.0831315i	−0.00157264	−	0.00484010i
$296$	0.171466	+	0.0763415i	0.00996625	+	0.00443726i
$297$	1.26623	+	0.269145i	0.0734739	+	0.0156174i
$298$	−15.7148	+	3.34029i	−0.910336	+	0.193498i
$299$	27.3652	−	12.1838i	1.58257	−	0.704607i
$300$	−0.413545	−	0.459289i	−0.0238761	−	0.0265170i
$301$	−0.144153	−	1.37152i	−0.00830884	−	0.0790534i
$302$	12.3519	−	8.97416i	0.710770	−	0.516405i
$303$	−1.12957	+	10.7471i	−0.0648920	+	0.617407i
$304$	−2.26909	−	3.93018i	−0.130141	−	0.225411i
$305$	−0.276949	+	0.479690i	−0.0158581	+	0.0274670i
$306$	−1.17524	−	0.853865i	−0.0671842	−	0.0488122i
$307$	20.3368	−	22.5863i	1.16068	−	1.28907i	0.210426	−	0.977610i	$-0.432515\pi$
$307$	20.3368	−	22.5863i	1.16068	−	1.28907i	0.950259	−	0.311461i	$-0.100818\pi$
$308$	−0.340596	+	1.04825i	−0.0194073	+	0.0597295i
$309$	2.42916			0.138190
$310$	−1.82019	+	5.26184i	−0.103380	+	0.298852i
$311$	−21.2495			−1.20495			−0.602476	−	0.798137i	$-0.705819\pi$
$311$	−21.2495			−1.20495			−0.602476	+	0.798137i	$0.705819\pi$
$312$	1.13095	−	3.48070i	0.0640274	−	0.197056i
$313$	5.88800	−	6.53929i	0.332809	−	0.369622i	−0.553393	−	0.832920i	$-0.686667\pi$
$313$	5.88800	−	6.53929i	0.332809	−	0.369622i	0.886203	+	0.463298i	$0.153334\pi$
$314$	−1.25542	−	0.912116i	−0.0708474	−	0.0514737i
$315$	3.86984	−	6.70276i	0.218041	−	0.377658i
$316$	6.32108	+	10.9484i	0.355588	+	0.615897i
$317$	−1.12591	+	10.7124i	−0.0632376	+	0.601666i	0.916312	+	0.400465i	$0.131151\pi$
$317$	−1.12591	+	10.7124i	−0.0632376	+	0.601666i	−0.979550	+	0.201201i	$0.935515\pi$
$318$	1.82614	−	1.32677i	0.102405	−	0.0744013i
$319$	−0.189821	−	1.80603i	−0.0106279	−	0.101118i
$320$	0.669131	+	0.743145i	0.0374055	+	0.0415431i
$321$	−1.20642	+	0.537133i	−0.0673358	+	0.0299798i
$322$	14.6276	−	3.10919i	0.815164	−	0.173268i
$323$	2.46310	+	0.523547i	0.137050	+	0.0291310i
$324$	5.21470	+	2.32174i	0.289706	+	0.128985i
$325$	−1.82991	−	5.63190i	−0.101505	−	0.312401i
$326$	−2.58209	−	7.94684i	−0.143009	−	0.440135i
$327$	5.21626	+	2.32243i	0.288460	+	0.128431i
$328$	0.0163289	+	0.00347083i	0.000901615	+	0.000191644i
$329$	27.7288	−	5.89393i	1.52874	−	0.324943i
$330$	0.210500	−	0.0937207i	0.0115877	−	0.00515916i
$331$	−6.68836	−	7.42818i	−0.367626	−	0.408290i	0.530742	−	0.847533i	$-0.321913\pi$
$331$	−6.68836	−	7.42818i	−0.367626	−	0.408290i	−0.898368	+	0.439244i	$0.855247\pi$
$332$	0.837204	+	7.96546i	0.0459475	+	0.437162i
$333$	0.397540	−	0.288829i	0.0217850	−	0.0158278i
$334$	2.10357	−	20.0142i	0.115102	−	1.09513i
$335$	−0.408977	−	0.708369i	−0.0223448	−	0.0387023i
$336$	0.913545	−	1.58231i	0.0498380	−	0.0863219i
$337$	−13.2342	−	9.61518i	−0.720911	−	0.523772i	0.165764	−	0.986165i	$-0.446991\pi$
$337$	−13.2342	−	9.61518i	−0.720911	−	0.523772i	−0.886675	+	0.462393i	$0.846991\pi$
$338$	14.7656	−	16.3989i	0.803143	−	0.891981i
$339$	−3.24005	+	9.97184i	−0.175975	+	0.541596i
$340$	−0.554875			−0.0300923
$341$	−1.65605	−	1.25162i	−0.0896799	−	0.0677792i
$342$	−11.8811			−0.642457
$343$	−4.80554	+	14.7899i	−0.259475	+	0.798581i
$344$	0.312142	−	0.346669i	0.0168296	−	0.0186911i
$345$	−2.52924	−	1.83760i	−0.136170	−	0.0989332i
$346$	−0.678267	+	1.17479i	−0.0364639	+	0.0631573i
$347$	7.06976	+	12.2452i	0.379525	+	0.657356i	0.990993	−	0.133913i	$-0.0427542\pi$
$347$	7.06976	+	12.2452i	0.379525	+	0.657356i	−0.611468	+	0.791269i	$0.709421\pi$
$348$	−0.314664	+	2.99383i	−0.0168678	+	0.160486i
$349$	12.0238	−	8.73582i	0.643620	−	0.467618i	−0.217472	−	0.976067i	$-0.569781\pi$
$349$	12.0238	−	8.73582i	0.643620	−	0.467618i	0.861092	+	0.508449i	$0.169781\pi$
$350$	−0.309017	−	2.94010i	−0.0165177	−	0.157155i
$351$	−13.7580	−	15.2798i	−0.734349	−	0.815577i
$352$	−0.340596	+	0.151643i	−0.0181539	+	0.00808262i
$353$	−24.9462	+	5.30247i	−1.32775	+	0.282222i	−0.816568	−	0.577250i	$-0.804126\pi$
$353$	−24.9462	+	5.30247i	−1.32775	+	0.282222i	−0.511183	+	0.859472i	$0.670793\pi$
$354$	−0.0528416	−	0.0112318i	−0.00280850	−	0.000596965i
$355$	−3.74064	−	1.66544i	−0.198532	−	0.0883923i
$356$	−0.384199	−	1.18244i	−0.0203625	−	0.0626694i
$357$	0.313284	+	0.964188i	0.0165807	+	0.0510302i
$358$	−0.863829	−	0.384601i	−0.0456548	−	0.0203268i
$359$	15.2112	+	3.23324i	0.802816	+	0.170644i	0.591006	−	0.806667i	$-0.298731\pi$
$359$	15.2112	+	3.23324i	0.802816	+	0.170644i	0.211810	+	0.977311i	$0.432064\pi$
$360$	2.56082	−	0.544320i	0.134967	−	0.0286882i
$361$	1.45719	−	0.648782i	0.0766941	−	0.0341464i
$362$	−6.66818	−	7.40576i	−0.350472	−	0.389238i
$363$	−0.701644	−	6.67569i	−0.0368267	−	0.350383i
$364$	14.1630	−	10.2900i	0.742340	−	0.539342i
$365$	−1.72664	+	16.4279i	−0.0903766	+	0.859876i
$366$	0.171164	+	0.296465i	0.00894689	+	0.0154965i
$367$	10.0577	−	17.4205i	0.525009	−	0.909343i	−0.474566	−	0.880220i	$-0.657395\pi$
$367$	10.0577	−	17.4205i	0.525009	−	0.909343i	0.999576	−	0.0291233i	$-0.00927153\pi$
$368$	4.09240	+	2.97330i	0.213331	+	0.154994i
$369$	0.0292442	−	0.0324790i	0.00152239	−	0.00169079i
$370$	0.0580002	−	0.178506i	0.00301529	−	0.00928011i
$371$	10.7972			0.560562
$372$	2.25384	+	2.60022i	0.116856	+	0.134815i
$373$	−36.5822			−1.89415			−0.947077	−	0.321006i	$-0.895979\pi$
$373$	−36.5822			−1.89415			−0.947077	+	0.321006i	$0.895979\pi$
$374$	0.0639275	−	0.196749i	0.00330561	−	0.0101736i
$375$	−0.413545	+	0.459289i	−0.0213554	+	0.0237176i
$376$	7.75776	+	5.63634i	0.400076	+	0.290672i
$377$	−14.4218	+	24.9792i	−0.742759	+	1.28650i
$378$	−5.13233	−	8.88946i	−0.263979	−	0.457224i
$379$	−2.43513	+	23.1687i	−0.125084	+	1.19010i	0.734321	+	0.678802i	$0.237501\pi$
$379$	−2.43513	+	23.1687i	−0.125084	+	1.19010i	−0.859405	+	0.511295i	$0.829166\pi$
$380$	−3.67147	+	2.66748i	−0.188342	+	0.136839i
$381$	−0.346180	−	3.29368i	−0.0177353	−	0.168741i
$382$	1.63105	+	1.81147i	0.0834518	+	0.0926827i
$383$	−17.2889	+	7.69753i	−0.883423	+	0.393325i	−0.797743	−	0.602997i	$-0.793973\pi$
$383$	−17.2889	+	7.69753i	−0.883423	+	0.393325i	−0.0856800	+	0.996323i	$0.527306\pi$
$384$	0.604528	−	0.128496i	0.0308497	−	0.00655731i
$385$	1.07811	+	0.229159i	0.0549455	+	0.0116790i
$386$	17.5250	+	7.80263i	0.891999	+	0.397144i
$387$	−0.377398	−	1.16151i	−0.0191842	−	0.0590429i
$388$	−5.24064	−	16.1290i	−0.266053	−	0.818827i
$389$	9.60837	+	4.27792i	0.487164	+	0.216899i	0.635594	−	0.772024i	$-0.280755\pi$
$389$	9.60837	+	4.27792i	0.487164	+	0.216899i	−0.148430	+	0.988923i	$0.547422\pi$
$390$	−3.57985	−	0.760921i	−0.181273	−	0.0385307i
$391$	−2.74549	+	0.583573i	−0.138846	+	0.0295125i
$392$	1.58928	−	0.707592i	0.0802707	−	0.0357388i
$393$	8.94183	+	9.93091i	0.451056	+	0.500948i
$394$	2.76485	+	26.3057i	0.139291	+	1.32526i
$395$	10.2277	−	7.43087i	0.514612	−	0.373888i
$396$	−0.102028	+	0.970733i	−0.00512710	+	0.0487811i
$397$	−7.82867	−	13.5597i	−0.392910	−	0.680540i	0.599922	−	0.800058i	$-0.295198\pi$
$397$	−7.82867	−	13.5597i	−0.392910	−	0.680540i	−0.992832	+	0.119519i	$0.961865\pi$
$398$	−8.07008	+	13.9778i	−0.404517	+	0.700644i
$399$	6.70810	+	4.87372i	0.335825	+	0.243991i
$400$	0.669131	−	0.743145i	0.0334565	−	0.0371572i
$401$	−2.50251	+	7.70194i	−0.124970	+	0.384617i	−0.993896	−	0.110325i	$-0.964811\pi$
$401$	−2.50251	+	7.70194i	−0.124970	+	0.384617i	0.868926	+	0.494942i	$0.164811\pi$
$402$	−0.505523			−0.0252132
$403$	9.59478	+	31.5438i	0.477950	+	1.57131i
$404$	−17.4850			−0.869912
$405$	1.76393	−	5.42882i	0.0876505	−	0.269760i
$406$	−9.63515	+	10.7009i	−0.478185	+	0.531078i
$407$	0.0566129	+	0.0411316i	0.00280619	+	0.00203882i
$408$	−0.171466	+	0.296988i	−0.00848882	+	0.0147031i
$409$	−4.73903	−	8.20824i	−0.234330	−	0.405871i	0.724748	−	0.689014i	$-0.241956\pi$
$409$	−4.73903	−	8.20824i	−0.234330	−	0.405871i	−0.959078	+	0.283143i	$0.908623\pi$
$410$	0.00174497	−	0.0166023i	8.61780e−5	−	0.000819929i
$411$	−6.85256	+	4.97867i	−0.338012	+	0.245580i
$412$	0.410845	+	3.90893i	0.0202409	+	0.192579i
$413$	−0.172909	−	0.192035i	−0.00850830	−	0.00944942i
$414$	12.0984	−	5.38653i	0.594602	−	0.264734i
$415$	7.83432	−	1.66524i	0.384572	−	0.0817432i
$416$	5.79232	+	1.23120i	0.283992	+	0.0603644i
$417$	−12.0916	−	5.38351i	−0.592126	−	0.263632i
$418$	−0.522846	−	1.60916i	−0.0255733	−	0.0787064i
$419$	2.30250	+	7.08636i	0.112484	+	0.346192i	0.991414	−	0.130760i	$-0.0417417\pi$
$419$	2.30250	+	7.08636i	0.112484	+	0.346192i	−0.878930	+	0.476952i	$0.841742\pi$
$420$	−1.66913	−	0.743145i	−0.0814452	−	0.0362618i
$421$	25.6780	+	5.45803i	1.25147	+	0.266008i	0.785538	−	0.618813i	$-0.212386\pi$
$421$	25.6780	+	5.45803i	1.25147	+	0.266008i	0.465931	+	0.884821i	$0.345720\pi$
$422$	2.89781	−	0.615948i	0.141063	−	0.0299839i
$423$	22.9342	−	10.2110i	1.11510	−	0.496474i
$424$	2.44385	+	2.71417i	0.118684	+	0.131812i
$425$	0.0580002	+	0.551835i	0.00281342	+	0.0267680i
$426$	−2.04732	+	1.48746i	−0.0991929	+	0.0720679i
$427$	−0.171164	+	1.62852i	−0.00828321	+	0.0788095i
$428$	−1.06838	−	1.85049i	−0.0516421	−	0.0894468i
$429$	0.682246	−	1.18168i	0.0329391	−	0.0570522i
$430$	−0.377398	−	0.274195i	−0.0181997	−	0.0132229i
$431$	0.418602	−	0.464905i	0.0201634	−	0.0223937i	−0.732979	−	0.680251i	$-0.761871\pi$
$431$	0.418602	−	0.464905i	0.0201634	−	0.0223937i	0.753142	+	0.657858i	$0.228537\pi$
$432$	1.07295	−	3.30220i	0.0516223	−	0.158877i
$433$	16.3338			0.784952			0.392476	−	0.919762i	$-0.371619\pi$
$433$	16.3338			0.784952			0.392476	+	0.919762i	$0.371619\pi$
$434$	1.41121	+	16.3993i	0.0677403	+	0.787194i
$435$	3.01032			0.144334
$436$	−2.85495	+	8.78665i	−0.136728	+	0.420804i
$437$	−15.3608	+	17.0599i	−0.734806	+	0.816085i
$438$	8.25920	+	6.00066i	0.394640	+	0.286723i
$439$	12.2570	−	21.2297i	0.584995	−	1.01324i	−0.409881	−	0.912139i	$-0.634430\pi$
$439$	12.2570	−	21.2297i	0.584995	−	1.01324i	0.994876	−	0.101102i	$-0.0322367\pi$
$440$	0.186415	+	0.322880i	0.00888697	+	0.0153927i
$441$	0.476080	−	4.52959i	0.0226705	−	0.215695i
$442$	−2.65828	+	1.93136i	−0.126442	+	0.0918652i
$443$	2.51078	+	23.8885i	0.119291	+	1.13498i	0.876365	+	0.481648i	$0.159962\pi$
$443$	2.51078	+	23.8885i	0.119291	+	1.13498i	−0.757074	+	0.653329i	$0.773372\pi$
$444$	−0.0776195	−	0.0862052i	−0.00368366	−	0.00409112i
$445$	−1.13581	+	0.505693i	−0.0538424	+	0.0239722i
$446$	3.61180	−	0.767711i	0.171024	−	0.0363522i
$447$	9.71231	+	2.06441i	0.459376	+	0.0976434i
$448$	2.70071	+	1.20243i	0.127597	+	0.0568096i
$449$	11.4690	+	35.2978i	0.541254	+	1.66581i	0.729734	+	0.683731i	$0.239644\pi$
$449$	11.4690	+	35.2978i	0.541254	+	1.66581i	−0.188481	+	0.982077i	$0.560356\pi$
$450$	−0.809017	−	2.48990i	−0.0381374	−	0.117375i
$451$	0.00568583	+	0.00253150i	0.000267735	+	0.000119203i
$452$	−16.5944	−	3.52724i	−0.780534	−	0.165908i
$453$	−9.22979	+	1.96185i	−0.433653	+	0.0921759i
$454$	−8.33393	+	3.71051i	−0.391131	+	0.174143i
$455$	−11.7141	−	13.0098i	−0.549163	−	0.609907i
$456$	0.293176	+	2.78939i	0.0137292	+	0.130625i
$457$	10.4041	−	7.55901i	0.486682	−	0.353595i	−0.317225	−	0.948350i	$-0.602751\pi$
$457$	10.4041	−	7.55901i	0.486682	−	0.353595i	0.803907	+	0.594755i	$0.202751\pi$
$458$	0.430727	−	4.09810i	0.0201266	−	0.191492i
$459$	0.963301	+	1.66849i	0.0449630	+	0.0778783i
$460$	2.52924	−	4.38078i	0.117927	−	0.204255i
$461$	6.91370	+	5.02310i	0.322003	+	0.233949i	0.737030	−	0.675860i	$-0.236228\pi$
$461$	6.91370	+	5.02310i	0.322003	+	0.233949i	−0.415027	+	0.909809i	$0.636228\pi$
$462$	0.455807	−	0.506225i	0.0212061	−	0.0235517i
$463$	−4.25601	+	13.0987i	−0.197794	+	0.608746i	0.802139	+	0.597137i	$0.203695\pi$
$463$	−4.25601	+	13.0987i	−0.197794	+	0.608746i	−0.999933	+	0.0116087i	$0.996305\pi$
$464$	−4.87080			−0.226121
$465$	2.35039	−	2.51329i	0.108997	−	0.116551i
$466$	3.69947			0.171374
$467$	6.80788	−	20.9525i	0.315031	−	0.969567i	−0.660710	−	0.750641i	$-0.729745\pi$
$467$	6.80788	−	20.9525i	0.315031	−	0.969567i	0.975742	−	0.218926i	$-0.0702552\pi$
$468$	10.3737	−	11.5212i	0.479525	−	0.532567i
$469$	−1.95630	−	1.42133i	−0.0903333	−	0.0656310i
$470$	4.79456	−	8.30442i	0.221156	−	0.383054i
$471$	0.479528	+	0.830566i	0.0220955	+	0.0382705i
$472$	0.00913679	−	0.0869308i	0.000420555	−	0.00400131i
$473$	0.140705	−	0.102228i	0.00646962	−	0.00470045i
$474$	−0.816711	−	7.77048i	−0.0375128	−	0.356910i
$475$	3.03664	+	3.37253i	0.139330	+	0.154742i
$476$	−1.49856	+	0.667200i	−0.0686862	+	0.0305811i
$477$	9.35282	−	1.98800i	0.428236	−	0.0910245i
$478$	−0.775404	−	0.164817i	−0.0354662	−	0.00753856i
$479$	34.4256	+	15.3273i	1.57295	+	0.700320i	0.993409	−	0.114626i	$-0.0365669\pi$
$479$	34.4256	+	15.3273i	1.57295	+	0.700320i	0.579537	+	0.814946i	$0.303234\pi$
$480$	−0.190983	−	0.587785i	−0.00871714	−	0.0268286i
$481$	−0.343462	−	1.05707i	−0.0156605	−	0.0481981i
$482$	26.8847	+	11.9698i	1.22456	+	0.545211i
$483$	−9.04035	−	1.92159i	−0.411350	−	0.0874352i
$484$	10.6237	−	2.25813i	0.482894	−	0.102642i
$485$	−15.4929	+	6.89787i	−0.703495	+	0.313216i
$486$	−9.33054	−	10.3626i	−0.423242	−	0.470058i
$487$	−2.96087	−	28.1708i	−0.134170	−	1.27654i	−0.829768	−	0.558109i	$-0.811527\pi$
$487$	−2.96087	−	28.1708i	−0.134170	−	1.27654i	0.695598	−	0.718431i	$-0.255139\pi$
$488$	−0.448113	+	0.325573i	−0.0202851	+	0.0147380i
$489$	−0.539803	+	5.13588i	−0.0244107	+	0.232253i
$490$	−0.869841	−	1.50661i	−0.0392954	−	0.0680616i
$491$	−7.47232	+	12.9424i	−0.337221	+	0.584084i	−0.983909	−	0.178671i	$-0.942820\pi$
$491$	−7.47232	+	12.9424i	−0.337221	+	0.584084i	0.646688	+	0.762755i	$0.276154\pi$
$492$	−0.00834687	−	0.00606436i	−0.000376306	−	0.000273402i
$493$	1.80845	−	2.00849i	0.0814484	−	0.0904576i
$494$	−8.30448	+	25.5586i	−0.373636	+	1.14993i
$495$	0.976080			0.0438715
$496$	−3.80301	+	4.06659i	−0.170760	+	0.182595i
$497$	−12.1050			−0.542981
$498$	1.52965	−	4.70777i	0.0685452	−	0.210960i
$499$	22.4583	−	24.9424i	1.00537	−	1.11658i	0.0121971	−	0.999926i	$-0.496117\pi$
$499$	22.4583	−	24.9424i	1.00537	−	1.11658i	0.993173	−	0.116651i	$-0.0372159\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	−6.21878	+	10.7712i	−0.277835	+	0.481224i
$502$	5.36419	+	9.29106i	0.239416	+	0.414680i
$503$	2.66750	−	25.3795i	0.118938	−	1.13162i	−0.758415	−	0.651772i	$-0.774026\pi$
$503$	2.66750	−	25.3795i	0.118938	−	1.13162i	0.877353	−	0.479846i	$-0.159307\pi$
$504$	6.26153	−	4.54927i	0.278911	−	0.202641i
$505$	1.82768	+	17.3892i	0.0813307	+	0.773810i
$506$	1.26195	+	1.40154i	0.0561004	+	0.0623059i
$507$	−12.4590	+	5.54710i	−0.553323	+	0.246355i
$508$	5.24155	−	1.11413i	0.232556	−	0.0494313i
$509$	−9.96013	−	2.11709i	−0.441475	−	0.0938384i	−0.0181892	−	0.999835i	$-0.505790\pi$
$509$	−9.96013	−	2.11709i	−0.441475	−	0.0938384i	−0.423286	+	0.905996i	$0.639123\pi$
$510$	0.313284	+	0.139483i	0.0138724	+	0.00617641i
$511$	15.0903	+	46.4432i	0.667556	+	2.05453i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	14.3949	+	6.40902i	0.635550	+	0.282965i
$514$	−11.2120	−	2.38318i	−0.494539	−	0.105118i
$515$	3.84457	−	0.817190i	0.169412	−	0.0360097i
$516$	−0.263381	+	0.117265i	−0.0115947	+	0.00516229i
$517$	2.39221	+	2.65682i	0.105209	+	0.116847i
$518$	−0.0580002	−	0.551835i	−0.00254838	−	0.0242463i
$519$	0.678267	−	0.492790i	0.0297726	−	0.0216311i
$520$	0.618989	−	5.88929i	0.0271445	−	0.258262i
$521$	−7.90589	−	13.6934i	−0.346363	−	0.599919i	0.639237	−	0.769010i	$-0.279250\pi$
$521$	−7.90589	−	13.6934i	−0.346363	−	0.599919i	−0.985600	+	0.169091i	$0.945917\pi$
$522$	−6.37595	+	11.0435i	−0.279068	+	0.483360i
$523$	−2.08215	−	1.51277i	−0.0910462	−	0.0661489i	0.541331	−	0.840810i	$-0.317921\pi$
$523$	−2.08215	−	1.51277i	−0.0910462	−	0.0661489i	−0.632377	+	0.774661i	$0.717921\pi$
$524$	−14.4682	+	16.0686i	−0.632046	+	0.701958i
$525$	−0.564602	+	1.73767i	−0.0246413	+	0.0758380i
$526$	25.5242			1.11291
$527$	−0.264874	−	3.07804i	−0.0115381	−	0.134081i
$528$	0.230421			0.0100278
$529$	0.799830	−	2.46162i	0.0347752	−	0.107027i
$530$	2.44385	−	2.71417i	0.106154	−	0.117896i
$531$	−0.185136	−	0.134510i	−0.00803424	−	0.00583722i
$532$	−6.70810	+	11.6188i	−0.290833	+	0.503738i
$533$	−0.0494279	−	0.0856117i	−0.00214096	−	0.00370825i
$534$	−0.0803195	+	0.764189i	−0.00347576	+	0.0330697i
$535$	−1.72868	+	1.25596i	−0.0747372	+	0.0542997i
$536$	−0.0854995	−	0.813473i	−0.00369302	−	0.0351367i
$537$	0.391040	+	0.434294i	0.0168746	+	0.0187412i
$538$	−20.7182	+	9.22434i	−0.893226	+	0.397690i
$539$	0.634430	−	0.134852i	0.0273269	−	0.00580850i
$540$	−3.39626	−	0.721898i	−0.146152	−	0.0310655i
$541$	−12.7255	−	5.66574i	−0.547111	−	0.243589i	0.114518	−	0.993421i	$-0.463468\pi$
$541$	−12.7255	−	5.66574i	−0.547111	−	0.243589i	−0.661628	+	0.749832i	$0.730134\pi$
$542$	1.54527	+	4.75586i	0.0663751	+	0.204282i
$543$	1.90323	+	5.85753i	0.0816753	+	0.251371i
$544$	−0.506904	−	0.225688i	−0.0217333	−	0.00967629i
$545$	9.03694	+	1.92086i	0.387100	+	0.0822806i
$546$	−10.5831	+	2.24951i	−0.452915	+	0.0962700i
$547$	26.7414	−	11.9060i	1.14338	−	0.509065i	0.254439	−	0.967089i	$-0.418109\pi$
$547$	26.7414	−	11.9060i	1.14338	−	0.509065i	0.888940	+	0.458024i	$0.151443\pi$
$548$	−9.17051	−	10.1849i	−0.391745	−	0.435077i
$549$	0.151579	+	1.44218i	0.00646925	+	0.0615508i
$550$	0.301625	−	0.219144i	0.0128613	−	0.00934431i
$551$	2.31056	−	21.9835i	0.0984330	−	0.936527i
$552$	−1.56316	−	2.70747i	−0.0665325	−	0.115238i
$553$	18.6870	−	32.3668i	0.794651	−	1.37638i
$554$	5.42577	+	3.94205i	0.230519	+	0.167482i
$555$	−0.0776195	+	0.0862052i	−0.00329476	+	0.00365921i
$556$	6.61793	−	20.3679i	0.280663	−	0.863791i
$557$	−24.7020			−1.04666			−0.523329	−	0.852131i	$-0.675310\pi$
$557$	−24.7020			−1.04666			−0.523329	+	0.852131i	$0.675310\pi$
$558$	4.24191	+	13.9457i	0.179575	+	0.590370i
$559$	−2.76242			−0.116838
$560$	0.913545	−	2.81160i	0.0386043	−	0.118812i
$561$	−0.0855517	+	0.0950147i	−0.00361199	+	0.00401153i
$562$	−12.7049	−	9.23066i	−0.535924	−	0.389372i
$563$	−19.4935	+	33.7637i	−0.821552	+	1.42297i	0.0829744	+	0.996552i	$0.473558\pi$
$563$	−19.4935	+	33.7637i	−0.821552	+	1.42297i	−0.904526	+	0.426418i	$0.859775\pi$
$564$	−2.96320	−	5.13241i	−0.124773	−	0.216113i
$565$	−1.77334	+	16.8722i	−0.0746048	+	0.709817i
$566$	−20.5455	+	14.9272i	−0.863592	+	0.627436i
$567$	−1.76393	−	16.7827i	−0.0740782	−	0.704807i
$568$	−2.73985	−	3.04291i	−0.114961	−	0.127678i
$569$	−5.03296	+	2.24082i	−0.210993	+	0.0939400i	−0.509512	−	0.860464i	$-0.670174\pi$
$569$	−5.03296	+	2.24082i	−0.210993	+	0.0939400i	0.298519	+	0.954404i	$0.403507\pi$
$570$	2.74346	−	0.583140i	0.114911	−	0.0244251i
$571$	28.4824	+	6.05411i	1.19195	+	0.253357i	0.760838	−	0.648942i	$-0.224788\pi$
$571$	28.4824	+	6.05411i	1.19195	+	0.253357i	0.431112	+	0.902299i	$0.358121\pi$
$572$	2.01692	+	0.897990i	0.0843316	+	0.0375469i
$573$	−0.465534	−	1.43277i	−0.0194480	−	0.0598547i
$574$	−0.0152505	−	0.0469362i	−0.000636543	−	0.00195908i
$575$	−4.62116	−	2.05747i	−0.192716	−	0.0858025i
$576$	2.56082	+	0.544320i	0.106701	+	0.0226800i
$577$	−3.46761	+	0.737063i	−0.144358	+	0.0306843i	−0.279524	−	0.960139i	$-0.590177\pi$
$577$	−3.46761	+	0.737063i	−0.144358	+	0.0306843i	0.135166	+	0.990823i	$0.456843\pi$
$578$	−15.2490	+	6.78929i	−0.634275	+	0.282397i
$579$	−7.93325	−	8.81077i	−0.329695	−	0.366163i
$580$	0.509137	+	4.84411i	0.0211408	+	0.201141i
$581$	19.1559	−	13.9176i	0.794720	−	0.577398i
$582$	−1.09559	+	10.4239i	−0.0454137	+	0.432083i
$583$	0.680837	+	1.17924i	0.0281974	+	0.0488393i
$584$	−8.25920	+	14.3054i	−0.341768	+	0.591960i
$585$	−12.5424	−	9.11260i	−0.518565	−	0.376760i
$586$	−13.0674	+	14.5128i	−0.539809	+	0.599519i
$587$	7.30292	−	22.4761i	0.301424	−	0.927687i	−0.679564	−	0.733616i	$-0.737831\pi$
$587$	7.30292	−	22.4761i	0.301424	−	0.927687i	0.980988	−	0.194070i	$-0.0621690\pi$
$588$	−1.07518			−0.0443398
$589$	−16.5498	−	19.0932i	−0.681922	−	0.786724i
$590$	−0.0874096			−0.00359860
$591$	5.05162	−	15.5473i	0.207796	−	0.639530i
$592$	0.125591	−	0.139483i	0.00516176	−	0.00573271i
$593$	32.1734	+	23.3754i	1.32120	+	0.959911i	0.999916	+	0.0129296i	$0.00411574\pi$
$593$	32.1734	+	23.3754i	1.32120	+	0.959911i	0.321288	+	0.946982i	$0.395884\pi$
$594$	0.647257	−	1.12108i	0.0265573	−	0.0459985i
$595$	0.820187	+	1.42061i	0.0336244	+	0.0582392i
$596$	−1.67935	+	15.9779i	−0.0687887	+	0.654481i
$597$	8.07008	−	5.86326i	0.330287	−	0.239967i
$598$	−3.13115	−	29.7909i	−0.128042	−	1.21824i
$599$	−32.0407	−	35.5848i	−1.30915	−	1.45396i	−0.808742	−	0.588164i	$-0.799851\pi$
$599$	−32.0407	−	35.5848i	−1.30915	−	1.45396i	−0.500406	−	0.865791i	$-0.666816\pi$
$600$	−0.564602	+	0.251377i	−0.0230498	+	0.0102624i
$601$	20.3496	−	4.32544i	0.830077	−	0.176438i	0.226771	−	0.973948i	$-0.427183\pi$
$601$	20.3496	−	4.32544i	0.830077	−	0.176438i	0.603306	+	0.797510i	$0.293850\pi$
$602$	−1.34894	−	0.286727i	−0.0549788	−	0.0116861i
$603$	−1.95630	−	0.870999i	−0.0796665	−	0.0354698i
$604$	−4.71799	−	14.5205i	−0.191972	−	0.590830i
$605$	−3.35623	−	10.3294i	−0.136450	−	0.419951i
$606$	9.87207	+	4.39533i	0.401026	+	0.178548i
$607$	42.3475	+	9.00124i	1.71883	+	0.365349i	0.958700	−	0.284420i	$-0.0918009\pi$
$607$	42.3475	+	9.00124i	1.71883	+	0.365349i	0.760132	+	0.649769i	$0.225134\pi$
$608$	−4.43901	+	0.943541i	−0.180026	+	0.0382656i
$609$	8.12999	−	3.61971i	0.329444	−	0.146678i
$610$	0.370631	+	0.411627i	0.0150064	+	0.0166663i
$611$	−5.93556	−	56.4730i	−0.240127	−	2.28465i
$612$	−1.17524	+	0.853865i	−0.0475064	+	0.0345154i
$613$	−1.41578	+	13.4702i	−0.0571828	+	0.544058i	0.928004	+	0.372571i	$0.121524\pi$
$613$	−1.41578	+	13.4702i	−0.0571828	+	0.544058i	−0.985186	+	0.171487i	$0.945143\pi$
$614$	−15.1965	−	26.3210i	−0.613279	−	1.06223i
$615$	−0.00515865	+	0.00893505i	−0.000208017	+	0.000360296i
$616$	0.891693	+	0.647853i	0.0359273	+	0.0261027i
$617$	−22.7539	+	25.2707i	−0.916036	+	1.01736i	0.0837459	+	0.996487i	$0.473312\pi$
$617$	−22.7539	+	25.2707i	−0.916036	+	1.01736i	−0.999782	+	0.0208741i	$0.993355\pi$
$618$	0.750652	−	2.31027i	0.0301956	−	0.0929327i
$619$	−9.93059			−0.399144			−0.199572	−	0.979883i	$-0.563955\pi$
$619$	−9.93059			−0.399144			−0.199572	+	0.979883i	$0.563955\pi$
$620$	4.44183	+	3.35710i	0.178388	+	0.134824i
$621$	−17.5638			−0.704809
$622$	−6.56647	+	20.2095i	−0.263291	+	0.810328i
$623$	−2.45942	+	2.73146i	−0.0985346	+	0.109434i
$624$	−2.96086	−	2.15119i	−0.118529	−	0.0861167i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−4.39974	−	7.62057i	−0.175849	−	0.304579i
$627$	−0.109305	+	1.03996i	−0.00436521	+	0.0415322i
$628$	−1.25542	+	0.912116i	−0.0500967	+	0.0363974i
$629$	0.0108862	+	0.103575i	0.000434062	+	0.00412983i
$630$	−5.17886	−	5.75170i	−0.206331	−	0.229153i
$631$	37.4747	−	16.6848i	1.49184	−	0.664211i	0.511101	−	0.859521i	$-0.329238\pi$
$631$	37.4747	−	16.6848i	1.49184	−	0.664211i	0.980742	+	0.195310i	$0.0625713\pi$
$632$	12.3659	−	2.62845i	0.491889	−	0.104554i
$633$	−1.79094	−	0.380677i	−0.0711836	−	0.0151305i
$634$	9.84013	+	4.38111i	0.390801	+	0.173996i
$635$	−1.65591	−	5.09638i	−0.0657129	−	0.202244i
$636$	−0.697522	−	2.14675i	−0.0276585	−	0.0851242i
$637$	−9.41127	−	4.19017i	−0.372888	−	0.166020i
$638$	−1.77629	−	0.377562i	−0.0703241	−	0.0149478i
$639$	−10.4856	+	2.22879i	−0.414806	+	0.0881696i
$640$	0.913545	−	0.406737i	0.0361111	−	0.0160777i
$641$	−10.8866	−	12.0907i	−0.429993	−	0.477556i	0.488743	−	0.872428i	$-0.337456\pi$
$641$	−10.8866	−	12.0907i	−0.429993	−	0.477556i	−0.918736	+	0.394872i	$0.870789\pi$
$642$	0.138039	+	1.31336i	0.00544798	+	0.0518341i
$643$	16.1181	−	11.7105i	0.635637	−	0.461817i	−0.222711	−	0.974884i	$-0.571491\pi$
$643$	16.1181	−	11.7105i	0.635637	−	0.461817i	0.858349	+	0.513067i	$0.171491\pi$
$644$	1.56316	−	14.8725i	0.0615971	−	0.586057i
$645$	0.144153	+	0.249680i	0.00567602	+	0.00983116i
$646$	1.25906	−	2.18076i	0.0495371	−	0.0858008i
$647$	1.54449	+	1.12214i	0.0607204	+	0.0441159i	0.617731	−	0.786389i	$-0.288052\pi$
$647$	1.54449	+	1.12214i	0.0607204	+	0.0441159i	−0.557011	+	0.830505i	$0.688052\pi$
$648$	3.81953	−	4.24202i	0.150045	−	0.166642i
$649$	0.0100705	−	0.0309938i	0.000395302	−	0.00121661i
$650$	−5.92173			−0.232269
$651$	3.32565	−	9.61385i	0.130342	−	0.376797i
$652$	−8.35581			−0.327239
$653$	7.26726	−	22.3663i	0.284390	−	0.875262i	−0.702191	−	0.711988i	$-0.747795\pi$
$653$	7.26726	−	22.3663i	0.284390	−	0.875262i	0.986581	−	0.163273i	$-0.0522052\pi$
$654$	3.82068	−	4.24329i	0.149400	−	0.165926i
$655$	17.4929	+	12.7093i	0.683503	+	0.496594i
$656$	0.00834687	−	0.0144572i	0.000325891	−	0.000564459i
$657$	21.6229	+	37.4519i	0.843588	+	1.46114i
$658$	2.96320	−	28.1930i	0.115518	−	1.09908i
$659$	−36.1412	+	26.2581i	−1.40786	+	1.02287i	−0.414232	+	0.910171i	$0.635950\pi$
$659$	−36.1412	+	26.2581i	−1.40786	+	1.02287i	−0.993629	+	0.112700i	$0.964050\pi$
$660$	−0.0240856	−	0.229159i	−0.000937529	−	0.00892000i
$661$	−25.2379	−	28.0295i	−0.981641	−	1.09022i	−0.995912	−	0.0903242i	$-0.971210\pi$
$661$	−25.2379	−	28.0295i	−0.981641	−	1.09022i	0.0142718	−	0.999898i	$-0.495457\pi$
$662$	−9.13144	+	4.06558i	−0.354903	+	0.158013i
$663$	1.98637	−	0.422216i	0.0771443	−	0.0163975i
$664$	7.83432	+	1.66524i	0.304030	+	0.0646237i
$665$	12.2563	+	5.45686i	0.475279	+	0.211608i
$666$	−0.151847	−	0.467336i	−0.00588394	−	0.0181089i
$667$	7.61383	+	23.4330i	0.294809	+	0.907328i
$668$	−18.3846	−	8.18533i	−0.711320	−	0.316700i
$669$	−2.23221	−	0.474472i	−0.0863023	−	0.0183441i
$670$	−0.800080	+	0.170062i	−0.0309098	+	0.00657008i
$671$	−0.188656	+	0.0839950i	−0.00728298	+	0.00324259i
$672$	−1.22256	−	1.35779i	−0.0471614	−	0.0523780i
$673$	−1.93647	−	18.4243i	−0.0746454	−	0.710204i	−0.966288	−	0.257464i	$-0.917113\pi$
$673$	−1.93647	−	18.4243i	−0.0746454	−	0.710204i	0.891643	−	0.452740i	$-0.149553\pi$
$674$	−13.2342	+	9.61518i	−0.509761	+	0.370363i
$675$	−0.362937	+	3.45312i	−0.0139695	+	0.132910i
$676$	−11.0334	−	19.1105i	−0.424363	−	0.735018i
$677$	9.41479	−	16.3069i	0.361840	−	0.626725i	−0.626424	−	0.779483i	$-0.715482\pi$
$677$	9.41479	−	16.3069i	0.361840	−	0.626725i	0.988264	+	0.152758i	$0.0488154\pi$
$678$	8.48255	+	6.16293i	0.325770	+	0.236686i
$679$	−33.5475	+	37.2583i	−1.28744	+	1.42984i
$680$	−0.171466	+	0.527718i	−0.00657541	+	0.0202370i
$681$	5.63809			0.216052
$682$	−1.70211	+	1.18822i	−0.0651772	+	0.0454993i
$683$	6.65036			0.254469			0.127235	−	0.991873i	$-0.459390\pi$
$683$	6.65036			0.254469			0.127235	+	0.991873i	$0.459390\pi$
$684$	−3.67147	+	11.2996i	−0.140382	+	0.432051i
$685$	−9.17051	+	10.1849i	−0.350387	+	0.389144i
$686$	12.5811	+	9.14068i	0.480347	+	0.348993i
$687$	−1.27336	+	2.20552i	−0.0485816	+	0.0841458i
$688$	−0.233245	−	0.403991i	−0.00889237	−	0.0154020i
$689$	2.26072	−	21.5093i	0.0861264	−	0.819438i
$690$	−2.52924	+	1.83760i	−0.0962867	+	0.0699564i
$691$	2.20089	+	20.9401i	0.0837257	+	0.796597i	0.953143	+	0.302519i	$0.0978276\pi$
$691$	2.20089	+	20.9401i	0.0837257	+	0.796597i	−0.869418	+	0.494078i	$0.835506\pi$
$692$	0.907699	+	1.00810i	0.0345055	+	0.0383223i
$693$	2.63611	−	1.17367i	0.100137	−	0.0445841i
$694$	13.8305	−	2.93977i	0.525000	−	0.111592i
$695$	−20.9481	−	4.45265i	−0.794606	−	0.168899i
$696$	2.75006	+	1.22441i	0.104241	+	0.0464110i
$697$	0.00286241	+	0.00880958i	0.000108421	+	0.000333687i
$698$	−4.59269	−	14.1349i	−0.173836	−	0.535012i
$699$	−2.08873	−	0.929961i	−0.0790029	−	0.0351744i
$700$	−2.89169	−	0.614648i	−0.109296	−	0.0232315i
$701$	−46.3326	+	9.84831i	−1.74996	+	0.371965i	−0.967919	−	0.251262i	$-0.919154\pi$
$701$	−46.3326	+	9.84831i	−1.74996	+	0.371965i	−0.782041	+	0.623227i	$0.785821\pi$
$702$	−18.7834	+	8.36293i	−0.708936	+	0.315638i
$703$	0.569954	+	0.632999i	0.0214962	+	0.0238740i
$704$	0.0389713	+	0.370787i	0.00146878	+	0.0139746i
$705$	−4.79456	+	3.48345i	−0.180573	+	0.131194i
$706$	−2.66584	+	25.3638i	−0.100330	+	0.954578i
$707$	25.8454	+	44.7656i	0.972017	+	1.68358i
$708$	−0.0270111	+	0.0467845i	−0.00101514	+	0.00175827i
$709$	−33.7365	−	24.5110i	−1.26700	−	0.920530i	−0.267921	−	0.963441i	$-0.586337\pi$
$709$	−33.7365	−	24.5110i	−1.26700	−	0.920530i	−0.999079	+	0.0429111i	$0.986337\pi$
$710$	−2.73985	+	3.04291i	−0.102825	+	0.114198i
$711$	10.2277	−	31.4777i	0.383570	−	1.18051i
$712$	−1.24329			−0.0465944
$713$	25.5087	+	11.9392i	0.955308	+	0.447126i
$714$	1.01381			0.0379408
$715$	0.682246	−	2.09974i	0.0255145	−	0.0785257i
$716$	−0.632716	+	0.702702i	−0.0236457	+	0.0262612i
$717$	0.396364	+	0.287975i	0.0148025	+	0.0107546i
$718$	7.77551	−	13.4676i	0.290179	−	0.502605i
$719$	9.37378	+	16.2359i	0.349583	+	0.605495i	0.986175	−	0.165705i	$-0.0529900\pi$
$719$	9.37378	+	16.2359i	0.349583	+	0.605495i	−0.636592	+	0.771200i	$0.719657\pi$
$720$	0.273659	−	2.60369i	0.0101987	−	0.0970339i
$721$	9.40047	−	6.82984i	0.350092	−	0.254356i
$722$	−0.166732	−	1.58635i	−0.00620513	−	0.0590379i
$723$	−12.1702	−	13.5164i	−0.452615	−	0.502680i
$724$	−9.10388	+	4.05331i	−0.338343	+	0.150640i
$725$	4.76436	−	1.01270i	0.176944	−	0.0376106i
$726$	−6.56578	−	1.39560i	−0.243679	−	0.0517956i
$727$	−23.7535	−	10.5758i	−0.880970	−	0.392233i	−0.0841525	−	0.996453i	$-0.526818\pi$
$727$	−23.7535	−	10.5758i	−0.880970	−	0.392233i	−0.796818	+	0.604220i	$0.793485\pi$
$728$	−5.40977	−	16.6496i	−0.200499	−	0.617073i
$729$	−2.62868	−	8.09024i	−0.0973584	−	0.299638i
$730$	15.0903	+	6.71864i	0.558517	+	0.248668i
$731$	0.253187	+	0.0538165i	0.00936445	+	0.00199048i
$732$	0.334848	−	0.0711740i	0.0123763	−	0.00263067i
$733$	−25.0717	+	11.1627i	−0.926045	+	0.412302i	−0.813646	−	0.581361i	$-0.802520\pi$
$733$	−25.0717	+	11.1627i	−0.926045	+	0.412302i	−0.112400	+	0.993663i	$0.535854\pi$
$734$	−13.4599	−	14.9487i	−0.496813	−	0.551767i
$735$	0.112387	+	1.06929i	0.00414546	+	0.0394414i
$736$	4.09240	−	2.97330i	0.150848	−	0.109597i
$737$	0.0318767	−	0.303287i	0.00117419	−	0.0111717i
$738$	−0.0218524	−	0.0378495i	−0.000804398	−	0.00139326i
$739$	−12.8005	+	22.1711i	−0.470874	+	0.815578i	−0.999445	−	0.0333112i	$-0.989395\pi$
$739$	−12.8005	+	22.1711i	−0.470874	+	0.815578i	0.528571	+	0.848889i	$0.322728\pi$
$740$	−0.151847	−	0.110323i	−0.00558199	−	0.00405555i
$741$	11.1136	−	12.3429i	0.408267	−	0.453427i
$742$	3.33652	−	10.2687i	0.122487	−	0.376977i
$743$	19.2574			0.706486			0.353243	−	0.935532i	$-0.385079\pi$
$743$	19.2574			0.706486			0.353243	+	0.935532i	$0.385079\pi$
$744$	3.16943	−	1.34002i	0.116197	−	0.0491274i
$745$	16.0659			0.588610
$746$	−11.3045	+	34.7917i	−0.413888	+	1.27382i
$747$	14.0308	−	15.5828i	0.513361	−	0.570145i
$748$	−0.167364	−	0.121597i	−0.00611944	−	0.00444604i
$749$	−3.15845	+	5.47059i	−0.115407	+	0.199891i
$750$	0.309017	+	0.535233i	0.0112837	+	0.0195440i
$751$	0.493975	−	4.69986i	0.0180254	−	0.171500i	−0.981805	−	0.189889i	$-0.939187\pi$
$751$	0.493975	−	4.69986i	0.0180254	−	0.171500i	0.999831	+	0.0183890i	$0.00585374\pi$
$752$	7.75776	−	5.63634i	0.282896	−	0.205536i
$753$	−0.693077	−	6.59419i	−0.0252571	−	0.240305i
$754$	19.3001	+	21.4349i	0.702868	+	0.780614i
$755$	−13.9478	+	6.20995i	−0.507612	+	0.226003i
$756$	−10.0404	+	2.13414i	−0.365164	+	0.0776180i
$757$	−17.2504	−	3.66668i	−0.626975	−	0.133268i	−0.116543	−	0.993186i	$-0.537181\pi$
$757$	−17.2504	−	3.66668i	−0.626975	−	0.133268i	−0.510432	+	0.859918i	$0.670515\pi$
$758$	21.2823	+	9.47548i	0.773007	+	0.344165i
$759$	−0.360185	−	1.10853i	−0.0130739	−	0.0402373i
$760$	1.40238	+	4.31607i	0.0508695	+	0.156560i
$761$	−42.6682	−	18.9971i	−1.54672	−	0.688645i	−0.556851	−	0.830612i	$-0.687991\pi$
$761$	−42.6682	−	18.9971i	−1.54672	−	0.688645i	−0.989871	+	0.141967i	$0.954657\pi$
$762$	−3.23946	−	0.688568i	−0.117353	−	0.0249442i
$763$	26.7159	−	5.67863i	0.967179	−	0.205580i
$764$	2.22683	−	0.991448i	0.0805639	−	0.0358693i
$765$	0.972034	+	1.07955i	0.0351440	+	0.0390313i
$766$	1.97821	+	18.8214i	0.0714757	+	0.680045i
$767$	−0.418760	+	0.304247i	−0.0151205	+	0.0109857i
$768$	0.0646021	−	0.614648i	0.00233113	−	0.0221792i
$769$	−21.5438	−	37.3150i	−0.776891	−	1.34561i	−0.933726	−	0.357989i	$-0.883462\pi$
$769$	−21.5438	−	37.3150i	−0.776891	−	1.34561i	0.156835	−	0.987625i	$-0.449871\pi$
$770$	0.551097	−	0.954527i	0.0198601	−	0.0343988i
$771$	5.73123	+	4.16398i	0.206405	+	0.149962i
$772$	12.8363	−	14.2561i	0.461987	−	0.513089i
$773$	−4.00760	+	12.3341i	−0.144143	+	0.443627i	−0.996900	−	0.0786813i	$-0.974929\pi$
$773$	−4.00760	+	12.3341i	−0.144143	+	0.443627i	0.852757	+	0.522308i	$0.174929\pi$
$774$	−1.22128			−0.0438982
$775$	2.87441	−	4.76841i	0.103252	−	0.171286i
$776$	−16.9591			−0.608795
$777$	−0.105972	+	0.326147i	−0.00380171	+	0.0117005i
$778$	7.03769	−	7.81615i	0.252314	−	0.280223i
$779$	0.0612905	+	0.0445302i	0.00219596	+	0.00159546i
$780$	−1.82991	+	3.16950i	−0.0655214	+	0.113486i
$781$	−0.763300	−	1.32207i	−0.0273130	−	0.0473075i
$782$	−0.293394	+	2.79145i	−0.0104917	+	0.0998222i
$783$	13.6821	−	9.94066i	0.488960	−	0.355250i
$784$	−0.181846	−	1.73015i	−0.00649451	−	0.0617911i
$785$	1.03835	+	1.15320i	0.0370602	+	0.0411595i
$786$	12.2080	−	5.43537i	0.435446	−	0.193873i
$787$	13.4274	−	2.85407i	0.478633	−	0.101737i	0.0377239	−	0.999288i	$-0.487989\pi$
$787$	13.4274	−	2.85407i	0.478633	−	0.101737i	0.440910	+	0.897552i	$0.354656\pi$
$788$	25.8726	+	5.49940i	0.921674	+	0.195908i
$789$	−14.4110	−	6.41621i	−0.513047	−	0.228423i
$790$	−3.90664	−	12.0234i	−0.138992	−	0.427774i
$791$	15.4984	+	47.6991i	0.551059	+	1.69599i
$792$	0.891693	+	0.397007i	0.0316849	+	0.0141070i
$793$	3.20836	+	0.681958i	0.113932	+	0.0242170i
$794$	−15.3152	+	3.25534i	−0.543516	+	0.115528i
$795$	−2.06208	+	0.918097i	−0.0731345	+	0.0325616i
$796$	10.7999	+	11.9945i	0.382792	+	0.425133i
$797$	0.330946	+	3.14874i	0.0117227	+	0.111534i	0.998818	−	0.0485970i	$-0.0154750\pi$
$797$	0.330946	+	3.14874i	0.0117227	+	0.111534i	−0.987096	+	0.160131i	$0.948808\pi$
$798$	6.70810	−	4.87372i	0.237464	−	0.172528i
$799$	−0.556171	+	5.29161i	−0.0196759	+	0.187204i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−1.62749	+	2.81890i	−0.0575047	+	0.0996010i
$802$	6.55167	+	4.76006i	0.231347	+	0.168084i
$803$	−4.12087	+	4.57669i	−0.145422	+	0.161508i
$804$	−0.156215	+	0.480781i	−0.00550929	+	0.0169559i
$805$	−14.9544			−0.527073
$806$	32.9649	+	0.622399i	1.16114	+	0.0219231i
$807$	14.0163			0.493398
$808$	−5.40317	+	16.6292i	−0.190083	+	0.585014i
$809$	−21.5913	+	23.9796i	−0.759110	+	0.843077i	−0.991576	−	0.129528i	$-0.958654\pi$
$809$	−21.5913	+	23.9796i	−0.759110	+	0.843077i	0.232466	+	0.972605i	$0.425321\pi$
$810$	−4.61803	−	3.35520i	−0.162261	−	0.117890i
$811$	−17.1213	+	29.6550i	−0.601210	+	1.04133i	0.391428	+	0.920209i	$0.371981\pi$
$811$	−17.1213	+	29.6550i	−0.601210	+	1.04133i	−0.992638	+	0.121118i	$0.961352\pi$
$812$	7.19975	+	12.4703i	0.252662	+	0.437623i
$813$	0.323050	−	3.07361i	0.0113298	−	0.107796i
$814$	0.0566129	−	0.0411316i	0.00198428	−	0.00144166i
$815$	0.873419	+	8.31003i	0.0305945	+	0.291088i
$816$	0.229466	+	0.254848i	0.00803292	+	0.00892146i
$817$	1.93399	−	0.861066i	0.0676616	−	0.0301249i
$818$	−9.27094	+	1.97060i	−0.324151	+	0.0689004i
$819$	−44.8307	−	9.52907i	−1.56651	−	0.332973i
$820$	−0.0152505	−	0.00678996i	−0.000532570	−	0.000237116i
$821$	−3.26980	−	10.0634i	−0.114117	−	0.351215i	0.877645	−	0.479311i	$-0.159113\pi$
$821$	−3.26980	−	10.0634i	−0.114117	−	0.351215i	−0.991762	+	0.128096i	$0.959113\pi$
$822$	2.61744	+	8.05566i	0.0912938	+	0.280974i
$823$	24.1442	+	10.7497i	0.841615	+	0.374711i	0.781824	−	0.623500i	$-0.214290\pi$
$823$	24.1442	+	10.7497i	0.841615	+	0.374711i	0.0597915	+	0.998211i	$0.480956\pi$
$824$	3.84457	+	0.817190i	0.133932	+	0.0284681i
$825$	−0.225386	+	0.0479072i	−0.00784693	+	0.00166792i
$826$	−0.236068	+	0.105104i	−0.00821386	+	0.00365704i
$827$	−11.1089	−	12.3377i	−0.386295	−	0.429024i	0.518364	−	0.855160i	$-0.326541\pi$
$827$	−11.1089	−	12.3377i	−0.386295	−	0.429024i	−0.904659	+	0.426136i	$0.859875\pi$
$828$	−1.38430	−	13.1707i	−0.0481078	−	0.457715i
$829$	10.7797	−	7.83192i	0.374395	−	0.272014i	−0.384636	−	0.923068i	$-0.625673\pi$
$829$	10.7797	−	7.83192i	0.374395	−	0.272014i	0.759031	+	0.651055i	$0.225673\pi$
$830$	0.837204	−	7.96546i	0.0290598	−	0.276485i
$831$	−2.07246	−	3.58961i	−0.0718929	−	0.124522i
$832$	2.96086	−	5.12837i	0.102649	−	0.177794i
$833$	0.780949	+	0.567393i	0.0270583	+	0.0196590i
$834$	−8.85652	+	9.83616i	−0.306676	+	0.340598i
$835$	−6.21878	+	19.1394i	−0.215210	+	0.662348i
$836$	−1.69197			−0.0585179
$837$	2.38332	−	19.1846i	0.0823798	−	0.663115i
$838$	7.45104			0.257392
$839$	6.58028	−	20.2520i	0.227176	−	0.699177i	−0.770887	−	0.636972i	$-0.780187\pi$
$839$	6.58028	−	20.2520i	0.227176	−	0.699177i	0.998063	−	0.0622052i	$-0.0198133\pi$
$840$	−1.22256	+	1.35779i	−0.0421824	+	0.0468483i
$841$	4.26785	+	3.10077i	0.147167	+	0.106923i
$842$	13.1258	−	22.7346i	0.452346	−	0.783486i
$843$	4.85285	+	8.40537i	0.167141	+	0.289496i
$844$	0.309670	−	2.94632i	0.0106593	−	0.101416i
$845$	−17.8525	+	12.9706i	−0.614143	+	0.446201i
$846$	−2.62415	−	24.9671i	−0.0902201	−	0.858386i
$847$	−21.4847	−	23.8611i	−0.738222	−	0.819878i
$848$	3.33652	−	1.48551i	0.114576	−	0.0510127i
$849$	15.3524	−	3.26325i	0.526893	−	0.111995i
$850$	0.542750	+	0.115365i	0.0186162	+	0.00395699i
$851$	−0.867358	−	0.386173i	−0.0297326	−	0.0132378i
$852$	0.782006	+	2.40677i	0.0267911	+	0.0824545i
$853$	−9.31052	−	28.6548i	−0.318786	−	0.981123i	−0.974168	−	0.225825i	$-0.927492\pi$
$853$	−9.31052	−	28.6548i	−0.318786	−	0.981123i	0.655382	−	0.755298i	$-0.272508\pi$
$854$	1.49592	+	0.666026i	0.0511893	+	0.0227910i
$855$	11.6215	+	2.47022i	0.397446	+	0.0844798i
$856$	−2.09007	+	0.444258i	−0.0714370	+	0.0151844i
$857$	−21.1543	+	9.41851i	−0.722618	+	0.321730i	−0.734882	−	0.678195i	$-0.762763\pi$
$857$	−21.1543	+	9.41851i	−0.722618	+	0.321730i	0.0122644	+	0.999925i	$0.496096\pi$
$858$	−0.913023	−	1.01401i	−0.0311701	−	0.0346179i
$859$	6.10830	+	58.1166i	0.208413	+	1.98291i	0.182225	+	0.983257i	$0.441670\pi$
$859$	6.10830	+	58.1166i	0.208413	+	1.98291i	0.0261876	+	0.999657i	$0.491663\pi$
$860$	−0.377398	+	0.274195i	−0.0128692	+	0.00934999i
$861$	−0.00318822	+	0.0303339i	−0.000108654	+	0.00103378i
$862$	−0.312795	−	0.541778i	−0.0106539	−	0.0184530i
$863$	−7.39945	+	12.8162i	−0.251880	+	0.436269i	−0.964043	−	0.265745i	$-0.914382\pi$
$863$	−7.39945	+	12.8162i	−0.251880	+	0.436269i	0.712163	+	0.702014i	$0.247716\pi$
$864$	−2.80902	−	2.04087i	−0.0955647	−	0.0694318i
$865$	0.907699	−	1.00810i	0.0308627	−	0.0342765i
$866$	5.04742	−	15.5344i	0.171518	−	0.527879i
$867$	10.3163			0.350360
$868$	16.0328	+	3.72554i	0.544189	+	0.126453i
$869$	4.71337			0.159890
$870$	0.930239	−	2.86298i	0.0315381	−	0.0970642i
$871$	−3.24107	+	3.59957i	−0.109819	+	0.121967i
$872$	7.47437	+	5.43045i	0.253114	+	0.183898i
$873$	−22.1997	+	38.4510i	−0.751346	+	1.30137i
$874$	11.4782	+	19.8808i	0.388255	+	0.672477i
$875$	−0.309017	+	2.94010i	−0.0104467	+	0.0993935i
$876$	8.25920	−	6.00066i	0.279052	−	0.202743i
$877$	−2.74852	−	26.1505i	−0.0928110	−	0.883038i	−0.937548	−	0.347856i	$-0.886910\pi$
$877$	−2.74852	−	26.1505i	−0.0928110	−	0.883038i	0.844737	−	0.535182i	$-0.179757\pi$
$878$	−16.4031	−	18.2175i	−0.553577	−	0.614809i
$879$	11.0261	−	4.90912i	0.371900	−	0.165581i
$880$	0.364682	−	0.0775156i	0.0122934	−	0.00261305i
$881$	39.7705	+	8.45348i	1.33990	+	0.284805i	0.821439	−	0.570296i	$-0.193171\pi$
$881$	39.7705	+	8.45348i	1.33990	+	0.284805i	0.518462	+	0.855101i	$0.326505\pi$
$882$	−4.16078	−	1.85250i	−0.140101	−	0.0623769i
$883$	0.151282	+	0.465599i	0.00509105	+	0.0156686i	0.953570	−	0.301172i	$-0.0973779\pi$
$883$	0.151282	+	0.465599i	0.00509105	+	0.0156686i	−0.948479	+	0.316841i	$0.897378\pi$
$884$	1.01537	+	3.12500i	0.0341507	+	0.105105i
$885$	0.0493516	+	0.0219728i	0.00165894	+	0.000738607i
$886$	23.4952	+	4.99406i	0.789337	+	0.167779i
$887$	−27.9318	+	5.93710i	−0.937859	+	0.199348i	−0.651392	−	0.758742i	$-0.725814\pi$
$887$	−27.9318	+	5.93710i	−0.937859	+	0.199348i	−0.286468	+	0.958090i	$0.592481\pi$
$888$	−0.105972	+	0.0471816i	−0.00355618	+	0.00158331i
$889$	−10.6002	−	11.7727i	−0.355519	−	0.394844i
$890$	0.129960	+	1.23648i	0.00435626	+	0.0414470i
$891$	1.72174	−	1.25092i	0.0576804	−	0.0419073i
$892$	0.385970	−	3.67226i	0.0129232	−	0.122956i
$893$	21.7586	+	37.6869i	0.728123	+	1.26115i
$894$	4.96464	−	8.59901i	0.166042	−	0.287594i
$895$	0.764989	+	0.555797i	0.0255708	+	0.0185782i
$896$	1.97815	−	2.19696i	0.0660853	−	0.0733951i
$897$	−5.72089	+	17.6071i	−0.191015	+	0.587884i
$898$	37.1143			1.23852
$899$	−26.6285	+	5.13669i	−0.888111	+	0.171318i
$900$	−2.61803			−0.0872678
$901$	−0.626240	+	1.92737i	−0.0208631	+	0.0642099i
$902$	0.00416461	−	0.00462527i	0.000138666	−	0.000154005i
$903$	0.689540	+	0.500980i	0.0229464	+	0.0166716i
$904$	−8.48255	+	14.6922i	−0.282125	+	0.488656i
$905$	4.98272	+	8.63032i	0.165631	+	0.286881i
$906$	−0.986329	+	9.38430i	−0.0327686	+	0.311772i
$907$	20.1177	−	14.6163i	0.667996	−	0.485328i	−0.201358	−	0.979518i	$-0.564535\pi$
$907$	20.1177	−	14.6163i	0.667996	−	0.485328i	0.869354	+	0.494190i	$0.164535\pi$
$908$	0.953574	+	9.07265i	0.0316455	+	0.301086i
$909$	30.6304	+	34.0185i	1.01594	+	1.12832i
$910$	−15.9929	+	7.12048i	−0.530158	+	0.236042i
$911$	35.9906	−	7.65004i	1.19242	−	0.253457i	0.431386	−	0.902167i	$-0.358025\pi$
$911$	35.9906	−	7.65004i	1.19242	−	0.253457i	0.761035	+	0.648710i	$0.224691\pi$
$912$	2.74346	+	0.583140i	0.0908450	+	0.0193097i
$913$	2.72795	+	1.21456i	0.0902821	+	0.0401962i
$914$	−3.97400	−	12.2307i	−0.131448	−	0.404557i
$915$	−0.105785	−	0.325573i	−0.00349715	−	0.0107631i
$916$	−3.76442	−	1.67603i	−0.124380	−	0.0553775i
$917$	62.5253	+	13.2902i	2.06477	+	0.438880i
$918$	1.88450	−	0.400563i	0.0621978	−	0.0132206i
$919$	−35.7164	+	15.9020i	−1.17818	+	0.524557i	−0.899965	−	0.435963i	$-0.856408\pi$
$919$	−35.7164	+	15.9020i	−1.17818	+	0.524557i	−0.278210	+	0.960520i	$0.589741\pi$
$920$	−3.38479	−	3.75919i	−0.111593	−	0.123937i
$921$	1.96345	+	18.6810i	0.0646978	+	0.615559i
$922$	6.91370	−	5.02310i	0.227691	−	0.165427i
$923$	−2.53453	+	24.1145i	−0.0834252	+	0.793738i
$924$	−0.340596	−	0.589930i	−0.0112048	−	0.0194073i
$925$	−0.0938464	+	0.162547i	−0.00308565	+	0.00534450i
$926$	11.1424	+	8.09541i	0.366161	+	0.266032i
$927$	6.88541	−	7.64703i	0.226147	−	0.251161i
$928$	−1.50516	+	4.63240i	−0.0494093	+	0.152066i
$929$	32.4177			1.06359			0.531794	−	0.846873i	$-0.321518\pi$
$929$	32.4177			1.06359			0.531794	+	0.846873i	$0.321518\pi$
$930$	−1.66397	−	3.01200i	−0.0545638	−	0.0987674i
$931$	7.89499			0.258748
$932$	1.14320	−	3.51840i	0.0374467	−	0.115249i
$933$	8.78765	−	9.75968i	0.287695	−	0.319517i
$934$	−17.8233	−	12.9494i	−0.583195	−	0.423716i
$935$	−0.103437	+	0.179158i	−0.00338275	+	0.00585909i
$936$	−7.75164	−	13.4262i	−0.253370	−	0.438850i
$937$	0.635543	−	6.04679i	0.0207623	−	0.197540i	−0.979224	−	0.202782i	$-0.935002\pi$
$937$	0.635543	−	6.04679i	0.0207623	−	0.197540i	0.999986	+	0.00524165i	$0.00166848\pi$
$938$	−1.95630	+	1.42133i	−0.0638753	+	0.0464081i
$939$	0.568465	+	5.40858i	0.0185512	+	0.176502i
$940$	−6.41637	−	7.12610i	−0.209279	−	0.232428i
$941$	26.4573	−	11.7795i	0.862483	−	0.384002i	0.0726746	−	0.997356i	$-0.476847\pi$
$941$	26.4573	−	11.7795i	0.862483	−	0.384002i	0.789809	+	0.613353i	$0.210180\pi$
$942$	0.938098	−	0.199399i	0.0305649	−	0.00649677i
$943$	−0.0825998	−	0.0175571i	−0.00268982	−	0.000571739i
$944$	−0.0798526	−	0.0355527i	−0.00259898	−	0.00115714i
$945$	3.17195	+	9.76227i	0.103184	+	0.317567i
$946$	−0.0537445	−	0.165408i	−0.00174738	−	0.00537789i
$947$	−18.5860	−	8.27502i	−0.603964	−	0.268902i	0.0818899	−	0.996641i	$-0.473904\pi$
$947$	−18.5860	−	8.27502i	−0.603964	−	0.268902i	−0.685854	+	0.727739i	$0.740571\pi$
$948$	−7.64254	−	1.62447i	−0.248218	−	0.0527604i
$949$	95.6799	−	20.3374i	3.10590	−	0.660180i
$950$	4.14583	−	1.84584i	0.134509	−	0.0598871i
$951$	−4.45445	−	4.94717i	−0.144445	−	0.160423i
$952$	0.171466	+	1.63139i	0.00555724	+	0.0528736i
$953$	30.0504	−	21.8329i	0.973429	−	0.707238i	0.0171986	−	0.999852i	$-0.494525\pi$
$953$	30.0504	−	21.8329i	0.973429	−	0.707238i	0.956231	+	0.292614i	$0.0945252\pi$
$954$	0.999477	−	9.50939i	0.0323593	−	0.307878i
$955$	−1.21878	−	2.11100i	−0.0394389	−	0.0683102i
$956$	−0.396364	+	0.686522i	−0.0128193	+	0.0222037i
$957$	0.907987	+	0.659692i	0.0293511	+	0.0213248i
$958$	25.2152	−	28.0043i	0.814666	−	0.904778i
$959$	−12.5202	+	38.5333i	−0.404300	+	1.24431i
$960$	−0.618034			−0.0199470
$961$	−16.5024	+	26.2426i	−0.532334	+	0.846534i
$962$	−1.11147			−0.0358351
$963$	−1.72868	+	5.32032i	−0.0557058	+	0.171445i
$964$	19.6918	−	21.8700i	0.634231	−	0.704384i
$965$	−15.5198	−	11.2758i	−0.499599	−	0.362980i
$966$	−4.62116	+	8.00408i	−0.148683	+	0.257527i
$967$	−15.7039	−	27.1999i	−0.505003	−	0.874691i	−0.999983	−	0.00578691i	$-0.998158\pi$
$967$	−15.7039	−	27.1999i	−0.505003	−	0.874691i	0.494980	−	0.868904i	$-0.335175\pi$
$968$	1.13528	−	10.8015i	0.0364894	−	0.347173i
$969$	−1.25906	+	0.914762i	−0.0404469	+	0.0293864i
$970$	1.77270	+	16.8662i	0.0569181	+	0.541540i
$971$	2.44309	+	2.71332i	0.0784023	+	0.0870746i	0.781070	−	0.624444i	$-0.214674\pi$
$971$	2.44309	+	2.71332i	0.0784023	+	0.0870746i	−0.702667	+	0.711519i	$0.748008\pi$
$972$	−12.7387	+	5.67165i	−0.408595	+	0.181918i
$973$	−61.9287	+	13.1634i	−1.98534	+	0.421998i
$974$	−27.7070	−	5.88930i	−0.887788	−	0.188705i
$975$	3.34342	+	1.48859i	0.107075	+	0.0476729i
$976$	0.171164	+	0.526789i	0.00547883	+	0.0168621i
$977$	8.56342	+	26.3555i	0.273968	+	0.843187i	0.989491	+	0.144597i	$0.0461887\pi$
$977$	8.56342	+	26.3555i	0.273968	+	0.843187i	−0.715523	+	0.698590i	$0.753811\pi$
$978$	4.71771	+	2.10046i	0.150856	+	0.0671652i
$979$	−0.453407	−	0.0963747i	−0.0144910	−	0.00308015i
$980$	−1.70167	+	0.361700i	−0.0543577	+	0.0115541i
$981$	22.0964	−	9.83797i	0.705485	−	0.314102i
$982$	9.99992	+	11.1060i	0.319110	+	0.354408i
$983$	−5.54120	−	52.7210i	−0.176737	−	1.68154i	−0.619576	−	0.784937i	$-0.712695\pi$
$983$	−5.54120	−	52.7210i	−0.176737	−	1.68154i	0.442839	−	0.896601i	$-0.353971\pi$
$984$	−0.00834687	+	0.00606436i	−0.000266089	+	0.000193325i
$985$	2.76485	−	26.3057i	0.0880953	−	0.838171i
$986$	−1.35134	−	2.34059i	−0.0430355	−	0.0745396i
$987$	−8.76009	+	15.1729i	−0.278837	+	0.482959i
$988$	21.7414	+	15.7961i	0.691687	+	0.502540i
$989$	−1.57897	+	1.75362i	−0.0502082	+	0.0557619i
$990$	0.301625	−	0.928307i	0.00958628	−	0.0295035i
$991$	−19.4946			−0.619268			−0.309634	−	0.950856i	$-0.600206\pi$
$991$	−19.4946			−0.619268			−0.309634	+	0.950856i	$0.600206\pi$
$992$	2.69236	+	4.87352i	0.0854826	+	0.154734i
$993$	6.17762			0.196041
$994$	−3.74064	+	11.5125i	−0.118646	+	0.365154i
$995$	10.7999	−	11.9945i	0.342379	−	0.380251i
$996$	−4.00467	−	2.90956i	−0.126893	−	0.0921930i
$997$	3.57123	−	6.18554i	0.113102	−	0.195898i	−0.803918	−	0.594741i	$-0.797255\pi$
$997$	3.57123	−	6.18554i	0.113102	−	0.195898i	0.917019	+	0.398843i	$0.130588\pi$
$998$	−16.7817	−	29.0667i	−0.531215	−	0.920091i
$999$	−0.0681206	+	0.648125i	−0.00215524	+	0.0205058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.q.b.231.1	yes	8
31.12	odd	30		9610.2.a.bn.1.4		4
31.19	even	15		9610.2.a.bw.1.2		4
31.20	even	15	inner	310.2.q.b.51.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.q.b.51.1	✓	8	31.20	even	15	inner
310.2.q.b.231.1	yes	8	1.1	even	1	trivial
9610.2.a.bn.1.4		4	31.12	odd	30
9610.2.a.bw.1.2		4	31.19	even	15

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:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.413545 + 0.459289i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.309017 + 0.535233i) q^{6} +(-0.309017 + 2.94010i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.273659 + 2.60369i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.413545 + 0.459289i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.309017 + 0.535233i) q^{6} +(-0.309017 + 2.94010i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.273659 + 2.60369i) q^{9} +(0.669131 + 0.743145i) q^{10} +(-0.340596 + 0.151643i) q^{11} +(0.604528 - 0.128496i) q^{12} +(5.79232 + 1.23120i) q^{13} +(2.70071 + 1.20243i) q^{14} +(-0.190983 - 0.587785i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.506904 - 0.225688i) q^{17} +(2.56082 + 0.544320i) q^{18} +(-4.43901 + 0.943541i) q^{19} +(0.913545 - 0.406737i) q^{20} +(-1.22256 - 1.35779i) q^{21} +(0.0389713 + 0.370787i) q^{22} +(4.09240 - 2.97330i) q^{23} +(0.0646021 - 0.614648i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.96086 - 5.12837i) q^{26} +(-2.80902 - 2.04087i) q^{27} +(1.97815 - 2.19696i) q^{28} +(-1.50516 + 4.63240i) q^{29} -0.618034 q^{30} +(2.69236 + 4.87352i) q^{31} +1.00000 q^{32} +(0.0712040 - 0.219144i) q^{33} +(-0.371284 + 0.412353i) q^{34} +(-2.39169 - 1.73767i) q^{35} +(1.30902 - 2.26728i) q^{36} +(-0.0938464 - 0.162547i) q^{37} +(-0.474369 + 4.51332i) q^{38} +(-2.96086 + 2.15119i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(-0.0111703 - 0.0124059i) q^{41} +(-1.66913 + 0.743145i) q^{42} +(-0.456295 + 0.0969885i) q^{43} +(0.364682 + 0.0775156i) q^{44} +(-2.39169 - 1.06485i) q^{45} +(-1.56316 - 4.81091i) q^{46} +(-2.96320 - 9.11979i) q^{47} +(-0.564602 - 0.251377i) q^{48} +(-1.70167 - 0.361700i) q^{49} +(-0.978148 + 0.207912i) q^{50} +(0.313284 - 0.139483i) q^{51} +(-3.96241 - 4.40070i) q^{52} +(-0.381766 - 3.63226i) q^{53} +(-2.80902 + 2.04087i) q^{54} +(0.0389713 - 0.370787i) q^{55} +(-1.47815 - 2.56023i) q^{56} +(1.40238 - 2.42899i) q^{57} +(3.94056 + 2.86298i) q^{58} +(-0.0584884 + 0.0649580i) q^{59} +(-0.190983 + 0.587785i) q^{60} +0.553899 q^{61} +(5.46698 - 1.05459i) q^{62} -7.73968 q^{63} +(0.309017 - 0.951057i) q^{64} +(-3.96241 + 4.40070i) q^{65} +(-0.186415 - 0.135438i) q^{66} +(-0.408977 + 0.708369i) q^{67} +(0.277438 + 0.480536i) q^{68} +(-0.326789 + 3.10919i) q^{69} +(-2.39169 + 1.73767i) q^{70} +(0.428006 + 4.07221i) q^{71} +(-1.75181 - 1.94558i) q^{72} +(15.0903 - 6.71864i) q^{73} +(-0.183591 + 0.0390235i) q^{74} +(0.604528 + 0.128496i) q^{75} +(4.14583 + 1.84584i) q^{76} +(-0.340596 - 1.04825i) q^{77} +(1.13095 + 3.48070i) q^{78} +(-11.5492 - 5.14203i) q^{79} +(-0.978148 - 0.207912i) q^{80} +(-5.58347 + 1.18680i) q^{81} +(-0.0152505 + 0.00678996i) q^{82} +(-5.35930 - 5.95210i) q^{83} +(0.190983 + 1.81708i) q^{84} +(0.448903 - 0.326147i) q^{85} +(-0.0487614 + 0.463934i) q^{86} +(-1.50516 - 2.60701i) q^{87} +(0.186415 - 0.322880i) q^{88} +(1.00585 + 0.730790i) q^{89} +(-1.75181 + 1.94558i) q^{90} +(-5.40977 + 16.6496i) q^{91} -5.05849 q^{92} +(-3.35177 - 0.778849i) q^{93} -9.58911 q^{94} +(1.40238 - 4.31607i) q^{95} +(-0.413545 + 0.459289i) q^{96} +(13.7202 + 9.96828i) q^{97} +(-0.869841 + 1.50661i) q^{98} +(-0.488040 - 0.845310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9} + q^{10} + 17 q^{11} + 3 q^{12} + 10 q^{13} + 2 q^{14} - 6 q^{15} - 2 q^{16} + 8 q^{17} + q^{18} - 8 q^{19} + q^{20} + q^{21} - 28 q^{22} - 2 q^{23} - 2 q^{24} - 4 q^{25} + 5 q^{26} - 18 q^{27} + 7 q^{28} + 11 q^{29} + 4 q^{30} - 14 q^{31} + 8 q^{32} + 3 q^{33} - 7 q^{34} - 4 q^{35} + 6 q^{36} + 6 q^{37} + 22 q^{38} - 5 q^{39} + q^{40} - 4 q^{41} - 9 q^{42} + 14 q^{43} + 2 q^{44} - 4 q^{45} + 18 q^{46} + 6 q^{47} - 2 q^{48} - 23 q^{49} + q^{50} + 14 q^{51} - 20 q^{52} - 8 q^{53} - 18 q^{54} - 28 q^{55} - 3 q^{56} + q^{57} + 11 q^{58} + 8 q^{59} - 6 q^{60} + 28 q^{61} + 31 q^{62} - 14 q^{63} - 2 q^{64} - 20 q^{65} - 7 q^{66} + 2 q^{67} + 13 q^{68} - 7 q^{69} - 4 q^{70} + 19 q^{71} + q^{72} + 12 q^{73} - 19 q^{74} + 3 q^{75} - 8 q^{76} + 17 q^{77} + 15 q^{78} - 39 q^{79} + q^{80} - 16 q^{81} - 4 q^{82} + 50 q^{83} + 6 q^{84} - q^{85} - 16 q^{86} + 11 q^{87} + 7 q^{88} - 12 q^{89} + q^{90} - 20 q^{91} - 32 q^{92} - 11 q^{93} - 24 q^{94} + q^{95} + 3 q^{96} + 42 q^{97} + 17 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9 + q^10 + 17 * q^11 + 3 * q^12 + 10 * q^13 + 2 * q^14 - 6 * q^15 - 2 * q^16 + 8 * q^17 + q^18 - 8 * q^19 + q^20 + q^21 - 28 * q^22 - 2 * q^23 - 2 * q^24 - 4 * q^25 + 5 * q^26 - 18 * q^27 + 7 * q^28 + 11 * q^29 + 4 * q^30 - 14 * q^31 + 8 * q^32 + 3 * q^33 - 7 * q^34 - 4 * q^35 + 6 * q^36 + 6 * q^37 + 22 * q^38 - 5 * q^39 + q^40 - 4 * q^41 - 9 * q^42 + 14 * q^43 + 2 * q^44 - 4 * q^45 + 18 * q^46 + 6 * q^47 - 2 * q^48 - 23 * q^49 + q^50 + 14 * q^51 - 20 * q^52 - 8 * q^53 - 18 * q^54 - 28 * q^55 - 3 * q^56 + q^57 + 11 * q^58 + 8 * q^59 - 6 * q^60 + 28 * q^61 + 31 * q^62 - 14 * q^63 - 2 * q^64 - 20 * q^65 - 7 * q^66 + 2 * q^67 + 13 * q^68 - 7 * q^69 - 4 * q^70 + 19 * q^71 + q^72 + 12 * q^73 - 19 * q^74 + 3 * q^75 - 8 * q^76 + 17 * q^77 + 15 * q^78 - 39 * q^79 + q^80 - 16 * q^81 - 4 * q^82 + 50 * q^83 + 6 * q^84 - q^85 - 16 * q^86 + 11 * q^87 + 7 * q^88 - 12 * q^89 + q^90 - 20 * q^91 - 32 * q^92 - 11 * q^93 - 24 * q^94 + q^95 + 3 * q^96 + 42 * q^97 + 17 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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