LMFDB - Embedded newform 1014.2.g.d.437.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(239,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("1014.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.3
Root			$0.500000 + 1.74530i$ of defining polynomial
Character	$\chi$	$=$	1014.437
Dual form			1014.2.g.d.239.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.796225 - 1.53819i) q^{3} -1.00000i q^{4} +(-2.76293 + 2.76293i) q^{5} +(0.524648 + 1.65068i) q^{6} +(1.79623 - 1.79623i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.73205 - 2.44949i) q^{9} -3.90738i q^{10} +(-0.412157 - 0.412157i) q^{11} +(-1.53819 - 0.796225i) q^{12} +2.54025i q^{14} +(2.05000 + 6.44983i) q^{15} -1.00000 q^{16} +1.09400 q^{17} +(2.95680 + 0.507306i) q^{18} +(0.971553 + 0.971553i) q^{19} +(2.76293 + 2.76293i) q^{20} +(-1.33273 - 4.19313i) q^{21} +0.582877 q^{22} -1.75292 q^{23} +(1.65068 - 0.524648i) q^{24} -10.2676i q^{25} +(-5.14688 + 0.713876i) q^{27} +(-1.79623 - 1.79623i) q^{28} -5.92330i q^{29} +(-6.01029 - 3.11115i) q^{30} +(-6.49983 - 6.49983i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.962144 + 0.305805i) q^{33} +(-0.773575 + 0.773575i) q^{34} +9.92570i q^{35} +(-2.44949 + 1.73205i) q^{36} +(-2.18840 + 2.18840i) q^{37} -1.37398 q^{38} -3.90738 q^{40} +(3.74650 - 3.74650i) q^{41} +(3.90738 + 2.02261i) q^{42} -3.76778i q^{43} +(-0.412157 + 0.412157i) q^{44} +(11.5533 + 1.98224i) q^{45} +(1.23950 - 1.23950i) q^{46} +(-5.51114 - 5.51114i) q^{47} +(-0.796225 + 1.53819i) q^{48} +0.547150i q^{49} +(7.26029 + 7.26029i) q^{50} +(0.871071 - 1.68278i) q^{51} -3.04435i q^{53} +(3.13461 - 4.14418i) q^{54} +2.27752 q^{55} +2.54025 q^{56} +(2.26801 - 0.720857i) q^{57} +(4.18840 + 4.18840i) q^{58} +(-5.99556 - 5.99556i) q^{59} +(6.44983 - 2.05000i) q^{60} +9.34533 q^{61} +9.19215 q^{62} +(-7.51099 - 1.28868i) q^{63} +1.00000i q^{64} +(0.464102 - 0.896575i) q^{66} +(-4.66788 - 4.66788i) q^{67} -1.09400i q^{68} +(-1.39572 + 2.69632i) q^{69} +(-7.01853 - 7.01853i) q^{70} +(0.601383 - 0.601383i) q^{71} +(0.507306 - 2.95680i) q^{72} +(5.18078 - 5.18078i) q^{73} -3.09487i q^{74} +(-15.7935 - 8.17533i) q^{75} +(0.971553 - 0.971553i) q^{76} -1.48065 q^{77} -13.1089 q^{79} +(2.76293 - 2.76293i) q^{80} +(-3.00000 + 8.48528i) q^{81} +5.29835i q^{82} +(-5.15394 + 5.15394i) q^{83} +(-4.19313 + 1.33273i) q^{84} +(-3.02265 + 3.02265i) q^{85} +(2.66422 + 2.66422i) q^{86} +(-9.11115 - 4.71628i) q^{87} -0.582877i q^{88} +(-6.85191 - 6.85191i) q^{89} +(-9.57108 + 6.76778i) q^{90} +1.75292i q^{92} +(-15.1733 + 4.82264i) q^{93} +7.79393 q^{94} -5.36867 q^{95} +(-0.524648 - 1.65068i) q^{96} +(-0.433704 - 0.433704i) q^{97} +(-0.386893 - 0.386893i) q^{98} +(-0.295697 + 1.72345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{7} + 24 q^{15} - 16 q^{16} - 32 q^{19} + 24 q^{21} - 16 q^{28} - 16 q^{31} - 24 q^{33} - 24 q^{34} + 8 q^{37} + 48 q^{45} + 48 q^{55} + 24 q^{57} + 24 q^{58} + 24 q^{60} + 48 q^{61} - 48 q^{66}+ \cdots - 16 q^{97}+O(q^{100}) $ 16 * q + 16 * q^7 + 24 * q^15 - 16 * q^16 - 32 * q^19 + 24 * q^21 - 16 * q^28 - 16 * q^31 - 24 * q^33 - 24 * q^34 + 8 * q^37 + 48 * q^45 + 48 * q^55 + 24 * q^57 + 24 * q^58 + 24 * q^60 + 48 * q^61 - 48 * q^66 - 32 * q^67 - 56 * q^73 - 32 * q^76 - 96 * q^79 - 48 * q^81 - 24 * q^84 - 24 * q^85 - 96 * q^87 - 48 * q^93 + 48 * q^94 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.796225	−	1.53819i	0.459701	−	0.888074i
$3$	0.796225	−	1.53819i	0.459701	−	0.888074i
$4$		−	1.00000i		−	0.500000i
$5$	−2.76293	+	2.76293i	−1.23562	+	1.23562i	−0.273849	+	0.961773i	$0.588297\pi$
$5$	−2.76293	+	2.76293i	−1.23562	+	1.23562i	−0.961773	+	0.273849i	$0.911703\pi$
$6$	0.524648	+	1.65068i	0.214186	+	0.673887i
$7$	1.79623	−	1.79623i	0.678909	−	0.678909i	−0.280844	−	0.959753i	$-0.590614\pi$
$7$	1.79623	−	1.79623i	0.678909	−	0.678909i	0.959753	+	0.280844i	$0.0906144\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.73205	−	2.44949i	−0.577350	−	0.816497i
$10$		−	3.90738i		−	1.23562i
$11$	−0.412157	−	0.412157i	−0.124270	−	0.124270i	0.642237	−	0.766506i	$-0.278007\pi$
$11$	−0.412157	−	0.412157i	−0.124270	−	0.124270i	−0.766506	+	0.642237i	$0.778007\pi$
$12$	−1.53819	−	0.796225i	−0.444037	−	0.229850i
$13$		0			0
$13$		0			0
$14$			2.54025i			0.678909i
$15$	2.05000	+	6.44983i	0.529307	+	1.66534i
$16$	−1.00000			−0.250000
$17$	1.09400			0.265334			0.132667	−	0.991161i	$-0.457646\pi$
$17$	1.09400			0.265334			0.132667	+	0.991161i	$0.457646\pi$
$18$	2.95680	+	0.507306i	0.696923	+	0.119573i
$19$	0.971553	+	0.971553i	0.222890	+	0.222890i	0.809714	−	0.586825i	$-0.199622\pi$
$19$	0.971553	+	0.971553i	0.222890	+	0.222890i	−0.586825	+	0.809714i	$0.699622\pi$
$20$	2.76293	+	2.76293i	0.617811	+	0.617811i
$21$	−1.33273	−	4.19313i	−0.290826	−	0.915017i
$22$	0.582877			0.124270
$23$	−1.75292			−0.365509			−0.182755	−	0.983159i	$-0.558501\pi$
$23$	−1.75292			−0.365509			−0.182755	+	0.983159i	$0.558501\pi$
$24$	1.65068	−	0.524648i	0.336944	−	0.107093i
$25$		−	10.2676i		−	2.05352i
$26$		0			0
$27$	−5.14688	+	0.713876i	−0.990518	+	0.137386i
$28$	−1.79623	−	1.79623i	−0.339455	−	0.339455i
$29$		−	5.92330i		−	1.09993i	−0.835188	−	0.549965i	$-0.814641\pi$
$29$		−	5.92330i		−	1.09993i	0.835188	−	0.549965i	$-0.185359\pi$
$30$	−6.01029	−	3.11115i	−1.09732	−	0.568016i
$31$	−6.49983	−	6.49983i	−1.16740	−	1.16740i	−0.982816	−	0.184588i	$-0.940905\pi$
$31$	−6.49983	−	6.49983i	−1.16740	−	1.16740i	−0.184588	−	0.982816i	$-0.559095\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.962144	+	0.305805i	−0.167488	+	0.0532339i
$34$	−0.773575	+	0.773575i	−0.132667	+	0.132667i
$35$			9.92570i			1.67775i
$36$	−2.44949	+	1.73205i	−0.408248	+	0.288675i
$37$	−2.18840	+	2.18840i	−0.359772	+	0.359772i	−0.863729	−	0.503957i	$-0.831877\pi$
$37$	−2.18840	+	2.18840i	−0.359772	+	0.359772i	0.503957	+	0.863729i	$0.331877\pi$
$38$	−1.37398			−0.222890
$39$		0			0
$40$	−3.90738			−0.617811
$41$	3.74650	−	3.74650i	0.585105	−	0.585105i	−0.351197	−	0.936302i	$-0.614225\pi$
$41$	3.74650	−	3.74650i	0.585105	−	0.585105i	0.936302	+	0.351197i	$0.114225\pi$
$42$	3.90738	+	2.02261i	0.602922	+	0.312095i
$43$		−	3.76778i		−	0.574581i	−0.957844	−	0.287290i	$-0.907246\pi$
$43$		−	3.76778i		−	0.574581i	0.957844	−	0.287290i	$-0.0927545\pi$
$44$	−0.412157	+	0.412157i	−0.0621349	+	0.0621349i
$45$	11.5533	+	1.98224i	1.72227	+	0.295494i
$46$	1.23950	−	1.23950i	0.182755	−	0.182755i
$47$	−5.51114	−	5.51114i	−0.803883	−	0.803883i	0.179817	−	0.983700i	$-0.442449\pi$
$47$	−5.51114	−	5.51114i	−0.803883	−	0.803883i	−0.983700	+	0.179817i	$0.942449\pi$
$48$	−0.796225	+	1.53819i	−0.114925	+	0.222018i
$49$			0.547150i			0.0781643i
$50$	7.26029	+	7.26029i	1.02676	+	1.02676i
$51$	0.871071	−	1.68278i	0.121974	−	0.235636i
$52$		0			0
$53$		−	3.04435i		−	0.418173i	−0.977897	−	0.209087i	$-0.932951\pi$
$53$		−	3.04435i		−	0.418173i	0.977897	−	0.209087i	$-0.0670490\pi$
$54$	3.13461	−	4.14418i	0.426566	−	0.563952i
$55$	2.27752			0.307101
$56$	2.54025			0.339455
$57$	2.26801	−	0.720857i	0.300405	−	0.0954799i
$58$	4.18840	+	4.18840i	0.549965	+	0.549965i
$59$	−5.99556	−	5.99556i	−0.780556	−	0.780556i	0.199369	−	0.979925i	$-0.436111\pi$
$59$	−5.99556	−	5.99556i	−0.780556	−	0.780556i	−0.979925	+	0.199369i	$0.936111\pi$
$60$	6.44983	−	2.05000i	0.832670	−	0.264653i
$61$	9.34533			1.19655			0.598273	−	0.801292i	$-0.295854\pi$
$61$	9.34533			1.19655			0.598273	+	0.801292i	$0.295854\pi$
$62$	9.19215			1.16740
$63$	−7.51099	−	1.28868i	−0.946296	−	0.162359i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	0.464102	−	0.896575i	0.0571270	−	0.110361i
$67$	−4.66788	−	4.66788i	−0.570272	−	0.570272i	0.361932	−	0.932204i	$-0.382117\pi$
$67$	−4.66788	−	4.66788i	−0.570272	−	0.570272i	−0.932204	+	0.361932i	$0.882117\pi$
$68$		−	1.09400i		−	0.132667i
$69$	−1.39572	+	2.69632i	−0.168025	+	0.324599i
$70$	−7.01853	−	7.01853i	−0.838875	−	0.838875i
$71$	0.601383	−	0.601383i	0.0713711	−	0.0713711i	−0.670520	−	0.741891i	$-0.733929\pi$
$71$	0.601383	−	0.601383i	0.0713711	−	0.0713711i	0.741891	+	0.670520i	$0.233929\pi$
$72$	0.507306	−	2.95680i	0.0597866	−	0.348462i
$73$	5.18078	−	5.18078i	0.606365	−	0.606365i	−0.335629	−	0.941994i	$-0.608949\pi$
$73$	5.18078	−	5.18078i	0.606365	−	0.606365i	0.941994	+	0.335629i	$0.108949\pi$
$74$		−	3.09487i		−	0.359772i
$75$	−15.7935	−	8.17533i	−1.82368	−	0.944006i
$76$	0.971553	−	0.971553i	0.111445	−	0.111445i
$77$	−1.48065			−0.168736
$78$		0			0
$79$	−13.1089			−1.47486			−0.737431	−	0.675422i	$-0.763961\pi$
$79$	−13.1089			−1.47486			−0.737431	+	0.675422i	$0.763961\pi$
$80$	2.76293	−	2.76293i	0.308905	−	0.308905i
$81$	−3.00000	+	8.48528i	−0.333333	+	0.942809i
$82$			5.29835i			0.585105i
$83$	−5.15394	+	5.15394i	−0.565719	+	0.565719i	−0.930926	−	0.365208i	$-0.880998\pi$
$83$	−5.15394	+	5.15394i	−0.565719	+	0.565719i	0.365208	+	0.930926i	$0.380998\pi$
$84$	−4.19313	+	1.33273i	−0.457508	+	0.145413i
$85$	−3.02265	+	3.02265i	−0.327852	+	0.327852i
$86$	2.66422	+	2.66422i	0.287290	+	0.287290i
$87$	−9.11115	−	4.71628i	−0.976818	−	0.505638i
$88$		−	0.582877i		−	0.0621349i
$89$	−6.85191	−	6.85191i	−0.726301	−	0.726301i	0.243580	−	0.969881i	$-0.421678\pi$
$89$	−6.85191	−	6.85191i	−0.726301	−	0.726301i	−0.969881	+	0.243580i	$0.921678\pi$
$90$	−9.57108	+	6.76778i	−1.00888	+	0.713386i
$91$		0			0
$92$			1.75292i			0.182755i
$93$	−15.1733	+	4.82264i	−1.57340	+	0.500084i
$94$	7.79393			0.803883
$95$	−5.36867			−0.550814
$96$	−0.524648	−	1.65068i	−0.0535466	−	0.168472i
$97$	−0.433704	−	0.433704i	−0.0440360	−	0.0440360i	0.684746	−	0.728782i	$-0.259913\pi$
$97$	−0.433704	−	0.433704i	−0.0440360	−	0.0440360i	−0.728782	+	0.684746i	$0.759913\pi$
$98$	−0.386893	−	0.386893i	−0.0390821	−	0.0390821i
$99$	−0.295697	+	1.72345i	−0.0297187	+	0.173213i
$100$	−10.2676			−1.02676
$101$	5.83579			0.580682			0.290341	−	0.956923i	$-0.406231\pi$
$101$	5.83579			0.580682			0.290341	+	0.956923i	$0.406231\pi$
$102$	0.573965	+	1.80584i	0.0568310	+	0.178805i
$103$		−	2.07313i		−	0.204272i	−0.994770	−	0.102136i	$-0.967432\pi$
$103$		−	2.07313i		−	0.204272i	0.994770	−	0.102136i	$-0.0325677\pi$
$104$		0			0
$105$	15.2676	+	7.90310i	1.48997	+	0.771263i
$106$	2.15268	+	2.15268i	0.209087	+	0.209087i
$107$		−	3.45856i		−	0.334351i	−0.985927	−	0.167176i	$-0.946535\pi$
$107$		−	3.45856i		−	0.334351i	0.985927	−	0.167176i	$-0.0534647\pi$
$108$	0.713876	+	5.14688i	0.0686928	+	0.495259i
$109$	10.9901	+	10.9901i	1.05266	+	1.05266i	0.998534	+	0.0541251i	$0.0172370\pi$
$109$	10.9901	+	10.9901i	1.05266	+	1.05266i	0.0541251	+	0.998534i	$0.482763\pi$
$110$	−1.61045	+	1.61045i	−0.153551	+	0.153551i
$111$	1.62372	+	5.10864i	0.154116	+	0.484891i
$112$	−1.79623	+	1.79623i	−0.169727	+	0.169727i
$113$		−	10.8971i		−	1.02512i	−0.858653	−	0.512558i	$-0.828698\pi$
$113$		−	10.8971i		−	1.02512i	0.858653	−	0.512558i	$-0.171302\pi$
$114$	−1.09400	+	2.11345i	−0.102463	+	0.197942i
$115$	4.84320	−	4.84320i	0.451631	−	0.451631i
$116$	−5.92330			−0.549965
$117$		0			0
$118$	8.47900			0.780556
$119$	1.96507	−	1.96507i	0.180138	−	0.180138i
$120$	−3.11115	+	6.01029i	−0.284008	+	0.548662i
$121$		−	10.6603i		−	0.969114i
$122$	−6.60814	+	6.60814i	−0.598273	+	0.598273i
$123$	−2.77977	−	8.74588i	−0.250643	−	0.788589i
$124$	−6.49983	+	6.49983i	−0.583702	+	0.583702i
$125$	14.5541	+	14.5541i	1.30175	+	1.30175i
$126$	6.22231	−	4.39984i	0.554327	−	0.391968i
$127$			9.31325i			0.826417i	0.910636	+	0.413209i	$0.135592\pi$
$127$			9.31325i			0.826417i	−0.910636	+	0.413209i	$0.864408\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−5.79555	−	3.00000i	−0.510270	−	0.264135i
$130$		0			0
$131$		−	0.917828i		−	0.0801910i	−0.999196	−	0.0400955i	$-0.987234\pi$
$131$		−	0.917828i		−	0.0801910i	0.999196	−	0.0400955i	$-0.0127662\pi$
$132$	0.305805	+	0.962144i	0.0266169	+	0.0837439i
$133$	3.49026			0.302644
$134$	6.60137			0.570272
$135$	12.2481	−	16.1929i	1.05415	−	1.39366i
$136$	0.773575	+	0.773575i	0.0663335	+	0.0663335i
$137$	−6.09427	−	6.09427i	−0.520669	−	0.520669i	0.397104	−	0.917773i	$-0.370015\pi$
$137$	−6.09427	−	6.09427i	−0.520669	−	0.520669i	−0.917773	+	0.397104i	$0.870015\pi$
$138$	−0.919666	−	2.89351i	−0.0782871	−	0.246312i
$139$	3.31325			0.281026			0.140513	−	0.990079i	$-0.455125\pi$
$139$	3.31325			0.281026			0.140513	+	0.990079i	$0.455125\pi$
$140$	9.92570			0.838875
$141$	−12.8653	+	4.08907i	−1.08345	+	0.344362i
$142$			0.850484i			0.0713711i
$143$		0			0
$144$	1.73205	+	2.44949i	0.144338	+	0.204124i
$145$	16.3657	+	16.3657i	1.35910	+	1.35910i
$146$			7.32673i			0.606365i
$147$	0.841620	+	0.435655i	0.0694156	+	0.0359322i
$148$	2.18840	+	2.18840i	0.179886	+	0.179886i
$149$	5.55437	−	5.55437i	0.455032	−	0.455032i	−0.441989	−	0.897021i	$-0.645727\pi$
$149$	5.55437	−	5.55437i	0.455032	−	0.455032i	0.897021	+	0.441989i	$0.145727\pi$
$150$	16.9485	−	5.38688i	1.38384	−	0.439837i
$151$	−10.2600	+	10.2600i	−0.834946	+	0.834946i	−0.988189	−	0.153243i	$-0.951028\pi$
$151$	−10.2600	+	10.2600i	−0.834946	+	0.834946i	0.153243	+	0.988189i	$0.451028\pi$
$152$			1.37398i			0.111445i
$153$	−1.89486	−	2.67974i	−0.153191	−	0.216644i
$154$	1.04698	−	1.04698i	0.0843680	−	0.0843680i
$155$	35.9172			2.88494
$156$		0			0
$157$	−6.71547			−0.535953			−0.267976	−	0.963425i	$-0.586355\pi$
$157$	−6.71547			−0.535953			−0.267976	+	0.963425i	$0.586355\pi$
$158$	9.26936	−	9.26936i	0.737431	−	0.737431i
$159$	−4.68278	−	2.42398i	−0.371369	−	0.192235i
$160$			3.90738i			0.308905i
$161$	−3.14864	+	3.14864i	−0.248148	+	0.248148i
$162$	−3.87868	−	8.12132i	−0.304738	−	0.638071i
$163$	1.11345	−	1.11345i	0.0872118	−	0.0872118i	−0.662155	−	0.749367i	$-0.730358\pi$
$163$	1.11345	−	1.11345i	0.0872118	−	0.0872118i	0.749367	+	0.662155i	$0.230358\pi$
$164$	−3.74650	−	3.74650i	−0.292552	−	0.292552i
$165$	1.81342	−	3.50326i	0.141175	−	0.272728i
$166$		−	7.28877i		−	0.565719i
$167$	17.2850	+	17.2850i	1.33755	+	1.33755i	0.898427	+	0.439123i	$0.144711\pi$
$167$	17.2850	+	17.2850i	1.33755	+	1.33755i	0.439123	+	0.898427i	$0.355289\pi$
$168$	2.02261	−	3.90738i	0.156048	−	0.301461i
$169$		0			0
$170$		−	4.27467i		−	0.327852i
$171$	0.697030	−	4.06259i	0.0533032	−	0.310674i
$172$	−3.76778			−0.287290
$173$	20.7673			1.57891			0.789456	−	0.613807i	$-0.210363\pi$
$173$	20.7673			1.57891			0.789456	+	0.613807i	$0.210363\pi$
$174$	9.77747	−	3.10764i	0.741228	−	0.235590i
$175$	−18.4429	−	18.4429i	−1.39415	−	1.39415i
$176$	0.412157	+	0.412157i	0.0310675	+	0.0310675i
$177$	−13.9961	+	4.44849i	−1.05201	+	0.334369i
$178$	9.69006			0.726301
$179$	14.0004			1.04644			0.523218	−	0.852199i	$-0.324731\pi$
$179$	14.0004			1.04644			0.523218	+	0.852199i	$0.324731\pi$
$180$	1.98224	−	11.5533i	0.147747	−	0.861134i
$181$			25.5405i			1.89841i	0.314653	+	0.949207i	$0.398112\pi$
$181$			25.5405i			1.89841i	−0.314653	+	0.949207i	$0.601888\pi$
$182$		0			0
$183$	7.44098	−	14.3749i	0.550053	−	1.06262i
$184$	−1.23950	−	1.23950i	−0.0913773	−	0.0913773i
$185$		−	12.0928i		−	0.889083i
$186$	7.31902	−	14.1393i	0.536656	−	1.03674i
$187$	−0.450899	−	0.450899i	−0.0329730	−	0.0329730i
$188$	−5.51114	+	5.51114i	−0.401941	+	0.401941i
$189$	−7.96267	+	10.5272i	−0.579199	+	0.765744i
$190$	3.79623	−	3.79623i	0.275407	−	0.275407i
$191$			23.6463i			1.71099i	0.517814	+	0.855493i	$0.326746\pi$
$191$			23.6463i			1.71099i	−0.517814	+	0.855493i	$0.673254\pi$
$192$	1.53819	+	0.796225i	0.111009	+	0.0574626i
$193$	7.49437	−	7.49437i	0.539457	−	0.539457i	−0.383913	−	0.923369i	$-0.625424\pi$
$193$	7.49437	−	7.49437i	0.539457	−	0.539457i	0.923369	+	0.383913i	$0.125424\pi$
$194$	0.613350			0.0440360
$195$		0			0
$196$	0.547150			0.0390821
$197$	−2.45207	+	2.45207i	−0.174703	+	0.174703i	−0.789042	−	0.614339i	$-0.789423\pi$
$197$	−2.45207	+	2.45207i	−0.174703	+	0.174703i	0.614339	+	0.789042i	$0.289423\pi$
$198$	−1.00957	−	1.42775i	−0.0717472	−	0.101466i
$199$			3.08804i			0.218905i	0.993992	+	0.109453i	$0.0349098\pi$
$199$			3.08804i			0.218905i	−0.993992	+	0.109453i	$0.965090\pi$
$200$	7.26029	−	7.26029i	0.513380	−	0.513380i
$201$	−10.8968	+	3.46340i	−0.768598	+	0.244289i
$202$	−4.12652	+	4.12652i	−0.290341	+	0.290341i
$203$	−10.6396	−	10.6396i	−0.746752	−	0.746752i
$204$	−1.68278	−	0.871071i	−0.117818	−	0.0609871i
$205$			20.7026i			1.44594i
$206$	1.46593	+	1.46593i	0.102136	+	0.102136i
$207$	3.03615	+	4.29376i	0.211027	+	0.298437i
$208$		0			0
$209$		−	0.800864i		−	0.0553969i
$210$	−16.3842	+	5.20750i	−1.13061	+	0.359351i
$211$	−4.95801			−0.341323			−0.170662	−	0.985330i	$-0.554591\pi$
$211$	−4.95801			−0.341323			−0.170662	+	0.985330i	$0.554591\pi$
$212$	−3.04435			−0.209087
$213$	−0.446205	−	1.40388i	−0.0305734	−	0.0961921i
$214$	2.44557	+	2.44557i	0.167176	+	0.167176i
$215$	10.4101	+	10.4101i	0.709964	+	0.709964i
$216$	−4.14418	−	3.13461i	−0.281976	−	0.213283i
$217$	−23.3503			−1.58512
$218$	−15.5423			−1.05266
$219$	−3.84395	−	12.0941i	−0.259750	−	0.817243i
$220$		−	2.27752i		−	0.153551i
$221$		0			0
$222$	−4.76050	−	2.46422i	−0.319504	−	0.165387i
$223$	−13.4803	−	13.4803i	−0.902710	−	0.902710i	0.0929595	−	0.995670i	$-0.470367\pi$
$223$	−13.4803	−	13.4803i	−0.902710	−	0.902710i	−0.995670	+	0.0929595i	$0.970367\pi$
$224$		−	2.54025i		−	0.169727i
$225$	−25.1504	+	17.7840i	−1.67669	+	1.18560i
$226$	7.70543	+	7.70543i	0.512558	+	0.512558i
$227$	−3.79025	+	3.79025i	−0.251568	+	0.251568i	−0.821613	−	0.570045i	$-0.806926\pi$
$227$	−3.79025	+	3.79025i	−0.251568	+	0.251568i	0.570045	+	0.821613i	$0.306926\pi$
$228$	−0.720857	−	2.26801i	−0.0477399	−	0.150202i
$229$	−2.78436	+	2.78436i	−0.183996	+	0.183996i	−0.793094	−	0.609099i	$-0.791531\pi$
$229$	−2.78436	+	2.78436i	−0.183996	+	0.183996i	0.609099	+	0.793094i	$0.291531\pi$
$230$			6.84932i			0.451631i
$231$	−1.17893	+	2.27752i	−0.0775681	+	0.149850i
$232$	4.18840	−	4.18840i	0.274982	−	0.274982i
$233$	3.83663			0.251346			0.125673	−	0.992072i	$-0.459891\pi$
$233$	3.83663			0.251346			0.125673	+	0.992072i	$0.459891\pi$
$234$		0			0
$235$	30.4538			1.98659
$236$	−5.99556	+	5.99556i	−0.390278	+	0.390278i
$237$	−10.4376	+	20.1639i	−0.677995	+	1.30979i
$238$			2.77903i			0.180138i
$239$	−0.751524	+	0.751524i	−0.0486121	+	0.0486121i	−0.730995	−	0.682383i	$-0.760944\pi$
$239$	−0.751524	+	0.751524i	−0.0486121	+	0.0486121i	0.682383	+	0.730995i	$0.260944\pi$
$240$	−2.05000	−	6.44983i	−0.132327	−	0.416335i
$241$	19.7732	−	19.7732i	1.27371	−	1.27371i	0.329577	−	0.944129i	$-0.393094\pi$
$241$	19.7732	−	19.7732i	1.27371	−	1.27371i	0.944129	−	0.329577i	$-0.106906\pi$
$242$	7.53794	+	7.53794i	0.484557	+	0.484557i
$243$	10.6633	+	11.3708i	0.684050	+	0.729435i
$244$		−	9.34533i		−	0.598273i
$245$	−1.51174	−	1.51174i	−0.0965815	−	0.0965815i
$246$	8.14986	+	4.21868i	0.519616	+	0.268973i
$247$		0			0
$248$		−	9.19215i		−	0.583702i
$249$	3.82404	+	12.0314i	0.242339	+	0.762461i
$250$	−20.5825			−1.30175
$251$	15.1264			0.954770			0.477385	−	0.878694i	$-0.341585\pi$
$251$	15.1264			0.954770			0.477385	+	0.878694i	$0.341585\pi$
$252$	−1.28868	+	7.51099i	−0.0811793	+	0.473148i
$253$	0.722478	+	0.722478i	0.0454218	+	0.0454218i
$254$	−6.58546	−	6.58546i	−0.413209	−	0.413209i
$255$	2.24270	+	7.05612i	0.140443	+	0.441871i
$256$	1.00000			0.0625000
$257$	0.357201			0.0222816			0.0111408	−	0.999938i	$-0.496454\pi$
$257$	0.357201			0.0222816			0.0111408	+	0.999938i	$0.496454\pi$
$258$	6.21940	−	1.97676i	0.387203	−	0.123067i
$259$			7.86174i			0.488505i
$260$		0			0
$261$	−14.5091	+	10.2595i	−0.898088	+	0.635044i
$262$	0.649002	+	0.649002i	0.0400955	+	0.0400955i
$263$			2.14777i			0.132437i	0.997805	+	0.0662186i	$0.0210935\pi$
$263$			2.14777i			0.132437i	−0.997805	+	0.0662186i	$0.978907\pi$
$264$	−0.896575	−	0.464102i	−0.0551804	−	0.0285635i
$265$	8.41133	+	8.41133i	0.516704	+	0.516704i
$266$	−2.46798	+	2.46798i	−0.151322	+	0.151322i
$267$	−15.9952	+	5.08387i	−0.978890	+	0.311128i
$268$	−4.66788	+	4.66788i	−0.285136	+	0.285136i
$269$		−	24.5235i		−	1.49522i	−0.664135	−	0.747612i	$-0.731200\pi$
$269$		−	24.5235i		−	1.49522i	0.664135	−	0.747612i	$-0.268800\pi$
$270$	2.78938	+	20.1108i	0.169756	+	1.22391i
$271$	−15.5041	+	15.5041i	−0.941805	+	0.941805i	−0.998397	−	0.0565921i	$-0.981977\pi$
$271$	−15.5041	+	15.5041i	−0.941805	+	0.941805i	0.0565921	+	0.998397i	$0.481977\pi$
$272$	−1.09400			−0.0663335
$273$		0			0
$274$	8.61860			0.520669
$275$	−4.23186	+	4.23186i	−0.255191	+	0.255191i
$276$	2.69632	+	1.39572i	0.162300	+	0.0840125i
$277$			18.6503i			1.12059i	0.828293	+	0.560295i	$0.189312\pi$
$277$			18.6503i			1.12059i	−0.828293	+	0.560295i	$0.810688\pi$
$278$	−2.34282	+	2.34282i	−0.140513	+	0.140513i
$279$	−4.66323	+	27.1793i	−0.279180	+	1.62718i
$280$	−7.01853	+	7.01853i	−0.419438	+	0.419438i
$281$	11.2782	+	11.2782i	0.672801	+	0.672801i	0.958361	−	0.285560i	$-0.0921797\pi$
$281$	11.2782	+	11.2782i	0.672801	+	0.672801i	−0.285560	+	0.958361i	$0.592180\pi$
$282$	6.20573	−	11.9885i	0.369546	−	0.713907i
$283$			4.71513i			0.280285i	0.990131	+	0.140143i	$0.0447561\pi$
$283$			4.71513i			0.280285i	−0.990131	+	0.140143i	$0.955244\pi$
$284$	−0.601383	−	0.601383i	−0.0356855	−	0.0356855i
$285$	−4.27467	+	8.25803i	−0.253210	+	0.489164i
$286$		0			0
$287$		−	13.4591i		−	0.794466i
$288$	−2.95680	−	0.507306i	−0.174231	−	0.0298933i
$289$	−15.8032			−0.929598
$290$	−23.1446			−1.35910
$291$	−1.01244	+	0.321793i	−0.0593505	+	0.0188638i
$292$	−5.18078	−	5.18078i	−0.303182	−	0.303182i
$293$	15.1005	+	15.1005i	0.882179	+	0.882179i	0.993756	−	0.111576i	$-0.0355900\pi$
$293$	15.1005	+	15.1005i	0.882179	+	0.882179i	−0.111576	+	0.993756i	$0.535590\pi$
$294$	−0.903170	+	0.287061i	−0.0526739	+	0.0167417i
$295$	33.1307			1.92894
$296$	−3.09487			−0.179886
$297$	2.41555	+	1.82709i	0.140164	+	0.106019i
$298$			7.85507i			0.455032i
$299$		0			0
$300$	−8.17533	+	15.7935i	−0.472003	+	0.911839i
$301$	−6.76778	−	6.76778i	−0.390088	−	0.390088i
$302$		−	14.5098i		−	0.834946i
$303$	4.64660	−	8.97654i	0.266940	−	0.515689i
$304$	−0.971553	−	0.971553i	−0.0557224	−	0.0557224i
$305$	−25.8205	+	25.8205i	−1.47848	+	1.47848i
$306$	3.23474	+	0.554993i	0.184917	+	0.0317268i
$307$	16.2259	−	16.2259i	0.926063	−	0.926063i	−0.0713857	−	0.997449i	$-0.522742\pi$
$307$	16.2259	−	16.2259i	0.926063	−	0.926063i	0.997449	+	0.0713857i	$0.0227421\pi$
$308$			1.48065i			0.0843680i
$309$	−3.18887	−	1.65068i	−0.181409	−	0.0939040i
$310$	−25.3973	+	25.3973i	−1.44247	+	1.44247i
$311$	−32.8464			−1.86255			−0.931275	−	0.364317i	$-0.881303\pi$
$311$	−32.8464			−1.86255			−0.931275	+	0.364317i	$0.881303\pi$
$312$		0			0
$313$	11.0629			0.625311			0.312655	−	0.949867i	$-0.398782\pi$
$313$	11.0629			0.625311			0.312655	+	0.949867i	$0.398782\pi$
$314$	4.74855	−	4.74855i	0.267976	−	0.267976i
$315$	24.3129	−	17.1918i	1.36988	−	0.968649i
$316$			13.1089i			0.737431i
$317$	−17.5500	+	17.5500i	−0.985704	+	0.985704i	−0.999899	−	0.0141948i	$-0.995481\pi$
$317$	−17.5500	+	17.5500i	−0.985704	+	0.985704i	0.0141948	+	0.999899i	$0.495481\pi$
$318$	5.02524	−	1.59721i	0.281802	−	0.0895670i
$319$	−2.44133	+	2.44133i	−0.136688	+	0.136688i
$320$	−2.76293	−	2.76293i	−0.154453	−	0.154453i
$321$	−5.31992	−	2.75379i	−0.296929	−	0.153702i
$322$		−	4.45285i		−	0.248148i
$323$	1.06288	+	1.06288i	0.0591402	+	0.0591402i
$324$	8.48528	+	3.00000i	0.471405	+	0.166667i
$325$		0			0
$326$			1.57465i			0.0872118i
$327$	25.6554	−	8.15424i	1.41875	−	0.450931i
$328$	5.29835			0.292552
$329$	−19.7985			−1.09153
$330$	1.19490	+	3.75946i	0.0657769	+	0.206952i
$331$	3.26963	+	3.26963i	0.179715	+	0.179715i	0.791232	−	0.611517i	$-0.209440\pi$
$331$	3.26963	+	3.26963i	0.179715	+	0.179715i	−0.611517	+	0.791232i	$0.709440\pi$
$332$	5.15394	+	5.15394i	0.282859	+	0.282859i
$333$	9.15090	+	1.57005i	0.501466	+	0.0860380i
$334$	−24.4446			−1.33755
$335$	25.7941			1.40928
$336$	1.33273	+	4.19313i	0.0727066	+	0.228754i
$337$			7.78436i			0.424041i	0.977265	+	0.212021i	$0.0680044\pi$
$337$			7.78436i			0.424041i	−0.977265	+	0.212021i	$0.931996\pi$
$338$		0			0
$339$	−16.7618	−	8.67656i	−0.910378	−	0.471246i
$340$	3.02265	+	3.02265i	0.163926	+	0.163926i
$341$			5.35789i			0.290146i
$342$	2.37981	+	3.36556i	0.128685	+	0.181989i
$343$	13.5564	+	13.5564i	0.731976	+	0.731976i
$344$	2.66422	−	2.66422i	0.143645	−	0.143645i
$345$	−3.59348	−	11.3060i	−0.193467	−	0.608697i
$346$	−14.6847	+	14.6847i	−0.789456	+	0.789456i
$347$			10.8435i			0.582111i	0.956706	+	0.291056i	$0.0940065\pi$
$347$			10.8435i			0.582111i	−0.956706	+	0.291056i	$0.905994\pi$
$348$	−4.71628	+	9.11115i	−0.252819	+	0.488409i
$349$	10.8700	−	10.8700i	0.581856	−	0.581856i	−0.353557	−	0.935413i	$-0.615028\pi$
$349$	10.8700	−	10.8700i	0.581856	−	0.581856i	0.935413	+	0.353557i	$0.115028\pi$
$350$	26.0822			1.39415
$351$		0			0
$352$	−0.582877			−0.0310675
$353$	1.32046	−	1.32046i	0.0702808	−	0.0702808i	−0.671093	−	0.741373i	$-0.734175\pi$
$353$	1.32046	−	1.32046i	0.0702808	−	0.0702808i	0.741373	+	0.671093i	$0.234175\pi$
$354$	6.75120	−	13.0423i	0.358822	−	0.693191i
$355$			3.32316i			0.176375i
$356$	−6.85191	+	6.85191i	−0.363150	+	0.363150i
$357$	−1.45801	−	4.58729i	−0.0771661	−	0.242785i
$358$	−9.89976	+	9.89976i	−0.523218	+	0.523218i
$359$	−12.1336	−	12.1336i	−0.640387	−	0.640387i	0.310264	−	0.950650i	$-0.399583\pi$
$359$	−12.1336	−	12.1336i	−0.640387	−	0.640387i	−0.950650	+	0.310264i	$0.899583\pi$
$360$	6.76778	+	9.57108i	0.356693	+	0.504440i
$361$		−	17.1122i		−	0.900641i
$362$	−18.0599	−	18.0599i	−0.949207	−	0.949207i
$363$	−16.3975	−	8.48796i	−0.860645	−	0.445503i
$364$		0			0
$365$			28.6283i			1.49847i
$366$	4.90300	+	15.4261i	0.256284	+	0.806337i
$367$	−9.06282			−0.473075			−0.236538	−	0.971622i	$-0.576013\pi$
$367$	−9.06282			−0.473075			−0.236538	+	0.971622i	$0.576013\pi$
$368$	1.75292			0.0913773
$369$	−15.6661	−	2.68788i	−0.815546	−	0.139926i
$370$	8.55093	+	8.55093i	0.444541	+	0.444541i
$371$	−5.46833	−	5.46833i	−0.283902	−	0.283902i
$372$	4.82264	+	15.1733i	0.250042	+	0.786699i
$373$	−7.57587			−0.392264			−0.196132	−	0.980578i	$-0.562838\pi$
$373$	−7.57587			−0.392264			−0.196132	+	0.980578i	$0.562838\pi$
$374$	0.637668			0.0329730
$375$	33.9752	−	10.7986i	1.75447	−	0.557636i
$376$		−	7.79393i		−	0.401941i
$377$		0			0
$378$	−1.81342	−	13.0743i	−0.0932723	−	0.672472i
$379$	−8.53980	−	8.53980i	−0.438660	−	0.438660i	0.452901	−	0.891561i	$-0.350389\pi$
$379$	−8.53980	−	8.53980i	−0.438660	−	0.438660i	−0.891561	+	0.452901i	$0.850389\pi$
$380$			5.36867i			0.275407i
$381$	14.3255	+	7.41544i	0.733920	+	0.379905i
$382$	−16.7205	−	16.7205i	−0.855493	−	0.855493i
$383$	26.0444	−	26.0444i	1.33081	−	1.33081i	0.426157	−	0.904649i	$-0.359867\pi$
$383$	26.0444	−	26.0444i	1.33081	−	1.33081i	0.904649	−	0.426157i	$-0.140133\pi$
$384$	−1.65068	+	0.524648i	−0.0842359	+	0.0267733i
$385$	4.09094	−	4.09094i	0.208494	−	0.208494i
$386$			10.5986i			0.539457i
$387$	−9.22913	+	6.52598i	−0.469143	+	0.331734i
$388$	−0.433704	+	0.433704i	−0.0220180	+	0.0220180i
$389$	−14.1012			−0.714961			−0.357481	−	0.933921i	$-0.616364\pi$
$389$	−14.1012			−0.714961			−0.357481	+	0.933921i	$0.616364\pi$
$390$		0			0
$391$	−1.91770			−0.0969820
$392$	−0.386893	+	0.386893i	−0.0195411	+	0.0195411i
$393$	−1.41179	−	0.730798i	−0.0712155	−	0.0368639i
$394$		−	3.46775i		−	0.174703i
$395$	36.2189	−	36.2189i	1.82237	−	1.82237i
$396$	1.72345	+	0.295697i	0.0866066	+	0.0148593i
$397$	5.55214	−	5.55214i	0.278654	−	0.278654i	−0.553918	−	0.832571i	$-0.686868\pi$
$397$	5.55214	−	5.55214i	0.278654	−	0.278654i	0.832571	+	0.553918i	$0.186868\pi$
$398$	−2.18357	−	2.18357i	−0.109453	−	0.109453i
$399$	2.77903	−	5.36867i	0.139126	−	0.268770i
$400$			10.2676i			0.513380i
$401$	−15.4546	−	15.4546i	−0.771764	−	0.771764i	0.206650	−	0.978415i	$-0.433744\pi$
$401$	−15.4546	−	15.4546i	−0.771764	−	0.771764i	−0.978415	+	0.206650i	$0.933744\pi$
$402$	5.25618	−	10.1542i	0.262154	−	0.506444i
$403$		0			0
$404$		−	5.83579i		−	0.290341i
$405$	−15.1555	−	31.7331i	−0.753081	−	1.57683i
$406$	15.0466			0.746752
$407$	1.80393			0.0894175
$408$	1.80584	−	0.573965i	0.0894026	−	0.0284155i
$409$	1.58498	+	1.58498i	0.0783720	+	0.0783720i	0.745206	−	0.666834i	$-0.232351\pi$
$409$	1.58498	+	1.58498i	0.0783720	+	0.0783720i	−0.666834	+	0.745206i	$0.732351\pi$
$410$	−14.6390	−	14.6390i	−0.722968	−	0.722968i
$411$	−14.2266	+	4.52173i	−0.701744	+	0.223041i
$412$	−2.07313			−0.102136
$413$	−21.5388			−1.05985
$414$	−5.18303	−	0.889267i	−0.254732	−	0.0437051i
$415$		−	28.4800i		−	1.39803i
$416$		0			0
$417$	2.63809	−	5.09640i	0.129188	−	0.249572i
$418$	0.566296	+	0.566296i	0.0276985	+	0.0276985i
$419$			33.3854i			1.63098i	0.578770	+	0.815491i	$0.303533\pi$
$419$			33.3854i			1.63098i	−0.578770	+	0.815491i	$0.696467\pi$
$420$	7.90310	−	15.2676i	0.385632	−	0.744983i
$421$	−2.25285	−	2.25285i	−0.109797	−	0.109797i	0.650074	−	0.759871i	$-0.274738\pi$
$421$	−2.25285	−	2.25285i	−0.109797	−	0.109797i	−0.759871	+	0.650074i	$0.774738\pi$
$422$	3.50584	−	3.50584i	0.170662	−	0.170662i
$423$	−3.95391	+	23.0451i	−0.192246	+	1.12049i
$424$	2.15268	−	2.15268i	0.104543	−	0.104543i
$425$		−	11.2328i		−	0.544869i
$426$	1.30821	+	0.677177i	0.0633828	+	0.0328093i
$427$	16.7863	−	16.7863i	0.812346	−	0.812346i
$428$	−3.45856			−0.167176
$429$		0			0
$430$	−14.7221			−0.709964
$431$	15.3329	−	15.3329i	0.738562	−	0.738562i	−0.233738	−	0.972300i	$-0.575096\pi$
$431$	15.3329	−	15.3329i	0.738562	−	0.738562i	0.972300	+	0.233738i	$0.0750958\pi$
$432$	5.14688	−	0.713876i	0.247629	−	0.0343464i
$433$		−	30.0520i		−	1.44421i	−0.691786	−	0.722103i	$-0.743176\pi$
$433$		−	30.0520i		−	1.44421i	0.691786	−	0.722103i	$-0.256824\pi$
$434$	16.5112	−	16.5112i	0.792561	−	0.792561i
$435$	38.2043	−	12.1427i	1.83176	−	0.582200i
$436$	10.9901	−	10.9901i	0.526330	−	0.526330i
$437$	−1.70306	−	1.70306i	−0.0814682	−	0.0814682i
$438$	11.2699	+	5.83373i	0.538497	+	0.278746i
$439$		−	20.8459i		−	0.994920i	−0.867487	−	0.497460i	$-0.834266\pi$
$439$		−	20.8459i		−	0.994920i	0.867487	−	0.497460i	$-0.165734\pi$
$440$	1.61045	+	1.61045i	0.0767753	+	0.0767753i
$441$	1.34024	−	0.947691i	0.0638209	−	0.0451282i
$442$		0			0
$443$		−	13.0363i		−	0.619374i	−0.950839	−	0.309687i	$-0.899776\pi$
$443$		−	13.0363i		−	0.619374i	0.950839	−	0.309687i	$-0.100224\pi$
$444$	5.10864	−	1.62372i	0.242445	−	0.0770582i
$445$	37.8627			1.79487
$446$	19.0641			0.902710
$447$	−4.12114	−	12.9662i	−0.194923	−	0.613281i
$448$	1.79623	+	1.79623i	0.0848637	+	0.0848637i
$449$	−13.4636	−	13.4636i	−0.635385	−	0.635385i	0.314028	−	0.949414i	$-0.398321\pi$
$449$	−13.4636	−	13.4636i	−0.635385	−	0.635385i	−0.949414	+	0.314028i	$0.898321\pi$
$450$	5.20882	−	30.3592i	0.245546	−	1.43115i
$451$	−3.08829			−0.145422
$452$	−10.8971			−0.512558
$453$	7.61254	+	23.9511i	0.357668	+	1.12532i
$454$		−	5.36023i		−	0.251568i
$455$		0			0
$456$	2.11345	+	1.09400i	0.0989712	+	0.0512313i
$457$	15.0333	+	15.0333i	0.703228	+	0.703228i	0.965102	−	0.261874i	$-0.0843406\pi$
$457$	15.0333	+	15.0333i	0.703228	+	0.703228i	−0.261874	+	0.965102i	$0.584341\pi$
$458$		−	3.93768i		−	0.183996i
$459$	−5.63069	+	0.780980i	−0.262818	+	0.0364530i
$460$	−4.84320	−	4.84320i	−0.225816	−	0.225816i
$461$	−1.07969	+	1.07969i	−0.0502864	+	0.0502864i	−0.731803	−	0.681516i	$-0.761321\pi$
$461$	−1.07969	+	1.07969i	−0.0502864	+	0.0502864i	0.681516	+	0.731803i	$0.261321\pi$
$462$	−0.776820	−	2.44408i	−0.0361410	−	0.113709i
$463$	21.3272	−	21.3272i	0.991159	−	0.991159i	−0.00880240	−	0.999961i	$-0.502802\pi$
$463$	21.3272	−	21.3272i	0.991159	−	0.991159i	0.999961	+	0.00880240i	$0.00280193\pi$
$464$			5.92330i			0.274982i
$465$	28.5982	−	55.2474i	1.32621	−	2.56204i
$466$	−2.71290	+	2.71290i	−0.125673	+	0.125673i
$467$	11.2935			0.522601			0.261300	−	0.965258i	$-0.415849\pi$
$467$	11.2935			0.522601			0.261300	+	0.965258i	$0.415849\pi$
$468$		0			0
$469$	−16.7691			−0.774326
$470$	−21.5341	+	21.5341i	−0.993295	+	0.993295i
$471$	−5.34703	+	10.3297i	−0.246378	+	0.475966i
$472$		−	8.47900i		−	0.390278i
$473$	−1.55291	+	1.55291i	−0.0714031	+	0.0714031i
$474$	−6.87753	−	21.6385i	−0.315896	−	0.993891i
$475$	9.97552	−	9.97552i	0.457708	−	0.457708i
$476$	−1.96507	−	1.96507i	−0.0900689	−	0.0900689i
$477$	−7.45709	+	5.27296i	−0.341437	+	0.241432i
$478$		−	1.06282i		−	0.0486121i
$479$	20.5591	+	20.5591i	0.939371	+	0.939371i	0.998264	−	0.0588932i	$-0.0187571\pi$
$479$	20.5591	+	20.5591i	0.939371	+	0.939371i	−0.0588932	+	0.998264i	$0.518757\pi$
$480$	6.01029	+	3.11115i	0.274331	+	0.142004i
$481$		0			0
$482$			27.9636i			1.27371i
$483$	2.33618	+	7.35023i	0.106300	+	0.334447i
$484$	−10.6603			−0.484557
$485$	2.39659			0.108824
$486$	−15.5804	−	0.500258i	−0.706743	−	0.0226921i
$487$	1.79164	+	1.79164i	0.0811869	+	0.0811869i	0.746534	−	0.665347i	$-0.231716\pi$
$487$	1.79164	+	1.79164i	0.0811869	+	0.0811869i	−0.665347	+	0.746534i	$0.731716\pi$
$488$	6.60814	+	6.60814i	0.299137	+	0.299137i
$489$	−0.826137	−	2.59924i	−0.0373592	−	0.117542i
$490$	2.13792			0.0965815
$491$	−36.9151			−1.66596			−0.832978	−	0.553307i	$-0.813366\pi$
$491$	−36.9151			−1.66596			−0.832978	+	0.553307i	$0.813366\pi$
$492$	−8.74588	+	2.77977i	−0.394295	+	0.125321i
$493$		−	6.48009i		−	0.291849i
$494$		0			0
$495$	−3.94478	−	5.57877i	−0.177305	−	0.250747i
$496$	6.49983	+	6.49983i	0.291851	+	0.291851i
$497$		−	2.16044i		−	0.0969090i
$498$	−11.2115	−	5.80351i	−0.502400	−	0.260061i
$499$	−22.3461	−	22.3461i	−1.00035	−	1.00035i	−1.00000		0.000347536i	$-0.999889\pi$
$499$	−22.3461	−	22.3461i	−1.00035	−	1.00035i	−0.000347536	−	1.00000i	$-0.500111\pi$
$500$	14.5541	−	14.5541i	0.650877	−	0.650877i
$501$	40.3502	−	12.8248i	1.80272	−	0.572970i
$502$	−10.6960	+	10.6960i	−0.477385	+	0.477385i
$503$		−	23.3454i		−	1.04092i	−0.853886	−	0.520460i	$-0.825760\pi$
$503$		−	23.3454i		−	1.04092i	0.853886	−	0.520460i	$-0.174240\pi$
$504$	−4.39984	−	6.22231i	−0.195984	−	0.277164i
$505$	−16.1239	+	16.1239i	−0.717504	+	0.717504i
$506$	−1.02174			−0.0454218
$507$		0			0
$508$	9.31325			0.413209
$509$	−13.1852	+	13.1852i	−0.584424	+	0.584424i	−0.936116	−	0.351692i	$-0.885606\pi$
$509$	−13.1852	+	13.1852i	−0.584424	+	0.584424i	0.351692	+	0.936116i	$0.385606\pi$
$510$	−6.57525	−	3.40360i	−0.291157	−	0.150714i
$511$		−	18.6117i		−	0.823333i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−5.69404	−	4.30690i	−0.251398	−	0.190154i
$514$	−0.252579	+	0.252579i	−0.0111408	+	0.0111408i
$515$	5.72793	+	5.72793i	0.252403	+	0.252403i
$516$	−3.00000	+	5.79555i	−0.132068	+	0.255135i
$517$			4.54291i			0.199797i
$518$	−5.55909	−	5.55909i	−0.244252	−	0.244252i
$519$	16.5355	−	31.9441i	0.725827	−	1.40219i
$520$		0			0
$521$			20.1922i			0.884637i	0.896858	+	0.442318i	$0.145844\pi$
$521$			20.1922i			0.884637i	−0.896858	+	0.442318i	$0.854156\pi$
$522$	3.00492	−	17.5140i	0.131522	−	0.766566i
$523$	28.2236			1.23413			0.617066	−	0.786912i	$-0.288321\pi$
$523$	28.2236			1.23413			0.617066	+	0.786912i	$0.288321\pi$
$524$	−0.917828			−0.0400955
$525$	−43.0534	+	13.6840i	−1.87901	+	0.597218i
$526$	−1.51870	−	1.51870i	−0.0662186	−	0.0662186i
$527$	−7.11081	−	7.11081i	−0.309752	−	0.309752i
$528$	0.962144	−	0.305805i	0.0418719	−	0.0133085i
$529$	−19.9273			−0.866403
$530$	−11.8954			−0.516704
$531$	−4.30145	+	25.0707i	−0.186667	+	1.08797i
$532$		−	3.49026i		−	0.151322i
$533$		0			0
$534$	7.71547	−	14.9051i	0.333881	−	0.645009i
$535$	9.55577	+	9.55577i	0.413132	+	0.413132i
$536$		−	6.60137i		−	0.285136i
$537$	11.1474	−	21.5352i	0.481048	−	0.929313i
$538$	17.3407	+	17.3407i	0.747612	+	0.747612i
$539$	0.225511	−	0.225511i	0.00971346	−	0.00971346i
$540$	−16.1929	−	12.2481i	−0.696831	−	0.527074i
$541$	13.2334	−	13.2334i	0.568947	−	0.568947i	−0.362887	−	0.931833i	$-0.618209\pi$
$541$	13.2334	−	13.2334i	0.568947	−	0.568947i	0.931833	+	0.362887i	$0.118209\pi$
$542$		−	21.9261i		−	0.941805i
$543$	39.2862	+	20.3360i	1.68593	+	0.872702i
$544$	0.773575	−	0.773575i	0.0331668	−	0.0331668i
$545$	−60.7298			−2.60138
$546$		0			0
$547$	−14.7212			−0.629433			−0.314717	−	0.949186i	$-0.601909\pi$
$547$	−14.7212			−0.629433			−0.314717	+	0.949186i	$0.601909\pi$
$548$	−6.09427	+	6.09427i	−0.260334	+	0.260334i
$549$	−16.1866	−	22.8913i	−0.690826	−	0.976976i
$550$		−	5.98476i		−	0.255191i
$551$	5.75480	−	5.75480i	0.245163	−	0.245163i
$552$	−2.89351	+	0.919666i	−0.123156	+	0.0391436i
$553$	−23.5465	+	23.5465i	−1.00130	+	1.00130i
$554$	−13.1878	−	13.1878i	−0.560295	−	0.560295i
$555$	−18.6011	−	9.62862i	−0.789571	−	0.408712i
$556$		−	3.31325i		−	0.140513i
$557$	8.71827	+	8.71827i	0.369405	+	0.369405i	0.867260	−	0.497855i	$-0.165879\pi$
$557$	8.71827	+	8.71827i	0.369405	+	0.369405i	−0.497855	+	0.867260i	$0.665879\pi$
$558$	−15.9213	−	22.5161i	−0.674001	−	0.953181i
$559$		0			0
$560$		−	9.92570i		−	0.419438i
$561$	−1.05259	+	0.334551i	−0.0444402	+	0.0141248i
$562$	−15.9498			−0.672801
$563$	−19.7326			−0.831628			−0.415814	−	0.909450i	$-0.636503\pi$
$563$	−19.7326			−0.831628			−0.415814	+	0.909450i	$0.636503\pi$
$564$	4.08907	+	12.8653i	0.172181	+	0.541726i
$565$	30.1080	+	30.1080i	1.26665	+	1.26665i
$566$	−3.33410	−	3.33410i	−0.140143	−	0.140143i
$567$	9.85280	+	20.6302i	0.413779	+	0.866385i
$568$	0.850484			0.0356855
$569$	34.9006			1.46311			0.731555	−	0.681782i	$-0.238795\pi$
$569$	34.9006			1.46311			0.731555	+	0.681782i	$0.238795\pi$
$570$	−2.81666	−	8.86196i	−0.117977	−	0.371187i
$571$			2.37582i			0.0994248i	0.998764	+	0.0497124i	$0.0158305\pi$
$571$			2.37582i			0.0994248i	−0.998764	+	0.0497124i	$0.984170\pi$
$572$		0			0
$573$	36.3725	+	18.8278i	1.51948	+	0.786542i
$574$	9.51702	+	9.51702i	0.397233	+	0.397233i
$575$			17.9983i			0.750581i
$576$	2.44949	−	1.73205i	0.102062	−	0.0721688i
$577$	−3.78848	−	3.78848i	−0.157716	−	0.157716i	0.623838	−	0.781554i	$-0.285573\pi$
$577$	−3.78848	−	3.78848i	−0.157716	−	0.157716i	−0.781554	+	0.623838i	$0.785573\pi$
$578$	11.1745	−	11.1745i	0.464799	−	0.464799i
$579$	−5.56055	−	17.4950i	−0.231089	−	0.727066i
$580$	16.3657	−	16.3657i	0.679548	−	0.679548i
$581$			18.5153i			0.768143i
$582$	0.488365	−	0.943448i	0.0202434	−	0.0391072i
$583$	−1.25475	+	1.25475i	−0.0519663	+	0.0519663i
$584$	7.32673			0.303182
$585$		0			0
$586$	−21.3553			−0.882179
$587$	7.18566	−	7.18566i	0.296584	−	0.296584i	−0.543090	−	0.839674i	$-0.682746\pi$
$587$	7.18566	−	7.18566i	0.296584	−	0.296584i	0.839674	+	0.543090i	$0.182746\pi$
$588$	0.435655	−	0.841620i	0.0179661	−	0.0347078i
$589$		−	12.6299i		−	0.520404i
$590$	−23.4269	+	23.4269i	−0.964471	+	0.964471i
$591$	1.81935	+	5.72415i	0.0748380	+	0.235460i
$592$	2.18840	−	2.18840i	0.0899429	−	0.0899429i
$593$	9.76893	+	9.76893i	0.401162	+	0.401162i	0.878642	−	0.477481i	$-0.158450\pi$
$593$	9.76893	+	9.76893i	0.401162	+	0.401162i	−0.477481	+	0.878642i	$0.658450\pi$
$594$	−3.00000	+	0.416102i	−0.123091	+	0.0170729i
$595$			10.8587i			0.445164i
$596$	−5.55437	−	5.55437i	−0.227516	−	0.227516i
$597$	4.74998	+	2.45877i	0.194404	+	0.100631i
$598$		0			0
$599$			35.2538i			1.44043i	0.693750	+	0.720216i	$0.255957\pi$
$599$			35.2538i			1.44043i	−0.693750	+	0.720216i	$0.744043\pi$
$600$	−5.38688	−	16.9485i	−0.219918	−	0.691921i
$601$	9.14384			0.372985			0.186493	−	0.982456i	$-0.440288\pi$
$601$	9.14384			0.372985			0.186493	+	0.982456i	$0.440288\pi$
$602$	9.57108			0.390088
$603$	−3.34892	+	19.5189i	−0.136378	+	0.794872i
$604$	10.2600	+	10.2600i	0.417473	+	0.417473i
$605$	29.4536	+	29.4536i	1.19746	+	1.19746i
$606$	3.06173	+	9.63301i	0.124374	+	0.391314i
$607$	−19.9279			−0.808847			−0.404423	−	0.914572i	$-0.632528\pi$
$607$	−19.9279			−0.808847			−0.404423	+	0.914572i	$0.632528\pi$
$608$	1.37398			0.0557224
$609$	−24.8372	+	7.89418i	−1.00645	+	0.319888i
$610$		−	36.5157i		−	1.47848i
$611$		0			0
$612$	−2.67974	+	1.89486i	−0.108322	+	0.0765953i
$613$	10.6247	+	10.6247i	0.429127	+	0.429127i	0.888331	−	0.459204i	$-0.151865\pi$
$613$	10.6247	+	10.6247i	0.429127	+	0.429127i	−0.459204	+	0.888331i	$0.651865\pi$
$614$			22.9469i			0.926063i
$615$	31.8446	+	16.4840i	1.28410	+	0.664698i
$616$	−1.04698	−	1.04698i	−0.0421840	−	0.0421840i
$617$	7.20247	−	7.20247i	0.289961	−	0.289961i	−0.547104	−	0.837065i	$-0.684270\pi$
$617$	7.20247	−	7.20247i	0.289961	−	0.289961i	0.837065	+	0.547104i	$0.184270\pi$
$618$	3.42208	−	1.08766i	0.137656	−	0.0437523i
$619$	−18.1131	+	18.1131i	−0.728027	+	0.728027i	−0.970226	−	0.242199i	$-0.922131\pi$
$619$	−18.1131	+	18.1131i	−0.728027	+	0.728027i	0.242199	+	0.970226i	$0.422131\pi$
$620$		−	35.9172i		−	1.44247i
$621$	9.02207	−	1.25137i	0.362043	−	0.0502157i
$622$	23.2259	−	23.2259i	0.931275	−	0.931275i
$623$	−24.6151			−0.986185
$624$		0			0
$625$	−29.0857			−1.16343
$626$	−7.82263	+	7.82263i	−0.312655	+	0.312655i
$627$	−1.23188	−	0.637668i	−0.0491965	−	0.0254660i
$628$			6.71547i			0.267976i
$629$	−2.39412	+	2.39412i	−0.0954596	+	0.0954596i
$630$	−5.03537	+	29.3483i	−0.200614	+	1.16926i
$631$	14.2008	−	14.2008i	0.565325	−	0.565325i	−0.365490	−	0.930815i	$-0.619099\pi$
$631$	14.2008	−	14.2008i	0.565325	−	0.565325i	0.930815	+	0.365490i	$0.119099\pi$
$632$	−9.26936	−	9.26936i	−0.368716	−	0.368716i
$633$	−3.94769	+	7.62635i	−0.156907	+	0.303120i
$634$		−	24.8194i		−	0.985704i
$635$	−25.7319	−	25.7319i	−1.02114	−	1.02114i
$636$	−2.42398	+	4.68278i	−0.0961173	+	0.185684i
$637$		0			0
$638$		−	3.45256i		−	0.136688i
$639$	−2.51471	−	0.431456i	−0.0994803	−	0.0170681i
$640$	3.90738			0.154453
$641$	−44.6833			−1.76489			−0.882443	−	0.470420i	$-0.844102\pi$
$641$	−44.6833			−1.76489			−0.882443	+	0.470420i	$0.844102\pi$
$642$	5.70897	−	1.81452i	0.225315	−	0.0716136i
$643$	6.35599	+	6.35599i	0.250656	+	0.250656i	0.821239	−	0.570584i	$-0.193283\pi$
$643$	6.35599	+	6.35599i	0.250656	+	0.250656i	−0.570584	+	0.821239i	$0.693283\pi$
$644$	3.14864	+	3.14864i	0.124074	+	0.124074i
$645$	24.3015	−	7.72393i	0.956872	−	0.304130i
$646$	−1.50314			−0.0591402
$647$	−37.9737			−1.49290			−0.746451	−	0.665441i	$-0.768244\pi$
$647$	−37.9737			−1.49290			−0.746451	+	0.665441i	$0.768244\pi$
$648$	−8.12132	+	3.87868i	−0.319036	+	0.152369i
$649$			4.94222i			0.193999i
$650$		0			0
$651$	−18.5921	+	35.9172i	−0.728682	+	1.40771i
$652$	−1.11345	−	1.11345i	−0.0436059	−	0.0436059i
$653$		−	18.4886i		−	0.723513i	−0.932273	−	0.361757i	$-0.882177\pi$
$653$		−	18.4886i		−	0.723513i	0.932273	−	0.361757i	$-0.117823\pi$
$654$	−12.3752	+	23.9070i	−0.483908	+	0.934839i
$655$	2.53590	+	2.53590i	0.0990857	+	0.0990857i
$656$	−3.74650	+	3.74650i	−0.146276	+	0.146276i
$657$	−21.6637	−	3.71690i	−0.845180	−	0.145010i
$658$	13.9997	−	13.9997i	0.545763	−	0.545763i
$659$			0.743853i			0.0289764i	0.999895	+	0.0144882i	$0.00461190\pi$
$659$			0.743853i			0.0289764i	−0.999895	+	0.0144882i	$0.995388\pi$
$660$	−3.50326	−	1.81342i	−0.136364	−	0.0705873i
$661$	19.8275	−	19.8275i	0.771200	−	0.771200i	−0.207116	−	0.978316i	$-0.566408\pi$
$661$	19.8275	−	19.8275i	0.771200	−	0.771200i	0.978316	+	0.207116i	$0.0664078\pi$
$662$	−4.62395			−0.179715
$663$		0			0
$664$	−7.28877			−0.282859
$665$	−9.64335	+	9.64335i	−0.373953	+	0.373953i
$666$	−7.58086	+	5.36048i	−0.293752	+	0.207714i
$667$			10.3831i			0.402034i
$668$	17.2850	−	17.2850i	0.668775	−	0.668775i
$669$	−31.4687	+	10.0019i	−1.21665	+	0.386697i
$670$	−18.2392	+	18.2392i	−0.704640	+	0.704640i
$671$	−3.85174	−	3.85174i	−0.148695	−	0.148695i
$672$	−3.90738	−	2.02261i	−0.150730	−	0.0780238i
$673$			27.6374i			1.06534i	0.846322	+	0.532672i	$0.178812\pi$
$673$			27.6374i			1.06534i	−0.846322	+	0.532672i	$0.821188\pi$
$674$	−5.50437	−	5.50437i	−0.212021	−	0.212021i
$675$	7.32980	+	52.8461i	0.282124	+	2.03405i
$676$		0			0
$677$		−	34.0927i		−	1.31029i	−0.755504	−	0.655145i	$-0.772608\pi$
$677$		−	34.0927i		−	1.31029i	0.755504	−	0.655145i	$-0.227392\pi$
$678$	17.9877	−	5.71715i	0.690812	−	0.219566i
$679$	−1.55806			−0.0597928
$680$	−4.27467			−0.163926
$681$	2.81223	+	8.84802i	0.107765	+	0.339057i
$682$	−3.78860	−	3.78860i	−0.145073	−	0.145073i
$683$	16.4785	+	16.4785i	0.630531	+	0.630531i	0.948201	−	0.317670i	$-0.102900\pi$
$683$	16.4785	+	16.4785i	0.630531	+	0.630531i	−0.317670	+	0.948201i	$0.602900\pi$
$684$	−4.06259	−	0.697030i	−0.155337	−	0.0266516i
$685$	33.6762			1.28670
$686$	−19.1716			−0.731976
$687$	2.06589	+	6.49985i	0.0788188	+	0.247985i
$688$			3.76778i			0.143645i
$689$		0			0
$690$	10.5356	+	5.45361i	0.401082	+	0.207615i
$691$	−7.22628	−	7.22628i	−0.274901	−	0.274901i	0.556169	−	0.831069i	$-0.312271\pi$
$691$	−7.22628	−	7.22628i	−0.274901	−	0.274901i	−0.831069	+	0.556169i	$0.812271\pi$
$692$		−	20.7673i		−	0.789456i
$693$	2.56456	+	3.62684i	0.0974197	+	0.137772i
$694$	−7.66753	−	7.66753i	−0.291056	−	0.291056i
$695$	−9.15429	+	9.15429i	−0.347242	+	0.347242i
$696$	−3.10764	−	9.77747i	−0.117795	−	0.370614i
$697$	4.09867	−	4.09867i	0.155248	−	0.155248i
$698$			15.3725i			0.581856i
$699$	3.05482	−	5.90146i	0.115544	−	0.223214i
$700$	−18.4429	+	18.4429i	−0.697077	+	0.697077i
$701$	31.9420			1.20643			0.603217	−	0.797577i	$-0.293885\pi$
$701$	31.9420			1.20643			0.603217	+	0.797577i	$0.293885\pi$
$702$		0			0
$703$	−4.25230			−0.160379
$704$	0.412157	−	0.412157i	0.0155337	−	0.0155337i
$705$	24.2481	−	46.8438i	0.913237	−	1.76424i
$706$			1.86741i			0.0702808i
$707$	10.4824	−	10.4824i	0.394231	−	0.394231i
$708$	4.44849	+	13.9961i	0.167184	+	0.526007i
$709$	−5.25088	+	5.25088i	−0.197201	+	0.197201i	−0.798799	−	0.601598i	$-0.794531\pi$
$709$	−5.25088	+	5.25088i	−0.197201	+	0.197201i	0.601598	+	0.798799i	$0.294531\pi$
$710$	−2.34983	−	2.34983i	−0.0881876	−	0.0881876i
$711$	22.7052	+	32.1100i	0.851512	+	1.20422i
$712$		−	9.69006i		−	0.363150i
$713$	11.3937	+	11.3937i	0.426697	+	0.426697i
$714$	4.27467	+	2.21273i	0.159976	+	0.0828095i
$715$		0			0
$716$		−	14.0004i		−	0.523218i
$717$	0.557604	+	1.75437i	0.0208241	+	0.0655181i
$718$	17.1595			0.640387
$719$	−28.9186			−1.07848			−0.539240	−	0.842152i	$-0.681289\pi$
$719$	−28.9186			−1.07848			−0.539240	+	0.842152i	$0.681289\pi$
$720$	−11.5533	−	1.98224i	−0.430567	−	0.0738736i
$721$	−3.72381	−	3.72381i	−0.138682	−	0.138682i
$722$	12.1001	+	12.1001i	0.450320	+	0.450320i
$723$	−14.6710	−	46.1589i	−0.545621	−	1.71667i
$724$	25.5405			0.949207
$725$	−60.8181			−2.25873
$726$	17.5967	−	5.59288i	0.653074	−	0.207571i
$727$			13.5518i			0.502608i	0.967908	+	0.251304i	$0.0808594\pi$
$727$			13.5518i			0.502608i	−0.967908	+	0.251304i	$0.919141\pi$
$728$		0			0
$729$	25.9808	−	7.34847i	0.962250	−	0.272166i
$730$	−20.2433	−	20.2433i	−0.749237	−	0.749237i
$731$		−	4.12195i		−	0.152456i
$732$	−14.3749	−	7.44098i	−0.531311	−	0.275027i
$733$	13.9665	+	13.9665i	0.515864	+	0.515864i	0.916317	−	0.400453i	$-0.131147\pi$
$733$	13.9665	+	13.9665i	0.515864	+	0.515864i	−0.400453	+	0.916317i	$0.631147\pi$
$734$	6.40838	−	6.40838i	0.236538	−	0.236538i
$735$	−3.52903	+	1.12166i	−0.130170	+	0.0413729i
$736$	−1.23950	+	1.23950i	−0.0456887	+	0.0456887i
$737$			3.84779i			0.141735i
$738$	12.9782	−	9.17701i	0.477736	−	0.337810i
$739$	−1.39265	+	1.39265i	−0.0512293	+	0.0512293i	−0.732257	−	0.681028i	$-0.761533\pi$
$739$	−1.39265	+	1.39265i	−0.0512293	+	0.0512293i	0.681028	+	0.732257i	$0.261533\pi$
$740$	−12.0928			−0.444541
$741$		0			0
$742$	7.73339			0.283902
$743$	4.23148	−	4.23148i	0.155238	−	0.155238i	−0.625215	−	0.780453i	$-0.714989\pi$
$743$	4.23148	−	4.23148i	0.155238	−	0.155238i	0.780453	+	0.625215i	$0.214989\pi$
$744$	−14.1393	−	7.31902i	−0.518370	−	0.268328i
$745$			30.6927i			1.12449i
$746$	5.35695	−	5.35695i	0.196132	−	0.196132i
$747$	21.5514	+	3.69764i	0.788525	+	0.135290i
$748$	−0.450899	+	0.450899i	−0.0164865	+	0.0164865i
$749$	−6.21235	−	6.21235i	−0.226994	−	0.226994i
$750$	−16.3883	+	31.6598i	−0.598417	+	1.15605i
$751$		−	17.5041i		−	0.638733i	−0.947631	−	0.319366i	$-0.896530\pi$
$751$		−	17.5041i		−	0.638733i	0.947631	−	0.319366i	$-0.103470\pi$
$752$	5.51114	+	5.51114i	0.200971	+	0.200971i
$753$	12.0440	−	23.2673i	0.438909	−	0.847906i
$754$		0			0
$755$		−	56.6953i		−	2.06335i
$756$	10.5272	+	7.96267i	0.382872	+	0.289600i
$757$	8.00336			0.290887			0.145443	−	0.989367i	$-0.453539\pi$
$757$	8.00336			0.290887			0.145443	+	0.989367i	$0.453539\pi$
$758$	12.0771			0.438660
$759$	1.68656	−	0.536052i	0.0612183	−	0.0194575i
$760$	−3.79623	−	3.79623i	−0.137704	−	0.137704i
$761$	−13.8584	−	13.8584i	−0.502368	−	0.502368i	0.409805	−	0.912173i	$-0.365597\pi$
$761$	−13.8584	−	13.8584i	−0.502368	−	0.502368i	−0.912173	+	0.409805i	$0.865597\pi$
$762$	−15.3732	+	4.88617i	−0.556912	+	0.177007i
$763$	39.4813			1.42932
$764$	23.6463			0.855493
$765$	12.6393	+	2.16857i	0.456976	+	0.0784047i
$766$			36.8323i			1.33081i
$767$		0			0
$768$	0.796225	−	1.53819i	0.0287313	−	0.0555046i
$769$	−30.3616	−	30.3616i	−1.09487	−	1.09487i	−0.995001	−	0.0998650i	$-0.968159\pi$
$769$	−30.3616	−	30.3616i	−1.09487	−	1.09487i	−0.0998650	−	0.995001i	$-0.531841\pi$
$770$			5.78547i			0.208494i
$771$	0.284412	−	0.549443i	0.0102429	−	0.0197877i
$772$	−7.49437	−	7.49437i	−0.269728	−	0.269728i
$773$	−6.55172	+	6.55172i	−0.235649	+	0.235649i	−0.815046	−	0.579397i	$-0.803288\pi$
$773$	−6.55172	+	6.55172i	−0.235649	+	0.235649i	0.579397	+	0.815046i	$0.303288\pi$
$774$	1.91142	−	11.1406i	0.0687044	−	0.400439i
$775$	−66.7377	+	66.7377i	−2.39729	+	2.39729i
$776$		−	0.613350i		−	0.0220180i
$777$	12.0928	+	6.25971i	0.433828	+	0.224566i
$778$	9.97109	−	9.97109i	0.357481	−	0.357481i
$779$	7.27984			0.260827
$780$		0			0
$781$	−0.495728			−0.0177385
$782$	1.35602	−	1.35602i	0.0484910	−	0.0484910i
$783$	4.22850	+	30.4865i	0.151114	+	1.08950i
$784$		−	0.547150i		−	0.0195411i
$785$	18.5544	−	18.5544i	0.662235	−	0.662235i
$786$	1.51504	−	0.481536i	0.0540397	−	0.0171758i
$787$	30.1223	−	30.1223i	1.07375	−	1.07375i	0.0766903	−	0.997055i	$-0.475565\pi$
$787$	30.1223	−	30.1223i	1.07375	−	1.07375i	0.997055	−	0.0766903i	$-0.0244353\pi$
$788$	2.45207	+	2.45207i	0.0873514	+	0.0873514i
$789$	3.30368	+	1.71011i	0.117614	+	0.0608815i
$790$			51.2213i			1.82237i
$791$	−19.5737	−	19.5737i	−0.695960	−	0.695960i
$792$	−1.42775	+	1.00957i	−0.0507330	+	0.0358736i
$793$		0			0
$794$			7.85191i			0.278654i
$795$	19.6355	−	6.24090i	0.696400	−	0.221342i
$796$	3.08804			0.109453
$797$	−21.0322			−0.744998			−0.372499	−	0.928033i	$-0.621499\pi$
$797$	−21.0322			−0.744998			−0.372499	+	0.928033i	$0.621499\pi$
$798$	1.83115	+	5.76130i	0.0648222	+	0.203948i
$799$	−6.02919	−	6.02919i	−0.213297	−	0.213297i
$800$	−7.26029	−	7.26029i	−0.256690	−	0.256690i
$801$	−4.91582	+	28.6515i	−0.173692	+	1.01235i
$802$	21.8561			0.771764
$803$	−4.27059			−0.150706
$804$	3.46340	+	10.8968i	0.122145	+	0.384299i
$805$		−	17.3990i		−	0.613233i
$806$		0			0
$807$	−37.7218	−	19.5262i	−1.32787	−	0.687356i
$808$	4.12652	+	4.12652i	0.145171	+	0.145171i
$809$			27.1206i			0.953508i	0.879037	+	0.476754i	$0.158187\pi$
$809$			27.1206i			0.953508i	−0.879037	+	0.476754i	$0.841813\pi$
$810$	33.1552	+	11.7221i	1.16496	+	0.411874i
$811$	−39.1597	−	39.1597i	−1.37508	−	1.37508i	−0.852726	−	0.522359i	$-0.825052\pi$
$811$	−39.1597	−	39.1597i	−1.37508	−	1.37508i	−0.522359	−	0.852726i	$-0.674948\pi$
$812$	−10.6396	+	10.6396i	−0.373376	+	0.373376i
$813$	11.5035	+	36.1929i	0.403444	+	1.26934i
$814$	−1.27557	+	1.27557i	−0.0447088	+	0.0447088i
$815$			6.15276i			0.215522i
$816$	−0.871071	+	1.68278i	−0.0304936	+	0.0589091i
$817$	3.66060	−	3.66060i	0.128068	−	0.128068i
$818$	−2.24149			−0.0783720
$819$		0			0
$820$	20.7026			0.722968
$821$	6.07641	−	6.07641i	0.212068	−	0.212068i	−0.593077	−	0.805145i	$-0.702087\pi$
$821$	6.07641	−	6.07641i	0.212068	−	0.212068i	0.805145	+	0.593077i	$0.202087\pi$
$822$	6.86235	−	13.2570i	0.239352	−	0.462392i
$823$			8.51217i			0.296715i	0.988934	+	0.148358i	$0.0473987\pi$
$823$			8.51217i			0.296715i	−0.988934	+	0.148358i	$0.952601\pi$
$824$	1.46593	−	1.46593i	0.0510680	−	0.0510680i
$825$	3.13989	+	9.87892i	0.109317	+	0.343940i
$826$	15.2302	−	15.2302i	0.529926	−	0.529926i
$827$	18.9976	+	18.9976i	0.660613	+	0.660613i	0.955524	−	0.294912i	$-0.0952903\pi$
$827$	18.9976	+	18.9976i	0.660613	+	0.660613i	−0.294912	+	0.955524i	$0.595290\pi$
$828$	4.29376	−	3.03615i	0.149219	−	0.105513i
$829$			16.5329i			0.574211i	0.957899	+	0.287106i	$0.0926931\pi$
$829$			16.5329i			0.574211i	−0.957899	+	0.287106i	$0.907307\pi$
$830$	20.1384	+	20.1384i	0.699014	+	0.699014i
$831$	28.6877	+	14.8499i	0.995167	+	0.515136i
$832$		0			0
$833$			0.598582i			0.0207396i
$834$	1.73829	+	5.46912i	0.0601920	+	0.189380i
$835$	−95.5144			−3.30541
$836$	−0.800864			−0.0276985
$837$	38.0939	+	28.8138i	1.31672	+	0.995950i
$838$	−23.6070	−	23.6070i	−0.815491	−	0.815491i
$839$	−29.3294	−	29.3294i	−1.01256	−	1.01256i	−0.999920	−	0.0126419i	$-0.995976\pi$
$839$	−29.3294	−	29.3294i	−1.01256	−	1.01256i	−0.0126419	−	0.999920i	$-0.504024\pi$
$840$	5.20750	+	16.3842i	0.179676	+	0.565307i
$841$	−6.08547			−0.209844
$842$	3.18601			0.109797
$843$	26.3280	−	8.36801i	0.906784	−	0.288210i
$844$			4.95801i			0.170662i
$845$		0			0
$846$	−13.4995	−	19.0912i	−0.464122	−	0.656368i
$847$	−19.1482	−	19.1482i	−0.657941	−	0.657941i
$848$			3.04435i			0.104543i
$849$	7.25276	+	3.75430i	0.248914	+	0.128847i
$850$	7.94276	+	7.94276i	0.272435	+	0.272435i
$851$	3.83610	−	3.83610i	0.131500	−	0.131500i
$852$	−1.40388	+	0.446205i	−0.0480961	+	0.0152867i
$853$	13.7858	−	13.7858i	0.472018	−	0.472018i	−0.430549	−	0.902567i	$-0.641680\pi$
$853$	13.7858	−	13.7858i	0.472018	−	0.472018i	0.902567	+	0.430549i	$0.141680\pi$
$854$			23.7394i			0.812346i
$855$	9.29881	+	13.1505i	0.318013	+	0.449738i
$856$	2.44557	−	2.44557i	0.0835879	−	0.0835879i
$857$	41.5499			1.41932			0.709659	−	0.704545i	$-0.248849\pi$
$857$	41.5499			1.41932			0.709659	+	0.704545i	$0.248849\pi$
$858$		0			0
$859$	44.2270			1.50900			0.754502	−	0.656298i	$-0.227878\pi$
$859$	44.2270			1.50900			0.754502	+	0.656298i	$0.227878\pi$
$860$	10.4101	−	10.4101i	0.354982	−	0.354982i
$861$	−20.7026	−	10.7165i	−0.705544	−	0.365217i
$862$			21.6840i			0.738562i
$863$	14.7459	−	14.7459i	0.501956	−	0.501956i	−0.410089	−	0.912045i	$-0.634502\pi$
$863$	14.7459	−	14.7459i	0.501956	−	0.501956i	0.912045	+	0.410089i	$0.134502\pi$
$864$	−3.13461	+	4.14418i	−0.106642	+	0.140988i
$865$	−57.3788	+	57.3788i	−1.95094	+	1.95094i
$866$	21.2499	+	21.2499i	0.722103	+	0.722103i
$867$	−12.5829	+	24.3083i	−0.427337	+	0.825552i
$868$			23.3503i			0.792561i
$869$	5.40290	+	5.40290i	0.183281	+	0.183281i
$870$	−18.4283	+	35.6007i	−0.624778	+	1.20698i
$871$		0			0
$872$			15.5423i			0.526330i
$873$	−0.311156	+	1.81355i	−0.0105310	+	0.0613794i
$874$	2.40848			0.0814682
$875$	52.2847			1.76755
$876$	−12.0941	+	3.84395i	−0.408622	+	0.129875i
$877$	−31.9277	−	31.9277i	−1.07812	−	1.07812i	−0.996678	−	0.0814427i	$-0.974047\pi$
$877$	−31.9277	−	31.9277i	−1.07812	−	1.07812i	−0.0814427	−	0.996678i	$-0.525953\pi$
$878$	14.7403	+	14.7403i	0.497460	+	0.497460i
$879$	35.2508	−	11.2040i	1.18898	−	0.377902i
$880$	−2.27752			−0.0767753
$881$	31.1330			1.04890			0.524448	−	0.851442i	$-0.324272\pi$
$881$	31.1330			1.04890			0.524448	+	0.851442i	$0.324272\pi$
$882$	−0.277572	+	1.61781i	−0.00934635	+	0.0544745i
$883$		−	45.7983i		−	1.54123i	−0.637298	−	0.770617i	$-0.719948\pi$
$883$		−	45.7983i		−	1.54123i	0.637298	−	0.770617i	$-0.280052\pi$
$884$		0			0
$885$	26.3795	−	50.9612i	0.886737	−	1.71304i
$886$	9.21806	+	9.21806i	0.309687	+	0.309687i
$887$		−	29.5730i		−	0.992965i	−0.868047	−	0.496482i	$-0.834625\pi$
$887$		−	29.5730i		−	0.992965i	0.868047	−	0.496482i	$-0.165375\pi$
$888$	−2.46422	+	4.76050i	−0.0826936	+	0.159752i
$889$	16.7287	+	16.7287i	0.561062	+	0.561062i
$890$	−26.7730	+	26.7730i	−0.897433	+	0.897433i
$891$	4.73373	−	2.26079i	0.158586	−	0.0757395i
$892$	−13.4803	+	13.4803i	−0.451355	+	0.451355i
$893$		−	10.7087i		−	0.358354i
$894$	12.0826	+	6.25440i	0.404102	+	0.209179i
$895$	−38.6821	+	38.6821i	−1.29300	+	1.29300i
$896$	−2.54025			−0.0848637
$897$		0			0
$898$	19.0404			0.635385
$899$	−38.5004	+	38.5004i	−1.28406	+	1.28406i
$900$	17.7840	+	25.1504i	0.592801	+	0.838347i
$901$		−	3.33051i		−	0.110956i
$902$	2.18375	−	2.18375i	0.0727109	−	0.0727109i
$903$	−15.7988	+	5.02145i	−0.525751	+	0.167103i
$904$	7.70543	−	7.70543i	0.256279	−	0.256279i
$905$	−70.5668	−	70.5668i	−2.34572	−	2.34572i
$906$	−22.3188	−	11.5531i	−0.741493	−	0.383825i
$907$		−	58.1044i		−	1.92933i	−0.263487	−	0.964663i	$-0.584873\pi$
$907$		−	58.1044i		−	1.92933i	0.263487	−	0.964663i	$-0.415127\pi$
$908$	3.79025	+	3.79025i	0.125784	+	0.125784i
$909$	−10.1079	−	14.2947i	−0.335257	−	0.474125i
$910$		0			0
$911$			52.8673i			1.75157i	0.482701	+	0.875785i	$0.339656\pi$
$911$			52.8673i			1.75157i	−0.482701	+	0.875785i	$0.660344\pi$
$912$	−2.26801	+	0.720857i	−0.0751012	+	0.0238700i
$913$	4.24846			0.140604
$914$	−21.2603			−0.703228
$915$	19.1579	+	60.2758i	0.633340	+	1.99266i
$916$	2.78436	+	2.78436i	0.0919978	+	0.0919978i
$917$	−1.64863	−	1.64863i	−0.0544424	−	0.0544424i
$918$	3.42926	−	4.53373i	0.113182	−	0.149636i
$919$	−6.15017			−0.202875			−0.101438	−	0.994842i	$-0.532344\pi$
$919$	−6.15017			−0.202875			−0.101438	+	0.994842i	$0.532344\pi$
$920$	6.84932			0.225816
$921$	−12.0391	−	37.8781i	−0.396700	−	1.24812i
$922$		−	1.52692i		−	0.0502864i
$923$		0			0
$924$	2.27752	+	1.17893i	0.0749250	+	0.0387840i
$925$	22.4697	+	22.4697i	0.738799	+	0.738799i
$926$			30.1612i			0.991159i
$927$	−5.07812	+	3.59077i	−0.166787	+	0.117936i
$928$	−4.18840	−	4.18840i	−0.137491	−	0.137491i
$929$	−25.3106	+	25.3106i	−0.830414	+	0.830414i	−0.987573	−	0.157160i	$-0.949766\pi$
$929$	−25.3106	+	25.3106i	−0.830414	+	0.830414i	0.157160	+	0.987573i	$0.449766\pi$
$930$	18.8439	+	59.2878i	0.617915	+	1.94412i
$931$	−0.531585	+	0.531585i	−0.0174220	+	0.0174220i
$932$		−	3.83663i		−	0.125673i
$933$	−26.1532	+	50.5240i	−0.856216	+	1.65408i
$934$	−7.98571	+	7.98571i	−0.261300	+	0.261300i
$935$	2.49161			0.0814844
$936$		0			0
$937$	−13.8585			−0.452737			−0.226369	−	0.974042i	$-0.572685\pi$
$937$	−13.8585			−0.452737			−0.226369	+	0.974042i	$0.572685\pi$
$938$	11.8576	−	11.8576i	0.387163	−	0.387163i
$939$	8.80854	−	17.0168i	0.287456	−	0.555322i
$940$		−	30.4538i		−	0.993295i
$941$	−10.8257	+	10.8257i	−0.352908	+	0.352908i	−0.861190	−	0.508283i	$-0.830281\pi$
$941$	−10.8257	+	10.8257i	−0.352908	+	0.352908i	0.508283	+	0.861190i	$0.330281\pi$
$942$	−3.52326	−	11.0851i	−0.114794	−	0.361172i
$943$	−6.56731	+	6.56731i	−0.213861	+	0.213861i
$944$	5.99556	+	5.99556i	0.195139	+	0.195139i
$945$	−7.08572	−	51.0864i	−0.230499	−	1.66184i
$946$		−	2.19615i		−	0.0714031i
$947$	−15.0501	−	15.0501i	−0.489061	−	0.489061i	0.418949	−	0.908010i	$-0.362399\pi$
$947$	−15.0501	−	15.0501i	−0.489061	−	0.489061i	−0.908010	+	0.418949i	$0.862399\pi$
$948$	20.1639	+	10.4376i	0.654893	+	0.338998i
$949$		0			0
$950$			14.1075i			0.457708i
$951$	13.0214	+	40.9689i	0.422249	+	1.32851i
$952$	2.77903			0.0900689
$953$	20.6433			0.668703			0.334351	−	0.942448i	$-0.391483\pi$
$953$	20.6433			0.668703			0.334351	+	0.942448i	$0.391483\pi$
$954$	1.54441	−	9.00151i	0.0500023	−	0.291435i
$955$	−65.3332	−	65.3332i	−2.11413	−	2.11413i
$956$	0.751524	+	0.751524i	0.0243060	+	0.0243060i
$957$	1.81138	+	5.69907i	0.0585535	+	0.184225i
$958$	−29.0750			−0.939371
$959$	−21.8934			−0.706974
$960$	−6.44983	+	2.05000i	−0.208167	+	0.0661634i
$961$			53.4956i			1.72566i
$962$		0			0
$963$	−8.47170	+	5.99040i	−0.272997	+	0.193038i
$964$	−19.7732	−	19.7732i	−0.636853	−	0.636853i
$965$			41.4129i			1.33313i
$966$	−6.84932	−	3.54547i	−0.220373	−	0.114074i
$967$	3.56933	+	3.56933i	0.114782	+	0.114782i	0.762165	−	0.647383i	$-0.224137\pi$
$967$	3.56933	+	3.56933i	0.114782	+	0.114782i	−0.647383	+	0.762165i	$0.724137\pi$
$968$	7.53794	−	7.53794i	0.242279	−	0.242279i
$969$	2.48120	−	0.788618i	0.0797076	−	0.0253341i
$970$	−1.69465	+	1.69465i	−0.0544118	+	0.0544118i
$971$		−	37.0559i		−	1.18918i	−0.804029	−	0.594590i	$-0.797314\pi$
$971$		−	37.0559i		−	1.18918i	0.804029	−	0.594590i	$-0.202686\pi$
$972$	11.3708	−	10.6633i	0.364717	−	0.342025i
$973$	5.95134	−	5.95134i	0.190791	−	0.190791i
$974$	−2.53376			−0.0811869
$975$		0			0
$976$	−9.34533			−0.299137
$977$	−34.5163	+	34.5163i	−1.10427	+	1.10427i	−0.110385	+	0.993889i	$0.535208\pi$
$977$	−34.5163	+	34.5163i	−1.10427	+	1.10427i	−0.993889	+	0.110385i	$0.964792\pi$
$978$	2.42211	+	1.25378i	0.0774505	+	0.0400914i
$979$			5.64812i			0.180515i
$980$	−1.51174	+	1.51174i	−0.0482907	+	0.0482907i
$981$	7.88471	−	45.9555i	0.251740	−	1.46725i
$982$	26.1029	−	26.1029i	0.832978	−	0.832978i
$983$	33.9032	+	33.9032i	1.08134	+	1.08134i	0.996384	+	0.0849587i	$0.0270758\pi$
$983$	33.9032	+	33.9032i	1.08134	+	1.08134i	0.0849587	+	0.996384i	$0.472924\pi$
$984$	4.21868	−	8.14986i	0.134487	−	0.259808i
$985$		−	13.5498i		−	0.431733i
$986$	4.58212	+	4.58212i	0.145924	+	0.145924i
$987$	−15.7641	+	30.4538i	−0.501776	+	0.969357i
$988$		0			0
$989$			6.60462i			0.210015i
$990$	6.73417	+	1.15540i	0.214026	+	0.0367210i
$991$	−48.7016			−1.54706			−0.773529	−	0.633761i	$-0.781510\pi$
$991$	−48.7016			−1.54706			−0.773529	+	0.633761i	$0.781510\pi$
$992$	−9.19215			−0.291851
$993$	7.63267	−	2.42595i	0.242215	−	0.0769850i
$994$	1.52766	+	1.52766i	0.0484545	+	0.0484545i
$995$	−8.53204	−	8.53204i	−0.270484	−	0.270484i
$996$	12.0314	−	3.82404i	0.381231	−	0.121169i
$997$	−5.53393			−0.175261			−0.0876306	−	0.996153i	$-0.527930\pi$
$997$	−5.53393			−0.175261			−0.0876306	+	0.996153i	$0.527930\pi$
$998$	31.6021			1.00035
$999$	9.70121	−	12.8257i	0.306933	−	0.405787i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.g.d.437.3		16
3.2	odd	2	inner	1014.2.g.d.437.7		16
13.4	even	6		78.2.k.a.11.1	✓	16
13.5	odd	4	inner	1014.2.g.d.239.7		16
13.8	odd	4		1014.2.g.c.239.3		16
13.11	odd	12		78.2.k.a.71.4	yes	16
13.12	even	2		1014.2.g.c.437.7		16
39.5	even	4	inner	1014.2.g.d.239.3		16
39.8	even	4		1014.2.g.c.239.7		16
39.11	even	12		78.2.k.a.71.1	yes	16
39.17	odd	6		78.2.k.a.11.4	yes	16
39.38	odd	2		1014.2.g.c.437.3		16
52.11	even	12		624.2.cn.d.305.2		16
52.43	odd	6		624.2.cn.d.401.4		16
156.11	odd	12		624.2.cn.d.305.4		16
156.95	even	6		624.2.cn.d.401.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.11.1	✓	16	13.4	even	6
78.2.k.a.11.4	yes	16	39.17	odd	6
78.2.k.a.71.1	yes	16	39.11	even	12
78.2.k.a.71.4	yes	16	13.11	odd	12
624.2.cn.d.305.2		16	52.11	even	12
624.2.cn.d.305.4		16	156.11	odd	12
624.2.cn.d.401.2		16	156.95	even	6
624.2.cn.d.401.4		16	52.43	odd	6
1014.2.g.c.239.3		16	13.8	odd	4
1014.2.g.c.239.7		16	39.8	even	4
1014.2.g.c.437.3		16	39.38	odd	2
1014.2.g.c.437.7		16	13.12	even	2
1014.2.g.d.239.3		16	39.5	even	4	inner
1014.2.g.d.239.7		16	13.5	odd	4	inner
1014.2.g.d.437.3		16	1.1	even	1	trivial
1014.2.g.d.437.7		16	3.2	odd	2	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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.796225 - 1.53819i) q^{3} -1.00000i q^{4} +(-2.76293 + 2.76293i) q^{5} +(0.524648 + 1.65068i) q^{6} +(1.79623 - 1.79623i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.73205 - 2.44949i) q^{9} -3.90738i q^{10} +(-0.412157 - 0.412157i) q^{11} +(-1.53819 - 0.796225i) q^{12} +2.54025i q^{14} +(2.05000 + 6.44983i) q^{15} -1.00000 q^{16} +1.09400 q^{17} +(2.95680 + 0.507306i) q^{18} +(0.971553 + 0.971553i) q^{19} +(2.76293 + 2.76293i) q^{20} +(-1.33273 - 4.19313i) q^{21} +0.582877 q^{22} -1.75292 q^{23} +(1.65068 - 0.524648i) q^{24} -10.2676i q^{25} +(-5.14688 + 0.713876i) q^{27} +(-1.79623 - 1.79623i) q^{28} -5.92330i q^{29} +(-6.01029 - 3.11115i) q^{30} +(-6.49983 - 6.49983i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.962144 + 0.305805i) q^{33} +(-0.773575 + 0.773575i) q^{34} +9.92570i q^{35} +(-2.44949 + 1.73205i) q^{36} +(-2.18840 + 2.18840i) q^{37} -1.37398 q^{38} -3.90738 q^{40} +(3.74650 - 3.74650i) q^{41} +(3.90738 + 2.02261i) q^{42} -3.76778i q^{43} +(-0.412157 + 0.412157i) q^{44} +(11.5533 + 1.98224i) q^{45} +(1.23950 - 1.23950i) q^{46} +(-5.51114 - 5.51114i) q^{47} +(-0.796225 + 1.53819i) q^{48} +0.547150i q^{49} +(7.26029 + 7.26029i) q^{50} +(0.871071 - 1.68278i) q^{51} -3.04435i q^{53} +(3.13461 - 4.14418i) q^{54} +2.27752 q^{55} +2.54025 q^{56} +(2.26801 - 0.720857i) q^{57} +(4.18840 + 4.18840i) q^{58} +(-5.99556 - 5.99556i) q^{59} +(6.44983 - 2.05000i) q^{60} +9.34533 q^{61} +9.19215 q^{62} +(-7.51099 - 1.28868i) q^{63} +1.00000i q^{64} +(0.464102 - 0.896575i) q^{66} +(-4.66788 - 4.66788i) q^{67} -1.09400i q^{68} +(-1.39572 + 2.69632i) q^{69} +(-7.01853 - 7.01853i) q^{70} +(0.601383 - 0.601383i) q^{71} +(0.507306 - 2.95680i) q^{72} +(5.18078 - 5.18078i) q^{73} -3.09487i q^{74} +(-15.7935 - 8.17533i) q^{75} +(0.971553 - 0.971553i) q^{76} -1.48065 q^{77} -13.1089 q^{79} +(2.76293 - 2.76293i) q^{80} +(-3.00000 + 8.48528i) q^{81} +5.29835i q^{82} +(-5.15394 + 5.15394i) q^{83} +(-4.19313 + 1.33273i) q^{84} +(-3.02265 + 3.02265i) q^{85} +(2.66422 + 2.66422i) q^{86} +(-9.11115 - 4.71628i) q^{87} -0.582877i q^{88} +(-6.85191 - 6.85191i) q^{89} +(-9.57108 + 6.76778i) q^{90} +1.75292i q^{92} +(-15.1733 + 4.82264i) q^{93} +7.79393 q^{94} -5.36867 q^{95} +(-0.524648 - 1.65068i) q^{96} +(-0.433704 - 0.433704i) q^{97} +(-0.386893 - 0.386893i) q^{98} +(-0.295697 + 1.72345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{7} + 24 q^{15} - 16 q^{16} - 32 q^{19} + 24 q^{21} - 16 q^{28} - 16 q^{31} - 24 q^{33} - 24 q^{34} + 8 q^{37} + 48 q^{45} + 48 q^{55} + 24 q^{57} + 24 q^{58} + 24 q^{60} + 48 q^{61} - 48 q^{66}+ \cdots - 16 q^{97}+O(q^{100}) \) 16 * q + 16 * q^7 + 24 * q^15 - 16 * q^16 - 32 * q^19 + 24 * q^21 - 16 * q^28 - 16 * q^31 - 24 * q^33 - 24 * q^34 + 8 * q^37 + 48 * q^45 + 48 * q^55 + 24 * q^57 + 24 * q^58 + 24 * q^60 + 48 * q^61 - 48 * q^66 - 32 * q^67 - 56 * q^73 - 32 * q^76 - 96 * q^79 - 48 * q^81 - 24 * q^84 - 24 * q^85 - 96 * q^87 - 48 * q^93 + 48 * q^94 - 16 * q^97

Introduction

L-functions

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