LMFDB - Embedded newform 1274.2.v.e.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(361,1274)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1274, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("1274.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.v (of order $6$, degree $2$, not 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:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.2
Root			$0.500000 + 0.399480i$ of defining polynomial
Character	$\chi$	$=$	1274.361
Dual form			1274.2.v.e.667.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} -0.466545 q^{3} +(0.500000 + 0.866025i) q^{4} +(2.93529 - 1.69469i) q^{5} +(0.404040 + 0.233273i) q^{6} -1.00000i q^{8} -2.78234 q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} -0.466545 q^{3} +(0.500000 + 0.866025i) q^{4} +(2.93529 - 1.69469i) q^{5} +(0.404040 + 0.233273i) q^{6} -1.00000i q^{8} -2.78234 q^{9} -3.38938 q^{10} +0.822730i q^{11} +(-0.233273 - 0.404040i) q^{12} +(-2.74987 + 2.33200i) q^{13} +(-1.36944 + 0.790648i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.29065 + 3.96752i) q^{17} +(2.40957 + 1.39117i) q^{18} +5.90621i q^{19} +(2.93529 + 1.69469i) q^{20} +(0.411365 - 0.712505i) q^{22} +(-3.06527 + 5.30921i) q^{23} +0.466545i q^{24} +(3.24394 - 5.61866i) q^{25} +(3.54746 - 0.644638i) q^{26} +2.69772 q^{27} +(3.43406 + 5.94797i) q^{29} +1.58130 q^{30} +(-3.71251 - 2.14342i) q^{31} +(0.866025 - 0.500000i) q^{32} -0.383841i q^{33} -4.58130i q^{34} +(-1.39117 - 2.40957i) q^{36} +(8.39253 + 4.84543i) q^{37} +(2.95310 - 5.11492i) q^{38} +(1.28294 - 1.08798i) q^{39} +(-1.69469 - 2.93529i) q^{40} +(-0.0774019 + 0.0446880i) q^{41} +(3.67687 - 6.36853i) q^{43} +(-0.712505 + 0.411365i) q^{44} +(-8.16695 + 4.71519i) q^{45} +(5.30921 - 3.06527i) q^{46} +(-9.67865 + 5.58797i) q^{47} +(0.233273 - 0.404040i) q^{48} +(-5.61866 + 3.24394i) q^{50} +(-1.06869 - 1.85103i) q^{51} +(-3.39451 - 1.21546i) q^{52} +(3.50765 - 6.07543i) q^{53} +(-2.33629 - 1.34886i) q^{54} +(1.39427 + 2.41495i) q^{55} -2.75551i q^{57} -6.86813i q^{58} +(-1.50790 + 0.870585i) q^{59} +(-1.36944 - 0.790648i) q^{60} +2.37945 q^{61} +(2.14342 + 3.71251i) q^{62} -1.00000 q^{64} +(-4.11964 + 11.5053i) q^{65} +(-0.191920 + 0.332416i) q^{66} +0.291719i q^{67} +(-2.29065 + 3.96752i) q^{68} +(1.43009 - 2.47698i) q^{69} +(9.48158 + 5.47419i) q^{71} +2.78234i q^{72} +(-11.0147 - 6.35934i) q^{73} +(-4.84543 - 8.39253i) q^{74} +(-1.51344 + 2.62136i) q^{75} +(-5.11492 + 2.95310i) q^{76} +(-1.65505 + 0.300752i) q^{78} +(-4.97801 - 8.62217i) q^{79} +3.38938i q^{80} +7.08840 q^{81} +0.0893760 q^{82} -3.23553i q^{83} +(13.4474 + 7.76387i) q^{85} +(-6.36853 + 3.67687i) q^{86} +(-1.60215 - 2.77500i) q^{87} +0.822730 q^{88} +(-6.96514 - 4.02133i) q^{89} +9.43038 q^{90} -6.13055 q^{92} +(1.73205 + 1.00000i) q^{93} +11.1759 q^{94} +(10.0092 + 17.3364i) q^{95} +(-0.404040 + 0.233273i) q^{96} +(12.7945 + 7.38693i) q^{97} -2.28911i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9	$ 12 q + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9} + 4 q^{10} + 2 q^{12} - 8 q^{13} - 6 q^{15} - 6 q^{16} + 4 q^{17} - 2 q^{22} - 6 q^{23} + 12 q^{25} + 16 q^{26} + 40 q^{27} - 10 q^{29} - 28 q^{30} - 18 q^{31} + 6 q^{36} + 6 q^{37} - 4 q^{38} + 30 q^{39} + 2 q^{40} - 24 q^{41} + 26 q^{43} + 18 q^{44} - 72 q^{45} + 6 q^{46} - 48 q^{47} - 2 q^{48} - 12 q^{50} + 18 q^{51} - 4 q^{52} - 18 q^{53} + 36 q^{54} - 6 q^{55} - 6 q^{59} - 6 q^{60} + 56 q^{61} - 2 q^{62} - 12 q^{64} + 38 q^{65} - 4 q^{68} + 32 q^{69} + 48 q^{71} + 48 q^{73} - 48 q^{75} + 12 q^{76} - 8 q^{78} - 22 q^{79} + 68 q^{81} - 12 q^{82} + 54 q^{85} - 6 q^{86} + 2 q^{87} - 4 q^{88} - 12 q^{89} + 12 q^{90} - 12 q^{92} - 16 q^{94} + 32 q^{95} - 6 q^{96} + 60 q^{97}+O(q^{100}) $ 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9 + 4 * q^10 + 2 * q^12 - 8 * q^13 - 6 * q^15 - 6 * q^16 + 4 * q^17 - 2 * q^22 - 6 * q^23 + 12 * q^25 + 16 * q^26 + 40 * q^27 - 10 * q^29 - 28 * q^30 - 18 * q^31 + 6 * q^36 + 6 * q^37 - 4 * q^38 + 30 * q^39 + 2 * q^40 - 24 * q^41 + 26 * q^43 + 18 * q^44 - 72 * q^45 + 6 * q^46 - 48 * q^47 - 2 * q^48 - 12 * q^50 + 18 * q^51 - 4 * q^52 - 18 * q^53 + 36 * q^54 - 6 * q^55 - 6 * q^59 - 6 * q^60 + 56 * q^61 - 2 * q^62 - 12 * q^64 + 38 * q^65 - 4 * q^68 + 32 * q^69 + 48 * q^71 + 48 * q^73 - 48 * q^75 + 12 * q^76 - 8 * q^78 - 22 * q^79 + 68 * q^81 - 12 * q^82 + 54 * q^85 - 6 * q^86 + 2 * q^87 - 4 * q^88 - 12 * q^89 + 12 * q^90 - 12 * q^92 - 16 * q^94 + 32 * q^95 - 6 * q^96 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.466545			−0.269360			−0.134680	−	0.990889i	$-0.543001\pi$
$3$	−0.466545			−0.269360			−0.134680	+	0.990889i	$0.543001\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.93529	−	1.69469i	1.31270	−	0.757888i	0.330157	−	0.943926i	$-0.392898\pi$
$5$	2.93529	−	1.69469i	1.31270	−	0.757888i	0.982542	+	0.186038i	$0.0595649\pi$
$6$	0.404040	+	0.233273i	0.164949	+	0.0952331i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−2.78234			−0.927445
$10$	−3.38938			−1.07181
$11$			0.822730i			0.248063i	0.992278	+	0.124031i	$0.0395823\pi$
$11$			0.822730i			0.248063i	−0.992278	+	0.124031i	$0.960418\pi$
$12$	−0.233273	−	0.404040i	−0.0673400	−	0.116636i
$13$	−2.74987	+	2.33200i	−0.762676	+	0.646781i
$13$	−2.74987	+	2.33200i	−0.762676	+	0.646781i
$14$		0			0
$15$	−1.36944	+	0.790648i	−0.353589	+	0.204145i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.29065	+	3.96752i	0.555564	+	0.962265i	0.997859	+	0.0653954i	$0.0208309\pi$
$17$	2.29065	+	3.96752i	0.555564	+	0.962265i	−0.442296	+	0.896869i	$0.645836\pi$
$18$	2.40957	+	1.39117i	0.567942	+	0.327901i
$19$			5.90621i			1.35498i	0.735534	+	0.677488i	$0.236932\pi$
$19$			5.90621i			1.35498i	−0.735534	+	0.677488i	$0.763068\pi$
$20$	2.93529	+	1.69469i	0.656350	+	0.378944i
$21$		0			0
$22$	0.411365	−	0.712505i	0.0877033	−	0.151907i
$23$	−3.06527	+	5.30921i	−0.639154	+	1.10705i	0.346465	+	0.938063i	$0.387382\pi$
$23$	−3.06527	+	5.30921i	−0.639154	+	1.10705i	−0.985619	+	0.168984i	$0.945951\pi$
$24$			0.466545i			0.0952331i
$25$	3.24394	−	5.61866i	0.648787	−	1.12373i
$26$	3.54746	−	0.644638i	0.695713	−	0.126424i
$27$	2.69772			0.519176
$28$		0			0
$29$	3.43406	+	5.94797i	0.637690	+	1.10451i	0.985938	+	0.167109i	$0.0534431\pi$
$29$	3.43406	+	5.94797i	0.637690	+	1.10451i	−0.348249	+	0.937402i	$0.613224\pi$
$30$	1.58130			0.288704
$31$	−3.71251	−	2.14342i	−0.666786	−	0.384969i	0.128072	−	0.991765i	$-0.459121\pi$
$31$	−3.71251	−	2.14342i	−0.666786	−	0.384969i	−0.794858	+	0.606796i	$0.792454\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		−	0.383841i		−	0.0668181i
$34$		−	4.58130i		−	0.785686i
$35$		0			0
$36$	−1.39117	−	2.40957i	−0.231861	−	0.401596i
$37$	8.39253	+	4.84543i	1.37972	+	0.796584i	0.992126	−	0.125245i	$-0.0399717\pi$
$37$	8.39253	+	4.84543i	1.37972	+	0.796584i	0.387598	+	0.921829i	$0.373305\pi$
$38$	2.95310	−	5.11492i	0.479057	−	0.829750i
$39$	1.28294	−	1.08798i	0.205434	−	0.174217i
$40$	−1.69469	−	2.93529i	−0.267954	−	0.464109i
$41$	−0.0774019	+	0.0446880i	−0.0120881	+	0.00697909i	−0.506032	−	0.862515i	$-0.668888\pi$
$41$	−0.0774019	+	0.0446880i	−0.0120881	+	0.00697909i	0.493944	+	0.869494i	$0.335555\pi$
$42$		0			0
$43$	3.67687	−	6.36853i	0.560718	−	0.971191i	−0.436716	−	0.899599i	$-0.643859\pi$
$43$	3.67687	−	6.36853i	0.560718	−	0.971191i	0.997434	−	0.0715921i	$-0.0228080\pi$
$44$	−0.712505	+	0.411365i	−0.107414	+	0.0620156i
$45$	−8.16695	+	4.71519i	−1.21746	+	0.702899i
$46$	5.30921	−	3.06527i	0.782800	−	0.451950i
$47$	−9.67865	+	5.58797i	−1.41178	+	0.815089i	−0.995556	−	0.0941741i	$-0.969979\pi$
$47$	−9.67865	+	5.58797i	−1.41178	+	0.815089i	−0.416221	+	0.909264i	$0.636646\pi$
$48$	0.233273	−	0.404040i	0.0336700	−	0.0583181i
$49$		0			0
$50$	−5.61866	+	3.24394i	−0.794599	+	0.458762i
$51$	−1.06869	−	1.85103i	−0.149647	−	0.259196i
$52$	−3.39451	−	1.21546i	−0.470733	−	0.168553i
$53$	3.50765	−	6.07543i	0.481813	−	0.834524i	−0.517969	−	0.855399i	$-0.673312\pi$
$53$	3.50765	−	6.07543i	0.481813	−	0.834524i	0.999782	+	0.0208750i	$0.00664521\pi$
$54$	−2.33629	−	1.34886i	−0.317929	−	0.183557i
$55$	1.39427	+	2.41495i	0.188003	+	0.325632i
$56$		0			0
$57$		−	2.75551i		−	0.364976i
$58$		−	6.86813i		−	0.901829i
$59$	−1.50790	+	0.870585i	−0.196311	+	0.113340i	−0.594934	−	0.803775i	$-0.702822\pi$
$59$	−1.50790	+	0.870585i	−0.196311	+	0.113340i	0.398622	+	0.917115i	$0.369488\pi$
$60$	−1.36944	−	0.790648i	−0.176794	−	0.102072i
$61$	2.37945			0.304657			0.152329	−	0.988330i	$-0.451323\pi$
$61$	2.37945			0.304657			0.152329	+	0.988330i	$0.451323\pi$
$62$	2.14342	+	3.71251i	0.272214	+	0.471489i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.11964	+	11.5053i	−0.510978	+	1.42705i
$66$	−0.191920	+	0.332416i	−0.0236238	+	0.0409176i
$67$			0.291719i			0.0356391i	0.999841	+	0.0178196i	$0.00567244\pi$
$67$			0.291719i			0.0356391i	−0.999841	+	0.0178196i	$0.994328\pi$
$68$	−2.29065	+	3.96752i	−0.277782	+	0.481132i
$69$	1.43009	−	2.47698i	0.172162	−	0.298194i
$70$		0			0
$71$	9.48158	+	5.47419i	1.12526	+	0.649667i	0.942738	−	0.333535i	$-0.108242\pi$
$71$	9.48158	+	5.47419i	1.12526	+	0.649667i	0.182519	+	0.983202i	$0.441575\pi$
$72$			2.78234i			0.327901i
$73$	−11.0147	−	6.35934i	−1.28917	−	0.744304i	−0.310666	−	0.950519i	$-0.600552\pi$
$73$	−11.0147	−	6.35934i	−1.28917	−	0.744304i	−0.978507	+	0.206215i	$0.933885\pi$
$74$	−4.84543	−	8.39253i	−0.563270	−	0.975612i
$75$	−1.51344	+	2.62136i	−0.174757	+	0.302688i
$76$	−5.11492	+	2.95310i	−0.586722	+	0.338744i
$77$		0			0
$78$	−1.65505	+	0.300752i	−0.187397	+	0.0340535i
$79$	−4.97801	−	8.62217i	−0.560070	−	0.970070i	−0.997490	−	0.0708122i	$-0.977441\pi$
$79$	−4.97801	−	8.62217i	−0.560070	−	0.970070i	0.437420	−	0.899257i	$-0.355892\pi$
$80$			3.38938i			0.378944i
$81$	7.08840			0.787600
$82$	0.0893760			0.00986993
$83$		−	3.23553i		−	0.355146i	−0.984108	−	0.177573i	$-0.943175\pi$
$83$		−	3.23553i		−	0.355146i	0.984108	−	0.177573i	$-0.0568246\pi$
$84$		0			0
$85$	13.4474	+	7.76387i	1.45858	+	0.842110i
$86$	−6.36853	+	3.67687i	−0.686736	+	0.396487i
$87$	−1.60215	−	2.77500i	−0.171768	−	0.297511i
$88$	0.822730			0.0877033
$89$	−6.96514	−	4.02133i	−0.738303	−	0.426260i	0.0831487	−	0.996537i	$-0.473502\pi$
$89$	−6.96514	−	4.02133i	−0.738303	−	0.426260i	−0.821452	+	0.570277i	$0.806836\pi$
$90$	9.43038			0.994050
$91$		0			0
$92$	−6.13055			−0.639154
$93$	1.73205	+	1.00000i	0.179605	+	0.103695i
$94$	11.1759			1.15271
$95$	10.0092	+	17.3364i	1.02692	+	1.77868i
$96$	−0.404040	+	0.233273i	−0.0412371	+	0.0238083i
$97$	12.7945	+	7.38693i	1.29909	+	0.750029i	0.980247	−	0.197778i	$-0.0633726\pi$
$97$	12.7945	+	7.38693i	1.29909	+	0.750029i	0.318842	+	0.947808i	$0.396706\pi$
$98$		0			0
$99$		−	2.28911i		−	0.230064i
$100$	6.48787			0.648787
$101$	8.23976			0.819887			0.409943	−	0.912111i	$-0.365548\pi$
$101$	8.23976			0.819887			0.409943	+	0.912111i	$0.365548\pi$
$102$			2.13738i			0.211632i
$103$	6.66156	+	11.5382i	0.656383	+	1.13689i	0.981545	+	0.191230i	$0.0612477\pi$
$103$	6.66156	+	11.5382i	0.656383	+	1.13689i	−0.325162	+	0.945658i	$0.605419\pi$
$104$	2.33200	+	2.74987i	0.228671	+	0.269647i
$105$		0			0
$106$	−6.07543	+	3.50765i	−0.590098	+	0.340693i
$107$	4.51325	−	7.81717i	0.436312	−	0.755715i	−0.561090	−	0.827755i	$-0.689618\pi$
$107$	4.51325	−	7.81717i	0.436312	−	0.755715i	0.997402	+	0.0720404i	$0.0229511\pi$
$108$	1.34886	+	2.33629i	0.129794	+	0.224810i
$109$	−0.343978	−	0.198596i	−0.0329471	−	0.0190220i	0.483436	−	0.875380i	$-0.339389\pi$
$109$	−0.343978	−	0.198596i	−0.0329471	−	0.0190220i	−0.516383	+	0.856358i	$0.672722\pi$
$110$		−	2.78854i		−	0.265877i
$111$	−3.91549	−	2.26061i	−0.371642	−	0.214568i
$112$		0			0
$113$	−2.23661	+	3.87392i	−0.210402	+	0.364428i	−0.951841	−	0.306594i	$-0.900811\pi$
$113$	−2.23661	+	3.87392i	−0.210402	+	0.364428i	0.741438	+	0.671021i	$0.234144\pi$
$114$	−1.37776	+	2.38634i	−0.129039	+	0.223501i
$115$			20.7787i			1.93763i
$116$	−3.43406	+	5.94797i	−0.318845	+	0.552255i
$117$	7.65106	−	6.48841i	0.707340	−	0.599854i
$118$	1.74117			0.160288
$119$		0			0
$120$	0.790648	+	1.36944i	0.0721760	+	0.125012i
$121$	10.3231			0.938465
$122$	−2.06066	−	1.18972i	−0.186564	−	0.107713i
$123$	0.0361115	−	0.0208490i	0.00325606	−	0.00187989i
$124$		−	4.28683i		−	0.384969i
$125$		−	5.04295i		−	0.451056i
$126$		0			0
$127$	−0.270063	−	0.467763i	−0.0239642	−	0.0415073i	0.853795	−	0.520610i	$-0.174295\pi$
$127$	−0.270063	−	0.467763i	−0.0239642	−	0.0415073i	−0.877759	+	0.479103i	$0.840962\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−1.71543	+	2.97120i	−0.151035	+	0.261600i
$130$	9.32034	−	7.90403i	0.817448	−	0.693229i
$131$	3.86307	+	6.69104i	0.337518	+	0.584599i	0.983965	−	0.178360i	$-0.0570792\pi$
$131$	3.86307	+	6.69104i	0.337518	+	0.584599i	−0.646447	+	0.762959i	$0.723746\pi$
$132$	0.332416	−	0.191920i	0.0289331	−	0.0167045i
$133$		0			0
$134$	0.145859	−	0.252636i	0.0126003	−	0.0218244i
$135$	7.91858	−	4.57179i	0.681523	−	0.393477i
$136$	3.96752	−	2.29065i	0.340212	−	0.196421i
$137$	−10.8600	+	6.27005i	−0.927837	+	0.535687i	−0.886127	−	0.463443i	$-0.846614\pi$
$137$	−10.8600	+	6.27005i	−0.927837	+	0.535687i	−0.0417099	+	0.999130i	$0.513281\pi$
$138$	−2.47698	+	1.43009i	−0.210855	+	0.121737i
$139$	−6.04868	+	10.4766i	−0.513042	+	0.888615i	0.486843	+	0.873489i	$0.338148\pi$
$139$	−6.04868	+	10.4766i	−0.513042	+	0.888615i	−0.999886	+	0.0151258i	$0.995185\pi$
$140$		0			0
$141$	4.51553	−	2.60704i	0.380276	−	0.219552i
$142$	−5.47419	−	9.48158i	−0.459384	−	0.795677i
$143$	−1.91861	−	2.26240i	−0.160442	−	0.189191i
$144$	1.39117	−	2.40957i	0.115931	−	0.200798i
$145$	20.1599	+	11.6393i	1.67419	+	0.966594i
$146$	6.35934	+	11.0147i	0.526303	+	0.911583i
$147$		0			0
$148$			9.69086i			0.796584i
$149$		−	17.0078i		−	1.39333i	−0.717395	−	0.696666i	$-0.754666\pi$
$149$		−	17.0078i		−	1.39333i	0.717395	−	0.696666i	$-0.245334\pi$
$150$	2.62136	−	1.51344i	0.214033	−	0.123572i
$151$	4.80269	+	2.77283i	0.390837	+	0.225650i	0.682523	−	0.730864i	$-0.260883\pi$
$151$	4.80269	+	2.77283i	0.390837	+	0.225650i	−0.291686	+	0.956514i	$0.594216\pi$
$152$	5.90621			0.479057
$153$	−6.37335	−	11.0390i	−0.515255	−	0.892448i
$154$		0			0
$155$	−14.5297			−1.16705
$156$	1.58369	+	0.567065i	0.126797	+	0.0454015i
$157$	−1.14676	+	1.98625i	−0.0915218	+	0.158520i	−0.908152	−	0.418641i	$-0.862506\pi$
$157$	−1.14676	+	1.98625i	−0.0915218	+	0.158520i	0.816630	+	0.577162i	$0.195840\pi$
$158$			9.95602i			0.792059i
$159$	−1.63648	+	2.83446i	−0.129781	+	0.224787i
$160$	1.69469	−	2.93529i	0.133977	−	0.232055i
$161$		0			0
$162$	−6.13873	−	3.54420i	−0.482304	−	0.278459i
$163$			23.3560i			1.82938i	0.404155	+	0.914691i	$0.367566\pi$
$163$			23.3560i			1.82938i	−0.404155	+	0.914691i	$0.632434\pi$
$164$	−0.0774019	−	0.0446880i	−0.00604407	−	0.00348955i
$165$	−0.650490	−	1.12668i	−0.0506406	−	0.0877121i
$166$	−1.61777	+	2.80205i	−0.125563	+	0.217482i
$167$	−18.8603	+	10.8890i	−1.45945	+	0.842614i	−0.998984	−	0.0450626i	$-0.985651\pi$
$167$	−18.8603	+	10.8890i	−1.45945	+	0.842614i	−0.460467	+	0.887677i	$0.652318\pi$
$168$		0			0
$169$	2.12355	−	12.8254i	0.163350	−	0.986568i
$170$	−7.76387	−	13.4474i	−0.595462	−	1.03137i
$171$		−	16.4330i		−	1.25667i
$172$	7.35374			0.560718
$173$	−8.09733			−0.615629			−0.307814	−	0.951446i	$-0.599598\pi$
$173$	−8.09733			−0.615629			−0.307814	+	0.951446i	$0.599598\pi$
$174$			3.20429i			0.242917i
$175$		0			0
$176$	−0.712505	−	0.411365i	−0.0537071	−	0.0310078i
$177$	0.703502	−	0.406167i	0.0528784	−	0.0305294i
$178$	4.02133	+	6.96514i	0.301411	+	0.522059i
$179$	−9.90883			−0.740621			−0.370310	−	0.928908i	$-0.620749\pi$
$179$	−9.90883			−0.740621			−0.370310	+	0.928908i	$0.620749\pi$
$180$	−8.16695	−	4.71519i	−0.608729	−	0.351450i
$181$	1.27902			0.0950685			0.0475343	−	0.998870i	$-0.484864\pi$
$181$	1.27902			0.0950685			0.0475343	+	0.998870i	$0.484864\pi$
$182$		0			0
$183$	−1.11012			−0.0820624
$184$	5.30921	+	3.06527i	0.391400	+	0.225975i
$185$	32.8460			2.41488
$186$	−1.00000	−	1.73205i	−0.0733236	−	0.127000i
$187$	−3.26420	+	1.88459i	−0.238702	+	0.137815i
$188$	−9.67865	−	5.58797i	−0.705888	−	0.407545i
$189$		0			0
$190$		−	20.0184i		−	1.45228i
$191$	−10.0342			−0.726050			−0.363025	−	0.931779i	$-0.618256\pi$
$191$	−10.0342			−0.726050			−0.363025	+	0.931779i	$0.618256\pi$
$192$	0.466545			0.0336700
$193$		−	15.8582i		−	1.14150i	−0.821124	−	0.570750i	$-0.806653\pi$
$193$		−	15.8582i		−	1.14150i	0.821124	−	0.570750i	$-0.193347\pi$
$194$	−7.38693	−	12.7945i	−0.530351	−	0.918595i
$195$	1.92200	−	5.36772i	0.137637	−	0.384390i
$196$		0			0
$197$	12.8242	−	7.40403i	0.913683	−	0.527515i	0.0320686	−	0.999486i	$-0.489790\pi$
$197$	12.8242	−	7.40403i	0.913683	−	0.527515i	0.881614	+	0.471971i	$0.156457\pi$
$198$	−1.14456	+	1.98243i	−0.0813400	+	0.140885i
$199$	−1.27771	−	2.21306i	−0.0905747	−	0.156880i	0.817178	−	0.576385i	$-0.195537\pi$
$199$	−1.27771	−	2.21306i	−0.0905747	−	0.156880i	−0.907753	+	0.419505i	$0.862204\pi$
$200$	−5.61866	−	3.24394i	−0.397299	−	0.229381i
$201$		−	0.136100i		−	0.00959974i
$202$	−7.13584	−	4.11988i	−0.502076	−	0.289874i
$203$		0			0
$204$	1.06869	−	1.85103i	0.0748233	−	0.129598i
$205$	−0.151464	+	0.262344i	−0.0105787	+	0.0183229i
$206$		−	13.3231i		−	0.928265i
$207$	8.52862	−	14.7720i	0.592780	−	1.02673i
$208$	−0.644638	−	3.54746i	−0.0446976	−	0.245972i
$209$	−4.85921			−0.336119
$210$		0			0
$211$	4.31824	+	7.47942i	0.297280	+	0.514904i	0.975513	−	0.219943i	$-0.0705872\pi$
$211$	4.31824	+	7.47942i	0.297280	+	0.514904i	−0.678233	+	0.734847i	$0.737254\pi$
$212$	7.01530			0.481813
$213$	−4.42359	−	2.55396i	−0.303099	−	0.174994i
$214$	−7.81717	+	4.51325i	−0.534371	+	0.308519i
$215$		−	24.9246i		−	1.69984i
$216$		−	2.69772i		−	0.183557i
$217$		0			0
$218$	0.198596	+	0.343978i	0.0134506	+	0.0232971i
$219$	5.13885	+	2.96692i	0.347251	+	0.200486i
$220$	−1.39427	+	2.41495i	−0.0940017	+	0.162816i
$221$	−15.5512	−	5.56836i	−1.04609	−	0.374569i
$222$	2.26061	+	3.91549i	0.151722	+	0.262791i
$223$	−17.2579	+	9.96384i	−1.15567	+	0.667228i	−0.950263	−	0.311448i	$-0.899186\pi$
$223$	−17.2579	+	9.96384i	−1.15567	+	0.667228i	−0.205410	+	0.978676i	$0.565853\pi$
$224$		0			0
$225$	−9.02572	+	15.6330i	−0.601715	+	1.04220i
$226$	3.87392	−	2.23661i	0.257689	−	0.148777i
$227$	−0.305381	+	0.176312i	−0.0202689	+	0.0117022i	−0.510100	−	0.860115i	$-0.670392\pi$
$227$	−0.305381	+	0.176312i	−0.0202689	+	0.0117022i	0.489831	+	0.871817i	$0.337058\pi$
$228$	2.38634	−	1.37776i	0.158039	−	0.0912441i
$229$	7.19942	−	4.15659i	0.475751	−	0.274675i	−0.242893	−	0.970053i	$-0.578096\pi$
$229$	7.19942	−	4.15659i	0.475751	−	0.274675i	0.718644	+	0.695378i	$0.244763\pi$
$230$	10.3894	−	17.9949i	0.685054	−	1.18655i
$231$		0			0
$232$	5.94797	−	3.43406i	0.390504	−	0.225457i
$233$	7.68988	+	13.3193i	0.503781	+	0.872574i	0.999990	+	0.00437153i	$0.00139151\pi$
$233$	7.68988	+	13.3193i	0.503781	+	0.872574i	−0.496209	+	0.868203i	$0.665275\pi$
$234$	−9.87021	+	1.79360i	−0.645236	+	0.117251i
$235$	−18.9397	+	32.8046i	−1.23549	+	2.13994i
$236$	−1.50790	−	0.870585i	−0.0981557	−	0.0566702i
$237$	2.32247	+	4.02263i	0.150860	+	0.261298i
$238$		0			0
$239$		−	2.88606i		−	0.186684i	−0.995634	−	0.0933418i	$-0.970245\pi$
$239$		−	2.88606i		−	0.186684i	0.995634	−	0.0933418i	$-0.0297549\pi$
$240$		−	1.58130i		−	0.102072i
$241$	5.42777	−	3.13372i	0.349633	−	0.201861i	−0.314891	−	0.949128i	$-0.601968\pi$
$241$	5.42777	−	3.13372i	0.349633	−	0.201861i	0.664524	+	0.747267i	$0.268634\pi$
$242$	−8.94008	−	5.16156i	−0.574690	−	0.331797i
$243$	−11.4002			−0.731324
$244$	1.18972	+	2.06066i	0.0761643	+	0.131920i
$245$		0			0
$246$	−0.0416979			−0.00265856
$247$	−13.7733	−	16.2413i	−0.876373	−	1.03341i
$248$	−2.14342	+	3.71251i	−0.136107	+	0.235744i
$249$			1.50952i			0.0956621i
$250$	−2.52148	+	4.36733i	−0.159472	+	0.276214i
$251$	8.63325	−	14.9532i	0.544926	−	0.943839i	−0.453686	−	0.891162i	$-0.649891\pi$
$251$	8.63325	−	14.9532i	0.544926	−	0.943839i	0.998612	−	0.0526775i	$-0.0167755\pi$
$252$		0			0
$253$	−4.36805	−	2.52189i	−0.274617	−	0.158550i
$254$			0.540127i			0.0338906i
$255$	−6.27382	−	3.62219i	−0.392882	−	0.226831i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.59655	+	9.69351i	−0.349103	+	0.604664i	−0.986090	−	0.166210i	$-0.946847\pi$
$257$	−5.59655	+	9.69351i	−0.349103	+	0.604664i	0.636987	+	0.770874i	$0.280180\pi$
$258$	2.97120	−	1.71543i	0.184979	−	0.106798i
$259$		0			0
$260$	−12.0237	+	2.18492i	−0.745676	+	0.135503i
$261$	−9.55472	−	16.5493i	−0.591422	−	1.02437i
$262$		−	7.72615i		−	0.477323i
$263$	−28.5826			−1.76248			−0.881240	−	0.472668i	$-0.843291\pi$
$263$	−28.5826			−1.76248			−0.881240	+	0.472668i	$0.843291\pi$
$264$	−0.383841			−0.0236238
$265$		−	23.7775i		−	1.46064i
$266$		0			0
$267$	3.24955	+	1.87613i	0.198869	+	0.114817i
$268$	−0.252636	+	0.145859i	−0.0154322	+	0.00890978i
$269$	9.18769	+	15.9135i	0.560183	+	0.970266i	0.997480	+	0.0709485i	$0.0226026\pi$
$269$	9.18769	+	15.9135i	0.560183	+	0.970266i	−0.437297	+	0.899317i	$0.644064\pi$
$270$	−9.14359			−0.556461
$271$	−17.6518	−	10.1913i	−1.07227	−	0.619075i	−0.143468	−	0.989655i	$-0.545826\pi$
$271$	−17.6518	−	10.1913i	−1.07227	−	0.619075i	−0.928801	+	0.370580i	$0.879159\pi$
$272$	−4.58130			−0.277782
$273$		0			0
$274$	12.5401			0.757575
$275$	4.62264	+	2.66888i	0.278756	+	0.160940i
$276$	2.86018			0.172162
$277$	3.61609	+	6.26326i	0.217270	+	0.376323i	0.953972	−	0.299894i	$-0.0969514\pi$
$277$	3.61609	+	6.26326i	0.217270	+	0.376323i	−0.736702	+	0.676217i	$0.763618\pi$
$278$	10.4766	−	6.04868i	0.628346	−	0.362776i
$279$	10.3294	+	5.96370i	0.618407	+	0.357038i
$280$		0			0
$281$		−	12.4585i		−	0.743215i	−0.928390	−	0.371607i	$-0.878807\pi$
$281$		−	12.4585i		−	0.743215i	0.928390	−	0.371607i	$-0.121193\pi$
$282$	−5.21408			−0.310494
$283$	−13.0607			−0.776378			−0.388189	−	0.921580i	$-0.626899\pi$
$283$	−13.0607			−0.776378			−0.388189	+	0.921580i	$0.626899\pi$
$284$			10.9484i			0.649667i
$285$	−4.66973	−	8.08821i	−0.276611	−	0.479104i
$286$	0.530363	+	2.91860i	0.0313610	+	0.172580i
$287$		0			0
$288$	−2.40957	+	1.39117i	−0.141985	+	0.0819754i
$289$	−1.99414	+	3.45395i	−0.117302	+	0.203174i
$290$	−11.6393	−	20.1599i	−0.683485	−	1.18383i
$291$	−5.96923	−	3.44634i	−0.349922	−	0.202028i
$292$		−	12.7187i		−	0.744304i
$293$	−12.6078	−	7.27909i	−0.736553	−	0.425249i	0.0842617	−	0.996444i	$-0.473147\pi$
$293$	−12.6078	−	7.27909i	−0.736553	−	0.425249i	−0.820815	+	0.571195i	$0.806480\pi$
$294$		0			0
$295$	−2.95074	+	5.11083i	−0.171799	+	0.297564i
$296$	4.84543	−	8.39253i	0.281635	−	0.487806i
$297$			2.21950i			0.128788i
$298$	−8.50389	+	14.7292i	−0.492617	+	0.853238i
$299$	−3.95198	−	21.7478i	−0.228549	−	1.25771i
$300$	−3.02688			−0.174757
$301$		0			0
$302$	−2.77283	−	4.80269i	−0.159559	−	0.276364i
$303$	−3.84422			−0.220845
$304$	−5.11492	−	2.95310i	−0.293361	−	0.169372i
$305$	6.98436	−	4.03242i	0.399923	−	0.230896i
$306$			12.7467i			0.728681i
$307$			3.24267i			0.185069i	0.995709	+	0.0925345i	$0.0294968\pi$
$307$			3.24267i			0.185069i	−0.995709	+	0.0925345i	$0.970503\pi$
$308$		0			0
$309$	−3.10792	−	5.38307i	−0.176803	−	0.306232i
$310$	12.5831	+	7.26484i	0.714671	+	0.412615i
$311$	5.13544	−	8.89484i	0.291204	−	0.504380i	−0.682891	−	0.730521i	$-0.739277\pi$
$311$	5.13544	−	8.89484i	0.291204	−	0.504380i	0.974095	+	0.226140i	$0.0726108\pi$
$312$	−1.08798	−	1.28294i	−0.0615949	−	0.0726320i
$313$	3.06691	+	5.31204i	0.173352	+	0.300254i	0.939590	−	0.342303i	$-0.111207\pi$
$313$	3.06691	+	5.31204i	0.173352	+	0.300254i	−0.766238	+	0.642557i	$0.777874\pi$
$314$	1.98625	−	1.14676i	0.112091	−	0.0647157i
$315$		0			0
$316$	4.97801	−	8.62217i	0.280035	−	0.485035i
$317$	−4.36899	+	2.52244i	−0.245387	+	0.141674i	−0.617650	−	0.786453i	$-0.711915\pi$
$317$	−4.36899	+	2.52244i	−0.245387	+	0.141674i	0.372263	+	0.928127i	$0.378582\pi$
$318$	2.83446	−	1.63648i	0.158949	−	0.0917690i
$319$	−4.89358	+	2.82531i	−0.273988	+	0.158187i
$320$	−2.93529	+	1.69469i	−0.164087	+	0.0947359i
$321$	−2.10563	+	3.64706i	−0.117525	+	0.203559i
$322$		0			0
$323$	−23.4330	+	13.5290i	−1.30385	+	0.752776i
$324$	3.54420	+	6.13873i	0.196900	+	0.341041i
$325$	4.18233	+	23.0154i	0.231994	+	1.27667i
$326$	11.6780	−	20.2269i	0.646784	−	1.12026i
$327$	0.160481	+	0.0926539i	0.00887463	+	0.00512377i
$328$	0.0446880	+	0.0774019i	0.00246748	+	0.00427380i
$329$		0			0
$330$			1.30098i			0.0716166i
$331$			23.0874i			1.26900i	0.772924	+	0.634499i	$0.218793\pi$
$331$			23.0874i			1.26900i	−0.772924	+	0.634499i	$0.781207\pi$
$332$	2.80205	−	1.61777i	0.153783	−	0.0887865i
$333$	−23.3508	−	13.4816i	−1.27962	−	0.738788i
$334$	21.7780			1.19164
$335$	0.494372	+	0.856278i	0.0270104	+	0.0467834i
$336$		0			0
$337$	29.1429			1.58751			0.793757	−	0.608235i	$-0.208122\pi$
$337$	29.1429			1.58751			0.793757	+	0.608235i	$0.208122\pi$
$338$	−8.25174	+	10.0453i	−0.448835	+	0.546394i
$339$	1.04348	−	1.80736i	0.0566740	−	0.0981622i
$340$			15.5277i			0.842110i
$341$	1.76345	−	3.05439i	0.0954963	−	0.165405i
$342$	−8.21652	+	14.2314i	−0.444299	+	0.769548i
$343$		0			0
$344$	−6.36853	−	3.67687i	−0.343368	−	0.198244i
$345$		−	9.69421i		−	0.521919i
$346$	7.01249	+	4.04866i	0.376994	+	0.217658i
$347$	14.5541	+	25.2085i	0.781306	+	1.35326i	0.931181	+	0.364557i	$0.118779\pi$
$347$	14.5541	+	25.2085i	0.781306	+	1.35326i	−0.149875	+	0.988705i	$0.547887\pi$
$348$	1.60215	−	2.77500i	0.0858840	−	0.148755i
$349$	22.3263	−	12.8901i	1.19510	−	0.689992i	0.235642	−	0.971840i	$-0.424281\pi$
$349$	22.3263	−	12.8901i	1.19510	−	0.689992i	0.959459	+	0.281848i	$0.0909475\pi$
$350$		0			0
$351$	−7.41837	+	6.29108i	−0.395963	+	0.335793i
$352$	0.411365	+	0.712505i	0.0219258	+	0.0379767i
$353$		−	9.91779i		−	0.527871i	−0.964540	−	0.263935i	$-0.914979\pi$
$353$		−	9.91779i		−	0.527871i	0.964540	−	0.263935i	$-0.0850206\pi$
$354$	−0.812334			−0.0431751
$355$	37.1082			1.96950
$356$		−	8.04265i		−	0.426260i
$357$		0			0
$358$	8.58130	+	4.95442i	0.453536	+	0.261849i
$359$	21.8829	−	12.6341i	1.15494	−	0.666804i	0.204852	−	0.978793i	$-0.434329\pi$
$359$	21.8829	−	12.6341i	1.15494	−	0.666804i	0.950086	+	0.311989i	$0.100995\pi$
$360$	4.71519	+	8.16695i	0.248512	+	0.430436i
$361$	−15.8833			−0.835962
$362$	−1.10766	−	0.639508i	−0.0582174	−	0.0336118i
$363$	−4.81620			−0.252785
$364$		0			0
$365$	−43.1084			−2.25640
$366$	0.961392	+	0.555060i	0.0502528	+	0.0290135i
$367$	35.7838			1.86790			0.933950	−	0.357404i	$-0.116338\pi$
$367$	35.7838			1.86790			0.933950	+	0.357404i	$0.116338\pi$
$368$	−3.06527	−	5.30921i	−0.159788	−	0.276762i
$369$	0.215358	−	0.124337i	0.0112111	−	0.00647273i
$370$	−28.4454	−	16.4230i	−1.47881	−	0.853790i
$371$		0			0
$372$			2.00000i			0.103695i
$373$	−23.3304			−1.20800			−0.604000	−	0.796984i	$-0.706427\pi$
$373$	−23.3304			−1.20800			−0.604000	+	0.796984i	$0.706427\pi$
$374$	3.76917			0.194899
$375$			2.35277i			0.121496i
$376$	5.58797	+	9.67865i	0.288178	+	0.499138i
$377$	−23.3139	−	8.34790i	−1.20073	−	0.429939i
$378$		0			0
$379$	21.0502	−	12.1533i	1.08127	−	0.624274i	0.150034	−	0.988681i	$-0.452062\pi$
$379$	21.0502	−	12.1533i	1.08127	−	0.624274i	0.931240	+	0.364407i	$0.118728\pi$
$380$	−10.0092	+	17.3364i	−0.513460	+	0.889339i
$381$	0.125997	+	0.218233i	0.00645501	+	0.0111804i
$382$	8.68988	+	5.01710i	0.444613	+	0.256697i
$383$		−	4.91150i		−	0.250966i	−0.992096	−	0.125483i	$-0.959952\pi$
$383$		−	4.91150i		−	0.250966i	0.992096	−	0.125483i	$-0.0400480\pi$
$384$	−0.404040	−	0.233273i	−0.0206186	−	0.0119041i
$385$		0			0
$386$	−7.92911	+	13.7336i	−0.403581	+	0.699023i
$387$	−10.2303	+	17.7194i	−0.520035	+	0.900727i
$388$			14.7739i			0.750029i
$389$	2.57261	−	4.45589i	0.130437	−	0.225923i	−0.793408	−	0.608690i	$-0.791695\pi$
$389$	2.57261	−	4.45589i	0.130437	−	0.225923i	0.923845	+	0.382767i	$0.125029\pi$
$390$	−4.34836	+	3.68758i	−0.220188	+	0.186728i
$391$	−28.0858			−1.42036
$392$		0			0
$393$	−1.80230	−	3.12167i	−0.0909139	−	0.157467i
$394$	−14.8081			−0.746019
$395$	−29.2238	−	16.8724i	−1.47041	−	0.848940i
$396$	1.98243	−	1.14456i	0.0996208	−	0.0575161i
$397$			12.3500i			0.619827i	0.950765	+	0.309913i	$0.100300\pi$
$397$			12.3500i			0.619827i	−0.950765	+	0.309913i	$0.899700\pi$
$398$			2.55543i			0.128092i
$399$		0			0
$400$	3.24394	+	5.61866i	0.162197	+	0.280933i
$401$	−28.1366	−	16.2447i	−1.40508	−	0.811221i	−0.410169	−	0.912010i	$-0.634530\pi$
$401$	−28.1366	−	16.2447i	−1.40508	−	0.811221i	−0.994908	+	0.100788i	$0.967864\pi$
$402$	−0.0680499	+	0.117866i	−0.00339402	+	0.00587862i
$403$	15.2073	−	2.76345i	0.757532	−	0.137657i
$404$	4.11988	+	7.13584i	0.204972	+	0.355021i
$405$	20.8065	−	12.0126i	1.03388	−	0.596912i
$406$		0			0
$407$	−3.98648	+	6.90479i	−0.197603	+	0.342258i
$408$	−1.85103	+	1.06869i	−0.0916395	+	0.0529081i
$409$	−3.26348	+	1.88417i	−0.161369	+	0.0931662i	−0.578510	−	0.815676i	$-0.696365\pi$
$409$	−3.26348	+	1.88417i	−0.161369	+	0.0931662i	0.417141	+	0.908842i	$0.363032\pi$
$410$	0.262344	−	0.151464i	0.0129563	−	0.00748029i
$411$	5.06670	−	2.92526i	0.249922	−	0.144293i
$412$	−6.66156	+	11.5382i	−0.328191	+	0.568444i
$413$		0			0
$414$	−14.7720	+	8.52862i	−0.726004	+	0.419159i
$415$	−5.48322	−	9.49722i	−0.269161	−	0.466200i
$416$	−1.21546	+	3.39451i	−0.0595926	+	0.166429i
$417$	2.82198	−	4.88781i	0.138193	−	0.239357i
$418$	4.20820	+	2.42961i	0.205830	+	0.118836i
$419$	5.26504	+	9.11931i	0.257214	+	0.445508i	0.965495	−	0.260423i	$-0.0838622\pi$
$419$	5.26504	+	9.11931i	0.257214	+	0.445508i	−0.708281	+	0.705931i	$0.750529\pi$
$420$		0			0
$421$		−	24.9973i		−	1.21830i	−0.793057	−	0.609148i	$-0.791512\pi$
$421$		−	24.9973i		−	1.21830i	0.793057	−	0.609148i	$-0.208488\pi$
$422$		−	8.63648i		−	0.420417i
$423$	26.9293	−	15.5476i	1.30935	−	0.755951i
$424$	−6.07543	−	3.50765i	−0.295049	−	0.170347i
$425$	29.7229			1.44177
$426$	2.55396	+	4.42359i	0.123740	+	0.214323i
$427$		0			0
$428$	9.02649			0.436312
$429$	0.895117	+	1.05551i	0.0432166	+	0.0509606i
$430$	−12.4623	+	21.5853i	−0.600985	+	1.04094i
$431$			11.9784i			0.576979i	0.957483	+	0.288489i	$0.0931530\pi$
$431$			11.9784i			0.576979i	−0.957483	+	0.288489i	$0.906847\pi$
$432$	−1.34886	+	2.33629i	−0.0648971	+	0.112405i
$433$	3.98475	−	6.90179i	0.191495	−	0.331679i	−0.754251	−	0.656586i	$-0.772000\pi$
$433$	3.98475	−	6.90179i	0.191495	−	0.331679i	0.945746	+	0.324907i	$0.105333\pi$
$434$		0			0
$435$	−9.40551	−	5.43027i	−0.450960	−	0.260362i
$436$		−	0.397192i		−	0.0190220i
$437$	−31.3573	−	18.1041i	−1.50002	−	0.866038i
$438$	−2.96692	−	5.13885i	−0.141765	−	0.245544i
$439$	2.17827	−	3.77288i	0.103963	−	0.180070i	−0.809351	−	0.587325i	$-0.800181\pi$
$439$	2.17827	−	3.77288i	0.103963	−	0.180070i	0.913314	+	0.407256i	$0.133514\pi$
$440$	2.41495	−	1.39427i	0.115128	−	0.0664693i
$441$		0			0
$442$	10.6836	+	12.5980i	0.508166	+	0.599224i
$443$	5.74117	+	9.94400i	0.272771	+	0.472454i	0.969570	−	0.244813i	$-0.0787265\pi$
$443$	5.74117	+	9.94400i	0.272771	+	0.472454i	−0.696799	+	0.717266i	$0.745393\pi$
$444$		−	4.52122i		−	0.214568i
$445$	−27.2596			−1.29223
$446$	19.9277			0.943603
$447$			7.93490i			0.375308i
$448$		0			0
$449$	−25.5692	−	14.7624i	−1.20669	−	0.696680i	−0.244652	−	0.969611i	$-0.578674\pi$
$449$	−25.5692	−	14.7624i	−1.20669	−	0.696680i	−0.962034	+	0.272931i	$0.912007\pi$
$450$	15.6330	−	9.02572i	0.736947	−	0.425476i
$451$	−0.0367662	−	0.0636809i	−0.00173125	−	0.00299861i
$452$	−4.47322			−0.210402
$453$	−2.24067	−	1.29365i	−0.105276	−	0.0607810i
$454$	0.352624			0.0165495
$455$		0			0
$456$	−2.75551			−0.129039
$457$	14.3744	+	8.29907i	0.672407	+	0.388214i	0.796988	−	0.603995i	$-0.206425\pi$
$457$	14.3744	+	8.29907i	0.672407	+	0.388214i	−0.124581	+	0.992209i	$0.539759\pi$
$458$	−8.31317			−0.388449
$459$	6.17953	+	10.7033i	0.288436	+	0.499585i
$460$	−17.9949	+	10.3894i	−0.839017	+	0.484407i
$461$	22.8996	+	13.2211i	1.06654	+	0.615769i	0.927235	−	0.374481i	$-0.122179\pi$
$461$	22.8996	+	13.2211i	1.06654	+	0.615769i	0.139308	+	0.990249i	$0.455512\pi$
$462$		0			0
$463$		−	10.4717i		−	0.486663i	−0.969943	−	0.243331i	$-0.921760\pi$
$463$		−	10.4717i		−	0.486663i	0.969943	−	0.243331i	$-0.0782403\pi$
$464$	−6.86813			−0.318845
$465$	6.77875			0.314357
$466$		−	15.3798i		−	0.712454i
$467$	−13.9505	−	24.1629i	−0.645551	−	1.11813i	−0.984174	−	0.177205i	$-0.943294\pi$
$467$	−13.9505	−	24.1629i	−0.645551	−	1.11813i	0.338623	−	0.940922i	$-0.390039\pi$
$468$	9.44465	+	3.38180i	0.436579	+	0.156324i
$469$		0			0
$470$	32.8046	−	18.9397i	1.51316	−	0.873625i
$471$	0.535017	−	0.926677i	0.0246523	−	0.0426990i
$472$	0.870585	+	1.50790i	0.0400719	+	0.0694066i
$473$	5.23958	+	3.02507i	0.240916	+	0.139093i
$474$		−	4.64493i		−	0.213349i
$475$	33.1850	+	19.1594i	1.52263	+	0.879091i
$476$		0			0
$477$	−9.75946	+	16.9039i	−0.446855	+	0.773975i
$478$	−1.44303	+	2.49940i	−0.0660026	+	0.114320i
$479$		−	6.88133i		−	0.314416i	−0.987566	−	0.157208i	$-0.949751\pi$
$479$		−	6.88133i		−	0.314416i	0.987566	−	0.157208i	$-0.0502493\pi$
$480$	−0.790648	+	1.36944i	−0.0360880	+	0.0625062i
$481$	−34.3779	+	6.24709i	−1.56750	+	0.284843i
$482$	−6.26744			−0.285474
$483$		0			0
$484$	5.16156	+	8.94008i	0.234616	+	0.406367i
$485$	50.0742			2.27375
$486$	9.87288	+	5.70011i	0.447843	+	0.258562i
$487$	35.3392	−	20.4031i	1.60137	−	0.924553i	0.610160	−	0.792278i	$-0.291105\pi$
$487$	35.3392	−	20.4031i	1.60137	−	0.924553i	0.991213	−	0.132275i	$-0.0422282\pi$
$488$		−	2.37945i		−	0.107713i
$489$		−	10.8966i		−	0.492762i
$490$		0			0
$491$	3.36353	+	5.82581i	0.151794	+	0.262915i	0.931887	−	0.362749i	$-0.118162\pi$
$491$	3.36353	+	5.82581i	0.151794	+	0.262915i	−0.780093	+	0.625664i	$0.784828\pi$
$492$	0.0361115	+	0.0208490i	0.00162803	+	0.000939944i
$493$	−15.7325	+	27.2494i	−0.708555	+	1.22725i
$494$	3.80736	+	20.9520i	0.171301	+	0.942675i
$495$	−3.87933	−	6.71920i	−0.174363	−	0.302005i
$496$	3.71251	−	2.14342i	0.166696	−	0.0962422i
$497$		0			0
$498$	0.754761	−	1.30728i	0.0338217	−	0.0585808i
$499$	−1.00633	+	0.581002i	−0.0450493	+	0.0260092i	−0.522355	−	0.852728i	$-0.674947\pi$
$499$	−1.00633	+	0.581002i	−0.0450493	+	0.0260092i	0.477306	+	0.878737i	$0.341613\pi$
$500$	4.36733	−	2.52148i	0.195313	−	0.112764i
$501$	8.79916	−	5.08020i	0.393118	−	0.226967i
$502$	−14.9532	+	8.63325i	−0.667395	+	0.385321i
$503$	−4.97527	+	8.61741i	−0.221836	+	0.384231i	−0.955366	−	0.295426i	$-0.904538\pi$
$503$	−4.97527	+	8.61741i	−0.221836	+	0.384231i	0.733529	+	0.679658i	$0.237872\pi$
$504$		0			0
$505$	24.1861	−	13.9638i	1.07627	−	0.621382i
$506$	2.52189	+	4.36805i	0.112112	+	0.194183i
$507$	−0.990731	+	5.98362i	−0.0439999	+	0.265742i
$508$	0.270063	−	0.467763i	0.0119821	−	0.0207536i
$509$	0.0452068	+	0.0261002i	0.00200376	+	0.00115687i	0.501002	−	0.865446i	$-0.332965\pi$
$509$	0.0452068	+	0.0261002i	0.00200376	+	0.00115687i	−0.498998	+	0.866603i	$0.666298\pi$
$510$	3.62219	+	6.27382i	0.160393	+	0.277810i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$			15.9333i			0.703472i
$514$	9.69351	−	5.59655i	0.427562	−	0.246853i
$515$	39.1072	+	22.5785i	1.72327	+	0.994929i
$516$	−3.43085			−0.151035
$517$	−4.59739	−	7.96292i	−0.202193	−	0.350209i
$518$		0			0
$519$	3.77777			0.165826
$520$	11.5053	+	4.11964i	0.504539	+	0.180658i
$521$	−13.0492	+	22.6019i	−0.571695	+	0.990206i	0.424697	+	0.905336i	$0.360381\pi$
$521$	−13.0492	+	22.6019i	−0.571695	+	0.990206i	−0.996392	+	0.0848699i	$0.972953\pi$
$522$			19.1094i			0.836397i
$523$	9.76606	−	16.9153i	0.427040	−	0.739655i	−0.569568	−	0.821944i	$-0.692890\pi$
$523$	9.76606	−	16.9153i	0.427040	−	0.739655i	0.996609	+	0.0822887i	$0.0262229\pi$
$524$	−3.86307	+	6.69104i	−0.168759	+	0.292299i
$525$		0			0
$526$	24.7533	+	14.2913i	1.07929	+	0.623131i
$527$		−	19.6392i		−	0.855499i
$528$	0.332416	+	0.191920i	0.0144665	+	0.00835226i
$529$	−7.29180	−	12.6298i	−0.317035	−	0.549120i
$530$	−11.8887	+	20.5919i	−0.516414	+	0.894455i
$531$	4.19548	−	2.42226i	0.182068	−	0.105117i
$532$		0			0
$533$	0.108633	−	0.303387i	0.00470540	−	0.0131412i
$534$	−1.87613	−	3.24955i	−0.0811881	−	0.140622i
$535$		−	30.5942i		−	1.32270i
$536$	0.291719			0.0126003
$537$	4.62292			0.199494
$538$		−	18.3754i		−	0.792219i
$539$		0			0
$540$	7.91858	+	4.57179i	0.340761	+	0.196739i
$541$	28.4750	−	16.4401i	1.22424	−	0.706814i	0.258419	−	0.966033i	$-0.416798\pi$
$541$	28.4750	−	16.4401i	1.22424	−	0.706814i	0.965819	+	0.259219i	$0.0834651\pi$
$542$	10.1913	+	17.6518i	0.437752	+	0.758209i
$543$	−0.596719			−0.0256077
$544$	3.96752	+	2.29065i	0.170106	+	0.0982107i
$545$	−1.34623			−0.0576662
$546$		0			0
$547$	−39.0180			−1.66829			−0.834144	−	0.551546i	$-0.814038\pi$
$547$	−39.0180			−1.66829			−0.834144	+	0.551546i	$0.814038\pi$
$548$	−10.8600	−	6.27005i	−0.463918	−	0.267843i
$549$	−6.62043			−0.282553
$550$	−2.66888	−	4.62264i	−0.113802	−	0.197110i
$551$	−35.1300	+	20.2823i	−1.49659	+	0.864055i
$552$	−2.47698	−	1.43009i	−0.105427	−	0.0608686i
$553$		0			0
$554$		−	7.23219i		−	0.307266i
$555$	−15.3241			−0.650473
$556$	−12.0974			−0.513042
$557$		−	29.5492i		−	1.25204i	−0.779807	−	0.626020i	$-0.784683\pi$
$557$		−	29.5492i		−	1.25204i	0.779807	−	0.626020i	$-0.215317\pi$
$558$	−5.96370	−	10.3294i	−0.252464	−	0.437280i
$559$	4.74050	+	26.0871i	0.200502	+	1.10337i
$560$		0			0
$561$	1.52290	−	0.879244i	0.0642967	−	0.0371217i
$562$	−6.22927	+	10.7894i	−0.262766	+	0.455124i
$563$	−13.5662	−	23.4973i	−0.571745	−	0.990292i	−0.996387	−	0.0849304i	$-0.972933\pi$
$563$	−13.5662	−	23.4973i	−0.571745	−	0.990292i	0.424642	−	0.905362i	$-0.360400\pi$
$564$	4.51553	+	2.60704i	0.190138	+	0.109776i
$565$			15.1614i			0.637845i
$566$	11.3109	+	6.53035i	0.475433	+	0.274491i
$567$		0			0
$568$	5.47419	−	9.48158i	0.229692	−	0.397838i
$569$	21.2297	−	36.7709i	0.889996	−	1.54152i	0.0501168	−	0.998743i	$-0.484041\pi$
$569$	21.2297	−	36.7709i	0.889996	−	1.54152i	0.839879	−	0.542774i	$-0.182626\pi$
$570$			9.33946i			0.391187i
$571$	5.63390	−	9.75820i	0.235771	−	0.408368i	−0.723725	−	0.690088i	$-0.757572\pi$
$571$	5.63390	−	9.75820i	0.235771	−	0.408368i	0.959497	+	0.281720i	$0.0909050\pi$
$572$	0.999992	−	2.79276i	0.0418118	−	0.116771i
$573$	4.68141			0.195569
$574$		0			0
$575$	19.8871	+	34.4455i	0.829349	+	1.43647i
$576$	2.78234			0.115931
$577$	19.8309	+	11.4494i	0.825570	+	0.476643i	0.852334	−	0.522999i	$-0.175187\pi$
$577$	19.8309	+	11.4494i	0.825570	+	0.476643i	−0.0267633	+	0.999642i	$0.508520\pi$
$578$	3.45395	−	1.99414i	0.143665	−	0.0829452i
$579$			7.39857i			0.307474i
$580$			23.2787i			0.966594i
$581$		0			0
$582$	3.44634	+	5.96923i	0.142855	+	0.247433i
$583$	4.99844	+	2.88585i	0.207014	+	0.119520i
$584$	−6.35934	+	11.0147i	−0.263151	+	0.455791i
$585$	11.4622	−	32.0115i	0.473904	−	1.32351i
$586$	7.27909	+	12.6078i	0.300696	+	0.520822i
$587$	31.0054	−	17.9010i	1.27973	−	0.738852i	0.302931	−	0.953013i	$-0.402035\pi$
$587$	31.0054	−	17.9010i	1.27973	−	0.738852i	0.976798	+	0.214161i	$0.0687016\pi$
$588$		0			0
$589$	12.6595	−	21.9268i	0.521624	−	0.903479i
$590$	5.11083	−	2.95074i	0.210410	−	0.121480i
$591$	−5.98304	+	3.45431i	−0.246110	+	0.142091i
$592$	−8.39253	+	4.84543i	−0.344931	+	0.199146i
$593$	−12.6520	+	7.30464i	−0.519555	+	0.299965i	−0.736753	−	0.676162i	$-0.763642\pi$
$593$	−12.6520	+	7.30464i	−0.519555	+	0.299965i	0.217197	+	0.976128i	$0.430308\pi$
$594$	1.10975	−	1.92214i	0.0455335	−	0.0788663i
$595$		0			0
$596$	14.7292	−	8.50389i	0.603331	−	0.348333i
$597$	0.596111	+	1.03249i	0.0243972	+	0.0422572i
$598$	−7.45140	+	20.8102i	−0.304711	+	0.850991i
$599$	18.7865	−	32.5391i	0.767594	−	1.32951i	−0.171270	−	0.985224i	$-0.554787\pi$
$599$	18.7865	−	32.5391i	0.767594	−	1.32951i	0.938864	−	0.344288i	$-0.111880\pi$
$600$	2.62136	+	1.51344i	0.107017	+	0.0617860i
$601$	2.72579	+	4.72121i	0.111187	+	0.192582i	0.916249	−	0.400609i	$-0.131201\pi$
$601$	2.72579	+	4.72121i	0.111187	+	0.192582i	−0.805062	+	0.593191i	$0.797868\pi$
$602$		0			0
$603$		−	0.811659i		−	0.0330533i
$604$			5.54567i			0.225650i
$605$	30.3013	−	17.4945i	1.23192	−	0.711251i
$606$	3.32919	+	1.92211i	0.135239	+	0.0780804i
$607$	−39.9387			−1.62106			−0.810531	−	0.585696i	$-0.800821\pi$
$607$	−39.9387			−1.62106			−0.810531	+	0.585696i	$0.800821\pi$
$608$	2.95310	+	5.11492i	0.119764	+	0.207438i
$609$		0			0
$610$	−8.06485			−0.326536
$611$	13.5839	−	37.9368i	0.549544	−	1.53476i
$612$	6.37335	−	11.0390i	0.257628	−	0.446224i
$613$			16.6552i			0.672696i	0.941738	+	0.336348i	$0.109192\pi$
$613$			16.6552i			0.672696i	−0.941738	+	0.336348i	$0.890808\pi$
$614$	1.62134	−	2.80824i	0.0654318	−	0.113331i
$615$	0.0706650	−	0.122395i	0.00284949	−	0.00493546i
$616$		0			0
$617$	−23.3525	−	13.4826i	−0.940137	−	0.542788i	−0.0501339	−	0.998743i	$-0.515965\pi$
$617$	−23.3525	−	13.4826i	−0.940137	−	0.542788i	−0.890003	+	0.455954i	$0.849298\pi$
$618$			6.21583i			0.250037i
$619$	11.0446	+	6.37663i	0.443922	+	0.256298i	0.705260	−	0.708949i	$-0.250830\pi$
$619$	11.0446	+	6.37663i	0.443922	+	0.256298i	−0.261338	+	0.965247i	$0.584164\pi$
$620$	−7.26484	−	12.5831i	−0.291763	−	0.505349i
$621$	−8.26925	+	14.3228i	−0.331833	+	0.574752i
$622$	−8.89484	+	5.13544i	−0.356651	+	0.205912i
$623$		0			0
$624$	0.300752	+	1.65505i	0.0120397	+	0.0662549i
$625$	7.67344	+	13.2908i	0.306938	+	0.531632i
$626$		−	6.13382i		−	0.245157i
$627$	2.26704			0.0905369
$628$	−2.29353			−0.0915218
$629$			44.3967i			1.77021i
$630$		0			0
$631$	32.5218	+	18.7764i	1.29467	+	0.747479i	0.979478	−	0.201549i	$-0.0645976\pi$
$631$	32.5218	+	18.7764i	1.29467	+	0.747479i	0.315193	+	0.949028i	$0.397931\pi$
$632$	−8.62217	+	4.97801i	−0.342971	+	0.198015i
$633$	−2.01465	−	3.48948i	−0.0800753	−	0.138695i
$634$	5.04487			0.200357
$635$	−1.58543	−	0.915346i	−0.0629157	−	0.0363244i
$636$	−3.27295			−0.129781
$637$		0			0
$638$	5.65062			0.223710
$639$	−26.3809	−	15.2310i	−1.04361	−	0.602531i
$640$	3.38938			0.133977
$641$	0.988115	+	1.71147i	0.0390282	+	0.0675988i	0.884880	−	0.465820i	$-0.154240\pi$
$641$	0.988115	+	1.71147i	0.0390282	+	0.0675988i	−0.845851	+	0.533418i	$0.820907\pi$
$642$	3.64706	−	2.10563i	0.143938	−	0.0831027i
$643$	−33.8360	−	19.5352i	−1.33436	−	0.770394i	−0.348397	−	0.937347i	$-0.613274\pi$
$643$	−33.8360	−	19.5352i	−1.33436	−	0.770394i	−0.985965	+	0.166953i	$0.946607\pi$
$644$		0			0
$645$			11.6284i			0.457870i
$646$	27.0581			1.06459
$647$	−12.1051			−0.475900			−0.237950	−	0.971277i	$-0.576475\pi$
$647$	−12.1051			−0.475900			−0.237950	+	0.971277i	$0.576475\pi$
$648$		−	7.08840i		−	0.278459i
$649$	−0.716256	−	1.24059i	−0.0281155	−	0.0486975i
$650$	7.88572	−	22.0231i	0.309303	−	0.863818i
$651$		0			0
$652$	−20.2269	+	11.6780i	−0.792145	+	0.457345i
$653$	−20.1232	+	34.8544i	−0.787481	+	1.36396i	0.140024	+	0.990148i	$0.455282\pi$
$653$	−20.1232	+	34.8544i	−0.787481	+	1.36396i	−0.927505	+	0.373810i	$0.878051\pi$
$654$	−0.0926539	−	0.160481i	−0.00362305	−	0.00627531i
$655$	22.6785	+	13.0934i	0.886120	+	0.511602i
$656$		−	0.0893760i		−	0.00348955i
$657$	30.6466	+	17.6938i	1.19564	+	0.690301i
$658$		0			0
$659$	1.81164	−	3.13785i	0.0705714	−	0.122233i	−0.828580	−	0.559870i	$-0.810851\pi$
$659$	1.81164	−	3.13785i	0.0705714	−	0.122233i	0.899152	+	0.437637i	$0.144184\pi$
$660$	0.650490	−	1.12668i	0.0253203	−	0.0438560i
$661$		−	23.6365i		−	0.919352i	−0.888087	−	0.459676i	$-0.847965\pi$
$661$		−	23.6365i		−	0.919352i	0.888087	−	0.459676i	$-0.152035\pi$
$662$	11.5437	−	19.9943i	0.448658	−	0.777099i
$663$	7.25535	+	2.59789i	0.281775	+	0.100894i
$664$	−3.23553			−0.125563
$665$		0			0
$666$	13.4816	+	23.3508i	0.522402	+	0.904827i
$667$	−42.1054			−1.63033
$668$	−18.8603	−	10.8890i	−0.729725	−	0.421307i
$669$	8.05157	−	4.64858i	0.311292	−	0.179724i
$670$		−	0.988744i		−	0.0381985i
$671$			1.95764i			0.0755740i
$672$		0			0
$673$	23.4355	+	40.5914i	0.903372	+	1.56469i	0.823088	+	0.567913i	$0.192249\pi$
$673$	23.4355	+	40.5914i	0.903372	+	1.56469i	0.0802832	+	0.996772i	$0.474418\pi$
$674$	−25.2385	−	14.5714i	−0.972150	−	0.561271i
$675$	8.75123	−	15.1576i	0.336835	−	0.583415i
$676$	12.1689	−	4.57365i	0.468034	−	0.175909i
$677$	6.86522	+	11.8909i	0.263852	+	0.457005i	0.967262	−	0.253779i	$-0.0816737\pi$
$677$	6.86522	+	11.8909i	0.263852	+	0.457005i	−0.703410	+	0.710784i	$0.748340\pi$
$678$	−1.80736	+	1.04348i	−0.0694112	+	0.0400745i
$679$		0			0
$680$	7.76387	−	13.4474i	0.297731	−	0.515685i
$681$	0.142474	−	0.0822575i	0.00545962	−	0.00315212i
$682$	−3.05439	+	1.76345i	−0.116959	+	0.0675261i
$683$	−3.03610	+	1.75289i	−0.116173	+	0.0670725i	−0.556961	−	0.830539i	$-0.688033\pi$
$683$	−3.03610	+	1.75289i	−0.116173	+	0.0670725i	0.440788	+	0.897611i	$0.354699\pi$
$684$	14.2314	−	8.21652i	0.544153	−	0.314167i
$685$	−21.2516	+	36.8088i	−0.811981	+	1.40639i
$686$		0			0
$687$	−3.35885	+	1.93923i	−0.128148	+	0.0739864i
$688$	3.67687	+	6.36853i	0.140179	+	0.242798i
$689$	4.52233	+	24.8865i	0.172287	+	0.948099i
$690$	−4.84711	+	8.39543i	−0.184526	+	0.319609i
$691$	27.5196	+	15.8885i	1.04690	+	0.604426i	0.921779	−	0.387716i	$-0.126736\pi$
$691$	27.5196	+	15.8885i	1.04690	+	0.604426i	0.125117	+	0.992142i	$0.460069\pi$
$692$	−4.04866	−	7.01249i	−0.153907	−	0.266575i
$693$		0			0
$694$		−	29.1082i		−	1.10493i
$695$			41.0025i			1.55531i
$696$	−2.77500	+	1.60215i	−0.105186	+	0.0607292i
$697$	−0.354601	−	0.204729i	−0.0134315	−	0.00775466i
$698$	−25.7802			−0.975796
$699$	−3.58768	−	6.21404i	−0.135698	−	0.235037i
$700$		0			0
$701$	−31.6828			−1.19664			−0.598322	−	0.801256i	$-0.704166\pi$
$701$	−31.6828			−1.19664			−0.598322	+	0.801256i	$0.704166\pi$
$702$	9.57004	−	1.73905i	0.361198	−	0.0656363i
$703$	−28.6181	+	49.5680i	−1.07935	+	1.86949i
$704$		−	0.822730i		−	0.0310078i
$705$	8.83624	−	15.3048i	0.332792	−	0.576413i
$706$	−4.95890	+	8.58906i	−0.186630	+	0.323253i
$707$		0			0
$708$	0.703502	+	0.406167i	0.0264392	+	0.0152647i
$709$			35.3147i			1.32627i	0.748498	+	0.663137i	$0.230775\pi$
$709$			35.3147i			1.32627i	−0.748498	+	0.663137i	$0.769225\pi$
$710$	−32.1367	−	18.5541i	−1.20607	−	0.696323i
$711$	13.8505	+	23.9898i	0.519434	+	0.899687i
$712$	−4.02133	+	6.96514i	−0.150706	+	0.261030i
$713$	22.7597	−	13.1403i	0.852357	−	0.492108i
$714$		0			0
$715$	−9.46572	−	3.38935i	−0.353998	−	0.126754i
$716$	−4.95442	−	8.58130i	−0.185155	−	0.320698i
$717$			1.34648i			0.0502850i
$718$	−25.2683			−0.943003
$719$	1.21956			0.0454818			0.0227409	−	0.999741i	$-0.492761\pi$
$719$	1.21956			0.0454818			0.0227409	+	0.999741i	$0.492761\pi$
$720$		−	9.43038i		−	0.351450i
$721$		0			0
$722$	13.7553	+	7.94164i	0.511920	+	0.295557i
$723$	−2.53230	+	1.46202i	−0.0941771	+	0.0543732i
$724$	0.639508	+	1.10766i	0.0237671	+	0.0411659i
$725$	44.5595			1.65490
$726$	4.17095	+	2.40810i	0.154798	+	0.0893729i
$727$	5.75380			0.213397			0.106698	−	0.994291i	$-0.465972\pi$
$727$	5.75380			0.213397			0.106698	+	0.994291i	$0.465972\pi$
$728$		0			0
$729$	−15.9465			−0.590611
$730$	37.3330	+	21.5542i	1.38175	+	0.797756i
$731$	33.6897			1.24606
$732$	−0.555060	−	0.961392i	−0.0205156	−	0.0355341i
$733$	30.5064	−	17.6129i	1.12678	−	0.650548i	0.183658	−	0.982990i	$-0.441206\pi$
$733$	30.5064	−	17.6129i	1.12678	−	0.650548i	0.943123	+	0.332443i	$0.107873\pi$
$734$	−30.9897	−	17.8919i	−1.14385	−	0.660402i
$735$		0			0
$736$			6.13055i			0.225975i
$737$	−0.240006			−0.00884073
$738$	−0.248674			−0.00915382
$739$		−	29.3524i		−	1.07975i	−0.841746	−	0.539873i	$-0.818472\pi$
$739$		−	29.3524i		−	1.07975i	0.841746	−	0.539873i	$-0.181528\pi$
$740$	16.4230	+	28.4454i	0.603721	+	1.04568i
$741$	6.42585	+	7.57729i	0.236060	+	0.278359i
$742$		0			0
$743$	−12.9763	+	7.49190i	−0.476056	+	0.274851i	−0.718771	−	0.695246i	$-0.755295\pi$
$743$	−12.9763	+	7.49190i	−0.476056	+	0.274851i	0.242715	+	0.970098i	$0.421962\pi$
$744$	1.00000	−	1.73205i	0.0366618	−	0.0635001i
$745$	−28.8229	−	49.9227i	−1.05599	−	1.82903i
$746$	20.2047	+	11.6652i	0.739746	+	0.427093i
$747$			9.00234i			0.329378i
$748$	−3.26420	−	1.88459i	−0.119351	−	0.0689073i
$749$		0			0
$750$	1.17638	−	2.03755i	0.0429554	−	0.0744010i
$751$	21.9195	−	37.9657i	0.799855	−	1.38539i	−0.119856	−	0.992791i	$-0.538243\pi$
$751$	21.9195	−	37.9657i	0.799855	−	1.38539i	0.919710	−	0.392598i	$-0.128424\pi$
$752$		−	11.1759i		−	0.407545i
$753$	−4.02780	+	6.97635i	−0.146781	+	0.254232i
$754$	16.0165	+	18.8864i	0.583286	+	0.687804i
$755$	18.7963			0.684069
$756$		0			0
$757$	18.1798	+	31.4884i	0.660758	+	1.14447i	0.980417	+	0.196933i	$0.0630983\pi$
$757$	18.1798	+	31.4884i	0.660758	+	1.14447i	−0.319659	+	0.947533i	$0.603568\pi$
$758$	−24.3066			−0.882856
$759$	2.03789	+	1.17658i	0.0739707	+	0.0427070i
$760$	17.3364	−	10.0092i	0.628857	−	0.363071i
$761$			18.2335i			0.660962i	0.943813	+	0.330481i	$0.107211\pi$
$761$			18.2335i			0.660962i	−0.943813	+	0.330481i	$0.892789\pi$
$762$		−	0.251993i		−	0.00912876i
$763$		0			0
$764$	−5.01710	−	8.68988i	−0.181512	−	0.314389i
$765$	−37.4152	−	21.6017i	−1.35275	−	0.781011i
$766$	−2.45575	+	4.25348i	−0.0887299	+	0.153685i
$767$	2.11631	−	5.91041i	0.0764157	−	0.213413i
$768$	0.233273	+	0.404040i	0.00841750	+	0.0145795i
$769$	−5.66870	+	3.27283i	−0.204419	+	0.118021i	−0.598715	−	0.800962i	$-0.704322\pi$
$769$	−5.66870	+	3.27283i	−0.204419	+	0.118021i	0.394296	+	0.918983i	$0.370988\pi$
$770$		0			0
$771$	2.61104	−	4.52246i	0.0940344	−	0.162872i
$772$	13.7336	−	7.92911i	0.494284	−	0.285375i
$773$	−38.6651	+	22.3233i	−1.39069	+	0.802913i	−0.993391	−	0.114778i	$-0.963384\pi$
$773$	−38.6651	+	22.3233i	−1.39069	+	0.802913i	−0.397295	+	0.917691i	$0.630051\pi$
$774$	17.7194	−	10.2303i	0.636910	−	0.367720i
$775$	−24.0863	+	13.9062i	−0.865204	+	0.499526i
$776$	7.38693	−	12.7945i	0.265175	−	0.459297i
$777$		0			0
$778$	−4.45589	+	2.57261i	−0.159752	+	0.0922326i
$779$	−0.263937	−	0.457151i	−0.00945651	−	0.0163792i
$780$	5.60958	−	1.01936i	0.200855	−	0.0364991i
$781$	−4.50379	+	7.80079i	−0.161158	+	0.279134i
$782$	24.3231	+	14.0429i	0.869791	+	0.502174i
$783$	9.26414	+	16.0460i	0.331073	+	0.573436i
$784$		0			0
$785$			7.77363i			0.277453i
$786$			3.60460i			0.128572i
$787$	−21.6962	+	12.5263i	−0.773385	+	0.446514i	−0.834081	−	0.551642i	$-0.814001\pi$
$787$	−21.6962	+	12.5263i	−0.773385	+	0.446514i	0.0606960	+	0.998156i	$0.480668\pi$
$788$	12.8242	+	7.40403i	0.456841	+	0.263758i
$789$	13.3351			0.474742
$790$	16.8724	+	29.2238i	0.600291	+	1.03974i
$791$		0			0
$792$	−2.28911			−0.0813400
$793$	−6.54317	+	5.54888i	−0.232355	+	0.197046i
$794$	6.17498	−	10.6954i	0.219142	−	0.379565i
$795$			11.0933i			0.393438i
$796$	1.27771	−	2.21306i	0.0452873	−	0.0784400i
$797$	13.9132	−	24.0984i	0.492831	−	0.853608i	−0.507135	−	0.861867i	$-0.669295\pi$
$797$	13.9132	−	24.0984i	0.492831	−	0.853608i	0.999966	+	0.00825861i	$0.00262883\pi$
$798$		0			0
$799$	−44.3408	−	25.6002i	−1.56866	−	0.905668i
$800$		−	6.48787i		−	0.229381i
$801$	19.3794	+	11.1887i	0.684736	+	0.395333i
$802$	16.2447	+	28.1366i	0.573620	+	0.993539i
$803$	5.23202	−	9.06213i	0.184634	−	0.319795i
$804$	0.117866	−	0.0680499i	0.00415681	−	0.00239994i
$805$		0			0
$806$	−14.5517	−	5.21045i	−0.512561	−	0.183530i
$807$	−4.28647	−	7.42438i	−0.150891	−	0.261351i
$808$		−	8.23976i		−	0.289874i
$809$	7.49650			0.263563			0.131781	−	0.991279i	$-0.457930\pi$
$809$	7.49650			0.263563			0.131781	+	0.991279i	$0.457930\pi$
$810$	−24.0253			−0.844161
$811$		−	9.88726i		−	0.347189i	−0.984817	−	0.173594i	$-0.944462\pi$
$811$		−	9.88726i		−	0.347189i	0.984817	−	0.173594i	$-0.0555381\pi$
$812$		0			0
$813$	8.23535	+	4.75468i	0.288826	+	0.166754i
$814$	6.90479	−	3.98648i	0.242013	−	0.139726i
$815$	39.5811	+	68.5565i	1.38647	+	2.40143i
$816$	2.13738			0.0748233
$817$	37.6138	+	21.7164i	1.31594	+	0.759759i
$818$	3.76834			0.131757
$819$		0			0
$820$	−0.302929			−0.0105787
$821$	−12.4426	−	7.18376i	−0.434251	−	0.250715i	0.266905	−	0.963723i	$-0.413999\pi$
$821$	−12.4426	−	7.18376i	−0.434251	−	0.250715i	−0.701156	+	0.713008i	$0.747332\pi$
$822$	−5.85052			−0.204060
$823$	5.94343	+	10.2943i	0.207175	+	0.358837i	0.950823	−	0.309733i	$-0.100240\pi$
$823$	5.94343	+	10.2943i	0.207175	+	0.358837i	−0.743649	+	0.668571i	$0.766906\pi$
$824$	11.5382	−	6.66156i	0.401951	−	0.232066i
$825$	−2.15667	−	1.24515i	−0.0750856	−	0.0433507i
$826$		0			0
$827$			29.0884i			1.01150i	0.862679	+	0.505752i	$0.168785\pi$
$827$			29.0884i			1.01150i	−0.862679	+	0.505752i	$0.831215\pi$
$828$	17.0572			0.592780
$829$	49.6286			1.72367			0.861836	−	0.507187i	$-0.169315\pi$
$829$	49.6286			1.72367			0.861836	+	0.507187i	$0.169315\pi$
$830$			10.9664i			0.380651i
$831$	−1.68707	−	2.92209i	−0.0585238	−	0.101366i
$832$	2.74987	−	2.33200i	0.0953345	−	0.0808476i
$833$		0			0
$834$	−4.88781	+	2.82198i	−0.169251	+	0.0977172i
$835$	−36.9068	+	63.9245i	−1.27721	+	2.21220i
$836$	−2.42961	−	4.20820i	−0.0840297	−	0.145544i
$837$	−10.0153	−	5.78234i	−0.346179	−	0.199867i
$838$		−	10.5301i		−	0.363755i
$839$	−3.99837	−	2.30846i	−0.138039	−	0.0796969i	0.429390	−	0.903119i	$-0.358729\pi$
$839$	−3.99837	−	2.30846i	−0.138039	−	0.0796969i	−0.567429	+	0.823422i	$0.692062\pi$
$840$		0			0
$841$	−9.08559	+	15.7367i	−0.313296	+	0.542645i
$842$	−12.4987	+	21.6483i	−0.430732	+	0.746051i
$843$			5.81247i			0.200192i
$844$	−4.31824	+	7.47942i	−0.148640	+	0.257452i
$845$	−15.5018	−	41.2449i	−0.533278	−	1.41887i
$846$	−31.0952			−1.06908
$847$		0			0
$848$	3.50765	+	6.07543i	0.120453	+	0.208631i
$849$	6.09341			0.209125
$850$	−25.7408	−	14.8614i	−0.882901	−	0.509743i
$851$	−51.4508	+	29.7051i	−1.76371	+	1.01828i
$852$		−	5.10792i		−	0.174994i
$853$		−	37.8266i		−	1.29516i	−0.761999	−	0.647579i	$-0.775782\pi$
$853$		−	37.8266i		−	1.29516i	0.761999	−	0.647579i	$-0.224218\pi$
$854$		0			0
$855$	−27.8489	−	48.2357i	−0.952412	−	1.64963i
$856$	−7.81717	−	4.51325i	−0.267185	−	0.154260i
$857$	−15.0826	+	26.1238i	−0.515211	+	0.892372i	0.484633	+	0.874718i	$0.338953\pi$
$857$	−15.0826	+	26.1238i	−0.515211	+	0.892372i	−0.999844	+	0.0176546i	$0.994380\pi$
$858$	−0.247438	−	1.36166i	−0.00844740	−	0.0464862i
$859$	−5.31579	−	9.20722i	−0.181372	−	0.314146i	0.760976	−	0.648780i	$-0.224721\pi$
$859$	−5.31579	−	9.20722i	−0.181372	−	0.314146i	−0.942348	+	0.334634i	$0.891387\pi$
$860$	21.5853	−	12.4623i	0.736054	−	0.424961i
$861$		0			0
$862$	5.98919	−	10.3736i	0.203993	−	0.353326i
$863$	20.6419	−	11.9176i	0.702659	−	0.405680i	−0.105678	−	0.994400i	$-0.533701\pi$
$863$	20.6419	−	11.9176i	0.702659	−	0.405680i	0.808337	+	0.588720i	$0.200368\pi$
$864$	2.33629	−	1.34886i	0.0794823	−	0.0458891i
$865$	−23.7680	+	13.7224i	−0.808135	+	0.466577i
$866$	−6.90179	+	3.98475i	−0.234532	+	0.135407i
$867$	0.930356	−	1.61142i	0.0315965	−	0.0547268i
$868$		0			0
$869$	7.09372	−	4.09556i	0.240638	−	0.138932i
$870$	5.43027	+	9.40551i	0.184104	+	0.318877i
$871$	−0.680288	−	0.802188i	−0.0230507	−	0.0271811i
$872$	−0.198596	+	0.343978i	−0.00672530	+	0.0116486i
$873$	−35.5987	−	20.5529i	−1.20483	−	0.695611i
$874$	18.1041	+	31.3573i	0.612381	+	1.06068i
$875$		0			0
$876$			5.93384i			0.200486i
$877$		−	28.4246i		−	0.959829i	−0.877315	−	0.479915i	$-0.840668\pi$
$877$		−	28.4246i		−	0.959829i	0.877315	−	0.479915i	$-0.159332\pi$
$878$	−3.77288	+	2.17827i	−0.127329	+	0.0735132i
$879$	5.88209	+	3.39602i	0.198398	+	0.114545i
$880$	−2.78854			−0.0940017
$881$	27.5915	+	47.7898i	0.929580	+	1.61008i	0.784025	+	0.620729i	$0.213163\pi$
$881$	27.5915	+	47.7898i	0.929580	+	1.61008i	0.145555	+	0.989350i	$0.453503\pi$
$882$		0			0
$883$	9.18216			0.309004			0.154502	−	0.987992i	$-0.450623\pi$
$883$	9.18216			0.309004			0.154502	+	0.987992i	$0.450623\pi$
$884$	−2.95328	−	16.2519i	−0.0993294	−	0.546612i
$885$	1.37665	−	2.38443i	0.0462757	−	0.0801518i
$886$		−	11.4823i		−	0.385757i
$887$	−16.7857	+	29.0737i	−0.563610	+	0.976201i	0.433568	+	0.901121i	$0.357254\pi$
$887$	−16.7857	+	29.0737i	−0.563610	+	0.976201i	−0.997178	+	0.0750798i	$0.976079\pi$
$888$	−2.26061	+	3.91549i	−0.0758611	+	0.131395i
$889$		0			0
$890$	23.6075	+	13.6298i	0.791325	+	0.456871i
$891$			5.83184i			0.195374i
$892$	−17.2579	−	9.96384i	−0.577836	−	0.333614i
$893$	−33.0037	−	57.1641i	−1.10443	−	1.91292i
$894$	3.96745	−	6.87182i	0.132691	−	0.229828i
$895$	−29.0853	+	16.7924i	−0.972213	+	0.561307i
$896$		0			0
$897$	1.84378	+	10.1463i	0.0615619	+	0.338777i
$898$	14.7624	+	25.5692i	0.492627	+	0.853255i
$899$		−	29.4425i		−	0.981963i
$900$	−18.0514			−0.601715
$901$	32.1392			1.07071
$902$			0.0735323i			0.00244836i
$903$		0			0
$904$	3.87392	+	2.23661i	0.128845	+	0.0743885i
$905$	3.75428	−	2.16753i	0.124796	−	0.0720513i
$906$	1.29365	+	2.24067i	0.0429787	+	0.0744413i
$907$	−11.0349			−0.366409			−0.183205	−	0.983075i	$-0.558647\pi$
$907$	−11.0349			−0.366409			−0.183205	+	0.983075i	$0.558647\pi$
$908$	−0.305381	−	0.176312i	−0.0101344	−	0.00585112i
$909$	−22.9258			−0.760400
$910$		0			0
$911$	59.9931			1.98766			0.993830	−	0.110917i	$-0.0353789\pi$
$911$	59.9931			1.98766			0.993830	+	0.110917i	$0.0353789\pi$
$912$	2.38634	+	1.37776i	0.0790197	+	0.0456220i
$913$	2.66197			0.0880984
$914$	−8.29907	−	14.3744i	−0.274509	−	0.475463i
$915$	−3.25852	+	1.88131i	−0.107723	+	0.0621941i
$916$	7.19942	+	4.15659i	0.237875	+	0.137337i
$917$		0			0
$918$		−	12.3591i		−	0.407910i
$919$	35.6537			1.17611			0.588053	−	0.808822i	$-0.299895\pi$
$919$	35.6537			1.17611			0.588053	+	0.808822i	$0.299895\pi$
$920$	20.7787			0.685054
$921$		−	1.51285i		−	0.0498502i
$922$	−13.2211	−	22.8996i	−0.435414	−	0.754159i
$923$	−38.8389	+	7.05774i	−1.27840	+	0.232308i
$924$		0			0
$925$	54.4497	−	31.4365i	1.79029	−	1.03363i
$926$	−5.23587	+	9.06879i	−0.172061	+	0.298019i
$927$	−18.5347	−	32.1030i	−0.608759	−	1.05440i
$928$	5.94797	+	3.43406i	0.195252	+	0.112729i
$929$		−	29.0302i		−	0.952450i	−0.879324	−	0.476225i	$-0.842005\pi$
$929$		−	29.0302i		−	0.952450i	0.879324	−	0.476225i	$-0.157995\pi$
$930$	−5.87057	−	3.38938i	−0.192504	−	0.111142i
$931$		0			0
$932$	−7.68988	+	13.3193i	−0.251891	+	0.436287i
$933$	−2.39591	+	4.14985i	−0.0784387	+	0.135860i
$934$			27.9010i			0.912947i
$935$	−6.38757	+	11.0636i	−0.208896	+	0.361818i
$936$	−6.48841	−	7.65106i	−0.212080	−	0.250083i
$937$	38.2635			1.25001			0.625006	−	0.780620i	$-0.285096\pi$
$937$	38.2635			1.25001			0.625006	+	0.780620i	$0.285096\pi$
$938$		0			0
$939$	−1.43085	−	2.47831i	−0.0466941	−	0.0808765i
$940$	−37.8795			−1.23549
$941$	−3.59180	−	2.07373i	−0.117089	−	0.0676017i	0.440311	−	0.897845i	$-0.354868\pi$
$941$	−3.59180	−	2.07373i	−0.117089	−	0.0676017i	−0.557401	+	0.830243i	$0.688201\pi$
$942$	−0.926677	+	0.535017i	−0.0301928	+	0.0174318i
$943$		−	0.547924i		−	0.0178428i
$944$		−	1.74117i		−	0.0566702i
$945$		0			0
$946$	−3.02507	−	5.23958i	−0.0983536	−	0.170353i
$947$	−0.872884	−	0.503960i	−0.0283649	−	0.0163765i	0.485750	−	0.874098i	$-0.338546\pi$
$947$	−0.872884	−	0.503960i	−0.0283649	−	0.0163765i	−0.514115	+	0.857721i	$0.671880\pi$
$948$	−2.32247	+	4.02263i	−0.0754302	+	0.130649i
$949$	45.1189	−	8.19894i	1.46462	−	0.266149i
$950$	−19.1594	−	33.1850i	−0.621611	−	1.07666i
$951$	2.03833	−	1.17683i	0.0660973	−	0.0381613i
$952$		0			0
$953$	8.25146	−	14.2919i	0.267291	−	0.462962i	−0.700870	−	0.713289i	$-0.747205\pi$
$953$	8.25146	−	14.2919i	0.267291	−	0.462962i	0.968161	+	0.250327i	$0.0805382\pi$
$954$	16.9039	−	9.75946i	0.547283	−	0.315974i
$955$	−29.4533	+	17.0048i	−0.953085	+	0.550264i
$956$	2.49940	−	1.44303i	0.0808363	−	0.0466709i
$957$	2.28307	−	1.31813i	0.0738013	−	0.0426092i
$958$	−3.44067	+	5.95941i	−0.111163	+	0.192540i
$959$		0			0
$960$	1.36944	−	0.790648i	0.0441986	−	0.0255181i
$961$	−6.31154	−	10.9319i	−0.203598	−	0.352642i
$962$	32.8957	+	11.7788i	1.06060	+	0.379764i
$963$	−12.5574	+	21.7500i	−0.404656	+	0.700884i
$964$	5.42777	+	3.13372i	0.174817	+	0.100930i
$965$	−26.8747	−	46.5484i	−0.865128	−	1.49845i
$966$		0			0
$967$		−	37.7765i		−	1.21481i	−0.794392	−	0.607406i	$-0.792210\pi$
$967$		−	37.7765i		−	1.21481i	0.794392	−	0.607406i	$-0.207790\pi$
$968$		−	10.3231i		−	0.331797i
$969$	10.9325	−	6.31191i	0.351204	−	0.202768i
$970$	−43.3655	−	25.0371i	−1.39238	−	0.803893i
$971$	−48.3122			−1.55041			−0.775206	−	0.631709i	$-0.782354\pi$
$971$	−48.3122			−1.55041			−0.775206	+	0.631709i	$0.782354\pi$
$972$	−5.70011	−	9.87288i	−0.182831	−	0.316673i
$973$		0			0
$974$	−40.8062			−1.30752
$975$	−1.95124	−	10.7377i	−0.0624898	−	0.343883i
$976$	−1.18972	+	2.06066i	−0.0380822	+	0.0659602i
$977$		−	16.3041i		−	0.521615i	−0.965391	−	0.260807i	$-0.916011\pi$
$977$		−	16.3041i		−	0.521615i	0.965391	−	0.260807i	$-0.0839888\pi$
$978$	−5.44831	+	9.43675i	−0.174218	+	0.301754i
$979$	3.30847	−	5.73043i	0.105739	−	0.183145i
$980$		0			0
$981$	0.957062	+	0.552560i	0.0305567	+	0.0176419i
$982$		−	6.72706i		−	0.214669i
$983$	−25.5583	−	14.7561i	−0.815182	−	0.470645i	0.0335703	−	0.999436i	$-0.489312\pi$
$983$	−25.5583	−	14.7561i	−0.815182	−	0.470645i	−0.848752	+	0.528791i	$0.822646\pi$
$984$	−0.0208490	−	0.0361115i	−0.000664641	−	0.00115119i
$985$	25.0950	−	43.4659i	0.799594	−	1.38494i
$986$	27.2494	−	15.7325i	0.867799	−	0.501024i
$987$		0			0
$988$	7.17873	−	20.0486i	0.228386	−	0.637833i
$989$	22.5412	+	39.0425i	0.716769	+	1.24148i
$990$			7.75866i			0.246586i
$991$	4.39245			0.139531			0.0697653	−	0.997563i	$-0.477775\pi$
$991$	4.39245			0.139531			0.0697653	+	0.997563i	$0.477775\pi$
$992$	−4.28683			−0.136107
$993$		−	10.7713i		−	0.341817i
$994$		0			0
$995$	−7.50091	−	4.33065i	−0.237795	−	0.137291i
$996$	−1.30728	+	0.754761i	−0.0414229	+	0.0239155i
$997$	−23.1669	−	40.1263i	−0.733704	−	1.27081i	−0.955290	−	0.295671i	$-0.904457\pi$
$997$	−23.1669	−	40.1263i	−0.733704	−	1.27081i	0.221586	−	0.975141i	$-0.428877\pi$
$998$	1.16200			0.0367826
$999$	22.6407	+	13.0716i	0.716320	+	0.413567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.v.e.361.2		12
7.2	even	3		1274.2.o.d.569.5		12
7.3	odd	6		1274.2.m.c.491.5		12
7.4	even	3		182.2.m.b.127.5	yes	12
7.5	odd	6		1274.2.o.e.569.5		12
7.6	odd	2		1274.2.v.d.361.2		12
13.4	even	6		1274.2.o.d.459.2		12
21.11	odd	6		1638.2.bj.g.127.1		12
28.11	odd	6		1456.2.cc.d.673.3		12
91.4	even	6		182.2.m.b.43.5	✓	12
91.11	odd	12		2366.2.a.bf.1.3		6
91.17	odd	6		1274.2.m.c.589.5		12
91.30	even	6	inner	1274.2.v.e.667.2		12
91.67	odd	12		2366.2.a.bh.1.3		6
91.69	odd	6		1274.2.o.e.459.2		12
91.81	even	3		2366.2.d.r.337.9		12
91.82	odd	6		1274.2.v.d.667.2		12
91.88	even	6		2366.2.d.r.337.3		12
273.95	odd	6		1638.2.bj.g.1135.3		12
364.95	odd	6		1456.2.cc.d.225.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.5	✓	12	91.4	even	6
182.2.m.b.127.5	yes	12	7.4	even	3
1274.2.m.c.491.5		12	7.3	odd	6
1274.2.m.c.589.5		12	91.17	odd	6
1274.2.o.d.459.2		12	13.4	even	6
1274.2.o.d.569.5		12	7.2	even	3
1274.2.o.e.459.2		12	91.69	odd	6
1274.2.o.e.569.5		12	7.5	odd	6
1274.2.v.d.361.2		12	7.6	odd	2
1274.2.v.d.667.2		12	91.82	odd	6
1274.2.v.e.361.2		12	1.1	even	1	trivial
1274.2.v.e.667.2		12	91.30	even	6	inner
1456.2.cc.d.225.3		12	364.95	odd	6
1456.2.cc.d.673.3		12	28.11	odd	6
1638.2.bj.g.127.1		12	21.11	odd	6
1638.2.bj.g.1135.3		12	273.95	odd	6
2366.2.a.bf.1.3		6	91.11	odd	12
2366.2.a.bh.1.3		6	91.67	odd	12
2366.2.d.r.337.3		12	91.88	even	6
2366.2.d.r.337.9		12	91.81	even	3

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:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.v (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} -0.466545 q^{3} +(0.500000 + 0.866025i) q^{4} +(2.93529 - 1.69469i) q^{5} +(0.404040 + 0.233273i) q^{6} -1.00000i q^{8} -2.78234 q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} -0.466545 q^{3} +(0.500000 + 0.866025i) q^{4} +(2.93529 - 1.69469i) q^{5} +(0.404040 + 0.233273i) q^{6} -1.00000i q^{8} -2.78234 q^{9} -3.38938 q^{10} +0.822730i q^{11} +(-0.233273 - 0.404040i) q^{12} +(-2.74987 + 2.33200i) q^{13} +(-1.36944 + 0.790648i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.29065 + 3.96752i) q^{17} +(2.40957 + 1.39117i) q^{18} +5.90621i q^{19} +(2.93529 + 1.69469i) q^{20} +(0.411365 - 0.712505i) q^{22} +(-3.06527 + 5.30921i) q^{23} +0.466545i q^{24} +(3.24394 - 5.61866i) q^{25} +(3.54746 - 0.644638i) q^{26} +2.69772 q^{27} +(3.43406 + 5.94797i) q^{29} +1.58130 q^{30} +(-3.71251 - 2.14342i) q^{31} +(0.866025 - 0.500000i) q^{32} -0.383841i q^{33} -4.58130i q^{34} +(-1.39117 - 2.40957i) q^{36} +(8.39253 + 4.84543i) q^{37} +(2.95310 - 5.11492i) q^{38} +(1.28294 - 1.08798i) q^{39} +(-1.69469 - 2.93529i) q^{40} +(-0.0774019 + 0.0446880i) q^{41} +(3.67687 - 6.36853i) q^{43} +(-0.712505 + 0.411365i) q^{44} +(-8.16695 + 4.71519i) q^{45} +(5.30921 - 3.06527i) q^{46} +(-9.67865 + 5.58797i) q^{47} +(0.233273 - 0.404040i) q^{48} +(-5.61866 + 3.24394i) q^{50} +(-1.06869 - 1.85103i) q^{51} +(-3.39451 - 1.21546i) q^{52} +(3.50765 - 6.07543i) q^{53} +(-2.33629 - 1.34886i) q^{54} +(1.39427 + 2.41495i) q^{55} -2.75551i q^{57} -6.86813i q^{58} +(-1.50790 + 0.870585i) q^{59} +(-1.36944 - 0.790648i) q^{60} +2.37945 q^{61} +(2.14342 + 3.71251i) q^{62} -1.00000 q^{64} +(-4.11964 + 11.5053i) q^{65} +(-0.191920 + 0.332416i) q^{66} +0.291719i q^{67} +(-2.29065 + 3.96752i) q^{68} +(1.43009 - 2.47698i) q^{69} +(9.48158 + 5.47419i) q^{71} +2.78234i q^{72} +(-11.0147 - 6.35934i) q^{73} +(-4.84543 - 8.39253i) q^{74} +(-1.51344 + 2.62136i) q^{75} +(-5.11492 + 2.95310i) q^{76} +(-1.65505 + 0.300752i) q^{78} +(-4.97801 - 8.62217i) q^{79} +3.38938i q^{80} +7.08840 q^{81} +0.0893760 q^{82} -3.23553i q^{83} +(13.4474 + 7.76387i) q^{85} +(-6.36853 + 3.67687i) q^{86} +(-1.60215 - 2.77500i) q^{87} +0.822730 q^{88} +(-6.96514 - 4.02133i) q^{89} +9.43038 q^{90} -6.13055 q^{92} +(1.73205 + 1.00000i) q^{93} +11.1759 q^{94} +(10.0092 + 17.3364i) q^{95} +(-0.404040 + 0.233273i) q^{96} +(12.7945 + 7.38693i) q^{97} -2.28911i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9	\( 12 q + 4 q^{3} + 6 q^{4} + 6 q^{6} + 12 q^{9} + 4 q^{10} + 2 q^{12} - 8 q^{13} - 6 q^{15} - 6 q^{16} + 4 q^{17} - 2 q^{22} - 6 q^{23} + 12 q^{25} + 16 q^{26} + 40 q^{27} - 10 q^{29} - 28 q^{30} - 18 q^{31} + 6 q^{36} + 6 q^{37} - 4 q^{38} + 30 q^{39} + 2 q^{40} - 24 q^{41} + 26 q^{43} + 18 q^{44} - 72 q^{45} + 6 q^{46} - 48 q^{47} - 2 q^{48} - 12 q^{50} + 18 q^{51} - 4 q^{52} - 18 q^{53} + 36 q^{54} - 6 q^{55} - 6 q^{59} - 6 q^{60} + 56 q^{61} - 2 q^{62} - 12 q^{64} + 38 q^{65} - 4 q^{68} + 32 q^{69} + 48 q^{71} + 48 q^{73} - 48 q^{75} + 12 q^{76} - 8 q^{78} - 22 q^{79} + 68 q^{81} - 12 q^{82} + 54 q^{85} - 6 q^{86} + 2 q^{87} - 4 q^{88} - 12 q^{89} + 12 q^{90} - 12 q^{92} - 16 q^{94} + 32 q^{95} - 6 q^{96} + 60 q^{97}+O(q^{100}) \) 12 * q + 4 * q^3 + 6 * q^4 + 6 * q^6 + 12 * q^9 + 4 * q^10 + 2 * q^12 - 8 * q^13 - 6 * q^15 - 6 * q^16 + 4 * q^17 - 2 * q^22 - 6 * q^23 + 12 * q^25 + 16 * q^26 + 40 * q^27 - 10 * q^29 - 28 * q^30 - 18 * q^31 + 6 * q^36 + 6 * q^37 - 4 * q^38 + 30 * q^39 + 2 * q^40 - 24 * q^41 + 26 * q^43 + 18 * q^44 - 72 * q^45 + 6 * q^46 - 48 * q^47 - 2 * q^48 - 12 * q^50 + 18 * q^51 - 4 * q^52 - 18 * q^53 + 36 * q^54 - 6 * q^55 - 6 * q^59 - 6 * q^60 + 56 * q^61 - 2 * q^62 - 12 * q^64 + 38 * q^65 - 4 * q^68 + 32 * q^69 + 48 * q^71 + 48 * q^73 - 48 * q^75 + 12 * q^76 - 8 * q^78 - 22 * q^79 + 68 * q^81 - 12 * q^82 + 54 * q^85 - 6 * q^86 + 2 * q^87 - 4 * q^88 - 12 * q^89 + 12 * q^90 - 12 * q^92 - 16 * q^94 + 32 * q^95 - 6 * q^96 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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