LMFDB - Embedded newform 1380.2.p.b.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(91,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))

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

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

chi := DirichletCharacter("1380.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.p (of order $2$, degree $1$, 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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.1
Character	$\chi$	$=$	1380.91
Dual form			1380.2.p.b.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41370 - 0.0379392i) q^{2} +1.00000i q^{3} +(1.99712 + 0.107270i) q^{4} -1.00000i q^{5} +(0.0379392 - 1.41370i) q^{6} +1.92200 q^{7} +(-2.81927 - 0.227417i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.41370 - 0.0379392i) q^{2} +1.00000i q^{3} +(1.99712 + 0.107270i) q^{4} -1.00000i q^{5} +(0.0379392 - 1.41370i) q^{6} +1.92200 q^{7} +(-2.81927 - 0.227417i) q^{8} -1.00000 q^{9} +(-0.0379392 + 1.41370i) q^{10} -6.24957 q^{11} +(-0.107270 + 1.99712i) q^{12} +1.29528 q^{13} +(-2.71714 - 0.0729192i) q^{14} +1.00000 q^{15} +(3.97699 + 0.428461i) q^{16} -0.0974606i q^{17} +(1.41370 + 0.0379392i) q^{18} +1.71456 q^{19} +(0.107270 - 1.99712i) q^{20} +1.92200i q^{21} +(8.83505 + 0.237104i) q^{22} +(-1.99929 - 4.35922i) q^{23} +(0.227417 - 2.81927i) q^{24} -1.00000 q^{25} +(-1.83114 - 0.0491420i) q^{26} -1.00000i q^{27} +(3.83846 + 0.206172i) q^{28} +6.14940 q^{29} +(-1.41370 - 0.0379392i) q^{30} -2.62644i q^{31} +(-5.60603 - 0.756602i) q^{32} -6.24957i q^{33} +(-0.00369758 + 0.137780i) q^{34} -1.92200i q^{35} +(-1.99712 - 0.107270i) q^{36} -9.78333i q^{37} +(-2.42388 - 0.0650490i) q^{38} +1.29528i q^{39} +(-0.227417 + 2.81927i) q^{40} +9.53279 q^{41} +(0.0729192 - 2.71714i) q^{42} -4.28963 q^{43} +(-12.4812 - 0.670390i) q^{44} +1.00000i q^{45} +(2.66102 + 6.23851i) q^{46} -4.88544i q^{47} +(-0.428461 + 3.97699i) q^{48} -3.30592 q^{49} +(1.41370 + 0.0379392i) q^{50} +0.0974606 q^{51} +(2.58683 + 0.138944i) q^{52} -2.10859i q^{53} +(-0.0379392 + 1.41370i) q^{54} +6.24957i q^{55} +(-5.41863 - 0.437095i) q^{56} +1.71456i q^{57} +(-8.69343 - 0.233303i) q^{58} +9.68115i q^{59} +(1.99712 + 0.107270i) q^{60} -6.28577i q^{61} +(-0.0996453 + 3.71302i) q^{62} -1.92200 q^{63} +(7.89656 + 1.28230i) q^{64} -1.29528i q^{65} +(-0.237104 + 8.83505i) q^{66} -4.41547 q^{67} +(0.0104546 - 0.194641i) q^{68} +(4.35922 - 1.99929i) q^{69} +(-0.0729192 + 2.71714i) q^{70} -10.2506i q^{71} +(2.81927 + 0.227417i) q^{72} -6.93152 q^{73} +(-0.371172 + 13.8307i) q^{74} -1.00000i q^{75} +(3.42418 + 0.183920i) q^{76} -12.0117 q^{77} +(0.0491420 - 1.83114i) q^{78} +7.77866 q^{79} +(0.428461 - 3.97699i) q^{80} +1.00000 q^{81} +(-13.4766 - 0.361667i) q^{82} -2.75387 q^{83} +(-0.206172 + 3.83846i) q^{84} -0.0974606 q^{85} +(6.06427 + 0.162745i) q^{86} +6.14940i q^{87} +(17.6192 + 1.42126i) q^{88} -7.14903i q^{89} +(0.0379392 - 1.41370i) q^{90} +2.48953 q^{91} +(-3.52522 - 8.92036i) q^{92} +2.62644 q^{93} +(-0.185350 + 6.90657i) q^{94} -1.71456i q^{95} +(0.756602 - 5.60603i) q^{96} -6.15320i q^{97} +(4.67359 + 0.125424i) q^{98} +6.24957 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} + 2 q^{10} - 20 q^{14} + 48 q^{15} - 6 q^{16} + 4 q^{18} - 16 q^{19} - 28 q^{22} - 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} - 4 q^{30} + 16 q^{32} + 28 q^{34} + 2 q^{36} - 2 q^{40} - 8 q^{41} + 26 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 16 q^{51} - 16 q^{52} + 2 q^{54} - 40 q^{56} - 8 q^{58} - 2 q^{60} + 24 q^{62} - 26 q^{64} + 48 q^{67} + 44 q^{68} - 8 q^{69} + 4 q^{72} - 20 q^{74} + 64 q^{76} + 32 q^{77} + 64 q^{79} - 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} + 40 q^{86} - 2 q^{90} - 28 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 + 2 * q^10 - 20 * q^14 + 48 * q^15 - 6 * q^16 + 4 * q^18 - 16 * q^19 - 28 * q^22 - 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 - 4 * q^30 + 16 * q^32 + 28 * q^34 + 2 * q^36 - 2 * q^40 - 8 * q^41 + 26 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 16 * q^51 - 16 * q^52 + 2 * q^54 - 40 * q^56 - 8 * q^58 - 2 * q^60 + 24 * q^62 - 26 * q^64 + 48 * q^67 + 44 * q^68 - 8 * q^69 + 4 * q^72 - 20 * q^74 + 64 * q^76 + 32 * q^77 + 64 * q^79 - 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 + 40 * q^86 - 2 * q^90 - 28 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.41370	−	0.0379392i	−0.999640	−	0.0268271i
$2$	−1.41370	−	0.0379392i	−0.999640	−	0.0268271i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.99712	+	0.107270i	0.998561	+	0.0536349i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.0379392	−	1.41370i	0.0154886	−	0.577142i
$7$	1.92200			0.726447			0.363224	−	0.931702i	$-0.381676\pi$
$7$	1.92200			0.726447			0.363224	+	0.931702i	$0.381676\pi$
$8$	−2.81927	−	0.227417i	−0.996762	−	0.0804041i
$9$	−1.00000			−0.333333
$10$	−0.0379392	+	1.41370i	−0.0119974	+	0.447053i
$11$	−6.24957			−1.88432			−0.942159	−	0.335167i	$-0.891207\pi$
$11$	−6.24957			−1.88432			−0.942159	+	0.335167i	$0.891207\pi$
$12$	−0.107270	+	1.99712i	−0.0309661	+	0.576519i
$13$	1.29528			0.359246			0.179623	−	0.983736i	$-0.442512\pi$
$13$	1.29528			0.359246			0.179623	+	0.983736i	$0.442512\pi$
$14$	−2.71714	−	0.0729192i	−0.726186	−	0.0194885i
$15$	1.00000			0.258199
$16$	3.97699	+	0.428461i	0.994247	+	0.107115i
$17$		−	0.0974606i		−	0.0236377i	−0.999930	−	0.0118188i	$-0.996238\pi$
$17$		−	0.0974606i		−	0.0236377i	0.999930	−	0.0118188i	$-0.00376214\pi$
$18$	1.41370	+	0.0379392i	0.333213	+	0.00894236i
$19$	1.71456			0.393346			0.196673	−	0.980469i	$-0.436986\pi$
$19$	1.71456			0.393346			0.196673	+	0.980469i	$0.436986\pi$
$20$	0.107270	−	1.99712i	0.0239862	−	0.446570i
$21$			1.92200i			0.419415i
$22$	8.83505	+	0.237104i	1.88364	+	0.0505508i
$23$	−1.99929	−	4.35922i	−0.416881	−	0.908961i
$23$	−1.99929	−	4.35922i	−0.416881	−	0.908961i
$24$	0.227417	−	2.81927i	0.0464213	−	0.575481i
$25$	−1.00000			−0.200000
$26$	−1.83114	−	0.0491420i	−0.359117	−	0.00963753i
$27$		−	1.00000i		−	0.192450i
$28$	3.83846	+	0.206172i	0.725402	+	0.0389629i
$29$	6.14940			1.14191			0.570957	−	0.820980i	$-0.306572\pi$
$29$	6.14940			1.14191			0.570957	+	0.820980i	$0.306572\pi$
$30$	−1.41370	−	0.0379392i	−0.258106	−	0.00692673i
$31$		−	2.62644i		−	0.471723i	−0.971787	−	0.235862i	$-0.924209\pi$
$31$		−	2.62644i		−	0.471723i	0.971787	−	0.235862i	$-0.0757912\pi$
$32$	−5.60603	−	0.756602i	−0.991015	−	0.133750i
$33$		−	6.24957i		−	1.08791i
$34$	−0.00369758	+	0.137780i	−0.000634130	+	0.0236291i
$35$		−	1.92200i		−	0.324877i
$36$	−1.99712	−	0.107270i	−0.332854	−	0.0178783i
$37$		−	9.78333i		−	1.60837i	−0.594379	−	0.804185i	$-0.702602\pi$
$37$		−	9.78333i		−	1.60837i	0.594379	−	0.804185i	$-0.297398\pi$
$38$	−2.42388	−	0.0650490i	−0.393205	−	0.0105523i
$39$			1.29528i			0.207411i
$40$	−0.227417	+	2.81927i	−0.0359578	+	0.445766i
$41$	9.53279			1.48877			0.744386	−	0.667750i	$-0.232742\pi$
$41$	9.53279			1.48877			0.744386	+	0.667750i	$0.232742\pi$
$42$	0.0729192	−	2.71714i	0.0112517	−	0.419264i
$43$	−4.28963			−0.654163			−0.327081	−	0.944996i	$-0.606065\pi$
$43$	−4.28963			−0.654163			−0.327081	+	0.944996i	$0.606065\pi$
$44$	−12.4812	−	0.670390i	−1.88161	−	0.101065i
$45$			1.00000i			0.149071i
$46$	2.66102	+	6.23851i	0.392347	+	0.919817i
$47$		−	4.88544i		−	0.712615i	−0.934369	−	0.356307i	$-0.884036\pi$
$47$		−	4.88544i		−	0.712615i	0.934369	−	0.356307i	$-0.115964\pi$
$48$	−0.428461	+	3.97699i	−0.0618431	+	0.574029i
$49$	−3.30592			−0.472274
$50$	1.41370	+	0.0379392i	0.199928	+	0.00536542i
$51$	0.0974606			0.0136472
$52$	2.58683	+	0.138944i	0.358729	+	0.0192681i
$53$		−	2.10859i		−	0.289637i	−0.989458	−	0.144818i	$-0.953740\pi$
$53$		−	2.10859i		−	0.289637i	0.989458	−	0.144818i	$-0.0462598\pi$
$54$	−0.0379392	+	1.41370i	−0.00516288	+	0.192381i
$55$			6.24957i			0.842692i
$56$	−5.41863	−	0.437095i	−0.724095	−	0.0584093i
$57$			1.71456i			0.227099i
$58$	−8.69343	−	0.233303i	−1.14150	−	0.0306342i
$59$			9.68115i			1.26038i	0.776442	+	0.630189i	$0.217023\pi$
$59$			9.68115i			1.26038i	−0.776442	+	0.630189i	$0.782977\pi$
$60$	1.99712	+	0.107270i	0.257827	+	0.0138485i
$61$		−	6.28577i		−	0.804811i	−0.915462	−	0.402405i	$-0.868174\pi$
$61$		−	6.28577i		−	0.804811i	0.915462	−	0.402405i	$-0.131826\pi$
$62$	−0.0996453	+	3.71302i	−0.0126550	+	0.471553i
$63$	−1.92200			−0.242149
$64$	7.89656	+	1.28230i	0.987070	+	0.160287i
$65$		−	1.29528i		−	0.160660i
$66$	−0.237104	+	8.83505i	−0.0291855	+	1.08752i
$67$	−4.41547			−0.539435			−0.269717	−	0.962939i	$-0.586930\pi$
$67$	−4.41547			−0.539435			−0.269717	+	0.962939i	$0.586930\pi$
$68$	0.0104546	−	0.194641i	0.00126780	−	0.0236036i
$69$	4.35922	−	1.99929i	0.524789	−	0.240687i
$70$	−0.0729192	+	2.71714i	−0.00871551	+	0.324760i
$71$		−	10.2506i		−	1.21653i	−0.793736	−	0.608263i	$-0.791867\pi$
$71$		−	10.2506i		−	1.21653i	0.793736	−	0.608263i	$-0.208133\pi$
$72$	2.81927	+	0.227417i	0.332254	+	0.0268014i
$73$	−6.93152			−0.811273			−0.405637	−	0.914034i	$-0.632950\pi$
$73$	−6.93152			−0.811273			−0.405637	+	0.914034i	$0.632950\pi$
$74$	−0.371172	+	13.8307i	−0.0431479	+	1.60779i
$75$		−	1.00000i		−	0.115470i
$76$	3.42418	+	0.183920i	0.392780	+	0.0210971i
$77$	−12.0117			−1.36886
$78$	0.0491420	−	1.83114i	0.00556423	−	0.207336i
$79$	7.77866			0.875168			0.437584	−	0.899178i	$-0.355834\pi$
$79$	7.77866			0.875168			0.437584	+	0.899178i	$0.355834\pi$
$80$	0.428461	−	3.97699i	0.0479034	−	0.444641i
$81$	1.00000			0.111111
$82$	−13.4766	−	0.361667i	−1.48824	−	0.0399394i
$83$	−2.75387			−0.302276			−0.151138	−	0.988513i	$-0.548294\pi$
$83$	−2.75387			−0.302276			−0.151138	+	0.988513i	$0.548294\pi$
$84$	−0.206172	+	3.83846i	−0.0224952	+	0.418811i
$85$	−0.0974606			−0.0105711
$86$	6.06427	+	0.162745i	0.653927	+	0.0175493i
$87$			6.14940i			0.659285i
$88$	17.6192	+	1.42126i	1.87822	+	0.151507i
$89$		−	7.14903i		−	0.757796i	−0.925439	−	0.378898i	$-0.876303\pi$
$89$		−	7.14903i		−	0.757796i	0.925439	−	0.378898i	$-0.123697\pi$
$90$	0.0379392	−	1.41370i	0.00399915	−	0.149018i
$91$	2.48953			0.260973
$92$	−3.52522	−	8.92036i	−0.367529	−	0.930012i
$93$	2.62644			0.272350
$94$	−0.185350	+	6.90657i	−0.0191174	+	0.712358i
$95$		−	1.71456i		−	0.175910i
$96$	0.756602	−	5.60603i	0.0772203	−	0.572163i
$97$		−	6.15320i		−	0.624763i	−0.949957	−	0.312381i	$-0.898873\pi$
$97$		−	6.15320i		−	0.624763i	0.949957	−	0.312381i	$-0.101127\pi$
$98$	4.67359	+	0.125424i	0.472104	+	0.0126697i
$99$	6.24957			0.628106
$100$	−1.99712	−	0.107270i	−0.199712	−	0.0107270i
$101$	9.08616			0.904107			0.452053	−	0.891991i	$-0.350692\pi$
$101$	9.08616			0.904107			0.452053	+	0.891991i	$0.350692\pi$
$102$	−0.137780	−	0.00369758i	−0.0136423	−	0.000366115i
$103$	6.18915			0.609835			0.304917	−	0.952379i	$-0.401371\pi$
$103$	6.18915			0.609835			0.304917	+	0.952379i	$0.401371\pi$
$104$	−3.65175	−	0.294569i	−0.358083	−	0.0288849i
$105$	1.92200			0.187568
$106$	−0.0799983	+	2.98092i	−0.00777012	+	0.289533i
$107$	−7.47731			−0.722859			−0.361429	−	0.932400i	$-0.617711\pi$
$107$	−7.47731			−0.722859			−0.361429	+	0.932400i	$0.617711\pi$
$108$	0.107270	−	1.99712i	0.0103220	−	0.192173i
$109$		−	9.73776i		−	0.932708i	−0.884598	−	0.466354i	$-0.845567\pi$
$109$		−	9.73776i		−	0.932708i	0.884598	−	0.466354i	$-0.154433\pi$
$110$	0.237104	−	8.83505i	0.0226070	−	0.842389i
$111$	9.78333			0.928593
$112$	7.64376	+	0.823502i	0.722268	+	0.0778137i
$113$		−	7.94496i		−	0.747399i	−0.927550	−	0.373699i	$-0.878089\pi$
$113$		−	7.94496i		−	0.747399i	0.927550	−	0.373699i	$-0.121911\pi$
$114$	0.0650490	−	2.42388i	0.00609239	−	0.227017i
$115$	−4.35922	+	1.99929i	−0.406500	+	0.186435i
$116$	12.2811	+	0.659644i	1.14027	+	0.0612464i
$117$	−1.29528			−0.119749
$118$	0.367296	−	13.6863i	0.0338123	−	1.25992i
$119$		−	0.187319i		−	0.0171715i
$120$	−2.81927	−	0.227417i	−0.257363	−	0.0207602i
$121$	28.0572			2.55065
$122$	−0.238478	+	8.88623i	−0.0215907	+	0.804521i
$123$			9.53279i			0.859543i
$124$	0.281738	−	5.24533i	0.0253008	−	0.471044i
$125$			1.00000i			0.0894427i
$126$	2.71714	+	0.0729192i	0.242062	+	0.00649616i
$127$		−	16.0271i		−	1.42218i	−0.703102	−	0.711089i	$-0.748202\pi$
$127$		−	16.0271i		−	1.42218i	0.703102	−	0.711089i	$-0.251798\pi$
$128$	−11.1148	−	2.11238i	−0.982415	−	0.186710i
$129$		−	4.28963i		−	0.377681i
$130$	−0.0491420	+	1.83114i	−0.00431004	+	0.160602i
$131$			3.02553i			0.264342i	0.991227	+	0.132171i	$0.0421948\pi$
$131$			3.02553i			0.264342i	−0.991227	+	0.132171i	$0.957805\pi$
$132$	0.670390	−	12.4812i	0.0583500	−	1.08635i
$133$	3.29538			0.285745
$134$	6.24216	+	0.167519i	0.539241	+	0.0144715i
$135$	−1.00000			−0.0860663
$136$	−0.0221642	+	0.274768i	−0.00190056	+	0.0235611i
$137$		−	9.42633i		−	0.805346i	−0.915344	−	0.402673i	$-0.868081\pi$
$137$		−	9.42633i		−	0.805346i	0.915344	−	0.402673i	$-0.131919\pi$
$138$	−6.23851	+	2.66102i	−0.531057	+	0.226521i
$139$			17.8819i			1.51672i	0.651836	+	0.758360i	$0.273999\pi$
$139$			17.8819i			1.51672i	−0.651836	+	0.758360i	$0.726001\pi$
$140$	0.206172	−	3.83846i	0.0174247	−	0.324409i
$141$	4.88544			0.411428
$142$	−0.388901	+	14.4914i	−0.0326358	+	1.21609i
$143$	−8.09495			−0.676934
$144$	−3.97699	−	0.428461i	−0.331416	−	0.0357051i
$145$		−	6.14940i		−	0.510680i
$146$	9.79913	+	0.262977i	0.810982	+	0.0217641i
$147$		−	3.30592i		−	0.272668i
$148$	1.04946	−	19.5385i	0.0862647	−	1.60605i
$149$		−	12.9361i		−	1.05977i	−0.848070	−	0.529884i	$-0.822235\pi$
$149$		−	12.9361i		−	1.05977i	0.848070	−	0.529884i	$-0.177765\pi$
$150$	−0.0379392	+	1.41370i	−0.00309773	+	0.115428i
$151$			1.71940i			0.139923i	0.997550	+	0.0699615i	$0.0222877\pi$
$151$			1.71940i			0.139923i	−0.997550	+	0.0699615i	$0.977712\pi$
$152$	−4.83380	−	0.389919i	−0.392073	−	0.0316266i
$153$			0.0974606i			0.00787922i
$154$	16.9810	+	0.455714i	1.36836	+	0.0367225i
$155$	−2.62644			−0.210961
$156$	−0.138944	+	2.58683i	−0.0111245	+	0.207112i
$157$		−	19.1021i		−	1.52452i	−0.647273	−	0.762258i	$-0.724091\pi$
$157$		−	19.1021i		−	1.52452i	0.647273	−	0.762258i	$-0.275909\pi$
$158$	−10.9967	−	0.295116i	−0.874853	−	0.0234782i
$159$	2.10859			0.167222
$160$	−0.756602	+	5.60603i	−0.0598146	+	0.443195i
$161$	−3.84264	−	8.37842i	−0.302842	−	0.660312i
$162$	−1.41370	−	0.0379392i	−0.111071	−	0.00298079i
$163$			12.7177i			0.996126i	0.867141	+	0.498063i	$0.165955\pi$
$163$			12.7177i			0.996126i	−0.867141	+	0.498063i	$0.834045\pi$
$164$	19.0381	+	1.02258i	1.48663	+	0.0798501i
$165$	−6.24957			−0.486529
$166$	3.89315	+	0.104480i	0.302167	+	0.00810919i
$167$			9.06933i			0.701806i	0.936412	+	0.350903i	$0.114125\pi$
$167$			9.06933i			0.701806i	−0.936412	+	0.350903i	$0.885875\pi$
$168$	0.437095	−	5.41863i	0.0337226	−	0.418057i
$169$	−11.3222			−0.870942
$170$	0.137780	+	0.00369758i	0.0105673	+	0.000283591i
$171$	−1.71456			−0.131115
$172$	−8.56692	−	0.460148i	−0.653221	−	0.0350859i
$173$	17.6920			1.34510			0.672548	−	0.740054i	$-0.265200\pi$
$173$	17.6920			1.34510			0.672548	+	0.740054i	$0.265200\pi$
$174$	0.233303	−	8.69343i	0.0176867	−	0.659047i
$175$	−1.92200			−0.145289
$176$	−24.8545	−	2.67770i	−1.87348	−	0.201839i
$177$	−9.68115			−0.727680
$178$	−0.271229	+	10.1066i	−0.0203295	+	0.757523i
$179$		−	10.3452i		−	0.773239i	−0.922239	−	0.386619i	$-0.873643\pi$
$179$		−	10.3452i		−	0.773239i	0.922239	−	0.386619i	$-0.126357\pi$
$180$	−0.107270	+	1.99712i	−0.00799542	+	0.148857i
$181$			25.6924i			1.90970i	0.297082	+	0.954852i	$0.403986\pi$
$181$			25.6924i			1.90970i	−0.297082	+	0.954852i	$0.596014\pi$
$182$	−3.51946	−	0.0944508i	−0.260880	−	0.00700116i
$183$	6.28577			0.464658
$184$	4.64519	+	12.7445i	0.342448	+	0.939537i
$185$	−9.78333			−0.719285
$186$	−3.71302	−	0.0996453i	−0.272251	−	0.00730635i
$187$			0.609087i			0.0445409i
$188$	0.524060	−	9.75682i	0.0382210	−	0.711589i
$189$		−	1.92200i		−	0.139805i
$190$	−0.0650490	+	2.42388i	−0.00471915	+	0.175846i
$191$	17.8099			1.28868			0.644339	−	0.764740i	$-0.277132\pi$
$191$	17.8099			1.28868			0.644339	+	0.764740i	$0.277132\pi$
$192$	−1.28230	+	7.89656i	−0.0925420	+	0.569885i
$193$	19.8025			1.42541			0.712707	−	0.701462i	$-0.247469\pi$
$193$	19.8025			1.42541			0.712707	+	0.701462i	$0.247469\pi$
$194$	−0.233448	+	8.69881i	−0.0167606	+	0.624538i
$195$	1.29528			0.0927570
$196$	−6.60232	−	0.354625i	−0.471595	−	0.0253304i
$197$	−5.77784			−0.411654			−0.205827	−	0.978588i	$-0.565988\pi$
$197$	−5.77784			−0.411654			−0.205827	+	0.978588i	$0.565988\pi$
$198$	−8.83505	−	0.237104i	−0.627880	−	0.0168503i
$199$	−15.9359			−1.12967			−0.564834	−	0.825204i	$-0.691060\pi$
$199$	−15.9359			−1.12967			−0.564834	+	0.825204i	$0.691060\pi$
$200$	2.81927	+	0.227417i	0.199352	+	0.0160808i
$201$		−	4.41547i		−	0.311443i
$202$	−12.8451	−	0.344722i	−0.903782	−	0.0242546i
$203$	11.8191			0.829541
$204$	0.194641	+	0.0104546i	0.0136276	+	0.000731966i
$205$		−	9.53279i		−	0.665799i
$206$	−8.74963	−	0.234812i	−0.609615	−	0.0163601i
$207$	1.99929	+	4.35922i	0.138960	+	0.302987i
$208$	5.15131	+	0.554978i	0.357179	+	0.0384808i
$209$	−10.7152			−0.741189
$210$	−2.71714	−	0.0729192i	−0.187500	−	0.00503190i
$211$		−	11.9753i		−	0.824413i	−0.911091	−	0.412206i	$-0.864758\pi$
$211$		−	11.9753i		−	0.824413i	0.911091	−	0.412206i	$-0.135242\pi$
$212$	0.226188	−	4.21111i	0.0155346	−	0.289220i
$213$	10.2506			0.702361
$214$	10.5707	+	0.283683i	0.722598	+	0.0193922i
$215$			4.28963i			0.292550i
$216$	−0.227417	+	2.81927i	−0.0154738	+	0.191827i
$217$		−	5.04802i		−	0.342682i
$218$	−0.369443	+	13.7663i	−0.0250218	+	0.932372i
$219$		−	6.93152i		−	0.468389i
$220$	−0.670390	+	12.4812i	−0.0451977	+	0.841479i
$221$		−	0.126239i		−	0.00849174i
$222$	−13.8307	−	0.371172i	−0.928258	−	0.0249114i
$223$		−	15.7556i		−	1.05507i	−0.849532	−	0.527537i	$-0.823116\pi$
$223$		−	15.7556i		−	1.05507i	0.849532	−	0.527537i	$-0.176884\pi$
$224$	−10.7748	−	1.45419i	−0.719920	−	0.0971620i
$225$	1.00000			0.0666667
$226$	−0.301426	+	11.2318i	−0.0200505	+	0.747130i
$227$	−19.1549			−1.27136			−0.635678	−	0.771954i	$-0.719280\pi$
$227$	−19.1549			−1.27136			−0.635678	+	0.771954i	$0.719280\pi$
$228$	−0.183920	+	3.42418i	−0.0121804	+	0.226772i
$229$			28.6485i			1.89315i	0.322485	+	0.946575i	$0.395482\pi$
$229$			28.6485i			1.89315i	−0.322485	+	0.946575i	$0.604518\pi$
$230$	6.23851	−	2.66102i	0.411355	−	0.175463i
$231$		−	12.0117i		−	0.790310i
$232$	−17.3368	−	1.39848i	−1.13822	−	0.0918145i
$233$	3.02005			0.197850			0.0989250	−	0.995095i	$-0.468460\pi$
$233$	3.02005			0.197850			0.0989250	+	0.995095i	$0.468460\pi$
$234$	1.83114	+	0.0491420i	0.119706	+	0.00321251i
$235$	−4.88544			−0.318691
$236$	−1.03849	+	19.3344i	−0.0676002	+	1.25856i
$237$			7.77866i			0.505278i
$238$	−0.00710674	+	0.264814i	−0.000460662	+	0.0171653i
$239$		−	14.7331i		−	0.953008i	−0.879172	−	0.476504i	$-0.841904\pi$
$239$		−	14.7331i		−	0.953008i	0.879172	−	0.476504i	$-0.158096\pi$
$240$	3.97699	+	0.428461i	0.256713	+	0.0276571i
$241$		−	17.3831i		−	1.11975i	−0.828578	−	0.559873i	$-0.810850\pi$
$241$		−	17.3831i		−	1.11975i	0.828578	−	0.559873i	$-0.189150\pi$
$242$	−39.6646	−	1.06447i	−2.54973	−	0.0684266i
$243$			1.00000i			0.0641500i
$244$	0.674273	−	12.5535i	0.0431659	−	0.803653i
$245$			3.30592i			0.211208i
$246$	0.361667	−	13.4766i	0.0230590	−	0.859234i
$247$	2.22083			0.141308
$248$	−0.597298	+	7.40465i	−0.0379285	+	0.470196i
$249$		−	2.75387i		−	0.174519i
$250$	0.0379392	−	1.41370i	0.00239949	−	0.0894105i
$251$	−2.22901			−0.140694			−0.0703468	−	0.997523i	$-0.522411\pi$
$251$	−2.22901			−0.140694			−0.0703468	+	0.997523i	$0.522411\pi$
$252$	−3.83846	−	0.206172i	−0.241801	−	0.0129876i
$253$	12.4947	+	27.2433i	0.785537	+	1.71277i
$254$	−0.608058	+	22.6576i	−0.0381529	+	1.42167i
$255$		−	0.0974606i		−	0.00610322i
$256$	15.6328	+	3.40797i	0.977053	+	0.212998i
$257$	−7.76681			−0.484480			−0.242240	−	0.970216i	$-0.577882\pi$
$257$	−7.76681			−0.484480			−0.242240	+	0.970216i	$0.577882\pi$
$258$	−0.162745	+	6.06427i	−0.0101321	+	0.377545i
$259$		−	18.8035i		−	1.16840i
$260$	0.138944	−	2.58683i	0.00861697	−	0.160429i
$261$	−6.14940			−0.380638
$262$	0.114786	−	4.27720i	0.00709152	−	0.264247i
$263$	18.5671			1.14490			0.572448	−	0.819941i	$-0.305994\pi$
$263$	18.5671			1.14490			0.572448	+	0.819941i	$0.305994\pi$
$264$	−1.42126	+	17.6192i	−0.0874725	+	1.08439i
$265$	−2.10859			−0.129530
$266$	−4.65869	−	0.125024i	−0.285642	−	0.00766572i
$267$	7.14903			0.437513
$268$	−8.81822	−	0.473646i	−0.538659	−	0.0289325i
$269$	−9.35582			−0.570434			−0.285217	−	0.958463i	$-0.592066\pi$
$269$	−9.35582			−0.570434			−0.285217	+	0.958463i	$0.592066\pi$
$270$	1.41370	+	0.0379392i	0.0860353	+	0.00230891i
$271$		−	2.98161i		−	0.181120i	−0.995891	−	0.0905601i	$-0.971134\pi$
$271$		−	2.98161i		−	0.181120i	0.995891	−	0.0905601i	$-0.0288657\pi$
$272$	0.0417581	−	0.387599i	0.00253196	−	0.0235017i
$273$			2.48953i			0.150673i
$274$	−0.357628	+	13.3260i	−0.0216051	+	0.805056i
$275$	6.24957			0.376864
$276$	8.92036	−	3.52522i	0.536943	−	0.212193i
$277$	−25.4380			−1.52842			−0.764210	−	0.644968i	$-0.776871\pi$
$277$	−25.4380			−1.52842			−0.764210	+	0.644968i	$0.776871\pi$
$278$	0.678424	−	25.2797i	0.0406892	−	1.51617i
$279$			2.62644i			0.157241i
$280$	−0.437095	+	5.41863i	−0.0261214	+	0.323825i
$281$			21.1926i			1.26425i	0.774868	+	0.632123i	$0.217816\pi$
$281$			21.1926i			1.26425i	−0.774868	+	0.632123i	$0.782184\pi$
$282$	−6.90657	−	0.185350i	−0.411280	−	0.0110374i
$283$	0.175124			0.0104101			0.00520503	−	0.999986i	$-0.498343\pi$
$283$	0.175124			0.0104101			0.00520503	+	0.999986i	$0.498343\pi$
$284$	1.09958	−	20.4717i	0.0652482	−	1.21477i
$285$	1.71456			0.101562
$286$	11.4439	+	0.307116i	0.676690	+	0.0181602i
$287$	18.3220			1.08151
$288$	5.60603	+	0.756602i	0.330338	+	0.0445832i
$289$	16.9905			0.999441
$290$	−0.233303	+	8.69343i	−0.0137000	+	0.510496i
$291$	6.15320			0.360707
$292$	−13.8431	−	0.743543i	−0.810106	−	0.0435126i
$293$			15.4948i			0.905215i	0.891710	+	0.452607i	$0.149506\pi$
$293$			15.4948i			0.905215i	−0.891710	+	0.452607i	$0.850494\pi$
$294$	−0.125424	+	4.67359i	−0.00731488	+	0.272570i
$295$	9.68115			0.563658
$296$	−2.22490	+	27.5818i	−0.129319	+	1.60316i
$297$			6.24957i			0.362637i
$298$	−0.490787	+	18.2879i	−0.0284305	+	1.05939i
$299$	−2.58965	−	5.64642i	−0.149763	−	0.326541i
$300$	0.107270	−	1.99712i	0.00619322	−	0.115304i
$301$	−8.24467			−0.475215
$302$	0.0652329	−	2.43073i	0.00375373	−	0.139873i
$303$			9.08616i			0.521986i
$304$	6.81877	+	0.734621i	0.391083	+	0.0421334i
$305$	−6.28577			−0.359922
$306$	0.00369758	−	0.137780i	0.000211377	−	0.00787638i
$307$		−	9.10944i		−	0.519903i	−0.965622	−	0.259952i	$-0.916293\pi$
$307$		−	9.10944i		−	0.519903i	0.965622	−	0.259952i	$-0.0837066\pi$
$308$	−23.9888	−	1.28849i	−1.36689	−	0.0734185i
$309$			6.18915i			0.352088i
$310$	3.71302	+	0.0996453i	0.210885	+	0.00565947i
$311$			32.3503i			1.83442i	0.398405	+	0.917210i	$0.369564\pi$
$311$			32.3503i			1.83442i	−0.398405	+	0.917210i	$0.630436\pi$
$312$	0.294569	−	3.65175i	0.0166767	−	0.206739i
$313$		−	1.50590i		−	0.0851185i	−0.999094	−	0.0425593i	$-0.986449\pi$
$313$		−	1.50590i		−	0.0851185i	0.999094	−	0.0425593i	$-0.0135511\pi$
$314$	−0.724721	+	27.0048i	−0.0408983	+	1.52397i
$315$			1.92200i			0.108292i
$316$	15.5349	+	0.834415i	0.873908	+	0.0469395i
$317$	0.340030			0.0190980			0.00954900	−	0.999954i	$-0.496960\pi$
$317$	0.340030			0.0190980			0.00954900	+	0.999954i	$0.496960\pi$
$318$	−2.98092	−	0.0799983i	−0.167162	−	0.00448608i
$319$	−38.4311			−2.15173
$320$	1.28230	−	7.89656i	0.0716827	−	0.441431i
$321$		−	7.47731i		−	0.417343i
$322$	5.11449	+	11.9904i	0.285019	+	0.668199i
$323$		−	0.167102i		−	0.00929778i
$324$	1.99712	+	0.107270i	0.110951	+	0.00595943i
$325$	−1.29528			−0.0718492
$326$	0.482499	−	17.9790i	0.0267232	−	0.995767i
$327$	9.73776			0.538499
$328$	−26.8755	−	2.16792i	−1.48395	−	0.119703i
$329$		−	9.38981i		−	0.517677i
$330$	8.83505	+	0.237104i	0.486354	+	0.0130522i
$331$			13.4000i			0.736533i	0.929720	+	0.368266i	$0.120049\pi$
$331$			13.4000i			0.736533i	−0.929720	+	0.368266i	$0.879951\pi$
$332$	−5.49980	−	0.295407i	−0.301841	−	0.0162125i
$333$			9.78333i			0.536123i
$334$	0.344084	−	12.8214i	0.0188274	−	0.701553i
$335$			4.41547i			0.241243i
$336$	−0.823502	+	7.64376i	−0.0449257	+	0.417001i
$337$			26.3640i			1.43614i	0.695971	+	0.718069i	$0.254974\pi$
$337$			26.3640i			1.43614i	−0.695971	+	0.718069i	$0.745026\pi$
$338$	16.0063	+	0.429557i	0.870629	+	0.0233648i
$339$	7.94496			0.431511
$340$	−0.194641	−	0.0104546i	−0.0105559	−	0.000566979i
$341$			16.4142i			0.888876i
$342$	2.42388	+	0.0650490i	0.131068	+	0.00351745i
$343$	−19.8080			−1.06953
$344$	12.0936	+	0.975535i	0.652045	+	0.0525973i
$345$	−1.99929	−	4.35922i	−0.107638	−	0.234693i
$346$	−25.0112	−	0.671220i	−1.34461	−	0.0360850i
$347$			12.2887i			0.659689i	0.944035	+	0.329845i	$0.106996\pi$
$347$			12.2887i			0.659689i	−0.944035	+	0.329845i	$0.893004\pi$
$348$	−0.659644	+	12.2811i	−0.0353606	+	0.658336i
$349$	−13.9251			−0.745391			−0.372696	−	0.927954i	$-0.621566\pi$
$349$	−13.9251			−0.745391			−0.372696	+	0.927954i	$0.621566\pi$
$350$	2.71714	+	0.0729192i	0.145237	+	0.00389769i
$351$		−	1.29528i		−	0.0691370i
$352$	35.0353	+	4.72844i	1.86739	+	0.252027i
$353$	17.1143			0.910900			0.455450	−	0.890261i	$-0.349478\pi$
$353$	17.1143			0.910900			0.455450	+	0.890261i	$0.349478\pi$
$354$	13.6863	+	0.367296i	0.727418	+	0.0195215i
$355$	−10.2506			−0.544047
$356$	0.766875	−	14.2775i	0.0406443	−	0.756705i
$357$	0.187319			0.00991398
$358$	−0.392490	+	14.6251i	−0.0207438	+	0.772961i
$359$	−36.8689			−1.94586			−0.972932	−	0.231092i	$-0.925770\pi$
$359$	−36.8689			−1.94586			−0.972932	+	0.231092i	$0.925770\pi$
$360$	0.227417	−	2.81927i	0.0119859	−	0.148589i
$361$	−16.0603			−0.845279
$362$	0.974752	−	36.3215i	0.0512318	−	1.90902i
$363$			28.0572i			1.47262i
$364$	4.97189	+	0.267051i	0.260598	+	0.0139973i
$365$			6.93152i			0.362813i
$366$	−8.88623	−	0.238478i	−0.464491	−	0.0124654i
$367$	13.2283			0.690514			0.345257	−	0.938508i	$-0.387792\pi$
$367$	13.2283			0.690514			0.345257	+	0.938508i	$0.387792\pi$
$368$	−6.08340	−	18.1932i	−0.317119	−	0.948386i
$369$	−9.53279			−0.496257
$370$	13.8307	+	0.371172i	0.719026	+	0.0192963i
$371$		−	4.05271i		−	0.210406i
$372$	5.24533	+	0.281738i	0.271957	+	0.0146074i
$373$			0.00180698i			9.35617e-5i	1.00000		4.67808e-5i	$1.48908e-5\pi$
$373$			0.00180698i			9.35617e-5i	−1.00000		4.67808e-5i	$0.999985\pi$
$374$	0.0231083	−	0.861069i	0.00119490	−	0.0445248i
$375$	−1.00000			−0.0516398
$376$	−1.11103	+	13.7734i	−0.0572971	+	0.710308i
$377$	7.96519			0.410228
$378$	−0.0729192	+	2.71714i	−0.00375056	+	0.139755i
$379$	0.264577			0.0135904			0.00679520	−	0.999977i	$-0.497837\pi$
$379$	0.264577			0.0135904			0.00679520	+	0.999977i	$0.497837\pi$
$380$	0.183920	−	3.42418i	0.00943490	−	0.175657i
$381$	16.0271			0.821095
$382$	−25.1779	−	0.675694i	−1.28822	−	0.0345715i
$383$	4.42959			0.226341			0.113171	−	0.993576i	$-0.463899\pi$
$383$	4.42959			0.226341			0.113171	+	0.993576i	$0.463899\pi$
$384$	2.11238	−	11.1148i	0.107797	−	0.567198i
$385$			12.0117i			0.612172i
$386$	−27.9949	−	0.751291i	−1.42490	−	0.0382397i
$387$	4.28963			0.218054
$388$	0.660052	−	12.2887i	0.0335091	−	0.623863i
$389$			29.3890i			1.49008i	0.667020	+	0.745040i	$0.267569\pi$
$389$			29.3890i			1.49008i	−0.667020	+	0.745040i	$0.732431\pi$
$390$	−1.83114	−	0.0491420i	−0.0927236	−	0.00248840i
$391$	−0.424852	+	0.194852i	−0.0214857	+	0.00985410i
$392$	9.32028	+	0.751823i	0.470745	+	0.0379728i
$393$	−3.02553			−0.152618
$394$	8.16815	+	0.219207i	0.411506	+	0.0110435i
$395$		−	7.77866i		−	0.391387i
$396$	12.4812	+	0.670390i	0.627202	+	0.0336884i
$397$	−15.5716			−0.781515			−0.390757	−	0.920494i	$-0.627787\pi$
$397$	−15.5716			−0.781515			−0.390757	+	0.920494i	$0.627787\pi$
$398$	22.5287	+	0.604597i	1.12926	+	0.0303057i
$399$			3.29538i			0.164975i
$400$	−3.97699	−	0.428461i	−0.198849	−	0.0214231i
$401$			25.7115i			1.28397i	0.766716	+	0.641986i	$0.221889\pi$
$401$			25.7115i			1.28397i	−0.766716	+	0.641986i	$0.778111\pi$
$402$	−0.167519	+	6.24216i	−0.00835511	+	0.311331i
$403$		−	3.40198i		−	0.169465i
$404$	18.1462	+	0.974670i	0.902806	+	0.0484917i
$405$		−	1.00000i		−	0.0496904i
$406$	−16.7088	−	0.448409i	−0.829242	−	0.0222542i
$407$			61.1416i			3.03068i
$408$	−0.274768	−	0.0221642i	−0.0136030	−	0.00109729i
$409$	1.10716			0.0547458			0.0273729	−	0.999625i	$-0.491286\pi$
$409$	1.10716			0.0547458			0.0273729	+	0.999625i	$0.491286\pi$
$410$	−0.361667	+	13.4766i	−0.0178615	+	0.665559i
$411$	9.42633			0.464967
$412$	12.3605	+	0.663908i	0.608957	+	0.0327084i
$413$			18.6072i			0.915599i
$414$	−2.66102	−	6.23851i	−0.130782	−	0.306606i
$415$			2.75387i			0.135182i
$416$	−7.26138	−	0.980012i	−0.356018	−	0.0480490i
$417$	−17.8819			−0.875678
$418$	15.1482	+	0.406528i	0.740922	+	0.0198840i
$419$	23.0762			1.12734			0.563672	−	0.825998i	$-0.309388\pi$
$419$	23.0762			1.12734			0.563672	+	0.825998i	$0.309388\pi$
$420$	3.83846	+	0.206172i	0.187298	+	0.0100602i
$421$		−	4.76852i		−	0.232404i	−0.993226	−	0.116202i	$-0.962928\pi$
$421$		−	4.76852i		−	0.232404i	0.993226	−	0.116202i	$-0.0370719\pi$
$422$	−0.454333	+	16.9295i	−0.0221166	+	0.824116i
$423$			4.88544i			0.237538i
$424$	−0.479529	+	5.94468i	−0.0232880	+	0.288699i
$425$			0.0974606i			0.00472753i
$426$	−14.4914	−	0.388901i	−0.702108	−	0.0188423i
$427$		−	12.0813i		−	0.584653i
$428$	−14.9331	−	0.802089i	−0.721818	−	0.0387704i
$429$		−	8.09495i		−	0.390828i
$430$	0.162745	−	6.06427i	0.00784828	−	0.292445i
$431$	−13.0482			−0.628512			−0.314256	−	0.949338i	$-0.601755\pi$
$431$	−13.0482			−0.628512			−0.314256	+	0.949338i	$0.601755\pi$
$432$	0.428461	−	3.97699i	0.0206144	−	0.191343i
$433$			21.6534i			1.04059i	0.853985	+	0.520297i	$0.174179\pi$
$433$			21.6534i			1.04059i	−0.853985	+	0.520297i	$0.825821\pi$
$434$	−0.191518	+	7.13641i	−0.00919316	+	0.342559i
$435$	6.14940			0.294841
$436$	1.04457	−	19.4475i	0.0500257	−	0.931365i
$437$	−3.42790	−	7.47413i	−0.163979	−	0.357536i
$438$	−0.262977	+	9.79913i	−0.0125655	+	0.468220i
$439$			18.4964i			0.882786i	0.897314	+	0.441393i	$0.145516\pi$
$439$			18.4964i			0.882786i	−0.897314	+	0.441393i	$0.854484\pi$
$440$	1.42126	−	17.6192i	0.0677559	−	0.839964i
$441$	3.30592			0.157425
$442$	−0.00478940	+	0.178464i	−0.000227809	+	0.00848868i
$443$		−	26.2925i		−	1.24919i	−0.780948	−	0.624597i	$-0.785263\pi$
$443$		−	26.2925i		−	1.24919i	0.780948	−	0.624597i	$-0.214737\pi$
$444$	19.5385	+	1.04946i	0.927256	+	0.0498049i
$445$	−7.14903			−0.338896
$446$	−0.597756	+	22.2738i	−0.0283046	+	1.05469i
$447$	12.9361			0.611858
$448$	15.1772	+	2.46458i	0.717055	+	0.116440i
$449$	4.40144			0.207717			0.103859	−	0.994592i	$-0.466881\pi$
$449$	4.40144			0.207717			0.103859	+	0.994592i	$0.466881\pi$
$450$	−1.41370	−	0.0379392i	−0.0666427	−	0.00178847i
$451$	−59.5759			−2.80532
$452$	0.852254	−	15.8670i	0.0400866	−	0.746323i
$453$	−1.71940			−0.0807846
$454$	27.0794	+	0.726723i	1.27090	+	0.0341068i
$455$		−	2.48953i		−	0.116711i
$456$	0.389919	−	4.83380i	0.0182596	−	0.226363i
$457$		−	8.03293i		−	0.375765i	−0.982192	−	0.187882i	$-0.939838\pi$
$457$		−	8.03293i		−	0.375765i	0.982192	−	0.187882i	$-0.0601623\pi$
$458$	1.08690	−	40.5006i	0.0507877	−	1.89247i
$459$	−0.0974606			−0.00454907
$460$	−8.92036	+	3.52522i	−0.415914	+	0.164364i
$461$	−18.0381			−0.840116			−0.420058	−	0.907497i	$-0.637990\pi$
$461$	−18.0381			−0.840116			−0.420058	+	0.907497i	$0.637990\pi$
$462$	−0.455714	+	16.9810i	−0.0212017	+	0.790026i
$463$			4.70440i			0.218632i	0.994007	+	0.109316i	$0.0348661\pi$
$463$			4.70440i			0.218632i	−0.994007	+	0.109316i	$0.965134\pi$
$464$	24.4561	+	2.63478i	1.13534	+	0.122317i
$465$		−	2.62644i		−	0.121798i
$466$	−4.26946	−	0.114578i	−0.197779	−	0.00530774i
$467$	−13.3561			−0.618045			−0.309022	−	0.951055i	$-0.600002\pi$
$467$	−13.3561			−0.618045			−0.309022	+	0.951055i	$0.600002\pi$
$468$	−2.58683	−	0.138944i	−0.119576	−	0.00642271i
$469$	−8.48652			−0.391871
$470$	6.90657	+	0.185350i	0.318576	+	0.00854955i
$471$	19.1021			0.880180
$472$	2.20166	−	27.2938i	0.101340	−	1.25630i
$473$	26.8084			1.23265
$474$	0.295116	−	10.9967i	0.0135551	−	0.505096i
$475$	−1.71456			−0.0786692
$476$	0.0200937	−	0.374099i	0.000920992	−	0.0171468i
$477$			2.10859i			0.0965457i
$478$	−0.558964	+	20.8283i	−0.0255664	+	0.952665i
$479$	41.2040			1.88266			0.941329	−	0.337490i	$-0.109578\pi$
$479$	41.2040			1.88266			0.941329	+	0.337490i	$0.109578\pi$
$480$	−5.60603	−	0.756602i	−0.255879	−	0.0345340i
$481$		−	12.6722i		−	0.577801i
$482$	−0.659503	+	24.5746i	−0.0300395	+	1.11934i
$483$	8.37842	−	3.84264i	0.381231	−	0.174846i
$484$	56.0336	+	3.00969i	2.54698	+	0.136804i
$485$	−6.15320			−0.279402
$486$	0.0379392	−	1.41370i	0.00172096	−	0.0641269i
$487$		−	32.4899i		−	1.47226i	−0.676842	−	0.736128i	$-0.736652\pi$
$487$		−	32.4899i		−	1.47226i	0.676842	−	0.736128i	$-0.263348\pi$
$488$	−1.42949	+	17.7213i	−0.0647101	+	0.802205i
$489$	−12.7177			−0.575114
$490$	0.125424	−	4.67359i	0.00566608	−	0.211131i
$491$		−	36.7932i		−	1.66045i	−0.557427	−	0.830226i	$-0.688211\pi$
$491$		−	36.7932i		−	1.66045i	0.557427	−	0.830226i	$-0.311789\pi$
$492$	−1.02258	+	19.0381i	−0.0461015	+	0.858306i
$493$		−	0.599324i		−	0.0269922i
$494$	−3.13960	−	0.0842567i	−0.141257	−	0.00379089i
$495$		−	6.24957i		−	0.280897i
$496$	1.12533	−	10.4453i	0.0505288	−	0.469009i
$497$		−	19.7017i		−	0.883742i
$498$	−0.104480	+	3.89315i	−0.00468184	+	0.174456i
$499$		−	41.1305i		−	1.84125i	−0.390444	−	0.920627i	$-0.627678\pi$
$499$		−	41.1305i		−	1.84125i	0.390444	−	0.920627i	$-0.372322\pi$
$500$	−0.107270	+	1.99712i	−0.00479725	+	0.0893140i
$501$	−9.06933			−0.405188
$502$	3.15116	+	0.0845668i	0.140643	+	0.00377440i
$503$	−15.8055			−0.704733			−0.352366	−	0.935862i	$-0.614623\pi$
$503$	−15.8055			−0.704733			−0.352366	+	0.935862i	$0.614623\pi$
$504$	5.41863	+	0.437095i	0.241365	+	0.0194698i
$505$		−	9.08616i		−	0.404329i
$506$	−16.6303	−	38.9880i	−0.739306	−	1.73323i
$507$		−	11.3222i		−	0.502839i
$508$	1.71923	−	32.0081i	0.0762784	−	1.42013i
$509$	−8.10190			−0.359111			−0.179555	−	0.983748i	$-0.557466\pi$
$509$	−8.10190			−0.359111			−0.179555	+	0.983748i	$0.557466\pi$
$510$	−0.00369758	+	0.137780i	−0.000163732	+	0.00610102i
$511$	−13.3224			−0.589347
$512$	−21.9709	−	5.41096i	−0.970987	−	0.239133i
$513$		−	1.71456i		−	0.0756995i
$514$	10.9800	+	0.294667i	0.484306	+	0.0129972i
$515$		−	6.18915i		−	0.272726i
$516$	0.460148	−	8.56692i	0.0202569	−	0.377137i
$517$			30.5319i			1.34279i
$518$	−0.713392	+	26.5827i	−0.0313447	+	1.16798i
$519$			17.6920i			0.776591i
$520$	−0.294569	+	3.65175i	−0.0129177	+	0.160140i
$521$		−	7.98084i		−	0.349647i	−0.984600	−	0.174824i	$-0.944065\pi$
$521$		−	7.98084i		−	0.349647i	0.984600	−	0.174824i	$-0.0559355\pi$
$522$	8.69343	+	0.233303i	0.380501	+	0.0102114i
$523$	−22.2528			−0.973047			−0.486524	−	0.873667i	$-0.661735\pi$
$523$	−22.2528			−0.973047			−0.486524	+	0.873667i	$0.661735\pi$
$524$	−0.324548	+	6.04235i	−0.0141779	+	0.263961i
$525$		−	1.92200i		−	0.0838829i
$526$	−26.2484	−	0.704421i	−1.14448	−	0.0307142i
$527$	−0.255975			−0.0111504
$528$	2.67770	−	24.8545i	0.116532	−	1.08165i
$529$	−15.0057	+	17.4307i	−0.652420	+	0.757858i
$530$	2.98092	+	0.0799983i	0.129483	+	0.00347490i
$531$		−	9.68115i		−	0.420126i
$532$	6.58126	+	0.353494i	0.285334	+	0.0153259i
$533$	12.3476			0.534836
$534$	−10.1066	−	0.271229i	−0.437356	−	0.0117372i
$535$			7.47731i			0.323272i
$536$	12.4484	+	1.00415i	0.537688	+	0.0433728i
$537$	10.3452			0.446430
$538$	13.2264	+	0.354953i	0.570229	+	0.0153031i
$539$	20.6606			0.889915
$540$	−1.99712	−	0.107270i	−0.0859424	−	0.00461616i
$541$	18.5599			0.797954			0.398977	−	0.916961i	$-0.369365\pi$
$541$	18.5599			0.797954			0.398977	+	0.916961i	$0.369365\pi$
$542$	−0.113120	+	4.21512i	−0.00485893	+	0.181055i
$543$	−25.6924			−1.10257
$544$	−0.0737388	+	0.546367i	−0.00316153	+	0.0234253i
$545$	−9.73776			−0.417120
$546$	0.0944508	−	3.51946i	0.00404212	−	0.150619i
$547$		−	24.6971i		−	1.05597i	−0.849253	−	0.527985i	$-0.822948\pi$
$547$		−	24.6971i		−	1.05597i	0.849253	−	0.527985i	$-0.177052\pi$
$548$	1.01116	−	18.8255i	0.0431946	−	0.804187i
$549$			6.28577i			0.268270i
$550$	−8.83505	−	0.237104i	−0.376728	−	0.0101102i
$551$	10.5435			0.449168
$552$	−12.7445	+	4.64519i	−0.542442	+	0.197712i
$553$	14.9506			0.635763
$554$	35.9618	+	0.965097i	1.52787	+	0.0410031i
$555$		−	9.78333i		−	0.415279i
$556$	−1.91818	+	35.7122i	−0.0813491	+	1.51454i
$557$			25.5238i			1.08148i	0.841191	+	0.540739i	$0.181855\pi$
$557$			25.5238i			1.08148i	−0.841191	+	0.540739i	$0.818145\pi$
$558$	0.0996453	−	3.71302i	0.00421832	−	0.157184i
$559$	−5.55628			−0.235006
$560$	0.823502	−	7.64376i	0.0347993	−	0.323008i
$561$	−0.609087			−0.0257157
$562$	0.804032	−	29.9601i	0.0339160	−	1.26379i
$563$	3.42487			0.144341			0.0721705	−	0.997392i	$-0.477007\pi$
$563$	3.42487			0.144341			0.0721705	+	0.997392i	$0.477007\pi$
$564$	9.75682	+	0.524060i	0.410836	+	0.0220669i
$565$	−7.94496			−0.334247
$566$	−0.247574	−	0.00664408i	−0.0104063	−	0.000279272i
$567$	1.92200			0.0807164
$568$	−2.33117	+	28.8993i	−0.0978136	+	1.21259i
$569$		−	25.0302i		−	1.04932i	−0.851311	−	0.524661i	$-0.824192\pi$
$569$		−	25.0302i		−	1.04932i	0.851311	−	0.524661i	$-0.175808\pi$
$570$	−2.42388	−	0.0650490i	−0.101525	−	0.00272460i
$571$	16.1945			0.677719			0.338859	−	0.940837i	$-0.389959\pi$
$571$	16.1945			0.677719			0.338859	+	0.940837i	$0.389959\pi$
$572$	−16.1666	−	0.868344i	−0.675960	−	0.0363073i
$573$			17.8099i			0.744019i
$574$	−25.9019	−	0.695123i	−1.08113	−	0.0290139i
$575$	1.99929	+	4.35922i	0.0833763	+	0.181792i
$576$	−7.89656	−	1.28230i	−0.329023	−	0.0534292i
$577$	11.5547			0.481027			0.240514	−	0.970646i	$-0.422684\pi$
$577$	11.5547			0.481027			0.240514	+	0.970646i	$0.422684\pi$
$578$	−24.0195	−	0.644607i	−0.999082	−	0.0268121i
$579$			19.8025i			0.822963i
$580$	0.659644	−	12.2811i	0.0273902	−	0.509945i
$581$	−5.29293			−0.219588
$582$	−8.69881	−	0.233448i	−0.360577	−	0.00967672i
$583$			13.1778i			0.545768i
$584$	19.5418	+	1.57635i	0.808647	+	0.0652297i
$585$			1.29528i			0.0535533i
$586$	0.587860	−	21.9050i	0.0242843	−	0.904889i
$587$			31.7042i			1.30857i	0.756246	+	0.654287i	$0.227031\pi$
$587$			31.7042i			1.30857i	−0.756246	+	0.654287i	$0.772969\pi$
$588$	0.354625	−	6.60232i	0.0146245	−	0.272275i
$589$		−	4.50319i		−	0.185551i
$590$	−13.6863	−	0.367296i	−0.563456	−	0.0151213i
$591$		−	5.77784i		−	0.237668i
$592$	4.19178	−	38.9082i	0.172281	−	1.59912i
$593$	7.40630			0.304140			0.152070	−	0.988370i	$-0.451406\pi$
$593$	7.40630			0.304140			0.152070	+	0.988370i	$0.451406\pi$
$594$	0.237104	−	8.83505i	0.00972850	−	0.362507i
$595$	−0.187319			−0.00767933
$596$	1.38765	−	25.8350i	0.0568406	−	1.05824i
$597$		−	15.9359i		−	0.652214i
$598$	3.44677	+	8.08062i	0.140949	+	0.330441i
$599$		−	22.6895i		−	0.927067i	−0.886079	−	0.463533i	$-0.846581\pi$
$599$		−	22.6895i		−	0.927067i	0.886079	−	0.463533i	$-0.153419\pi$
$600$	−0.227417	+	2.81927i	−0.00928426	+	0.115096i
$601$	−12.9957			−0.530107			−0.265054	−	0.964234i	$-0.585390\pi$
$601$	−12.9957			−0.530107			−0.265054	+	0.964234i	$0.585390\pi$
$602$	11.6555	+	0.312796i	0.475044	+	0.0127486i
$603$	4.41547			0.179812
$604$	−0.184440	+	3.43386i	−0.00750476	+	0.139722i
$605$		−	28.0572i		−	1.14069i
$606$	0.344722	−	12.8451i	0.0140034	−	0.521798i
$607$		−	5.65504i		−	0.229531i	−0.993393	−	0.114766i	$-0.963388\pi$
$607$		−	5.65504i		−	0.229531i	0.993393	−	0.114766i	$-0.0366117\pi$
$608$	−9.61185	−	1.29724i	−0.389812	−	0.0526099i
$609$			11.8191i			0.478935i
$610$	8.88623	+	0.238478i	0.359793	+	0.00965567i
$611$		−	6.32802i		−	0.256004i
$612$	−0.0104546	+	0.194641i	−0.000422601	+	0.00786788i
$613$		−	10.0957i		−	0.407760i	−0.978996	−	0.203880i	$-0.934645\pi$
$613$		−	10.0957i		−	0.407760i	0.978996	−	0.203880i	$-0.0653552\pi$
$614$	−0.345605	+	12.8781i	−0.0139475	+	0.519716i
$615$	9.53279			0.384399
$616$	33.8641	+	2.73166i	1.36443	+	0.110062i
$617$		−	44.6135i		−	1.79607i	−0.439921	−	0.898036i	$-0.644994\pi$
$617$		−	44.6135i		−	1.79607i	0.439921	−	0.898036i	$-0.355006\pi$
$618$	0.234812	−	8.74963i	0.00944551	−	0.351962i
$619$	32.5331			1.30762			0.653808	−	0.756661i	$-0.273171\pi$
$619$	32.5331			1.30762			0.653808	+	0.756661i	$0.273171\pi$
$620$	−5.24533	−	0.281738i	−0.210657	−	0.0113149i
$621$	−4.35922	+	1.99929i	−0.174930	+	0.0802289i
$622$	1.22735	−	45.7338i	0.0492121	−	1.83376i
$623$		−	13.7404i		−	0.550499i
$624$	−0.554978	+	5.15131i	−0.0222169	+	0.206218i
$625$	1.00000			0.0400000
$626$	−0.0571327	+	2.12890i	−0.00228348	+	0.0850879i
$627$		−	10.7152i		−	0.427926i
$628$	2.04908	−	38.1493i	0.0817673	−	1.52232i
$629$	−0.953489			−0.0380181
$630$	0.0729192	−	2.71714i	0.00290517	−	0.108253i
$631$	5.60626			0.223182			0.111591	−	0.993754i	$-0.464405\pi$
$631$	5.60626			0.223182			0.111591	+	0.993754i	$0.464405\pi$
$632$	−21.9301	−	1.76900i	−0.872334	−	0.0703670i
$633$	11.9753			0.475975
$634$	−0.480702	−	0.0129005i	−0.0190911	−	0.000512344i
$635$	−16.0271			−0.636018
$636$	4.21111	+	0.226188i	0.166981	+	0.00896893i
$637$	−4.28209			−0.169663
$638$	54.3302	+	1.45805i	2.15095	+	0.0577246i
$639$			10.2506i			0.405508i
$640$	−2.11238	+	11.1148i	−0.0834993	+	0.439349i
$641$			42.5788i			1.68176i	0.541221	+	0.840880i	$0.317962\pi$
$641$			42.5788i			1.68176i	−0.541221	+	0.840880i	$0.682038\pi$
$642$	−0.283683	+	10.5707i	−0.0111961	+	0.417192i
$643$	−31.0918			−1.22614			−0.613071	−	0.790027i	$-0.710066\pi$
$643$	−31.0918			−1.22614			−0.613071	+	0.790027i	$0.710066\pi$
$644$	−6.77547	−	17.1449i	−0.266991	−	0.675605i
$645$	−4.28963			−0.168904
$646$	−0.00633971	+	0.236232i	−0.000249433	+	0.00929444i
$647$			7.49238i			0.294556i	0.989095	+	0.147278i	$0.0470511\pi$
$647$			7.49238i			0.294556i	−0.989095	+	0.147278i	$0.952949\pi$
$648$	−2.81927	−	0.227417i	−0.110751	−	0.00893378i
$649$		−	60.5031i		−	2.37495i
$650$	1.83114	+	0.0491420i	0.0718234	+	0.00192751i
$651$	5.04802			0.197848
$652$	−1.36422	+	25.3988i	−0.0534271	+	0.994692i
$653$	−27.9116			−1.09227			−0.546134	−	0.837698i	$-0.683901\pi$
$653$	−27.9116			−1.09227			−0.546134	+	0.837698i	$0.683901\pi$
$654$	−13.7663	−	0.369443i	−0.538305	−	0.0144464i
$655$	3.02553			0.118217
$656$	37.9118	+	4.08443i	1.48021	+	0.159470i
$657$	6.93152			0.270424
$658$	−0.356242	+	13.2744i	−0.0138878	+	0.517491i
$659$	−7.36762			−0.287002			−0.143501	−	0.989650i	$-0.545836\pi$
$659$	−7.36762			−0.287002			−0.143501	+	0.989650i	$0.545836\pi$
$660$	−12.4812	−	0.670390i	−0.485828	−	0.0260949i
$661$		−	1.11554i		−	0.0433895i	−0.999765	−	0.0216948i	$-0.993094\pi$
$661$		−	1.11554i		−	0.0433895i	0.999765	−	0.0216948i	$-0.00690620\pi$
$662$	0.508387	−	18.9437i	0.0197590	−	0.736268i
$663$	0.126239			0.00490271
$664$	7.76389	+	0.626276i	0.301297	+	0.0243042i
$665$		−	3.29538i		−	0.127789i
$666$	0.371172	−	13.8307i	0.0143826	−	0.535930i
$667$	−12.2944	−	26.8066i	−0.476043	−	1.03796i
$668$	−0.972865	+	18.1126i	−0.0376413	+	0.700796i
$669$	15.7556			0.609147
$670$	0.167519	−	6.24216i	0.00647184	−	0.241156i
$671$			39.2834i			1.51652i
$672$	1.45419	−	10.7748i	0.0560965	−	0.415646i
$673$	8.98117			0.346199			0.173099	−	0.984904i	$-0.444622\pi$
$673$	8.98117			0.346199			0.173099	+	0.984904i	$0.444622\pi$
$674$	1.00023	−	37.2709i	0.0385274	−	1.43562i
$675$			1.00000i			0.0384900i
$676$	−22.6119	−	1.21453i	−0.869689	−	0.0467129i
$677$			14.9183i			0.573357i	0.958027	+	0.286679i	$0.0925512\pi$
$677$			14.9183i			0.573357i	−0.958027	+	0.286679i	$0.907449\pi$
$678$	−11.2318	−	0.301426i	−0.431356	−	0.0115762i
$679$		−	11.8264i		−	0.453857i
$680$	0.274768	+	0.0221642i	0.0105369	+	0.000849958i
$681$		−	19.1549i		−	0.734018i
$682$	0.622741	−	23.2048i	0.0238460	−	0.888556i
$683$			5.21749i			0.199642i	0.995005	+	0.0998209i	$0.0318270\pi$
$683$			5.21749i			0.199642i	−0.995005	+	0.0998209i	$0.968173\pi$
$684$	−3.42418	−	0.183920i	−0.130927	−	0.00703236i
$685$	−9.42633			−0.360162
$686$	28.0026	+	0.751499i	1.06914	+	0.0286924i
$687$	−28.6485			−1.09301
$688$	−17.0598	−	1.83794i	−0.650399	−	0.0700709i
$689$		−	2.73121i		−	0.104051i
$690$	2.66102	+	6.23851i	0.101303	+	0.237496i
$691$			24.5730i			0.934801i	0.884046	+	0.467400i	$0.154809\pi$
$691$			24.5730i			0.934801i	−0.884046	+	0.467400i	$0.845191\pi$
$692$	35.3330	+	1.89781i	1.34316	+	0.0721440i
$693$	12.0117			0.456286
$694$	0.466222	−	17.3725i	0.0176976	−	0.659452i
$695$	17.8819			0.678298
$696$	1.39848	−	17.3368i	0.0530091	−	0.657150i
$697$		−	0.929071i		−	0.0351911i
$698$	19.6859	+	0.528306i	0.745123	+	0.0199967i
$699$			3.02005i			0.114229i
$700$	−3.83846	−	0.206172i	−0.145080	−	0.00779258i
$701$		−	48.3487i		−	1.82611i	−0.407840	−	0.913053i	$-0.633718\pi$
$701$		−	48.3487i		−	1.82611i	0.407840	−	0.913053i	$-0.366282\pi$
$702$	−0.0491420	+	1.83114i	−0.00185474	+	0.0691121i
$703$		−	16.7741i		−	0.632646i
$704$	−49.3502	−	8.01383i	−1.85995	−	0.302032i
$705$		−	4.88544i		−	0.183996i
$706$	−24.1945	−	0.649302i	−0.910572	−	0.0244368i
$707$	17.4636			0.656786
$708$	−19.3344	−	1.03849i	−0.726632	−	0.0390290i
$709$			18.8401i			0.707554i	0.935330	+	0.353777i	$0.115103\pi$
$709$			18.8401i			0.707554i	−0.935330	+	0.353777i	$0.884897\pi$
$710$	14.4914	+	0.388901i	0.543851	+	0.0145952i
$711$	−7.77866			−0.291723
$712$	−1.62581	+	20.1550i	−0.0609298	+	0.755342i
$713$	−11.4493	+	5.25103i	−0.428778	+	0.196653i
$714$	−0.264814	−	0.00710674i	−0.00991041	−	0.000265963i
$715$			8.09495i			0.302734i
$716$	1.10973	−	20.6607i	0.0414726	−	0.772126i
$717$	14.7331			0.550219
$718$	52.1217	+	1.39878i	1.94516	+	0.0522019i
$719$			9.18403i			0.342506i	0.985227	+	0.171253i	$0.0547816\pi$
$719$			9.18403i			0.342506i	−0.985227	+	0.171253i	$0.945218\pi$
$720$	−0.428461	+	3.97699i	−0.0159678	+	0.148214i
$721$	11.8955			0.443013
$722$	22.7045	+	0.609315i	0.844975	+	0.0226764i
$723$	17.3831			0.646486
$724$	−2.75602	+	51.3109i	−0.102427	+	1.90695i
$725$	−6.14940			−0.228383
$726$	1.06447	−	39.6646i	0.0395061	−	1.47209i
$727$	−41.8557			−1.55234			−0.776171	−	0.630522i	$-0.782841\pi$
$727$	−41.8557			−1.55234			−0.776171	+	0.630522i	$0.782841\pi$
$728$	−7.01865	−	0.566161i	−0.260128	−	0.0209833i
$729$	−1.00000			−0.0370370
$730$	0.262977	−	9.79913i	0.00973321	−	0.362682i
$731$			0.418070i			0.0154629i
$732$	12.5535	+	0.674273i	0.463989	+	0.0249219i
$733$		−	36.1122i		−	1.33384i	−0.745131	−	0.666918i	$-0.767613\pi$
$733$		−	36.1122i		−	1.33384i	0.745131	−	0.666918i	$-0.232387\pi$
$734$	−18.7010	−	0.501873i	−0.690265	−	0.0185245i
$735$	−3.30592			−0.121941
$736$	7.90990	+	25.9506i	0.291563	+	0.956552i
$737$	27.5948			1.01647
$738$	13.4766	+	0.361667i	0.496079	+	0.0133131i
$739$			40.4886i			1.48940i	0.667401	+	0.744698i	$0.267407\pi$
$739$			40.4886i			1.48940i	−0.667401	+	0.744698i	$0.732593\pi$
$740$	−19.5385	−	1.04946i	−0.718249	−	0.0385787i
$741$			2.22083i			0.0815843i
$742$	−0.153757	+	5.72933i	−0.00564458	+	0.210330i
$743$	11.5177			0.422542			0.211271	−	0.977428i	$-0.432240\pi$
$743$	11.5177			0.422542			0.211271	+	0.977428i	$0.432240\pi$
$744$	−7.40465	−	0.597298i	−0.271468	−	0.0218980i
$745$	−12.9361			−0.473943
$746$	6.85553e−5	−	0.00255453i	2.50999e−6	−	9.35280e-5i
$747$	2.75387			0.100759
$748$	−0.0653366	+	1.21642i	−0.00238894	+	0.0444767i
$749$	−14.3714			−0.525119
$750$	1.41370	+	0.0379392i	0.0516212	+	0.00138535i
$751$	−9.05061			−0.330261			−0.165131	−	0.986272i	$-0.552805\pi$
$751$	−9.05061			−0.330261			−0.165131	+	0.986272i	$0.552805\pi$
$752$	2.09322	−	19.4293i	0.0763320	−	0.708515i
$753$		−	2.22901i		−	0.0812295i
$754$	−11.2604	−	0.302193i	−0.410081	−	0.0110052i
$755$	1.71940			0.0625755
$756$	0.206172	−	3.83846i	0.00749842	−	0.139604i
$757$			28.4467i			1.03391i	0.856012	+	0.516956i	$0.172935\pi$
$757$			28.4467i			1.03391i	−0.856012	+	0.516956i	$0.827065\pi$
$758$	−0.374034	−	0.0100378i	−0.0135855	−	0.000364591i
$759$	−27.2433	+	12.4947i	−0.988869	+	0.453530i
$760$	−0.389919	+	4.83380i	−0.0141439	+	0.175340i
$761$	25.1836			0.912906			0.456453	−	0.889748i	$-0.349120\pi$
$761$	25.1836			0.912906			0.456453	+	0.889748i	$0.349120\pi$
$762$	−22.6576	−	0.608058i	−0.820800	−	0.0220276i
$763$		−	18.7160i		−	0.677563i
$764$	35.5685	+	1.91046i	1.28682	+	0.0691181i
$765$	0.0974606			0.00352369
$766$	−6.26213	−	0.168055i	−0.226260	−	0.00607208i
$767$			12.5398i			0.452786i
$768$	−3.40797	+	15.6328i	−0.122975	+	0.564102i
$769$		−	9.04015i		−	0.325996i	−0.986626	−	0.162998i	$-0.947884\pi$
$769$		−	9.04015i		−	0.325996i	0.986626	−	0.162998i	$-0.0521165\pi$
$770$	0.455714	−	16.9810i	0.0164228	−	0.611951i
$771$		−	7.76681i		−	0.279715i
$772$	39.5479	+	2.12421i	1.42336	+	0.0764519i
$773$			33.1305i			1.19162i	0.803125	+	0.595810i	$0.203169\pi$
$773$			33.1305i			1.19162i	−0.803125	+	0.595810i	$0.796831\pi$
$774$	−6.06427	−	0.162745i	−0.217976	−	0.00584976i
$775$			2.62644i			0.0943446i
$776$	−1.39934	+	17.3475i	−0.0502335	+	0.622740i
$777$	18.8035			0.674574
$778$	1.11499	−	41.5473i	0.0399745	−	1.48954i
$779$	16.3445			0.585603
$780$	2.58683	+	0.138944i	0.0926235	+	0.00497501i
$781$			64.0620i			2.29232i
$782$	0.608008	−	0.259345i	0.0217423	−	0.00927416i
$783$		−	6.14940i		−	0.219762i
$784$	−13.1476	−	1.41646i	−0.469557	−	0.0505878i
$785$	−19.1021			−0.681785
$786$	4.27720	+	0.114786i	0.152563	+	0.00409429i
$787$	−1.91035			−0.0680967			−0.0340484	−	0.999420i	$-0.510840\pi$
$787$	−1.91035			−0.0680967			−0.0340484	+	0.999420i	$0.510840\pi$
$788$	−11.5390	−	0.619787i	−0.411061	−	0.0220790i
$789$			18.5671i			0.661006i
$790$	−0.295116	+	10.9967i	−0.0104998	+	0.391246i
$791$		−	15.2702i		−	0.542946i
$792$	−17.6192	−	1.42126i	−0.626072	−	0.0505023i
$793$		−	8.14184i		−	0.289125i
$794$	22.0136	+	0.590774i	0.781233	+	0.0209658i
$795$		−	2.10859i		−	0.0747839i
$796$	−31.8260	−	1.70944i	−1.12804	−	0.0605896i
$797$			48.9032i			1.73224i	0.499835	+	0.866120i	$0.333394\pi$
$797$			48.9032i			1.73224i	−0.499835	+	0.866120i	$0.666606\pi$
$798$	0.125024	−	4.65869i	0.00442580	−	0.164916i
$799$	−0.476138			−0.0168445
$800$	5.60603	+	0.756602i	0.198203	+	0.0267499i
$801$			7.14903i			0.252599i
$802$	0.975476	−	36.3485i	0.0344452	−	1.28351i
$803$	43.3191			1.52870
$804$	0.473646	−	8.81822i	0.0167042	−	0.310995i
$805$	−8.37842	+	3.84264i	−0.295301	+	0.135435i
$806$	−0.129069	+	4.80940i	−0.00454625	+	0.169404i
$807$		−	9.35582i		−	0.329340i
$808$	−25.6163	−	2.06635i	−0.901180	−	0.0726939i
$809$	14.9980			0.527303			0.263651	−	0.964618i	$-0.415073\pi$
$809$	14.9980			0.527303			0.263651	+	0.964618i	$0.415073\pi$
$810$	−0.0379392	+	1.41370i	−0.00133305	+	0.0496725i
$811$			48.0636i			1.68774i	0.536547	+	0.843871i	$0.319729\pi$
$811$			48.0636i			1.68774i	−0.536547	+	0.843871i	$0.680271\pi$
$812$	23.6042	+	1.26784i	0.828346	+	0.0444923i
$813$	2.98161			0.104570
$814$	2.31967	−	86.4362i	0.0813043	−	3.02959i
$815$	12.7177			0.445481
$816$	0.387599	+	0.0417581i	0.0135687	+	0.00146183i
$817$	−7.35482			−0.257312
$818$	−1.56520	−	0.0420050i	−0.0547261	−	0.00146867i
$819$	−2.48953			−0.0869911
$820$	1.02258	−	19.0381i	0.0357101	−	0.664841i
$821$	−3.52398			−0.122988			−0.0614939	−	0.998107i	$-0.519586\pi$
$821$	−3.52398			−0.122988			−0.0614939	+	0.998107i	$0.519586\pi$
$822$	−13.3260	−	0.357628i	−0.464799	−	0.0124737i
$823$			50.0037i			1.74302i	0.490377	+	0.871510i	$0.336859\pi$
$823$			50.0037i			1.74302i	−0.490377	+	0.871510i	$0.663141\pi$
$824$	−17.4489	−	1.40752i	−0.607860	−	0.0490332i
$825$			6.24957i			0.217582i
$826$	0.705942	−	26.3050i	0.0245628	−	0.915269i
$827$	−45.8710			−1.59509			−0.797546	−	0.603259i	$-0.793869\pi$
$827$	−45.8710			−1.59509			−0.797546	+	0.603259i	$0.793869\pi$
$828$	3.52522	+	8.92036i	0.122510	+	0.310004i
$829$	−20.9201			−0.726586			−0.363293	−	0.931675i	$-0.618348\pi$
$829$	−20.9201			−0.726586			−0.363293	+	0.931675i	$0.618348\pi$
$830$	0.104480	−	3.89315i	0.00362654	−	0.135133i
$831$		−	25.4380i		−	0.882433i
$832$	10.2283	+	1.66094i	0.354601	+	0.0575827i
$833$			0.322197i			0.0111635i
$834$	25.2797	+	0.678424i	0.875363	+	0.0234919i
$835$	9.06933			0.313857
$836$	−21.3997	−	1.14942i	−0.740122	−	0.0397536i
$837$	−2.62644			−0.0907832
$838$	−32.6229	−	0.875492i	−1.12694	−	0.0302434i
$839$	40.0855			1.38390			0.691952	−	0.721944i	$-0.256751\pi$
$839$	40.0855			1.38390			0.691952	+	0.721944i	$0.256751\pi$
$840$	−5.41863	−	0.437095i	−0.186961	−	0.0150812i
$841$	8.81508			0.303968
$842$	−0.180914	+	6.74128i	−0.00623471	+	0.232320i
$843$	−21.1926			−0.729913
$844$	1.28459	−	23.9161i	0.0442173	−	0.823226i
$845$			11.3222i			0.389497i
$846$	0.185350	−	6.90657i	0.00637246	−	0.237453i
$847$	53.9259			1.85291
$848$	0.903449	−	8.38583i	0.0310246	−	0.287971i
$849$			0.175124i			0.00601025i
$850$	0.00369758	−	0.137780i	0.000126826	−	0.00472583i
$851$	−42.6477	+	19.5597i	−1.46194	+	0.670499i
$852$	20.4717	+	1.09958i	0.701350	+	0.0376711i
$853$	41.1666			1.40952			0.704758	−	0.709448i	$-0.251056\pi$
$853$	41.1666			1.40952			0.704758	+	0.709448i	$0.251056\pi$
$854$	−0.458353	+	17.0793i	−0.0156845	+	0.584442i
$855$			1.71456i			0.0586366i
$856$	21.0805	+	1.70047i	0.720518	+	0.0581208i
$857$	20.1321			0.687700			0.343850	−	0.939025i	$-0.388269\pi$
$857$	20.1321			0.687700			0.343850	+	0.939025i	$0.388269\pi$
$858$	−0.307116	+	11.4439i	−0.0104848	+	0.390687i
$859$		−	7.30027i		−	0.249082i	−0.992214	−	0.124541i	$-0.960254\pi$
$859$		−	7.30027i		−	0.249082i	0.992214	−	0.124541i	$-0.0397458\pi$
$860$	−0.460148	+	8.56692i	−0.0156909	+	0.292129i
$861$			18.3220i			0.624413i
$862$	18.4464	+	0.495040i	0.628286	+	0.0168611i
$863$		−	43.9395i		−	1.49572i	−0.663858	−	0.747859i	$-0.731082\pi$
$863$		−	43.9395i		−	1.49572i	0.663858	−	0.747859i	$-0.268918\pi$
$864$	−0.756602	+	5.60603i	−0.0257401	+	0.190721i
$865$		−	17.6920i		−	0.601545i
$866$	0.821512	−	30.6115i	0.0279161	−	1.04022i
$867$			16.9905i			0.577028i
$868$	0.541500	−	10.0815i	0.0183797	−	0.342189i
$869$	−48.6133			−1.64909
$870$	−8.69343	−	0.233303i	−0.294735	−	0.00790973i
$871$	−5.71927			−0.193790
$872$	−2.21453	+	27.4534i	−0.0749935	+	0.929688i
$873$			6.15320i			0.208254i
$874$	4.56248	+	10.6963i	0.154328	+	0.361807i
$875$			1.92200i			0.0649754i
$876$	0.743543	−	13.8431i	0.0251220	−	0.467715i
$877$	14.0592			0.474746			0.237373	−	0.971419i	$-0.423714\pi$
$877$	14.0592			0.474746			0.237373	+	0.971419i	$0.423714\pi$
$878$	0.701740	−	26.1485i	0.0236826	−	0.882469i
$879$	−15.4948			−0.522626
$880$	−2.67770	+	24.8545i	−0.0902653	+	0.837844i
$881$		−	42.7469i		−	1.44018i	−0.693881	−	0.720090i	$-0.744101\pi$
$881$		−	42.7469i		−	1.44018i	0.693881	−	0.720090i	$-0.255899\pi$
$882$	−4.67359	−	0.125424i	−0.157368	−	0.00422325i
$883$			30.0392i			1.01090i	0.862856	+	0.505450i	$0.168674\pi$
$883$			30.0392i			1.01090i	−0.862856	+	0.505450i	$0.831326\pi$
$884$	0.0135416	−	0.252114i	0.000455453	−	0.00847952i
$885$			9.68115i			0.325428i
$886$	−0.997516	+	37.1698i	−0.0335122	+	1.24874i
$887$			13.9244i			0.467536i	0.972292	+	0.233768i	$0.0751057\pi$
$887$			13.9244i			0.467536i	−0.972292	+	0.233768i	$0.924894\pi$
$888$	−27.5818	−	2.22490i	−0.925586	−	0.0746626i
$889$		−	30.8041i		−	1.03314i
$890$	10.1066	+	0.271229i	0.338775	+	0.00909161i
$891$	−6.24957			−0.209369
$892$	1.69010	−	31.4659i	0.0565887	−	1.05355i
$893$		−	8.37636i		−	0.280304i
$894$	−18.2879	−	0.490787i	−0.611637	−	0.0164144i
$895$	−10.3452			−0.345803
$896$	−21.3626	−	4.06000i	−0.713673	−	0.135635i
$897$	5.64642	−	2.58965i	0.188528	−	0.0864658i
$898$	−6.22234	−	0.166987i	−0.207642	−	0.00557244i
$899$		−	16.1510i		−	0.538667i
$900$	1.99712	+	0.107270i	0.0665707	+	0.00357566i
$901$	−0.205504			−0.00684634
$902$	84.2227	+	2.26026i	2.80431	+	0.0752586i
$903$		−	8.24467i		−	0.274365i
$904$	−1.80682	+	22.3990i	−0.0600939	+	0.744979i
$905$	25.6924			0.854045
$906$	2.43073	+	0.0652329i	0.0807555	+	0.00216722i
$907$	50.7791			1.68609			0.843046	−	0.537842i	$-0.180760\pi$
$907$	50.7791			1.68609			0.843046	+	0.537842i	$0.180760\pi$
$908$	−38.2547	−	2.05474i	−1.26953	−	0.0681891i
$909$	−9.08616			−0.301369
$910$	−0.0944508	+	3.51946i	−0.00313101	+	0.116669i
$911$	24.6076			0.815285			0.407642	−	0.913142i	$-0.366351\pi$
$911$	24.6076			0.815285			0.407642	+	0.913142i	$0.366351\pi$
$912$	−0.734621	+	6.81877i	−0.0243257	+	0.225792i
$913$	17.2105			0.569584
$914$	−0.304763	+	11.3562i	−0.0100807	+	0.375629i
$915$		−	6.28577i		−	0.207801i
$916$	−3.07312	+	57.2146i	−0.101539	+	1.89042i
$917$			5.81506i			0.192030i
$918$	0.137780	+	0.00369758i	0.00454743	+	0.000122038i
$919$	−11.5691			−0.381631			−0.190815	−	0.981626i	$-0.561113\pi$
$919$	−11.5691			−0.381631			−0.190815	+	0.981626i	$0.561113\pi$
$920$	12.7445	−	4.64519i	0.420174	−	0.153147i
$921$	9.10944			0.300166
$922$	25.5005	+	0.684350i	0.839813	+	0.0225379i
$923$		−	13.2774i		−	0.437032i
$924$	1.28849	−	23.9888i	0.0423882	−	0.789173i
$925$			9.78333i			0.321674i
$926$	0.178481	−	6.65063i	0.00586526	−	0.218553i
$927$	−6.18915			−0.203278
$928$	−34.4737	−	4.65264i	−1.13165	−	0.152731i
$929$	−54.9587			−1.80314			−0.901569	−	0.432636i	$-0.857584\pi$
$929$	−54.9587			−1.80314			−0.901569	+	0.432636i	$0.857584\pi$
$930$	−0.0996453	+	3.71302i	−0.00326750	+	0.121755i
$931$	−5.66819			−0.185767
$932$	6.03141	+	0.323960i	0.197565	+	0.0106117i
$933$	−32.3503			−1.05910
$934$	18.8815	+	0.506719i	0.617822	+	0.0165803i
$935$	0.609087			0.0199193
$936$	3.65175	+	0.294569i	0.119361	+	0.00962828i
$937$			33.0245i			1.07886i	0.842029	+	0.539432i	$0.181361\pi$
$937$			33.0245i			1.07886i	−0.842029	+	0.539432i	$0.818639\pi$
$938$	11.9974	+	0.321972i	0.391730	+	0.0105128i
$939$	1.50590			0.0491432
$940$	−9.75682	−	0.524060i	−0.318232	−	0.0170930i
$941$		−	47.3005i		−	1.54195i	−0.636863	−	0.770977i	$-0.719768\pi$
$941$		−	47.3005i		−	1.54195i	0.636863	−	0.770977i	$-0.280232\pi$
$942$	−27.0048	−	0.724721i	−0.879863	−	0.0236127i
$943$	−19.0588	−	41.5556i	−0.620641	−	1.35324i
$944$	−4.14800	+	38.5018i	−0.135006	+	1.25313i
$945$	−1.92200			−0.0625226
$946$	−37.8991	−	1.01709i	−1.23221	−	0.0330684i
$947$			37.8773i			1.23085i	0.788197	+	0.615423i	$0.211015\pi$
$947$			37.8773i			1.23085i	−0.788197	+	0.615423i	$0.788985\pi$
$948$	−0.834415	+	15.5349i	−0.0271005	+	0.504551i
$949$	−8.97827			−0.291447
$950$	2.42388	+	0.0650490i	0.0786409	+	0.00211047i
$951$			0.340030i			0.0110262i
$952$	−0.0425995	+	0.528103i	−0.00138066	+	0.0171159i
$953$			29.5065i			0.955809i	0.878412	+	0.477904i	$0.158603\pi$
$953$			29.5065i			0.955809i	−0.878412	+	0.477904i	$0.841397\pi$
$954$	0.0799983	−	2.98092i	0.00259004	−	0.0965109i
$955$		−	17.8099i		−	0.576315i
$956$	1.58042	−	29.4239i	0.0511145	−	0.951636i
$957$		−	38.4311i		−	1.24230i
$958$	−58.2503	−	1.56325i	−1.88198	−	0.0505063i
$959$		−	18.1174i		−	0.585041i
$960$	7.89656	+	1.28230i	0.254860	+	0.0413860i
$961$	24.1018			0.777477
$962$	−0.480772	+	17.9147i	−0.0155007	+	0.577593i
$963$	7.47731			0.240953
$964$	1.86469	−	34.7162i	0.0600575	−	1.11813i
$965$		−	19.8025i		−	0.637464i
$966$	−11.9904	+	5.11449i	−0.385785	+	0.164556i
$967$		−	26.5405i		−	0.853486i	−0.904373	−	0.426743i	$-0.859661\pi$
$967$		−	26.5405i		−	0.853486i	0.904373	−	0.426743i	$-0.140339\pi$
$968$	−79.1008	−	6.38068i	−2.54239	−	0.205083i
$969$	0.167102			0.00536808
$970$	8.69881	+	0.233448i	0.279302	+	0.00749555i
$971$	26.8740			0.862426			0.431213	−	0.902250i	$-0.358086\pi$
$971$	26.8740			0.862426			0.431213	+	0.902250i	$0.358086\pi$
$972$	−0.107270	+	1.99712i	−0.00344068	+	0.0640577i
$973$			34.3689i			1.10182i
$974$	−1.23264	+	45.9311i	−0.0394964	+	1.47173i
$975$		−	1.29528i		−	0.0414822i
$976$	2.69321	−	24.9984i	0.0862076	−	0.800181i
$977$			4.62588i			0.147995i	0.997258	+	0.0739975i	$0.0235757\pi$
$977$			4.62588i			0.147995i	−0.997258	+	0.0739975i	$0.976424\pi$
$978$	17.9790	+	0.482499i	0.574907	+	0.0154286i
$979$			44.6784i			1.42793i
$980$	−0.354625	+	6.60232i	−0.0113281	+	0.210904i
$981$			9.73776i			0.310903i
$982$	−1.39590	+	52.0147i	−0.0445451	+	1.65985i
$983$	48.0686			1.53315			0.766576	−	0.642154i	$-0.221959\pi$
$983$	48.0686			1.53315			0.766576	+	0.642154i	$0.221959\pi$
$984$	2.16792	−	26.8755i	0.0691107	−	0.856760i
$985$			5.77784i			0.184097i
$986$	−0.0227379	+	0.847267i	−0.000724122	+	0.0269825i
$987$	9.38981			0.298881
$988$	4.43527	+	0.238228i	0.141105	+	0.00757904i
$989$	8.57623	+	18.6995i	0.272708	+	0.594608i
$990$	−0.237104	+	8.83505i	−0.00753566	+	0.280796i
$991$			23.1744i			0.736159i	0.929794	+	0.368080i	$0.119985\pi$
$991$			23.1744i			0.736159i	−0.929794	+	0.368080i	$0.880015\pi$
$992$	−1.98717	+	14.7239i	−0.0630928	+	0.467485i
$993$	−13.4000			−0.425237
$994$	−0.747467	+	27.8524i	−0.0237082	+	0.883423i
$995$			15.9359i			0.505203i
$996$	0.295407	−	5.49980i	0.00936031	−	0.174268i
$997$	42.9920			1.36157			0.680786	−	0.732482i	$-0.261638\pi$
$997$	42.9920			1.36157			0.680786	+	0.732482i	$0.261638\pi$
$998$	−1.56046	+	58.1464i	−0.0493955	+	1.84059i
$999$	−9.78333			−0.309531

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.p.b.91.1	yes	48
4.3	odd	2		1380.2.p.a.91.2	yes	48
23.22	odd	2		1380.2.p.a.91.1	✓	48
92.91	even	2	inner	1380.2.p.b.91.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.p.a.91.1	✓	48	23.22	odd	2
1380.2.p.a.91.2	yes	48	4.3	odd	2
1380.2.p.b.91.1	yes	48	1.1	even	1	trivial
1380.2.p.b.91.2	yes	48	92.91	even	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:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41370 - 0.0379392i) q^{2} +1.00000i q^{3} +(1.99712 + 0.107270i) q^{4} -1.00000i q^{5} +(0.0379392 - 1.41370i) q^{6} +1.92200 q^{7} +(-2.81927 - 0.227417i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.41370 - 0.0379392i) q^{2} +1.00000i q^{3} +(1.99712 + 0.107270i) q^{4} -1.00000i q^{5} +(0.0379392 - 1.41370i) q^{6} +1.92200 q^{7} +(-2.81927 - 0.227417i) q^{8} -1.00000 q^{9} +(-0.0379392 + 1.41370i) q^{10} -6.24957 q^{11} +(-0.107270 + 1.99712i) q^{12} +1.29528 q^{13} +(-2.71714 - 0.0729192i) q^{14} +1.00000 q^{15} +(3.97699 + 0.428461i) q^{16} -0.0974606i q^{17} +(1.41370 + 0.0379392i) q^{18} +1.71456 q^{19} +(0.107270 - 1.99712i) q^{20} +1.92200i q^{21} +(8.83505 + 0.237104i) q^{22} +(-1.99929 - 4.35922i) q^{23} +(0.227417 - 2.81927i) q^{24} -1.00000 q^{25} +(-1.83114 - 0.0491420i) q^{26} -1.00000i q^{27} +(3.83846 + 0.206172i) q^{28} +6.14940 q^{29} +(-1.41370 - 0.0379392i) q^{30} -2.62644i q^{31} +(-5.60603 - 0.756602i) q^{32} -6.24957i q^{33} +(-0.00369758 + 0.137780i) q^{34} -1.92200i q^{35} +(-1.99712 - 0.107270i) q^{36} -9.78333i q^{37} +(-2.42388 - 0.0650490i) q^{38} +1.29528i q^{39} +(-0.227417 + 2.81927i) q^{40} +9.53279 q^{41} +(0.0729192 - 2.71714i) q^{42} -4.28963 q^{43} +(-12.4812 - 0.670390i) q^{44} +1.00000i q^{45} +(2.66102 + 6.23851i) q^{46} -4.88544i q^{47} +(-0.428461 + 3.97699i) q^{48} -3.30592 q^{49} +(1.41370 + 0.0379392i) q^{50} +0.0974606 q^{51} +(2.58683 + 0.138944i) q^{52} -2.10859i q^{53} +(-0.0379392 + 1.41370i) q^{54} +6.24957i q^{55} +(-5.41863 - 0.437095i) q^{56} +1.71456i q^{57} +(-8.69343 - 0.233303i) q^{58} +9.68115i q^{59} +(1.99712 + 0.107270i) q^{60} -6.28577i q^{61} +(-0.0996453 + 3.71302i) q^{62} -1.92200 q^{63} +(7.89656 + 1.28230i) q^{64} -1.29528i q^{65} +(-0.237104 + 8.83505i) q^{66} -4.41547 q^{67} +(0.0104546 - 0.194641i) q^{68} +(4.35922 - 1.99929i) q^{69} +(-0.0729192 + 2.71714i) q^{70} -10.2506i q^{71} +(2.81927 + 0.227417i) q^{72} -6.93152 q^{73} +(-0.371172 + 13.8307i) q^{74} -1.00000i q^{75} +(3.42418 + 0.183920i) q^{76} -12.0117 q^{77} +(0.0491420 - 1.83114i) q^{78} +7.77866 q^{79} +(0.428461 - 3.97699i) q^{80} +1.00000 q^{81} +(-13.4766 - 0.361667i) q^{82} -2.75387 q^{83} +(-0.206172 + 3.83846i) q^{84} -0.0974606 q^{85} +(6.06427 + 0.162745i) q^{86} +6.14940i q^{87} +(17.6192 + 1.42126i) q^{88} -7.14903i q^{89} +(0.0379392 - 1.41370i) q^{90} +2.48953 q^{91} +(-3.52522 - 8.92036i) q^{92} +2.62644 q^{93} +(-0.185350 + 6.90657i) q^{94} -1.71456i q^{95} +(0.756602 - 5.60603i) q^{96} -6.15320i q^{97} +(4.67359 + 0.125424i) q^{98} +6.24957 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} + 2 q^{10} - 20 q^{14} + 48 q^{15} - 6 q^{16} + 4 q^{18} - 16 q^{19} - 28 q^{22} - 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} - 4 q^{30} + 16 q^{32} + 28 q^{34} + 2 q^{36} - 2 q^{40} - 8 q^{41} + 26 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 16 q^{51} - 16 q^{52} + 2 q^{54} - 40 q^{56} - 8 q^{58} - 2 q^{60} + 24 q^{62} - 26 q^{64} + 48 q^{67} + 44 q^{68} - 8 q^{69} + 4 q^{72} - 20 q^{74} + 64 q^{76} + 32 q^{77} + 64 q^{79} - 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} + 40 q^{86} - 2 q^{90} - 28 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 + 2 * q^10 - 20 * q^14 + 48 * q^15 - 6 * q^16 + 4 * q^18 - 16 * q^19 - 28 * q^22 - 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 - 4 * q^30 + 16 * q^32 + 28 * q^34 + 2 * q^36 - 2 * q^40 - 8 * q^41 + 26 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 16 * q^51 - 16 * q^52 + 2 * q^54 - 40 * q^56 - 8 * q^58 - 2 * q^60 + 24 * q^62 - 26 * q^64 + 48 * q^67 + 44 * q^68 - 8 * q^69 + 4 * q^72 - 20 * q^74 + 64 * q^76 + 32 * q^77 + 64 * q^79 - 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 + 40 * q^86 - 2 * q^90 - 28 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Introduction

L-functions

Modular forms

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Database

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