LMFDB - Embedded newform 1380.2.p.a.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.a.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} +(-2.99180 + 6.08680i) 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} +(4.46044 - 8.49143i) 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} + 14 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} - 4 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 + 14 * 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 - 4 * 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	$-0.618324\pi$
$7$	−1.92200			−0.726447			−0.363224	+	0.931702i	$0.618324\pi$
$8$	−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	$-0.108793\pi$
$11$	6.24957			1.88432			0.942159	+	0.335167i	$0.108793\pi$
$12$	−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	$0.00376214\pi$
$17$			0.0974606i			0.0236377i	−0.999930	+	0.0118188i	$0.996238\pi$
$18$	1.41370	+	0.0379392i	0.333213	+	0.00894236i
$19$	−1.71456			−0.393346			−0.196673	−	0.980469i	$-0.563014\pi$
$19$	−1.71456			−0.393346			−0.196673	+	0.980469i	$0.563014\pi$
$20$	−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	$0.297398\pi$
$37$			9.78333i			1.60837i	−0.594379	+	0.804185i	$0.702602\pi$
$38$	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	$-0.393935\pi$
$43$	4.28963			0.654163			0.327081	+	0.944996i	$0.393935\pi$
$44$	12.4812	+	0.670390i	1.88161	+	0.101065i
$45$		−	1.00000i		−	0.149071i
$46$	−2.99180	+	6.08680i	−0.441116	+	0.897450i
$47$		−	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	$0.0462598\pi$
$53$			2.10859i			0.289637i	−0.989458	+	0.144818i	$0.953740\pi$
$54$	−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	$0.131826\pi$
$61$			6.28577i			0.804811i	−0.915462	+	0.402405i	$0.868174\pi$
$62$	−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	$-0.413070\pi$
$67$	4.41547			0.539435			0.269717	+	0.962939i	$0.413070\pi$
$68$	−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	$-0.644166\pi$
$79$	−7.77866			−0.875168			−0.437584	+	0.899178i	$0.644166\pi$
$80$	−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	$-0.451706\pi$
$83$	2.75387			0.302276			0.151138	+	0.988513i	$0.451706\pi$
$84$	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	$0.123697\pi$
$89$			7.14903i			0.757796i	−0.925439	+	0.378898i	$0.876303\pi$
$90$	−0.0379392	+	1.41370i	−0.00399915	+	0.149018i
$91$	−2.48953			−0.260973
$92$	4.46044	−	8.49143i	0.465033	−	0.885293i
$93$	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	$0.101127\pi$
$97$			6.15320i			0.624763i	−0.949957	+	0.312381i	$0.898873\pi$
$98$	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	$-0.598629\pi$
$103$	−6.18915			−0.609835			−0.304917	+	0.952379i	$0.598629\pi$
$104$	−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	$-0.382289\pi$
$107$	7.47731			0.722859			0.361429	+	0.932400i	$0.382289\pi$
$108$	0.107270	−	1.99712i	0.0103220	−	0.192173i
$109$			9.73776i			0.932708i	0.884598	+	0.466354i	$0.154433\pi$
$109$			9.73776i			0.932708i	−0.884598	+	0.466354i	$0.845567\pi$
$110$	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	$0.121911\pi$
$113$			7.94496i			0.747399i	−0.927550	+	0.373699i	$0.878089\pi$
$114$	−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	$0.131919\pi$
$137$			9.42633i			0.805346i	−0.915344	+	0.402673i	$0.868081\pi$
$138$	−6.08680	−	2.99180i	−0.518143	−	0.254679i
$139$			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	$0.177765\pi$
$149$			12.9361i			1.05977i	−0.848070	+	0.529884i	$0.822235\pi$
$150$	−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	$0.275909\pi$
$157$			19.1021i			1.52452i	−0.647273	+	0.762258i	$0.724091\pi$
$158$	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	$-0.596014\pi$
$181$		−	25.6924i		−	1.90970i	0.297082	−	0.954852i	$-0.403986\pi$
$182$	3.51946	+	0.0944508i	0.260880	+	0.00700116i
$183$	−6.28577			−0.464658
$184$	−6.62791	+	11.8352i	−0.488616	+	0.872499i
$185$	−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	$-0.722868\pi$
$191$	−17.8099			−1.28868			−0.644339	+	0.764740i	$0.722868\pi$
$192$	−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	$-0.308940\pi$
$199$	15.9359			1.12967			0.564834	+	0.825204i	$0.308940\pi$
$200$	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	$-0.280720\pi$
$227$	19.1549			1.27136			0.635678	+	0.771954i	$0.280720\pi$
$228$	0.183920	−	3.42418i	0.0121804	−	0.226772i
$229$		−	28.6485i		−	1.89315i	−0.322485	−	0.946575i	$-0.604518\pi$
$229$		−	28.6485i		−	1.89315i	0.322485	−	0.946575i	$-0.395482\pi$
$230$	−6.08680	−	2.99180i	−0.401352	−	0.197273i
$231$		−	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	$0.189150\pi$
$241$			17.3831i			1.11975i	−0.828578	+	0.559873i	$0.810850\pi$
$242$	−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	$-0.477589\pi$
$251$	2.22901			0.140694			0.0703468	+	0.997523i	$0.477589\pi$
$252$	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	$-0.694006\pi$
$263$	−18.5671			−1.14490			−0.572448	+	0.819941i	$0.694006\pi$
$264$	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
$276$	8.49143	+	4.46044i	0.511124	+	0.268487i
$277$	−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	$-0.782184\pi$
$281$		−	21.1926i		−	1.26425i	0.774868	−	0.632123i	$-0.217816\pi$
$282$	−6.90657	−	0.185350i	−0.411280	−	0.0110374i
$283$	−0.175124			−0.0104101			−0.00520503	−	0.999986i	$-0.501657\pi$
$283$	−0.175124			−0.0104101			−0.00520503	+	0.999986i	$0.501657\pi$
$284$	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	$-0.850494\pi$
$293$		−	15.4948i		−	0.905215i	0.891710	−	0.452607i	$-0.149506\pi$
$294$	−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	$0.0135511\pi$
$313$			1.50590i			0.0851185i	−0.999094	+	0.0425593i	$0.986449\pi$
$314$	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
$322$	5.75023	−	11.6988i	0.320448	−	0.651950i
$323$		−	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	$-0.745026\pi$
$337$		−	26.3640i		−	1.43614i	0.695971	−	0.718069i	$-0.254974\pi$
$338$	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	$-0.0742300\pi$
$359$	36.8689			1.94586			0.972932	+	0.231092i	$0.0742300\pi$
$360$	−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	$-0.612208\pi$
$367$	−13.2283			−0.690514			−0.345257	+	0.938508i	$0.612208\pi$
$368$	9.81892	−	16.4800i	0.511847	−	0.859077i
$369$	−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	$-0.999985\pi$
$373$		−	0.00180698i		−	9.35617e-5i	1.00000		4.67808e-5i	$-1.48908e-5\pi$
$374$	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	$-0.502163\pi$
$379$	−0.264577			−0.0135904			−0.00679520	+	0.999977i	$0.502163\pi$
$380$	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	$-0.536101\pi$
$383$	−4.42959			−0.226341			−0.113171	+	0.993576i	$0.536101\pi$
$384$	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	$-0.732431\pi$
$389$		−	29.3890i		−	1.49008i	0.667020	−	0.745040i	$-0.267569\pi$
$390$	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	$-0.778111\pi$
$401$		−	25.7115i		−	1.28397i	0.766716	−	0.641986i	$-0.221889\pi$
$402$	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
$414$	2.99180	−	6.08680i	0.147039	−	0.299150i
$415$			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	$-0.690612\pi$
$419$	−23.0762			−1.12734			−0.563672	+	0.825998i	$0.690612\pi$
$420$	3.83846	+	0.206172i	0.187298	+	0.0100602i
$421$			4.76852i			0.232404i	0.993226	+	0.116202i	$0.0370719\pi$
$421$			4.76852i			0.232404i	−0.993226	+	0.116202i	$0.962928\pi$
$422$	−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	$-0.398245\pi$
$431$	13.0482			0.628512			0.314256	+	0.949338i	$0.398245\pi$
$432$	0.428461	−	3.97699i	0.0206144	−	0.191343i
$433$		−	21.6534i		−	1.04059i	−0.853985	−	0.520297i	$-0.825821\pi$
$433$		−	21.6534i		−	1.04059i	0.853985	−	0.520297i	$-0.174179\pi$
$434$	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	$0.0601623\pi$
$457$			8.03293i			0.375765i	−0.982192	+	0.187882i	$0.939838\pi$
$458$	−1.08690	+	40.5006i	−0.0507877	+	1.89247i
$459$	0.0974606			0.00454907
$460$	8.49143	+	4.46044i	0.395915	+	0.207969i
$461$	−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	$-0.399998\pi$
$467$	13.3561			0.618045			0.309022	+	0.951055i	$0.399998\pi$
$468$	−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	$-0.890422\pi$
$479$	−41.2040			−1.88266			−0.941329	+	0.337490i	$0.890422\pi$
$480$	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	$-0.385377\pi$
$503$	15.8055			0.704733			0.352366	+	0.935862i	$0.385377\pi$
$504$	−5.41863	−	0.437095i	−0.241365	−	0.0194698i
$505$			9.08616i			0.404329i
$506$	−18.6974	+	38.0399i	−0.831203	+	1.69108i
$507$		−	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	$0.0559355\pi$
$521$			7.98084i			0.349647i	−0.984600	+	0.174824i	$0.944065\pi$
$522$	8.69343	+	0.233303i	0.380501	+	0.0102114i
$523$	22.2528			0.973047			0.486524	−	0.873667i	$-0.338265\pi$
$523$	22.2528			0.973047			0.486524	+	0.873667i	$0.338265\pi$
$524$	−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
$552$	−11.8352	−	6.62791i	−0.503738	−	0.282103i
$553$	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	$-0.818145\pi$
$557$		−	25.5238i		−	1.08148i	0.841191	−	0.540739i	$-0.181855\pi$
$558$	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	$-0.522993\pi$
$563$	−3.42487			−0.144341			−0.0721705	+	0.997392i	$0.522993\pi$
$564$	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	$0.175808\pi$
$569$			25.0302i			1.04932i	−0.851311	+	0.524661i	$0.824192\pi$
$570$	−2.42388	−	0.0650490i	−0.101525	−	0.00272460i
$571$	−16.1945			−0.677719			−0.338859	−	0.940837i	$-0.610041\pi$
$571$	−16.1945			−0.677719			−0.338859	+	0.940837i	$0.610041\pi$
$572$	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
$598$	−3.87521	+	7.88412i	−0.158469	+	0.322406i
$599$		−	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	$0.0653552\pi$
$613$			10.0957i			0.407760i	−0.978996	+	0.203880i	$0.934645\pi$
$614$	−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	$0.355006\pi$
$617$			44.6135i			1.79607i	−0.439921	+	0.898036i	$0.644994\pi$
$618$	−0.234812	+	8.74963i	−0.00944551	+	0.351962i
$619$	−32.5331			−1.30762			−0.653808	−	0.756661i	$-0.726829\pi$
$619$	−32.5331			−1.30762			−0.653808	+	0.756661i	$0.726829\pi$
$620$	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	$-0.535595\pi$
$631$	−5.60626			−0.223182			−0.111591	+	0.993754i	$0.535595\pi$
$632$	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	$-0.682038\pi$
$641$		−	42.5788i		−	1.68176i	0.541221	−	0.840880i	$-0.317962\pi$
$642$	0.283683	−	10.5707i	0.0111961	−	0.417192i
$643$	31.0918			1.22614			0.613071	−	0.790027i	$-0.289934\pi$
$643$	31.0918			1.22614			0.613071	+	0.790027i	$0.289934\pi$
$644$	−8.57297	+	16.3205i	−0.337822	+	0.643119i
$645$	−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	$-0.454164\pi$
$659$	7.36762			0.287002			0.143501	+	0.989650i	$0.454164\pi$
$660$	−12.4812	−	0.670390i	−0.485828	−	0.0260949i
$661$			1.11554i			0.0433895i	0.999765	+	0.0216948i	$0.00690620\pi$
$661$			1.11554i			0.0433895i	−0.999765	+	0.0216948i	$0.993094\pi$
$662$	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	$-0.907449\pi$
$677$		−	14.9183i		−	0.573357i	0.958027	−	0.286679i	$-0.0925512\pi$
$678$	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
$690$	2.99180	−	6.08680i	0.113896	−	0.231721i
$691$			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	$0.366282\pi$
$701$			48.3487i			1.82611i	−0.407840	+	0.913053i	$0.633718\pi$
$702$	−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	$-0.884897\pi$
$709$		−	18.8401i		−	0.707554i	0.935330	−	0.353777i	$-0.115103\pi$
$710$	−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	$-0.217159\pi$
$727$	41.8557			1.55234			0.776171	+	0.630522i	$0.217159\pi$
$728$	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	$0.232387\pi$
$733$			36.1122i			1.33384i	−0.745131	+	0.666918i	$0.767613\pi$
$734$	18.7010	+	0.501873i	0.690265	+	0.0185245i
$735$	3.30592			0.121941
$736$	−14.5063	+	22.9253i	−0.534709	+	0.845036i
$737$	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	$-0.567760\pi$
$743$	−11.5177			−0.422542			−0.211271	+	0.977428i	$0.567760\pi$
$744$	−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	$-0.447195\pi$
$751$	9.05061			0.330261			0.165131	+	0.986272i	$0.447195\pi$
$752$	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	$-0.827065\pi$
$757$		−	28.4467i		−	1.03391i	0.856012	−	0.516956i	$-0.172935\pi$
$758$	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	$0.0521165\pi$
$769$			9.04015i			0.325996i	−0.986626	+	0.162998i	$0.947884\pi$
$770$	−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	$-0.796831\pi$
$773$		−	33.1305i		−	1.19162i	0.803125	−	0.595810i	$-0.203169\pi$
$774$	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
$782$	−0.593223	−	0.291582i	−0.0212136	−	0.0104270i
$783$		−	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	$-0.489160\pi$
$787$	1.91035			0.0680967			0.0340484	+	0.999420i	$0.489160\pi$
$788$	−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	$-0.666606\pi$
$797$		−	48.9032i		−	1.73224i	0.499835	−	0.866120i	$-0.333394\pi$
$798$	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	$-0.206131\pi$
$827$	45.8710			1.59509			0.797546	+	0.603259i	$0.206131\pi$
$828$	−4.46044	+	8.49143i	−0.155011	+	0.295098i
$829$	−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	$-0.743249\pi$
$839$	−40.0855			−1.38390			−0.691952	+	0.721944i	$0.743249\pi$
$840$	−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
$874$	5.12960	−	10.4362i	0.173511	−	0.353009i
$875$			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	$0.255899\pi$
$881$			42.7469i			1.44018i	−0.693881	+	0.720090i	$0.744101\pi$
$882$	−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	$-0.819240\pi$
$907$	−50.7791			−1.68609			−0.843046	+	0.537842i	$0.819240\pi$
$908$	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	$-0.633649\pi$
$911$	−24.6076			−0.815285			−0.407642	+	0.913142i	$0.633649\pi$
$912$	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	$-0.438887\pi$
$919$	11.5691			0.381631			0.190815	+	0.981626i	$0.438887\pi$
$920$	−11.8352	−	6.62791i	−0.390193	−	0.218516i
$921$	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	$-0.818639\pi$
$937$		−	33.0245i		−	1.07886i	0.842029	−	0.539432i	$-0.181361\pi$
$938$	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	$0.280232\pi$
$941$			47.3005i			1.54195i	−0.636863	+	0.770977i	$0.719768\pi$
$942$	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	$-0.841397\pi$
$953$		−	29.5065i		−	0.955809i	0.878412	−	0.477904i	$-0.158603\pi$
$954$	−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
$966$	11.6988	+	5.75023i	0.376404	+	0.185011i
$967$		−	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	$-0.641914\pi$
$971$	−26.8740			−0.862426			−0.431213	+	0.902250i	$0.641914\pi$
$972$	−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	$-0.976424\pi$
$977$		−	4.62588i		−	0.147995i	0.997258	−	0.0739975i	$-0.0235757\pi$
$978$	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	$-0.778041\pi$
$983$	−48.0686			−1.53315			−0.766576	+	0.642154i	$0.778041\pi$
$984$	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.a.91.1	✓	48
4.3	odd	2		1380.2.p.b.91.2	yes	48
23.22	odd	2		1380.2.p.b.91.1	yes	48
92.91	even	2	inner	1380.2.p.a.91.2	yes	48

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

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} +(-2.99180 + 6.08680i) 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} +(4.46044 - 8.49143i) 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	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} - 2 q^{10} + 20 q^{14} - 48 q^{15} - 6 q^{16} + 4 q^{18} + 16 q^{19} + 28 q^{22} + 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} + 4 q^{30} + 16 q^{32} - 28 q^{34} + 2 q^{36} + 2 q^{40} - 8 q^{41} + 14 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} + 16 q^{51} - 16 q^{52} + 2 q^{54} + 40 q^{56} - 8 q^{58} + 2 q^{60} + 24 q^{62} - 26 q^{64} - 48 q^{67} - 44 q^{68} - 8 q^{69} + 4 q^{72} + 20 q^{74} - 64 q^{76} + 32 q^{77} - 64 q^{79} + 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} - 40 q^{86} + 2 q^{90} - 4 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) \) 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 + 14 * 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 - 4 * 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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