LMFDB - Embedded newform 1183.2.c.h.337.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(337,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1183.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 96x^{8} + 266x^{6} + 332x^{4} + 141x^{2} + 1 $ x^12 + 16x^10 + 96x^8 + 266x^6 + 332x^4 + 141*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.10
Root			$-1.54570i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.h.337.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.93488i q^{2} -2.54570 q^{3} -1.74376 q^{4} +0.312100i q^{5} -4.92562i q^{6} +1.00000i q^{7} +0.495793i q^{8} +3.48058 q^{9} +O(q^{10})$	\(q+1.93488i q^{2} -2.54570 q^{3} -1.74376 q^{4} +0.312100i q^{5} -4.92562i q^{6} +1.00000i q^{7} +0.495793i q^{8} +3.48058 q^{9} -0.603875 q^{10} -4.16701i q^{11} +4.43909 q^{12} -1.93488 q^{14} -0.794512i q^{15} -4.44682 q^{16} +5.20672 q^{17} +6.73450i q^{18} -4.87572i q^{19} -0.544227i q^{20} -2.54570i q^{21} +8.06266 q^{22} -3.39655 q^{23} -1.26214i q^{24} +4.90259 q^{25} -1.22341 q^{27} -1.74376i q^{28} +3.54362 q^{29} +1.53728 q^{30} -9.52510i q^{31} -7.61248i q^{32} +10.6079i q^{33} +10.0744i q^{34} -0.312100 q^{35} -6.06929 q^{36} +11.7368i q^{37} +9.43392 q^{38} -0.154737 q^{40} -0.433763i q^{41} +4.92562 q^{42} +8.96489 q^{43} +7.26626i q^{44} +1.08629i q^{45} -6.57192i q^{46} -8.62354i q^{47} +11.3203 q^{48} -1.00000 q^{49} +9.48593i q^{50} -13.2547 q^{51} -1.14124 q^{53} -2.36714i q^{54} +1.30052 q^{55} -0.495793 q^{56} +12.4121i q^{57} +6.85649i q^{58} +11.7192i q^{59} +1.38544i q^{60} -4.87971 q^{61} +18.4299 q^{62} +3.48058i q^{63} +5.83559 q^{64} -20.5251 q^{66} +8.71761i q^{67} -9.07927 q^{68} +8.64660 q^{69} -0.603875i q^{70} +6.09160i q^{71} +1.72565i q^{72} +3.59203i q^{73} -22.7092 q^{74} -12.4805 q^{75} +8.50208i q^{76} +4.16701 q^{77} +9.90686 q^{79} -1.38785i q^{80} -7.32731 q^{81} +0.839279 q^{82} -0.500966i q^{83} +4.43909i q^{84} +1.62502i q^{85} +17.3460i q^{86} -9.02100 q^{87} +2.06597 q^{88} -10.5068i q^{89} -2.10184 q^{90} +5.92277 q^{92} +24.2480i q^{93} +16.6855 q^{94} +1.52171 q^{95} +19.3791i q^{96} -2.35258i q^{97} -1.93488i q^{98} -14.5036i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{3} - 16 q^{4}+O(q^{10}) $ 12 * q - 8 * q^3 - 16 * q^4	$ 12 q - 8 q^{3} - 16 q^{4} + 28 q^{10} + 46 q^{12} - 4 q^{14} + 46 q^{17} - 8 q^{22} + 36 q^{23} + 20 q^{25} - 20 q^{27} - 30 q^{29} - 28 q^{30} - 4 q^{35} - 44 q^{36} + 22 q^{38} - 28 q^{40} + 16 q^{42} + 36 q^{43} - 22 q^{48} - 12 q^{49} - 28 q^{51} - 50 q^{53} + 6 q^{56} + 32 q^{61} + 18 q^{62} + 14 q^{64} + 32 q^{66} - 68 q^{68} + 2 q^{69} - 28 q^{74} - 30 q^{75} + 16 q^{77} + 4 q^{79} - 12 q^{81} + 20 q^{82} + 26 q^{87} + 96 q^{88} - 64 q^{92} - 28 q^{94} + 14 q^{95}+O(q^{100}) $ 12 * q - 8 * q^3 - 16 * q^4 + 28 * q^10 + 46 * q^12 - 4 * q^14 + 46 * q^17 - 8 * q^22 + 36 * q^23 + 20 * q^25 - 20 * q^27 - 30 * q^29 - 28 * q^30 - 4 * q^35 - 44 * q^36 + 22 * q^38 - 28 * q^40 + 16 * q^42 + 36 * q^43 - 22 * q^48 - 12 * q^49 - 28 * q^51 - 50 * q^53 + 6 * q^56 + 32 * q^61 + 18 * q^62 + 14 * q^64 + 32 * q^66 - 68 * q^68 + 2 * q^69 - 28 * q^74 - 30 * q^75 + 16 * q^77 + 4 * q^79 - 12 * q^81 + 20 * q^82 + 26 * q^87 + 96 * q^88 - 64 * q^92 - 28 * q^94 + 14 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.93488i	1.36817i	0.729404	+	0.684083i	$0.239798\pi$
$2$	1.93488i	1.36817i	−0.729404	+	0.684083i	$0.760202\pi$
$3$	−2.54570	−1.46976	−0.734880	−	0.678198i	$-0.762761\pi$
$3$	−2.54570	−1.46976	−0.734880	+	0.678198i	$0.762761\pi$
$4$	−1.74376	−0.871880
$5$	0.312100i	0.139575i	0.997562	+	0.0697876i	$0.0222322\pi$
$5$	0.312100i	0.139575i	−0.997562	+	0.0697876i	$0.977768\pi$
$6$	− 4.92562i	− 2.01088i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	0.495793i	0.175289i
$9$	3.48058	1.16019
$10$	−0.603875	−0.190962
$11$	− 4.16701i	− 1.25640i	−0.778052	−	0.628200i	$-0.783792\pi$
$11$	− 4.16701i	− 1.25640i	0.778052	−	0.628200i	$-0.216208\pi$
$12$	4.43909	1.28145
$13$	0	0
$13$	0	0
$14$	−1.93488	−0.517118
$15$	− 0.794512i	− 0.205142i
$16$	−4.44682	−1.11171
$17$	5.20672	1.26281	0.631407	−	0.775451i	$-0.282478\pi$
$17$	5.20672	1.26281	0.631407	+	0.775451i	$0.282478\pi$
$18$	6.73450i	1.58734i
$19$	− 4.87572i	− 1.11857i	−0.828977	−	0.559283i	$-0.811077\pi$
$19$	− 4.87572i	− 1.11857i	0.828977	−	0.559283i	$-0.188923\pi$
$20$	− 0.544227i	− 0.121693i
$21$	− 2.54570i	− 0.555517i
$22$	8.06266	1.71896
$23$	−3.39655	−0.708230	−0.354115	−	0.935202i	$-0.615218\pi$
$23$	−3.39655	−0.708230	−0.354115	+	0.935202i	$0.615218\pi$
$24$	− 1.26214i	− 0.257633i
$25$	4.90259	0.980519
$26$	0	0
$27$	−1.22341	−0.235445
$28$	− 1.74376i	− 0.329540i
$29$	3.54362	0.658034	0.329017	−	0.944324i	$-0.393283\pi$
$29$	3.54362	0.658034	0.329017	+	0.944324i	$0.393283\pi$
$30$	1.53728	0.280668
$31$	− 9.52510i	− 1.71076i	−0.518002	−	0.855380i	$-0.673324\pi$
$31$	− 9.52510i	− 1.71076i	0.518002	−	0.855380i	$-0.326676\pi$
$32$	− 7.61248i	− 1.34571i
$33$	10.6079i	1.84661i
$34$	10.0744i	1.72774i
$35$	−0.312100	−0.0527545
$36$	−6.06929	−1.01155
$37$	11.7368i	1.92951i	0.263146	+	0.964756i	$0.415240\pi$
$37$	11.7368i	1.92951i	−0.263146	+	0.964756i	$0.584760\pi$
$38$	9.43392	1.53038
$39$	0	0
$40$	−0.154737	−0.0244661
$41$	− 0.433763i	− 0.0677424i	−0.999426	−	0.0338712i	$-0.989216\pi$
$41$	− 0.433763i	− 0.0677424i	0.999426	−	0.0338712i	$-0.0107836\pi$
$42$	4.92562	0.760040
$43$	8.96489	1.36713	0.683567	−	0.729888i	$-0.260428\pi$
$43$	8.96489	1.36713	0.683567	+	0.729888i	$0.260428\pi$
$44$	7.26626i	1.09543i
$45$	1.08629i	0.161934i
$46$	− 6.57192i	− 0.968977i
$47$	− 8.62354i	− 1.25787i	−0.777457	−	0.628936i	$-0.783491\pi$
$47$	− 8.62354i	− 1.25787i	0.777457	−	0.628936i	$-0.216509\pi$
$48$	11.3203	1.63394
$49$	−1.00000	−0.142857
$50$	9.48593i	1.34151i
$51$	−13.2547	−1.85603
$52$	0	0
$53$	−1.14124	−0.156761	−0.0783807	−	0.996924i	$-0.524975\pi$
$53$	−1.14124	−0.156761	−0.0783807	+	0.996924i	$0.524975\pi$
$54$	− 2.36714i	− 0.322127i
$55$	1.30052	0.175362
$56$	−0.495793	−0.0662532
$57$	12.4121i	1.64402i
$58$	6.85649i	0.900301i
$59$	11.7192i	1.52571i	0.646569	+	0.762855i	$0.276203\pi$
$59$	11.7192i	1.52571i	−0.646569	+	0.762855i	$0.723797\pi$
$60$	1.38544i	0.178859i
$61$	−4.87971	−0.624783	−0.312392	−	0.949953i	$-0.601130\pi$
$61$	−4.87971	−0.624783	−0.312392	+	0.949953i	$0.601130\pi$
$62$	18.4299	2.34060
$63$	3.48058i	0.438512i
$64$	5.83559	0.729448
$65$	0	0
$66$	−20.5251	−2.52646
$67$	8.71761i	1.06503i	0.846422	+	0.532513i	$0.178752\pi$
$67$	8.71761i	1.06503i	−0.846422	+	0.532513i	$0.821248\pi$
$68$	−9.07927	−1.10102
$69$	8.64660	1.04093
$70$	− 0.603875i	− 0.0721769i
$71$	6.09160i	0.722939i	0.932384	+	0.361470i	$0.117725\pi$
$71$	6.09160i	0.722939i	−0.932384	+	0.361470i	$0.882275\pi$
$72$	1.72565i	0.203369i
$73$	3.59203i	0.420415i	0.977657	+	0.210208i	$0.0674140\pi$
$73$	3.59203i	0.420415i	−0.977657	+	0.210208i	$0.932586\pi$
$74$	−22.7092	−2.63989
$75$	−12.4805	−1.44113
$76$	8.50208i	0.975255i
$77$	4.16701	0.474875
$78$	0	0
$79$	9.90686	1.11461	0.557304	−	0.830308i	$-0.311836\pi$
$79$	9.90686	1.11461	0.557304	+	0.830308i	$0.311836\pi$
$80$	− 1.38785i	− 0.155167i
$81$	−7.32731	−0.814146
$82$	0.839279	0.0926829
$83$	− 0.500966i	− 0.0549882i	−0.999622	−	0.0274941i	$-0.991247\pi$
$83$	− 0.500966i	− 0.0549882i	0.999622	−	0.0274941i	$-0.00875274\pi$
$84$	4.43909i	0.484344i
$85$	1.62502i	0.176258i
$86$	17.3460i	1.87047i
$87$	−9.02100	−0.967152
$88$	2.06597	0.220234
$89$	− 10.5068i	− 1.11372i	−0.830606	−	0.556861i	$-0.812006\pi$
$89$	− 10.5068i	− 1.11372i	0.830606	−	0.556861i	$-0.187994\pi$
$90$	−2.10184	−0.221553
$91$	0	0
$92$	5.92277	0.617492
$93$	24.2480i	2.51440i
$94$	16.6855	1.72098
$95$	1.52171	0.156124
$96$	19.3791i	1.97787i
$97$	− 2.35258i	− 0.238868i	−0.992842	−	0.119434i	$-0.961892\pi$
$97$	− 2.35258i	− 0.238868i	0.992842	−	0.119434i	$-0.0381080\pi$
$98$	− 1.93488i	− 0.195452i
$99$	− 14.5036i	− 1.45767i
$100$	−8.54895	−0.854895
$101$	6.26932	0.623821	0.311910	−	0.950112i	$-0.399031\pi$
$101$	6.26932	0.623821	0.311910	+	0.950112i	$0.399031\pi$
$102$	− 25.6463i	− 2.53936i
$103$	3.76722	0.371195	0.185598	−	0.982626i	$-0.440578\pi$
$103$	3.76722	0.371195	0.185598	+	0.982626i	$0.440578\pi$
$104$	0	0
$105$	0.794512	0.0775364
$106$	− 2.20816i	− 0.214476i
$107$	4.01657	0.388296	0.194148	−	0.980972i	$-0.437806\pi$
$107$	4.01657	0.388296	0.194148	+	0.980972i	$0.437806\pi$
$108$	2.13333	0.205279
$109$	4.97360i	0.476384i	0.971218	+	0.238192i	$0.0765548\pi$
$109$	4.97360i	0.476384i	−0.971218	+	0.238192i	$0.923445\pi$
$110$	2.51635i	0.239925i
$111$	− 29.8783i	− 2.83592i
$112$	− 4.44682i	− 0.420185i
$113$	−13.0735	−1.22985	−0.614925	−	0.788586i	$-0.710814\pi$
$113$	−13.0735	−1.22985	−0.614925	+	0.788586i	$0.710814\pi$
$114$	−24.0159	−2.24930
$115$	− 1.06006i	− 0.0988514i
$116$	−6.17923	−0.573727
$117$	0	0
$118$	−22.6753	−2.08743
$119$	5.20672i	0.477299i
$120$	0.393914	0.0359592
$121$	−6.36395	−0.578541
$122$	− 9.44166i	− 0.854807i
$123$	1.10423i	0.0995650i
$124$	16.6095i	1.49158i
$125$	3.09060i	0.276431i
$126$	−6.73450	−0.599957
$127$	10.8005	0.958389	0.479194	−	0.877709i	$-0.340929\pi$
$127$	10.8005	0.958389	0.479194	+	0.877709i	$0.340929\pi$
$128$	− 3.93379i	− 0.347701i
$129$	−22.8219	−2.00936
$130$	0	0
$131$	12.6661	1.10664	0.553320	−	0.832969i	$-0.313361\pi$
$131$	12.6661	1.10664	0.553320	+	0.832969i	$0.313361\pi$
$132$	− 18.4977i	− 1.61002i
$133$	4.87572	0.422778
$134$	−16.8675	−1.45713
$135$	− 0.381825i	− 0.0328622i
$136$	2.58146i	0.221358i
$137$	− 14.7249i	− 1.25803i	−0.777391	−	0.629017i	$-0.783457\pi$
$137$	− 14.7249i	− 1.25803i	0.777391	−	0.629017i	$-0.216543\pi$
$138$	16.7301i	1.42416i
$139$	22.7805	1.93222	0.966111	−	0.258129i	$-0.0831059\pi$
$139$	22.7805	1.93222	0.966111	+	0.258129i	$0.0831059\pi$
$140$	0.544227	0.0459956
$141$	21.9529i	1.84877i
$142$	−11.7865	−0.989102
$143$	0	0
$144$	−15.4775	−1.28979
$145$	1.10596i	0.0918453i
$146$	−6.95014	−0.575198
$147$	2.54570	0.209966
$148$	− 20.4661i	− 1.68230i
$149$	7.21670i	0.591215i	0.955309	+	0.295608i	$0.0955221\pi$
$149$	7.21670i	0.591215i	−0.955309	+	0.295608i	$0.904478\pi$
$150$	− 24.1483i	− 1.97170i
$151$	0.657085i	0.0534728i	0.999643	+	0.0267364i	$0.00851148\pi$
$151$	0.657085i	0.0534728i	−0.999643	+	0.0267364i	$0.991489\pi$
$152$	2.41735	0.196073
$153$	18.1224	1.46511
$154$	8.06266i	0.649708i
$155$	2.97278	0.238780
$156$	0	0
$157$	−8.62702	−0.688511	−0.344255	−	0.938876i	$-0.611869\pi$
$157$	−8.62702	−0.688511	−0.344255	+	0.938876i	$0.611869\pi$
$158$	19.1686i	1.52497i
$159$	2.90525	0.230401
$160$	2.37585	0.187828
$161$	− 3.39655i	− 0.267686i
$162$	− 14.1775i	− 1.11389i
$163$	− 11.5337i	− 0.903386i	−0.892173	−	0.451693i	$-0.850820\pi$
$163$	− 11.5337i	− 0.903386i	0.892173	−	0.451693i	$-0.149180\pi$
$164$	0.756378i	0.0590632i
$165$	−3.31074	−0.257740
$166$	0.969309	0.0752330
$167$	− 10.7650i	− 0.833020i	−0.909131	−	0.416510i	$-0.863253\pi$
$167$	− 10.7650i	− 0.833020i	0.909131	−	0.416510i	$-0.136747\pi$
$168$	1.26214	0.0973762
$169$	0	0
$170$	−3.14421	−0.241150
$171$	− 16.9703i	− 1.29775i
$172$	−15.6326	−1.19198
$173$	10.1547	0.772045	0.386022	−	0.922489i	$-0.373849\pi$
$173$	10.1547	0.772045	0.386022	+	0.922489i	$0.373849\pi$
$174$	− 17.4545i	− 1.32323i
$175$	4.90259i	0.370601i
$176$	18.5299i	1.39675i
$177$	− 29.8336i	− 2.24243i
$178$	20.3295	1.52376
$179$	7.03271	0.525650	0.262825	−	0.964844i	$-0.415346\pi$
$179$	7.03271	0.525650	0.262825	+	0.964844i	$0.415346\pi$
$180$	− 1.89422i	− 0.141187i
$181$	21.0737	1.56640	0.783198	−	0.621773i	$-0.213587\pi$
$181$	21.0737	1.56640	0.783198	+	0.621773i	$0.213587\pi$
$182$	0	0
$183$	12.4223	0.918281
$184$	− 1.68399i	− 0.124145i
$185$	−3.66304	−0.269312
$186$	−46.9170	−3.44012
$187$	− 21.6964i	− 1.58660i
$188$	15.0374i	1.09671i
$189$	− 1.22341i	− 0.0889897i
$190$	2.94432i	0.213604i
$191$	−18.1189	−1.31104	−0.655520	−	0.755178i	$-0.727550\pi$
$191$	−18.1189	−1.31104	−0.655520	+	0.755178i	$0.727550\pi$
$192$	−14.8556	−1.07211
$193$	1.53602i	0.110565i	0.998471	+	0.0552827i	$0.0176060\pi$
$193$	1.53602i	0.110565i	−0.998471	+	0.0552827i	$0.982394\pi$
$194$	4.55195	0.326811
$195$	0	0
$196$	1.74376	0.124554
$197$	6.72807i	0.479355i	0.970853	+	0.239677i	$0.0770417\pi$
$197$	6.72807i	0.479355i	−0.970853	+	0.239677i	$0.922958\pi$
$198$	28.0627	1.99433
$199$	−0.640433	−0.0453991	−0.0226995	−	0.999742i	$-0.507226\pi$
$199$	−0.640433	−0.0453991	−0.0226995	+	0.999742i	$0.507226\pi$
$200$	2.43067i	0.171875i
$201$	− 22.1924i	− 1.56533i
$202$	12.1304i	0.853491i
$203$	3.54362i	0.248714i
$204$	23.1131	1.61824
$205$	0.135377	0.00945516
$206$	7.28911i	0.507857i
$207$	−11.8220	−0.821683
$208$	0	0
$209$	−20.3171	−1.40537
$210$	1.53728i	0.106083i
$211$	17.5658	1.20928	0.604638	−	0.796500i	$-0.293318\pi$
$211$	17.5658	1.20928	0.604638	+	0.796500i	$0.293318\pi$
$212$	1.99005	0.136677
$213$	− 15.5074i	− 1.06255i
$214$	7.77157i	0.531254i
$215$	2.79794i	0.190818i
$216$	− 0.606556i	− 0.0412709i
$217$	9.52510	0.646606
$218$	−9.62331	−0.651773
$219$	− 9.14422i	− 0.617909i
$220$	−2.26780	−0.152895
$221$	0	0
$222$	57.8108	3.88001
$223$	− 18.3241i	− 1.22707i	−0.789667	−	0.613535i	$-0.789747\pi$
$223$	− 18.3241i	− 1.22707i	0.789667	−	0.613535i	$-0.210253\pi$
$224$	7.61248	0.508630
$225$	17.0639	1.13759
$226$	− 25.2956i	− 1.68264i
$227$	0.673988i	0.0447342i	0.999750	+	0.0223671i	$0.00712026\pi$
$227$	0.673988i	0.0447342i	−0.999750	+	0.0223671i	$0.992880\pi$
$228$	− 21.6437i	− 1.43339i
$229$	− 19.4805i	− 1.28730i	−0.765318	−	0.643652i	$-0.777418\pi$
$229$	− 19.4805i	− 1.28730i	0.765318	−	0.643652i	$-0.222582\pi$
$230$	2.05110	0.135245
$231$	−10.6079	−0.697951
$232$	1.75691i	0.115346i
$233$	30.1222	1.97337	0.986686	−	0.162637i	$-0.0520001\pi$
$233$	30.1222	1.97337	0.986686	+	0.162637i	$0.0520001\pi$
$234$	0	0
$235$	2.69140	0.175568
$236$	− 20.4355i	− 1.33024i
$237$	−25.2199	−1.63821
$238$	−10.0744	−0.653025
$239$	13.2375i	0.856266i	0.903716	+	0.428133i	$0.140828\pi$
$239$	13.2375i	0.856266i	−0.903716	+	0.428133i	$0.859172\pi$
$240$	3.53305i	0.228057i
$241$	− 13.3135i	− 0.857596i	−0.903400	−	0.428798i	$-0.858937\pi$
$241$	− 13.3135i	− 0.857596i	0.903400	−	0.428798i	$-0.141063\pi$
$242$	− 12.3135i	− 0.791540i
$243$	22.3233	1.43204
$244$	8.50905	0.544736
$245$	− 0.312100i	− 0.0199393i
$246$	−2.13655	−0.136222
$247$	0	0
$248$	4.72248	0.299878
$249$	1.27531i	0.0808194i
$250$	−5.97993	−0.378204
$251$	−25.5724	−1.61411	−0.807056	−	0.590474i	$-0.798941\pi$
$251$	−25.5724	−1.61411	−0.807056	+	0.590474i	$0.798941\pi$
$252$	− 6.06929i	− 0.382330i
$253$	14.1535i	0.889820i
$254$	20.8977i	1.31124i
$255$	− 4.13680i	− 0.259056i
$256$	19.2826	1.20516
$257$	−0.589113	−0.0367478	−0.0183739	−	0.999831i	$-0.505849\pi$
$257$	−0.589113	−0.0367478	−0.0183739	+	0.999831i	$0.505849\pi$
$258$	− 44.1577i	− 2.74914i
$259$	−11.7368	−0.729287
$260$	0	0
$261$	12.3339	0.763447
$262$	24.5073i	1.51407i
$263$	−18.5016	−1.14085	−0.570427	−	0.821348i	$-0.693222\pi$
$263$	−18.5016	−1.14085	−0.570427	+	0.821348i	$0.693222\pi$
$264$	−5.25935	−0.323690
$265$	− 0.356181i	− 0.0218800i
$266$	9.43392i	0.578431i
$267$	26.7472i	1.63690i
$268$	− 15.2014i	− 0.928575i
$269$	−2.70804	−0.165112	−0.0825560	−	0.996586i	$-0.526308\pi$
$269$	−2.70804	−0.165112	−0.0825560	+	0.996586i	$0.526308\pi$
$270$	0.738785	0.0449610
$271$	11.7872i	0.716018i	0.933718	+	0.358009i	$0.116544\pi$
$271$	11.7872i	0.716018i	−0.933718	+	0.358009i	$0.883456\pi$
$272$	−23.1533	−1.40388
$273$	0	0
$274$	28.4910	1.72120
$275$	− 20.4291i	− 1.23192i
$276$	−15.0776	−0.907564
$277$	24.0504	1.44505	0.722523	−	0.691347i	$-0.242982\pi$
$277$	24.0504	1.44505	0.722523	+	0.691347i	$0.242982\pi$
$278$	44.0776i	2.64360i
$279$	− 33.1529i	− 1.98481i
$280$	− 0.154737i	− 0.00924730i
$281$	19.1899i	1.14477i	0.819983	+	0.572387i	$0.193983\pi$
$281$	19.1899i	1.14477i	−0.819983	+	0.572387i	$0.806017\pi$
$282$	−42.4763	−2.52943
$283$	12.2120	0.725930	0.362965	−	0.931803i	$-0.381765\pi$
$283$	12.2120	0.725930	0.362965	+	0.931803i	$0.381765\pi$
$284$	− 10.6223i	− 0.630316i
$285$	−3.87381	−0.229465
$286$	0	0
$287$	0.433763	0.0256042
$288$	− 26.4958i	− 1.56128i
$289$	10.1099	0.594702
$290$	−2.13991	−0.125660
$291$	5.98895i	0.351078i
$292$	− 6.26364i	− 0.366552i
$293$	11.3644i	0.663914i	0.943295	+	0.331957i	$0.107709\pi$
$293$	11.3644i	0.663914i	−0.943295	+	0.331957i	$0.892291\pi$
$294$	4.92562i	0.287268i
$295$	−3.65756	−0.212951
$296$	−5.81901	−0.338223
$297$	5.09794i	0.295813i
$298$	−13.9635	−0.808881
$299$	0	0
$300$	21.7630	1.25649
$301$	8.96489i	0.516728i
$302$	−1.27138	−0.0731597
$303$	−15.9598	−0.916867
$304$	21.6814i	1.24352i
$305$	− 1.52296i	− 0.0872043i
$306$	35.0647i	2.00451i
$307$	− 8.19392i	− 0.467652i	−0.972278	−	0.233826i	$-0.924875\pi$
$307$	− 8.19392i	− 0.467652i	0.972278	−	0.233826i	$-0.0751246\pi$
$308$	−7.26626	−0.414034
$309$	−9.59020	−0.545567
$310$	5.75198i	0.326690i
$311$	−28.5674	−1.61991	−0.809954	−	0.586493i	$-0.800508\pi$
$311$	−28.5674	−1.61991	−0.809954	+	0.586493i	$0.800508\pi$
$312$	0	0
$313$	9.40971	0.531869	0.265934	−	0.963991i	$-0.414320\pi$
$313$	9.40971	0.531869	0.265934	+	0.963991i	$0.414320\pi$
$314$	− 16.6922i	− 0.941998i
$315$	−1.08629	−0.0612054
$316$	−17.2752	−0.971805
$317$	− 1.95188i	− 0.109628i	−0.998497	−	0.0548142i	$-0.982543\pi$
$317$	− 1.95188i	− 0.109628i	0.998497	−	0.0548142i	$-0.0174567\pi$
$318$	5.62131i	0.315228i
$319$	− 14.7663i	− 0.826754i
$320$	1.82129i	0.101813i
$321$	−10.2250	−0.570702
$322$	6.57192	0.366239
$323$	− 25.3865i	− 1.41254i
$324$	12.7771	0.709837
$325$	0	0
$326$	22.3162	1.23598
$327$	− 12.6613i	− 0.700170i
$328$	0.215057	0.0118745
$329$	8.62354	0.475431
$330$	− 6.40588i	− 0.352632i
$331$	− 7.34325i	− 0.403622i	−0.979425	−	0.201811i	$-0.935317\pi$
$331$	− 7.34325i	− 0.403622i	0.979425	−	0.201811i	$-0.0646826\pi$
$332$	0.873565i	0.0479431i
$333$	40.8507i	2.23861i
$334$	20.8290	1.13971
$335$	−2.72076	−0.148651
$336$	11.3203i	0.617571i
$337$	23.0416	1.25516	0.627579	−	0.778553i	$-0.284046\pi$
$337$	23.0416	1.25516	0.627579	+	0.778553i	$0.284046\pi$
$338$	0	0
$339$	33.2811	1.80758
$340$	− 2.83364i	− 0.153676i
$341$	−39.6912	−2.14940
$342$	32.8355	1.77554
$343$	− 1.00000i	− 0.0539949i
$344$	4.44473i	0.239644i
$345$	2.69860i	0.145288i
$346$	19.6480i	1.05629i
$347$	−25.2471	−1.35533	−0.677667	−	0.735369i	$-0.737009\pi$
$347$	−25.2471	−1.35533	−0.677667	+	0.735369i	$0.737009\pi$
$348$	15.7305	0.843241
$349$	2.03258i	0.108802i	0.998519	+	0.0544008i	$0.0173249\pi$
$349$	2.03258i	0.108802i	−0.998519	+	0.0544008i	$0.982675\pi$
$350$	−9.48593	−0.507044
$351$	0	0
$352$	−31.7212	−1.69075
$353$	− 9.68813i	− 0.515647i	−0.966192	−	0.257824i	$-0.916995\pi$
$353$	− 9.68813i	− 0.515647i	0.966192	−	0.257824i	$-0.0830053\pi$
$354$	57.7243	3.06801
$355$	−1.90119	−0.100904
$356$	18.3214i	0.971032i
$357$	− 13.2547i	− 0.701515i
$358$	13.6075i	0.719176i
$359$	− 26.9664i	− 1.42323i	−0.702569	−	0.711616i	$-0.747964\pi$
$359$	− 26.9664i	− 1.42323i	0.702569	−	0.711616i	$-0.252036\pi$
$360$	−0.538574	−0.0283853
$361$	−4.77260	−0.251189
$362$	40.7751i	2.14309i
$363$	16.2007	0.850316
$364$	0	0
$365$	−1.12107	−0.0586796
$366$	24.0356i	1.25636i
$367$	−6.58796	−0.343888	−0.171944	−	0.985107i	$-0.555005\pi$
$367$	−6.58796	−0.343888	−0.171944	+	0.985107i	$0.555005\pi$
$368$	15.1039	0.787343
$369$	− 1.50975i	− 0.0785942i
$370$	− 7.08754i	− 0.368464i
$371$	− 1.14124i	− 0.0592502i
$372$	− 42.2828i	− 2.19226i
$373$	16.5944	0.859225	0.429613	−	0.903013i	$-0.358650\pi$
$373$	16.5944	0.859225	0.429613	+	0.903013i	$0.358650\pi$
$374$	41.9800	2.17073
$375$	− 7.86773i	− 0.406288i
$376$	4.27549	0.220492
$377$	0	0
$378$	2.36714	0.121753
$379$	− 30.7940i	− 1.58178i	−0.611959	−	0.790890i	$-0.709618\pi$
$379$	− 30.7940i	− 1.58178i	0.611959	−	0.790890i	$-0.290382\pi$
$380$	−2.65350	−0.136121
$381$	−27.4948	−1.40860
$382$	− 35.0579i	− 1.79372i
$383$	28.2978i	1.44595i	0.690875	+	0.722974i	$0.257226\pi$
$383$	28.2978i	1.44595i	−0.690875	+	0.722974i	$0.742774\pi$
$384$	10.0142i	0.511038i
$385$	1.30052i	0.0662807i
$386$	−2.97202	−0.151272
$387$	31.2030	1.58614
$388$	4.10233i	0.208264i
$389$	−12.9393	−0.656047	−0.328024	−	0.944670i	$-0.606383\pi$
$389$	−12.9393	−0.656047	−0.328024	+	0.944670i	$0.606383\pi$
$390$	0	0
$391$	−17.6849	−0.894364
$392$	− 0.495793i	− 0.0250413i
$393$	−32.2440	−1.62650
$394$	−13.0180	−0.655837
$395$	3.09193i	0.155572i
$396$	25.2908i	1.27091i
$397$	18.3110i	0.919004i	0.888177	+	0.459502i	$0.151972\pi$
$397$	18.3110i	0.919004i	−0.888177	+	0.459502i	$0.848028\pi$
$398$	− 1.23916i	− 0.0621135i
$399$	−12.4121	−0.621382
$400$	−21.8010	−1.09005
$401$	1.31244i	0.0655402i	0.999463	+	0.0327701i	$0.0104329\pi$
$401$	1.31244i	0.0655402i	−0.999463	+	0.0327701i	$0.989567\pi$
$402$	42.9397	2.14164
$403$	0	0
$404$	−10.9322	−0.543897
$405$	− 2.28685i	− 0.113635i
$406$	−6.85649	−0.340282
$407$	48.9072	2.42424
$408$	− 6.57161i	− 0.325343i
$409$	29.3018i	1.44888i	0.689338	+	0.724440i	$0.257901\pi$
$409$	29.3018i	1.44888i	−0.689338	+	0.724440i	$0.742099\pi$
$410$	0.261939i	0.0129362i
$411$	37.4852i	1.84901i
$412$	−6.56912	−0.323638
$413$	−11.7192	−0.576664
$414$	− 22.8741i	− 1.12420i
$415$	0.156351	0.00767499
$416$	0	0
$417$	−57.9924	−2.83990
$418$	− 39.3112i	− 1.92277i
$419$	−0.303569	−0.0148303	−0.00741516	−	0.999973i	$-0.502360\pi$
$419$	−0.303569	−0.0148303	−0.00741516	+	0.999973i	$0.502360\pi$
$420$	−1.38544	−0.0676024
$421$	− 1.19312i	− 0.0581492i	−0.999577	−	0.0290746i	$-0.990744\pi$
$421$	− 1.19312i	− 0.0581492i	0.999577	−	0.0290746i	$-0.00925604\pi$
$422$	33.9876i	1.65449i
$423$	− 30.0149i	− 1.45937i
$424$	− 0.565819i	− 0.0274786i
$425$	25.5264	1.23821
$426$	30.0049	1.45374
$427$	− 4.87971i	− 0.236146i
$428$	−7.00393	−0.338548
$429$	0	0
$430$	−5.41368	−0.261071
$431$	− 22.7978i	− 1.09813i	−0.835780	−	0.549065i	$-0.814984\pi$
$431$	− 22.7978i	− 1.09813i	0.835780	−	0.549065i	$-0.185016\pi$
$432$	5.44027	0.261745
$433$	4.00964	0.192691	0.0963455	−	0.995348i	$-0.469285\pi$
$433$	4.00964	0.192691	0.0963455	+	0.995348i	$0.469285\pi$
$434$	18.4299i	0.884665i
$435$	− 2.81545i	− 0.134991i
$436$	− 8.67276i	− 0.415350i
$437$	16.5606i	0.792202i
$438$	17.6930	0.845403
$439$	2.55835	0.122103	0.0610516	−	0.998135i	$-0.480555\pi$
$439$	2.55835	0.122103	0.0610516	+	0.998135i	$0.480555\pi$
$440$	0.644790i	0.0307392i
$441$	−3.48058	−0.165742
$442$	0	0
$443$	0.363292	0.0172605	0.00863026	−	0.999963i	$-0.497253\pi$
$443$	0.363292	0.0172605	0.00863026	+	0.999963i	$0.497253\pi$
$444$	52.1005i	2.47258i
$445$	3.27918	0.155448
$446$	35.4549	1.67884
$447$	− 18.3715i	− 0.868944i
$448$	5.83559i	0.275706i
$449$	− 15.3032i	− 0.722202i	−0.932527	−	0.361101i	$-0.882401\pi$
$449$	− 15.3032i	− 0.722202i	0.932527	−	0.361101i	$-0.117599\pi$
$450$	33.0165i	1.55641i
$451$	−1.80749	−0.0851115
$452$	22.7970	1.07228
$453$	− 1.67274i	− 0.0785922i
$454$	−1.30409	−0.0612038
$455$	0	0
$456$	−6.15383	−0.288180
$457$	− 8.91104i	− 0.416841i	−0.978039	−	0.208420i	$-0.933168\pi$
$457$	− 8.91104i	− 0.416841i	0.978039	−	0.208420i	$-0.0668322\pi$
$458$	37.6923	1.76125
$459$	−6.36993	−0.297323
$460$	1.84850i	0.0861866i
$461$	− 21.4636i	− 0.999657i	−0.866124	−	0.499829i	$-0.833396\pi$
$461$	− 21.4636i	− 0.999657i	0.866124	−	0.499829i	$-0.166604\pi$
$462$	− 20.5251i	− 0.954914i
$463$	3.09472i	0.143824i	0.997411	+	0.0719119i	$0.0229101\pi$
$463$	3.09472i	0.143824i	−0.997411	+	0.0719119i	$0.977090\pi$
$464$	−15.7579	−0.731540
$465$	−7.56781	−0.350949
$466$	58.2829i	2.69990i
$467$	−20.9079	−0.967503	−0.483751	−	0.875205i	$-0.660726\pi$
$467$	−20.9079	−0.967503	−0.483751	+	0.875205i	$0.660726\pi$
$468$	0	0
$469$	−8.71761	−0.402542
$470$	5.20755i	0.240206i
$471$	21.9618	1.01195
$472$	−5.81030	−0.267441
$473$	− 37.3568i	− 1.71767i
$474$	− 48.7974i	− 2.24134i
$475$	− 23.9037i	− 1.09677i
$476$	− 9.07927i	− 0.416148i
$477$	−3.97217	−0.181873
$478$	−25.6131	−1.17151
$479$	− 18.3562i	− 0.838715i	−0.907821	−	0.419357i	$-0.862255\pi$
$479$	− 18.3562i	− 0.838715i	0.907821	−	0.419357i	$-0.137745\pi$
$480$	−6.04820	−0.276061
$481$	0	0
$482$	25.7600	1.17333
$483$	8.64660i	0.393434i
$484$	11.0972	0.504418
$485$	0.734238	0.0333400
$486$	43.1930i	1.95927i
$487$	− 13.3086i	− 0.603070i	−0.953455	−	0.301535i	$-0.902501\pi$
$487$	− 13.3086i	− 0.603070i	0.953455	−	0.301535i	$-0.0974990\pi$
$488$	− 2.41933i	− 0.109518i
$489$	29.3612i	1.32776i
$490$	0.603875	0.0272803
$491$	14.5460	0.656452	0.328226	−	0.944599i	$-0.393549\pi$
$491$	14.5460	0.656452	0.328226	+	0.944599i	$0.393549\pi$
$492$	− 1.92551i	− 0.0868087i
$493$	18.4507	0.830976
$494$	0	0
$495$	4.52657	0.203454
$496$	42.3564i	1.90186i
$497$	−6.09160	−0.273245
$498$	−2.46757	−0.110574
$499$	31.7570i	1.42164i	0.703375	+	0.710819i	$0.251675\pi$
$499$	31.7570i	1.42164i	−0.703375	+	0.710819i	$0.748325\pi$
$500$	− 5.38926i	− 0.241015i
$501$	27.4044i	1.22434i
$502$	− 49.4794i	− 2.20838i
$503$	−16.6463	−0.742224	−0.371112	−	0.928588i	$-0.621023\pi$
$503$	−16.6463	−0.742224	−0.371112	+	0.928588i	$0.621023\pi$
$504$	−1.72565	−0.0768664
$505$	1.95665i	0.0870699i
$506$	−27.3852	−1.21742
$507$	0	0
$508$	−18.8335	−0.835600
$509$	25.1990i	1.11693i	0.829529	+	0.558463i	$0.188609\pi$
$509$	25.1990i	1.11693i	−0.829529	+	0.558463i	$0.811391\pi$
$510$	8.00421	0.354432
$511$	−3.59203	−0.158902
$512$	29.4419i	1.30116i
$513$	5.96498i	0.263360i
$514$	− 1.13986i	− 0.0502772i
$515$	1.17575i	0.0518096i
$516$	39.7959	1.75192
$517$	−35.9344	−1.58039
$518$	− 22.7092i	− 0.997786i
$519$	−25.8507	−1.13472
$520$	0	0
$521$	−23.9887	−1.05096	−0.525481	−	0.850805i	$-0.676115\pi$
$521$	−23.9887	−1.05096	−0.525481	+	0.850805i	$0.676115\pi$
$522$	23.8645i	1.04452i
$523$	12.9042	0.564259	0.282130	−	0.959376i	$-0.408959\pi$
$523$	12.9042	0.564259	0.282130	+	0.959376i	$0.408959\pi$
$524$	−22.0866	−0.964858
$525$	− 12.4805i	− 0.544695i
$526$	− 35.7983i	− 1.56088i
$527$	− 49.5945i	− 2.16037i
$528$	− 47.1716i	− 2.05288i
$529$	−11.4634	−0.498410
$530$	0.689167	0.0299355
$531$	40.7896i	1.77012i
$532$	−8.50208	−0.368612
$533$	0	0
$534$	−51.7526	−2.23956
$535$	1.25357i	0.0541965i
$536$	−4.32213	−0.186688
$537$	−17.9032	−0.772579
$538$	− 5.23973i	− 0.225901i
$539$	4.16701i	0.179486i
$540$	0.665811i	0.0286519i
$541$	− 11.5539i	− 0.496739i	−0.968665	−	0.248370i	$-0.920105\pi$
$541$	− 11.5539i	− 0.496739i	0.968665	−	0.248370i	$-0.0798948\pi$
$542$	−22.8067	−0.979633
$543$	−53.6473	−2.30222
$544$	− 39.6360i	− 1.69938i
$545$	−1.55226	−0.0664914
$546$	0	0
$547$	−31.4142	−1.34318	−0.671588	−	0.740925i	$-0.734387\pi$
$547$	−31.4142	−1.34318	−0.671588	+	0.740925i	$0.734387\pi$
$548$	25.6767i	1.09686i
$549$	−16.9842	−0.724869
$550$	39.5279	1.68548
$551$	− 17.2777i	− 0.736055i
$552$	4.28693i	0.182464i
$553$	9.90686i	0.421283i
$554$	46.5345i	1.97706i
$555$	9.32499	0.395824
$556$	−39.7238	−1.68467
$557$	37.9319i	1.60723i	0.595151	+	0.803614i	$0.297092\pi$
$557$	37.9319i	1.60723i	−0.595151	+	0.803614i	$0.702908\pi$
$558$	64.1468	2.71555
$559$	0	0
$560$	1.38785	0.0586474
$561$	55.2326i	2.33192i
$562$	−37.1302	−1.56624
$563$	−22.3144	−0.940438	−0.470219	−	0.882550i	$-0.655825\pi$
$563$	−22.3144	−0.940438	−0.470219	+	0.882550i	$0.655825\pi$
$564$	− 38.2806i	− 1.61191i
$565$	− 4.08023i	− 0.171657i
$566$	23.6288i	0.993193i
$567$	− 7.32731i	− 0.307718i
$568$	−3.02017	−0.126724
$569$	4.83382	0.202644	0.101322	−	0.994854i	$-0.467693\pi$
$569$	4.83382	0.202644	0.101322	+	0.994854i	$0.467693\pi$
$570$	− 7.49536i	− 0.313946i
$571$	8.46200	0.354124	0.177062	−	0.984200i	$-0.443341\pi$
$571$	8.46200	0.354124	0.177062	+	0.984200i	$0.443341\pi$
$572$	0	0
$573$	46.1253	1.92691
$574$	0.839279i	0.0350308i
$575$	−16.6519	−0.694433
$576$	20.3112	0.846301
$577$	− 9.70860i	− 0.404174i	−0.979368	−	0.202087i	$-0.935228\pi$
$577$	− 9.70860i	− 0.404174i	0.979368	−	0.202087i	$-0.0647724\pi$
$578$	19.5615i	0.813651i
$579$	− 3.91026i	− 0.162505i
$580$	− 1.92854i	− 0.0800781i
$581$	0.500966	0.0207836
$582$	−11.5879	−0.480333
$583$	4.75555i	0.196955i
$584$	−1.78090	−0.0736943
$585$	0	0
$586$	−21.9887	−0.908344
$587$	5.01204i	0.206869i	0.994636	+	0.103434i	$0.0329832\pi$
$587$	5.01204i	0.206869i	−0.994636	+	0.103434i	$0.967017\pi$
$588$	−4.43909	−0.183065
$589$	−46.4417	−1.91360
$590$	− 7.07694i	− 0.291353i
$591$	− 17.1276i	− 0.704536i
$592$	− 52.1913i	− 2.14505i
$593$	7.85096i	0.322400i	0.986922	+	0.161200i	$0.0515365\pi$
$593$	7.85096i	0.322400i	−0.986922	+	0.161200i	$0.948464\pi$
$594$	−9.86390	−0.404721
$595$	−1.62502	−0.0666191
$596$	− 12.5842i	− 0.515469i
$597$	1.63035	0.0667257
$598$	0	0
$599$	−28.9758	−1.18392	−0.591960	−	0.805967i	$-0.701646\pi$
$599$	−28.9758	−1.18392	−0.591960	+	0.805967i	$0.701646\pi$
$600$	− 6.18776i	− 0.252614i
$601$	7.84625	0.320055	0.160028	−	0.987113i	$-0.448842\pi$
$601$	7.84625	0.320055	0.160028	+	0.987113i	$0.448842\pi$
$602$	−17.3460	−0.706970
$603$	30.3423i	1.23564i
$604$	− 1.14580i	− 0.0466219i
$605$	− 1.98619i	− 0.0807500i
$606$	− 30.8803i	− 1.25443i
$607$	−41.8833	−1.69999	−0.849995	−	0.526791i	$-0.823395\pi$
$607$	−41.8833	−1.69999	−0.849995	+	0.526791i	$0.823395\pi$
$608$	−37.1163	−1.50526
$609$	− 9.02100i	− 0.365549i
$610$	2.94674	0.119310
$611$	0	0
$612$	−31.6011	−1.27740
$613$	19.3299i	0.780725i	0.920661	+	0.390363i	$0.127650\pi$
$613$	19.3299i	0.780725i	−0.920661	+	0.390363i	$0.872350\pi$
$614$	15.8543	0.639826
$615$	−0.344630	−0.0138968
$616$	2.06597i	0.0832405i
$617$	− 39.7821i	− 1.60157i	−0.598955	−	0.800783i	$-0.704417\pi$
$617$	− 39.7821i	− 1.60157i	0.598955	−	0.800783i	$-0.295583\pi$
$618$	− 18.5559i	− 0.746427i
$619$	− 14.2327i	− 0.572059i	−0.958221	−	0.286029i	$-0.907665\pi$
$619$	− 14.2327i	− 0.572059i	0.958221	−	0.286029i	$-0.0923355\pi$
$620$	−5.18382	−0.208187
$621$	4.15536	0.166749
$622$	− 55.2745i	− 2.21630i
$623$	10.5068	0.420947
$624$	0	0
$625$	23.5484	0.941936
$626$	18.2067i	0.727685i
$627$	51.7213	2.06555
$628$	15.0434	0.600299
$629$	61.1100i	2.43662i
$630$	− 2.10184i	− 0.0837391i
$631$	22.2652i	0.886364i	0.896432	+	0.443182i	$0.146150\pi$
$631$	22.2652i	0.886364i	−0.896432	+	0.443182i	$0.853850\pi$
$632$	4.91175i	0.195379i
$633$	−44.7171	−1.77735
$634$	3.77665	0.149990
$635$	3.37083i	0.133767i
$636$	−5.06606	−0.200882
$637$	0	0
$638$	28.5710	1.13114
$639$	21.2023i	0.838749i
$640$	1.22774	0.0485305
$641$	−4.25054	−0.167886	−0.0839430	−	0.996471i	$-0.526751\pi$
$641$	−4.25054	−0.167886	−0.0839430	+	0.996471i	$0.526751\pi$
$642$	− 19.7841i	− 0.780815i
$643$	26.5252i	1.04605i	0.852317	+	0.523026i	$0.175197\pi$
$643$	26.5252i	1.04605i	−0.852317	+	0.523026i	$0.824803\pi$
$644$	5.92277i	0.233390i
$645$	− 7.12271i	− 0.280456i
$646$	49.1198	1.93259
$647$	−15.4298	−0.606607	−0.303304	−	0.952894i	$-0.598090\pi$
$647$	−15.4298	−0.606607	−0.303304	+	0.952894i	$0.598090\pi$
$648$	− 3.63283i	− 0.142711i
$649$	48.8340	1.91690
$650$	0	0
$651$	−24.2480	−0.950355
$652$	20.1119i	0.787644i
$653$	15.8223	0.619176	0.309588	−	0.950871i	$-0.399809\pi$
$653$	15.8223	0.619176	0.309588	+	0.950871i	$0.399809\pi$
$654$	24.4980	0.957949
$655$	3.95308i	0.154460i
$656$	1.92887i	0.0753096i
$657$	12.5023i	0.487763i
$658$	16.6855i	0.650469i
$659$	32.7593	1.27612	0.638061	−	0.769986i	$-0.279737\pi$
$659$	32.7593	1.27612	0.638061	+	0.769986i	$0.279737\pi$
$660$	5.77313	0.224719
$661$	− 14.4345i	− 0.561436i	−0.959790	−	0.280718i	$-0.909427\pi$
$661$	− 14.4345i	− 0.561436i	0.959790	−	0.280718i	$-0.0905725\pi$
$662$	14.2083	0.552222
$663$	0	0
$664$	0.248376	0.00963884
$665$	1.52171i	0.0590094i
$666$	−79.0412	−3.06279
$667$	−12.0361	−0.466040
$668$	18.7716i	0.726294i
$669$	46.6475i	1.80350i
$670$	− 5.26435i	− 0.203380i
$671$	20.3338i	0.784978i
$672$	−19.3791	−0.747564
$673$	17.6481	0.680284	0.340142	−	0.940374i	$-0.389525\pi$
$673$	17.6481	0.680284	0.340142	+	0.940374i	$0.389525\pi$
$674$	44.5828i	1.71726i
$675$	−5.99786	−0.230858
$676$	0	0
$677$	10.0522	0.386338	0.193169	−	0.981165i	$-0.438123\pi$
$677$	10.0522	0.386338	0.193169	+	0.981165i	$0.438123\pi$
$678$	64.3950i	2.47307i
$679$	2.35258	0.0902835
$680$	−0.805672	−0.0308961
$681$	− 1.71577i	− 0.0657485i
$682$	− 76.7977i	− 2.94073i
$683$	28.7118i	1.09863i	0.835616	+	0.549313i	$0.185111\pi$
$683$	28.7118i	1.09863i	−0.835616	+	0.549313i	$0.814889\pi$
$684$	29.5921i	1.13148i
$685$	4.59564	0.175591
$686$	1.93488	0.0738741
$687$	49.5914i	1.89203i
$688$	−39.8653	−1.51985
$689$	0	0
$690$	−5.22147	−0.198778
$691$	− 39.7668i	− 1.51280i	−0.654109	−	0.756400i	$-0.726956\pi$
$691$	− 39.7668i	− 1.51280i	0.654109	−	0.756400i	$-0.273044\pi$
$692$	−17.7073	−0.673130
$693$	14.5036	0.550946
$694$	− 48.8501i	− 1.85432i
$695$	7.10980i	0.269690i
$696$	− 4.47255i	− 0.169532i
$697$	− 2.25848i	− 0.0855461i
$698$	−3.93280	−0.148859
$699$	−76.6821	−2.90038
$700$	− 8.54895i	− 0.323120i
$701$	−10.4132	−0.393301	−0.196651	−	0.980474i	$-0.563006\pi$
$701$	−10.4132	−0.393301	−0.196651	+	0.980474i	$0.563006\pi$
$702$	0	0
$703$	57.2251	2.15829
$704$	− 24.3169i	− 0.916479i
$705$	−6.85150	−0.258043
$706$	18.7454	0.705491
$707$	6.26932i	0.235782i
$708$	52.0226i	1.95513i
$709$	− 33.7060i	− 1.26586i	−0.774210	−	0.632928i	$-0.781853\pi$
$709$	− 33.7060i	− 1.26586i	0.774210	−	0.632928i	$-0.218147\pi$
$710$	− 3.67857i	− 0.138054i
$711$	34.4816	1.29316
$712$	5.20922	0.195224
$713$	32.3525i	1.21161i
$714$	25.6463	0.959789
$715$	0	0
$716$	−12.2634	−0.458304
$717$	− 33.6988i	− 1.25850i
$718$	52.1767	1.94722
$719$	42.0927	1.56979	0.784896	−	0.619628i	$-0.212716\pi$
$719$	42.0927	1.56979	0.784896	+	0.619628i	$0.212716\pi$
$720$	− 4.83053i	− 0.180023i
$721$	3.76722i	0.140299i
$722$	− 9.23440i	− 0.343669i
$723$	33.8921i	1.26046i
$724$	−36.7475	−1.36571
$725$	17.3729	0.645215
$726$	31.3464i	1.16337i
$727$	19.9921	0.741465	0.370733	−	0.928740i	$-0.379107\pi$
$727$	19.9921	0.741465	0.370733	+	0.928740i	$0.379107\pi$
$728$	0	0
$729$	−34.8465	−1.29061
$730$	− 2.16914i	− 0.0802834i
$731$	46.6777	1.72644
$732$	−21.6615	−0.800631
$733$	20.7416i	0.766108i	0.923726	+	0.383054i	$0.125128\pi$
$733$	20.7416i	0.766108i	−0.923726	+	0.383054i	$0.874872\pi$
$734$	− 12.7469i	− 0.470497i
$735$	0.794512i	0.0293060i
$736$	25.8562i	0.953072i
$737$	36.3264	1.33810
$738$	2.92118	0.107530
$739$	22.5049i	0.827855i	0.910310	+	0.413927i	$0.135843\pi$
$739$	22.5049i	0.827855i	−0.910310	+	0.413927i	$0.864157\pi$
$740$	6.38746	0.234808
$741$	0	0
$742$	2.20816	0.0810642
$743$	− 3.81492i	− 0.139956i	−0.997549	−	0.0699780i	$-0.977707\pi$
$743$	− 3.81492i	− 0.139956i	0.997549	−	0.0699780i	$-0.0222929\pi$
$744$	−12.0220	−0.440748
$745$	−2.25233	−0.0825190
$746$	32.1082i	1.17556i
$747$	− 1.74365i	− 0.0637969i
$748$	37.8334i	1.38333i
$749$	4.01657i	0.146762i
$750$	15.2231	0.555869
$751$	30.1283	1.09940	0.549699	−	0.835363i	$-0.314742\pi$
$751$	30.1283	1.09940	0.549699	+	0.835363i	$0.314742\pi$
$752$	38.3473i	1.39838i
$753$	65.0995	2.37236
$754$	0	0
$755$	−0.205076	−0.00746348
$756$	2.13333i	0.0775883i
$757$	34.9608	1.27067	0.635335	−	0.772237i	$-0.280862\pi$
$757$	34.9608	1.27067	0.635335	+	0.772237i	$0.280862\pi$
$758$	59.5826	2.16414
$759$	− 36.0304i	− 1.30782i
$760$	0.754453i	0.0273669i
$761$	14.6724i	0.531875i	0.963990	+	0.265938i	$0.0856815\pi$
$761$	14.6724i	0.531875i	−0.963990	+	0.265938i	$0.914318\pi$
$762$	− 53.1991i	− 1.92720i
$763$	−4.97360	−0.180056
$764$	31.5951	1.14307
$765$	5.65599i	0.204493i
$766$	−54.7528	−1.97830
$767$	0	0
$768$	−49.0877	−1.77130
$769$	− 8.21482i	− 0.296234i	−0.988970	−	0.148117i	$-0.952679\pi$
$769$	− 8.21482i	− 0.296234i	0.988970	−	0.148117i	$-0.0473212\pi$
$770$	−2.51635	−0.0906831
$771$	1.49970	0.0540105
$772$	− 2.67846i	− 0.0963998i
$773$	46.8567i	1.68532i	0.538448	+	0.842659i	$0.319011\pi$
$773$	46.8567i	1.68532i	−0.538448	+	0.842659i	$0.680989\pi$
$774$	60.3741i	2.17010i
$775$	− 46.6977i	− 1.67743i
$776$	1.16639	0.0418710
$777$	29.8783	1.07188
$778$	− 25.0359i	− 0.897582i
$779$	−2.11490	−0.0757743
$780$	0	0
$781$	25.3837	0.908301
$782$	− 34.2182i	− 1.22364i
$783$	−4.33529	−0.154931
$784$	4.44682	0.158815
$785$	− 2.69249i	− 0.0960991i
$786$	− 62.3883i	− 2.22532i
$787$	39.4146i	1.40498i	0.711693	+	0.702490i	$0.247929\pi$
$787$	39.4146i	1.40498i	−0.711693	+	0.702490i	$0.752071\pi$
$788$	− 11.7321i	− 0.417940i
$789$	47.0994	1.67678
$790$	−5.98251	−0.212848
$791$	− 13.0735i	− 0.464839i
$792$	7.19078	0.255513
$793$	0	0
$794$	−35.4296	−1.25735
$795$	0.906728i	0.0321583i
$796$	1.11676	0.0395826
$797$	−19.5718	−0.693267	−0.346634	−	0.938001i	$-0.612675\pi$
$797$	−19.5718	−0.693267	−0.346634	+	0.938001i	$0.612675\pi$
$798$	− 24.0159i	− 0.850154i
$799$	− 44.9004i	− 1.58846i
$800$	− 37.3209i	− 1.31949i
$801$	− 36.5698i	− 1.29213i
$802$	−2.53942	−0.0896699
$803$	14.9680	0.528210
$804$	38.6982i	1.36478i
$805$	1.06006	0.0373623
$806$	0	0
$807$	6.89385	0.242675
$808$	3.10829i	0.109349i
$809$	0.917176	0.0322462	0.0161231	−	0.999870i	$-0.494868\pi$
$809$	0.917176	0.0322462	0.0161231	+	0.999870i	$0.494868\pi$
$810$	4.42478	0.155471
$811$	55.0717i	1.93383i	0.255098	+	0.966915i	$0.417892\pi$
$811$	55.0717i	1.93383i	−0.255098	+	0.966915i	$0.582108\pi$
$812$	− 6.17923i	− 0.216848i
$813$	− 30.0065i	− 1.05237i
$814$	94.6295i	3.31676i
$815$	3.59965	0.126090
$816$	58.9414	2.06336
$817$	− 43.7103i	− 1.52923i
$818$	−56.6954	−1.98231
$819$	0	0
$820$	−0.236066	−0.00824377
$821$	− 19.9874i	− 0.697564i	−0.937204	−	0.348782i	$-0.886595\pi$
$821$	− 19.9874i	− 0.697564i	0.937204	−	0.348782i	$-0.113405\pi$
$822$	−72.5294	−2.52975
$823$	−4.78565	−0.166817	−0.0834087	−	0.996515i	$-0.526581\pi$
$823$	−4.78565	−0.166817	−0.0834087	+	0.996515i	$0.526581\pi$
$824$	1.86776i	0.0650666i
$825$	52.0064i	1.81063i
$826$	− 22.6753i	− 0.788973i
$827$	19.7389i	0.686390i	0.939264	+	0.343195i	$0.111509\pi$
$827$	19.7389i	0.686390i	−0.939264	+	0.343195i	$0.888491\pi$
$828$	20.6147	0.716409
$829$	−15.5467	−0.539959	−0.269980	−	0.962866i	$-0.587017\pi$
$829$	−15.5467	−0.539959	−0.269980	+	0.962866i	$0.587017\pi$
$830$	0.302521i	0.0105007i
$831$	−61.2249	−2.12387
$832$	0	0
$833$	−5.20672	−0.180402
$834$	− 112.208i	− 3.88546i
$835$	3.35975	0.116269
$836$	35.4282	1.22531
$837$	11.6531i	0.402789i
$838$	− 0.587369i	− 0.0202903i
$839$	28.9070i	0.997982i	0.866607	+	0.498991i	$0.166296\pi$
$839$	28.9070i	0.997982i	−0.866607	+	0.498991i	$0.833704\pi$
$840$	0.393914i	0.0135913i
$841$	−16.4427	−0.566991
$842$	2.30855	0.0795579
$843$	− 48.8517i	− 1.68254i
$844$	−30.6305	−1.05434
$845$	0	0
$846$	58.0752	1.99667
$847$	− 6.36395i	− 0.218668i
$848$	5.07489	0.174272
$849$	−31.0881	−1.06694
$850$	49.3906i	1.69408i
$851$	− 39.8645i	− 1.36654i
$852$	27.0411i	0.926413i
$853$	− 0.564390i	− 0.0193244i	−0.999953	−	0.00966218i	$-0.996924\pi$
$853$	− 0.564390i	− 0.0193244i	0.999953	−	0.00966218i	$-0.00307562\pi$
$854$	9.44166	0.323087
$855$	5.29643	0.181134
$856$	1.99139i	0.0680642i
$857$	39.8324	1.36065	0.680325	−	0.732911i	$-0.261839\pi$
$857$	39.8324	1.36065	0.680325	+	0.732911i	$0.261839\pi$
$858$	0	0
$859$	−48.3937	−1.65117	−0.825585	−	0.564278i	$-0.809155\pi$
$859$	−48.3937	−1.65117	−0.825585	+	0.564278i	$0.809155\pi$
$860$	− 4.87894i	− 0.166370i
$861$	−1.10423	−0.0376320
$862$	44.1110	1.50243
$863$	− 3.81608i	− 0.129901i	−0.997888	−	0.0649505i	$-0.979311\pi$
$863$	− 3.81608i	− 0.129901i	0.997888	−	0.0649505i	$-0.0206889\pi$
$864$	9.31315i	0.316840i
$865$	3.16927i	0.107758i
$866$	7.75817i	0.263633i
$867$	−25.7368	−0.874068
$868$	−16.6095	−0.563763
$869$	− 41.2820i	− 1.40039i
$870$	5.44756	0.184690
$871$	0	0
$872$	−2.46588	−0.0835051
$873$	− 8.18832i	− 0.277133i
$874$	−32.0428	−1.08386
$875$	−3.09060	−0.104481
$876$	15.9453i	0.538743i
$877$	3.07809i	0.103940i	0.998649	+	0.0519699i	$0.0165500\pi$
$877$	3.07809i	0.103940i	−0.998649	+	0.0519699i	$0.983450\pi$
$878$	4.95009i	0.167058i
$879$	− 28.9303i	− 0.975793i
$880$	−5.78319	−0.194951
$881$	34.7729	1.17153	0.585764	−	0.810482i	$-0.300795\pi$
$881$	34.7729	1.17153	0.585764	+	0.810482i	$0.300795\pi$
$882$	− 6.73450i	− 0.226762i
$883$	17.6873	0.595224	0.297612	−	0.954687i	$-0.403810\pi$
$883$	17.6873	0.595224	0.297612	+	0.954687i	$0.403810\pi$
$884$	0	0
$885$	9.31104	0.312987
$886$	0.702926i	0.0236153i
$887$	39.2893	1.31921	0.659603	−	0.751614i	$-0.270725\pi$
$887$	39.2893	1.31921	0.659603	+	0.751614i	$0.270725\pi$
$888$	14.8134	0.497106
$889$	10.8005i	0.362237i
$890$	6.34482i	0.212679i
$891$	30.5330i	1.02289i
$892$	31.9528i	1.06986i
$893$	−42.0459	−1.40701
$894$	35.5467	1.18886
$895$	2.19491i	0.0733677i
$896$	3.93379	0.131419
$897$	0	0
$898$	29.6098	0.988093
$899$	− 33.7534i	− 1.12574i
$900$	−29.7553	−0.991843
$901$	−5.94211	−0.197961
$902$	− 3.49728i	− 0.116447i
$903$	− 22.8219i	− 0.759466i
$904$	− 6.48174i	− 0.215580i
$905$	6.57709i	0.218630i
$906$	3.23655	0.107527
$907$	−42.6219	−1.41524	−0.707618	−	0.706595i	$-0.750230\pi$
$907$	−42.6219	−1.41524	−0.707618	+	0.706595i	$0.750230\pi$
$908$	− 1.17527i	− 0.0390028i
$909$	21.8209	0.723752
$910$	0	0
$911$	56.5310	1.87296	0.936478	−	0.350727i	$-0.114065\pi$
$911$	56.5310	1.87296	0.936478	+	0.350727i	$0.114065\pi$
$912$	− 55.1944i	− 1.82767i
$913$	−2.08753	−0.0690871
$914$	17.2418	0.570308
$915$	3.87699i	0.128169i
$916$	33.9692i	1.12238i
$917$	12.6661i	0.418271i
$918$	− 12.3251i	− 0.406787i
$919$	−35.2658	−1.16331	−0.581655	−	0.813435i	$-0.697595\pi$
$919$	−35.2658	−1.16331	−0.581655	+	0.813435i	$0.697595\pi$
$920$	0.525572	0.0173276
$921$	20.8593i	0.687336i
$922$	41.5294	1.36770
$923$	0	0
$924$	18.4977	0.608530
$925$	57.5406i	1.89192i
$926$	−5.98791	−0.196775
$927$	13.1121	0.430658
$928$	− 26.9758i	− 0.885523i
$929$	− 5.51296i	− 0.180874i	−0.995902	−	0.0904372i	$-0.971174\pi$
$929$	− 5.51296i	− 0.180874i	0.995902	−	0.0904372i	$-0.0288264\pi$
$930$	− 14.6428i	− 0.480156i
$931$	4.87572i	0.159795i
$932$	−52.5259	−1.72054
$933$	72.7239	2.38088
$934$	− 40.4543i	− 1.32371i
$935$	6.77145	0.221450
$936$	0	0
$937$	44.2496	1.44557	0.722785	−	0.691073i	$-0.242861\pi$
$937$	44.2496	1.44557	0.722785	+	0.691073i	$0.242861\pi$
$938$	− 16.8675i	− 0.550745i
$939$	−23.9543	−0.781719
$940$	−4.69316	−0.153074
$941$	− 46.2818i	− 1.50874i	−0.656448	−	0.754372i	$-0.727942\pi$
$941$	− 46.2818i	− 1.50874i	0.656448	−	0.754372i	$-0.272058\pi$
$942$	42.4934i	1.38451i
$943$	1.47330i	0.0479772i
$944$	− 52.1132i	− 1.69614i
$945$	0.381825	0.0124208
$946$	72.2809	2.35005
$947$	− 55.7472i	− 1.81154i	−0.423769	−	0.905770i	$-0.639293\pi$
$947$	− 55.7472i	− 1.81154i	0.423769	−	0.905770i	$-0.360707\pi$
$948$	43.9774	1.42832
$949$	0	0
$950$	46.2507	1.50057
$951$	4.96889i	0.161127i
$952$	−2.58146	−0.0836655
$953$	4.03648	0.130754	0.0653772	−	0.997861i	$-0.479175\pi$
$953$	4.03648	0.130754	0.0653772	+	0.997861i	$0.479175\pi$
$954$	− 7.68568i	− 0.248833i
$955$	− 5.65491i	− 0.182989i
$956$	− 23.0831i	− 0.746561i
$957$	37.5906i	1.21513i
$958$	35.5170	1.14750
$959$	14.7249	0.475492
$960$	− 4.63644i	− 0.149641i
$961$	−59.7276	−1.92670
$962$	0	0
$963$	13.9800	0.450498
$964$	23.2155i	0.747721i
$965$	−0.479393	−0.0154322
$966$	−16.7301	−0.538283
$967$	52.0755i	1.67463i	0.546717	+	0.837317i	$0.315877\pi$
$967$	52.0755i	1.67463i	−0.546717	+	0.837317i	$0.684123\pi$
$968$	− 3.15520i	− 0.101412i
$969$	64.6263i	2.07610i
$970$	1.42066i	0.0456147i
$971$	16.0432	0.514851	0.257426	−	0.966298i	$-0.417126\pi$
$971$	16.0432	0.514851	0.257426	+	0.966298i	$0.417126\pi$
$972$	−38.9265	−1.24857
$973$	22.7805i	0.730311i
$974$	25.7505	0.825101
$975$	0	0
$976$	21.6992	0.694575
$977$	− 10.0736i	− 0.322284i	−0.986931	−	0.161142i	$-0.948482\pi$
$977$	− 10.0736i	− 0.322284i	0.986931	−	0.161142i	$-0.0515177\pi$
$978$	−56.8104	−1.81660
$979$	−43.7820	−1.39928
$980$	0.544227i	0.0173847i
$981$	17.3110i	0.552697i
$982$	28.1448i	0.898136i
$983$	52.7163i	1.68139i	0.541509	+	0.840695i	$0.317853\pi$
$983$	52.7163i	1.68139i	−0.541509	+	0.840695i	$0.682147\pi$
$984$	−0.547470	−0.0174527
$985$	−2.09983	−0.0669061
$986$	35.6998i	1.13691i
$987$	−21.9529	−0.698769
$988$	0	0
$989$	−30.4497	−0.968245
$990$	8.75836i	0.278359i
$991$	−62.8727	−1.99722	−0.998609	−	0.0527258i	$-0.983209\pi$
$991$	−62.8727	−1.99722	−0.998609	+	0.0527258i	$0.983209\pi$
$992$	−72.5096	−2.30218
$993$	18.6937i	0.593227i
$994$	− 11.7865i	− 0.373845i
$995$	− 0.199879i	− 0.00633659i
$996$	− 2.22383i	− 0.0704648i
$997$	33.1634	1.05030	0.525148	−	0.851011i	$-0.324010\pi$
$997$	33.1634	1.05030	0.525148	+	0.851011i	$0.324010\pi$
$998$	−61.4460	−1.94504
$999$	− 14.3588i	− 0.454293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.h.337.10		12
13.5	odd	4		1183.2.a.o.1.5	yes	6
13.8	odd	4		1183.2.a.n.1.2	✓	6
13.12	even	2	inner	1183.2.c.h.337.3		12
91.34	even	4		8281.2.a.cb.1.2		6
91.83	even	4		8281.2.a.cg.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.n.1.2	✓	6	13.8	odd	4
1183.2.a.o.1.5	yes	6	13.5	odd	4
1183.2.c.h.337.3		12	13.12	even	2	inner
1183.2.c.h.337.10		12	1.1	even	1	trivial
8281.2.a.cb.1.2		6	91.34	even	4
8281.2.a.cg.1.5		6	91.83	even	4

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.93488i q^{2} -2.54570 q^{3} -1.74376 q^{4} +0.312100i q^{5} -4.92562i q^{6} +1.00000i q^{7} +0.495793i q^{8} +3.48058 q^{9} +O(q^{10})\)	\(q+1.93488i q^{2} -2.54570 q^{3} -1.74376 q^{4} +0.312100i q^{5} -4.92562i q^{6} +1.00000i q^{7} +0.495793i q^{8} +3.48058 q^{9} -0.603875 q^{10} -4.16701i q^{11} +4.43909 q^{12} -1.93488 q^{14} -0.794512i q^{15} -4.44682 q^{16} +5.20672 q^{17} +6.73450i q^{18} -4.87572i q^{19} -0.544227i q^{20} -2.54570i q^{21} +8.06266 q^{22} -3.39655 q^{23} -1.26214i q^{24} +4.90259 q^{25} -1.22341 q^{27} -1.74376i q^{28} +3.54362 q^{29} +1.53728 q^{30} -9.52510i q^{31} -7.61248i q^{32} +10.6079i q^{33} +10.0744i q^{34} -0.312100 q^{35} -6.06929 q^{36} +11.7368i q^{37} +9.43392 q^{38} -0.154737 q^{40} -0.433763i q^{41} +4.92562 q^{42} +8.96489 q^{43} +7.26626i q^{44} +1.08629i q^{45} -6.57192i q^{46} -8.62354i q^{47} +11.3203 q^{48} -1.00000 q^{49} +9.48593i q^{50} -13.2547 q^{51} -1.14124 q^{53} -2.36714i q^{54} +1.30052 q^{55} -0.495793 q^{56} +12.4121i q^{57} +6.85649i q^{58} +11.7192i q^{59} +1.38544i q^{60} -4.87971 q^{61} +18.4299 q^{62} +3.48058i q^{63} +5.83559 q^{64} -20.5251 q^{66} +8.71761i q^{67} -9.07927 q^{68} +8.64660 q^{69} -0.603875i q^{70} +6.09160i q^{71} +1.72565i q^{72} +3.59203i q^{73} -22.7092 q^{74} -12.4805 q^{75} +8.50208i q^{76} +4.16701 q^{77} +9.90686 q^{79} -1.38785i q^{80} -7.32731 q^{81} +0.839279 q^{82} -0.500966i q^{83} +4.43909i q^{84} +1.62502i q^{85} +17.3460i q^{86} -9.02100 q^{87} +2.06597 q^{88} -10.5068i q^{89} -2.10184 q^{90} +5.92277 q^{92} +24.2480i q^{93} +16.6855 q^{94} +1.52171 q^{95} +19.3791i q^{96} -2.35258i q^{97} -1.93488i q^{98} -14.5036i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{3} - 16 q^{4}+O(q^{10}) \) 12 * q - 8 * q^3 - 16 * q^4	\( 12 q - 8 q^{3} - 16 q^{4} + 28 q^{10} + 46 q^{12} - 4 q^{14} + 46 q^{17} - 8 q^{22} + 36 q^{23} + 20 q^{25} - 20 q^{27} - 30 q^{29} - 28 q^{30} - 4 q^{35} - 44 q^{36} + 22 q^{38} - 28 q^{40} + 16 q^{42} + 36 q^{43} - 22 q^{48} - 12 q^{49} - 28 q^{51} - 50 q^{53} + 6 q^{56} + 32 q^{61} + 18 q^{62} + 14 q^{64} + 32 q^{66} - 68 q^{68} + 2 q^{69} - 28 q^{74} - 30 q^{75} + 16 q^{77} + 4 q^{79} - 12 q^{81} + 20 q^{82} + 26 q^{87} + 96 q^{88} - 64 q^{92} - 28 q^{94} + 14 q^{95}+O(q^{100}) \) 12 * q - 8 * q^3 - 16 * q^4 + 28 * q^10 + 46 * q^12 - 4 * q^14 + 46 * q^17 - 8 * q^22 + 36 * q^23 + 20 * q^25 - 20 * q^27 - 30 * q^29 - 28 * q^30 - 4 * q^35 - 44 * q^36 + 22 * q^38 - 28 * q^40 + 16 * q^42 + 36 * q^43 - 22 * q^48 - 12 * q^49 - 28 * q^51 - 50 * q^53 + 6 * q^56 + 32 * q^61 + 18 * q^62 + 14 * q^64 + 32 * q^66 - 68 * q^68 + 2 * q^69 - 28 * q^74 - 30 * q^75 + 16 * q^77 + 4 * q^79 - 12 * q^81 + 20 * q^82 + 26 * q^87 + 96 * q^88 - 64 * q^92 - 28 * q^94 + 14 * q^95

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