LMFDB - Embedded newform 1183.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

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, 0]))

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

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

chi := DirichletCharacter("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.a (trivial)

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:	yes
Analytic conductor:	$9.44630255912$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.1279733.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 6x^{4} + 10x^{3} + 10x^{2} - 11x - 1 $ x^6 - 2x^5 - 6x^4 + 10x^3 + 10x^2 - 11*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.10066$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.93488 q^{2} -2.54570 q^{3} +1.74376 q^{4} -0.312100 q^{5} +4.92562 q^{6} +1.00000 q^{7} +0.495793 q^{8} +3.48058 q^{9} +O(q^{10})$	\(q-1.93488 q^{2} -2.54570 q^{3} +1.74376 q^{4} -0.312100 q^{5} +4.92562 q^{6} +1.00000 q^{7} +0.495793 q^{8} +3.48058 q^{9} +0.603875 q^{10} -4.16701 q^{11} -4.43909 q^{12} -1.93488 q^{14} +0.794512 q^{15} -4.44682 q^{16} -5.20672 q^{17} -6.73450 q^{18} +4.87572 q^{19} -0.544227 q^{20} -2.54570 q^{21} +8.06266 q^{22} +3.39655 q^{23} -1.26214 q^{24} -4.90259 q^{25} -1.22341 q^{27} +1.74376 q^{28} +3.54362 q^{29} -1.53728 q^{30} +9.52510 q^{31} +7.61248 q^{32} +10.6079 q^{33} +10.0744 q^{34} -0.312100 q^{35} +6.06929 q^{36} +11.7368 q^{37} -9.43392 q^{38} -0.154737 q^{40} +0.433763 q^{41} +4.92562 q^{42} -8.96489 q^{43} -7.26626 q^{44} -1.08629 q^{45} -6.57192 q^{46} -8.62354 q^{47} +11.3203 q^{48} +1.00000 q^{49} +9.48593 q^{50} +13.2547 q^{51} -1.14124 q^{53} +2.36714 q^{54} +1.30052 q^{55} +0.495793 q^{56} -12.4121 q^{57} -6.85649 q^{58} +11.7192 q^{59} +1.38544 q^{60} -4.87971 q^{61} -18.4299 q^{62} +3.48058 q^{63} -5.83559 q^{64} -20.5251 q^{66} -8.71761 q^{67} -9.07927 q^{68} -8.64660 q^{69} +0.603875 q^{70} -6.09160 q^{71} +1.72565 q^{72} +3.59203 q^{73} -22.7092 q^{74} +12.4805 q^{75} +8.50208 q^{76} -4.16701 q^{77} +9.90686 q^{79} +1.38785 q^{80} -7.32731 q^{81} -0.839279 q^{82} +0.500966 q^{83} -4.43909 q^{84} +1.62502 q^{85} +17.3460 q^{86} -9.02100 q^{87} -2.06597 q^{88} -10.5068 q^{89} +2.10184 q^{90} +5.92277 q^{92} -24.2480 q^{93} +16.6855 q^{94} -1.52171 q^{95} -19.3791 q^{96} +2.35258 q^{97} -1.93488 q^{98} -14.5036 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 8 q^{6} + 6 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 8 * q^6 + 6 * q^7 - 3 * q^8	$ 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 8 q^{6} + 6 q^{7} - 3 q^{8} - 14 q^{10} - 8 q^{11} - 23 q^{12} - 2 q^{14} - 3 q^{15} - 23 q^{17} - 26 q^{18} + 13 q^{19} + 4 q^{20} - 4 q^{21} - 4 q^{22} - 18 q^{23} + 26 q^{24} - 10 q^{25} - 10 q^{27} + 8 q^{28} - 15 q^{29} + 14 q^{30} - 3 q^{31} - 28 q^{32} - 3 q^{33} + 29 q^{34} - 2 q^{35} + 22 q^{36} + 13 q^{37} - 11 q^{38} - 14 q^{40} + 4 q^{41} + 8 q^{42} - 18 q^{43} + 19 q^{45} - 10 q^{46} + 16 q^{47} - 11 q^{48} + 6 q^{49} + 10 q^{50} + 14 q^{51} - 25 q^{53} + 31 q^{54} - 3 q^{56} + 4 q^{57} + 13 q^{58} - 18 q^{59} - 22 q^{60} + 16 q^{61} - 9 q^{62} - 7 q^{64} + 16 q^{66} - 16 q^{67} - 34 q^{68} - q^{69} - 14 q^{70} - 25 q^{71} - 39 q^{72} + 5 q^{73} - 14 q^{74} + 15 q^{75} - 7 q^{76} - 8 q^{77} + 2 q^{79} + 27 q^{80} - 6 q^{81} - 10 q^{82} + 7 q^{83} - 23 q^{84} - 9 q^{85} + 3 q^{86} + 13 q^{87} - 48 q^{88} + 10 q^{89} - 32 q^{92} - 35 q^{93} - 14 q^{94} - 7 q^{95} + 14 q^{96} + 5 q^{97} - 2 q^{98} + 15 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 8 * q^6 + 6 * q^7 - 3 * q^8 - 14 * q^10 - 8 * q^11 - 23 * q^12 - 2 * q^14 - 3 * q^15 - 23 * q^17 - 26 * q^18 + 13 * q^19 + 4 * q^20 - 4 * q^21 - 4 * q^22 - 18 * q^23 + 26 * q^24 - 10 * q^25 - 10 * q^27 + 8 * q^28 - 15 * q^29 + 14 * q^30 - 3 * q^31 - 28 * q^32 - 3 * q^33 + 29 * q^34 - 2 * q^35 + 22 * q^36 + 13 * q^37 - 11 * q^38 - 14 * q^40 + 4 * q^41 + 8 * q^42 - 18 * q^43 + 19 * q^45 - 10 * q^46 + 16 * q^47 - 11 * q^48 + 6 * q^49 + 10 * q^50 + 14 * q^51 - 25 * q^53 + 31 * q^54 - 3 * q^56 + 4 * q^57 + 13 * q^58 - 18 * q^59 - 22 * q^60 + 16 * q^61 - 9 * q^62 - 7 * q^64 + 16 * q^66 - 16 * q^67 - 34 * q^68 - q^69 - 14 * q^70 - 25 * q^71 - 39 * q^72 + 5 * q^73 - 14 * q^74 + 15 * q^75 - 7 * q^76 - 8 * q^77 + 2 * q^79 + 27 * q^80 - 6 * q^81 - 10 * q^82 + 7 * q^83 - 23 * q^84 - 9 * q^85 + 3 * q^86 + 13 * q^87 - 48 * q^88 + 10 * q^89 - 32 * q^92 - 35 * q^93 - 14 * q^94 - 7 * q^95 + 14 * q^96 + 5 * q^97 - 2 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.93488	−1.36817	−0.684083	−	0.729404i	$-0.739798\pi$
$2$	−1.93488	−1.36817	−0.684083	+	0.729404i	$0.739798\pi$
$3$	−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
$5$	−0.312100	−0.139575	−0.0697876	−	0.997562i	$-0.522232\pi$
$5$	−0.312100	−0.139575	−0.0697876	+	0.997562i	$0.522232\pi$
$6$	4.92562	2.01088
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.495793	0.175289
$9$	3.48058	1.16019
$10$	0.603875	0.190962
$11$	−4.16701	−1.25640	−0.628200	−	0.778052i	$-0.716208\pi$
$11$	−4.16701	−1.25640	−0.628200	+	0.778052i	$0.716208\pi$
$12$	−4.43909	−1.28145
$13$	0	0
$13$	0	0
$14$	−1.93488	−0.517118
$15$	0.794512	0.205142
$16$	−4.44682	−1.11171
$17$	−5.20672	−1.26281	−0.631407	−	0.775451i	$-0.717522\pi$
$17$	−5.20672	−1.26281	−0.631407	+	0.775451i	$0.717522\pi$
$18$	−6.73450	−1.58734
$19$	4.87572	1.11857	0.559283	−	0.828977i	$-0.311077\pi$
$19$	4.87572	1.11857	0.559283	+	0.828977i	$0.311077\pi$
$20$	−0.544227	−0.121693
$21$	−2.54570	−0.555517
$22$	8.06266	1.71896
$23$	3.39655	0.708230	0.354115	−	0.935202i	$-0.384782\pi$
$23$	3.39655	0.708230	0.354115	+	0.935202i	$0.384782\pi$
$24$	−1.26214	−0.257633
$25$	−4.90259	−0.980519
$26$	0	0
$27$	−1.22341	−0.235445
$28$	1.74376	0.329540
$29$	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
$31$	9.52510	1.71076	0.855380	−	0.518002i	$-0.173324\pi$
$31$	9.52510	1.71076	0.855380	+	0.518002i	$0.173324\pi$
$32$	7.61248	1.34571
$33$	10.6079	1.84661
$34$	10.0744	1.72774
$35$	−0.312100	−0.0527545
$36$	6.06929	1.01155
$37$	11.7368	1.92951	0.964756	−	0.263146i	$-0.0847602\pi$
$37$	11.7368	1.92951	0.964756	+	0.263146i	$0.0847602\pi$
$38$	−9.43392	−1.53038
$39$	0	0
$40$	−0.154737	−0.0244661
$41$	0.433763	0.0677424	0.0338712	−	0.999426i	$-0.489216\pi$
$41$	0.433763	0.0677424	0.0338712	+	0.999426i	$0.489216\pi$
$42$	4.92562	0.760040
$43$	−8.96489	−1.36713	−0.683567	−	0.729888i	$-0.739572\pi$
$43$	−8.96489	−1.36713	−0.683567	+	0.729888i	$0.739572\pi$
$44$	−7.26626	−1.09543
$45$	−1.08629	−0.161934
$46$	−6.57192	−0.968977
$47$	−8.62354	−1.25787	−0.628936	−	0.777457i	$-0.716509\pi$
$47$	−8.62354	−1.25787	−0.628936	+	0.777457i	$0.716509\pi$
$48$	11.3203	1.63394
$49$	1.00000	0.142857
$50$	9.48593	1.34151
$51$	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	$0.524975\pi$
$54$	2.36714	0.322127
$55$	1.30052	0.175362
$56$	0.495793	0.0662532
$57$	−12.4121	−1.64402
$58$	−6.85649	−0.900301
$59$	11.7192	1.52571	0.762855	−	0.646569i	$-0.223797\pi$
$59$	11.7192	1.52571	0.762855	+	0.646569i	$0.223797\pi$
$60$	1.38544	0.178859
$61$	−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
$63$	3.48058	0.438512
$64$	−5.83559	−0.729448
$65$	0	0
$66$	−20.5251	−2.52646
$67$	−8.71761	−1.06503	−0.532513	−	0.846422i	$-0.678752\pi$
$67$	−8.71761	−1.06503	−0.532513	+	0.846422i	$0.678752\pi$
$68$	−9.07927	−1.10102
$69$	−8.64660	−1.04093
$70$	0.603875	0.0721769
$71$	−6.09160	−0.722939	−0.361470	−	0.932384i	$-0.617725\pi$
$71$	−6.09160	−0.722939	−0.361470	+	0.932384i	$0.617725\pi$
$72$	1.72565	0.203369
$73$	3.59203	0.420415	0.210208	−	0.977657i	$-0.432586\pi$
$73$	3.59203	0.420415	0.210208	+	0.977657i	$0.432586\pi$
$74$	−22.7092	−2.63989
$75$	12.4805	1.44113
$76$	8.50208	0.975255
$77$	−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	$0.311836\pi$
$80$	1.38785	0.155167
$81$	−7.32731	−0.814146
$82$	−0.839279	−0.0926829
$83$	0.500966	0.0549882	0.0274941	−	0.999622i	$-0.491247\pi$
$83$	0.500966	0.0549882	0.0274941	+	0.999622i	$0.491247\pi$
$84$	−4.43909	−0.484344
$85$	1.62502	0.176258
$86$	17.3460	1.87047
$87$	−9.02100	−0.967152
$88$	−2.06597	−0.220234
$89$	−10.5068	−1.11372	−0.556861	−	0.830606i	$-0.687994\pi$
$89$	−10.5068	−1.11372	−0.556861	+	0.830606i	$0.687994\pi$
$90$	2.10184	0.221553
$91$	0	0
$92$	5.92277	0.617492
$93$	−24.2480	−2.51440
$94$	16.6855	1.72098
$95$	−1.52171	−0.156124
$96$	−19.3791	−1.97787
$97$	2.35258	0.238868	0.119434	−	0.992842i	$-0.461892\pi$
$97$	2.35258	0.238868	0.119434	+	0.992842i	$0.461892\pi$
$98$	−1.93488	−0.195452
$99$	−14.5036	−1.45767
$100$	−8.54895	−0.854895
$101$	−6.26932	−0.623821	−0.311910	−	0.950112i	$-0.600969\pi$
$101$	−6.26932	−0.623821	−0.311910	+	0.950112i	$0.600969\pi$
$102$	−25.6463	−2.53936
$103$	−3.76722	−0.371195	−0.185598	−	0.982626i	$-0.559422\pi$
$103$	−3.76722	−0.371195	−0.185598	+	0.982626i	$0.559422\pi$
$104$	0	0
$105$	0.794512	0.0775364
$106$	2.20816	0.214476
$107$	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
$109$	−4.97360	−0.476384	−0.238192	−	0.971218i	$-0.576555\pi$
$109$	−4.97360	−0.476384	−0.238192	+	0.971218i	$0.576555\pi$
$110$	−2.51635	−0.239925
$111$	−29.8783	−2.83592
$112$	−4.44682	−0.420185
$113$	−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
$115$	−1.06006	−0.0988514
$116$	6.17923	0.573727
$117$	0	0
$118$	−22.6753	−2.08743
$119$	−5.20672	−0.477299
$120$	0.393914	0.0359592
$121$	6.36395	0.578541
$122$	9.44166	0.854807
$123$	−1.10423	−0.0995650
$124$	16.6095	1.49158
$125$	3.09060	0.276431
$126$	−6.73450	−0.599957
$127$	−10.8005	−0.958389	−0.479194	−	0.877709i	$-0.659071\pi$
$127$	−10.8005	−0.958389	−0.479194	+	0.877709i	$0.659071\pi$
$128$	−3.93379	−0.347701
$129$	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	$0.313361\pi$
$132$	18.4977	1.61002
$133$	4.87572	0.422778
$134$	16.8675	1.45713
$135$	0.381825	0.0328622
$136$	−2.58146	−0.221358
$137$	−14.7249	−1.25803	−0.629017	−	0.777391i	$-0.716543\pi$
$137$	−14.7249	−1.25803	−0.629017	+	0.777391i	$0.716543\pi$
$138$	16.7301	1.42416
$139$	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
$141$	21.9529	1.84877
$142$	11.7865	0.989102
$143$	0	0
$144$	−15.4775	−1.28979
$145$	−1.10596	−0.0918453
$146$	−6.95014	−0.575198
$147$	−2.54570	−0.209966
$148$	20.4661	1.68230
$149$	−7.21670	−0.591215	−0.295608	−	0.955309i	$-0.595522\pi$
$149$	−7.21670	−0.591215	−0.295608	+	0.955309i	$0.595522\pi$
$150$	−24.1483	−1.97170
$151$	0.657085	0.0534728	0.0267364	−	0.999643i	$-0.491489\pi$
$151$	0.657085	0.0534728	0.0267364	+	0.999643i	$0.491489\pi$
$152$	2.41735	0.196073
$153$	−18.1224	−1.46511
$154$	8.06266	0.649708
$155$	−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	$0.611869\pi$
$158$	−19.1686	−1.52497
$159$	2.90525	0.230401
$160$	−2.37585	−0.187828
$161$	3.39655	0.267686
$162$	14.1775	1.11389
$163$	−11.5337	−0.903386	−0.451693	−	0.892173i	$-0.649180\pi$
$163$	−11.5337	−0.903386	−0.451693	+	0.892173i	$0.649180\pi$
$164$	0.756378	0.0590632
$165$	−3.31074	−0.257740
$166$	−0.969309	−0.0752330
$167$	−10.7650	−0.833020	−0.416510	−	0.909131i	$-0.636747\pi$
$167$	−10.7650	−0.833020	−0.416510	+	0.909131i	$0.636747\pi$
$168$	−1.26214	−0.0973762
$169$	0	0
$170$	−3.14421	−0.241150
$171$	16.9703	1.29775
$172$	−15.6326	−1.19198
$173$	−10.1547	−0.772045	−0.386022	−	0.922489i	$-0.626151\pi$
$173$	−10.1547	−0.772045	−0.386022	+	0.922489i	$0.626151\pi$
$174$	17.4545	1.32323
$175$	−4.90259	−0.370601
$176$	18.5299	1.39675
$177$	−29.8336	−2.24243
$178$	20.3295	1.52376
$179$	−7.03271	−0.525650	−0.262825	−	0.964844i	$-0.584654\pi$
$179$	−7.03271	−0.525650	−0.262825	+	0.964844i	$0.584654\pi$
$180$	−1.89422	−0.141187
$181$	−21.0737	−1.56640	−0.783198	−	0.621773i	$-0.786413\pi$
$181$	−21.0737	−1.56640	−0.783198	+	0.621773i	$0.786413\pi$
$182$	0	0
$183$	12.4223	0.918281
$184$	1.68399	0.124145
$185$	−3.66304	−0.269312
$186$	46.9170	3.44012
$187$	21.6964	1.58660
$188$	−15.0374	−1.09671
$189$	−1.22341	−0.0889897
$190$	2.94432	0.213604
$191$	−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
$193$	1.53602	0.110565	0.0552827	−	0.998471i	$-0.482394\pi$
$193$	1.53602	0.110565	0.0552827	+	0.998471i	$0.482394\pi$
$194$	−4.55195	−0.326811
$195$	0	0
$196$	1.74376	0.124554
$197$	−6.72807	−0.479355	−0.239677	−	0.970853i	$-0.577042\pi$
$197$	−6.72807	−0.479355	−0.239677	+	0.970853i	$0.577042\pi$
$198$	28.0627	1.99433
$199$	0.640433	0.0453991	0.0226995	−	0.999742i	$-0.492774\pi$
$199$	0.640433	0.0453991	0.0226995	+	0.999742i	$0.492774\pi$
$200$	−2.43067	−0.171875
$201$	22.1924	1.56533
$202$	12.1304	0.853491
$203$	3.54362	0.248714
$204$	23.1131	1.61824
$205$	−0.135377	−0.00945516
$206$	7.28911	0.507857
$207$	11.8220	0.821683
$208$	0	0
$209$	−20.3171	−1.40537
$210$	−1.53728	−0.106083
$211$	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
$213$	15.5074	1.06255
$214$	−7.77157	−0.531254
$215$	2.79794	0.190818
$216$	−0.606556	−0.0412709
$217$	9.52510	0.646606
$218$	9.62331	0.651773
$219$	−9.14422	−0.617909
$220$	2.26780	0.152895
$221$	0	0
$222$	57.8108	3.88001
$223$	18.3241	1.22707	0.613535	−	0.789667i	$-0.289747\pi$
$223$	18.3241	1.22707	0.613535	+	0.789667i	$0.289747\pi$
$224$	7.61248	0.508630
$225$	−17.0639	−1.13759
$226$	25.2956	1.68264
$227$	−0.673988	−0.0447342	−0.0223671	−	0.999750i	$-0.507120\pi$
$227$	−0.673988	−0.0447342	−0.0223671	+	0.999750i	$0.507120\pi$
$228$	−21.6437	−1.43339
$229$	−19.4805	−1.28730	−0.643652	−	0.765318i	$-0.722582\pi$
$229$	−19.4805	−1.28730	−0.643652	+	0.765318i	$0.722582\pi$
$230$	2.05110	0.135245
$231$	10.6079	0.697951
$232$	1.75691	0.115346
$233$	−30.1222	−1.97337	−0.986686	−	0.162637i	$-0.948000\pi$
$233$	−30.1222	−1.97337	−0.986686	+	0.162637i	$0.948000\pi$
$234$	0	0
$235$	2.69140	0.175568
$236$	20.4355	1.33024
$237$	−25.2199	−1.63821
$238$	10.0744	0.653025
$239$	−13.2375	−0.856266	−0.428133	−	0.903716i	$-0.640828\pi$
$239$	−13.2375	−0.856266	−0.428133	+	0.903716i	$0.640828\pi$
$240$	−3.53305	−0.228057
$241$	−13.3135	−0.857596	−0.428798	−	0.903400i	$-0.641063\pi$
$241$	−13.3135	−0.857596	−0.428798	+	0.903400i	$0.641063\pi$
$242$	−12.3135	−0.791540
$243$	22.3233	1.43204
$244$	−8.50905	−0.544736
$245$	−0.312100	−0.0199393
$246$	2.13655	0.136222
$247$	0	0
$248$	4.72248	0.299878
$249$	−1.27531	−0.0808194
$250$	−5.97993	−0.378204
$251$	25.5724	1.61411	0.807056	−	0.590474i	$-0.201059\pi$
$251$	25.5724	1.61411	0.807056	+	0.590474i	$0.201059\pi$
$252$	6.06929	0.382330
$253$	−14.1535	−0.889820
$254$	20.8977	1.31124
$255$	−4.13680	−0.259056
$256$	19.2826	1.20516
$257$	0.589113	0.0367478	0.0183739	−	0.999831i	$-0.494151\pi$
$257$	0.589113	0.0367478	0.0183739	+	0.999831i	$0.494151\pi$
$258$	−44.1577	−2.74914
$259$	11.7368	0.729287
$260$	0	0
$261$	12.3339	0.763447
$262$	−24.5073	−1.51407
$263$	−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
$265$	0.356181	0.0218800
$266$	−9.43392	−0.578431
$267$	26.7472	1.63690
$268$	−15.2014	−0.928575
$269$	−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
$271$	11.7872	0.716018	0.358009	−	0.933718i	$-0.383456\pi$
$271$	11.7872	0.716018	0.358009	+	0.933718i	$0.383456\pi$
$272$	23.1533	1.40388
$273$	0	0
$274$	28.4910	1.72120
$275$	20.4291	1.23192
$276$	−15.0776	−0.907564
$277$	−24.0504	−1.44505	−0.722523	−	0.691347i	$-0.757018\pi$
$277$	−24.0504	−1.44505	−0.722523	+	0.691347i	$0.757018\pi$
$278$	−44.0776	−2.64360
$279$	33.1529	1.98481
$280$	−0.154737	−0.00924730
$281$	19.1899	1.14477	0.572387	−	0.819983i	$-0.306017\pi$
$281$	19.1899	1.14477	0.572387	+	0.819983i	$0.306017\pi$
$282$	−42.4763	−2.52943
$283$	−12.2120	−0.725930	−0.362965	−	0.931803i	$-0.618235\pi$
$283$	−12.2120	−0.725930	−0.362965	+	0.931803i	$0.618235\pi$
$284$	−10.6223	−0.630316
$285$	3.87381	0.229465
$286$	0	0
$287$	0.433763	0.0256042
$288$	26.4958	1.56128
$289$	10.1099	0.594702
$290$	2.13991	0.125660
$291$	−5.98895	−0.351078
$292$	6.26364	0.366552
$293$	11.3644	0.663914	0.331957	−	0.943295i	$-0.392291\pi$
$293$	11.3644	0.663914	0.331957	+	0.943295i	$0.392291\pi$
$294$	4.92562	0.287268
$295$	−3.65756	−0.212951
$296$	5.81901	0.338223
$297$	5.09794	0.295813
$298$	13.9635	0.808881
$299$	0	0
$300$	21.7630	1.25649
$301$	−8.96489	−0.516728
$302$	−1.27138	−0.0731597
$303$	15.9598	0.916867
$304$	−21.6814	−1.24352
$305$	1.52296	0.0872043
$306$	35.0647	2.00451
$307$	−8.19392	−0.467652	−0.233826	−	0.972278i	$-0.575125\pi$
$307$	−8.19392	−0.467652	−0.233826	+	0.972278i	$0.575125\pi$
$308$	−7.26626	−0.414034
$309$	9.59020	0.545567
$310$	5.75198	0.326690
$311$	28.5674	1.61991	0.809954	−	0.586493i	$-0.199492\pi$
$311$	28.5674	1.61991	0.809954	+	0.586493i	$0.199492\pi$
$312$	0	0
$313$	9.40971	0.531869	0.265934	−	0.963991i	$-0.414320\pi$
$313$	9.40971	0.531869	0.265934	+	0.963991i	$0.414320\pi$
$314$	16.6922	0.941998
$315$	−1.08629	−0.0612054
$316$	17.2752	0.971805
$317$	1.95188	0.109628	0.0548142	−	0.998497i	$-0.482543\pi$
$317$	1.95188	0.109628	0.0548142	+	0.998497i	$0.482543\pi$
$318$	−5.62131	−0.315228
$319$	−14.7663	−0.826754
$320$	1.82129	0.101813
$321$	−10.2250	−0.570702
$322$	−6.57192	−0.366239
$323$	−25.3865	−1.41254
$324$	−12.7771	−0.709837
$325$	0	0
$326$	22.3162	1.23598
$327$	12.6613	0.700170
$328$	0.215057	0.0118745
$329$	−8.62354	−0.475431
$330$	6.40588	0.352632
$331$	7.34325	0.403622	0.201811	−	0.979425i	$-0.435317\pi$
$331$	7.34325	0.403622	0.201811	+	0.979425i	$0.435317\pi$
$332$	0.873565	0.0479431
$333$	40.8507	2.23861
$334$	20.8290	1.13971
$335$	2.72076	0.148651
$336$	11.3203	0.617571
$337$	−23.0416	−1.25516	−0.627579	−	0.778553i	$-0.715954\pi$
$337$	−23.0416	−1.25516	−0.627579	+	0.778553i	$0.715954\pi$
$338$	0	0
$339$	33.2811	1.80758
$340$	2.83364	0.153676
$341$	−39.6912	−2.14940
$342$	−32.8355	−1.77554
$343$	1.00000	0.0539949
$344$	−4.44473	−0.239644
$345$	2.69860	0.145288
$346$	19.6480	1.05629
$347$	−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
$349$	2.03258	0.108802	0.0544008	−	0.998519i	$-0.482675\pi$
$349$	2.03258	0.108802	0.0544008	+	0.998519i	$0.482675\pi$
$350$	9.48593	0.507044
$351$	0	0
$352$	−31.7212	−1.69075
$353$	9.68813	0.515647	0.257824	−	0.966192i	$-0.416995\pi$
$353$	9.68813	0.515647	0.257824	+	0.966192i	$0.416995\pi$
$354$	57.7243	3.06801
$355$	1.90119	0.100904
$356$	−18.3214	−0.971032
$357$	13.2547	0.701515
$358$	13.6075	0.719176
$359$	−26.9664	−1.42323	−0.711616	−	0.702569i	$-0.752036\pi$
$359$	−26.9664	−1.42323	−0.711616	+	0.702569i	$0.752036\pi$
$360$	−0.538574	−0.0283853
$361$	4.77260	0.251189
$362$	40.7751	2.14309
$363$	−16.2007	−0.850316
$364$	0	0
$365$	−1.12107	−0.0586796
$366$	−24.0356	−1.25636
$367$	−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
$369$	1.50975	0.0785942
$370$	7.08754	0.368464
$371$	−1.14124	−0.0592502
$372$	−42.2828	−2.19226
$373$	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
$375$	−7.86773	−0.406288
$376$	−4.27549	−0.220492
$377$	0	0
$378$	2.36714	0.121753
$379$	30.7940	1.58178	0.790890	−	0.611959i	$-0.209618\pi$
$379$	30.7940	1.58178	0.790890	+	0.611959i	$0.209618\pi$
$380$	−2.65350	−0.136121
$381$	27.4948	1.40860
$382$	35.0579	1.79372
$383$	−28.2978	−1.44595	−0.722974	−	0.690875i	$-0.757226\pi$
$383$	−28.2978	−1.44595	−0.722974	+	0.690875i	$0.757226\pi$
$384$	10.0142	0.511038
$385$	1.30052	0.0662807
$386$	−2.97202	−0.151272
$387$	−31.2030	−1.58614
$388$	4.10233	0.208264
$389$	12.9393	0.656047	0.328024	−	0.944670i	$-0.393617\pi$
$389$	12.9393	0.656047	0.328024	+	0.944670i	$0.393617\pi$
$390$	0	0
$391$	−17.6849	−0.894364
$392$	0.495793	0.0250413
$393$	−32.2440	−1.62650
$394$	13.0180	0.655837
$395$	−3.09193	−0.155572
$396$	−25.2908	−1.27091
$397$	18.3110	0.919004	0.459502	−	0.888177i	$-0.348028\pi$
$397$	18.3110	0.919004	0.459502	+	0.888177i	$0.348028\pi$
$398$	−1.23916	−0.0621135
$399$	−12.4121	−0.621382
$400$	21.8010	1.09005
$401$	1.31244	0.0655402	0.0327701	−	0.999463i	$-0.489567\pi$
$401$	1.31244	0.0655402	0.0327701	+	0.999463i	$0.489567\pi$
$402$	−42.9397	−2.14164
$403$	0	0
$404$	−10.9322	−0.543897
$405$	2.28685	0.113635
$406$	−6.85649	−0.340282
$407$	−48.9072	−2.42424
$408$	6.57161	0.325343
$409$	−29.3018	−1.44888	−0.724440	−	0.689338i	$-0.757901\pi$
$409$	−29.3018	−1.44888	−0.724440	+	0.689338i	$0.757901\pi$
$410$	0.261939	0.0129362
$411$	37.4852	1.84901
$412$	−6.56912	−0.323638
$413$	11.7192	0.576664
$414$	−22.8741	−1.12420
$415$	−0.156351	−0.00767499
$416$	0	0
$417$	−57.9924	−2.83990
$418$	39.3112	1.92277
$419$	−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
$421$	1.19312	0.0581492	0.0290746	−	0.999577i	$-0.490744\pi$
$421$	1.19312	0.0581492	0.0290746	+	0.999577i	$0.490744\pi$
$422$	−33.9876	−1.65449
$423$	−30.0149	−1.45937
$424$	−0.565819	−0.0274786
$425$	25.5264	1.23821
$426$	−30.0049	−1.45374
$427$	−4.87971	−0.236146
$428$	7.00393	0.338548
$429$	0	0
$430$	−5.41368	−0.261071
$431$	22.7978	1.09813	0.549065	−	0.835780i	$-0.314984\pi$
$431$	22.7978	1.09813	0.549065	+	0.835780i	$0.314984\pi$
$432$	5.44027	0.261745
$433$	−4.00964	−0.192691	−0.0963455	−	0.995348i	$-0.530715\pi$
$433$	−4.00964	−0.192691	−0.0963455	+	0.995348i	$0.530715\pi$
$434$	−18.4299	−0.884665
$435$	2.81545	0.134991
$436$	−8.67276	−0.415350
$437$	16.5606	0.792202
$438$	17.6930	0.845403
$439$	−2.55835	−0.122103	−0.0610516	−	0.998135i	$-0.519445\pi$
$439$	−2.55835	−0.122103	−0.0610516	+	0.998135i	$0.519445\pi$
$440$	0.644790	0.0307392
$441$	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	$0.497253\pi$
$444$	−52.1005	−2.47258
$445$	3.27918	0.155448
$446$	−35.4549	−1.67884
$447$	18.3715	0.868944
$448$	−5.83559	−0.275706
$449$	−15.3032	−0.722202	−0.361101	−	0.932527i	$-0.617599\pi$
$449$	−15.3032	−0.722202	−0.361101	+	0.932527i	$0.617599\pi$
$450$	33.0165	1.55641
$451$	−1.80749	−0.0851115
$452$	−22.7970	−1.07228
$453$	−1.67274	−0.0785922
$454$	1.30409	0.0612038
$455$	0	0
$456$	−6.15383	−0.288180
$457$	8.91104	0.416841	0.208420	−	0.978039i	$-0.433168\pi$
$457$	8.91104	0.416841	0.208420	+	0.978039i	$0.433168\pi$
$458$	37.6923	1.76125
$459$	6.36993	0.297323
$460$	−1.84850	−0.0861866
$461$	21.4636	0.999657	0.499829	−	0.866124i	$-0.333396\pi$
$461$	21.4636	0.999657	0.499829	+	0.866124i	$0.333396\pi$
$462$	−20.5251	−0.954914
$463$	3.09472	0.143824	0.0719119	−	0.997411i	$-0.477090\pi$
$463$	3.09472	0.143824	0.0719119	+	0.997411i	$0.477090\pi$
$464$	−15.7579	−0.731540
$465$	7.56781	0.350949
$466$	58.2829	2.69990
$467$	20.9079	0.967503	0.483751	−	0.875205i	$-0.339274\pi$
$467$	20.9079	0.967503	0.483751	+	0.875205i	$0.339274\pi$
$468$	0	0
$469$	−8.71761	−0.402542
$470$	−5.20755	−0.240206
$471$	21.9618	1.01195
$472$	5.81030	0.267441
$473$	37.3568	1.71767
$474$	48.7974	2.24134
$475$	−23.9037	−1.09677
$476$	−9.07927	−0.416148
$477$	−3.97217	−0.181873
$478$	25.6131	1.17151
$479$	−18.3562	−0.838715	−0.419357	−	0.907821i	$-0.637745\pi$
$479$	−18.3562	−0.838715	−0.419357	+	0.907821i	$0.637745\pi$
$480$	6.04820	0.276061
$481$	0	0
$482$	25.7600	1.17333
$483$	−8.64660	−0.393434
$484$	11.0972	0.504418
$485$	−0.734238	−0.0333400
$486$	−43.1930	−1.95927
$487$	13.3086	0.603070	0.301535	−	0.953455i	$-0.402501\pi$
$487$	13.3086	0.603070	0.301535	+	0.953455i	$0.402501\pi$
$488$	−2.41933	−0.109518
$489$	29.3612	1.32776
$490$	0.603875	0.0272803
$491$	−14.5460	−0.656452	−0.328226	−	0.944599i	$-0.606451\pi$
$491$	−14.5460	−0.656452	−0.328226	+	0.944599i	$0.606451\pi$
$492$	−1.92551	−0.0868087
$493$	−18.4507	−0.830976
$494$	0	0
$495$	4.52657	0.203454
$496$	−42.3564	−1.90186
$497$	−6.09160	−0.273245
$498$	2.46757	0.110574
$499$	−31.7570	−1.42164	−0.710819	−	0.703375i	$-0.751675\pi$
$499$	−31.7570	−1.42164	−0.710819	+	0.703375i	$0.751675\pi$
$500$	5.38926	0.241015
$501$	27.4044	1.22434
$502$	−49.4794	−2.20838
$503$	−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
$505$	1.95665	0.0870699
$506$	27.3852	1.21742
$507$	0	0
$508$	−18.8335	−0.835600
$509$	−25.1990	−1.11693	−0.558463	−	0.829529i	$-0.688609\pi$
$509$	−25.1990	−1.11693	−0.558463	+	0.829529i	$0.688609\pi$
$510$	8.00421	0.354432
$511$	3.59203	0.158902
$512$	−29.4419	−1.30116
$513$	−5.96498	−0.263360
$514$	−1.13986	−0.0502772
$515$	1.17575	0.0518096
$516$	39.7959	1.75192
$517$	35.9344	1.58039
$518$	−22.7092	−0.997786
$519$	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	$0.676115\pi$
$522$	−23.8645	−1.04452
$523$	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
$525$	12.4805	0.544695
$526$	35.7983	1.56088
$527$	−49.5945	−2.16037
$528$	−47.1716	−2.05288
$529$	−11.4634	−0.498410
$530$	−0.689167	−0.0299355
$531$	40.7896	1.77012
$532$	8.50208	0.368612
$533$	0	0
$534$	−51.7526	−2.23956
$535$	−1.25357	−0.0541965
$536$	−4.32213	−0.186688
$537$	17.9032	0.772579
$538$	5.23973	0.225901
$539$	−4.16701	−0.179486
$540$	0.665811	0.0286519
$541$	−11.5539	−0.496739	−0.248370	−	0.968665i	$-0.579895\pi$
$541$	−11.5539	−0.496739	−0.248370	+	0.968665i	$0.579895\pi$
$542$	−22.8067	−0.979633
$543$	53.6473	2.30222
$544$	−39.6360	−1.69938
$545$	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	$0.734387\pi$
$548$	−25.6767	−1.09686
$549$	−16.9842	−0.724869
$550$	−39.5279	−1.68548
$551$	17.2777	0.736055
$552$	−4.28693	−0.182464
$553$	9.90686	0.421283
$554$	46.5345	1.97706
$555$	9.32499	0.395824
$556$	39.7238	1.68467
$557$	37.9319	1.60723	0.803614	−	0.595151i	$-0.202908\pi$
$557$	37.9319	1.60723	0.803614	+	0.595151i	$0.202908\pi$
$558$	−64.1468	−2.71555
$559$	0	0
$560$	1.38785	0.0586474
$561$	−55.2326	−2.33192
$562$	−37.1302	−1.56624
$563$	22.3144	0.940438	0.470219	−	0.882550i	$-0.344175\pi$
$563$	22.3144	0.940438	0.470219	+	0.882550i	$0.344175\pi$
$564$	38.2806	1.61191
$565$	4.08023	0.171657
$566$	23.6288	0.993193
$567$	−7.32731	−0.307718
$568$	−3.02017	−0.126724
$569$	−4.83382	−0.202644	−0.101322	−	0.994854i	$-0.532307\pi$
$569$	−4.83382	−0.202644	−0.101322	+	0.994854i	$0.532307\pi$
$570$	−7.49536	−0.313946
$571$	−8.46200	−0.354124	−0.177062	−	0.984200i	$-0.556659\pi$
$571$	−8.46200	−0.354124	−0.177062	+	0.984200i	$0.556659\pi$
$572$	0	0
$573$	46.1253	1.92691
$574$	−0.839279	−0.0350308
$575$	−16.6519	−0.694433
$576$	−20.3112	−0.846301
$577$	9.70860	0.404174	0.202087	−	0.979368i	$-0.435228\pi$
$577$	9.70860	0.404174	0.202087	+	0.979368i	$0.435228\pi$
$578$	−19.5615	−0.813651
$579$	−3.91026	−0.162505
$580$	−1.92854	−0.0800781
$581$	0.500966	0.0207836
$582$	11.5879	0.480333
$583$	4.75555	0.196955
$584$	1.78090	0.0736943
$585$	0	0
$586$	−21.9887	−0.908344
$587$	−5.01204	−0.206869	−0.103434	−	0.994636i	$-0.532983\pi$
$587$	−5.01204	−0.206869	−0.103434	+	0.994636i	$0.532983\pi$
$588$	−4.43909	−0.183065
$589$	46.4417	1.91360
$590$	7.07694	0.291353
$591$	17.1276	0.704536
$592$	−52.1913	−2.14505
$593$	7.85096	0.322400	0.161200	−	0.986922i	$-0.448464\pi$
$593$	7.85096	0.322400	0.161200	+	0.986922i	$0.448464\pi$
$594$	−9.86390	−0.404721
$595$	1.62502	0.0666191
$596$	−12.5842	−0.515469
$597$	−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	$0.701646\pi$
$600$	6.18776	0.252614
$601$	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
$603$	−30.3423	−1.23564
$604$	1.14580	0.0466219
$605$	−1.98619	−0.0807500
$606$	−30.8803	−1.25443
$607$	−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
$609$	−9.02100	−0.365549
$610$	−2.94674	−0.119310
$611$	0	0
$612$	−31.6011	−1.27740
$613$	−19.3299	−0.780725	−0.390363	−	0.920661i	$-0.627650\pi$
$613$	−19.3299	−0.780725	−0.390363	+	0.920661i	$0.627650\pi$
$614$	15.8543	0.639826
$615$	0.344630	0.0138968
$616$	−2.06597	−0.0832405
$617$	39.7821	1.60157	0.800783	−	0.598955i	$-0.204417\pi$
$617$	39.7821	1.60157	0.800783	+	0.598955i	$0.204417\pi$
$618$	−18.5559	−0.746427
$619$	−14.2327	−0.572059	−0.286029	−	0.958221i	$-0.592335\pi$
$619$	−14.2327	−0.572059	−0.286029	+	0.958221i	$0.592335\pi$
$620$	−5.18382	−0.208187
$621$	−4.15536	−0.166749
$622$	−55.2745	−2.21630
$623$	−10.5068	−0.420947
$624$	0	0
$625$	23.5484	0.941936
$626$	−18.2067	−0.727685
$627$	51.7213	2.06555
$628$	−15.0434	−0.600299
$629$	−61.1100	−2.43662
$630$	2.10184	0.0837391
$631$	22.2652	0.886364	0.443182	−	0.896432i	$-0.353850\pi$
$631$	22.2652	0.886364	0.443182	+	0.896432i	$0.353850\pi$
$632$	4.91175	0.195379
$633$	−44.7171	−1.77735
$634$	−3.77665	−0.149990
$635$	3.37083	0.133767
$636$	5.06606	0.200882
$637$	0	0
$638$	28.5710	1.13114
$639$	−21.2023	−0.838749
$640$	1.22774	0.0485305
$641$	4.25054	0.167886	0.0839430	−	0.996471i	$-0.473249\pi$
$641$	4.25054	0.167886	0.0839430	+	0.996471i	$0.473249\pi$
$642$	19.7841	0.780815
$643$	−26.5252	−1.04605	−0.523026	−	0.852317i	$-0.675197\pi$
$643$	−26.5252	−1.04605	−0.523026	+	0.852317i	$0.675197\pi$
$644$	5.92277	0.233390
$645$	−7.12271	−0.280456
$646$	49.1198	1.93259
$647$	15.4298	0.606607	0.303304	−	0.952894i	$-0.401910\pi$
$647$	15.4298	0.606607	0.303304	+	0.952894i	$0.401910\pi$
$648$	−3.63283	−0.142711
$649$	−48.8340	−1.91690
$650$	0	0
$651$	−24.2480	−0.950355
$652$	−20.1119	−0.787644
$653$	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
$655$	−3.95308	−0.154460
$656$	−1.92887	−0.0753096
$657$	12.5023	0.487763
$658$	16.6855	0.650469
$659$	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
$661$	−14.4345	−0.561436	−0.280718	−	0.959790i	$-0.590573\pi$
$661$	−14.4345	−0.561436	−0.280718	+	0.959790i	$0.590573\pi$
$662$	−14.2083	−0.552222
$663$	0	0
$664$	0.248376	0.00963884
$665$	−1.52171	−0.0590094
$666$	−79.0412	−3.06279
$667$	12.0361	0.466040
$668$	−18.7716	−0.726294
$669$	−46.6475	−1.80350
$670$	−5.26435	−0.203380
$671$	20.3338	0.784978
$672$	−19.3791	−0.747564
$673$	−17.6481	−0.680284	−0.340142	−	0.940374i	$-0.610475\pi$
$673$	−17.6481	−0.680284	−0.340142	+	0.940374i	$0.610475\pi$
$674$	44.5828	1.71726
$675$	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	$0.438123\pi$
$678$	−64.3950	−2.47307
$679$	2.35258	0.0902835
$680$	0.805672	0.0308961
$681$	1.71577	0.0657485
$682$	76.7977	2.94073
$683$	28.7118	1.09863	0.549313	−	0.835616i	$-0.314889\pi$
$683$	28.7118	1.09863	0.549313	+	0.835616i	$0.314889\pi$
$684$	29.5921	1.13148
$685$	4.59564	0.175591
$686$	−1.93488	−0.0738741
$687$	49.5914	1.89203
$688$	39.8653	1.51985
$689$	0	0
$690$	−5.22147	−0.198778
$691$	39.7668	1.51280	0.756400	−	0.654109i	$-0.226956\pi$
$691$	39.7668	1.51280	0.756400	+	0.654109i	$0.226956\pi$
$692$	−17.7073	−0.673130
$693$	−14.5036	−0.550946
$694$	48.8501	1.85432
$695$	−7.10980	−0.269690
$696$	−4.47255	−0.169532
$697$	−2.25848	−0.0855461
$698$	−3.93280	−0.148859
$699$	76.6821	2.90038
$700$	−8.54895	−0.323120
$701$	10.4132	0.393301	0.196651	−	0.980474i	$-0.436994\pi$
$701$	10.4132	0.393301	0.196651	+	0.980474i	$0.436994\pi$
$702$	0	0
$703$	57.2251	2.15829
$704$	24.3169	0.916479
$705$	−6.85150	−0.258043
$706$	−18.7454	−0.705491
$707$	−6.26932	−0.235782
$708$	−52.0226	−1.95513
$709$	−33.7060	−1.26586	−0.632928	−	0.774210i	$-0.718147\pi$
$709$	−33.7060	−1.26586	−0.632928	+	0.774210i	$0.718147\pi$
$710$	−3.67857	−0.138054
$711$	34.4816	1.29316
$712$	−5.20922	−0.195224
$713$	32.3525	1.21161
$714$	−25.6463	−0.959789
$715$	0	0
$716$	−12.2634	−0.458304
$717$	33.6988	1.25850
$718$	52.1767	1.94722
$719$	−42.0927	−1.56979	−0.784896	−	0.619628i	$-0.787284\pi$
$719$	−42.0927	−1.56979	−0.784896	+	0.619628i	$0.787284\pi$
$720$	4.83053	0.180023
$721$	−3.76722	−0.140299
$722$	−9.23440	−0.343669
$723$	33.8921	1.26046
$724$	−36.7475	−1.36571
$725$	−17.3729	−0.645215
$726$	31.3464	1.16337
$727$	−19.9921	−0.741465	−0.370733	−	0.928740i	$-0.620893\pi$
$727$	−19.9921	−0.741465	−0.370733	+	0.928740i	$0.620893\pi$
$728$	0	0
$729$	−34.8465	−1.29061
$730$	2.16914	0.0802834
$731$	46.6777	1.72644
$732$	21.6615	0.800631
$733$	−20.7416	−0.766108	−0.383054	−	0.923726i	$-0.625128\pi$
$733$	−20.7416	−0.766108	−0.383054	+	0.923726i	$0.625128\pi$
$734$	12.7469	0.470497
$735$	0.794512	0.0293060
$736$	25.8562	0.953072
$737$	36.3264	1.33810
$738$	−2.92118	−0.107530
$739$	22.5049	0.827855	0.413927	−	0.910310i	$-0.364157\pi$
$739$	22.5049	0.827855	0.413927	+	0.910310i	$0.364157\pi$
$740$	−6.38746	−0.234808
$741$	0	0
$742$	2.20816	0.0810642
$743$	3.81492	0.139956	0.0699780	−	0.997549i	$-0.477707\pi$
$743$	3.81492	0.139956	0.0699780	+	0.997549i	$0.477707\pi$
$744$	−12.0220	−0.440748
$745$	2.25233	0.0825190
$746$	−32.1082	−1.17556
$747$	1.74365	0.0637969
$748$	37.8334	1.38333
$749$	4.01657	0.146762
$750$	15.2231	0.555869
$751$	−30.1283	−1.09940	−0.549699	−	0.835363i	$-0.685258\pi$
$751$	−30.1283	−1.09940	−0.549699	+	0.835363i	$0.685258\pi$
$752$	38.3473	1.39838
$753$	−65.0995	−2.37236
$754$	0	0
$755$	−0.205076	−0.00746348
$756$	−2.13333	−0.0775883
$757$	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
$759$	36.0304	1.30782
$760$	−0.754453	−0.0273669
$761$	14.6724	0.531875	0.265938	−	0.963990i	$-0.414318\pi$
$761$	14.6724	0.531875	0.265938	+	0.963990i	$0.414318\pi$
$762$	−53.1991	−1.92720
$763$	−4.97360	−0.180056
$764$	−31.5951	−1.14307
$765$	5.65599	0.204493
$766$	54.7528	1.97830
$767$	0	0
$768$	−49.0877	−1.77130
$769$	8.21482	0.296234	0.148117	−	0.988970i	$-0.452679\pi$
$769$	8.21482	0.296234	0.148117	+	0.988970i	$0.452679\pi$
$770$	−2.51635	−0.0906831
$771$	−1.49970	−0.0540105
$772$	2.67846	0.0963998
$773$	−46.8567	−1.68532	−0.842659	−	0.538448i	$-0.819011\pi$
$773$	−46.8567	−1.68532	−0.842659	+	0.538448i	$0.819011\pi$
$774$	60.3741	2.17010
$775$	−46.6977	−1.67743
$776$	1.16639	0.0418710
$777$	−29.8783	−1.07188
$778$	−25.0359	−0.897582
$779$	2.11490	0.0757743
$780$	0	0
$781$	25.3837	0.908301
$782$	34.2182	1.22364
$783$	−4.33529	−0.154931
$784$	−4.44682	−0.158815
$785$	2.69249	0.0960991
$786$	62.3883	2.22532
$787$	39.4146	1.40498	0.702490	−	0.711693i	$-0.252071\pi$
$787$	39.4146	1.40498	0.702490	+	0.711693i	$0.252071\pi$
$788$	−11.7321	−0.417940
$789$	47.0994	1.67678
$790$	5.98251	0.212848
$791$	−13.0735	−0.464839
$792$	−7.19078	−0.255513
$793$	0	0
$794$	−35.4296	−1.25735
$795$	−0.906728	−0.0321583
$796$	1.11676	0.0395826
$797$	19.5718	0.693267	0.346634	−	0.938001i	$-0.387325\pi$
$797$	19.5718	0.693267	0.346634	+	0.938001i	$0.387325\pi$
$798$	24.0159	0.850154
$799$	44.9004	1.58846
$800$	−37.3209	−1.31949
$801$	−36.5698	−1.29213
$802$	−2.53942	−0.0896699
$803$	−14.9680	−0.528210
$804$	38.6982	1.36478
$805$	−1.06006	−0.0373623
$806$	0	0
$807$	6.89385	0.242675
$808$	−3.10829	−0.109349
$809$	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
$811$	−55.0717	−1.93383	−0.966915	−	0.255098i	$-0.917892\pi$
$811$	−55.0717	−1.93383	−0.966915	+	0.255098i	$0.917892\pi$
$812$	6.17923	0.216848
$813$	−30.0065	−1.05237
$814$	94.6295	3.31676
$815$	3.59965	0.126090
$816$	−58.9414	−2.06336
$817$	−43.7103	−1.52923
$818$	56.6954	1.98231
$819$	0	0
$820$	−0.236066	−0.00824377
$821$	19.9874	0.697564	0.348782	−	0.937204i	$-0.386595\pi$
$821$	19.9874	0.697564	0.348782	+	0.937204i	$0.386595\pi$
$822$	−72.5294	−2.52975
$823$	4.78565	0.166817	0.0834087	−	0.996515i	$-0.473419\pi$
$823$	4.78565	0.166817	0.0834087	+	0.996515i	$0.473419\pi$
$824$	−1.86776	−0.0650666
$825$	−52.0064	−1.81063
$826$	−22.6753	−0.788973
$827$	19.7389	0.686390	0.343195	−	0.939264i	$-0.388491\pi$
$827$	19.7389	0.686390	0.343195	+	0.939264i	$0.388491\pi$
$828$	20.6147	0.716409
$829$	15.5467	0.539959	0.269980	−	0.962866i	$-0.412983\pi$
$829$	15.5467	0.539959	0.269980	+	0.962866i	$0.412983\pi$
$830$	0.302521	0.0105007
$831$	61.2249	2.12387
$832$	0	0
$833$	−5.20672	−0.180402
$834$	112.208	3.88546
$835$	3.35975	0.116269
$836$	−35.4282	−1.22531
$837$	−11.6531	−0.402789
$838$	0.587369	0.0202903
$839$	28.9070	0.997982	0.498991	−	0.866607i	$-0.333704\pi$
$839$	28.9070	0.997982	0.498991	+	0.866607i	$0.333704\pi$
$840$	0.393914	0.0135913
$841$	−16.4427	−0.566991
$842$	−2.30855	−0.0795579
$843$	−48.8517	−1.68254
$844$	30.6305	1.05434
$845$	0	0
$846$	58.0752	1.99667
$847$	6.36395	0.218668
$848$	5.07489	0.174272
$849$	31.0881	1.06694
$850$	−49.3906	−1.69408
$851$	39.8645	1.36654
$852$	27.0411	0.926413
$853$	−0.564390	−0.0193244	−0.00966218	−	0.999953i	$-0.503076\pi$
$853$	−0.564390	−0.0193244	−0.00966218	+	0.999953i	$0.503076\pi$
$854$	9.44166	0.323087
$855$	−5.29643	−0.181134
$856$	1.99139	0.0680642
$857$	−39.8324	−1.36065	−0.680325	−	0.732911i	$-0.738161\pi$
$857$	−39.8324	−1.36065	−0.680325	+	0.732911i	$0.738161\pi$
$858$	0	0
$859$	−48.3937	−1.65117	−0.825585	−	0.564278i	$-0.809155\pi$
$859$	−48.3937	−1.65117	−0.825585	+	0.564278i	$0.809155\pi$
$860$	4.87894	0.166370
$861$	−1.10423	−0.0376320
$862$	−44.1110	−1.50243
$863$	3.81608	0.129901	0.0649505	−	0.997888i	$-0.479311\pi$
$863$	3.81608	0.129901	0.0649505	+	0.997888i	$0.479311\pi$
$864$	−9.31315	−0.316840
$865$	3.16927	0.107758
$866$	7.75817	0.263633
$867$	−25.7368	−0.874068
$868$	16.6095	0.563763
$869$	−41.2820	−1.40039
$870$	−5.44756	−0.184690
$871$	0	0
$872$	−2.46588	−0.0835051
$873$	8.18832	0.277133
$874$	−32.0428	−1.08386
$875$	3.09060	0.104481
$876$	−15.9453	−0.538743
$877$	−3.07809	−0.103940	−0.0519699	−	0.998649i	$-0.516550\pi$
$877$	−3.07809	−0.103940	−0.0519699	+	0.998649i	$0.516550\pi$
$878$	4.95009	0.167058
$879$	−28.9303	−0.975793
$880$	−5.78319	−0.194951
$881$	−34.7729	−1.17153	−0.585764	−	0.810482i	$-0.699205\pi$
$881$	−34.7729	−1.17153	−0.585764	+	0.810482i	$0.699205\pi$
$882$	−6.73450	−0.226762
$883$	−17.6873	−0.595224	−0.297612	−	0.954687i	$-0.596190\pi$
$883$	−17.6873	−0.595224	−0.297612	+	0.954687i	$0.596190\pi$
$884$	0	0
$885$	9.31104	0.312987
$886$	−0.702926	−0.0236153
$887$	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
$889$	−10.8005	−0.362237
$890$	−6.34482	−0.212679
$891$	30.5330	1.02289
$892$	31.9528	1.06986
$893$	−42.0459	−1.40701
$894$	−35.5467	−1.18886
$895$	2.19491	0.0733677
$896$	−3.93379	−0.131419
$897$	0	0
$898$	29.6098	0.988093
$899$	33.7534	1.12574
$900$	−29.7553	−0.991843
$901$	5.94211	0.197961
$902$	3.49728	0.116447
$903$	22.8219	0.759466
$904$	−6.48174	−0.215580
$905$	6.57709	0.218630
$906$	3.23655	0.107527
$907$	42.6219	1.41524	0.707618	−	0.706595i	$-0.249770\pi$
$907$	42.6219	1.41524	0.707618	+	0.706595i	$0.249770\pi$
$908$	−1.17527	−0.0390028
$909$	−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	$0.114065\pi$
$912$	55.1944	1.82767
$913$	−2.08753	−0.0690871
$914$	−17.2418	−0.570308
$915$	−3.87699	−0.128169
$916$	−33.9692	−1.12238
$917$	12.6661	0.418271
$918$	−12.3251	−0.406787
$919$	−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
$921$	20.8593	0.687336
$922$	−41.5294	−1.36770
$923$	0	0
$924$	18.4977	0.608530
$925$	−57.5406	−1.89192
$926$	−5.98791	−0.196775
$927$	−13.1121	−0.430658
$928$	26.9758	0.885523
$929$	5.51296	0.180874	0.0904372	−	0.995902i	$-0.471174\pi$
$929$	5.51296	0.180874	0.0904372	+	0.995902i	$0.471174\pi$
$930$	−14.6428	−0.480156
$931$	4.87572	0.159795
$932$	−52.5259	−1.72054
$933$	−72.7239	−2.38088
$934$	−40.4543	−1.32371
$935$	−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	$0.242861\pi$
$938$	16.8675	0.550745
$939$	−23.9543	−0.781719
$940$	4.69316	0.153074
$941$	46.2818	1.50874	0.754372	−	0.656448i	$-0.227942\pi$
$941$	46.2818	1.50874	0.754372	+	0.656448i	$0.227942\pi$
$942$	−42.4934	−1.38451
$943$	1.47330	0.0479772
$944$	−52.1132	−1.69614
$945$	0.381825	0.0124208
$946$	−72.2809	−2.35005
$947$	−55.7472	−1.81154	−0.905770	−	0.423769i	$-0.860707\pi$
$947$	−55.7472	−1.81154	−0.905770	+	0.423769i	$0.860707\pi$
$948$	−43.9774	−1.42832
$949$	0	0
$950$	46.2507	1.50057
$951$	−4.96889	−0.161127
$952$	−2.58146	−0.0836655
$953$	−4.03648	−0.130754	−0.0653772	−	0.997861i	$-0.520825\pi$
$953$	−4.03648	−0.130754	−0.0653772	+	0.997861i	$0.520825\pi$
$954$	7.68568	0.248833
$955$	5.65491	0.182989
$956$	−23.0831	−0.746561
$957$	37.5906	1.21513
$958$	35.5170	1.14750
$959$	−14.7249	−0.475492
$960$	−4.63644	−0.149641
$961$	59.7276	1.92670
$962$	0	0
$963$	13.9800	0.450498
$964$	−23.2155	−0.747721
$965$	−0.479393	−0.0154322
$966$	16.7301	0.538283
$967$	−52.0755	−1.67463	−0.837317	−	0.546717i	$-0.815877\pi$
$967$	−52.0755	−1.67463	−0.837317	+	0.546717i	$0.815877\pi$
$968$	3.15520	0.101412
$969$	64.6263	2.07610
$970$	1.42066	0.0456147
$971$	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
$973$	22.7805	0.730311
$974$	−25.7505	−0.825101
$975$	0	0
$976$	21.6992	0.694575
$977$	10.0736	0.322284	0.161142	−	0.986931i	$-0.448482\pi$
$977$	10.0736	0.322284	0.161142	+	0.986931i	$0.448482\pi$
$978$	−56.8104	−1.81660
$979$	43.7820	1.39928
$980$	−0.544227	−0.0173847
$981$	−17.3110	−0.552697
$982$	28.1448	0.898136
$983$	52.7163	1.68139	0.840695	−	0.541509i	$-0.182147\pi$
$983$	52.7163	1.68139	0.840695	+	0.541509i	$0.182147\pi$
$984$	−0.547470	−0.0174527
$985$	2.09983	0.0669061
$986$	35.6998	1.13691
$987$	21.9529	0.698769
$988$	0	0
$989$	−30.4497	−0.968245
$990$	−8.75836	−0.278359
$991$	−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
$993$	−18.6937	−0.593227
$994$	11.7865	0.373845
$995$	−0.199879	−0.00633659
$996$	−2.22383	−0.0704648
$997$	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
$999$	−14.3588	−0.454293

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.n.1.2	✓	6	1.1	even	1	trivial
1183.2.a.o.1.5	yes	6	13.12	even	2
1183.2.c.h.337.3		12	13.8	odd	4
1183.2.c.h.337.10		12	13.5	odd	4
8281.2.a.cb.1.2		6	7.6	odd	2
8281.2.a.cg.1.5		6	91.90	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q-1.93488 q^{2} -2.54570 q^{3} +1.74376 q^{4} -0.312100 q^{5} +4.92562 q^{6} +1.00000 q^{7} +0.495793 q^{8} +3.48058 q^{9} +O(q^{10})\)	\(q-1.93488 q^{2} -2.54570 q^{3} +1.74376 q^{4} -0.312100 q^{5} +4.92562 q^{6} +1.00000 q^{7} +0.495793 q^{8} +3.48058 q^{9} +0.603875 q^{10} -4.16701 q^{11} -4.43909 q^{12} -1.93488 q^{14} +0.794512 q^{15} -4.44682 q^{16} -5.20672 q^{17} -6.73450 q^{18} +4.87572 q^{19} -0.544227 q^{20} -2.54570 q^{21} +8.06266 q^{22} +3.39655 q^{23} -1.26214 q^{24} -4.90259 q^{25} -1.22341 q^{27} +1.74376 q^{28} +3.54362 q^{29} -1.53728 q^{30} +9.52510 q^{31} +7.61248 q^{32} +10.6079 q^{33} +10.0744 q^{34} -0.312100 q^{35} +6.06929 q^{36} +11.7368 q^{37} -9.43392 q^{38} -0.154737 q^{40} +0.433763 q^{41} +4.92562 q^{42} -8.96489 q^{43} -7.26626 q^{44} -1.08629 q^{45} -6.57192 q^{46} -8.62354 q^{47} +11.3203 q^{48} +1.00000 q^{49} +9.48593 q^{50} +13.2547 q^{51} -1.14124 q^{53} +2.36714 q^{54} +1.30052 q^{55} +0.495793 q^{56} -12.4121 q^{57} -6.85649 q^{58} +11.7192 q^{59} +1.38544 q^{60} -4.87971 q^{61} -18.4299 q^{62} +3.48058 q^{63} -5.83559 q^{64} -20.5251 q^{66} -8.71761 q^{67} -9.07927 q^{68} -8.64660 q^{69} +0.603875 q^{70} -6.09160 q^{71} +1.72565 q^{72} +3.59203 q^{73} -22.7092 q^{74} +12.4805 q^{75} +8.50208 q^{76} -4.16701 q^{77} +9.90686 q^{79} +1.38785 q^{80} -7.32731 q^{81} -0.839279 q^{82} +0.500966 q^{83} -4.43909 q^{84} +1.62502 q^{85} +17.3460 q^{86} -9.02100 q^{87} -2.06597 q^{88} -10.5068 q^{89} +2.10184 q^{90} +5.92277 q^{92} -24.2480 q^{93} +16.6855 q^{94} -1.52171 q^{95} -19.3791 q^{96} +2.35258 q^{97} -1.93488 q^{98} -14.5036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 8 q^{6} + 6 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 8 * q^6 + 6 * q^7 - 3 * q^8	\( 6 q - 2 q^{2} - 4 q^{3} + 8 q^{4} - 2 q^{5} + 8 q^{6} + 6 q^{7} - 3 q^{8} - 14 q^{10} - 8 q^{11} - 23 q^{12} - 2 q^{14} - 3 q^{15} - 23 q^{17} - 26 q^{18} + 13 q^{19} + 4 q^{20} - 4 q^{21} - 4 q^{22} - 18 q^{23} + 26 q^{24} - 10 q^{25} - 10 q^{27} + 8 q^{28} - 15 q^{29} + 14 q^{30} - 3 q^{31} - 28 q^{32} - 3 q^{33} + 29 q^{34} - 2 q^{35} + 22 q^{36} + 13 q^{37} - 11 q^{38} - 14 q^{40} + 4 q^{41} + 8 q^{42} - 18 q^{43} + 19 q^{45} - 10 q^{46} + 16 q^{47} - 11 q^{48} + 6 q^{49} + 10 q^{50} + 14 q^{51} - 25 q^{53} + 31 q^{54} - 3 q^{56} + 4 q^{57} + 13 q^{58} - 18 q^{59} - 22 q^{60} + 16 q^{61} - 9 q^{62} - 7 q^{64} + 16 q^{66} - 16 q^{67} - 34 q^{68} - q^{69} - 14 q^{70} - 25 q^{71} - 39 q^{72} + 5 q^{73} - 14 q^{74} + 15 q^{75} - 7 q^{76} - 8 q^{77} + 2 q^{79} + 27 q^{80} - 6 q^{81} - 10 q^{82} + 7 q^{83} - 23 q^{84} - 9 q^{85} + 3 q^{86} + 13 q^{87} - 48 q^{88} + 10 q^{89} - 32 q^{92} - 35 q^{93} - 14 q^{94} - 7 q^{95} + 14 q^{96} + 5 q^{97} - 2 q^{98} + 15 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^3 + 8 * q^4 - 2 * q^5 + 8 * q^6 + 6 * q^7 - 3 * q^8 - 14 * q^10 - 8 * q^11 - 23 * q^12 - 2 * q^14 - 3 * q^15 - 23 * q^17 - 26 * q^18 + 13 * q^19 + 4 * q^20 - 4 * q^21 - 4 * q^22 - 18 * q^23 + 26 * q^24 - 10 * q^25 - 10 * q^27 + 8 * q^28 - 15 * q^29 + 14 * q^30 - 3 * q^31 - 28 * q^32 - 3 * q^33 + 29 * q^34 - 2 * q^35 + 22 * q^36 + 13 * q^37 - 11 * q^38 - 14 * q^40 + 4 * q^41 + 8 * q^42 - 18 * q^43 + 19 * q^45 - 10 * q^46 + 16 * q^47 - 11 * q^48 + 6 * q^49 + 10 * q^50 + 14 * q^51 - 25 * q^53 + 31 * q^54 - 3 * q^56 + 4 * q^57 + 13 * q^58 - 18 * q^59 - 22 * q^60 + 16 * q^61 - 9 * q^62 - 7 * q^64 + 16 * q^66 - 16 * q^67 - 34 * q^68 - q^69 - 14 * q^70 - 25 * q^71 - 39 * q^72 + 5 * q^73 - 14 * q^74 + 15 * q^75 - 7 * q^76 - 8 * q^77 + 2 * q^79 + 27 * q^80 - 6 * q^81 - 10 * q^82 + 7 * q^83 - 23 * q^84 - 9 * q^85 + 3 * q^86 + 13 * q^87 - 48 * q^88 + 10 * q^89 - 32 * q^92 - 35 * q^93 - 14 * q^94 - 7 * q^95 + 14 * q^96 + 5 * q^97 - 2 * q^98 + 15 * q^99

Introduction

L-functions

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