LMFDB - Embedded newform 100.4.e.e.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,4,Mod(7,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("100.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	100.e (of order $4$, degree $2$, 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:	$5.90019100057$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
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} - 7x^{10} + 44x^{8} - 156x^{6} + 704x^{4} - 1792x^{2} + 4096 $ x^12 - 7x^10 + 44x^8 - 156x^6 + 704x^4 - 1792*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$-1.76129 + 0.947553i$ of defining polynomial
Character	$\chi$	$=$	100.7
Dual form			100.4.e.e.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.70884 + 0.813737i) q^{2} +(2.61822 + 2.61822i) q^{3} +(6.67566 - 4.40857i) q^{4} +(-9.22289 - 4.96181i) q^{6} +(17.7783 - 17.7783i) q^{7} +(-14.4959 + 17.3744i) q^{8} -13.2899i q^{9} +O(q^{10})$	\(q+(-2.70884 + 0.813737i) q^{2} +(2.61822 + 2.61822i) q^{3} +(6.67566 - 4.40857i) q^{4} +(-9.22289 - 4.96181i) q^{6} +(17.7783 - 17.7783i) q^{7} +(-14.4959 + 17.3744i) q^{8} -13.2899i q^{9} -7.37590i q^{11} +(29.0210 + 5.93575i) q^{12} +(2.68249 - 2.68249i) q^{13} +(-33.6917 + 62.6254i) q^{14} +(25.1290 - 58.8603i) q^{16} +(20.2367 + 20.2367i) q^{17} +(10.8144 + 36.0001i) q^{18} +135.808 q^{19} +93.0948 q^{21} +(6.00204 + 19.9802i) q^{22} +(71.0426 + 71.0426i) q^{23} +(-83.4434 + 7.53642i) q^{24} +(-5.08361 + 9.44930i) q^{26} +(105.488 - 105.488i) q^{27} +(40.3050 - 197.059i) q^{28} -34.2890i q^{29} +187.974i q^{31} +(-20.1737 + 179.892i) q^{32} +(19.3117 - 19.3117i) q^{33} +(-71.2855 - 38.3507i) q^{34} +(-58.5893 - 88.7186i) q^{36} +(-250.679 - 250.679i) q^{37} +(-367.882 + 110.512i) q^{38} +14.0467 q^{39} -211.105 q^{41} +(-252.179 + 75.7547i) q^{42} +(-46.7326 - 46.7326i) q^{43} +(-32.5172 - 49.2390i) q^{44} +(-250.253 - 134.633i) q^{46} +(-189.707 + 189.707i) q^{47} +(219.902 - 88.3159i) q^{48} -289.134i q^{49} +105.968i q^{51} +(6.08147 - 29.7334i) q^{52} +(74.5742 - 74.5742i) q^{53} +(-199.910 + 371.589i) q^{54} +(51.1739 + 566.598i) q^{56} +(355.575 + 355.575i) q^{57} +(27.9022 + 92.8835i) q^{58} +101.072 q^{59} +232.112 q^{61} +(-152.961 - 509.191i) q^{62} +(-236.271 - 236.271i) q^{63} +(-91.7370 - 503.715i) q^{64} +(-36.5978 + 68.0271i) q^{66} +(34.7419 - 34.7419i) q^{67} +(224.309 + 45.8785i) q^{68} +372.010i q^{69} -614.600i q^{71} +(230.903 + 192.649i) q^{72} +(37.4378 - 37.4378i) q^{73} +(883.036 + 475.063i) q^{74} +(906.607 - 598.718i) q^{76} +(-131.131 - 131.131i) q^{77} +(-38.0504 + 11.4303i) q^{78} -1002.91 q^{79} +193.554 q^{81} +(571.850 - 171.784i) q^{82} +(423.190 + 423.190i) q^{83} +(621.470 - 410.415i) q^{84} +(164.619 + 88.5632i) q^{86} +(89.7761 - 89.7761i) q^{87} +(128.152 + 106.920i) q^{88} +1049.38i q^{89} -95.3802i q^{91} +(787.453 + 161.060i) q^{92} +(-492.156 + 492.156i) q^{93} +(359.514 - 668.257i) q^{94} +(-523.815 + 418.177i) q^{96} +(536.526 + 536.526i) q^{97} +(235.279 + 783.218i) q^{98} -98.0246 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 8 q^{6} + 12 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 + 8 * q^6 + 12 * q^8	$ 12 q + 6 q^{2} + 8 q^{6} + 12 q^{8} + 80 q^{12} - 116 q^{13} + 312 q^{16} + 332 q^{17} - 198 q^{18} - 144 q^{21} - 360 q^{22} - 164 q^{26} + 880 q^{28} + 376 q^{32} - 80 q^{33} + 460 q^{36} - 508 q^{37} - 1600 q^{38} - 656 q^{41} - 1160 q^{42} - 1432 q^{46} + 2720 q^{48} + 932 q^{52} + 644 q^{53} + 2048 q^{56} + 960 q^{57} - 1576 q^{58} - 896 q^{61} - 2440 q^{62} - 1680 q^{66} + 844 q^{68} + 3036 q^{72} - 1436 q^{73} + 800 q^{76} - 3120 q^{77} - 3720 q^{78} + 5988 q^{81} + 1352 q^{82} - 2552 q^{86} + 2400 q^{88} + 1840 q^{92} + 3280 q^{93} + 1088 q^{96} + 4772 q^{97} - 1698 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 + 8 * q^6 + 12 * q^8 + 80 * q^12 - 116 * q^13 + 312 * q^16 + 332 * q^17 - 198 * q^18 - 144 * q^21 - 360 * q^22 - 164 * q^26 + 880 * q^28 + 376 * q^32 - 80 * q^33 + 460 * q^36 - 508 * q^37 - 1600 * q^38 - 656 * q^41 - 1160 * q^42 - 1432 * q^46 + 2720 * q^48 + 932 * q^52 + 644 * q^53 + 2048 * q^56 + 960 * q^57 - 1576 * q^58 - 896 * q^61 - 2440 * q^62 - 1680 * q^66 + 844 * q^68 + 3036 * q^72 - 1436 * q^73 + 800 * q^76 - 3120 * q^77 - 3720 * q^78 + 5988 * q^81 + 1352 * q^82 - 2552 * q^86 + 2400 * q^88 + 1840 * q^92 + 3280 * q^93 + 1088 * q^96 + 4772 * q^97 - 1698 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−2.70884	+	0.813737i	−0.957721	+	0.287699i
$2$	−2.70884	+	0.813737i	−0.957721	+	0.287699i
$3$	2.61822	+	2.61822i	0.503877	+	0.503877i	0.912640	−	0.408764i	$-0.134040\pi$
$3$	2.61822	+	2.61822i	0.503877	+	0.503877i	−0.408764	+	0.912640i	$0.634040\pi$
$4$	6.67566	−	4.40857i	0.834458	−	0.551071i
$5$		0			0
$5$		0			0
$6$	−9.22289	−	4.96181i	−0.627538	−	0.337608i
$7$	17.7783	−	17.7783i	0.959936	−	0.959936i	−0.0392914	−	0.999228i	$-0.512510\pi$
$7$	17.7783	−	17.7783i	0.959936	−	0.959936i	0.999228	+	0.0392914i	$0.0125101\pi$
$8$	−14.4959	+	17.3744i	−0.640635	+	0.767846i
$9$		−	13.2899i		−	0.492217i
$10$		0			0
$11$		−	7.37590i		−	0.202174i	−0.994878	−	0.101087i	$-0.967768\pi$
$11$		−	7.37590i		−	0.202174i	0.994878	−	0.101087i	$-0.0322321\pi$
$12$	29.0210	+	5.93575i	0.698136	+	0.142792i
$13$	2.68249	−	2.68249i	0.0572300	−	0.0572300i	−0.677913	−	0.735143i	$-0.737115\pi$
$13$	2.68249	−	2.68249i	0.0572300	−	0.0572300i	0.735143	+	0.677913i	$0.237115\pi$
$14$	−33.6917	+	62.6254i	−0.643178	+	1.19552i
$15$		0			0
$16$	25.1290	−	58.8603i	0.392641	−	0.919692i
$17$	20.2367	+	20.2367i	0.288713	+	0.288713i	0.836571	−	0.547858i	$-0.184557\pi$
$17$	20.2367	+	20.2367i	0.288713	+	0.288713i	−0.547858	+	0.836571i	$0.684557\pi$
$18$	10.8144	+	36.0001i	0.141610	+	0.471406i
$19$	135.808			1.63981			0.819906	−	0.572498i	$-0.194025\pi$
$19$	135.808			1.63981			0.819906	+	0.572498i	$0.194025\pi$
$20$		0			0
$21$	93.0948			0.967379
$22$	6.00204	+	19.9802i	0.0581654	+	0.193627i
$23$	71.0426	+	71.0426i	0.644061	+	0.644061i	0.951551	−	0.307490i	$-0.0994892\pi$
$23$	71.0426	+	71.0426i	0.644061	+	0.644061i	−0.307490	+	0.951551i	$0.599489\pi$
$24$	−83.4434	+	7.53642i	−0.709700	+	0.0640985i
$25$		0			0
$26$	−5.08361	+	9.44930i	−0.0383453	+	0.0712754i
$27$	105.488	−	105.488i	0.751893	−	0.751893i
$28$	40.3050	−	197.059i	0.272033	−	1.33002i
$29$		−	34.2890i		−	0.219562i	−0.993956	−	0.109781i	$-0.964985\pi$
$29$		−	34.2890i		−	0.219562i	0.993956	−	0.109781i	$-0.0350150\pi$
$30$		0			0
$31$			187.974i			1.08907i	0.838739	+	0.544533i	$0.183293\pi$
$31$			187.974i			1.08907i	−0.838739	+	0.544533i	$0.816707\pi$
$32$	−20.1737	+	179.892i	−0.111445	+	0.993771i
$33$	19.3117	−	19.3117i	0.101871	−	0.101871i
$34$	−71.2855	−	38.3507i	−0.359569	−	0.193444i
$35$		0			0
$36$	−58.5893	−	88.7186i	−0.271247	−	0.410734i
$37$	−250.679	−	250.679i	−1.11382	−	1.11382i	−0.992629	−	0.121190i	$-0.961329\pi$
$37$	−250.679	−	250.679i	−1.11382	−	1.11382i	−0.121190	−	0.992629i	$-0.538671\pi$
$38$	−367.882	+	110.512i	−1.57048	+	0.471773i
$39$	14.0467			0.0576737
$40$		0			0
$41$	−211.105			−0.804122			−0.402061	−	0.915613i	$-0.631706\pi$
$41$	−211.105			−0.804122			−0.402061	+	0.915613i	$0.631706\pi$
$42$	−252.179	+	75.7547i	−0.926479	+	0.278314i
$43$	−46.7326	−	46.7326i	−0.165736	−	0.165736i	0.619366	−	0.785102i	$-0.287390\pi$
$43$	−46.7326	−	46.7326i	−0.165736	−	0.165736i	−0.785102	+	0.619366i	$0.787390\pi$
$44$	−32.5172	−	49.2390i	−0.111412	−	0.168706i
$45$		0			0
$46$	−250.253	−	134.633i	−0.802126	−	0.431535i
$47$	−189.707	+	189.707i	−0.588757	+	0.588757i	−0.937295	−	0.348538i	$-0.886678\pi$
$47$	−189.707	+	189.707i	−0.588757	+	0.588757i	0.348538	+	0.937295i	$0.386678\pi$
$48$	219.902	−	88.3159i	0.661254	−	0.265569i
$49$		−	289.134i		−	0.842956i
$50$		0			0
$51$			105.968i			0.290952i
$52$	6.08147	−	29.7334i	0.0162182	−	0.0792939i
$53$	74.5742	−	74.5742i	0.193275	−	0.193275i	−0.603835	−	0.797109i	$-0.706361\pi$
$53$	74.5742	−	74.5742i	0.193275	−	0.193275i	0.797109	+	0.603835i	$0.206361\pi$
$54$	−199.910	+	371.589i	−0.503784	+	0.936423i
$55$		0			0
$56$	51.1739	+	566.598i	0.122114	+	1.35205i
$57$	355.575	+	355.575i	0.826263	+	0.826263i
$58$	27.9022	+	92.8835i	0.0631679	+	0.210279i
$59$	101.072			0.223024			0.111512	−	0.993763i	$-0.464431\pi$
$59$	101.072			0.223024			0.111512	+	0.993763i	$0.464431\pi$
$60$		0			0
$61$	232.112			0.487196			0.243598	−	0.969876i	$-0.421672\pi$
$61$	232.112			0.487196			0.243598	+	0.969876i	$0.421672\pi$
$62$	−152.961	−	509.191i	−0.313324	−	1.04302i
$63$	−236.271	−	236.271i	−0.472497	−	0.472497i
$64$	−91.7370	−	503.715i	−0.179174	−	0.983817i
$65$		0			0
$66$	−36.5978	+	68.0271i	−0.0682557	+	0.126872i
$67$	34.7419	−	34.7419i	0.0633493	−	0.0633493i	−0.674722	−	0.738072i	$-0.735737\pi$
$67$	34.7419	−	34.7419i	0.0633493	−	0.0633493i	0.738072	+	0.674722i	$0.235737\pi$
$68$	224.309	+	45.8785i	0.400021	+	0.0818175i
$69$			372.010i			0.649054i
$70$		0			0
$71$		−	614.600i		−	1.02732i	−0.857994	−	0.513660i	$-0.828289\pi$
$71$		−	614.600i		−	1.02732i	0.857994	−	0.513660i	$-0.171711\pi$
$72$	230.903	+	192.649i	0.377946	+	0.315331i
$73$	37.4378	−	37.4378i	0.0600242	−	0.0600242i	−0.676457	−	0.736482i	$-0.736486\pi$
$73$	37.4378	−	37.4378i	0.0600242	−	0.0600242i	0.736482	+	0.676457i	$0.236486\pi$
$74$	883.036	+	475.063i	1.38717	+	0.746283i
$75$		0			0
$76$	906.607	−	598.718i	1.36836	−	0.903654i
$77$	−131.131	−	131.131i	−0.194074	−	0.194074i
$78$	−38.0504	+	11.4303i	−0.0552353	+	0.0165927i
$79$	−1002.91			−1.42831			−0.714153	−	0.699990i	$-0.753188\pi$
$79$	−1002.91			−1.42831			−0.714153	+	0.699990i	$0.753188\pi$
$80$		0			0
$81$	193.554			0.265506
$82$	571.850	−	171.784i	0.770125	−	0.231346i
$83$	423.190	+	423.190i	0.559652	+	0.559652i	0.929208	−	0.369556i	$-0.120490\pi$
$83$	423.190	+	423.190i	0.559652	+	0.559652i	−0.369556	+	0.929208i	$0.620490\pi$
$84$	621.470	−	410.415i	0.807237	−	0.533095i
$85$		0			0
$86$	164.619	+	88.5632i	0.206411	+	0.111047i
$87$	89.7761	−	89.7761i	0.110632	−	0.110632i
$88$	128.152	+	106.920i	0.155239	+	0.129520i
$89$			1049.38i			1.24982i	0.780695	+	0.624912i	$0.214865\pi$
$89$			1049.38i			1.24982i	−0.780695	+	0.624912i	$0.785135\pi$
$90$		0			0
$91$		−	95.3802i		−	0.109874i
$92$	787.453	+	161.060i	0.892365	+	0.182518i
$93$	−492.156	+	492.156i	−0.548755	+	0.548755i
$94$	359.514	−	668.257i	0.394479	−	0.733249i
$95$		0			0
$96$	−523.815	+	418.177i	−0.556892	+	0.444583i
$97$	536.526	+	536.526i	0.561608	+	0.561608i	0.929764	−	0.368156i	$-0.120011\pi$
$97$	536.526	+	536.526i	0.561608	+	0.561608i	−0.368156	+	0.929764i	$0.620011\pi$
$98$	235.279	+	783.218i	0.242518	+	0.807316i
$99$	−98.0246			−0.0995136
$100$		0			0
$101$	−1415.80			−1.39483			−0.697414	−	0.716668i	$-0.745666\pi$
$101$	−1415.80			−1.39483			−0.697414	+	0.716668i	$0.745666\pi$
$102$	−86.2303	−	287.052i	−0.0837066	−	0.278650i
$103$	−284.920	−	284.920i	−0.272563	−	0.272563i	0.557568	−	0.830131i	$-0.311735\pi$
$103$	−284.920	−	284.920i	−0.272563	−	0.272563i	−0.830131	+	0.557568i	$0.811735\pi$
$104$	7.72143	+	85.4919i	0.00728027	+	0.0806074i
$105$		0			0
$106$	−141.326	+	262.694i	−0.129498	+	0.240708i
$107$	−464.315	+	464.315i	−0.419505	+	0.419505i	−0.885033	−	0.465528i	$-0.845864\pi$
$107$	−464.315	+	464.315i	−0.419505	+	0.419505i	0.465528	+	0.885033i	$0.345864\pi$
$108$	239.150	−	1169.25i	0.213076	−	1.04177i
$109$		−	638.365i		−	0.560957i	−0.959860	−	0.280478i	$-0.909507\pi$
$109$		−	638.365i		−	0.560957i	0.959860	−	0.280478i	$-0.0904931\pi$
$110$		0			0
$111$		−	1312.66i		−	1.12246i
$112$	−599.684	−	1493.18i	−0.505936	−	1.25976i
$113$	−1001.84	+	1001.84i	−0.834027	+	0.834027i	−0.988065	−	0.154038i	$-0.950772\pi$
$113$	−1001.84	+	1001.84i	−0.834027	+	0.834027i	0.154038	+	0.988065i	$0.450772\pi$
$114$	−1252.54	−	673.852i	−1.02905	−	0.553614i
$115$		0			0
$116$	−151.165	−	228.902i	−0.120994	−	0.183216i
$117$	−35.6500	−	35.6500i	−0.0281696	−	0.0281696i
$118$	−273.787	+	82.2456i	−0.213594	+	0.0641638i
$119$	719.548			0.554293
$120$		0			0
$121$	1276.60			0.959126
$122$	−628.756	+	188.878i	−0.466598	+	0.140166i
$123$	−552.718	−	552.718i	−0.405178	−	0.405178i
$124$	828.695	+	1254.85i	0.600153	+	0.908780i
$125$		0			0
$126$	832.282	+	447.758i	0.588457	+	0.316583i
$127$	−619.456	+	619.456i	−0.432818	+	0.432818i	−0.889586	−	0.456768i	$-0.849007\pi$
$127$	−619.456	+	619.456i	−0.432818	+	0.432818i	0.456768	+	0.889586i	$0.349007\pi$
$128$	658.392	+	1289.83i	0.454642	+	0.890674i
$129$		−	244.712i		−	0.167021i
$130$		0			0
$131$			1620.12i			1.08054i	0.841491	+	0.540270i	$0.181678\pi$
$131$			1620.12i			1.08054i	−0.841491	+	0.540270i	$0.818322\pi$
$132$	43.7815	−	214.056i	0.0288689	−	0.141145i
$133$	2414.43	−	2414.43i	1.57412	−	1.57412i
$134$	−65.8397	+	122.381i	−0.0424454	+	0.0788965i
$135$		0			0
$136$	−644.950	+	58.2504i	−0.406647	+	0.0367274i
$137$	−825.076	−	825.076i	−0.514533	−	0.514533i	0.401379	−	0.915912i	$-0.368531\pi$
$137$	−825.076	−	825.076i	−0.514533	−	0.514533i	−0.915912	+	0.401379i	$0.868531\pi$
$138$	−302.718	−	1007.72i	−0.186733	−	0.621613i
$139$	−1264.21			−0.771430			−0.385715	−	0.922618i	$-0.626045\pi$
$139$	−1264.21			−0.771430			−0.385715	+	0.922618i	$0.626045\pi$
$140$		0			0
$141$	−993.387			−0.593321
$142$	500.123	+	1664.86i	0.295559	+	0.983885i
$143$	−19.7858	−	19.7858i	−0.0115704	−	0.0115704i
$144$	−782.244	−	333.961i	−0.452688	−	0.193264i
$145$		0			0
$146$	−70.9487	+	131.878i	−0.0402175	+	0.0747553i
$147$	757.016	−	757.016i	0.424746	−	0.424746i
$148$	−2778.58	−	568.312i	−1.54323	−	0.315642i
$149$		−	1351.49i		−	0.743079i	−0.928417	−	0.371539i	$-0.878830\pi$
$149$		−	1351.49i		−	0.743079i	0.928417	−	0.371539i	$-0.121170\pi$
$150$		0			0
$151$			2325.64i			1.25336i	0.779275	+	0.626682i	$0.215588\pi$
$151$			2325.64i			1.25336i	−0.779275	+	0.626682i	$0.784412\pi$
$152$	−1968.66	+	2359.57i	−1.05052	+	1.25912i
$153$	268.943	−	268.943i	0.142109	−	0.142109i
$154$	461.918	+	248.507i	0.241704	+	0.130034i
$155$		0			0
$156$	93.7712	−	61.9260i	0.0481263	−	0.0317823i
$157$	−162.486	−	162.486i	−0.0825976	−	0.0825976i	0.664601	−	0.747199i	$-0.268602\pi$
$157$	−162.486	−	162.486i	−0.0825976	−	0.0825976i	−0.747199	+	0.664601i	$0.768602\pi$
$158$	2716.73	−	816.105i	1.36792	−	0.410923i
$159$	390.503			0.194773
$160$		0			0
$161$	2526.03			1.23651
$162$	−524.307	+	157.502i	−0.254281	+	0.0763859i
$163$	932.441	+	932.441i	0.448064	+	0.448064i	0.894710	−	0.446647i	$-0.147382\pi$
$163$	932.441	+	932.441i	0.448064	+	0.448064i	−0.446647	+	0.894710i	$0.647382\pi$
$164$	−1409.26	+	930.670i	−0.671006	+	0.443129i
$165$		0			0
$166$	−1490.72	−	801.990i	−0.697002	−	0.374979i
$167$	976.461	−	976.461i	0.452460	−	0.452460i	−0.443710	−	0.896170i	$-0.646338\pi$
$167$	976.461	−	976.461i	0.452460	−	0.452460i	0.896170	+	0.443710i	$0.146338\pi$
$168$	−1349.49	+	1617.46i	−0.619737	+	0.742798i
$169$			2182.61i			0.993449i
$170$		0			0
$171$		−	1804.87i		−	0.807143i
$172$	−517.995	−	105.947i	−0.229632	−	0.0469674i
$173$	−761.698	+	761.698i	−0.334745	+	0.334745i	−0.854385	−	0.519640i	$-0.826066\pi$
$173$	−761.698	+	761.698i	−0.334745	+	0.334745i	0.519640	+	0.854385i	$0.326066\pi$
$174$	−170.135	+	316.244i	−0.0741260	+	0.137784i
$175$		0			0
$176$	−434.148	−	185.349i	−0.185938	−	0.0793818i
$177$	264.628	+	264.628i	0.112376	+	0.112376i
$178$	−853.921	−	2842.61i	−0.359574	−	1.19698i
$179$	4003.32			1.67163			0.835816	−	0.549009i	$-0.184995\pi$
$179$	4003.32			1.67163			0.835816	+	0.549009i	$0.184995\pi$
$180$		0			0
$181$	−1950.00			−0.800785			−0.400392	−	0.916344i	$-0.631126\pi$
$181$	−1950.00			−0.800785			−0.400392	+	0.916344i	$0.631126\pi$
$182$	77.6144	+	258.370i	0.0316108	+	0.105229i
$183$	607.721	+	607.721i	0.245487	+	0.245487i
$184$	−2264.15	+	204.493i	−0.907147	+	0.0819315i
$185$		0			0
$186$	932.688	−	1733.66i	0.367677	−	0.683430i
$187$	149.264	−	149.264i	0.0583704	−	0.0583704i
$188$	−430.083	+	2102.75i	−0.166846	+	0.815740i
$189$		−	3750.78i		−	1.44354i
$190$		0			0
$191$			1458.80i			0.552644i	0.961065	+	0.276322i	$0.0891156\pi$
$191$			1458.80i			0.552644i	−0.961065	+	0.276322i	$0.910884\pi$
$192$	1078.65	−	1559.02i	0.405441	−	0.586004i
$193$	−2264.70	+	2264.70i	−0.844647	+	0.844647i	−0.989459	−	0.144812i	$-0.953742\pi$
$193$	−2264.70	+	2264.70i	−0.844647	+	0.844647i	0.144812	+	0.989459i	$0.453742\pi$
$194$	−1889.96	−	1016.77i	−0.699438	−	0.376289i
$195$		0			0
$196$	−1274.67	−	1930.16i	−0.464529	−	0.703411i
$197$	−2092.70	−	2092.70i	−0.756845	−	0.756845i	0.218902	−	0.975747i	$-0.429753\pi$
$197$	−2092.70	−	2092.70i	−0.756845	−	0.756845i	−0.975747	+	0.218902i	$0.929753\pi$
$198$	265.533	−	79.7662i	0.0953062	−	0.0286300i
$199$	2087.70			0.743683			0.371842	−	0.928296i	$-0.378726\pi$
$199$	2087.70			0.743683			0.371842	+	0.928296i	$0.378726\pi$
$200$		0			0
$201$	181.924			0.0638405
$202$	3835.19	−	1152.09i	1.33586	−	0.401291i
$203$	−609.599	−	609.599i	−0.210766	−	0.210766i
$204$	467.169	+	707.409i	0.160335	+	0.242787i
$205$		0			0
$206$	1003.65	+	539.954i	0.339456	+	0.182623i
$207$	944.145	−	944.145i	0.317018	−	0.317018i
$208$	−90.4840	−	225.301i	−0.0301632	−	0.0751048i
$209$		−	1001.70i		−	0.331528i
$210$		0			0
$211$		−	199.597i		−	0.0651223i	−0.999470	−	0.0325611i	$-0.989634\pi$
$211$		−	199.597i		−	0.0651223i	0.999470	−	0.0325611i	$-0.0103664\pi$
$212$	169.067	−	826.598i	0.0547714	−	0.267788i
$213$	1609.16	−	1609.16i	0.517642	−	0.517642i
$214$	879.926	−	1635.59i	0.281077	−	0.522460i
$215$		0			0
$216$	303.641	+	3361.92i	0.0956489	+	1.05903i
$217$	3341.84	+	3341.84i	1.04543	+	1.04543i
$218$	519.461	+	1729.23i	0.161387	+	0.537240i
$219$	196.041			0.0604896
$220$		0			0
$221$	108.570			0.0330461
$222$	1068.16	+	3555.80i	0.322930	+	1.07500i
$223$	3340.24	+	3340.24i	1.00304	+	1.00304i	0.999995	+	0.00304854i	$0.000970381\pi$
$223$	3340.24	+	3340.24i	1.00304	+	1.00304i	0.00304854	+	0.999995i	$0.499030\pi$
$224$	2839.51	+	3556.82i	0.846976	+	1.06094i
$225$		0			0
$226$	1898.59	−	3529.06i	0.558816	−	1.03871i
$227$	824.316	−	824.316i	0.241021	−	0.241021i	−0.576251	−	0.817272i	$-0.695485\pi$
$227$	824.316	−	824.316i	0.241021	−	0.241021i	0.817272	+	0.576251i	$0.195485\pi$
$228$	3941.27	+	806.121i	1.14481	+	0.234152i
$229$			4512.23i			1.30208i	0.759043	+	0.651041i	$0.225667\pi$
$229$			4512.23i			1.30208i	−0.759043	+	0.651041i	$0.774333\pi$
$230$		0			0
$231$		−	686.658i		−	0.195579i
$232$	595.749	+	497.050i	0.168590	+	0.140659i
$233$	292.574	−	292.574i	0.0822625	−	0.0822625i	−0.664778	−	0.747041i	$-0.731474\pi$
$233$	292.574	−	292.574i	0.0822625	−	0.0822625i	0.747041	+	0.664778i	$0.231474\pi$
$234$	125.580	+	67.5605i	0.0350829	+	0.0188742i
$235$		0			0
$236$	674.720	−	445.581i	0.186104	−	0.122902i
$237$	−2625.84	−	2625.84i	−0.719690	−	0.719690i
$238$	−1949.14	+	585.522i	−0.530858	+	0.159470i
$239$	−2925.20			−0.791696			−0.395848	−	0.918316i	$-0.629549\pi$
$239$	−2925.20			−0.791696			−0.395848	+	0.918316i	$0.629549\pi$
$240$		0			0
$241$	4259.40			1.13847			0.569236	−	0.822174i	$-0.307239\pi$
$241$	4259.40			1.13847			0.569236	+	0.822174i	$0.307239\pi$
$242$	−3458.10	+	1038.81i	−0.918574	+	0.275940i
$243$	−2341.40	−	2341.40i	−0.618111	−	0.618111i
$244$	1549.50	−	1023.28i	0.406544	−	0.268480i
$245$		0			0
$246$	1947.00	+	1047.46i	0.504617	+	0.271478i
$247$	364.304	−	364.304i	0.0938465	−	0.0938465i
$248$	−3265.92	−	2724.85i	−0.836235	−	0.697694i
$249$			2216.01i			0.563991i
$250$		0			0
$251$		−	5268.72i		−	1.32493i	−0.749091	−	0.662467i	$-0.769509\pi$
$251$		−	5268.72i		−	1.32493i	0.749091	−	0.662467i	$-0.230491\pi$
$252$	−2618.88	−	535.647i	−0.654658	−	0.133899i
$253$	524.003	−	524.003i	0.130213	−	0.130213i
$254$	1173.94	−	2182.08i	0.289997	−	0.539040i
$255$		0			0
$256$	−2833.07	−	2958.20i	−0.691667	−	0.722217i
$257$	5635.08	+	5635.08i	1.36773	+	1.36773i	0.863668	+	0.504061i	$0.168161\pi$
$257$	5635.08	+	5635.08i	1.36773	+	1.36773i	0.504061	+	0.863668i	$0.331839\pi$
$258$	199.132	+	662.888i	0.0480519	+	0.159960i
$259$	−8913.27			−2.13839
$260$		0			0
$261$	−455.696			−0.108072
$262$	−1318.35	−	4388.66i	−0.310871	−	1.03486i
$263$	−2721.99	−	2721.99i	−0.638195	−	0.638195i	0.311915	−	0.950110i	$-0.399030\pi$
$263$	−2721.99	−	2721.99i	−0.638195	−	0.638195i	−0.950110	+	0.311915i	$0.899030\pi$
$264$	55.5878	+	615.470i	0.0129591	+	0.143483i
$265$		0			0
$266$	−4575.60	+	8505.01i	−1.05469	+	1.96044i
$267$	−2747.51	+	2747.51i	−0.629757	+	0.629757i
$268$	78.7632	−	385.088i	0.0179523	−	0.0877723i
$269$		−	603.964i		−	0.136893i	−0.997655	−	0.0684467i	$-0.978196\pi$
$269$		−	603.964i		−	0.136893i	0.997655	−	0.0684467i	$-0.0218043\pi$
$270$		0			0
$271$			4232.24i			0.948672i	0.880344	+	0.474336i	$0.157312\pi$
$271$			4232.24i			0.948672i	−0.880344	+	0.474336i	$0.842688\pi$
$272$	1699.67	−	682.611i	0.378888	−	0.152167i
$273$	249.726	−	249.726i	0.0553631	−	0.0553631i
$274$	2906.40	+	1563.61i	0.640810	+	0.344748i
$275$		0			0
$276$	1640.03	+	2483.41i	0.357675	+	0.541609i
$277$	−3214.07	−	3214.07i	−0.697165	−	0.697165i	0.266633	−	0.963798i	$-0.414089\pi$
$277$	−3214.07	−	3214.07i	−0.697165	−	0.697165i	−0.963798	+	0.266633i	$0.914089\pi$
$278$	3424.54	−	1028.73i	0.738815	−	0.221940i
$279$	2498.14			0.536056
$280$		0			0
$281$	−7574.78			−1.60809			−0.804046	−	0.594567i	$-0.797323\pi$
$281$	−7574.78			−1.60809			−0.804046	+	0.594567i	$0.797323\pi$
$282$	2690.93	−	808.356i	0.568236	−	0.170698i
$283$	−504.094	−	504.094i	−0.105884	−	0.105884i	0.652180	−	0.758064i	$-0.273855\pi$
$283$	−504.094	−	504.094i	−0.105884	−	0.105884i	−0.758064	+	0.652180i	$0.773855\pi$
$284$	−2709.51	−	4102.87i	−0.566126	−	0.857255i
$285$		0			0
$286$	69.6971	+	37.4962i	0.0144101	+	0.00775244i
$287$	−3753.08	+	3753.08i	−0.771906	+	0.771906i
$288$	2390.73	+	268.106i	0.489150	+	0.0548552i
$289$		−	4093.95i		−	0.833289i
$290$		0			0
$291$			2809.49i			0.565962i
$292$	84.8750	−	414.970i	0.0170101	−	0.0831653i
$293$	244.144	−	244.144i	0.0486793	−	0.0486793i	−0.682348	−	0.731027i	$-0.739041\pi$
$293$	244.144	−	244.144i	0.0486793	−	0.0486793i	0.731027	+	0.682348i	$0.239041\pi$
$294$	−1434.63	+	2666.65i	−0.284589	+	0.528987i
$295$		0			0
$296$	7989.20	−	721.566i	1.56879	−	0.141690i
$297$	−778.066	−	778.066i	−0.152013	−	0.152013i
$298$	1099.76	+	3660.99i	0.213783	+	0.711662i
$299$	381.143			0.0737192
$300$		0			0
$301$	−1661.65			−0.318192
$302$	−1892.46	−	6299.80i	−0.360592	−	1.20037i
$303$	−3706.88	−	3706.88i	−0.702822	−	0.702822i
$304$	3412.71	−	7993.69i	0.643857	−	1.50812i
$305$		0			0
$306$	−509.676	+	947.373i	−0.0952164	+	0.176986i
$307$	−6853.22	+	6853.22i	−1.27405	+	1.27405i	−0.330110	+	0.943942i	$0.607086\pi$
$307$	−6853.22	+	6853.22i	−1.27405	+	1.27405i	−0.943942	+	0.330110i	$0.892914\pi$
$308$	−1453.48	−	297.286i	−0.268896	−	0.0549981i
$309$		−	1491.97i		−	0.274676i
$310$		0			0
$311$		−	10802.7i		−	1.96966i	−0.173510	−	0.984832i	$-0.555511\pi$
$311$		−	10802.7i		−	1.96966i	0.173510	−	0.984832i	$-0.444489\pi$
$312$	−203.620	+	244.053i	−0.0369478	+	0.0442845i
$313$	−2618.43	+	2618.43i	−0.472851	+	0.472851i	−0.902836	−	0.429985i	$-0.858519\pi$
$313$	−2618.43	+	2618.43i	−0.472851	+	0.472851i	0.429985	+	0.902836i	$0.358519\pi$
$314$	572.372	+	307.929i	0.102869	+	0.0553422i
$315$		0			0
$316$	−6695.09	+	4421.40i	−1.19186	+	0.787098i
$317$	−3652.64	−	3652.64i	−0.647170	−	0.647170i	0.305138	−	0.952308i	$-0.401297\pi$
$317$	−3652.64	−	3652.64i	−0.647170	−	0.647170i	−0.952308	+	0.305138i	$0.901297\pi$
$318$	−1057.81	+	317.767i	−0.186538	+	0.0560361i
$319$	−252.912			−0.0443898
$320$		0			0
$321$	−2431.36			−0.422757
$322$	−6842.61	+	2055.52i	−1.18424	+	0.355745i
$323$	2748.30	+	2748.30i	0.473436	+	0.473436i
$324$	1292.10	−	853.296i	0.221554	−	0.146313i
$325$		0			0
$326$	−3284.60	−	1767.07i	−0.558028	−	0.300212i
$327$	1671.38	−	1671.38i	0.282653	−	0.282653i
$328$	3060.16	−	3667.81i	0.515149	−	0.617442i
$329$			6745.31i			1.13034i
$330$		0			0
$331$			7839.91i			1.30187i	0.759131	+	0.650937i	$0.225624\pi$
$331$			7839.91i			1.30187i	−0.759131	+	0.650937i	$0.774376\pi$
$332$	4690.74	+	959.411i	0.775415	+	0.158598i
$333$	−3331.48	+	3331.48i	−0.548241	+	0.548241i
$334$	−1850.50	+	3439.66i	−0.303158	+	0.563503i
$335$		0			0
$336$	2339.38	−	5479.59i	0.379832	−	0.889691i
$337$	4503.23	+	4503.23i	0.727912	+	0.727912i	0.970204	−	0.242291i	$-0.0778990\pi$
$337$	4503.23	+	4503.23i	0.727912	+	0.727912i	−0.242291	+	0.970204i	$0.577899\pi$
$338$	−1776.07	−	5912.34i	−0.285815	−	0.951447i
$339$	−5246.07			−0.840494
$340$		0			0
$341$	1386.47			0.220181
$342$	1468.69	+	4889.10i	0.232215	+	0.773018i
$343$	957.648	+	957.648i	0.150753	+	0.150753i
$344$	1489.38	−	134.517i	0.233436	−	0.0210834i
$345$		0			0
$346$	1443.50	−	2683.14i	0.224286	−	0.416898i
$347$	8458.77	−	8458.77i	1.30862	−	1.30862i	0.386205	−	0.922413i	$-0.373786\pi$
$347$	8458.77	−	8458.77i	1.30862	−	1.30862i	0.922413	−	0.386205i	$-0.126214\pi$
$348$	203.531	−	995.100i	0.0313517	−	0.153284i
$349$			5515.41i			0.845941i	0.906144	+	0.422970i	$0.139013\pi$
$349$			5515.41i			0.845941i	−0.906144	+	0.422970i	$0.860987\pi$
$350$		0			0
$351$		−	565.940i		−	0.0860617i
$352$	1326.86	+	148.799i	0.200915	+	0.0225314i
$353$	761.447	−	761.447i	0.114810	−	0.114810i	−0.647368	−	0.762178i	$-0.724130\pi$
$353$	761.447	−	761.447i	0.114810	−	0.114810i	0.762178	+	0.647368i	$0.224130\pi$
$354$	−932.172	−	501.497i	−0.139956	−	0.0752946i
$355$		0			0
$356$	4626.28	+	7005.33i	0.688742	+	1.04293i
$357$	1883.93	+	1883.93i	0.279295	+	0.279295i
$358$	−10844.4	+	3257.65i	−1.60096	+	0.480928i
$359$	−3564.71			−0.524062			−0.262031	−	0.965059i	$-0.584392\pi$
$359$	−3564.71			−0.524062			−0.262031	+	0.965059i	$0.584392\pi$
$360$		0			0
$361$	11584.8			1.68899
$362$	5282.23	−	1586.78i	0.766928	−	0.230385i
$363$	3342.41	+	3342.41i	0.483281	+	0.483281i
$364$	−420.491	−	636.726i	−0.0605486	−	0.0916855i
$365$		0			0
$366$	−2140.75	−	1151.70i	−0.305734	−	0.164481i
$367$	4407.82	−	4407.82i	0.626939	−	0.626939i	−0.320358	−	0.947297i	$-0.603803\pi$
$367$	4407.82	−	4407.82i	0.626939	−	0.626939i	0.947297	+	0.320358i	$0.103803\pi$
$368$	5966.81	−	2396.36i	0.845222	−	0.339453i
$369$			2805.55i			0.395802i
$370$		0			0
$371$		−	2651.60i		−	0.371063i
$372$	−1115.76	+	5455.17i	−0.155510	+	0.760316i
$373$	8371.19	−	8371.19i	1.16205	−	1.16205i	0.178021	−	0.984027i	$-0.443030\pi$
$373$	8371.19	−	8371.19i	1.16205	−	1.16205i	0.984027	−	0.178021i	$-0.0569696\pi$
$374$	−282.871	+	525.794i	−0.0391094	+	0.0726957i
$375$		0			0
$376$	−546.061	−	6046.00i	−0.0748962	−	0.829252i
$377$	−91.9800	−	91.9800i	−0.0125656	−	0.0125656i
$378$	3052.15	+	10160.3i	0.415305	+	1.38251i
$379$	11130.1			1.50848			0.754240	−	0.656599i	$-0.228006\pi$
$379$	11130.1			1.50848			0.754240	+	0.656599i	$0.228006\pi$
$380$		0			0
$381$	−3243.75			−0.436174
$382$	−1187.08	−	3951.66i	−0.158995	−	0.529279i
$383$	1006.62	+	1006.62i	0.134297	+	0.134297i	0.771060	−	0.636763i	$-0.219727\pi$
$383$	1006.62	+	1006.62i	0.134297	+	0.134297i	−0.636763	+	0.771060i	$0.719727\pi$
$384$	−1653.25	+	5100.88i	−0.219706	+	0.677873i
$385$		0			0
$386$	4291.85	−	7977.60i	0.565932	−	1.05194i
$387$	−621.069	+	621.069i	−0.0815781	+	0.0815781i
$388$	5946.98	+	1216.35i	0.778124	+	0.159152i
$389$		−	13548.4i		−	1.76589i	−0.469478	−	0.882944i	$-0.655558\pi$
$389$		−	13548.4i		−	1.76589i	0.469478	−	0.882944i	$-0.344442\pi$
$390$		0			0
$391$			2875.34i			0.371898i
$392$	5023.52	+	4191.26i	0.647260	+	0.540027i
$393$	−4241.84	+	4241.84i	−0.544459	+	0.544459i
$394$	7371.69	+	3965.88i	0.942590	+	0.507102i
$395$		0			0
$396$	−654.379	+	432.148i	−0.0830399	+	0.0548391i
$397$	−1822.81	−	1822.81i	−0.230439	−	0.230439i	0.582437	−	0.812876i	$-0.302099\pi$
$397$	−1822.81	−	1822.81i	−0.230439	−	0.230439i	−0.812876	+	0.582437i	$0.802099\pi$
$398$	−5655.25	+	1698.84i	−0.712241	+	0.213957i
$399$	12643.0			1.58632
$400$		0			0
$401$	5922.04			0.737488			0.368744	−	0.929531i	$-0.379788\pi$
$401$	5922.04			0.737488			0.368744	+	0.929531i	$0.379788\pi$
$402$	−492.804	+	148.038i	−0.0611413	+	0.0183669i
$403$	504.238	+	504.238i	0.0623273	+	0.0623273i
$404$	−9451.43	+	6241.67i	−1.16393	+	0.768650i
$405$		0			0
$406$	2147.36	+	1155.25i	0.262492	+	0.141218i
$407$	−1848.98	+	1848.98i	−0.225186	+	0.225186i
$408$	−1841.13	−	1536.11i	−0.223406	−	0.186394i
$409$		−	8533.05i		−	1.03162i	−0.856703	−	0.515809i	$-0.827491\pi$
$409$		−	8533.05i		−	1.03162i	0.856703	−	0.515809i	$-0.172509\pi$
$410$		0			0
$411$		−	4320.46i		−	0.518522i
$412$	−3158.12	−	645.940i	−0.377644	−	0.0772408i
$413$	1796.88	−	1796.88i	0.214088	−	0.214088i
$414$	−1789.26	+	3325.83i	−0.212408	+	0.394820i
$415$		0			0
$416$	428.443	+	536.674i	0.0504955	+	0.0632515i
$417$	−3309.98	−	3309.98i	−0.388706	−	0.388706i
$418$	815.124	+	2713.46i	0.0953804	+	0.317511i
$419$	7128.02			0.831089			0.415545	−	0.909573i	$-0.363591\pi$
$419$	7128.02			0.831089			0.415545	+	0.909573i	$0.363591\pi$
$420$		0			0
$421$	−611.239			−0.0707601			−0.0353800	−	0.999374i	$-0.511264\pi$
$421$	−611.239			−0.0707601			−0.0353800	+	0.999374i	$0.511264\pi$
$422$	162.419	+	540.676i	0.0187356	+	0.0623690i
$423$	2521.17	+	2521.17i	0.289796	+	0.289796i
$424$	214.658	+	2376.70i	0.0245866	+	0.272223i
$425$		0			0
$426$	−3049.53	+	5668.39i	−0.346831	+	0.644682i
$427$	4126.56	−	4126.56i	0.467677	−	0.467677i
$428$	−1052.65	+	5146.58i	−0.118882	+	0.581236i
$429$		−	103.607i		−	0.0116601i
$430$		0			0
$431$			9361.72i			1.04626i	0.852253	+	0.523130i	$0.175236\pi$
$431$			9361.72i			1.04626i	−0.852253	+	0.523130i	$0.824764\pi$
$432$	−3558.24	−	8859.84i	−0.396286	−	0.986734i
$433$	1769.48	−	1769.48i	0.196388	−	0.196388i	−0.602062	−	0.798450i	$-0.705654\pi$
$433$	1769.48	−	1769.48i	0.196388	−	0.196388i	0.798450	+	0.602062i	$0.205654\pi$
$434$	−11771.9	−	6333.15i	−1.30200	−	0.700463i
$435$		0			0
$436$	−2814.28	−	4261.51i	−0.309127	−	0.468095i
$437$	9648.13	+	9648.13i	1.05614	+	1.05614i
$438$	−531.044	+	159.526i	−0.0579321	+	0.0174028i
$439$	−7823.34			−0.850541			−0.425271	−	0.905066i	$-0.639821\pi$
$439$	−7823.34			−0.850541			−0.425271	+	0.905066i	$0.639821\pi$
$440$		0			0
$441$	−3842.54			−0.414917
$442$	−294.099	+	88.3472i	−0.0316490	+	0.00950735i
$443$	−9066.48	−	9066.48i	−0.972374	−	0.972374i	0.0272545	−	0.999629i	$-0.491324\pi$
$443$	−9066.48	−	9066.48i	−0.972374	−	0.972374i	−0.999629	+	0.0272545i	$0.991324\pi$
$444$	−5786.97	−	8762.91i	−0.618553	−	0.936642i
$445$		0			0
$446$	−11766.3	−	6330.10i	−1.24921	−	0.672061i
$447$	3538.51	−	3538.51i	0.374420	−	0.374420i
$448$	−10586.1	−	7324.25i	−1.11640	−	0.772407i
$449$			3381.93i			0.355464i	0.984079	+	0.177732i	$0.0568759\pi$
$449$			3381.93i			0.355464i	−0.984079	+	0.177732i	$0.943124\pi$
$450$		0			0
$451$			1557.09i			0.162573i
$452$	−2271.26	+	11104.6i	−0.236352	+	1.15557i
$453$	−6089.04	+	6089.04i	−0.631541	+	0.631541i
$454$	−1562.17	+	2903.72i	−0.161489	+	0.300173i
$455$		0			0
$456$	−11332.3	+	1023.50i	−1.16378	+	0.105110i
$457$	−10289.7	−	10289.7i	−1.05324	−	1.05324i	−0.998501	−	0.0547399i	$-0.982567\pi$
$457$	−10289.7	−	10289.7i	−1.05324	−	1.05324i	−0.0547399	−	0.998501i	$-0.517433\pi$
$458$	−3671.77	−	12222.9i	−0.374608	−	1.24703i
$459$	4269.45			0.434163
$460$		0			0
$461$	−5310.20			−0.536488			−0.268244	−	0.963351i	$-0.586443\pi$
$461$	−5310.20			−0.536488			−0.268244	+	0.963351i	$0.586443\pi$
$462$	558.759	+	1860.05i	0.0562680	+	0.187310i
$463$	7686.78	+	7686.78i	0.771566	+	0.771566i	0.978380	−	0.206814i	$-0.0663096\pi$
$463$	7686.78	+	7686.78i	0.771566	+	0.771566i	−0.206814	+	0.978380i	$0.566310\pi$
$464$	−2018.26	−	861.648i	−0.201930	−	0.0862091i
$465$		0			0
$466$	−554.459	+	1030.62i	−0.0551176	+	0.102451i
$467$	4535.99	−	4535.99i	0.449466	−	0.449466i	−0.445711	−	0.895177i	$-0.647049\pi$
$467$	4535.99	−	4535.99i	0.449466	−	0.449466i	0.895177	+	0.445711i	$0.147049\pi$
$468$	−395.153	−	80.8218i	−0.0390298	−	0.00798288i
$469$		−	1235.30i		−	0.121623i
$470$		0			0
$471$		−	850.850i		−	0.0832380i
$472$	−1465.12	+	1756.05i	−0.142877	+	0.171248i
$473$	−344.695	+	344.695i	−0.0335076	+	0.0335076i
$474$	9249.72	+	4976.24i	0.896316	+	0.482208i
$475$		0			0
$476$	4803.46	−	3172.18i	0.462534	−	0.305455i
$477$	−991.080	−	991.080i	−0.0951330	−	0.0951330i
$478$	7923.91	−	2380.34i	0.758224	−	0.227771i
$479$	−10969.6			−1.04638			−0.523189	−	0.852217i	$-0.675258\pi$
$479$	−10969.6			−1.04638			−0.523189	+	0.852217i	$0.675258\pi$
$480$		0			0
$481$	−1344.89			−0.127488
$482$	−11538.0	+	3466.03i	−1.09034	+	0.327538i
$483$	6613.70	+	6613.70i	0.623051	+	0.623051i
$484$	8522.13	−	5627.97i	0.800350	−	0.528547i
$485$		0			0
$486$	8247.77	+	4437.20i	0.769808	+	0.414147i
$487$	−12736.0	+	12736.0i	−1.18506	+	1.18506i	−0.206646	+	0.978416i	$0.566255\pi$
$487$	−12736.0	+	12736.0i	−1.18506	+	1.18506i	−0.978416	+	0.206646i	$0.933745\pi$
$488$	−3364.68	+	4032.80i	−0.312115	+	0.374091i
$489$			4882.67i			0.451538i
$490$		0			0
$491$			10518.6i			0.966796i	0.875401	+	0.483398i	$0.160598\pi$
$491$			10518.6i			0.966796i	−0.875401	+	0.483398i	$0.839402\pi$
$492$	−6126.46	−	1253.06i	−0.561387	−	0.114822i
$493$	693.897	−	693.897i	0.0633905	−	0.0633905i
$494$	−690.394	+	1283.29i	−0.0628792	+	0.116878i
$495$		0			0
$496$	11064.2	+	4723.59i	1.00161	+	0.427612i
$497$	−10926.5	−	10926.5i	−0.986161	−	0.986161i
$498$	−1803.25	−	6002.82i	−0.162260	−	0.540146i
$499$	2445.26			0.219368			0.109684	−	0.993966i	$-0.465016\pi$
$499$	2445.26			0.219368			0.109684	+	0.993966i	$0.465016\pi$
$500$		0			0
$501$	5113.18			0.455968
$502$	4287.35	+	14272.1i	0.381183	+	1.26892i
$503$	−12216.7	−	12216.7i	−1.08293	−	1.08293i	−0.996235	−	0.0866986i	$-0.972368\pi$
$503$	−12216.7	−	12216.7i	−1.08293	−	1.08293i	−0.0866986	−	0.996235i	$-0.527632\pi$
$504$	7530.01	−	680.093i	0.665502	−	0.0601066i
$505$		0			0
$506$	−993.041	+	1845.84i	−0.0872452	+	0.162169i
$507$	−5714.55	+	5714.55i	−0.500576	+	0.500576i
$508$	−1404.37	+	6866.20i	−0.122655	+	0.599682i
$509$			5615.75i			0.489025i	0.969646	+	0.244512i	$0.0786279\pi$
$509$			5615.75i			0.489025i	−0.969646	+	0.244512i	$0.921372\pi$
$510$		0			0
$511$		−	1331.16i		−	0.115239i
$512$	10081.5	+	5707.93i	0.870205	+	0.492690i
$513$	14326.0	−	14326.0i	1.23296	−	1.23296i
$514$	−19850.0	−	10679.1i	−1.70340	−	0.916408i
$515$		0			0
$516$	−1078.83	−	1633.62i	−0.0920406	−	0.139372i
$517$	1399.26	+	1399.26i	0.119031	+	0.119031i
$518$	24144.6	−	7253.05i	2.04798	−	0.615214i
$519$	−3988.58			−0.337340
$520$		0			0
$521$	5287.10			0.444591			0.222296	−	0.974979i	$-0.428645\pi$
$521$	5287.10			0.444591			0.222296	+	0.974979i	$0.428645\pi$
$522$	1234.41	−	370.816i	0.103503	−	0.0310923i
$523$	4328.34	+	4328.34i	0.361883	+	0.361883i	0.864506	−	0.502623i	$-0.167631\pi$
$523$	4328.34	+	4328.34i	0.361883	+	0.361883i	−0.502623	+	0.864506i	$0.667631\pi$
$524$	7142.43	+	10815.4i	0.595455	+	0.901666i
$525$		0			0
$526$	9588.45	+	5158.47i	0.794821	+	0.427605i
$527$	−3803.97	+	3803.97i	−0.314428	+	0.314428i
$528$	−651.409	−	1621.98i	−0.0536912	−	0.133688i
$529$		−	2072.91i		−	0.170371i
$530$		0			0
$531$		−	1343.23i		−	0.109776i
$532$	5473.73	−	26762.1i	0.446083	−	2.18098i
$533$	−566.287	+	566.287i	−0.0460199	+	0.0460199i
$534$	5206.83	−	9678.34i	0.421951	−	0.784312i
$535$		0			0
$536$	100.003	+	1107.23i	0.00805871	+	0.0892262i
$537$	10481.6	+	10481.6i	0.842297	+	0.842297i
$538$	491.468	+	1636.04i	0.0393841	+	0.131106i
$539$	−2132.62			−0.170424
$540$		0			0
$541$	−13608.6			−1.08148			−0.540739	−	0.841190i	$-0.681855\pi$
$541$	−13608.6			−1.08148			−0.540739	+	0.841190i	$0.681855\pi$
$542$	−3443.93	−	11464.5i	−0.272932	−	0.908563i
$543$	−5105.52	−	5105.52i	−0.403497	−	0.403497i
$544$	−4048.67	+	3232.17i	−0.319090	+	0.254739i
$545$		0			0
$546$	−473.258	+	879.681i	−0.0370945	+	0.0689503i
$547$	2884.33	−	2884.33i	0.225457	−	0.225457i	−0.585335	−	0.810792i	$-0.699037\pi$
$547$	2884.33	−	2884.33i	0.225457	−	0.225457i	0.810792	+	0.585335i	$0.199037\pi$
$548$	−9145.34	−	1870.52i	−0.712901	−	0.145812i
$549$		−	3084.74i		−	0.239806i
$550$		0			0
$551$		−	4656.71i		−	0.360041i
$552$	−6463.44	−	5392.63i	−0.498374	−	0.415807i
$553$	−17830.0	+	17830.0i	−1.37108	+	1.37108i
$554$	11321.8	+	6091.00i	0.868263	+	0.467115i
$555$		0			0
$556$	−8439.43	+	5573.35i	−0.643726	+	0.425113i
$557$	6538.87	+	6538.87i	0.497416	+	0.497416i	0.910633	−	0.413216i	$-0.135595\pi$
$557$	6538.87	+	6538.87i	0.497416	+	0.497416i	−0.413216	+	0.910633i	$0.635595\pi$
$558$	−6767.07	+	2032.83i	−0.513392	+	0.154223i
$559$	−250.720			−0.0189702
$560$		0			0
$561$	781.612			0.0588229
$562$	20518.9	−	6163.88i	1.54010	−	0.462647i
$563$	−6499.93	−	6499.93i	−0.486571	−	0.486571i	0.420651	−	0.907222i	$-0.361802\pi$
$563$	−6499.93	−	6499.93i	−0.486571	−	0.486571i	−0.907222	+	0.420651i	$0.861802\pi$
$564$	−6631.52	+	4379.42i	−0.495102	+	0.326962i
$565$		0			0
$566$	1775.71	+	955.311i	0.131870	+	0.0709447i
$567$	3441.05	−	3441.05i	0.254869	−	0.254869i
$568$	10678.3	+	8909.19i	0.788822	+	0.658136i
$569$		−	5264.67i		−	0.387885i	−0.981013	−	0.193942i	$-0.937872\pi$
$569$		−	5264.67i		−	0.387885i	0.981013	−	0.193942i	$-0.0621275\pi$
$570$		0			0
$571$		−	22034.0i		−	1.61488i	−0.589952	−	0.807438i	$-0.700853\pi$
$571$		−	22034.0i		−	1.61488i	0.589952	−	0.807438i	$-0.299147\pi$
$572$	−219.311	−	44.8563i	−0.0160312	−	0.00327891i
$573$	−3819.46	+	3819.46i	−0.278464	+	0.278464i
$574$	7112.48	−	13220.5i	0.517194	−	0.961348i
$575$		0			0
$576$	−6694.29	+	1219.17i	−0.484251	+	0.0881924i
$577$	9208.58	+	9208.58i	0.664399	+	0.664399i	0.956414	−	0.292015i	$-0.0943257\pi$
$577$	9208.58	+	9208.58i	0.664399	+	0.664399i	−0.292015	+	0.956414i	$0.594326\pi$
$578$	3331.40	+	11089.9i	0.239737	+	0.798059i
$579$	−11859.0			−0.851196
$580$		0			0
$581$	15047.2			1.07446
$582$	−2286.18	−	7610.46i	−0.162827	−	0.542034i
$583$	−550.052	−	550.052i	−0.0390751	−	0.0390751i
$584$	107.763	+	1193.15i	0.00763572	+	0.0845429i
$585$		0			0
$586$	−462.679	+	860.016i	−0.0326162	+	0.0606262i
$587$	−6536.20	+	6536.20i	−0.459587	+	0.459587i	−0.898520	−	0.438933i	$-0.855357\pi$
$587$	−6536.20	+	6536.20i	−0.459587	+	0.459587i	0.438933	+	0.898520i	$0.355357\pi$
$588$	1716.23	−	8390.94i	0.120367	−	0.588498i
$589$			25528.3i			1.78586i
$590$		0			0
$591$		−	10958.3i		−	0.762713i
$592$	−21054.3	+	8455.72i	−1.46170	+	0.587040i
$593$	11033.7	−	11033.7i	0.764079	−	0.764079i	−0.212978	−	0.977057i	$-0.568316\pi$
$593$	11033.7	−	11033.7i	0.764079	−	0.764079i	0.977057	+	0.212978i	$0.0683163\pi$
$594$	2740.80	+	1474.52i	0.189321	+	0.101852i
$595$		0			0
$596$	−5958.16	−	9022.12i	−0.409489	−	0.620068i
$597$	5466.05	+	5466.05i	0.374725	+	0.374725i
$598$	−1032.46	+	310.150i	−0.0706024	+	0.0212090i
$599$	1861.62			0.126985			0.0634923	−	0.997982i	$-0.479776\pi$
$599$	1861.62			0.126985			0.0634923	+	0.997982i	$0.479776\pi$
$600$		0			0
$601$	−21693.2			−1.47235			−0.736177	−	0.676789i	$-0.763371\pi$
$601$	−21693.2			−1.47235			−0.736177	+	0.676789i	$0.763371\pi$
$602$	4501.15	−	1352.15i	0.304739	−	0.0915437i
$603$	−461.715	−	461.715i	−0.0311816	−	0.0311816i
$604$	10252.8	+	15525.2i	0.690693	+	1.04588i
$605$		0			0
$606$	13057.8	+	7024.94i	0.875308	+	0.470905i
$607$	−617.817	+	617.817i	−0.0413121	+	0.0413121i	−0.727461	−	0.686149i	$-0.759300\pi$
$607$	−617.817	+	617.817i	−0.0413121	+	0.0413121i	0.686149	+	0.727461i	$0.259300\pi$
$608$	−2739.75	+	24430.7i	−0.182749	+	1.62960i
$609$		−	3192.13i		−	0.212400i
$610$		0			0
$611$			1017.77i			0.0673891i
$612$	609.719	−	2981.03i	0.0402719	−	0.196897i
$613$	−5656.87	+	5656.87i	−0.372722	+	0.372722i	−0.868468	−	0.495745i	$-0.834895\pi$
$613$	−5656.87	+	5656.87i	−0.372722	+	0.372722i	0.495745	+	0.868468i	$0.334895\pi$
$614$	12987.6	−	24141.0i	0.853642	−	1.58673i
$615$		0			0
$616$	4179.17	−	377.453i	0.273350	−	0.0246884i
$617$	−12811.8	−	12811.8i	−0.835953	−	0.835953i	0.152370	−	0.988323i	$-0.451309\pi$
$617$	−12811.8	−	12811.8i	−0.835953	−	0.835953i	−0.988323	+	0.152370i	$0.951309\pi$
$618$	1214.07	+	4041.50i	0.0790243	+	0.263063i
$619$	−12163.2			−0.789788			−0.394894	−	0.918727i	$-0.629219\pi$
$619$	−12163.2			−0.789788			−0.394894	+	0.918727i	$0.629219\pi$
$620$		0			0
$621$	14988.2			0.968530
$622$	8790.56	+	29262.9i	0.566671	+	1.88639i
$623$	18656.2	+	18656.2i	1.19975	+	1.19975i
$624$	352.980	−	826.794i	0.0226450	−	0.0530421i
$625$		0			0
$626$	4962.20	−	9223.62i	0.316820	−	0.588898i
$627$	2622.68	−	2622.68i	0.167049	−	0.167049i
$628$	−1801.04	−	368.372i	−0.114441	−	0.0234071i
$629$		−	10145.8i		−	0.643149i
$630$		0			0
$631$		−	3347.17i		−	0.211171i	−0.994410	−	0.105585i	$-0.966328\pi$
$631$		−	3347.17i		−	0.211171i	0.994410	−	0.105585i	$-0.0336716\pi$
$632$	14538.1	−	17424.9i	0.915023	−	1.09672i
$633$	522.588	−	522.588i	0.0328136	−	0.0328136i
$634$	12866.7	+	6922.14i	0.805998	+	0.433617i
$635$		0			0
$636$	2606.87	−	1721.56i	0.162530	−	0.107334i
$637$	−775.600	−	775.600i	−0.0482424	−	0.0482424i
$638$	685.099	−	205.804i	0.0425131	−	0.0127709i
$639$	−8167.95			−0.505664
$640$		0			0
$641$	−24791.3			−1.52761			−0.763803	−	0.645449i	$-0.776670\pi$
$641$	−24791.3			−1.52761			−0.763803	+	0.645449i	$0.776670\pi$
$642$	6586.17	−	1978.48i	0.404884	−	0.121627i
$643$	−12922.9	−	12922.9i	−0.792583	−	0.792583i	0.189330	−	0.981913i	$-0.439368\pi$
$643$	−12922.9	−	12922.9i	−0.792583	−	0.792583i	−0.981913	+	0.189330i	$0.939368\pi$
$644$	16862.9	−	11136.2i	1.03182	−	0.681408i
$645$		0			0
$646$	−9681.12	−	5208.33i	−0.589626	−	0.317212i
$647$	16924.5	−	16924.5i	1.02840	−	1.02840i	0.0288113	−	0.999585i	$-0.490828\pi$
$647$	16924.5	−	16924.5i	1.02840	−	1.02840i	0.999585	−	0.0288113i	$-0.00917218\pi$
$648$	−2805.74	+	3362.88i	−0.170092	+	0.203868i
$649$		−	745.493i		−	0.0450896i
$650$		0			0
$651$			17499.4i			1.05354i
$652$	10335.4	+	2113.93i	0.620806	+	0.126975i
$653$	−10391.0	+	10391.0i	−0.622715	+	0.622715i	−0.946225	−	0.323510i	$-0.895137\pi$
$653$	−10391.0	+	10391.0i	−0.622715	+	0.622715i	0.323510	+	0.946225i	$0.395137\pi$
$654$	−3167.44	+	5887.57i	−0.189384	+	0.352022i
$655$		0			0
$656$	−5304.85	+	12425.7i	−0.315731	+	0.739545i
$657$	−497.543	−	497.543i	−0.0295449	−	0.0295449i
$658$	−5488.91	−	18272.0i	−0.325197	−	1.08255i
$659$	773.045			0.0456958			0.0228479	−	0.999739i	$-0.492727\pi$
$659$	773.045			0.0456958			0.0228479	+	0.999739i	$0.492727\pi$
$660$		0			0
$661$	17856.3			1.05073			0.525364	−	0.850878i	$-0.323929\pi$
$661$	17856.3			1.05073			0.525364	+	0.850878i	$0.323929\pi$
$662$	−6379.62	−	21237.1i	−0.374549	−	1.24683i
$663$	284.260	+	284.260i	0.0166512	+	0.0166512i
$664$	−13487.2	+	1218.13i	−0.788259	+	0.0711938i
$665$		0			0
$666$	6313.51	−	11735.4i	0.367333	−	0.682790i
$667$	2435.98	−	2435.98i	0.141411	−	0.141411i
$668$	2213.73	−	10823.3i	0.128221	−	0.626896i
$669$			17490.9i			1.01082i
$670$		0			0
$671$		−	1712.04i		−	0.0984985i
$672$	−1878.07	+	16747.0i	−0.107810	+	0.961353i
$673$	19931.6	−	19931.6i	1.14161	−	1.14161i	0.153459	−	0.988155i	$-0.450959\pi$
$673$	19931.6	−	19931.6i	1.14161	−	1.14161i	0.988155	−	0.153459i	$-0.0490414\pi$
$674$	−15863.0	−	8534.10i	−0.906557	−	0.487717i
$675$		0			0
$676$	9622.18	+	14570.4i	0.547462	+	0.828992i
$677$	5515.73	+	5515.73i	0.313126	+	0.313126i	0.846120	−	0.532993i	$-0.178933\pi$
$677$	5515.73	+	5515.73i	0.313126	+	0.313126i	−0.532993	+	0.846120i	$0.678933\pi$
$678$	14210.8	−	4268.92i	0.804958	−	0.241810i
$679$	19077.0			1.07822
$680$		0			0
$681$	4316.48			0.242890
$682$	−3755.74	+	1128.22i	−0.210872	+	0.0633460i
$683$	19946.1	+	19946.1i	1.11745	+	1.11745i	0.992115	+	0.125331i	$0.0399992\pi$
$683$	19946.1	+	19946.1i	1.11745	+	1.11745i	0.125331	+	0.992115i	$0.460001\pi$
$684$	−7956.88	−	12048.7i	−0.444794	−	0.673527i
$685$		0			0
$686$	−3373.39	−	1814.85i	−0.187750	−	0.101007i
$687$	−11814.0	+	11814.0i	−0.656089	+	0.656089i
$688$	−3925.04	+	1576.35i	−0.217501	+	0.0873515i
$689$		−	400.090i		−	0.0221222i
$690$		0			0
$691$			356.654i			0.0196350i	0.999952	+	0.00981748i	$0.00312505\pi$
$691$			356.654i			0.0196350i	−0.999952	+	0.00981748i	$0.996875\pi$
$692$	−1726.84	+	8442.84i	−0.0948621	+	0.463798i
$693$	−1742.71	+	1742.71i	−0.0955267	+	0.0955267i
$694$	−16030.3	+	29796.7i	−0.876802	+	1.62978i
$695$		0			0
$696$	258.416	+	2861.19i	0.0140736	+	0.155823i
$697$	−4272.07	−	4272.07i	−0.232161	−	0.232161i
$698$	−4488.09	−	14940.4i	−0.243377	−	0.810175i
$699$	1532.05			0.0829003
$700$		0			0
$701$	17230.0			0.928343			0.464172	−	0.885745i	$-0.346352\pi$
$701$	17230.0			0.928343			0.464172	+	0.885745i	$0.346352\pi$
$702$	460.526	+	1533.04i	0.0247599	+	0.0824231i
$703$	−34044.1	−	34044.1i	−1.82646	−	1.82646i
$704$	−3715.35	+	676.643i	−0.198903	+	0.0362243i
$705$		0			0
$706$	−1443.02	+	2682.26i	−0.0769248	+	0.142986i
$707$	−25170.5	+	25170.5i	−1.33895	+	1.33895i
$708$	2933.19	+	599.935i	0.155701	+	0.0318460i
$709$		−	8153.11i		−	0.431871i	−0.976408	−	0.215935i	$-0.930720\pi$
$709$		−	8153.11i		−	0.431871i	0.976408	−	0.215935i	$-0.0692801\pi$
$710$		0			0
$711$			13328.5i			0.703036i
$712$	−18232.4	−	15211.8i	−0.959672	−	0.800681i
$713$	−13354.1	+	13354.1i	−0.701425	+	0.701425i
$714$	−6636.31	−	3570.26i	−0.347840	−	0.187134i
$715$		0			0
$716$	26724.8	−	17648.9i	1.39491	−	0.921189i
$717$	−7658.81	−	7658.81i	−0.398917	−	0.398917i
$718$	9656.25	−	2900.74i	0.501905	−	0.150772i
$719$	17219.3			0.893147			0.446573	−	0.894747i	$-0.352644\pi$
$719$	17219.3			0.893147			0.446573	+	0.894747i	$0.352644\pi$
$720$		0			0
$721$	−10130.8			−0.523287
$722$	−31381.3	+	9426.94i	−1.61758	+	0.485920i
$723$	11152.0	+	11152.0i	0.573649	+	0.573649i
$724$	−13017.5	+	8596.70i	−0.668221	+	0.441290i
$725$		0			0
$726$	−11773.9	−	6334.22i	−0.601888	−	0.323809i
$727$	8881.73	−	8881.73i	0.453102	−	0.453102i	−0.443281	−	0.896383i	$-0.646186\pi$
$727$	8881.73	−	8881.73i	0.453102	−	0.453102i	0.896383	+	0.443281i	$0.146186\pi$
$728$	1657.17	+	1382.62i	0.0843665	+	0.0703893i
$729$		−	17486.6i		−	0.888409i
$730$		0			0
$731$		−	1891.43i		−	0.0957004i
$732$	6736.12	+	1377.76i	0.340129	+	0.0695676i
$733$	−4401.20	+	4401.20i	−0.221776	+	0.221776i	−0.809246	−	0.587470i	$-0.800124\pi$
$733$	−4401.20	+	4401.20i	−0.221776	+	0.221776i	0.587470	+	0.809246i	$0.300124\pi$
$734$	−8353.30	+	15526.9i	−0.420062	+	0.780802i
$735$		0			0
$736$	−14213.2	+	11346.8i	−0.711826	+	0.568271i
$737$	−256.253	−	256.253i	−0.0128076	−	0.0128076i
$738$	−2282.98	−	7599.79i	−0.113872	−	0.379068i
$739$	23097.8			1.14975			0.574875	−	0.818241i	$-0.305051\pi$
$739$	23097.8			1.14975			0.574875	+	0.818241i	$0.305051\pi$
$740$		0			0
$741$	1907.65			0.0945741
$742$	2157.70	+	7182.77i	0.106754	+	0.355374i
$743$	17404.1	+	17404.1i	0.859348	+	0.859348i	0.991261	−	0.131913i	$-0.0421119\pi$
$743$	17404.1	+	17404.1i	0.859348	+	0.859348i	−0.131913	+	0.991261i	$0.542112\pi$
$744$	−1416.65	−	15685.1i	−0.0698075	−	0.772911i
$745$		0			0
$746$	−15864.3	+	29488.2i	−0.778597	+	1.44724i
$747$	5624.13	−	5624.13i	0.275470	−	0.275470i
$748$	338.395	−	1654.48i	0.0165414	−	0.0808739i
$749$			16509.4i			0.805396i
$750$		0			0
$751$		−	2347.75i		−	0.114075i	−0.998372	−	0.0570377i	$-0.981834\pi$
$751$		−	2347.75i		−	0.114075i	0.998372	−	0.0570377i	$-0.0181655\pi$
$752$	6399.05	+	15933.3i	0.310305	+	0.772644i
$753$	13794.7	−	13794.7i	0.667604	−	0.667604i
$754$	324.007	+	174.312i	0.0156494	+	0.00841919i
$755$		0			0
$756$	−16535.6	−	25038.9i	−0.795493	−	1.20457i
$757$	7078.12	+	7078.12i	0.339840	+	0.339840i	0.856307	−	0.516467i	$-0.172753\pi$
$757$	7078.12	+	7078.12i	0.339840	+	0.339840i	−0.516467	+	0.856307i	$0.672753\pi$
$758$	−30149.6	+	9056.95i	−1.44470	+	0.433989i
$759$	2743.91			0.131222
$760$		0			0
$761$	−27017.6			−1.28697			−0.643486	−	0.765458i	$-0.722513\pi$
$761$	−27017.6			−1.28697			−0.643486	+	0.765458i	$0.722513\pi$
$762$	8786.80	−	2639.56i	0.417732	−	0.125487i
$763$	−11349.0	−	11349.0i	−0.538483	−	0.538483i
$764$	6431.22	+	9738.45i	0.304546	+	0.461158i
$765$		0			0
$766$	−3545.90	−	1907.65i	−0.167257	−	0.0899821i
$767$	271.124	−	271.124i	0.0127636	−	0.0127636i
$768$	327.626	−	15162.8i	0.0153935	−	0.712423i
$769$		−	41584.0i		−	1.95001i	−0.222183	−	0.975005i	$-0.571318\pi$
$769$		−	41584.0i		−	1.95001i	0.222183	−	0.975005i	$-0.428682\pi$
$770$		0			0
$771$			29507.7i			1.37833i
$772$	−5134.29	+	25102.5i	−0.239362	+	1.17028i
$773$	19799.8	−	19799.8i	0.921280	−	0.921280i	−0.0758404	−	0.997120i	$-0.524164\pi$
$773$	19799.8	−	19799.8i	0.921280	−	0.921280i	0.997120	+	0.0758404i	$0.0241639\pi$
$774$	1176.99	−	2187.77i	0.0546591	−	0.101599i
$775$		0			0
$776$	−17099.2	+	1544.36i	−0.791014	+	0.0714426i
$777$	−23336.9	−	23336.9i	−1.07749	−	1.07749i
$778$	11024.8	+	36700.5i	0.508045	+	1.69123i
$779$	−28669.7			−1.31861
$780$		0			0
$781$	−4533.23			−0.207697
$782$	−2339.77	−	7788.84i	−0.106995	−	0.356174i
$783$	−3617.07	−	3617.07i	−0.165087	−	0.165087i
$784$	−17018.5	−	7265.64i	−0.775260	−	0.330979i
$785$		0			0
$786$	8038.74	−	14942.2i	0.364799	−	0.678081i
$787$	23772.7	−	23772.7i	1.07675	−	1.07675i	0.0799542	−	0.996799i	$-0.474523\pi$
$787$	23772.7	−	23772.7i	1.07675	−	1.07675i	0.996799	−	0.0799542i	$-0.0254774\pi$
$788$	−23195.9	−	4744.34i	−1.04863	−	0.214480i
$789$		−	14253.6i		−	0.643144i
$790$		0			0
$791$			35621.9i			1.60123i
$792$	1420.96	−	1703.11i	0.0637519	−	0.0764110i
$793$	622.640	−	622.640i	0.0278822	−	0.0278822i
$794$	6420.99	+	3454.42i	0.286993	+	0.154399i
$795$		0			0
$796$	13936.8	−	9203.77i	0.620573	−	0.409823i
$797$	−8760.69	−	8760.69i	−0.389359	−	0.389359i	0.485100	−	0.874459i	$-0.338783\pi$
$797$	−8760.69	−	8760.69i	−0.389359	−	0.389359i	−0.874459	+	0.485100i	$0.838783\pi$
$798$	−34247.9	+	10288.1i	−1.51925	+	0.456383i
$799$	−7678.08			−0.339964
$800$		0			0
$801$	13946.1			0.615184
$802$	−16041.9	+	4818.98i	−0.706308	+	0.212175i
$803$	−276.138	−	276.138i	−0.0121353	−	0.0121353i
$804$	1214.46	−	802.025i	0.0532722	−	0.0351806i
$805$		0			0
$806$	−1776.22	−	955.585i	−0.0776236	−	0.0417606i
$807$	1581.31	−	1581.31i	0.0689774	−	0.0689774i
$808$	20523.4	−	24598.7i	0.893576	−	1.07101i
$809$			27571.0i			1.19820i	0.800673	+	0.599102i	$0.204475\pi$
$809$			27571.0i			1.19820i	−0.800673	+	0.599102i	$0.795525\pi$
$810$		0			0
$811$		−	20085.4i		−	0.869661i	−0.900512	−	0.434831i	$-0.856808\pi$
$811$		−	20085.4i		−	0.869661i	0.900512	−	0.434831i	$-0.143192\pi$
$812$	−6756.94	−	1382.02i	−0.292022	−	0.0597282i
$813$	−11080.9	+	11080.9i	−0.478014	+	0.478014i
$814$	3504.02	−	6513.18i	0.150879	−	0.280451i
$815$		0			0
$816$	6237.33	+	2662.88i	0.267586	+	0.114239i
$817$	−6346.65	−	6346.65i	−0.271776	−	0.271776i
$818$	6943.65	+	23114.7i	0.296796	+	0.988002i
$819$	−1267.59			−0.0540820
$820$		0			0
$821$	14867.5			0.632008			0.316004	−	0.948758i	$-0.397659\pi$
$821$	14867.5			0.632008			0.316004	+	0.948758i	$0.397659\pi$
$822$	3515.72	+	11703.5i	0.149179	+	0.496600i
$823$	23345.7	+	23345.7i	0.988797	+	0.988797i	0.999938	−	0.0111410i	$-0.00354636\pi$
$823$	23345.7	+	23345.7i	0.988797	+	0.988797i	−0.0111410	+	0.999938i	$0.503546\pi$
$824$	9080.48	−	820.128i	0.383900	−	0.0346730i
$825$		0			0
$826$	−3405.27	+	6329.64i	−0.143444	+	0.266630i
$827$	−3330.46	+	3330.46i	−0.140038	+	0.140038i	−0.773651	−	0.633613i	$-0.781571\pi$
$827$	−3330.46	+	3330.46i	−0.140038	+	0.140038i	0.633613	+	0.773651i	$0.281571\pi$
$828$	2140.47	−	10465.1i	0.0898385	−	0.439237i
$829$		−	11521.6i		−	0.482703i	−0.970438	−	0.241351i	$-0.922409\pi$
$829$		−	11521.6i		−	0.482703i	0.970438	−	0.241351i	$-0.0775906\pi$
$830$		0			0
$831$		−	16830.3i		−	0.702570i
$832$	−1597.30	−	1105.13i	−0.0665580	−	0.0460498i
$833$	5851.12	−	5851.12i	0.243372	−	0.243372i
$834$	11659.7	+	6272.76i	0.484102	+	0.260441i
$835$		0			0
$836$	−4416.09	−	6687.04i	−0.182696	−	0.276646i
$837$	19828.9	+	19828.9i	0.818861	+	0.818861i
$838$	−19308.7	+	5800.33i	−0.795951	+	0.239104i
$839$	33130.1			1.36326			0.681631	−	0.731696i	$-0.261271\pi$
$839$	33130.1			1.36326			0.681631	+	0.731696i	$0.261271\pi$
$840$		0			0
$841$	23213.3			0.951792
$842$	1655.75	−	497.388i	0.0677684	−	0.0203576i
$843$	−19832.5	−	19832.5i	−0.810280	−	0.810280i
$844$	−879.936	−	1332.44i	−0.0358870	−	0.0543418i
$845$		0			0
$846$	−8881.03	−	4777.89i	−0.360918	−	0.194169i
$847$	22695.7	−	22695.7i	0.920699	−	0.920699i
$848$	−2515.48	−	6263.43i	−0.101866	−	0.253641i
$849$		−	2639.66i		−	0.106705i
$850$		0			0
$851$		−	35617.7i		−	1.43474i
$852$	3648.11	−	17836.3i	0.146693	−	0.717208i
$853$	−12007.8	+	12007.8i	−0.481994	+	0.481994i	−0.905768	−	0.423774i	$-0.860705\pi$
$853$	−12007.8	+	12007.8i	−0.481994	+	0.481994i	0.423774	+	0.905768i	$0.360705\pi$
$854$	−7820.26	+	14536.1i	−0.313354	+	0.582454i
$855$		0			0
$856$	−1336.51	−	14797.8i	−0.0533655	−	0.590864i
$857$	9369.48	+	9369.48i	0.373460	+	0.373460i	0.868736	−	0.495276i	$-0.164933\pi$
$857$	9369.48	+	9369.48i	0.373460	+	0.373460i	−0.495276	+	0.868736i	$0.664933\pi$
$858$	84.3090	+	280.656i	0.00335462	+	0.0111672i
$859$	17337.1			0.688630			0.344315	−	0.938854i	$-0.388111\pi$
$859$	17337.1			0.688630			0.344315	+	0.938854i	$0.388111\pi$
$860$		0			0
$861$	−19652.8			−0.777891
$862$	−7617.98	−	25359.4i	−0.301009	−	1.00203i
$863$	17345.8	+	17345.8i	0.684191	+	0.684191i	0.960942	−	0.276751i	$-0.0892576\pi$
$863$	17345.8	+	17345.8i	0.684191	+	0.684191i	−0.276751	+	0.960942i	$0.589258\pi$
$864$	16848.3	+	21104.4i	0.663414	+	0.831004i
$865$		0			0
$866$	−3353.36	+	6233.15i	−0.131584	+	0.244586i
$867$	10718.9	−	10718.9i	0.419875	−	0.419875i
$868$	37041.8	+	7576.27i	1.44848	+	0.296262i
$869$			7397.36i			0.288767i
$870$		0			0
$871$		−	186.390i		−	0.00725096i
$872$	11091.2	+	9253.69i	0.430728	+	0.359368i
$873$	7130.35	−	7130.35i	0.276433	−	0.276433i
$874$	−33986.3	−	18284.2i	−1.31534	−	0.707636i
$875$		0			0
$876$	1308.70	−	864.260i	0.0504760	−	0.0333341i
$877$	18857.4	+	18857.4i	0.726075	+	0.726075i	0.969836	−	0.243760i	$-0.0783810\pi$
$877$	18857.4	+	18857.4i	0.726075	+	0.726075i	−0.243760	+	0.969836i	$0.578381\pi$
$878$	21192.2	−	6366.14i	0.814581	−	0.244700i
$879$	1278.44			0.0490567
$880$		0			0
$881$	27095.7			1.03618			0.518092	−	0.855325i	$-0.326643\pi$
$881$	27095.7			1.03618			0.518092	+	0.855325i	$0.326643\pi$
$882$	10408.9	−	3126.82i	0.397374	−	0.119371i
$883$	2484.93	+	2484.93i	0.0947049	+	0.0947049i	0.752872	−	0.658167i	$-0.228668\pi$
$883$	2484.93	+	2484.93i	0.0947049	+	0.0947049i	−0.658167	+	0.752872i	$0.728668\pi$
$884$	724.775	−	478.638i	0.0275756	−	0.0182108i
$885$		0			0
$886$	31937.4	+	17182.0i	1.21101	+	0.651511i
$887$	−26609.3	+	26609.3i	−1.00727	+	1.00727i	−0.00730049	+	0.999973i	$0.502324\pi$
$887$	−26609.3	+	26609.3i	−1.00727	+	1.00727i	−0.999973	+	0.00730049i	$0.997676\pi$
$888$	22806.7	+	19028.3i	0.861873	+	0.719084i
$889$			22025.7i			0.830955i
$890$		0			0
$891$		−	1427.63i		−	0.0536785i
$892$	37024.0	+	7572.63i	1.38975	+	0.284249i
$893$	−25763.6	+	25763.6i	−0.965451	+	0.965451i
$894$	−6705.85	+	12464.7i	−0.250869	+	0.466310i
$895$		0			0
$896$	34636.1	+	11225.9i	1.29142	+	0.418563i
$897$	997.915	+	997.915i	0.0371454	+	0.0371454i
$898$	−2752.00	−	9161.12i	−0.102267	−	0.340435i
$899$	6445.42			0.239118
$900$		0			0
$901$	3018.27			0.111602
$902$	−1267.06	−	4217.90i	−0.0467721	−	0.155699i
$903$	−4350.56	−	4350.56i	−0.160330	−	0.160330i
$904$	−2883.74	−	31928.9i	−0.106097	−	1.17471i
$905$		0			0
$906$	11539.4	−	21449.1i	0.423146	−	0.786534i
$907$	−23802.0	+	23802.0i	−0.871369	+	0.871369i	−0.992622	−	0.121252i	$-0.961309\pi$
$907$	−23802.0	+	23802.0i	−0.871369	+	0.871369i	0.121252	+	0.992622i	$0.461309\pi$
$908$	1868.80	−	9136.92i	0.0683022	−	0.333942i
$909$			18815.8i			0.686558i
$910$		0			0
$911$			36580.4i			1.33036i	0.746681	+	0.665182i	$0.231646\pi$
$911$			36580.4i			1.33036i	−0.746681	+	0.665182i	$0.768354\pi$
$912$	29864.5	−	11994.0i	1.08433	−	0.435483i
$913$	3121.41	−	3121.41i	0.113147	−	0.113147i
$914$	36246.2	+	19500.0i	1.31173	+	0.705694i
$915$		0			0
$916$	19892.5	+	30122.2i	0.717540	+	1.08653i
$917$	28803.0	+	28803.0i	1.03725	+	1.03725i
$918$	−11565.3	+	3474.21i	−0.415807	+	0.124908i
$919$	−32910.8			−1.18131			−0.590657	−	0.806923i	$-0.701131\pi$
$919$	−32910.8			−1.18131			−0.590657	+	0.806923i	$0.701131\pi$
$920$		0			0
$921$	−35886.5			−1.28393
$922$	14384.5	−	4321.11i	0.513806	−	0.154347i
$923$	−1648.66	−	1648.66i	−0.0587935	−	0.0587935i
$924$	−3027.18	−	4583.90i	−0.107778	−	0.163203i
$925$		0			0
$926$	−27077.3	−	14567.3i	−0.960924	−	0.516966i
$927$	−3786.55	+	3786.55i	−0.134160	+	0.134160i
$928$	6168.30	+	691.737i	0.218195	+	0.0244692i
$929$			2662.19i			0.0940190i	0.998894	+	0.0470095i	$0.0149691\pi$
$929$			2662.19i			0.0940190i	−0.998894	+	0.0470095i	$0.985031\pi$
$930$		0			0
$931$		−	39266.6i		−	1.38229i
$932$	663.293	−	3242.96i	0.0233121	−	0.113977i
$933$	28283.9	−	28283.9i	0.992468	−	0.992468i
$934$	−8596.18	+	15978.4i	−0.301152	+	0.559774i
$935$		0			0
$936$	1136.17	−	102.617i	0.0396763	−	0.00358347i
$937$	−37885.5	−	37885.5i	−1.32088	−	1.32088i	−0.913063	−	0.407818i	$-0.866290\pi$
$937$	−37885.5	−	37885.5i	−1.32088	−	1.32088i	−0.407818	−	0.913063i	$-0.633710\pi$
$938$	1005.21	+	3346.24i	0.0349907	+	0.116480i
$939$	−13711.2			−0.476517
$940$		0			0
$941$	−6516.65			−0.225756			−0.112878	−	0.993609i	$-0.536007\pi$
$941$	−6516.65			−0.225756			−0.112878	+	0.993609i	$0.536007\pi$
$942$	692.368	+	2304.82i	0.0239475	+	0.0797188i
$943$	−14997.4	−	14997.4i	−0.517904	−	0.517904i
$944$	2539.83	−	5949.10i	0.0875681	−	0.205113i
$945$		0			0
$946$	653.234	−	1214.22i	0.0224508	−	0.0417310i
$947$	10250.1	−	10250.1i	0.351724	−	0.351724i	−0.509026	−	0.860751i	$-0.669994\pi$
$947$	10250.1	−	10250.1i	0.351724	−	0.351724i	0.860751	+	0.509026i	$0.169994\pi$
$948$	−29105.4	−	5953.02i	−0.997152	−	0.203951i
$949$		−	200.854i		−	0.00687037i
$950$		0			0
$951$		−	19126.8i		−	0.652187i
$952$	−10430.5	+	12501.7i	−0.355099	+	0.425611i
$953$	−19249.8	+	19249.8i	−0.654314	+	0.654314i	−0.954029	−	0.299715i	$-0.903109\pi$
$953$	−19249.8	+	19249.8i	−0.654314	+	0.654314i	0.299715	+	0.954029i	$0.403109\pi$
$954$	3491.16	+	1878.20i	0.118481	+	0.0637411i
$955$		0			0
$956$	−19527.7	+	12896.0i	−0.660637	+	0.436281i
$957$	−662.180	−	662.180i	−0.0223670	−	0.0223670i
$958$	29715.0	−	8926.38i	1.00214	−	0.301042i
$959$	−29336.9			−0.987838
$960$		0			0
$961$	−5543.06			−0.186065
$962$	3643.09	−	1094.39i	0.122098	−	0.0366782i
$963$	6170.68	+	6170.68i	0.206487	+	0.206487i
$964$	28434.3	−	18777.8i	0.950007	−	0.627379i
$965$		0			0
$966$	−23297.3	−	12533.7i	−0.775960	−	0.417457i
$967$	−3744.56	+	3744.56i	−0.124526	+	0.124526i	−0.766623	−	0.642097i	$-0.778065\pi$
$967$	−3744.56	+	3744.56i	−0.124526	+	0.124526i	0.642097	+	0.766623i	$0.278065\pi$
$968$	−18505.4	+	22180.0i	−0.614449	+	0.736460i
$969$			14391.3i			0.477106i
$970$		0			0
$971$			29491.0i			0.974677i	0.873213	+	0.487338i	$0.162032\pi$
$971$			29491.0i			0.974677i	−0.873213	+	0.487338i	$0.837968\pi$
$972$	−25952.6	−	5308.17i	−0.856411	−	0.175164i
$973$	−22475.4	+	22475.4i	−0.740524	+	0.740524i
$974$	24136.1	−	44863.7i	0.794016	−	1.47590i
$975$		0			0
$976$	5832.75	−	13662.2i	0.191293	−	0.448070i
$977$	−13592.2	−	13592.2i	−0.445092	−	0.445092i	0.448627	−	0.893719i	$-0.351913\pi$
$977$	−13592.2	−	13592.2i	−0.445092	−	0.445092i	−0.893719	+	0.448627i	$0.851913\pi$
$978$	−3973.21	−	13226.4i	−0.129907	−	0.432447i
$979$	7740.14			0.252682
$980$		0			0
$981$	−8483.78			−0.276112
$982$	−8559.36	−	28493.2i	−0.278147	−	0.925921i
$983$	−12087.1	−	12087.1i	−0.392185	−	0.392185i	0.483280	−	0.875466i	$-0.339445\pi$
$983$	−12087.1	−	12087.1i	−0.392185	−	0.392185i	−0.875466	+	0.483280i	$0.839445\pi$
$984$	17615.3	−	1590.97i	0.570686	−	0.0515430i
$985$		0			0
$986$	−1315.01	+	2444.31i	−0.0424730	+	0.0789478i
$987$	−17660.7	+	17660.7i	−0.569551	+	0.569551i
$988$	825.910	−	4038.03i	0.0265949	−	0.130027i
$989$		−	6640.01i		−	0.213488i
$990$		0			0
$991$		−	52539.6i		−	1.68413i	−0.539374	−	0.842066i	$-0.681339\pi$
$991$		−	52539.6i		−	1.68413i	0.539374	−	0.842066i	$-0.318661\pi$
$992$	−33814.9	−	3792.13i	−1.08228	−	0.121371i
$993$	−20526.6	+	20526.6i	−0.655984	+	0.655984i
$994$	38489.6	+	20706.9i	1.22818	+	0.660749i
$995$		0			0
$996$	9769.43	+	14793.3i	0.310799	+	0.470627i
$997$	−12067.7	−	12067.7i	−0.383337	−	0.383337i	0.488966	−	0.872303i	$-0.337374\pi$
$997$	−12067.7	−	12067.7i	−0.383337	−	0.383337i	−0.872303	+	0.488966i	$0.837374\pi$
$998$	−6623.82	+	1989.80i	−0.210094	+	0.0631121i
$999$	−52887.0			−1.67495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.e.e.7.1		12
4.3	odd	2	inner	100.4.e.e.7.4		12
5.2	odd	4		20.4.e.b.3.3	✓	12
5.3	odd	4	inner	100.4.e.e.43.4		12
5.4	even	2		20.4.e.b.7.6	yes	12
15.2	even	4		180.4.k.e.163.4		12
15.14	odd	2		180.4.k.e.127.1		12
20.3	even	4	inner	100.4.e.e.43.1		12
20.7	even	4		20.4.e.b.3.6	yes	12
20.19	odd	2		20.4.e.b.7.3	yes	12
40.19	odd	2		320.4.n.k.127.3		12
40.27	even	4		320.4.n.k.63.4		12
40.29	even	2		320.4.n.k.127.4		12
40.37	odd	4		320.4.n.k.63.3		12
60.47	odd	4		180.4.k.e.163.1		12
60.59	even	2		180.4.k.e.127.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.4.e.b.3.3	✓	12	5.2	odd	4
20.4.e.b.3.6	yes	12	20.7	even	4
20.4.e.b.7.3	yes	12	20.19	odd	2
20.4.e.b.7.6	yes	12	5.4	even	2
100.4.e.e.7.1		12	1.1	even	1	trivial
100.4.e.e.7.4		12	4.3	odd	2	inner
100.4.e.e.43.1		12	20.3	even	4	inner
100.4.e.e.43.4		12	5.3	odd	4	inner
180.4.k.e.127.1		12	15.14	odd	2
180.4.k.e.127.4		12	60.59	even	2
180.4.k.e.163.1		12	60.47	odd	4
180.4.k.e.163.4		12	15.2	even	4
320.4.n.k.63.3		12	40.37	odd	4
320.4.n.k.63.4		12	40.27	even	4
320.4.n.k.127.3		12	40.19	odd	2
320.4.n.k.127.4		12	40.29	even	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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.70884 + 0.813737i) q^{2} +(2.61822 + 2.61822i) q^{3} +(6.67566 - 4.40857i) q^{4} +(-9.22289 - 4.96181i) q^{6} +(17.7783 - 17.7783i) q^{7} +(-14.4959 + 17.3744i) q^{8} -13.2899i q^{9} +O(q^{10})\)	\(q+(-2.70884 + 0.813737i) q^{2} +(2.61822 + 2.61822i) q^{3} +(6.67566 - 4.40857i) q^{4} +(-9.22289 - 4.96181i) q^{6} +(17.7783 - 17.7783i) q^{7} +(-14.4959 + 17.3744i) q^{8} -13.2899i q^{9} -7.37590i q^{11} +(29.0210 + 5.93575i) q^{12} +(2.68249 - 2.68249i) q^{13} +(-33.6917 + 62.6254i) q^{14} +(25.1290 - 58.8603i) q^{16} +(20.2367 + 20.2367i) q^{17} +(10.8144 + 36.0001i) q^{18} +135.808 q^{19} +93.0948 q^{21} +(6.00204 + 19.9802i) q^{22} +(71.0426 + 71.0426i) q^{23} +(-83.4434 + 7.53642i) q^{24} +(-5.08361 + 9.44930i) q^{26} +(105.488 - 105.488i) q^{27} +(40.3050 - 197.059i) q^{28} -34.2890i q^{29} +187.974i q^{31} +(-20.1737 + 179.892i) q^{32} +(19.3117 - 19.3117i) q^{33} +(-71.2855 - 38.3507i) q^{34} +(-58.5893 - 88.7186i) q^{36} +(-250.679 - 250.679i) q^{37} +(-367.882 + 110.512i) q^{38} +14.0467 q^{39} -211.105 q^{41} +(-252.179 + 75.7547i) q^{42} +(-46.7326 - 46.7326i) q^{43} +(-32.5172 - 49.2390i) q^{44} +(-250.253 - 134.633i) q^{46} +(-189.707 + 189.707i) q^{47} +(219.902 - 88.3159i) q^{48} -289.134i q^{49} +105.968i q^{51} +(6.08147 - 29.7334i) q^{52} +(74.5742 - 74.5742i) q^{53} +(-199.910 + 371.589i) q^{54} +(51.1739 + 566.598i) q^{56} +(355.575 + 355.575i) q^{57} +(27.9022 + 92.8835i) q^{58} +101.072 q^{59} +232.112 q^{61} +(-152.961 - 509.191i) q^{62} +(-236.271 - 236.271i) q^{63} +(-91.7370 - 503.715i) q^{64} +(-36.5978 + 68.0271i) q^{66} +(34.7419 - 34.7419i) q^{67} +(224.309 + 45.8785i) q^{68} +372.010i q^{69} -614.600i q^{71} +(230.903 + 192.649i) q^{72} +(37.4378 - 37.4378i) q^{73} +(883.036 + 475.063i) q^{74} +(906.607 - 598.718i) q^{76} +(-131.131 - 131.131i) q^{77} +(-38.0504 + 11.4303i) q^{78} -1002.91 q^{79} +193.554 q^{81} +(571.850 - 171.784i) q^{82} +(423.190 + 423.190i) q^{83} +(621.470 - 410.415i) q^{84} +(164.619 + 88.5632i) q^{86} +(89.7761 - 89.7761i) q^{87} +(128.152 + 106.920i) q^{88} +1049.38i q^{89} -95.3802i q^{91} +(787.453 + 161.060i) q^{92} +(-492.156 + 492.156i) q^{93} +(359.514 - 668.257i) q^{94} +(-523.815 + 418.177i) q^{96} +(536.526 + 536.526i) q^{97} +(235.279 + 783.218i) q^{98} -98.0246 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 8 q^{6} + 12 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 + 8 * q^6 + 12 * q^8	\( 12 q + 6 q^{2} + 8 q^{6} + 12 q^{8} + 80 q^{12} - 116 q^{13} + 312 q^{16} + 332 q^{17} - 198 q^{18} - 144 q^{21} - 360 q^{22} - 164 q^{26} + 880 q^{28} + 376 q^{32} - 80 q^{33} + 460 q^{36} - 508 q^{37} - 1600 q^{38} - 656 q^{41} - 1160 q^{42} - 1432 q^{46} + 2720 q^{48} + 932 q^{52} + 644 q^{53} + 2048 q^{56} + 960 q^{57} - 1576 q^{58} - 896 q^{61} - 2440 q^{62} - 1680 q^{66} + 844 q^{68} + 3036 q^{72} - 1436 q^{73} + 800 q^{76} - 3120 q^{77} - 3720 q^{78} + 5988 q^{81} + 1352 q^{82} - 2552 q^{86} + 2400 q^{88} + 1840 q^{92} + 3280 q^{93} + 1088 q^{96} + 4772 q^{97} - 1698 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 + 8 * q^6 + 12 * q^8 + 80 * q^12 - 116 * q^13 + 312 * q^16 + 332 * q^17 - 198 * q^18 - 144 * q^21 - 360 * q^22 - 164 * q^26 + 880 * q^28 + 376 * q^32 - 80 * q^33 + 460 * q^36 - 508 * q^37 - 1600 * q^38 - 656 * q^41 - 1160 * q^42 - 1432 * q^46 + 2720 * q^48 + 932 * q^52 + 644 * q^53 + 2048 * q^56 + 960 * q^57 - 1576 * q^58 - 896 * q^61 - 2440 * q^62 - 1680 * q^66 + 844 * q^68 + 3036 * q^72 - 1436 * q^73 + 800 * q^76 - 3120 * q^77 - 3720 * q^78 + 5988 * q^81 + 1352 * q^82 - 2552 * q^86 + 2400 * q^88 + 1840 * q^92 + 3280 * q^93 + 1088 * q^96 + 4772 * q^97 - 1698 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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