LMFDB - Embedded newform 200.4.k.j.43.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,4,Mod(43,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("200.43");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	200.k (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:	$11.8003820011$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.10
Character	$\chi$	$=$	200.43
Dual form			200.4.k.j.107.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.607409 + 2.76244i) q^{2} +(2.02737 + 2.02737i) q^{3} +(-7.26211 + 3.35586i) q^{4} +(-4.36904 + 6.83193i) q^{6} +(-1.63237 - 1.63237i) q^{7} +(-13.6814 - 18.0227i) q^{8} -18.7795i q^{9} +O(q^{10})$	\(q+(0.607409 + 2.76244i) q^{2} +(2.02737 + 2.02737i) q^{3} +(-7.26211 + 3.35586i) q^{4} +(-4.36904 + 6.83193i) q^{6} +(-1.63237 - 1.63237i) q^{7} +(-13.6814 - 18.0227i) q^{8} -18.7795i q^{9} -62.3878 q^{11} +(-21.5266 - 7.91943i) q^{12} +(-47.3701 + 47.3701i) q^{13} +(3.51780 - 5.50083i) q^{14} +(41.4765 - 48.7412i) q^{16} +(-26.6151 + 26.6151i) q^{17} +(51.8773 - 11.4068i) q^{18} -59.7713i q^{19} -6.61884i q^{21} +(-37.8949 - 172.342i) q^{22} +(-6.56082 + 6.56082i) q^{23} +(8.80150 - 64.2761i) q^{24} +(-159.630 - 102.084i) q^{26} +(92.8121 - 92.8121i) q^{27} +(17.3324 + 6.37645i) q^{28} -73.0449 q^{29} +168.579i q^{31} +(159.838 + 84.9703i) q^{32} +(-126.483 - 126.483i) q^{33} +(-89.6887 - 57.3562i) q^{34} +(63.0214 + 136.379i) q^{36} +(97.0101 + 97.0101i) q^{37} +(165.114 - 36.3056i) q^{38} -192.074 q^{39} +27.5126 q^{41} +(18.2841 - 4.02034i) q^{42} +(-204.855 - 204.855i) q^{43} +(453.067 - 209.364i) q^{44} +(-22.1089 - 14.1387i) q^{46} +(165.258 + 165.258i) q^{47} +(182.905 - 14.7283i) q^{48} -337.671i q^{49} -107.917 q^{51} +(185.040 - 502.974i) q^{52} +(-372.552 + 372.552i) q^{53} +(312.762 + 200.013i) q^{54} +(-7.08666 + 51.7529i) q^{56} +(121.179 - 121.179i) q^{57} +(-44.3681 - 201.782i) q^{58} -67.1632i q^{59} +659.080i q^{61} +(-465.688 + 102.396i) q^{62} +(-30.6551 + 30.6551i) q^{63} +(-137.638 + 493.153i) q^{64} +(272.575 - 426.229i) q^{66} +(-506.483 + 506.483i) q^{67} +(103.965 - 282.598i) q^{68} -26.6024 q^{69} -1147.99i q^{71} +(-338.459 + 256.930i) q^{72} +(685.459 + 685.459i) q^{73} +(-209.060 + 326.909i) q^{74} +(200.584 + 434.066i) q^{76} +(101.840 + 101.840i) q^{77} +(-116.667 - 530.591i) q^{78} -751.180 q^{79} -130.718 q^{81} +(16.7114 + 76.0018i) q^{82} +(-251.518 - 251.518i) q^{83} +(22.2119 + 48.0667i) q^{84} +(441.468 - 690.329i) q^{86} +(-148.089 - 148.089i) q^{87} +(853.553 + 1124.40i) q^{88} +497.545i q^{89} +154.651 q^{91} +(25.6282 - 69.6625i) q^{92} +(-341.772 + 341.772i) q^{93} +(-356.135 + 556.893i) q^{94} +(151.784 + 496.316i) q^{96} +(-305.299 + 305.299i) q^{97} +(932.794 - 205.104i) q^{98} +1171.61i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 4 q^{3} - 16 q^{6} + 44 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 4 * q^3 - 16 * q^6 + 44 * q^8	$ 32 q + 2 q^{2} + 4 q^{3} - 16 q^{6} + 44 q^{8} - 8 q^{11} - 28 q^{12} + 72 q^{16} - 48 q^{17} + 278 q^{18} - 68 q^{22} - 92 q^{26} - 104 q^{27} - 620 q^{28} - 288 q^{32} + 112 q^{33} + 476 q^{36} - 636 q^{38} - 8 q^{41} - 1020 q^{42} + 868 q^{43} + 1328 q^{46} + 784 q^{48} + 1480 q^{51} + 1900 q^{52} - 2392 q^{56} - 104 q^{57} + 700 q^{58} + 2880 q^{62} - 4360 q^{66} + 1852 q^{67} - 1196 q^{68} - 5596 q^{72} + 744 q^{73} + 4312 q^{76} - 2240 q^{78} - 1240 q^{81} - 5828 q^{82} - 2676 q^{83} + 6976 q^{86} + 2864 q^{88} - 1704 q^{91} + 7500 q^{92} - 10656 q^{96} + 584 q^{97} + 3814 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 4 * q^3 - 16 * q^6 + 44 * q^8 - 8 * q^11 - 28 * q^12 + 72 * q^16 - 48 * q^17 + 278 * q^18 - 68 * q^22 - 92 * q^26 - 104 * q^27 - 620 * q^28 - 288 * q^32 + 112 * q^33 + 476 * q^36 - 636 * q^38 - 8 * q^41 - 1020 * q^42 + 868 * q^43 + 1328 * q^46 + 784 * q^48 + 1480 * q^51 + 1900 * q^52 - 2392 * q^56 - 104 * q^57 + 700 * q^58 + 2880 * q^62 - 4360 * q^66 + 1852 * q^67 - 1196 * q^68 - 5596 * q^72 + 744 * q^73 + 4312 * q^76 - 2240 * q^78 - 1240 * q^81 - 5828 * q^82 - 2676 * q^83 + 6976 * q^86 + 2864 * q^88 - 1704 * q^91 + 7500 * q^92 - 10656 * q^96 + 584 * q^97 + 3814 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.607409	+	2.76244i	0.214751	+	0.976669i
$2$	0.607409	+	2.76244i	0.214751	+	0.976669i
$3$	2.02737	+	2.02737i	0.390168	+	0.390168i	0.874747	−	0.484579i	$-0.161027\pi$
$3$	2.02737	+	2.02737i	0.390168	+	0.390168i	−0.484579	+	0.874747i	$0.661027\pi$
$4$	−7.26211	+	3.35586i	−0.907764	+	0.419482i
$5$		0			0
$5$		0			0
$6$	−4.36904	+	6.83193i	−0.297276	+	0.464854i
$7$	−1.63237	−	1.63237i	−0.0881396	−	0.0881396i	0.661662	−	0.749802i	$-0.269851\pi$
$7$	−1.63237	−	1.63237i	−0.0881396	−	0.0881396i	−0.749802	+	0.661662i	$0.769851\pi$
$8$	−13.6814	−	18.0227i	−0.604638	−	0.796500i
$9$		−	18.7795i		−	0.695538i
$10$		0			0
$11$	−62.3878			−1.71006			−0.855028	−	0.518581i	$-0.826460\pi$
$11$	−62.3878			−1.71006			−0.855028	+	0.518581i	$0.826460\pi$
$12$	−21.5266	−	7.91943i	−0.517849	−	0.190512i
$13$	−47.3701	+	47.3701i	−1.01062	+	1.01062i	−0.0106811	+	0.999943i	$0.503400\pi$
$13$	−47.3701	+	47.3701i	−1.01062	+	1.01062i	−0.999943	+	0.0106811i	$0.996600\pi$
$14$	3.51780	−	5.50083i	0.0671551	−	0.105011i
$15$		0			0
$16$	41.4765	−	48.7412i	0.648070	−	0.761581i
$17$	−26.6151	+	26.6151i	−0.379712	+	0.379712i	−0.870998	−	0.491286i	$-0.836527\pi$
$17$	−26.6151	+	26.6151i	−0.379712	+	0.379712i	0.491286	+	0.870998i	$0.336527\pi$
$18$	51.8773	−	11.4068i	0.679310	−	0.149368i
$19$		−	59.7713i		−	0.721710i	−0.932622	−	0.360855i	$-0.882485\pi$
$19$		−	59.7713i		−	0.721710i	0.932622	−	0.360855i	$-0.117515\pi$
$20$		0			0
$21$		−	6.61884i		−	0.0687785i
$22$	−37.8949	−	172.342i	−0.367237	−	1.67016i
$23$	−6.56082	+	6.56082i	−0.0594793	+	0.0594793i	−0.736221	−	0.676741i	$-0.763392\pi$
$23$	−6.56082	+	6.56082i	−0.0594793	+	0.0594793i	0.676741	+	0.736221i	$0.263392\pi$
$24$	8.80150	−	64.2761i	0.0748583	−	0.546679i
$25$		0			0
$26$	−159.630	−	102.084i	−1.20408	−	0.770012i
$27$	92.8121	−	92.8121i	0.661544	−	0.661544i
$28$	17.3324	+	6.37645i	0.116983	+	0.0430370i
$29$	−73.0449			−0.467728			−0.233864	−	0.972269i	$-0.575137\pi$
$29$	−73.0449			−0.467728			−0.233864	+	0.972269i	$0.575137\pi$
$30$		0			0
$31$			168.579i			0.976699i	0.872648	+	0.488349i	$0.162401\pi$
$31$			168.579i			0.976699i	−0.872648	+	0.488349i	$0.837599\pi$
$32$	159.838	+	84.9703i	0.882986	+	0.469399i
$33$	−126.483	−	126.483i	−0.667209	−	0.667209i
$34$	−89.6887	−	57.3562i	−0.452397	−	0.289309i
$35$		0			0
$36$	63.0214	+	136.379i	0.291766	+	0.631384i
$37$	97.0101	+	97.0101i	0.431037	+	0.431037i	0.888981	−	0.457944i	$-0.151414\pi$
$37$	97.0101	+	97.0101i	0.431037	+	0.431037i	−0.457944	+	0.888981i	$0.651414\pi$
$38$	165.114	−	36.3056i	0.704871	−	0.154988i
$39$	−192.074			−0.788626
$40$		0			0
$41$	27.5126			0.104799			0.0523993	−	0.998626i	$-0.483313\pi$
$41$	27.5126			0.104799			0.0523993	+	0.998626i	$0.483313\pi$
$42$	18.2841	−	4.02034i	0.0671738	−	0.0147703i
$43$	−204.855	−	204.855i	−0.726513	−	0.726513i	0.243411	−	0.969923i	$-0.421734\pi$
$43$	−204.855	−	204.855i	−0.726513	−	0.726513i	−0.969923	+	0.243411i	$0.921734\pi$
$44$	453.067	−	209.364i	1.55233	−	0.717338i
$45$		0			0
$46$	−22.1089	−	14.1387i	−0.0708649	−	0.0453183i
$47$	165.258	+	165.258i	0.512879	+	0.512879i	0.915407	−	0.402529i	$-0.131869\pi$
$47$	165.258	+	165.258i	0.512879	+	0.512879i	−0.402529	+	0.915407i	$0.631869\pi$
$48$	182.905	−	14.7283i	0.550000	−	0.0442884i
$49$		−	337.671i		−	0.984463i
$50$		0			0
$51$	−107.917			−0.296303
$52$	185.040	−	502.974i	0.493469	−	1.34135i
$53$	−372.552	+	372.552i	−0.965546	+	0.965546i	−0.999426	−	0.0338796i	$-0.989214\pi$
$53$	−372.552	+	372.552i	−0.965546	+	0.965546i	0.0338796	+	0.999426i	$0.489214\pi$
$54$	312.762	+	200.013i	0.788177	+	0.504042i
$55$		0			0
$56$	−7.08666	+	51.7529i	−0.0169106	+	0.123496i
$57$	121.179	−	121.179i	0.281588	−	0.281588i
$58$	−44.3681	−	201.782i	−0.100445	−	0.456815i
$59$		−	67.1632i		−	0.148202i	−0.997251	−	0.0741009i	$-0.976391\pi$
$59$		−	67.1632i		−	0.148202i	0.997251	−	0.0741009i	$-0.0236087\pi$
$60$		0			0
$61$			659.080i			1.38339i	0.722192	+	0.691693i	$0.243135\pi$
$61$			659.080i			1.38339i	−0.722192	+	0.691693i	$0.756865\pi$
$62$	−465.688	+	102.396i	−0.953911	+	0.209747i
$63$	−30.6551	+	30.6551i	−0.0613045	+	0.0613045i
$64$	−137.638	+	493.153i	−0.268825	+	0.963189i
$65$		0			0
$66$	272.575	−	426.229i	0.508358	−	0.794926i
$67$	−506.483	+	506.483i	−0.923533	+	0.923533i	−0.997277	−	0.0737437i	$-0.976505\pi$
$67$	−506.483	+	506.483i	−0.923533	+	0.923533i	0.0737437	+	0.997277i	$0.476505\pi$
$68$	103.965	−	282.598i	0.185406	−	0.503971i
$69$	−26.6024			−0.0464139
$70$		0			0
$71$		−	1147.99i		−	1.91889i	−0.281902	−	0.959443i	$-0.590965\pi$
$71$		−	1147.99i		−	1.91889i	0.281902	−	0.959443i	$-0.409035\pi$
$72$	−338.459	+	256.930i	−0.553996	+	0.420549i
$73$	685.459	+	685.459i	1.09900	+	1.09900i	0.994528	+	0.104470i	$0.0333146\pi$
$73$	685.459	+	685.459i	1.09900	+	1.09900i	0.104470	+	0.994528i	$0.466685\pi$
$74$	−209.060	+	326.909i	−0.328415	+	0.513546i
$75$		0			0
$76$	200.584	+	434.066i	0.302744	+	0.655142i
$77$	101.840	+	101.840i	0.150724	+	0.150724i
$78$	−116.667	−	530.591i	−0.169359	−	0.770226i
$79$	−751.180			−1.06980			−0.534901	−	0.844915i	$-0.679651\pi$
$79$	−751.180			−1.06980			−0.534901	+	0.844915i	$0.679651\pi$
$80$		0			0
$81$	−130.718			−0.179311
$82$	16.7114	+	76.0018i	0.0225056	+	0.102354i
$83$	−251.518	−	251.518i	−0.332622	−	0.332622i	0.520959	−	0.853582i	$-0.325574\pi$
$83$	−251.518	−	251.518i	−0.332622	−	0.332622i	−0.853582	+	0.520959i	$0.825574\pi$
$84$	22.2119	+	48.0667i	0.0288513	+	0.0624346i
$85$		0			0
$86$	441.468	−	690.329i	0.553543	−	0.865582i
$87$	−148.089	−	148.089i	−0.182492	−	0.182492i
$88$	853.553	+	1124.40i	1.03397	+	1.36206i
$89$			497.545i			0.592581i	0.955098	+	0.296291i	$0.0957497\pi$
$89$			497.545i			0.592581i	−0.955098	+	0.296291i	$0.904250\pi$
$90$		0			0
$91$	154.651			0.178152
$92$	25.6282	−	69.6625i	0.0290427	−	0.0789437i
$93$	−341.772	+	341.772i	−0.381076	+	0.381076i
$94$	−356.135	+	556.893i	−0.390771	+	0.611054i
$95$		0			0
$96$	151.784	+	496.316i	0.161368	+	0.527657i
$97$	−305.299	+	305.299i	−0.319572	+	0.319572i	−0.848603	−	0.529031i	$-0.822556\pi$
$97$	−305.299	+	305.299i	−0.319572	+	0.319572i	0.529031	+	0.848603i	$0.322556\pi$
$98$	932.794	−	205.104i	0.961494	−	0.211415i
$99$			1171.61i			1.18941i
$100$		0			0
$101$			942.824i			0.928857i	0.885611	+	0.464428i	$0.153740\pi$
$101$			942.824i			0.928857i	−0.885611	+	0.464428i	$0.846260\pi$
$102$	−65.5499	−	298.115i	−0.0636315	−	0.289390i
$103$	−250.655	+	250.655i	−0.239784	+	0.239784i	−0.816761	−	0.576977i	$-0.804232\pi$
$103$	−250.655	+	250.655i	−0.239784	+	0.239784i	0.576977	+	0.816761i	$0.304232\pi$
$104$	1501.83	+	205.650i	1.41602	+	0.193900i
$105$		0			0
$106$	−1255.44	−	802.860i	−1.15037	−	0.735666i
$107$	−347.839	+	347.839i	−0.314270	+	0.314270i	−0.846561	−	0.532292i	$-0.821331\pi$
$107$	−347.839	+	347.839i	−0.314270	+	0.314270i	0.532292	+	0.846561i	$0.321331\pi$
$108$	−362.548	+	985.476i	−0.323020	+	0.878032i
$109$	822.067			0.722383			0.361191	−	0.932492i	$-0.382370\pi$
$109$	822.067			0.722383			0.361191	+	0.932492i	$0.382370\pi$
$110$		0			0
$111$			393.351i			0.336354i
$112$	−147.268	+	11.8587i	−0.124246	+	0.0100048i
$113$	−698.411	−	698.411i	−0.581425	−	0.581425i	0.353870	−	0.935295i	$-0.384866\pi$
$113$	−698.411	−	698.411i	−0.581425	−	0.581425i	−0.935295	+	0.353870i	$0.884866\pi$
$114$	408.353	+	261.143i	0.335489	+	0.214547i
$115$		0			0
$116$	530.460	−	245.128i	0.424586	−	0.196203i
$117$	889.589	+	889.589i	0.702928	+	0.702928i
$118$	185.534	−	40.7955i	0.144744	−	0.0318266i
$119$	86.8913			0.0669354
$120$		0			0
$121$	2561.24			1.92429
$122$	−1820.67	+	400.331i	−1.35111	+	0.297084i
$123$	55.7782	+	55.7782i	0.0408890	+	0.0408890i
$124$	−565.726	−	1224.24i	−0.409707	−	0.886611i
$125$		0			0
$126$	−103.303	−	66.0626i	−0.0730394	−	0.0467090i
$127$	−952.133	−	952.133i	−0.665261	−	0.665261i	0.291354	−	0.956615i	$-0.405894\pi$
$127$	−952.133	−	952.133i	−0.665261	−	0.665261i	−0.956615	+	0.291354i	$0.905894\pi$
$128$	−1445.91	−	80.6717i	−0.998447	−	0.0557066i
$129$		−	830.633i		−	0.566924i
$130$		0			0
$131$	−2296.26			−1.53149			−0.765744	−	0.643146i	$-0.777629\pi$
$131$	−2296.26			−1.53149			−0.765744	+	0.643146i	$0.777629\pi$
$132$	1342.99	+	494.076i	0.885550	+	0.325786i
$133$	−97.5689	+	97.5689i	−0.0636112	+	0.0636112i
$134$	−1706.77	−	1091.48i	−1.10032	−	0.703656i
$135$		0			0
$136$	843.808	+	115.545i	0.532029	+	0.0728522i
$137$	1005.61	−	1005.61i	0.627119	−	0.627119i	−0.320223	−	0.947342i	$-0.603758\pi$
$137$	1005.61	−	1005.61i	0.627119	−	0.627119i	0.947342	+	0.320223i	$0.103758\pi$
$138$	−16.1585	−	73.4875i	−0.00996744	−	0.0453310i
$139$			407.100i			0.248416i	0.992256	+	0.124208i	$0.0396389\pi$
$139$			407.100i			0.248416i	−0.992256	+	0.124208i	$0.960361\pi$
$140$		0			0
$141$			670.077i			0.400218i
$142$	3171.24	−	697.297i	1.87412	−	0.412084i
$143$	2955.32	−	2955.32i	1.72822	−	1.72822i
$144$	−915.336	−	778.909i	−0.529709	−	0.450757i
$145$		0			0
$146$	−1477.18	+	2309.89i	−0.837346	+	1.30937i
$147$	684.584	−	684.584i	0.384106	−	0.384106i
$148$	−1030.05	−	378.946i	−0.572092	−	0.210467i
$149$	2180.37			1.19881			0.599405	−	0.800446i	$-0.295404\pi$
$149$	2180.37			1.19881			0.599405	+	0.800446i	$0.295404\pi$
$150$		0			0
$151$		−	2581.10i		−	1.39104i	−0.718506	−	0.695520i	$-0.755174\pi$
$151$		−	2581.10i		−	1.39104i	0.718506	−	0.695520i	$-0.244826\pi$
$152$	−1077.24	+	817.756i	−0.574842	+	0.436373i
$153$	499.819	+	499.819i	0.264104	+	0.264104i
$154$	−219.468	+	343.185i	−0.114839	+	0.179575i
$155$		0			0
$156$	1394.86	−	644.572i	0.715886	−	0.330814i
$157$	549.008	+	549.008i	0.279080	+	0.279080i	0.832742	−	0.553662i	$-0.186770\pi$
$157$	549.008	+	549.008i	0.279080	+	0.279080i	−0.553662	+	0.832742i	$0.686770\pi$
$158$	−456.274	−	2075.09i	−0.229742	−	1.04484i
$159$	−1510.60			−0.753450
$160$		0			0
$161$	21.4194			0.0104850
$162$	−79.3993	−	361.100i	−0.0385074	−	0.175128i
$163$	317.555	+	317.555i	0.152594	+	0.152594i	0.779276	−	0.626681i	$-0.215587\pi$
$163$	317.555	+	317.555i	0.152594	+	0.152594i	−0.626681	+	0.779276i	$0.715587\pi$
$164$	−199.799	+	92.3282i	−0.0951324	+	0.0439611i
$165$		0			0
$166$	542.028	−	847.576i	0.253431	−	0.396293i
$167$	−1146.69	−	1146.69i	−0.531338	−	0.531338i	0.389633	−	0.920970i	$-0.372602\pi$
$167$	−1146.69	−	1146.69i	−0.531338	−	0.531338i	−0.920970	+	0.389633i	$0.872602\pi$
$168$	−119.290	+	90.5550i	−0.0547821	+	0.0415861i
$169$		−	2290.86i		−	1.04272i
$170$		0			0
$171$	−1122.48			−0.501977
$172$	2175.14	+	800.215i	0.964261	+	0.354743i
$173$	−186.798	+	186.798i	−0.0820922	+	0.0820922i	−0.746961	−	0.664868i	$-0.768488\pi$
$173$	−186.798	+	186.798i	−0.0820922	+	0.0820922i	0.664868	+	0.746961i	$0.268488\pi$
$174$	319.136	−	499.038i	0.139044	−	0.217425i
$175$		0			0
$176$	−2587.63	+	3040.85i	−1.10824	+	1.30235i
$177$	136.165	−	136.165i	0.0578236	−	0.0578236i
$178$	−1374.44	+	302.213i	−0.578755	+	0.127258i
$179$		−	2285.01i		−	0.954134i	−0.878867	−	0.477067i	$-0.841700\pi$
$179$		−	2285.01i		−	0.954134i	0.878867	−	0.477067i	$-0.158300\pi$
$180$		0			0
$181$		−	32.6132i		−	0.0133929i	−0.999978	−	0.00669646i	$-0.997868\pi$
$181$		−	32.6132i		−	0.0133929i	0.999978	−	0.00669646i	$-0.00213157\pi$
$182$	93.9364	+	427.214i	0.0382584	+	0.173996i
$183$	−1336.20	+	1336.20i	−0.539753	+	0.539753i
$184$	208.005	+	28.4827i	0.0833388	+	0.0114118i
$185$		0			0
$186$	−1151.72	−	736.528i	−0.454022	−	0.290349i
$187$	1660.46	−	1660.46i	0.649329	−	0.649329i
$188$	−1754.70	−	645.538i	−0.680716	−	0.250429i
$189$	−303.007			−0.116617
$190$		0			0
$191$		−	896.187i		−	0.339507i	−0.985487	−	0.169753i	$-0.945703\pi$
$191$		−	896.187i		−	0.339507i	0.985487	−	0.169753i	$-0.0542972\pi$
$192$	−1278.85	+	720.760i	−0.480692	+	0.270919i
$193$	2046.33	+	2046.33i	0.763202	+	0.763202i	0.976900	−	0.213698i	$-0.0685509\pi$
$193$	2046.33	+	2046.33i	0.763202	+	0.763202i	−0.213698	+	0.976900i	$0.568551\pi$
$194$	−1028.81	−	657.928i	−0.380744	−	0.243487i
$195$		0			0
$196$	1133.17	+	2452.20i	0.412964	+	0.893660i
$197$	−2980.13	−	2980.13i	−1.07779	−	1.07779i	−0.996707	−	0.0810878i	$-0.974161\pi$
$197$	−2980.13	−	2980.13i	−1.07779	−	1.07779i	−0.0810878	−	0.996707i	$-0.525839\pi$
$198$	−3236.51	+	711.648i	−1.16166	+	0.255427i
$199$	4534.78			1.61539			0.807693	−	0.589603i	$-0.200716\pi$
$199$	4534.78			1.61539			0.807693	+	0.589603i	$0.200716\pi$
$200$		0			0
$201$	−2053.66			−0.720666
$202$	−2604.49	+	572.680i	−0.907185	+	0.199473i
$203$	119.236	+	119.236i	0.0412254	+	0.0412254i
$204$	783.707	−	362.155i	0.268973	−	0.124294i
$205$		0			0
$206$	−844.668	−	540.168i	−0.285683	−	0.182696i
$207$	123.209	+	123.209i	0.0413702	+	0.0413702i
$208$	344.130	+	4273.62i	0.114717	+	1.42463i
$209$			3729.00i			1.23416i
$210$		0			0
$211$	3171.97			1.03492			0.517459	−	0.855708i	$-0.326878\pi$
$211$	3171.97			1.03492			0.517459	+	0.855708i	$0.326878\pi$
$212$	1455.28	−	3955.74i	0.471459	−	1.28152i
$213$	2327.40	−	2327.40i	0.748688	−	0.748688i
$214$	−1172.16	−	749.602i	−0.374427	−	0.239447i
$215$		0			0
$216$	−2942.53	−	402.928i	−0.926915	−	0.126925i
$217$	275.183	−	275.183i	0.0860859	−	0.0860859i
$218$	499.330	+	2270.91i	0.155133	+	0.705529i
$219$			2779.36i			0.857587i
$220$		0			0
$221$		−	2521.52i		−	0.767492i
$222$	−1086.61	+	238.925i	−0.328506	+	0.0722324i
$223$	3221.86	−	3221.86i	0.967497	−	0.967497i	−0.0319913	−	0.999488i	$-0.510185\pi$
$223$	3221.86	−	3221.86i	0.967497	−	0.967497i	0.999488	+	0.0319913i	$0.0101849\pi$
$224$	−122.211	−	399.617i	−0.0364534	−	0.119199i
$225$		0			0
$226$	1505.09	−	2353.54i	0.442997	−	0.692721i
$227$	−2709.11	+	2709.11i	−0.792113	+	0.792113i	−0.981837	−	0.189724i	$-0.939241\pi$
$227$	−2709.11	+	2709.11i	−0.792113	+	0.792113i	0.189724	+	0.981837i	$0.439241\pi$
$228$	−473.355	+	1286.67i	−0.137494	+	0.373736i
$229$	−1946.36			−0.561657			−0.280828	−	0.959758i	$-0.590609\pi$
$229$	−1946.36			−0.561657			−0.280828	+	0.959758i	$0.590609\pi$
$230$		0			0
$231$			412.935i			0.117615i
$232$	999.358	+	1316.47i	0.282806	+	0.372545i
$233$	−1215.55	−	1215.55i	−0.341774	−	0.341774i	0.515260	−	0.857034i	$-0.327695\pi$
$233$	−1215.55	−	1215.55i	−0.341774	−	0.341774i	−0.857034	+	0.515260i	$0.827695\pi$
$234$	−1917.09	+	2997.78i	−0.535573	+	0.837482i
$235$		0			0
$236$	225.390	+	487.747i	0.0621680	+	0.134532i
$237$	−1522.92	−	1522.92i	−0.417403	−	0.417403i
$238$	52.7785	+	240.032i	0.0143745	+	0.0653737i
$239$	−4078.95			−1.10396			−0.551978	−	0.833859i	$-0.686127\pi$
$239$	−4078.95			−1.10396			−0.551978	+	0.833859i	$0.686127\pi$
$240$		0			0
$241$	−1100.86			−0.294242			−0.147121	−	0.989118i	$-0.547001\pi$
$241$	−1100.86			−0.294242			−0.147121	+	0.989118i	$0.547001\pi$
$242$	1555.72	+	7075.25i	0.413245	+	1.87940i
$243$	−2770.94	−	2770.94i	−0.731506	−	0.731506i
$244$	−2211.78	−	4786.31i	−0.580306	−	1.25579i
$245$		0			0
$246$	−120.204	+	187.964i	−0.0311541	+	0.0487160i
$247$	2831.38	+	2831.38i	0.729377	+	0.729377i
$248$	3038.25	−	2306.40i	0.777940	−	0.590549i
$249$		−	1019.84i		−	0.259557i
$250$		0			0
$251$	3914.44			0.984372			0.492186	−	0.870490i	$-0.336198\pi$
$251$	3914.44			0.984372			0.492186	+	0.870490i	$0.336198\pi$
$252$	119.747	−	325.495i	0.0299339	−	0.0813661i
$253$	409.315	−	409.315i	0.101713	−	0.101713i
$254$	2051.87	−	3208.54i	0.506874	−	0.792606i
$255$		0			0
$256$	−655.405	−	4043.22i	−0.160011	−	0.987115i
$257$	1389.39	−	1389.39i	0.337229	−	0.337229i	−0.518094	−	0.855324i	$-0.673358\pi$
$257$	1389.39	−	1389.39i	0.337229	−	0.337229i	0.855324	+	0.518094i	$0.173358\pi$
$258$	2294.57	−	504.534i	0.553697	−	0.121748i
$259$		−	316.713i		−	0.0759829i
$260$		0			0
$261$			1371.75i			0.325323i
$262$	−1394.77	−	6343.26i	−0.328889	−	1.49576i
$263$	−4340.69	+	4340.69i	−1.01771	+	1.01771i	−0.0178731	+	0.999840i	$0.505689\pi$
$263$	−4340.69	+	4340.69i	−1.01771	+	1.01771i	−0.999840	+	0.0178731i	$0.994311\pi$
$264$	−549.106	+	4010.04i	−0.128012	+	0.934852i
$265$		0			0
$266$	−328.792	−	210.264i	−0.0757877	−	0.0484665i
$267$	−1008.71	+	1008.71i	−0.231206	+	0.231206i
$268$	1978.45	−	5377.82i	0.450945	−	1.22576i
$269$	2033.97			0.461017			0.230508	−	0.973070i	$-0.425961\pi$
$269$	2033.97			0.461017			0.230508	+	0.973070i	$0.425961\pi$
$270$		0			0
$271$			3331.79i			0.746833i	0.927664	+	0.373416i	$0.121814\pi$
$271$			3331.79i			0.746833i	−0.927664	+	0.373416i	$0.878186\pi$
$272$	193.351	+	2401.15i	0.0431015	+	0.535261i
$273$	313.535	+	313.535i	0.0695092	+	0.0695092i
$274$	3388.76	+	2167.12i	0.747162	+	0.477813i
$275$		0			0
$276$	193.190	−	89.2739i	0.0421328	−	0.0194698i
$277$	2835.89	+	2835.89i	0.615134	+	0.615134i	0.944279	−	0.329145i	$-0.106761\pi$
$277$	2835.89	+	2835.89i	0.615134	+	0.615134i	−0.329145	+	0.944279i	$0.606761\pi$
$278$	−1124.59	+	247.276i	−0.242620	+	0.0533476i
$279$	3165.83			0.679331
$280$		0			0
$281$	480.154			0.101935			0.0509673	−	0.998700i	$-0.483770\pi$
$281$	480.154			0.101935			0.0509673	+	0.998700i	$0.483770\pi$
$282$	−1851.05	+	407.011i	−0.390880	+	0.0859473i
$283$	3181.67	+	3181.67i	0.668305	+	0.668305i	0.957324	−	0.289018i	$-0.0933288\pi$
$283$	3181.67	+	3181.67i	0.668305	+	0.668305i	−0.289018	+	0.957324i	$0.593329\pi$
$284$	3852.48	+	8336.80i	0.804938	+	1.74190i
$285$		0			0
$286$	9958.96	+	6368.79i	2.05904	+	1.31676i
$287$	−44.9107	−	44.9107i	−0.00923691	−	0.00923691i
$288$	1595.70	−	3001.67i	0.326485	−	0.614151i
$289$			3496.27i			0.711637i
$290$		0			0
$291$	−1237.91			−0.249373
$292$	−7278.17	−	2677.58i	−1.45864	−	0.536621i
$293$	−3468.44	+	3468.44i	−0.691564	+	0.691564i	−0.962576	−	0.271012i	$-0.912642\pi$
$293$	−3468.44	+	3468.44i	−0.691564	+	0.691564i	0.271012	+	0.962576i	$0.412642\pi$
$294$	2306.94	+	1475.30i	0.457631	+	0.292657i
$295$		0			0
$296$	421.153	−	3075.62i	0.0826995	−	0.603943i
$297$	−5790.34	+	5790.34i	−1.13128	+	1.13128i
$298$	1324.37	+	6023.13i	0.257446	+	1.17084i
$299$		−	621.574i		−	0.120223i
$300$		0			0
$301$			668.797i			0.128069i
$302$	7130.13	−	1567.78i	1.35859	−	0.298728i
$303$	−1911.46	+	1911.46i	−0.362410	+	0.362410i
$304$	−2913.32	−	2479.10i	−0.549640	−	0.467718i
$305$		0			0
$306$	−1077.12	+	1684.31i	−0.201226	+	0.314659i
$307$	4035.38	−	4035.38i	0.750201	−	0.750201i	−0.224316	−	0.974516i	$-0.572015\pi$
$307$	4035.38	−	4035.38i	0.750201	−	0.750201i	0.974516	+	0.224316i	$0.0720147\pi$
$308$	−1081.33	−	397.812i	−0.200048	−	0.0735957i
$309$	−1016.34			−0.187112
$310$		0			0
$311$			4519.57i			0.824055i	0.911171	+	0.412027i	$0.135179\pi$
$311$			4519.57i			0.824055i	−0.911171	+	0.412027i	$0.864821\pi$
$312$	2627.84	+	3461.70i	0.476834	+	0.628141i
$313$	−36.2445	−	36.2445i	−0.00654525	−	0.00654525i	0.703827	−	0.710372i	$-0.251473\pi$
$313$	−36.2445	−	36.2445i	−0.00654525	−	0.00654525i	−0.710372	+	0.703827i	$0.751473\pi$
$314$	−1183.13	+	1850.07i	−0.212636	+	0.332502i
$315$		0			0
$316$	5455.15	−	2520.85i	0.971128	−	0.448763i
$317$	1598.38	+	1598.38i	0.283199	+	0.283199i	0.834383	−	0.551184i	$-0.185824\pi$
$317$	1598.38	+	1598.38i	0.283199	+	0.283199i	−0.551184	+	0.834383i	$0.685824\pi$
$318$	−917.553	−	4172.94i	−0.161804	−	0.735871i
$319$	4557.11			0.799841
$320$		0			0
$321$	−1410.40			−0.245236
$322$	13.0103	+	59.1696i	0.00225166	+	0.0102403i
$323$	1590.82	+	1590.82i	0.274042	+	0.274042i
$324$	949.289	−	438.671i	0.162772	−	0.0752179i
$325$		0			0
$326$	−684.340	+	1070.11i	−0.116264	+	0.181804i
$327$	1666.63	+	1666.63i	0.281850	+	0.281850i
$328$	−376.411	−	495.852i	−0.0633653	−	0.0834721i
$329$		−	539.523i		−	0.0904099i
$330$		0			0
$331$	−2971.73			−0.493477			−0.246739	−	0.969082i	$-0.579359\pi$
$331$	−2971.73			−0.493477			−0.246739	+	0.969082i	$0.579359\pi$
$332$	2670.61	+	982.492i	0.441471	+	0.162413i
$333$	1821.80	−	1821.80i	0.299803	−	0.299803i
$334$	2471.14	−	3864.16i	0.404835	−	0.633046i
$335$		0			0
$336$	−322.610	−	274.526i	−0.0523804	−	0.0445733i
$337$	−2602.78	+	2602.78i	−0.420719	+	0.420719i	−0.885451	−	0.464732i	$-0.846151\pi$
$337$	−2602.78	+	2602.78i	−0.420719	+	0.420719i	0.464732	+	0.885451i	$0.346151\pi$
$338$	6328.36	−	1391.49i	1.01839	−	0.223926i
$339$		−	2831.88i		−	0.453706i
$340$		0			0
$341$		−	10517.3i		−	1.67021i
$342$	−681.802	−	3100.77i	−0.107800	−	0.490265i
$343$	−1111.11	+	1111.11i	−0.174910	+	0.174910i
$344$	−889.343	+	6494.74i	−0.139390	+	1.01795i
$345$		0			0
$346$	−629.479	−	402.554i	−0.0978063	−	0.0625475i
$347$	771.195	−	771.195i	0.119308	−	0.119308i	−0.644932	−	0.764240i	$-0.723114\pi$
$347$	771.195	−	771.195i	0.119308	−	0.119308i	0.764240	+	0.644932i	$0.223114\pi$
$348$	1572.41	+	578.474i	0.242212	+	0.0891077i
$349$	−12180.8			−1.86826			−0.934130	−	0.356933i	$-0.883822\pi$
$349$	−12180.8			−1.86826			−0.934130	+	0.356933i	$0.883822\pi$
$350$		0			0
$351$			8793.05i			1.33715i
$352$	−9971.91	−	5301.11i	−1.50996	−	0.802699i
$353$	−7908.15	−	7908.15i	−1.19238	−	1.19238i	−0.976398	−	0.215977i	$-0.930706\pi$
$353$	−7908.15	−	7908.15i	−1.19238	−	1.19238i	−0.215977	−	0.976398i	$-0.569294\pi$
$354$	458.854	+	293.439i	0.0688922	+	0.0440568i
$355$		0			0
$356$	−1669.69	−	3613.23i	−0.248577	−	0.537924i
$357$	176.161	+	176.161i	0.0261160	+	0.0261160i
$358$	6312.21	−	1387.94i	0.931873	−	0.204902i
$359$	−6142.68			−0.903060			−0.451530	−	0.892256i	$-0.649122\pi$
$359$	−6142.68			−0.903060			−0.451530	+	0.892256i	$0.649122\pi$
$360$		0			0
$361$	3286.39			0.479135
$362$	90.0919	−	19.8095i	0.0130805	−	0.00287615i
$363$	5192.58	+	5192.58i	0.750798	+	0.750798i
$364$	−1123.09	+	518.987i	−0.161720	+	0.0747316i
$365$		0			0
$366$	−4502.79	−	2879.55i	−0.643072	−	0.411247i
$367$	2826.77	+	2826.77i	0.402061	+	0.402061i	0.878959	−	0.476898i	$-0.158239\pi$
$367$	2826.77	+	2826.77i	0.402061	+	0.402061i	−0.476898	+	0.878959i	$0.658239\pi$
$368$	47.6624	+	591.902i	0.00675157	+	0.0838451i
$369$		−	516.673i		−	0.0728914i
$370$		0			0
$371$	1216.28			0.170206
$372$	1335.05	−	3628.92i	0.186073	−	0.505782i
$373$	765.331	−	765.331i	0.106240	−	0.106240i	−0.651989	−	0.758228i	$-0.726065\pi$
$373$	765.331	−	765.331i	0.106240	−	0.106240i	0.758228	+	0.651989i	$0.226065\pi$
$374$	5595.48	+	3578.33i	0.773624	+	0.494735i
$375$		0			0
$376$	717.439	−	5239.35i	0.0984018	−	0.718614i
$377$	3460.15	−	3460.15i	0.472697	−	0.472697i
$378$	−184.049	−	837.038i	−0.0250436	−	0.113896i
$379$		−	3482.43i		−	0.471980i	−0.971755	−	0.235990i	$-0.924167\pi$
$379$		−	3482.43i		−	0.471980i	0.971755	−	0.235990i	$-0.0758333\pi$
$380$		0			0
$381$		−	3860.66i		−	0.519127i
$382$	2475.66	−	544.352i	0.331586	−	0.0729096i
$383$	−9322.29	+	9322.29i	−1.24373	+	1.24373i	−0.285282	+	0.958444i	$0.592087\pi$
$383$	−9322.29	+	9322.29i	−1.24373	+	1.24373i	−0.958444	+	0.285282i	$0.907913\pi$
$384$	−2767.84	−	3094.94i	−0.367827	−	0.411297i
$385$		0			0
$386$	−4409.89	+	6895.81i	−0.581496	+	0.909294i
$387$	−3847.07	+	3847.07i	−0.505317	+	0.505317i
$388$	1192.58	−	3241.66i	0.156041	−	0.424150i
$389$	−7236.20			−0.943161			−0.471581	−	0.881823i	$-0.656316\pi$
$389$	−7236.20			−0.943161			−0.471581	+	0.881823i	$0.656316\pi$
$390$		0			0
$391$		−	349.233i		−	0.0451701i
$392$	−6085.75	+	4619.81i	−0.784125	+	0.595244i
$393$	−4655.36	−	4655.36i	−0.597537	−	0.597537i
$394$	6422.27	−	10042.6i	0.821191	−	1.28411i
$395$		0			0
$396$	−3931.76	−	8508.38i	−0.498936	−	1.07970i
$397$	−3899.18	−	3899.18i	−0.492933	−	0.492933i	0.416296	−	0.909229i	$-0.363328\pi$
$397$	−3899.18	−	3899.18i	−0.492933	−	0.492933i	−0.909229	+	0.416296i	$0.863328\pi$
$398$	2754.46	+	12527.0i	0.346906	+	1.57770i
$399$	−395.617			−0.0496381
$400$		0			0
$401$	−7856.60			−0.978403			−0.489202	−	0.872171i	$-0.662712\pi$
$401$	−7856.60			−0.978403			−0.489202	+	0.872171i	$0.662712\pi$
$402$	−1247.41	−	5673.10i	−0.154764	−	0.703852i
$403$	−7985.60	−	7985.60i	−0.987075	−	0.987075i
$404$	−3163.98	−	6846.89i	−0.389639	−	0.843182i
$405$		0			0
$406$	−256.958	+	401.808i	−0.0314103	+	0.0491167i
$407$	−6052.25	−	6052.25i	−0.737098	−	0.737098i
$408$	1476.46	+	1944.97i	0.179156	+	0.236005i
$409$		−	278.474i		−	0.0336666i	−0.999858	−	0.0168333i	$-0.994642\pi$
$409$		−	278.474i		−	0.0336666i	0.999858	−	0.0168333i	$-0.00535846\pi$
$410$		0			0
$411$	4077.50			0.489363
$412$	979.121	−	2661.44i	0.117082	−	0.318252i
$413$	−109.635	+	109.635i	−0.0130625	+	0.0130625i
$414$	−265.519	+	415.195i	−0.0315206	+	0.0492892i
$415$		0			0
$416$	−11596.6	+	3546.47i	−1.36675	+	0.417981i
$417$	−825.343	+	825.343i	−0.0969238	+	0.0969238i
$418$	−10301.1	+	2265.03i	−1.20537	+	0.265039i
$419$		−	4588.99i		−	0.535052i	−0.963551	−	0.267526i	$-0.913794\pi$
$419$		−	4588.99i		−	0.535052i	0.963551	−	0.267526i	$-0.0862062\pi$
$420$		0			0
$421$			5953.12i			0.689162i	0.938757	+	0.344581i	$0.111979\pi$
$421$			5953.12i			0.689162i	−0.938757	+	0.344581i	$0.888021\pi$
$422$	1926.68	+	8762.38i	0.222250	+	1.01077i
$423$	3103.46	−	3103.46i	0.356727	−	0.356727i
$424$	11811.4	+	1617.37i	1.35286	+	0.185251i
$425$		0			0
$426$	7842.96	+	5015.60i	0.892002	+	0.570438i
$427$	1075.86	−	1075.86i	0.121931	−	0.121931i
$428$	1358.75	−	3693.34i	0.153452	−	0.417113i
$429$	11983.1			1.34860
$430$		0			0
$431$		−	4163.99i		−	0.465365i	−0.972553	−	0.232683i	$-0.925250\pi$
$431$		−	4163.99i		−	0.465365i	0.972553	−	0.232683i	$-0.0747504\pi$
$432$	−674.253	−	8373.29i	−0.0750927	−	0.932547i
$433$	2024.70	+	2024.70i	0.224713	+	0.224713i	0.810480	−	0.585767i	$-0.199207\pi$
$433$	2024.70	+	2024.70i	0.224713	+	0.224713i	−0.585767	+	0.810480i	$0.699207\pi$
$434$	927.324	+	593.027i	0.102564	+	0.0655903i
$435$		0			0
$436$	−5969.94	+	2758.74i	−0.655753	+	0.303026i
$437$	392.149	+	392.149i	0.0429268	+	0.0429268i
$438$	−7677.80	+	1688.21i	−0.837579	+	0.184168i
$439$	−3583.38			−0.389580			−0.194790	−	0.980845i	$-0.562403\pi$
$439$	−3583.38			−0.389580			−0.194790	+	0.980845i	$0.562403\pi$
$440$		0			0
$441$	−6341.30			−0.684731
$442$	6965.54	−	1531.59i	0.749586	−	0.164820i
$443$	−1001.91	−	1001.91i	−0.107454	−	0.107454i	0.651336	−	0.758790i	$-0.274209\pi$
$443$	−1001.91	−	1001.91i	−0.107454	−	0.107454i	−0.758790	+	0.651336i	$0.774209\pi$
$444$	−1320.03	−	2856.56i	−0.141094	−	0.305330i
$445$		0			0
$446$	10857.2	+	6943.20i	1.15270	+	0.737153i
$447$	4420.41	+	4420.41i	0.467737	+	0.467737i
$448$	1029.68	−	580.331i	0.108589	−	0.0612010i
$449$		−	7881.21i		−	0.828368i	−0.910193	−	0.414184i	$-0.864067\pi$
$449$		−	7881.21i		−	0.828368i	0.910193	−	0.414184i	$-0.135933\pi$
$450$		0			0
$451$	−1716.45			−0.179212
$452$	7415.70	+	2728.17i	0.771693	+	0.283899i
$453$	5232.85	−	5232.85i	0.542739	−	0.542739i
$454$	−9129.27	−	5838.20i	−0.943739	−	0.603525i
$455$		0			0
$456$	−3841.87	−	526.077i	−0.394544	−	0.0540259i
$457$	7151.43	−	7151.43i	0.732013	−	0.732013i	−0.239006	−	0.971018i	$-0.576821\pi$
$457$	7151.43	−	7151.43i	0.732013	−	0.732013i	0.971018	+	0.239006i	$0.0768214\pi$
$458$	−1182.24	−	5376.71i	−0.120617	−	0.548552i
$459$			4940.40i			0.502393i
$460$		0			0
$461$			5918.81i			0.597975i	0.954257	+	0.298987i	$0.0966488\pi$
$461$			5918.81i			0.597975i	−0.954257	+	0.298987i	$0.903351\pi$
$462$	−1140.71	+	250.820i	−0.114871	+	0.0252580i
$463$	−4849.09	+	4849.09i	−0.486731	+	0.486731i	−0.907273	−	0.420542i	$-0.861840\pi$
$463$	−4849.09	+	4849.09i	−0.486731	+	0.486731i	0.420542	+	0.907273i	$0.361840\pi$
$464$	−3029.65	+	3560.30i	−0.303120	+	0.356213i
$465$		0			0
$466$	2619.54	−	4096.21i	0.260403	−	0.407196i
$467$	2370.31	−	2370.31i	0.234871	−	0.234871i	−0.579851	−	0.814722i	$-0.696889\pi$
$467$	2370.31	−	2370.31i	0.234871	−	0.234871i	0.814722	+	0.579851i	$0.196889\pi$
$468$	−9445.62	−	3474.96i	−0.932958	−	0.343227i
$469$	1653.53			0.162800
$470$		0			0
$471$			2226.09i			0.217776i
$472$	−1210.47	+	918.887i	−0.118043	+	0.0896085i
$473$	12780.4	+	12780.4i	1.24238	+	1.24238i
$474$	3281.94	−	5132.01i	0.318026	−	0.497302i
$475$		0			0
$476$	−631.014	+	291.595i	−0.0607615	+	0.0280782i
$477$	6996.35	+	6996.35i	0.671574	+	0.671574i
$478$	−2477.59	−	11267.8i	−0.237076	−	1.07820i
$479$	11996.7			1.14435			0.572174	−	0.820132i	$-0.306100\pi$
$479$	11996.7			1.14435			0.572174	+	0.820132i	$0.306100\pi$
$480$		0			0
$481$	−9190.77			−0.871233
$482$	−668.669	−	3041.04i	−0.0631889	−	0.287377i
$483$	43.4250	+	43.4250i	0.00409090	+	0.00409090i
$484$	−18600.0	+	8595.14i	−1.74680	+	0.807207i
$485$		0			0
$486$	5971.45	−	9337.64i	0.557347	−	0.871531i
$487$	6021.08	+	6021.08i	0.560249	+	0.560249i	0.929378	−	0.369129i	$-0.120344\pi$
$487$	6021.08	+	6021.08i	0.560249	+	0.560249i	−0.369129	+	0.929378i	$0.620344\pi$
$488$	11878.4	−	9017.14i	1.10187	−	0.836449i
$489$			1287.60i			0.119075i
$490$		0			0
$491$	9946.16			0.914183			0.457092	−	0.889420i	$-0.348891\pi$
$491$	9946.16			0.914183			0.457092	+	0.889420i	$0.348891\pi$
$492$	−592.251	−	217.884i	−0.0542698	−	0.0199654i
$493$	1944.10	−	1944.10i	0.177602	−	0.177602i
$494$	−6101.69	+	9541.30i	−0.555725	+	0.868995i
$495$		0			0
$496$	8216.73	+	6992.06i	0.743835	+	0.632969i
$497$	−1873.94	+	1873.94i	−0.169130	+	0.169130i
$498$	2817.24	−	619.459i	0.253501	−	0.0557402i
$499$		−	15650.8i		−	1.40406i	−0.712148	−	0.702029i	$-0.752278\pi$
$499$		−	15650.8i		−	1.40406i	0.712148	−	0.702029i	$-0.247722\pi$
$500$		0			0
$501$		−	4649.52i		−	0.414622i
$502$	2377.67	+	10813.4i	0.211395	+	0.961405i
$503$	6492.90	−	6492.90i	0.575555	−	0.575555i	−0.358120	−	0.933675i	$-0.616582\pi$
$503$	6492.90	−	6492.90i	0.575555	−	0.575555i	0.933675	+	0.358120i	$0.116582\pi$
$504$	971.894	+	133.084i	0.0858961	+	0.0117620i
$505$		0			0
$506$	1379.33	+	882.085i	0.121183	+	0.0774970i
$507$	4644.42	−	4644.42i	0.406837	−	0.406837i
$508$	10109.7	+	3719.27i	0.882965	+	0.324835i
$509$	−9155.78			−0.797294			−0.398647	−	0.917104i	$-0.630520\pi$
$509$	−9155.78			−0.797294			−0.398647	+	0.917104i	$0.630520\pi$
$510$		0			0
$511$		−	2237.84i		−	0.193731i
$512$	10771.1	−	4266.40i	0.929722	−	0.368262i
$513$	−5547.50	−	5547.50i	−0.477443	−	0.477443i
$514$	4682.04	+	2994.18i	0.401782	+	0.256941i
$515$		0			0
$516$	2787.48	+	6032.15i	0.237814	+	0.514633i
$517$	−10310.1	−	10310.1i	−0.877052	−	0.877052i
$518$	874.899	−	192.374i	0.0742101	−	0.0163174i
$519$	−757.416			−0.0640595
$520$		0			0
$521$	8890.03			0.747561			0.373781	−	0.927517i	$-0.378061\pi$
$521$	8890.03			0.747561			0.373781	+	0.927517i	$0.378061\pi$
$522$	−3789.37	+	833.213i	−0.317732	+	0.0698635i
$523$	9129.71	+	9129.71i	0.763316	+	0.763316i	0.976920	−	0.213604i	$-0.0685203\pi$
$523$	9129.71	+	9129.71i	0.763316	+	0.763316i	−0.213604	+	0.976920i	$0.568520\pi$
$524$	16675.7	−	7705.90i	1.39023	−	0.642431i
$525$		0			0
$526$	−14627.5	−	9354.31i	−1.21252	−	0.775413i
$527$	−4486.74	−	4486.74i	−0.370864	−	0.370864i
$528$	−11411.0	+	918.864i	−0.940532	+	0.0757357i
$529$			12080.9i			0.992924i
$530$		0			0
$531$	−1261.29			−0.103080
$532$	381.129	−	1035.98i	0.0310602	−	0.0844277i
$533$	−1303.27	+	1303.27i	−0.105912	+	0.105912i
$534$	−3399.19	−	2173.80i	−0.275464	−	0.176160i
$535$		0			0
$536$	16057.6	+	2198.81i	1.29400	+	0.177191i
$537$	4632.57	−	4632.57i	0.372272	−	0.372272i
$538$	1235.45	+	5618.72i	0.0990040	+	0.450261i
$539$			21066.5i			1.68349i
$540$		0			0
$541$		−	8774.26i		−	0.697292i	−0.937254	−	0.348646i	$-0.886642\pi$
$541$		−	8774.26i		−	0.697292i	0.937254	−	0.348646i	$-0.113358\pi$
$542$	−9203.85	+	2023.76i	−0.729408	+	0.160383i
$543$	66.1191	−	66.1191i	0.00522549	−	0.00522549i
$544$	−6515.58	+	1992.60i	−0.513517	+	0.157044i
$545$		0			0
$546$	−675.677	+	1056.57i	−0.0529603	+	0.0828147i
$547$	−14817.9	+	14817.9i	−1.15826	+	1.15826i	−0.173406	+	0.984850i	$0.555477\pi$
$547$	−14817.9	+	14817.9i	−1.15826	+	1.15826i	−0.984850	+	0.173406i	$0.944523\pi$
$548$	−3928.18	+	10677.6i	−0.306211	+	0.832341i
$549$	12377.2			0.962198
$550$		0			0
$551$			4365.99i			0.337564i
$552$	363.959	+	479.449i	0.0280636	+	0.0369686i
$553$	1226.20	+	1226.20i	0.0942920	+	0.0942920i
$554$	−6111.42	+	9556.51i	−0.468681	+	0.732883i
$555$		0			0
$556$	−1366.17	−	2956.40i	−0.104206	−	0.225503i
$557$	−13934.8	−	13934.8i	−1.06003	−	1.06003i	−0.998079	−	0.0619489i	$-0.980268\pi$
$557$	−13934.8	−	13934.8i	−1.06003	−	1.06003i	−0.0619489	−	0.998079i	$-0.519732\pi$
$558$	1922.95	+	8745.41i	0.145887	+	0.663481i
$559$	19408.0			1.46846
$560$		0			0
$561$	6732.72			0.506695
$562$	291.650	+	1326.40i	0.0218906	+	0.0995563i
$563$	−7373.79	−	7373.79i	−0.551986	−	0.551986i	0.375027	−	0.927014i	$-0.377633\pi$
$563$	−7373.79	−	7373.79i	−0.551986	−	0.551986i	−0.927014	+	0.375027i	$0.877633\pi$
$564$	−2248.68	−	4866.17i	−0.167884	−	0.363303i
$565$		0			0
$566$	−6856.58	+	10721.7i	−0.509194	+	0.796233i
$567$	213.380	+	213.380i	0.0158044	+	0.0158044i
$568$	−20689.9	+	15706.1i	−1.52839	+	1.16023i
$569$			8066.19i			0.594292i	0.954832	+	0.297146i	$0.0960349\pi$
$569$			8066.19i			0.594292i	−0.954832	+	0.297146i	$0.903965\pi$
$570$		0			0
$571$	1577.74			0.115633			0.0578164	−	0.998327i	$-0.481586\pi$
$571$	1577.74			0.115633			0.0578164	+	0.998327i	$0.481586\pi$
$572$	−11544.2	+	31379.5i	−0.843861	+	2.29378i
$573$	1816.90	−	1816.90i	0.132465	−	0.132465i
$574$	96.7838	−	151.342i	0.00703776	−	0.0110050i
$575$		0			0
$576$	9261.18	+	2584.78i	0.669935	+	0.186978i
$577$	−14468.0	+	14468.0i	−1.04387	+	1.04387i	−0.0448739	+	0.998993i	$0.514289\pi$
$577$	−14468.0	+	14468.0i	−1.04387	+	1.04387i	−0.998993	+	0.0448739i	$0.985711\pi$
$578$	−9658.24	+	2123.67i	−0.695034	+	0.152825i
$579$			8297.33i			0.595553i
$580$		0			0
$581$			821.139i			0.0586344i
$582$	−751.917	−	3419.65i	−0.0535532	−	0.243555i
$583$	23242.7	−	23242.7i	1.65114	−	1.65114i
$584$	2975.80	−	21731.9i	0.210856	−	1.53985i
$585$		0			0
$586$	−11688.1	−	7474.58i	−0.823943	−	0.526915i
$587$	16990.1	−	16990.1i	1.19465	−	1.19465i	0.218898	−	0.975748i	$-0.429754\pi$
$587$	16990.1	−	16990.1i	1.19465	−	1.19465i	0.975748	−	0.218898i	$-0.0702463\pi$
$588$	−2674.16	+	7268.89i	−0.187552	+	0.509803i
$589$	10076.2			0.704893
$590$		0			0
$591$		−	12083.7i		−	0.841042i
$592$	8752.03	−	704.751i	0.607612	−	0.0489275i
$593$	67.7222	+	67.7222i	0.00468974	+	0.00468974i	0.709448	−	0.704758i	$-0.248944\pi$
$593$	67.7222	+	67.7222i	0.00468974	+	0.00468974i	−0.704758	+	0.709448i	$0.748944\pi$
$594$	−19512.6	−	12478.3i	−1.34783	−	0.861941i
$595$		0			0
$596$	−15834.1	+	7317.00i	−1.08824	+	0.502879i
$597$	9193.68	+	9193.68i	0.630272	+	0.630272i
$598$	1717.06	−	377.549i	0.117418	−	0.0258180i
$599$	−12494.2			−0.852252			−0.426126	−	0.904664i	$-0.640122\pi$
$599$	−12494.2			−0.852252			−0.426126	+	0.904664i	$0.640122\pi$
$600$		0			0
$601$	19551.9			1.32702			0.663508	−	0.748169i	$-0.269067\pi$
$601$	19551.9			1.32702			0.663508	+	0.748169i	$0.269067\pi$
$602$	−1847.51	+	406.233i	−0.125081	+	0.0275030i
$603$	9511.51	+	9511.51i	0.642353	+	0.642353i
$604$	8661.81	+	18744.2i	0.583516	+	1.26274i
$605$		0			0
$606$	−6441.31	−	4119.24i	−0.431783	−	0.276126i
$607$	−6194.33	−	6194.33i	−0.414201	−	0.414201i	0.468998	−	0.883199i	$-0.344615\pi$
$607$	−6194.33	−	6194.33i	−0.414201	−	0.414201i	−0.883199	+	0.468998i	$0.844615\pi$
$608$	5078.79	−	9553.70i	0.338770	−	0.637260i
$609$			483.473i			0.0321696i
$610$		0			0
$611$	−15656.6			−1.03666
$612$	−5307.06	−	1952.42i	−0.350531	−	0.128957i
$613$	−4151.90	+	4151.90i	−0.273562	+	0.273562i	−0.830532	−	0.556970i	$-0.811964\pi$
$613$	−4151.90	+	4151.90i	−0.273562	+	0.273562i	0.556970	+	0.830532i	$0.311964\pi$
$614$	13598.6	+	8696.37i	0.893804	+	0.571591i
$615$		0			0
$616$	442.121	−	3228.75i	0.0289181	−	0.211185i
$617$	−9127.15	+	9127.15i	−0.595535	+	0.595535i	−0.939121	−	0.343586i	$-0.888358\pi$
$617$	−9127.15	+	9127.15i	−0.595535	+	0.595535i	0.343586	+	0.939121i	$0.388358\pi$
$618$	−617.334	−	2807.58i	−0.0401825	−	0.182746i
$619$			9443.78i			0.613211i	0.951837	+	0.306605i	$0.0991932\pi$
$619$			9443.78i			0.613211i	−0.951837	+	0.306605i	$0.900807\pi$
$620$		0			0
$621$			1217.85i			0.0786965i
$622$	−12485.0	+	2745.22i	−0.804829	+	0.176967i
$623$	812.178	−	812.178i	0.0522299	−	0.0522299i
$624$	−7966.54	+	9361.90i	−0.511085	+	0.600603i
$625$		0			0
$626$	78.1080	−	122.138i	0.00498694	−	0.00779814i
$627$	−7560.07	+	7560.07i	−0.481531	+	0.481531i
$628$	−5829.35	−	2144.56i	−0.370408	−	0.136270i
$629$	−5163.87			−0.327340
$630$		0			0
$631$			3283.13i			0.207130i	0.994623	+	0.103565i	$0.0330251\pi$
$631$			3283.13i			0.207130i	−0.994623	+	0.103565i	$0.966975\pi$
$632$	10277.2	+	13538.3i	0.646844	+	0.852098i
$633$	6430.77	+	6430.77i	0.403792	+	0.403792i
$634$	−3444.56	+	5386.30i	−0.215774	+	0.337409i
$635$		0			0
$636$	10970.2	−	5069.36i	0.683955	−	0.316059i
$637$	15995.5	+	15995.5i	0.994922	+	0.994922i
$638$	2768.03	+	12588.7i	0.171767	+	0.781180i
$639$	−21558.6			−1.33466
$640$		0			0
$641$	17569.8			1.08263			0.541316	−	0.840819i	$-0.317926\pi$
$641$	17569.8			1.08263			0.541316	+	0.840819i	$0.317926\pi$
$642$	−856.687	−	3896.13i	−0.0526647	−	0.239514i
$643$	−6841.79	−	6841.79i	−0.419617	−	0.419617i	0.465455	−	0.885072i	$-0.345891\pi$
$643$	−6841.79	−	6841.79i	−0.419617	−	0.419617i	−0.885072	+	0.465455i	$0.845891\pi$
$644$	−155.550	+	71.8802i	−0.00951788	+	0.00439826i
$645$		0			0
$646$	−3428.26	+	5360.81i	−0.208797	+	0.326499i
$647$	−20801.5	−	20801.5i	−1.26398	−	1.26398i	−0.949149	−	0.314827i	$-0.898054\pi$
$647$	−20801.5	−	20801.5i	−1.26398	−	1.26398i	−0.314827	−	0.949149i	$-0.601946\pi$
$648$	1788.41	+	2355.90i	0.108419	+	0.142822i
$649$			4190.17i			0.253434i
$650$		0			0
$651$	1115.80			0.0671759
$652$	−3371.79	−	1240.45i	−0.202530	−	0.0745089i
$653$	−6791.66	+	6791.66i	−0.407011	+	0.407011i	−0.880695	−	0.473684i	$-0.842924\pi$
$653$	−6791.66	+	6791.66i	−0.407011	+	0.407011i	0.473684	+	0.880695i	$0.342924\pi$
$654$	−3591.64	+	5616.30i	−0.214747	+	0.335802i
$655$		0			0
$656$	1141.12	−	1341.00i	0.0679168	−	0.0798126i
$657$	12872.6	−	12872.6i	0.764395	−	0.764395i
$658$	1490.40	−	327.711i	0.0883005	−	0.0194157i
$659$			2846.76i			0.168276i	0.996454	+	0.0841381i	$0.0268137\pi$
$659$			2846.76i			0.168276i	−0.996454	+	0.0841381i	$0.973186\pi$
$660$		0			0
$661$			20101.9i			1.18286i	0.806355	+	0.591432i	$0.201437\pi$
$661$			20101.9i			1.18286i	−0.806355	+	0.591432i	$0.798563\pi$
$662$	−1805.05	−	8209.21i	−0.105975	−	0.481964i
$663$	5112.06	−	5112.06i	0.299451	−	0.299451i
$664$	−1091.92	+	7974.15i	−0.0638175	+	0.466050i
$665$		0			0
$666$	6139.20	+	3926.04i	0.357191	+	0.228425i
$667$	479.235	−	479.235i	0.0278201	−	0.0278201i
$668$	12175.5	+	4479.25i	0.705215	+	0.259442i
$669$	13063.8			0.754972
$670$		0			0
$671$		−	41118.6i		−	2.36567i
$672$	562.405	−	1057.94i	0.0322846	−	0.0607305i
$673$	7942.65	+	7942.65i	0.454928	+	0.454928i	0.896986	−	0.442058i	$-0.145752\pi$
$673$	7942.65	+	7942.65i	0.454928	+	0.454928i	−0.442058	+	0.896986i	$0.645752\pi$
$674$	−8770.95	−	5609.05i	−0.501253	−	0.320553i
$675$		0			0
$676$	7687.80	+	16636.5i	0.437403	+	0.946545i
$677$	−1214.74	−	1214.74i	−0.0689604	−	0.0689604i	0.671785	−	0.740746i	$-0.265528\pi$
$677$	−1214.74	−	1214.74i	−0.0689604	−	0.0689604i	−0.740746	+	0.671785i	$0.765528\pi$
$678$	7822.88	−	1720.11i	0.443121	−	0.0974341i
$679$	996.722			0.0563339
$680$		0			0
$681$	−10984.7			−0.618114
$682$	29053.3	−	6388.28i	1.63124	−	0.358680i
$683$	2979.54	+	2979.54i	0.166924	+	0.166924i	0.785626	−	0.618702i	$-0.212341\pi$
$683$	2979.54	+	2979.54i	0.166924	+	0.166924i	−0.618702	+	0.785626i	$0.712341\pi$
$684$	8151.55	−	3766.87i	0.455676	−	0.210570i
$685$		0			0
$686$	−3744.25	−	2394.46i	−0.208391	−	0.133267i
$687$	−3946.00	−	3946.00i	−0.219140	−	0.219140i
$688$	−18481.5	+	1488.21i	−1.02413	+	0.0824673i
$689$		−	35295.7i		−	1.95161i
$690$		0			0
$691$	−24835.3			−1.36726			−0.683631	−	0.729827i	$-0.739600\pi$
$691$	−24835.3			−1.36726			−0.683631	+	0.729827i	$0.739600\pi$
$692$	729.679	−	1983.41i	0.0400841	−	0.108957i
$693$	1912.51	−	1912.51i	0.104834	−	0.104834i
$694$	2598.81	+	1661.95i	0.142146	+	0.0909030i
$695$		0			0
$696$	−642.905	+	4695.04i	−0.0350133	+	0.255697i
$697$	−732.250	+	732.250i	−0.0397933	+	0.0397933i
$698$	−7398.72	−	33648.7i	−0.401211	−	1.82467i
$699$		−	4928.74i		−	0.266698i
$700$		0			0
$701$		−	16050.4i		−	0.864787i	−0.901685	−	0.432394i	$-0.857669\pi$
$701$		−	16050.4i		−	0.864787i	0.901685	−	0.432394i	$-0.142331\pi$
$702$	−24290.2	+	5340.97i	−1.30595	+	0.287154i
$703$	5798.42	−	5798.42i	0.311084	−	0.311084i
$704$	8586.95	−	30766.7i	0.459706	−	1.64711i
$705$		0			0
$706$	17042.3	−	26649.2i	0.908491	−	1.42062i
$707$	1539.04	−	1539.04i	0.0818691	−	0.0818691i
$708$	−531.894	+	1445.79i	−0.0282342	+	0.0767461i
$709$	13000.2			0.688620			0.344310	−	0.938856i	$-0.388113\pi$
$709$	13000.2			0.688620			0.344310	+	0.938856i	$0.388113\pi$
$710$		0			0
$711$			14106.8i			0.744088i
$712$	8967.13	−	6807.12i	0.471991	−	0.358297i
$713$	−1106.02	−	1106.02i	−0.0580934	−	0.0580934i
$714$	−379.632	+	593.635i	−0.0198983	+	0.0311152i
$715$		0			0
$716$	7668.18	+	16594.0i	0.400242	+	0.866128i
$717$	−8269.55	−	8269.55i	−0.430728	−	0.430728i
$718$	−3731.12	−	16968.8i	−0.193933	−	0.881990i
$719$	−724.797			−0.0375944			−0.0187972	−	0.999823i	$-0.505984\pi$
$719$	−724.797			−0.0375944			−0.0187972	+	0.999823i	$0.505984\pi$
$720$		0			0
$721$	818.322			0.0422689
$722$	1996.18	+	9078.44i	0.102895	+	0.467956i
$723$	−2231.84	−	2231.84i	−0.114804	−	0.114804i
$724$	109.445	+	236.841i	0.00561809	+	0.0121576i
$725$		0			0
$726$	−11190.1	+	17498.2i	−0.572046	+	0.894516i
$727$	22261.1	+	22261.1i	1.13565	+	1.13565i	0.989221	+	0.146430i	$0.0467784\pi$
$727$	22261.1	+	22261.1i	1.13565	+	1.13565i	0.146430	+	0.989221i	$0.453222\pi$
$728$	−2115.84	−	2787.24i	−0.107718	−	0.141898i
$729$		−	7706.07i		−	0.391509i
$730$		0			0
$731$	10904.4			0.551731
$732$	5219.54	−	14187.7i	0.263551	−	0.716385i
$733$	−8886.09	+	8886.09i	−0.447770	+	0.447770i	−0.894613	−	0.446843i	$-0.852548\pi$
$733$	−8886.09	+	8886.09i	−0.447770	+	0.447770i	0.446843	+	0.894613i	$0.352548\pi$
$734$	−6091.77	+	9525.78i	−0.306337	+	0.479023i
$735$		0			0
$736$	−1606.14	+	491.191i	−0.0804390	+	0.0245999i
$737$	31598.4	−	31598.4i	1.57929	−	1.57929i
$738$	1427.28	−	313.832i	0.0711908	−	0.0156535i
$739$		−	21372.7i		−	1.06388i	−0.846783	−	0.531939i	$-0.821464\pi$
$739$		−	21372.7i		−	1.06388i	0.846783	−	0.531939i	$-0.178536\pi$
$740$		0			0
$741$			11480.5i			0.569159i
$742$	738.782	+	3359.91i	0.0365519	+	0.166235i
$743$	−17304.4	+	17304.4i	−0.854421	+	0.854421i	−0.990674	−	0.136253i	$-0.956494\pi$
$743$	−17304.4	+	17304.4i	−0.854421	+	0.854421i	0.136253	+	0.990674i	$0.456494\pi$
$744$	10835.6	+	1483.75i	0.533941	+	0.0731140i
$745$		0			0
$746$	2579.05	+	1649.31i	0.126576	+	0.0809458i
$747$	−4723.38	+	4723.38i	−0.231351	+	0.231351i
$748$	−6486.16	+	17630.7i	−0.317056	+	0.861819i
$749$	1135.60			0.0553992
$750$		0			0
$751$		−	9428.24i		−	0.458111i	−0.973413	−	0.229055i	$-0.926436\pi$
$751$		−	9428.24i		−	0.458111i	0.973413	−	0.229055i	$-0.0735637\pi$
$752$	14909.2	−	1200.55i	0.722980	−	0.0582174i
$753$	7936.03	+	7936.03i	0.384070	+	0.384070i
$754$	11660.2	+	7456.72i	0.563181	+	0.360156i
$755$		0			0
$756$	2200.47	−	1016.85i	0.105860	−	0.0489185i
$757$	−642.402	−	642.402i	−0.0308435	−	0.0308435i	0.691517	−	0.722360i	$-0.256943\pi$
$757$	−642.402	−	642.402i	−0.0308435	−	0.0308435i	−0.722360	+	0.691517i	$0.756943\pi$
$758$	9619.99	−	2115.26i	0.460968	−	0.101358i
$759$	1659.67			0.0793703
$760$		0			0
$761$	−20575.9			−0.980124			−0.490062	−	0.871688i	$-0.663026\pi$
$761$	−20575.9			−0.980124			−0.490062	+	0.871688i	$0.663026\pi$
$762$	10664.8	−	2345.00i	0.507015	−	0.111483i
$763$	−1341.92	−	1341.92i	−0.0636705	−	0.0636705i
$764$	3007.48	+	6508.21i	0.142417	+	0.308192i
$765$		0			0
$766$	−31414.7	−	20089.8i	−1.48180	−	0.947616i
$767$	3181.53	+	3181.53i	0.149776	+	0.149776i
$768$	6868.37	−	9525.87i	0.322709	−	0.447572i
$769$			14159.5i			0.663987i	0.943282	+	0.331994i	$0.107721\pi$
$769$			14159.5i			0.663987i	−0.943282	+	0.331994i	$0.892279\pi$
$770$		0			0
$771$	5633.63			0.263152
$772$	−21727.8	−	7993.48i	−1.01296	−	0.372657i
$773$	4651.93	−	4651.93i	0.216453	−	0.216453i	−0.590549	−	0.807002i	$-0.701089\pi$
$773$	4651.93	−	4651.93i	0.216453	−	0.216453i	0.807002	+	0.590549i	$0.201089\pi$
$774$	−12964.0	−	8290.55i	−0.602045	−	0.385010i
$775$		0			0
$776$	9679.25	+	1325.41i	0.447764	+	0.0613135i
$777$	642.094	−	642.094i	0.0296461	−	0.0296461i
$778$	−4395.33	−	19989.5i	−0.202545	−	0.921156i
$779$		−	1644.46i		−	0.0756342i
$780$		0			0
$781$			71620.3i			3.28140i
$782$	964.735	−	212.127i	0.0441162	−	0.00970033i
$783$	−6779.46	+	6779.46i	−0.309423	+	0.309423i
$784$	−16458.5	−	14005.4i	−0.749748	−	0.638001i
$785$		0			0
$786$	10032.4	−	15687.9i	0.455274	−	0.711918i
$787$	−11118.1	+	11118.1i	−0.503581	+	0.503581i	−0.912549	−	0.408968i	$-0.865889\pi$
$787$	−11118.1	+	11118.1i	−0.503581	+	0.503581i	0.408968	+	0.912549i	$0.365889\pi$
$788$	31642.9	+	11641.2i	1.43050	+	0.526268i
$789$	−17600.4			−0.794158
$790$		0			0
$791$			2280.13i			0.102493i
$792$	21115.7	−	16029.3i	0.947365	−	0.719163i
$793$	−31220.7	−	31220.7i	−1.39808	−	1.39808i
$794$	8402.85	−	13139.6i	0.375574	−	0.587290i
$795$		0			0
$796$	−32932.1	+	15218.1i	−1.46639	+	0.677625i
$797$	26274.8	+	26274.8i	1.16776	+	1.16776i	0.982734	+	0.185021i	$0.0592354\pi$
$797$	26274.8	+	26274.8i	1.16776	+	1.16776i	0.185021	+	0.982734i	$0.440765\pi$
$798$	−240.301	−	1092.87i	−0.0106599	−	0.0484800i
$799$	−8796.69			−0.389493
$800$		0			0
$801$	9343.67			0.412163
$802$	−4772.16	−	21703.3i	−0.210113	−	0.955576i
$803$	−42764.2	−	42764.2i	−1.87935	−	1.87935i
$804$	14913.9	−	6891.78i	0.654195	−	0.302306i
$805$		0			0
$806$	17209.2	−	26910.2i	0.752070	−	1.17602i
$807$	4123.62	+	4123.62i	0.179874	+	0.179874i
$808$	16992.3	−	12899.2i	0.739834	−	0.561622i
$809$		−	29424.6i		−	1.27876i	−0.768892	−	0.639379i	$-0.779192\pi$
$809$		−	29424.6i		−	1.27876i	0.768892	−	0.639379i	$-0.220808\pi$
$810$		0			0
$811$	−15648.6			−0.677554			−0.338777	−	0.940867i	$-0.610013\pi$
$811$	−15648.6			−0.677554			−0.338777	+	0.940867i	$0.610013\pi$
$812$	−1266.05	−	465.767i	−0.0547162	−	0.0201296i
$813$	−6754.77	+	6754.77i	−0.291390	+	0.291390i
$814$	13042.8	−	20395.1i	0.561608	−	0.878193i
$815$		0			0
$816$	−4476.03	+	5260.02i	−0.192025	+	0.225659i
$817$	−12244.4	+	12244.4i	−0.524331	+	0.524331i
$818$	769.266	−	169.147i	0.0328811	−	0.00722995i
$819$		−	2904.27i		−	0.123912i
$820$		0			0
$821$		−	3218.41i		−	0.136813i	−0.997658	−	0.0684064i	$-0.978209\pi$
$821$		−	3218.41i		−	0.136813i	0.997658	−	0.0684064i	$-0.0217915\pi$
$822$	2476.71	+	11263.8i	0.105091	+	0.477946i
$823$	−4720.16	+	4720.16i	−0.199920	+	0.199920i	−0.799966	−	0.600046i	$-0.795149\pi$
$823$	−4720.16	+	4720.16i	−0.199920	+	0.199920i	0.600046	+	0.799966i	$0.295149\pi$
$824$	7946.79	+	1088.18i	0.335970	+	0.0460053i
$825$		0			0
$826$	−369.454	−	236.267i	−0.0155629	−	0.00995251i
$827$	−4751.81	+	4751.81i	−0.199802	+	0.199802i	−0.799915	−	0.600113i	$-0.795122\pi$
$827$	−4751.81	+	4751.81i	−0.199802	+	0.199802i	0.600113	+	0.799915i	$0.295122\pi$
$828$	−1308.23	−	481.286i	−0.0549084	−	0.0202003i
$829$	−35341.2			−1.48064			−0.740319	−	0.672255i	$-0.765326\pi$
$829$	−35341.2			−1.48064			−0.740319	+	0.672255i	$0.765326\pi$
$830$		0			0
$831$			11498.8i			0.480011i
$832$	−16840.8	−	29880.7i	−0.701741	−	1.24510i
$833$	8987.13	+	8987.13i	0.373812	+	0.373812i
$834$	−2781.28	−	1778.64i	−0.115477	−	0.0738479i
$835$		0			0
$836$	−12514.0	−	27080.4i	−0.517710	−	1.12033i
$837$	15646.2	+	15646.2i	0.646129	+	0.646129i
$838$	12676.8	−	2787.39i	0.522569	−	0.114903i
$839$	−33758.3			−1.38911			−0.694557	−	0.719438i	$-0.744400\pi$
$839$	−33758.3			−1.38911			−0.694557	+	0.719438i	$0.744400\pi$
$840$		0			0
$841$	−19053.4			−0.781231
$842$	−16445.1	+	3615.97i	−0.673083	+	0.147998i
$843$	973.451	+	973.451i	0.0397716	+	0.0397716i
$844$	−23035.2	+	10644.7i	−0.939461	+	0.434129i
$845$		0			0
$846$	10458.2	+	6688.04i	0.425011	+	0.271796i
$847$	−4180.88	−	4180.88i	−0.169607	−	0.169607i
$848$	2706.48	+	33610.8i	0.109600	+	1.36108i
$849$			12900.8i			0.521503i
$850$		0			0
$851$	−1272.93			−0.0512756
$852$	−9091.40	+	24712.2i	−0.365571	+	0.993693i
$853$	−27284.0	+	27284.0i	−1.09518	+	1.09518i	−0.100210	+	0.994966i	$0.531951\pi$
$853$	−27284.0	+	27284.0i	−1.09518	+	1.09518i	−0.994966	+	0.100210i	$0.968049\pi$
$854$	3625.49	+	2318.51i	0.145271	+	0.0929015i
$855$		0			0
$856$	11027.9	+	1510.08i	0.440335	+	0.0602963i
$857$	−8957.01	+	8957.01i	−0.357019	+	0.357019i	−0.862713	−	0.505694i	$-0.831237\pi$
$857$	−8957.01	+	8957.01i	−0.357019	+	0.357019i	0.505694	+	0.862713i	$0.331237\pi$
$858$	7278.61	+	33102.4i	0.289613	+	1.31713i
$859$			34133.2i			1.35578i	0.735166	+	0.677888i	$0.237104\pi$
$859$			34133.2i			1.35578i	−0.735166	+	0.677888i	$0.762896\pi$
$860$		0			0
$861$		−	182.101i		−	0.00720789i
$862$	11502.8	−	2529.25i	0.454508	−	0.0999379i
$863$	−2289.06	+	2289.06i	−0.0902901	+	0.0902901i	−0.750809	−	0.660519i	$-0.770336\pi$
$863$	−2289.06	+	2289.06i	−0.0902901	+	0.0902901i	0.660519	+	0.750809i	$0.270336\pi$
$864$	22721.1	−	6948.59i	0.894663	−	0.273606i
$865$		0			0
$866$	−4363.28	+	6822.91i	−0.171213	+	0.267727i
$867$	−7088.25	+	7088.25i	−0.277658	+	0.277658i
$868$	−1074.93	+	2921.88i	−0.0420342	+	0.114257i
$869$	46864.5			1.82942
$870$		0			0
$871$		−	47984.3i		−	1.86669i
$872$	−11247.0	−	14815.9i	−0.436780	−	0.575378i
$873$	5733.38	+	5733.38i	0.222274	+	0.222274i
$874$	−845.091	+	1321.48i	−0.0327067	+	0.0511439i
$875$		0			0
$876$	−9327.12	−	20184.0i	−0.359742	−	0.778487i
$877$	−26605.5	−	26605.5i	−1.02441	−	1.02441i	−0.999695	−	0.0247110i	$-0.992133\pi$
$877$	−26605.5	−	26605.5i	−1.02441	−	1.02441i	−0.0247110	−	0.999695i	$-0.507867\pi$
$878$	−2176.58	−	9898.87i	−0.0836628	−	0.380491i
$879$	−14063.6			−0.539652
$880$		0			0
$881$	17574.1			0.672061			0.336031	−	0.941851i	$-0.390915\pi$
$881$	17574.1			0.672061			0.336031	+	0.941851i	$0.390915\pi$
$882$	−3851.76	−	17517.4i	−0.147047	−	0.668756i
$883$	−7230.39	−	7230.39i	−0.275563	−	0.275563i	0.555772	−	0.831335i	$-0.312423\pi$
$883$	−7230.39	−	7230.39i	−0.275563	−	0.275563i	−0.831335	+	0.555772i	$0.812423\pi$
$884$	8461.86	+	18311.6i	0.321949	+	0.696702i
$885$		0			0
$886$	2159.14	−	3376.27i	0.0818709	−	0.128023i
$887$	−27480.2	−	27480.2i	−1.04024	−	1.04024i	−0.999156	−	0.0410876i	$-0.986918\pi$
$887$	−27480.2	−	27480.2i	−1.04024	−	1.04024i	−0.0410876	−	0.999156i	$-0.513082\pi$
$888$	7089.27	−	5381.60i	0.267906	−	0.203372i
$889$			3108.47i			0.117272i
$890$		0			0
$891$	8155.21			0.306633
$892$	−12585.4	+	34209.6i	−0.472411	+	1.28411i
$893$	9877.67	−	9877.67i	0.370149	−	0.370149i
$894$	−9526.12	+	14896.1i	−0.356377	+	0.557271i
$895$		0			0
$896$	2228.57	+	2491.94i	0.0830928	+	0.0929127i
$897$	1260.16	−	1260.16i	0.0469070	−	0.0469070i
$898$	21771.4	−	4787.12i	0.809042	−	0.177893i
$899$		−	12313.8i		−	0.456829i
$900$		0			0
$901$		−	19831.0i		−	0.733259i
$902$	−1042.59	−	4741.58i	−0.0384859	−	0.175030i
$903$	−1355.90	+	1355.90i	−0.0499685	+	0.0499685i
$904$	−3032.04	+	22142.5i	−0.111553	+	0.814656i
$905$		0			0
$906$	17633.9	+	11276.9i	0.646631	+	0.413522i
$907$	32472.3	−	32472.3i	1.18878	−	1.18878i	0.211377	−	0.977405i	$-0.432205\pi$
$907$	32472.3	−	32472.3i	1.18878	−	1.18878i	0.977405	−	0.211377i	$-0.0677946\pi$
$908$	10582.5	−	28765.2i	0.386774	−	1.05133i
$909$	17705.8			0.646055
$910$		0			0
$911$			33425.7i			1.21564i	0.794077	+	0.607818i	$0.207955\pi$
$911$			33425.7i			1.21564i	−0.794077	+	0.607818i	$0.792045\pi$
$912$	−880.328	−	10932.5i	−0.0319634	−	0.396941i
$913$	15691.6	+	15691.6i	0.568803	+	0.568803i
$914$	24099.2	+	15411.5i	0.872135	+	0.557733i
$915$		0			0
$916$	14134.7	−	6531.72i	0.509851	−	0.235605i
$917$	3748.34	+	3748.34i	0.134985	+	0.134985i
$918$	−13647.6	+	3000.84i	−0.490671	+	0.107890i
$919$	27640.7			0.992145			0.496072	−	0.868281i	$-0.334775\pi$
$919$	27640.7			0.992145			0.496072	+	0.868281i	$0.334775\pi$
$920$		0			0
$921$	16362.4			0.585408
$922$	−16350.3	+	3595.13i	−0.584023	+	0.128416i
$923$	54380.3	+	54380.3i	1.93927	+	1.93927i
$924$	−1385.75	−	2998.78i	−0.0493374	−	0.106767i
$925$		0			0
$926$	−16340.7	−	10449.9i	−0.579901	−	0.370849i
$927$	4707.18	+	4707.18i	0.166779	+	0.166779i
$928$	−11675.3	−	6206.65i	−0.412997	−	0.219551i
$929$		−	4275.33i		−	0.150989i	−0.997146	−	0.0754946i	$-0.975946\pi$
$929$		−	4275.33i		−	0.150989i	0.997146	−	0.0754946i	$-0.0240536\pi$
$930$		0			0
$931$	−20183.0			−0.710496
$932$	12906.7	+	4748.25i	0.453618	+	0.166882i
$933$	−9162.84	+	9162.84i	−0.321520	+	0.321520i
$934$	7987.58	+	5108.08i	0.279830	+	0.178952i
$935$		0			0
$936$	3862.00	−	28203.7i	0.134865	−	0.984899i
$937$	−4338.96	+	4338.96i	−0.151278	+	0.151278i	−0.778689	−	0.627410i	$-0.784115\pi$
$937$	−4338.96	+	4338.96i	−0.151278	+	0.151278i	0.627410	+	0.778689i	$0.284115\pi$
$938$	1004.37	+	4567.78i	0.0349615	+	0.159002i
$939$		−	146.962i		−	0.00510749i
$940$		0			0
$941$		−	29214.9i		−	1.01209i	−0.862506	−	0.506047i	$-0.831106\pi$
$941$		−	29214.9i		−	1.01209i	0.862506	−	0.506047i	$-0.168894\pi$
$942$	−6149.42	+	1352.14i	−0.212695	+	0.0467678i
$943$	−180.505	+	180.505i	−0.00623335	+	0.00623335i
$944$	−3273.62	−	2785.69i	−0.112868	−	0.0960451i
$945$		0			0
$946$	−27542.2	+	43068.1i	−0.946589	+	1.48019i
$947$	−35030.7	+	35030.7i	−1.20205	+	1.20205i	−0.228512	+	0.973541i	$0.573386\pi$
$947$	−35030.7	+	35030.7i	−1.20205	+	1.20205i	−0.973541	+	0.228512i	$0.926614\pi$
$948$	16170.3	+	5948.92i	0.553996	+	0.203810i
$949$	−64940.5			−2.22135
$950$		0			0
$951$			6481.03i			0.220990i
$952$	−1188.79	−	1566.02i	−0.0404717	−	0.0533140i
$953$	−25184.3	−	25184.3i	−0.856035	−	0.856035i	0.134834	−	0.990868i	$-0.456950\pi$
$953$	−25184.3	−	25184.3i	−0.856035	−	0.856035i	−0.990868	+	0.134834i	$0.956950\pi$
$954$	−15077.3	+	23576.6i	−0.511684	+	0.800127i
$955$		0			0
$956$	29621.8	−	13688.4i	1.00213	−	0.463090i
$957$	9238.96	+	9238.96i	0.312072	+	0.312072i
$958$	7286.89	+	33140.1i	0.245750	+	1.11765i
$959$	−3283.06			−0.110548
$960$		0			0
$961$	1372.17			0.0460599
$962$	−5582.55	−	25388.9i	−0.187098	−	0.850906i
$963$	6532.25	+	6532.25i	0.218586	+	0.218586i
$964$	7994.53	−	3694.31i	0.267102	−	0.123429i
$965$		0			0
$966$	−93.5820	+	146.335i	−0.00311693	+	0.00487398i
$967$	35241.6	+	35241.6i	1.17197	+	1.17197i	0.981740	+	0.190228i	$0.0609226\pi$
$967$	35241.6	+	35241.6i	1.17197	+	1.17197i	0.190228	+	0.981740i	$0.439077\pi$
$968$	−35041.3	−	46160.5i	−1.16350	−	1.53270i
$969$			6450.36i			0.213845i
$970$		0			0
$971$	16611.5			0.549010			0.274505	−	0.961586i	$-0.411486\pi$
$971$	16611.5			0.549010			0.274505	+	0.961586i	$0.411486\pi$
$972$	29421.8	+	10824.0i	0.970888	+	0.357181i
$973$	664.537	−	664.537i	0.0218953	−	0.0218953i
$974$	−12975.6	+	20290.1i	−0.426863	+	0.667492i
$975$		0			0
$976$	32124.3	+	27336.3i	1.05356	+	0.896531i
$977$	−17592.3	+	17592.3i	−0.576076	+	0.576076i	−0.933820	−	0.357744i	$-0.883546\pi$
$977$	−17592.3	+	17592.3i	−0.576076	+	0.576076i	0.357744	+	0.933820i	$0.383546\pi$
$978$	−3556.92	+	782.102i	−0.116296	+	0.0255714i
$979$		−	31040.8i		−	1.01335i
$980$		0			0
$981$		−	15438.0i		−	0.502445i
$982$	6041.39	+	27475.6i	0.196322	+	0.892854i
$983$	−10007.4	+	10007.4i	−0.324705	+	0.324705i	−0.850569	−	0.525864i	$-0.823742\pi$
$983$	−10007.4	+	10007.4i	−0.324705	+	0.324705i	0.525864	+	0.850569i	$0.323742\pi$
$984$	242.152	−	1768.40i	0.00784504	−	0.0572912i
$985$		0			0
$986$	6551.31	+	4189.58i	0.211598	+	0.135318i
$987$	1093.81	−	1093.81i	0.0352750	−	0.0352750i
$988$	−30063.4	−	11060.1i	−0.968062	−	0.356142i
$989$	2688.03			0.0864250
$990$		0			0
$991$			54042.7i			1.73231i	0.499772	+	0.866157i	$0.333417\pi$
$991$			54042.7i			1.73231i	−0.499772	+	0.866157i	$0.666583\pi$
$992$	−14324.2	+	26945.2i	−0.458461	+	0.862411i
$993$	−6024.80	−	6024.80i	−0.192539	−	0.192539i
$994$	−6314.88	−	4038.39i	−0.201505	−	0.128863i
$995$		0			0
$996$	3422.43	+	7406.19i	0.108879	+	0.235616i
$997$	−2684.64	−	2684.64i	−0.0852791	−	0.0852791i	0.663180	−	0.748460i	$-0.269206\pi$
$997$	−2684.64	−	2684.64i	−0.0852791	−	0.0852791i	−0.748460	+	0.663180i	$0.769206\pi$
$998$	43234.3	−	9506.42i	1.37130	−	0.301523i
$999$	18007.4			0.570300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.4.k.j.43.10		32
5.2	odd	4	inner	200.4.k.j.107.1		32
5.3	odd	4		40.4.k.a.27.16	yes	32
5.4	even	2		40.4.k.a.3.7	✓	32
8.3	odd	2	inner	200.4.k.j.43.1		32
20.3	even	4		160.4.o.a.47.12		32
20.19	odd	2		160.4.o.a.143.11		32
40.3	even	4		40.4.k.a.27.7	yes	32
40.13	odd	4		160.4.o.a.47.11		32
40.19	odd	2		40.4.k.a.3.16	yes	32
40.27	even	4	inner	200.4.k.j.107.10		32
40.29	even	2		160.4.o.a.143.12		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.k.a.3.7	✓	32	5.4	even	2
40.4.k.a.3.16	yes	32	40.19	odd	2
40.4.k.a.27.7	yes	32	40.3	even	4
40.4.k.a.27.16	yes	32	5.3	odd	4
160.4.o.a.47.11		32	40.13	odd	4
160.4.o.a.47.12		32	20.3	even	4
160.4.o.a.143.11		32	20.19	odd	2
160.4.o.a.143.12		32	40.29	even	2
200.4.k.j.43.1		32	8.3	odd	2	inner
200.4.k.j.43.10		32	1.1	even	1	trivial
200.4.k.j.107.1		32	5.2	odd	4	inner
200.4.k.j.107.10		32	40.27	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	200.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.607409 + 2.76244i) q^{2} +(2.02737 + 2.02737i) q^{3} +(-7.26211 + 3.35586i) q^{4} +(-4.36904 + 6.83193i) q^{6} +(-1.63237 - 1.63237i) q^{7} +(-13.6814 - 18.0227i) q^{8} -18.7795i q^{9} +O(q^{10})\)	\(q+(0.607409 + 2.76244i) q^{2} +(2.02737 + 2.02737i) q^{3} +(-7.26211 + 3.35586i) q^{4} +(-4.36904 + 6.83193i) q^{6} +(-1.63237 - 1.63237i) q^{7} +(-13.6814 - 18.0227i) q^{8} -18.7795i q^{9} -62.3878 q^{11} +(-21.5266 - 7.91943i) q^{12} +(-47.3701 + 47.3701i) q^{13} +(3.51780 - 5.50083i) q^{14} +(41.4765 - 48.7412i) q^{16} +(-26.6151 + 26.6151i) q^{17} +(51.8773 - 11.4068i) q^{18} -59.7713i q^{19} -6.61884i q^{21} +(-37.8949 - 172.342i) q^{22} +(-6.56082 + 6.56082i) q^{23} +(8.80150 - 64.2761i) q^{24} +(-159.630 - 102.084i) q^{26} +(92.8121 - 92.8121i) q^{27} +(17.3324 + 6.37645i) q^{28} -73.0449 q^{29} +168.579i q^{31} +(159.838 + 84.9703i) q^{32} +(-126.483 - 126.483i) q^{33} +(-89.6887 - 57.3562i) q^{34} +(63.0214 + 136.379i) q^{36} +(97.0101 + 97.0101i) q^{37} +(165.114 - 36.3056i) q^{38} -192.074 q^{39} +27.5126 q^{41} +(18.2841 - 4.02034i) q^{42} +(-204.855 - 204.855i) q^{43} +(453.067 - 209.364i) q^{44} +(-22.1089 - 14.1387i) q^{46} +(165.258 + 165.258i) q^{47} +(182.905 - 14.7283i) q^{48} -337.671i q^{49} -107.917 q^{51} +(185.040 - 502.974i) q^{52} +(-372.552 + 372.552i) q^{53} +(312.762 + 200.013i) q^{54} +(-7.08666 + 51.7529i) q^{56} +(121.179 - 121.179i) q^{57} +(-44.3681 - 201.782i) q^{58} -67.1632i q^{59} +659.080i q^{61} +(-465.688 + 102.396i) q^{62} +(-30.6551 + 30.6551i) q^{63} +(-137.638 + 493.153i) q^{64} +(272.575 - 426.229i) q^{66} +(-506.483 + 506.483i) q^{67} +(103.965 - 282.598i) q^{68} -26.6024 q^{69} -1147.99i q^{71} +(-338.459 + 256.930i) q^{72} +(685.459 + 685.459i) q^{73} +(-209.060 + 326.909i) q^{74} +(200.584 + 434.066i) q^{76} +(101.840 + 101.840i) q^{77} +(-116.667 - 530.591i) q^{78} -751.180 q^{79} -130.718 q^{81} +(16.7114 + 76.0018i) q^{82} +(-251.518 - 251.518i) q^{83} +(22.2119 + 48.0667i) q^{84} +(441.468 - 690.329i) q^{86} +(-148.089 - 148.089i) q^{87} +(853.553 + 1124.40i) q^{88} +497.545i q^{89} +154.651 q^{91} +(25.6282 - 69.6625i) q^{92} +(-341.772 + 341.772i) q^{93} +(-356.135 + 556.893i) q^{94} +(151.784 + 496.316i) q^{96} +(-305.299 + 305.299i) q^{97} +(932.794 - 205.104i) q^{98} +1171.61i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 4 q^{3} - 16 q^{6} + 44 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 4 * q^3 - 16 * q^6 + 44 * q^8	\( 32 q + 2 q^{2} + 4 q^{3} - 16 q^{6} + 44 q^{8} - 8 q^{11} - 28 q^{12} + 72 q^{16} - 48 q^{17} + 278 q^{18} - 68 q^{22} - 92 q^{26} - 104 q^{27} - 620 q^{28} - 288 q^{32} + 112 q^{33} + 476 q^{36} - 636 q^{38} - 8 q^{41} - 1020 q^{42} + 868 q^{43} + 1328 q^{46} + 784 q^{48} + 1480 q^{51} + 1900 q^{52} - 2392 q^{56} - 104 q^{57} + 700 q^{58} + 2880 q^{62} - 4360 q^{66} + 1852 q^{67} - 1196 q^{68} - 5596 q^{72} + 744 q^{73} + 4312 q^{76} - 2240 q^{78} - 1240 q^{81} - 5828 q^{82} - 2676 q^{83} + 6976 q^{86} + 2864 q^{88} - 1704 q^{91} + 7500 q^{92} - 10656 q^{96} + 584 q^{97} + 3814 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 4 * q^3 - 16 * q^6 + 44 * q^8 - 8 * q^11 - 28 * q^12 + 72 * q^16 - 48 * q^17 + 278 * q^18 - 68 * q^22 - 92 * q^26 - 104 * q^27 - 620 * q^28 - 288 * q^32 + 112 * q^33 + 476 * q^36 - 636 * q^38 - 8 * q^41 - 1020 * q^42 + 868 * q^43 + 1328 * q^46 + 784 * q^48 + 1480 * q^51 + 1900 * q^52 - 2392 * q^56 - 104 * q^57 + 700 * q^58 + 2880 * q^62 - 4360 * q^66 + 1852 * q^67 - 1196 * q^68 - 5596 * q^72 + 744 * q^73 + 4312 * q^76 - 2240 * q^78 - 1240 * q^81 - 5828 * q^82 - 2676 * q^83 + 6976 * q^86 + 2864 * q^88 - 1704 * q^91 + 7500 * q^92 - 10656 * q^96 + 584 * q^97 + 3814 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more