LMFDB - Embedded newform 28.4.d.b.27.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [28,4,Mod(27,28)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("28.27"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	28.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.65205348016$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 30x^{6} + 84x^{5} + 493x^{4} - 464x^{3} - 3172x^{2} + 1072x + 8978 $ x^8 - 4x^7 - 30x^6 + 84x^5 + 493x^4 - 464x^3 - 3172x^2 + 1072*x + 8978
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			27.7
Root			$-2.56684 + 1.39897i$ of defining polynomial
Character	$\chi$	$=$	28.27
Dual form			28.4.d.b.27.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.414214 + 2.79793i) q^{2} -7.54788 q^{3} +(-7.65685 + 2.31788i) q^{4} +8.74756i q^{5} +(-3.12644 - 21.1185i) q^{6} +(13.8008 + 12.3507i) q^{7} +(-9.65685 - 20.4633i) q^{8} +29.9706 q^{9} +(-24.4751 + 3.62336i) q^{10} +0.397686i q^{11} +(57.7931 - 17.4951i) q^{12} +75.7263i q^{13} +(-28.8399 + 43.7294i) q^{14} -66.0256i q^{15} +(53.2548 - 35.4954i) q^{16} -84.4739i q^{17} +(12.4142 + 83.8556i) q^{18} -20.0536 q^{19} +(-20.2758 - 66.9788i) q^{20} +(-104.167 - 93.2214i) q^{21} +(-1.11270 + 0.164727i) q^{22} +122.382i q^{23} +(72.8888 + 154.454i) q^{24} +48.4802 q^{25} +(-211.877 + 31.3669i) q^{26} -22.4215 q^{27} +(-134.298 - 62.5788i) q^{28} -175.823 q^{29} +(184.735 - 27.3487i) q^{30} +128.092 q^{31} +(121.373 + 134.301i) q^{32} -3.00169i q^{33} +(236.352 - 34.9902i) q^{34} +(-108.038 + 120.723i) q^{35} +(-229.480 + 69.4683i) q^{36} +253.196 q^{37} +(-8.30649 - 56.1087i) q^{38} -571.574i q^{39} +(179.004 - 84.4739i) q^{40} -81.4722i q^{41} +(217.680 - 330.065i) q^{42} +69.1388i q^{43} +(-0.921790 - 3.04502i) q^{44} +262.169i q^{45} +(-342.416 + 50.6922i) q^{46} +147.923 q^{47} +(-401.961 + 267.915i) q^{48} +(37.9218 + 340.897i) q^{49} +(20.0812 + 135.644i) q^{50} +637.599i q^{51} +(-175.525 - 579.826i) q^{52} +283.921 q^{53} +(-9.28727 - 62.7337i) q^{54} -3.47878 q^{55} +(119.463 - 401.677i) q^{56} +151.362 q^{57} +(-72.8284 - 491.942i) q^{58} -632.911 q^{59} +(153.040 + 505.548i) q^{60} +3.25919i q^{61} +(53.0574 + 358.392i) q^{62} +(413.616 + 370.157i) q^{63} +(-325.490 + 395.222i) q^{64} -662.420 q^{65} +(8.39852 - 1.24334i) q^{66} -551.508i q^{67} +(195.801 + 646.804i) q^{68} -923.724i q^{69} +(-382.525 - 252.279i) q^{70} -486.278i q^{71} +(-289.421 - 613.296i) q^{72} +165.946i q^{73} +(104.877 + 708.425i) q^{74} -365.923 q^{75} +(153.548 - 46.4820i) q^{76} +(-4.91169 + 5.48837i) q^{77} +(1599.22 - 236.754i) q^{78} -279.010i q^{79} +(310.498 + 465.850i) q^{80} -639.971 q^{81} +(227.954 - 33.7469i) q^{82} +622.183 q^{83} +(1013.66 + 472.337i) q^{84} +738.940 q^{85} +(-193.446 + 28.6382i) q^{86} +1327.09 q^{87} +(8.13795 - 3.84039i) q^{88} -696.803i q^{89} +(-733.532 + 108.594i) q^{90} +(-935.271 + 1045.08i) q^{91} +(-283.667 - 937.060i) q^{92} -966.823 q^{93} +(61.2718 + 413.879i) q^{94} -175.420i q^{95} +(-916.106 - 1013.69i) q^{96} +1623.01i q^{97} +(-938.100 + 247.307i) q^{98} +11.9189i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 16 q^{4} - 32 q^{8} + 104 q^{9} - 152 q^{14} + 64 q^{16} + 88 q^{18} - 64 q^{21} + 240 q^{22} - 472 q^{25} - 48 q^{28} - 592 q^{29} + 256 q^{30} + 1152 q^{32} - 976 q^{36} + 1392 q^{37}+ \cdots - 3144 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 - 16 * q^4 - 32 * q^8 + 104 * q^9 - 152 * q^14 + 64 * q^16 + 88 * q^18 - 64 * q^21 + 240 * q^22 - 472 * q^25 - 48 * q^28 - 592 * q^29 + 256 * q^30 + 1152 * q^32 - 976 * q^36 + 1392 * q^37 - 1024 * q^42 - 1184 * q^44 - 816 * q^46 + 1480 * q^49 + 1688 * q^50 - 1168 * q^53 + 800 * q^56 - 192 * q^57 - 560 * q^58 + 2944 * q^60 - 3328 * q^64 + 448 * q^65 - 3200 * q^70 - 1184 * q^72 - 496 * q^74 + 368 * q^77 + 7680 * q^78 - 4984 * q^81 + 4480 * q^84 + 1024 * q^85 + 240 * q^86 + 3776 * q^88 - 3808 * q^92 - 2304 * q^93 - 3144 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.414214	+	2.79793i	0.146447	+	0.989219i
$2$	0.414214	+	2.79793i	0.146447	+	0.989219i
$3$	−7.54788			−1.45259			−0.726296	−	0.687383i	$-0.758760\pi$
$3$	−7.54788			−1.45259			−0.726296	+	0.687383i	$0.758760\pi$
$4$	−7.65685	+	2.31788i	−0.957107	+	0.289735i
$5$			8.74756i			0.782405i	0.920305	+	0.391203i	$0.127941\pi$
$5$			8.74756i			0.782405i	−0.920305	+	0.391203i	$0.872059\pi$
$6$	−3.12644	−	21.1185i	−0.212727	−	1.43693i
$7$	13.8008	+	12.3507i	0.745171	+	0.666874i
$7$	13.8008	+	12.3507i	0.745171	+	0.666874i
$8$	−9.65685	−	20.4633i	−0.426777	−	0.904357i
$9$	29.9706			1.11002
$10$	−24.4751	+	3.62336i	−0.773970	+	0.114581i
$11$			0.397686i			0.0109006i	0.999985	+	0.00545031i	$0.00173490\pi$
$11$			0.397686i			0.0109006i	−0.999985	+	0.00545031i	$0.998265\pi$
$12$	57.7931	−	17.4951i	1.39028	−	0.420867i
$13$			75.7263i			1.61559i	0.589462	+	0.807796i	$0.299340\pi$
$13$			75.7263i			1.61559i	−0.589462	+	0.807796i	$0.700660\pi$
$14$	−28.8399	+	43.7294i	−0.550556	+	0.834798i
$15$		−	66.0256i		−	1.13652i
$16$	53.2548	−	35.4954i	0.832107	−	0.554615i
$17$		−	84.4739i		−	1.20517i	−0.798054	−	0.602586i	$-0.794137\pi$
$17$		−	84.4739i		−	1.20517i	0.798054	−	0.602586i	$-0.205863\pi$
$18$	12.4142	+	83.8556i	0.162559	+	1.09805i
$19$	−20.0536			−0.242138			−0.121069	−	0.992644i	$-0.538632\pi$
$19$	−20.0536			−0.242138			−0.121069	+	0.992644i	$0.538632\pi$
$20$	−20.2758	−	66.9788i	−0.226691	−	0.748845i
$21$	−104.167	−	93.2214i	−1.08243	−	0.968695i
$22$	−1.11270	+	0.164727i	−0.0107831	+	0.00159636i
$23$			122.382i			1.10950i	0.832019	+	0.554748i	$0.187185\pi$
$23$			122.382i			1.10950i	−0.832019	+	0.554748i	$0.812815\pi$
$24$	72.8888	+	154.454i	0.619932	+	1.31366i
$25$	48.4802			0.387842
$26$	−211.877	+	31.3669i	−1.59817	+	0.236598i
$27$	−22.4215			−0.159815
$28$	−134.298	−	62.5788i	−0.906425	−	0.422367i
$29$	−175.823			−1.12585			−0.562924	−	0.826509i	$-0.690324\pi$
$29$	−175.823			−1.12585			−0.562924	+	0.826509i	$0.690324\pi$
$30$	184.735	−	27.3487i	1.12426	−	0.166439i
$31$	128.092			0.742128			0.371064	−	0.928607i	$-0.378993\pi$
$31$	128.092			0.742128			0.371064	+	0.928607i	$0.378993\pi$
$32$	121.373	+	134.301i	0.670495	+	0.741914i
$33$		−	3.00169i		−	0.0158341i
$34$	236.352	−	34.9902i	1.19218	−	0.176493i
$35$	−108.038	+	120.723i	−0.521765	+	0.583026i
$36$	−229.480	+	69.4683i	−1.06241	+	0.321612i
$37$	253.196			1.12500			0.562502	−	0.826796i	$-0.309839\pi$
$37$	253.196			1.12500			0.562502	+	0.826796i	$0.309839\pi$
$38$	−8.30649	−	56.1087i	−0.0354603	−	0.239527i
$39$		−	571.574i		−	2.34680i
$40$	179.004	−	84.4739i	0.707574	−	0.333912i
$41$		−	81.4722i		−	0.310337i	−0.987888	−	0.155169i	$-0.950408\pi$
$41$		−	81.4722i		−	0.310337i	0.987888	−	0.155169i	$-0.0495921\pi$
$42$	217.680	−	330.065i	0.799733	−	1.21262i
$43$			69.1388i			0.245199i	0.992456	+	0.122600i	$0.0391231\pi$
$43$			69.1388i			0.245199i	−0.992456	+	0.122600i	$0.960877\pi$
$44$	−0.921790	−	3.04502i	−0.00315830	−	0.0104331i
$45$			262.169i			0.868486i
$46$	−342.416	+	50.6922i	−1.09753	+	0.162482i
$47$	147.923			0.459081			0.229541	−	0.973299i	$-0.426278\pi$
$47$	147.923			0.459081			0.229541	+	0.973299i	$0.426278\pi$
$48$	−401.961	+	267.915i	−1.20871	+	0.805629i
$49$	37.9218	+	340.897i	0.110559	+	0.993870i
$50$	20.0812	+	135.644i	0.0567981	+	0.383660i
$51$			637.599i			1.75062i
$52$	−175.525	−	579.826i	−0.468094	−	1.54629i
$53$	283.921			0.735840			0.367920	−	0.929857i	$-0.380070\pi$
$53$	283.921			0.735840			0.367920	+	0.929857i	$0.380070\pi$
$54$	−9.28727	−	62.7337i	−0.0234044	−	0.158092i
$55$	−3.47878			−0.00852870
$56$	119.463	−	401.677i	0.285070	−	0.958507i
$57$	151.362			0.351727
$58$	−72.8284	−	491.942i	−0.164877	−	1.11371i
$59$	−632.911			−1.39658			−0.698288	−	0.715816i	$-0.746055\pi$
$59$	−632.911			−1.39658			−0.698288	+	0.715816i	$0.746055\pi$
$60$	153.040	+	505.548i	0.329289	+	1.08777i
$61$			3.25919i			0.00684093i	0.999994	+	0.00342046i	$0.00108877\pi$
$61$			3.25919i			0.00684093i	−0.999994	+	0.00342046i	$0.998911\pi$
$62$	53.0574	+	358.392i	0.108682	+	0.734127i
$63$	413.616	+	370.157i	0.827155	+	0.740244i
$64$	−325.490	+	395.222i	−0.635723	+	0.771917i
$65$	−662.420			−1.26405
$66$	8.39852	−	1.24334i	0.0156634	−	0.00231886i
$67$		−	551.508i		−	1.00563i	−0.864393	−	0.502817i	$-0.832297\pi$
$67$		−	551.508i		−	1.00563i	0.864393	−	0.502817i	$-0.167703\pi$
$68$	195.801	+	646.804i	0.349181	+	1.15348i
$69$		−	923.724i		−	1.61164i
$70$	−382.525	−	252.279i	−0.653151	−	0.430758i
$71$		−	486.278i		−	0.812825i	−0.913690	−	0.406412i	$-0.866780\pi$
$71$		−	486.278i		−	0.812825i	0.913690	−	0.406412i	$-0.133220\pi$
$72$	−289.421	−	613.296i	−0.473731	−	1.00386i
$73$			165.946i			0.266062i	0.991112	+	0.133031i	$0.0424710\pi$
$73$			165.946i			0.266062i	−0.991112	+	0.133031i	$0.957529\pi$
$74$	104.877	+	708.425i	0.164753	+	1.11288i
$75$	−365.923			−0.563376
$76$	153.548	−	46.4820i	0.231752	−	0.0701559i
$77$	−4.91169	+	5.48837i	−0.00726934	+	0.00812282i
$78$	1599.22	−	236.754i	2.32149	−	0.343680i
$79$		−	279.010i		−	0.397355i	−0.980065	−	0.198677i	$-0.936335\pi$
$79$		−	279.010i		−	0.397355i	0.980065	−	0.198677i	$-0.0636646\pi$
$80$	310.498	+	465.850i	0.433934	+	0.651045i
$81$	−639.971			−0.877875
$82$	227.954	−	33.7469i	0.306991	−	0.0454478i
$83$	622.183			0.822813			0.411406	−	0.911452i	$-0.365038\pi$
$83$	622.183			0.822813			0.411406	+	0.911452i	$0.365038\pi$
$84$	1013.66	+	472.337i	1.31666	+	0.613526i
$85$	738.940			0.942933
$86$	−193.446	+	28.6382i	−0.242556	+	0.0359086i
$87$	1327.09			1.63540
$88$	8.13795	−	3.84039i	0.00985805	−	0.00465213i
$89$		−	696.803i		−	0.829898i	−0.909845	−	0.414949i	$-0.863799\pi$
$89$		−	696.803i		−	0.829898i	0.909845	−	0.414949i	$-0.136201\pi$
$90$	−733.532	+	108.594i	−0.859123	+	0.127187i
$91$	−935.271	+	1045.08i	−1.07740	+	1.20389i
$92$	−283.667	−	937.060i	−0.321460	−	1.06191i
$93$	−966.823			−1.07801
$94$	61.2718	+	413.879i	0.0672309	+	0.454132i
$95$		−	175.420i		−	0.189450i
$96$	−916.106	−	1013.69i	−0.973955	−	1.07770i
$97$			1623.01i			1.69889i	0.527679	+	0.849444i	$0.323062\pi$
$97$			1623.01i			1.69889i	−0.527679	+	0.849444i	$0.676938\pi$
$98$	−938.100	+	247.307i	−0.966963	+	0.254916i
$99$			11.9189i			0.0120999i
$100$	−371.206	+	112.372i	−0.371206	+	0.112372i
$101$		−	774.501i		−	0.763027i	−0.924363	−	0.381513i	$-0.875403\pi$
$101$		−	774.501i		−	0.763027i	0.924363	−	0.381513i	$-0.124597\pi$
$102$	−1783.96	+	264.102i	−1.73175	+	0.256373i
$103$	28.8584			0.0276068			0.0138034	−	0.999905i	$-0.495606\pi$
$103$	28.8584			0.0276068			0.0138034	+	0.999905i	$0.495606\pi$
$104$	1549.61	−	731.278i	1.46107	−	0.689497i
$105$	815.460	−	911.203i	0.757912	−	0.846898i
$106$	117.604	+	794.392i	0.107761	+	0.727907i
$107$			51.9136i			0.0469035i	0.999725	+	0.0234517i	$0.00746561\pi$
$107$			51.9136i			0.0469035i	−0.999725	+	0.0234517i	$0.992534\pi$
$108$	171.678	−	51.9703i	0.152960	−	0.0463042i
$109$	132.197			0.116167			0.0580833	−	0.998312i	$-0.481501\pi$
$109$	132.197			0.116167			0.0580833	+	0.998312i	$0.481501\pi$
$110$	−1.44096	−	9.73339i	−0.00124900	−	0.00843675i
$111$	−1911.09			−1.63417
$112$	1173.35	+	167.870i	0.989920	+	0.141627i
$113$	318.049			0.264774			0.132387	−	0.991198i	$-0.457736\pi$
$113$	318.049			0.264774			0.132387	+	0.991198i	$0.457736\pi$
$114$	62.6964	+	423.502i	0.0515093	+	0.347935i
$115$	−1070.54			−0.868075
$116$	1346.25	−	407.538i	1.07756	−	0.326198i
$117$			2269.56i			1.79334i
$118$	−262.160	−	1770.84i	−0.204524	−	1.38152i
$119$	1043.31	−	1165.80i	0.803698	−	0.898059i
$120$	−1351.10	+	637.599i	−1.02782	+	0.485038i
$121$	1330.84			0.999881
$122$	−9.11900	+	1.35000i	−0.00676717	+	0.00100183i
$123$			614.943i			0.450793i
$124$	−980.781	+	296.902i	−0.710296	+	0.215021i
$125$			1517.53i			1.08585i
$126$	−864.348	+	1310.59i	−0.611129	+	0.926643i
$127$			845.289i			0.590608i	0.955403	+	0.295304i	$0.0954209\pi$
$127$			845.289i			0.590608i	−0.955403	+	0.295304i	$0.904579\pi$
$128$	−1240.63	−	746.994i	−0.856694	−	0.515825i
$129$		−	521.852i		−	0.356174i
$130$	−274.384	−	1853.41i	−0.185116	−	1.25042i
$131$	1464.88			0.977001			0.488501	−	0.872564i	$-0.337544\pi$
$131$	1464.88			0.977001			0.488501	+	0.872564i	$0.337544\pi$
$132$	6.95756	+	22.9835i	0.00458771	+	0.0151550i
$133$	−276.755	−	247.676i	−0.180434	−	0.161475i
$134$	1543.08	−	228.442i	0.994791	−	0.147272i
$135$		−	196.133i		−	0.125040i
$136$	−1728.61	+	815.752i	−1.08991	+	0.514339i
$137$	747.803			0.466344			0.233172	−	0.972436i	$-0.425089\pi$
$137$	747.803			0.466344			0.233172	+	0.972436i	$0.425089\pi$
$138$	2584.52	−	382.619i	1.59427	−	0.236020i
$139$	2129.17			1.29924			0.649618	−	0.760261i	$-0.274929\pi$
$139$	2129.17			1.29924			0.649618	+	0.760261i	$0.274929\pi$
$140$	547.411	−	1174.78i	0.330462	−	0.709192i
$141$	−1116.51			−0.666858
$142$	1360.57	−	201.423i	0.804061	−	0.119035i
$143$	−30.1153			−0.0176110
$144$	1596.08	−	1063.82i	0.923656	−	0.615635i
$145$		−	1538.03i		−	0.880869i
$146$	−464.306	+	68.7371i	−0.263193	+	0.0389639i
$147$	−286.229	−	2573.05i	−0.160597	−	1.44369i
$148$	−1938.68	+	586.879i	−1.07675	+	0.325954i
$149$	−843.177			−0.463596			−0.231798	−	0.972764i	$-0.574461\pi$
$149$	−843.177			−0.463596			−0.231798	+	0.972764i	$0.574461\pi$
$150$	−151.570	−	1023.83i	−0.0825044	−	0.557302i
$151$			2088.40i			1.12551i	0.826625	+	0.562753i	$0.190258\pi$
$151$			2088.40i			1.12551i	−0.826625	+	0.562753i	$0.809742\pi$
$152$	193.655	+	410.363i	0.103339	+	0.218979i
$153$		−	2531.73i		−	1.33777i
$154$	−17.3906	−	11.4692i	−0.00909982	−	0.00600140i
$155$			1120.49i			0.580645i
$156$	1324.84	+	4376.46i	0.679950	+	2.24613i
$157$			168.690i			0.0857513i	0.999080	+	0.0428756i	$0.0136519\pi$
$157$			168.690i			0.0857513i	−0.999080	+	0.0428756i	$0.986348\pi$
$158$	780.650	−	115.570i	0.393071	−	0.0581913i
$159$	−2143.00			−1.06888
$160$	−1174.80	+	1061.71i	−0.580477	+	0.524599i
$161$	−1511.50	+	1688.96i	−0.739893	+	0.826763i
$162$	−265.084	−	1790.59i	−0.128562	−	0.868410i
$163$		−	2882.96i		−	1.38534i	−0.721254	−	0.692670i	$-0.756434\pi$
$163$		−	2882.96i		−	1.38534i	0.721254	−	0.692670i	$-0.243566\pi$
$164$	188.843	+	623.821i	0.0899156	+	0.297026i
$165$	26.2574			0.0123887
$166$	257.717	+	1740.83i	0.120498	+	0.813942i
$167$	−1988.79			−0.921542			−0.460771	−	0.887519i	$-0.652427\pi$
$167$	−1988.79			−0.921542			−0.460771	+	0.887519i	$0.652427\pi$
$168$	−901.694	+	3031.81i	−0.414091	+	1.39232i
$169$	−3537.48			−1.61014
$170$	306.079	+	2067.51i	0.138089	+	0.932767i
$171$	−601.019			−0.268778
$172$	−160.256	−	529.386i	−0.0710429	−	0.234682i
$173$		−	2516.46i		−	1.10591i	−0.833210	−	0.552957i	$-0.813499\pi$
$173$		−	2516.46i		−	1.10591i	0.833210	−	0.552957i	$-0.186501\pi$
$174$	549.701	+	3713.12i	0.239498	+	1.61776i
$175$	669.064	+	598.763i	0.289008	+	0.258641i
$176$	14.1160	+	21.1787i	0.00604565	+	0.00907048i
$177$	4777.14			2.02866
$178$	1949.61	−	288.625i	0.820951	−	0.121536i
$179$			2602.74i			1.08681i	0.839472	+	0.543403i	$0.182864\pi$
$179$			2602.74i			1.08681i	−0.839472	+	0.543403i	$0.817136\pi$
$180$	−607.678	−	2007.39i	−0.251631	−	0.831234i
$181$		−	2374.53i		−	0.975125i	−0.873088	−	0.487562i	$-0.837886\pi$
$181$		−	2374.53i		−	0.975125i	0.873088	−	0.487562i	$-0.162114\pi$
$182$	−3311.47	−	2183.94i	−1.34869	−	0.889474i
$183$		−	24.6000i		−	0.00993707i
$184$	2504.33	−	1181.82i	1.00338	−	0.473507i
$185$			2214.85i			0.880209i
$186$	−400.471	−	2705.10i	−0.157871	−	1.06639i
$187$	33.5941			0.0131371
$188$	−1132.63	+	342.869i	−0.439390	+	0.133012i
$189$	−309.433	−	276.920i	−0.119090	−	0.106577i
$190$	490.814	−	72.6615i	0.187407	−	0.0277443i
$191$			322.049i			0.122004i	0.998138	+	0.0610018i	$0.0194295\pi$
$191$			322.049i			0.122004i	−0.998138	+	0.0610018i	$0.980570\pi$
$192$	2456.76	−	2983.09i	0.923446	−	1.12128i
$193$	−3949.91			−1.47316			−0.736582	−	0.676349i	$-0.763561\pi$
$193$	−3949.91			−1.47316			−0.736582	+	0.676349i	$0.763561\pi$
$194$	−4541.08	+	672.274i	−1.68057	+	0.248796i
$195$	4999.87			1.83615
$196$	−1080.52	−	2522.30i	−0.393776	−	0.919206i
$197$	2712.37			0.980957			0.490478	−	0.871453i	$-0.336822\pi$
$197$	2712.37			0.980957			0.490478	+	0.871453i	$0.336822\pi$
$198$	−33.3482	+	4.93696i	−0.0119695	+	0.00177199i
$199$	2828.98			1.00774			0.503872	−	0.863779i	$-0.331908\pi$
$199$	2828.98			1.00774			0.503872	+	0.863779i	$0.331908\pi$
$200$	−468.167	−	992.064i	−0.165522	−	0.350748i
$201$			4162.72i			1.46077i
$202$	2167.00	−	320.809i	0.754800	−	0.111743i
$203$	−2426.50	−	2171.54i	−0.838949	−	0.750798i
$204$	−1477.88	−	4882.00i	−0.507217	−	1.67553i
$205$	712.683			0.242809
$206$	11.9535	+	80.7439i	0.00404293	+	0.0273092i
$207$			3667.85i			1.23156i
$208$	2687.94	+	4032.79i	0.896033	+	1.34435i
$209$		−	7.97505i		−	0.00263945i
$210$	2887.26	+	1904.17i	0.948761	+	0.625715i
$211$		−	4950.07i		−	1.61506i	−0.589828	−	0.807529i	$-0.700804\pi$
$211$		−	4950.07i		−	1.61506i	0.589828	−	0.807529i	$-0.299196\pi$
$212$	−2173.94	+	658.096i	−0.704278	+	0.213199i
$213$			3670.37i			1.18070i
$214$	−145.251	+	21.5033i	−0.0463978	+	0.00686886i
$215$	−604.796			−0.191845
$216$	216.521	+	458.816i	0.0682054	+	0.144530i
$217$	1767.76	+	1582.02i	0.553012	+	0.494906i
$218$	54.7577	+	369.878i	0.0170122	+	0.114914i
$219$		−	1252.54i		−	0.386479i
$220$	26.6365	−	8.06341i	0.00816288	−	0.00247107i
$221$	6396.90			1.94707
$222$	−791.601	−	5347.11i	−0.239319	−	1.61655i
$223$	−5958.68			−1.78934			−0.894669	−	0.446729i	$-0.852589\pi$
$223$	−5958.68			−1.78934			−0.894669	+	0.446729i	$0.852589\pi$
$224$	16.3288	+	3352.49i	0.00487059	+	0.999988i
$225$	1452.98			0.430513
$226$	131.740	+	889.879i	0.0387753	+	0.261920i
$227$	−817.324			−0.238977			−0.119488	−	0.992836i	$-0.538125\pi$
$227$	−817.324			−0.238977			−0.119488	+	0.992836i	$0.538125\pi$
$228$	−1158.96	+	350.841i	−0.336640	+	0.101908i
$229$		−	3095.86i		−	0.893364i	−0.894693	−	0.446682i	$-0.852606\pi$
$229$		−	3095.86i		−	0.893364i	0.894693	−	0.446682i	$-0.147394\pi$
$230$	−443.433	−	2995.31i	−0.127127	−	0.858716i
$231$	37.0729	−	41.4256i	0.0105594	−	0.0117991i
$232$	1697.90	+	3597.92i	0.480486	+	1.01817i
$233$	−2649.92			−0.745072			−0.372536	−	0.928018i	$-0.621512\pi$
$233$	−2649.92			−0.745072			−0.372536	+	0.928018i	$0.621512\pi$
$234$	−6350.08	+	940.083i	−1.77401	+	0.262629i
$235$			1293.97i			0.359188i
$236$	4846.11	−	1467.01i	1.33667	−	0.404638i
$237$			2105.93i			0.577194i
$238$	3693.99	+	2436.22i	1.00608	+	0.663515i
$239$			4292.34i			1.16171i	0.814007	+	0.580855i	$0.197282\pi$
$239$			4292.34i			1.16171i	−0.814007	+	0.580855i	$0.802718\pi$
$240$	−2343.60	−	3516.18i	−0.630329	−	0.945702i
$241$		−	5048.97i		−	1.34951i	−0.738041	−	0.674756i	$-0.764249\pi$
$241$		−	5048.97i		−	1.34951i	0.738041	−	0.674756i	$-0.235751\pi$
$242$	551.253	+	3723.61i	0.146429	+	0.989101i
$243$	5435.80			1.43501
$244$	−7.55443	−	24.9552i	−0.00198206	−	0.00654750i
$245$	−2982.02	+	331.723i	−0.777609	+	0.0865021i
$246$	−1720.57	+	254.718i	−0.445933	+	0.0660171i
$247$		−	1518.59i		−	0.391196i
$248$	−1236.96	−	2621.18i	−0.316723	−	0.671149i
$249$	−4696.17			−1.19521
$250$	−4245.94	+	628.581i	−1.07415	+	0.159020i
$251$	−478.767			−0.120396			−0.0601982	−	0.998186i	$-0.519173\pi$
$251$	−478.767			−0.120396			−0.0601982	+	0.998186i	$0.519173\pi$
$252$	−4024.98	−	1875.52i	−1.00615	−	0.468836i
$253$	−48.6696			−0.0120942
$254$	−2365.06	+	350.130i	−0.584241	+	0.0864926i
$255$	−5577.44			−1.36970
$256$	1576.15	−	3780.60i	0.384803	−	0.922999i
$257$			2082.43i			0.505442i	0.967539	+	0.252721i	$0.0813255\pi$
$257$			2082.43i			0.505442i	−0.967539	+	0.252721i	$0.918674\pi$
$258$	1460.11	−	216.158i	0.352334	−	0.0521605i
$259$	3494.30	+	3127.14i	0.838320	+	0.750236i
$260$	5072.06	−	1535.41i	1.20983	−	0.366240i
$261$	−5269.53			−1.24971
$262$	606.773	+	4098.64i	0.143079	+	0.966468i
$263$		−	4105.49i		−	0.962568i	−0.876565	−	0.481284i	$-0.840171\pi$
$263$		−	4105.49i		−	0.962568i	0.876565	−	0.481284i	$-0.159829\pi$
$264$	−61.4243	+	28.9869i	−0.0143197	+	0.00675764i
$265$			2483.61i			0.575725i
$266$	578.344	−	876.933i	0.133310	−	0.202136i
$267$			5259.39i			1.20550i
$268$	1278.33	+	4222.82i	0.291368	+	0.962498i
$269$		−	6020.46i		−	1.36459i	−0.731078	−	0.682294i	$-0.760983\pi$
$269$		−	6020.46i		−	1.36459i	0.731078	−	0.682294i	$-0.239017\pi$
$270$	548.767	−	81.2410i	0.123692	−	0.0183117i
$271$	−108.476			−0.0243153			−0.0121577	−	0.999926i	$-0.503870\pi$
$271$	−108.476			−0.0243153			−0.0121577	+	0.999926i	$0.503870\pi$
$272$	−2998.43	−	4498.64i	−0.668407	−	1.00283i
$273$	7059.32	−	7888.15i	1.56502	−	1.74876i
$274$	309.750	+	2092.30i	0.0682945	+	0.461316i
$275$			19.2799i			0.00422772i
$276$	2141.09	+	7072.82i	0.466950	+	1.54251i
$277$	−1079.19			−0.234088			−0.117044	−	0.993127i	$-0.537342\pi$
$277$	−1079.19			−0.234088			−0.117044	+	0.993127i	$0.537342\pi$
$278$	881.931	+	5957.27i	0.190269	+	1.28523i
$279$	3838.98			0.823778
$280$	3513.69	+	1045.01i	0.749941	+	0.223041i
$281$	482.626			0.102459			0.0512296	−	0.998687i	$-0.483686\pi$
$281$	482.626			0.102459			0.0512296	+	0.998687i	$0.483686\pi$
$282$	−462.473	−	3123.91i	−0.0976590	−	0.659668i
$283$	2476.45			0.520175			0.260088	−	0.965585i	$-0.416249\pi$
$283$	2476.45			0.520175			0.260088	+	0.965585i	$0.416249\pi$
$284$	1127.14	+	3723.36i	0.235504	+	0.777960i
$285$			1324.05i			0.275193i
$286$	−12.4742	−	84.2606i	−0.00257907	−	0.0174211i
$287$	1006.24	−	1124.38i	0.206956	−	0.231254i
$288$	3637.60	+	4025.07i	0.744264	+	0.823540i
$289$	−2222.84			−0.452440
$290$	4303.29	−	637.071i	0.871372	−	0.129000i
$291$		−	12250.3i		−	2.46779i
$292$	−384.644	−	1270.63i	−0.0770876	−	0.254650i
$293$			4641.77i			0.925513i	0.886485	+	0.462757i	$0.153140\pi$
$293$			4641.77i			0.925513i	−0.886485	+	0.462757i	$0.846860\pi$
$294$	7080.67	−	1866.64i	1.40460	−	0.370289i
$295$		−	5536.43i		−	1.09269i
$296$	−2445.08	−	5181.22i	−0.480126	−	1.01741i
$297$		−	8.91670i		−	0.00174209i
$298$	−349.256	−	2359.15i	−0.0678921	−	0.458598i
$299$	−9267.53			−1.79249
$300$	2801.82	−	848.167i	0.539211	−	0.163230i
$301$	−853.911	+	954.168i	−0.163517	+	0.182715i
$302$	−5843.20	+	865.043i	−1.11337	+	0.164827i
$303$			5845.84i			1.10837i
$304$	−1067.95	+	711.811i	−0.201485	+	0.134293i
$305$	−28.5100			−0.00535238
$306$	7083.61	−	1048.68i	1.32334	−	0.195911i
$307$	−1544.80			−0.287187			−0.143594	−	0.989637i	$-0.545866\pi$
$307$	−1544.80			−0.287187			−0.143594	+	0.989637i	$0.545866\pi$
$308$	24.8867	−	53.4083i	0.00460406	−	0.00988059i
$309$	−217.820			−0.0401014
$310$	−3135.06	+	464.123i	−0.574385	+	0.0850335i
$311$	8897.39			1.62227			0.811133	−	0.584862i	$-0.198851\pi$
$311$	8897.39			1.62227			0.811133	+	0.584862i	$0.198851\pi$
$312$	−11696.3	+	5519.60i	−2.12234	+	1.00156i
$313$		−	1960.82i		−	0.354096i	−0.984202	−	0.177048i	$-0.943345\pi$
$313$		−	1960.82i		−	0.354096i	0.984202	−	0.177048i	$-0.0566548\pi$
$314$	−471.984	+	69.8738i	−0.0848268	+	0.0125580i
$315$	−3237.97	+	3618.13i	−0.579171	+	0.647171i
$316$	646.712	+	2136.34i	0.115128	+	0.380311i
$317$	−4234.84			−0.750322			−0.375161	−	0.926960i	$-0.622413\pi$
$317$	−4234.84			−0.750322			−0.375161	+	0.926960i	$0.622413\pi$
$318$	−887.661	−	5995.98i	−0.156533	−	1.05735i
$319$		−	69.9225i		−	0.0122724i
$320$	−3457.22	−	2847.25i	−0.603952	−	0.497393i
$321$		−	391.838i		−	0.0681316i
$322$	−5351.69	−	3529.48i	−0.926205	−	0.610839i
$323$			1694.01i			0.291818i
$324$	4900.16	−	1483.38i	0.840220	−	0.254351i
$325$			3671.23i			0.626594i
$326$	8066.32	−	1194.16i	1.37040	−	0.202878i
$327$	−997.806			−0.168743
$328$	−1667.19	+	786.765i	−0.280656	+	0.132445i
$329$	2041.45	+	1826.95i	0.342094	+	0.306149i
$330$	10.8762	+	73.4665i	0.00181429	+	0.0122551i
$331$			9859.53i			1.63725i	0.574330	+	0.818624i	$0.305262\pi$
$331$			9859.53i			1.63725i	−0.574330	+	0.818624i	$0.694738\pi$
$332$	−4763.97	+	1442.15i	−0.787520	+	0.238398i
$333$	7588.43			1.24878
$334$	−823.786	−	5564.51i	−0.134957	−	0.911607i
$335$	4824.35			0.786813
$336$	−8856.30	−	1267.06i	−1.43795	−	0.205726i
$337$	6869.41			1.11039			0.555194	−	0.831721i	$-0.312644\pi$
$337$	6869.41			1.11039			0.555194	+	0.831721i	$0.312644\pi$
$338$	−1465.27	−	9897.62i	−0.235800	−	1.59278i
$339$	−2400.60			−0.384609
$340$	−5657.96	+	1712.78i	−0.902488	+	0.273201i
$341$			50.9403i			0.00808966i
$342$	−248.950	−	1681.61i	−0.0393616	−	0.265880i
$343$	−3686.96	+	5173.00i	−0.580400	+	0.814332i
$344$	1414.81	−	667.663i	0.221748	−	0.104645i
$345$	8080.33			1.26096
$346$	7040.90	−	1042.35i	1.09399	−	0.161957i
$347$			257.299i			0.0398055i	0.999802	+	0.0199028i	$0.00633567\pi$
$347$			257.299i			0.0398055i	−0.999802	+	0.0199028i	$0.993664\pi$
$348$	−10161.4	+	3076.05i	−1.56525	+	0.473832i
$349$		−	2840.72i		−	0.435703i	−0.975982	−	0.217851i	$-0.930095\pi$
$349$		−	2840.72i		−	0.435703i	0.975982	−	0.217851i	$-0.0699048\pi$
$350$	−1398.16	+	2120.01i	−0.213529	+	0.323770i
$351$		−	1697.90i		−	0.258196i
$352$	−53.4095	+	48.2682i	−0.00808732	+	0.00730881i
$353$			11322.4i			1.70717i	0.520953	+	0.853585i	$0.325577\pi$
$353$			11322.4i			1.70717i	−0.520953	+	0.853585i	$0.674423\pi$
$354$	1978.76	+	13366.1i	0.297090	+	2.00678i
$355$	4253.74			0.635959
$356$	1615.11	+	5335.32i	0.240451	+	0.794301i
$357$	−7874.78	+	8799.35i	−1.16744	+	1.30451i
$358$	−7282.30	+	1078.09i	−1.07509	+	0.159159i
$359$		−	5421.36i		−	0.797014i	−0.917165	−	0.398507i	$-0.869528\pi$
$359$		−	5421.36i		−	0.797014i	0.917165	−	0.398507i	$-0.130472\pi$
$360$	5364.84	−	2531.73i	0.785422	−	0.370650i
$361$	−6456.85			−0.941369
$362$	6643.78	−	983.563i	0.964611	−	0.142804i
$363$	−10045.0			−1.45242
$364$	4738.86	−	10169.9i	0.682373	−	1.46441i
$365$	−1451.62			−0.208168
$366$	68.8291	−	10.1897i	0.00982994	−	0.00145525i
$367$	−10941.3			−1.55622			−0.778109	−	0.628129i	$-0.783821\pi$
$367$	−10941.3			−1.55622			−0.778109	+	0.628129i	$0.783821\pi$
$368$	4343.99	+	6517.43i	0.615343	+	0.923218i
$369$		−	2441.77i		−	0.344481i
$370$	−6196.99	+	917.419i	−0.870719	+	0.128904i
$371$	3918.32	+	3506.61i	0.548327	+	0.490713i
$372$	7402.82	−	2240.98i	1.03177	−	0.312337i
$373$	389.936			0.0541290			0.0270645	−	0.999634i	$-0.491384\pi$
$373$	389.936			0.0541290			0.0270645	+	0.999634i	$0.491384\pi$
$374$	13.9151	+	93.9940i	0.00192389	+	0.0129955i
$375$		−	11454.1i		−	1.57730i
$376$	−1428.47	−	3026.99i	−0.195925	−	0.415174i
$377$		−	13314.5i		−	1.81891i
$378$	646.633	−	980.477i	0.0879873	−	0.133414i
$379$		−	12927.3i		−	1.75207i	−0.482252	−	0.876033i	$-0.660181\pi$
$379$		−	12927.3i		−	1.75207i	0.482252	−	0.876033i	$-0.339819\pi$
$380$	406.604	+	1343.17i	0.0548903	+	0.181324i
$381$		−	6380.14i		−	0.857912i
$382$	−901.072	+	133.397i	−0.120688	+	0.0178670i
$383$	12981.5			1.73192			0.865960	−	0.500113i	$-0.166708\pi$
$383$	12981.5			1.73192			0.865960	+	0.500113i	$0.166708\pi$
$384$	9364.10	+	5638.22i	1.24443	+	0.749282i
$385$	−48.0098	−	42.9653i	−0.00635534	−	0.00568757i
$386$	−1636.11	−	11051.6i	−0.215740	−	1.45728i
$387$			2072.13i			0.272176i
$388$	−3761.96	−	12427.2i	−0.492228	−	1.62602i
$389$	12562.9			1.63745			0.818723	−	0.574188i	$-0.194682\pi$
$389$	12562.9			1.63745			0.818723	+	0.574188i	$0.194682\pi$
$390$	2071.02	+	13989.3i	0.268897	+	1.81635i
$391$	10338.1			1.33713
$392$	6609.67	−	4068.00i	0.851629	−	0.524145i
$393$	−11056.7			−1.41918
$394$	1123.50	+	7589.03i	0.143658	+	0.970381i
$395$	2440.65			0.310893
$396$	−27.6266	−	91.2611i	−0.00350577	−	0.0115809i
$397$			5874.41i			0.742640i	0.928505	+	0.371320i	$0.121095\pi$
$397$			5874.41i			0.742640i	−0.928505	+	0.371320i	$0.878905\pi$
$398$	1171.80	+	7915.29i	0.147581	+	0.996878i
$399$	2088.92	+	1869.43i	0.262097	+	0.234558i
$400$	2581.81	−	1720.82i	0.322726	−	0.215103i
$401$	4771.54			0.594213			0.297106	−	0.954844i	$-0.403978\pi$
$401$	4771.54			0.594213			0.297106	+	0.954844i	$0.403978\pi$
$402$	−11647.0	+	1724.25i	−1.44502	+	0.213925i
$403$			9699.93i			1.19898i
$404$	1795.20	+	5930.24i	0.221076	+	0.730298i
$405$		−	5598.18i		−	0.686854i
$406$	5070.73	−	7688.65i	0.619842	−	0.939856i
$407$			100.692i			0.0122632i
$408$	13047.4	−	6157.20i	1.58319	−	0.747125i
$409$			2248.81i			0.271874i	0.990718	+	0.135937i	$0.0434044\pi$
$409$			2248.81i			0.271874i	−0.990718	+	0.135937i	$0.956596\pi$
$410$	295.203	+	1994.04i	0.0355586	+	0.240192i
$411$	−5644.33			−0.677407
$412$	−220.965	+	66.8904i	−0.0264227	+	0.00799868i
$413$	−8734.66	−	7816.88i	−1.04069	−	0.931340i
$414$	−10262.4	+	1519.28i	−1.21828	+	0.180358i
$415$			5442.58i			0.643773i
$416$	−10170.1	+	9191.10i	−1.19863	+	1.08325i
$417$	−16070.7			−1.88726
$418$	22.3136	−	3.30337i	0.00261099	−	0.000386539i
$419$	−10323.4			−1.20366			−0.601829	−	0.798625i	$-0.705561\pi$
$419$	−10323.4			−1.20366			−0.601829	+	0.798625i	$0.705561\pi$
$420$	−4131.80	+	8867.09i	−0.480026	+	1.03017i
$421$	3245.09			0.375668			0.187834	−	0.982201i	$-0.439853\pi$
$421$	3245.09			0.375668			0.187834	+	0.982201i	$0.439853\pi$
$422$	13850.0	−	2050.39i	1.59765	−	0.236520i
$423$	4433.34			0.509590
$424$	−2741.78	−	5809.95i	−0.314040	−	0.665462i
$425$		−	4095.31i		−	0.467416i
$426$	−10269.4	+	1520.32i	−1.16797	+	0.172910i
$427$	−40.2532	+	44.9793i	−0.00456204	+	0.00509766i
$428$	−120.330	−	397.495i	−0.0135896	−	0.0448916i
$429$	227.307			0.0255815
$430$	−250.515	−	1692.18i	−0.0280951	−	0.189777i
$431$		−	9556.09i		−	1.06798i	−0.845490	−	0.533992i	$-0.820691\pi$
$431$		−	9556.09i		−	1.06798i	0.845490	−	0.533992i	$-0.179309\pi$
$432$	−1194.05	+	795.859i	−0.132983	+	0.0886360i
$433$			5658.90i			0.628058i	0.949413	+	0.314029i	$0.101679\pi$
$433$			5658.90i			0.628058i	−0.949413	+	0.314029i	$0.898321\pi$
$434$	−3694.15	+	5601.38i	−0.408583	+	0.619527i
$435$			11608.8i			1.27954i
$436$	−1012.21	+	306.417i	−0.111184	+	0.0336576i
$437$		−	2454.20i		−	0.268651i
$438$	3504.53	−	518.820i	0.382312	−	0.0565986i
$439$	−3329.73			−0.362003			−0.181001	−	0.983483i	$-0.557934\pi$
$439$	−3329.73			−0.362003			−0.181001	+	0.983483i	$0.557934\pi$
$440$	33.5941	+	71.1872i	0.00363985	+	0.00771299i
$441$	1136.54	+	10216.9i	0.122723	+	1.10322i
$442$	2649.68	+	17898.1i	0.285141	+	1.92608i
$443$			6566.55i			0.704257i	0.935952	+	0.352129i	$0.114542\pi$
$443$			6566.55i			0.704257i	−0.935952	+	0.352129i	$0.885458\pi$
$444$	14633.0	−	4429.69i	1.56408	−	0.473477i
$445$	6095.32			0.649317
$446$	−2468.16	−	16672.0i	−0.262043	−	1.77005i
$447$	6364.21			0.673415
$448$	−9373.26	+	1434.33i	−0.988494	+	0.151263i
$449$	−15156.4			−1.59304			−0.796518	−	0.604615i	$-0.793327\pi$
$449$	−15156.4			−1.59304			−0.796518	+	0.604615i	$0.793327\pi$
$450$	601.844	+	4065.34i	0.0630471	+	0.425871i
$451$	32.4003			0.00338287
$452$	−2435.25	+	737.200i	−0.253417	+	0.0767145i
$453$		−	15763.0i		−	1.63490i
$454$	−338.547	−	2286.82i	−0.0349973	−	0.236400i
$455$	−9141.90	−	8181.34i	−0.941932	−	0.842961i
$456$	−1461.69	−	3097.37i	−0.150109	−	0.318087i
$457$	16572.9			1.69638			0.848191	−	0.529690i	$-0.177692\pi$
$457$	16572.9			1.69638			0.848191	+	0.529690i	$0.177692\pi$
$458$	8662.02	−	1282.35i	0.883732	−	0.130830i
$459$			1894.03i			0.192605i
$460$	8196.99	−	2481.39i	0.830840	−	0.251512i
$461$			5823.47i			0.588343i	0.955753	+	0.294171i	$0.0950436\pi$
$461$			5823.47i			0.588343i	−0.955753	+	0.294171i	$0.904956\pi$
$462$	131.262	+	86.5683i	0.0132183	+	0.00871758i
$463$		−	12952.0i		−	1.30007i	−0.759906	−	0.650033i	$-0.774755\pi$
$463$		−	12952.0i		−	1.30007i	0.759906	−	0.650033i	$-0.225245\pi$
$464$	−9363.44	+	6240.92i	−0.936825	+	0.624412i
$465$		−	8457.34i		−	0.843440i
$466$	−1097.63	−	7414.29i	−0.109113	−	0.737039i
$467$	−7199.70			−0.713410			−0.356705	−	0.934217i	$-0.616100\pi$
$467$	−7199.70			−0.713410			−0.356705	+	0.934217i	$0.616100\pi$
$468$	−5260.58	−	17377.7i	−0.519595	−	1.71642i
$469$	6811.50	−	7611.23i	0.670630	−	0.749369i
$470$	−3620.43	+	535.979i	−0.355315	+	0.0526018i
$471$		−	1273.25i		−	0.124562i
$472$	6111.93	+	12951.4i	0.596027	+	1.26300i
$473$	−27.4955			−0.00267282
$474$	−5892.26	+	872.306i	−0.570971	+	0.0845281i
$475$	−972.205			−0.0939112
$476$	−5286.27	+	11344.7i	−0.509025	+	1.09240i
$477$	8509.27			0.816798
$478$	−12009.7	+	1777.95i	−1.14918	+	0.170128i
$479$	−10505.0			−1.00205			−0.501027	−	0.865431i	$-0.667044\pi$
$479$	−10505.0			−1.00205			−0.501027	+	0.865431i	$0.667044\pi$
$480$	8867.28	−	8013.69i	0.843196	−	0.762028i
$481$			19173.6i			1.81755i
$482$	14126.7	−	2091.35i	1.33496	−	0.197632i
$483$	11408.6	−	12748.1i	1.07476	−	1.20095i
$484$	−10190.1	+	3084.74i	−0.956993	+	0.289701i
$485$	−14197.4			−1.32922
$486$	2251.58	+	15209.0i	0.210152	+	1.41954i
$487$			14612.5i			1.35966i	0.733369	+	0.679831i	$0.237947\pi$
$487$			14612.5i			1.35966i	−0.733369	+	0.679831i	$0.762053\pi$
$488$	66.6937	−	31.4735i	0.00618664	−	0.00291955i
$489$			21760.2i			2.01233i
$490$	−2163.33	−	8206.08i	−0.199448	−	0.756557i
$491$			16952.7i			1.55818i	0.626913	+	0.779089i	$0.284318\pi$
$491$			16952.7i			1.55818i	−0.626913	+	0.779089i	$0.715682\pi$
$492$	−1425.37	−	4708.53i	−0.130611	−	0.431457i
$493$			14852.5i			1.35684i
$494$	4248.91	−	629.020i	0.386978	−	0.0572893i
$495$	−104.261			−0.00946704
$496$	6821.51	−	4546.67i	0.617530	−	0.411596i
$497$	6005.86	−	6711.00i	0.542051	−	0.605693i
$498$	−1945.22	−	13139.6i	−0.175035	−	1.18232i
$499$		−	17687.3i		−	1.58676i	−0.608727	−	0.793379i	$-0.708320\pi$
$499$		−	17687.3i		−	1.58676i	0.608727	−	0.793379i	$-0.291680\pi$
$500$	−3517.45	−	11619.5i	−0.314611	−	1.03928i
$501$	15011.2			1.33862
$502$	−198.312	−	1339.56i	−0.0176316	−	0.119098i
$503$	14327.9			1.27008			0.635038	−	0.772481i	$-0.280984\pi$
$503$	14327.9			1.27008			0.635038	+	0.772481i	$0.280984\pi$
$504$	3580.38	−	12038.5i	0.316434	−	1.06396i
$505$	6774.99			0.596996
$506$	−20.1596	−	136.174i	−0.00177115	−	0.0119638i
$507$	26700.5			2.33888
$508$	−1959.28	−	6472.25i	−0.171120	−	0.565275i
$509$			16759.3i			1.45941i	0.683759	+	0.729707i	$0.260344\pi$
$509$			16759.3i			1.45941i	−0.683759	+	0.729707i	$0.739656\pi$
$510$	−2310.25	−	15605.3i	−0.200587	−	1.35493i
$511$	−2049.55	+	2290.18i	−0.177430	+	0.198262i
$512$	11230.7	+	2844.00i	0.969400	+	0.245485i
$513$	449.632			0.0386973
$514$	−5826.51	+	862.572i	−0.499993	+	0.0740203i
$515$			252.441i			0.0215997i
$516$	1209.59	+	3995.74i	0.103196	+	0.340897i
$517$			58.8270i			0.00500427i
$518$	−7302.14	+	11072.1i	−0.619378	+	0.939152i
$519$			18994.0i			1.60644i
$520$	6396.90	+	13555.3i	0.539466	+	1.14315i
$521$		−	18219.8i		−	1.53210i	−0.642783	−	0.766049i	$-0.722220\pi$
$521$		−	18219.8i		−	1.53210i	0.642783	−	0.766049i	$-0.277780\pi$
$522$	−2182.71	−	14743.8i	−0.183016	−	1.23624i
$523$	−8500.33			−0.710695			−0.355348	−	0.934734i	$-0.615638\pi$
$523$	−8500.33			−0.710695			−0.355348	+	0.934734i	$0.615638\pi$
$524$	−11216.4	+	3395.42i	−0.935094	+	0.283072i
$525$	−5050.02	−	4519.40i	−0.419811	−	0.375700i
$526$	11486.9	−	1700.55i	0.952190	−	0.140965i
$527$		−	10820.4i		−	0.894392i
$528$	−106.546	−	159.854i	−0.00878186	−	0.0131757i
$529$	−2810.33			−0.230980
$530$	−6948.99	+	1028.75i	−0.569518	+	0.0843130i
$531$	−18968.7			−1.55023
$532$	2693.16	+	1254.93i	0.219480	+	0.102271i
$533$	6169.59			0.501378
$534$	−14715.4	+	2178.51i	−1.19251	+	0.176542i
$535$	−454.117			−0.0366975
$536$	−11285.7	+	5325.83i	−0.909452	+	0.429181i
$537$		−	19645.2i		−	1.57868i
$538$	16844.8	−	2493.76i	1.34988	−	0.199839i
$539$	−135.570	+	15.0810i	−0.0108338	+	0.00120516i
$540$	454.614	+	1501.76i	0.0362286	+	0.119677i
$541$	−18444.5			−1.46579			−0.732895	−	0.680342i	$-0.761831\pi$
$541$	−18444.5			−1.46579			−0.732895	+	0.680342i	$0.761831\pi$
$542$	−44.9323	−	303.509i	−0.00356090	−	0.0240532i
$543$			17922.7i			1.41646i
$544$	11344.9	−	10252.8i	0.894134	−	0.808062i
$545$			1156.40i			0.0908894i
$546$	24994.6	+	16484.1i	1.95910	+	1.29204i
$547$		−	16381.3i		−	1.28046i	−0.768182	−	0.640232i	$-0.778838\pi$
$547$		−	16381.3i		−	1.28046i	0.768182	−	0.640232i	$-0.221162\pi$
$548$	−5725.82	+	1733.32i	−0.446341	+	0.135116i
$549$			97.6798i			0.00759357i
$550$	−53.9439	+	7.98600i	−0.00418214	+	0.000619135i
$551$	3525.90			0.272610
$552$	−18902.4	+	8920.27i	−1.45750	+	0.687812i
$553$	3445.96	−	3850.54i	0.264985	−	0.296097i
$554$	−447.015	−	3019.50i	−0.0342813	−	0.231564i
$555$		−	16717.4i		−	1.27858i
$556$	−16302.7	+	4935.17i	−1.24351	+	0.376435i
$557$	−22097.0			−1.68094			−0.840468	−	0.541862i	$-0.817720\pi$
$557$	−22097.0			−1.68094			−0.840468	+	0.541862i	$0.817720\pi$
$558$	1590.16	+	10741.2i	0.120639	+	0.814896i
$559$	−5235.63			−0.396142
$560$	−1468.45	+	10263.9i	−0.110810	+	0.774519i
$561$	−253.564			−0.0190829
$562$	199.910	+	1350.35i	0.0150048	+	0.101355i
$563$	−22890.4			−1.71353			−0.856764	−	0.515709i	$-0.827528\pi$
$563$	−22890.4			−1.71353			−0.856764	+	0.515709i	$0.827528\pi$
$564$	8548.94	−	2587.94i	0.638254	−	0.193212i
$565$			2782.15i			0.207161i
$566$	1025.78	+	6928.94i	0.0761779	+	0.514567i
$567$	−8832.08	−	7904.07i	−0.654167	−	0.585431i
$568$	−9950.83	+	4695.91i	−0.735084	+	0.346895i
$569$	11664.1			0.859375			0.429688	−	0.902978i	$-0.358624\pi$
$569$	11664.1			0.859375			0.429688	+	0.902978i	$0.358624\pi$
$570$	−3704.61	+	548.440i	−0.272226	+	0.0403011i
$571$			11808.4i			0.865439i	0.901529	+	0.432720i	$0.142446\pi$
$571$			11808.4i			0.865439i	−0.901529	+	0.432720i	$0.857554\pi$
$572$	230.588	−	69.8037i	0.0168556	−	0.00510252i
$573$		−	2430.79i		−	0.177221i
$574$	3562.73	+	2349.65i	0.259069	+	0.170858i
$575$			5933.10i			0.430309i
$576$	−9755.13	+	11845.0i	−0.705666	+	0.856844i
$577$		−	14572.9i		−	1.05144i	−0.850659	−	0.525718i	$-0.823797\pi$
$577$		−	14572.9i		−	1.05144i	0.850659	−	0.525718i	$-0.176203\pi$
$578$	−920.730	−	6219.35i	−0.0662583	−	0.447562i
$579$	29813.4			2.13990
$580$	3564.96	+	11776.4i	0.255219	+	0.843086i
$581$	8586.60	+	7684.38i	0.613136	+	0.548712i
$582$	34275.6	−	5074.25i	2.44118	−	0.361399i
$583$			112.911i			0.00802112i
$584$	3395.80	−	1602.52i	0.240615	−	0.113549i
$585$	−19853.1			−1.40312
$586$	−12987.4	+	1922.69i	−0.915535	+	0.135538i
$587$	5506.03			0.387152			0.193576	−	0.981085i	$-0.437991\pi$
$587$	5506.03			0.387152			0.193576	+	0.981085i	$0.437991\pi$
$588$	8155.65	+	19038.0i	0.571996	+	1.33523i
$589$	−2568.71			−0.179697
$590$	15490.6	−	2293.26i	1.08091	−	0.160021i
$591$	−20472.7			−1.42493
$592$	13483.9	−	8987.29i	0.936124	−	0.623945i
$593$		−	7223.08i		−	0.500197i	−0.968220	−	0.250098i	$-0.919537\pi$
$593$		−	7223.08i		−	0.500197i	0.968220	−	0.250098i	$-0.0804629\pi$
$594$	24.9483	−	3.69342i	0.00172330	−	0.000255123i
$595$	10197.9	+	9126.41i	0.702646	+	0.628817i
$596$	6456.09	−	1954.39i	0.443711	−	0.134320i
$597$	−21352.8			−1.46384
$598$	−3838.74	−	25929.9i	−0.262504	−	1.77317i
$599$			11260.6i			0.768107i	0.923311	+	0.384054i	$0.125472\pi$
$599$			11260.6i			0.768107i	−0.923311	+	0.384054i	$0.874528\pi$
$600$	3533.67	+	7487.98i	0.240436	+	0.509493i
$601$		−	25380.2i		−	1.72259i	−0.508103	−	0.861296i	$-0.669653\pi$
$601$		−	25380.2i		−	1.72259i	0.508103	−	0.861296i	$-0.330347\pi$
$602$	−3023.40	−	1993.96i	−0.204692	−	0.134996i
$603$		−	16529.0i		−	1.11627i
$604$	−4840.67	−	15990.6i	−0.326099	−	1.07723i
$605$			11641.6i			0.782312i
$606$	−16356.3	+	2421.43i	−1.09642	+	0.162316i
$607$	9071.99			0.606624			0.303312	−	0.952891i	$-0.401908\pi$
$607$	9071.99			0.606624			0.303312	+	0.952891i	$0.401908\pi$
$608$	−2433.96	−	2693.22i	−0.162352	−	0.179645i
$609$	18314.9	+	16390.5i	1.21865	+	1.09060i
$610$	−11.8092	−	79.7690i	−0.000783838	−	0.00529467i
$611$			11201.7i			0.741689i
$612$	5868.25	+	19385.1i	0.387598	+	1.28039i
$613$	10393.9			0.684837			0.342419	−	0.939547i	$-0.388754\pi$
$613$	10393.9			0.684837			0.342419	+	0.939547i	$0.388754\pi$
$614$	−639.878	−	4322.25i	−0.0420576	−	0.284091i
$615$	−5379.25			−0.352703
$616$	159.741	+	47.5088i	0.0104483	+	0.00310744i
$617$	16600.4			1.08316			0.541578	−	0.840651i	$-0.317827\pi$
$617$	16600.4			1.08316			0.541578	+	0.840651i	$0.317827\pi$
$618$	−90.2240	−	609.445i	−0.00587272	−	0.0396691i
$619$	25628.2			1.66411			0.832054	−	0.554695i	$-0.187165\pi$
$619$	25628.2			1.66411			0.832054	+	0.554695i	$0.187165\pi$
$620$	−2597.17	−	8579.44i	−0.168233	−	0.555739i
$621$		−	2743.98i		−	0.177314i
$622$	3685.42	+	24894.3i	0.237575	+	1.60478i
$623$	8605.98	−	9616.41i	0.553437	−	0.618416i
$624$	−20288.2	−	30439.1i	−1.30157	−	1.95278i
$625$	−7214.64			−0.461737
$626$	5486.25	−	812.199i	0.350279	−	0.0518562i
$627$			60.1947i			0.00383404i
$628$	−391.004	−	1291.64i	−0.0248452	−	0.0820731i
$629$		−	21388.4i		−	1.35582i
$630$	−11464.5	−	7560.93i	−0.725011	−	0.478150i
$631$		−	6093.01i		−	0.384404i	−0.981355	−	0.192202i	$-0.938437\pi$
$631$		−	6093.01i		−	0.384404i	0.981355	−	0.192202i	$-0.0615628\pi$
$632$	−5709.45	+	2694.36i	−0.359351	+	0.169582i
$633$			37362.6i			2.34602i
$634$	−1754.13	−	11848.8i	−0.109882	−	0.742233i
$635$	−7394.21			−0.462095
$636$	16408.7	−	4967.23i	1.02303	−	0.309691i
$637$	−25814.9	+	2871.68i	−1.60569	+	0.178619i
$638$	195.638	−	28.9628i	0.0121401	−	0.00179726i
$639$		−	14574.0i		−	0.902253i
$640$	6534.37	−	10852.4i	0.403584	−	0.670282i
$641$	−9793.98			−0.603493			−0.301747	−	0.953388i	$-0.597570\pi$
$641$	−9793.98			−0.603493			−0.301747	+	0.953388i	$0.597570\pi$
$642$	1096.34	−	162.304i	0.0673970	−	0.00997764i
$643$	15275.5			0.936868			0.468434	−	0.883499i	$-0.344818\pi$
$643$	15275.5			0.936868			0.468434	+	0.883499i	$0.344818\pi$
$644$	7658.51	−	16435.6i	0.468614	−	1.00567i
$645$	4564.93			0.278673
$646$	−4739.72	+	701.681i	−0.288672	+	0.0427357i
$647$	10058.4			0.611184			0.305592	−	0.952163i	$-0.401146\pi$
$647$	10058.4			0.611184			0.305592	+	0.952163i	$0.401146\pi$
$648$	6180.10	+	13095.9i	0.374656	+	0.793912i
$649$		−	251.700i		−	0.0152236i
$650$	−10271.9	+	1520.67i	−0.619839	+	0.0917626i
$651$	−13342.9	−	11940.9i	−0.803301	−	0.718896i
$652$	6682.35	+	22074.4i	0.401382	+	1.32592i
$653$	24996.0			1.49796			0.748981	−	0.662592i	$-0.230544\pi$
$653$	24996.0			1.49796			0.748981	+	0.662592i	$0.230544\pi$
$654$	−413.305	−	2791.80i	−0.0247118	−	0.166923i
$655$			12814.1i			0.764411i
$656$	−2891.89	−	4338.79i	−0.172118	−	0.258234i
$657$			4973.50i			0.295334i
$658$	−4266.09	+	6468.60i	−0.252750	+	0.383240i
$659$			15031.5i			0.888532i	0.895895	+	0.444266i	$0.146536\pi$
$659$			15031.5i			0.888532i	−0.895895	+	0.444266i	$0.853464\pi$
$660$	−201.049	+	60.8617i	−0.0118573	+	0.00358945i
$661$		−	6084.60i		−	0.358039i	−0.983846	−	0.179019i	$-0.942708\pi$
$661$		−	6084.60i		−	0.358039i	0.983846	−	0.179019i	$-0.0572924\pi$
$662$	−27586.3	+	4083.95i	−1.61960	+	0.239769i
$663$	−48283.0			−2.82829
$664$	−6008.33	−	12731.9i	−0.351157	−	0.744117i
$665$	2166.56	−	2420.93i	0.126339	−	0.141173i
$666$	3143.23	+	21231.9i	0.182879	+	1.23531i
$667$		−	21517.6i		−	1.24912i
$668$	15227.9	−	4609.79i	0.882014	−	0.267003i
$669$	44975.4			2.59918
$670$	1998.31	+	13498.2i	0.115226	+	0.778330i
$671$	−1.29613			−7.45704e−5
$672$	−123.248	−	25304.2i	−0.00707497	−	1.45257i
$673$	−9507.60			−0.544563			−0.272282	−	0.962218i	$-0.587778\pi$
$673$	−9507.60			−0.544563			−0.272282	+	0.962218i	$0.587778\pi$
$674$	2845.40	+	19220.1i	0.162612	+	1.09842i
$675$	−1087.00			−0.0619831
$676$	27086.0	−	8199.46i	1.54108	−	0.466515i
$677$			19963.6i			1.13333i	0.823948	+	0.566665i	$0.191767\pi$
$677$			19963.6i			1.13333i	−0.823948	+	0.566665i	$0.808233\pi$
$678$	−994.359	−	6716.70i	−0.0563247	−	0.380462i
$679$	−20045.3	+	22398.8i	−1.13294	+	1.26596i
$680$	−7135.84	−	15121.1i	−0.402422	−	0.852748i
$681$	6169.07			0.347135
$682$	−142.528	+	21.1002i	−0.00800244	+	0.00118470i
$683$		−	21589.2i		−	1.20950i	−0.796415	−	0.604751i	$-0.793273\pi$
$683$		−	21589.2i		−	1.20950i	0.796415	−	0.604751i	$-0.206727\pi$
$684$	4601.91	−	1393.09i	0.257249	−	0.0778745i
$685$			6541.45i			0.364870i
$686$	−16000.9	−	8173.14i	−0.890550	−	0.454886i
$687$			23367.2i			1.29769i
$688$	2454.11	+	3681.98i	0.135991	+	0.204032i
$689$			21500.3i			1.18882i
$690$	3346.98	+	22608.2i	0.184663	+	1.24736i
$691$	−8948.20			−0.492628			−0.246314	−	0.969190i	$-0.579219\pi$
$691$	−8948.20			−0.492628			−0.246314	+	0.969190i	$0.579219\pi$
$692$	5832.87	+	19268.2i	0.320423	+	1.05848i
$693$	−147.206	+	164.489i	−0.00806911	+	0.00901650i
$694$	−719.905	+	106.577i	−0.0393764	+	0.00582939i
$695$			18625.0i			1.01653i
$696$	−12815.6	−	27156.7i	−0.697949	−	1.47898i
$697$	−6882.27			−0.374010
$698$	7948.14	−	1176.66i	0.431005	−	0.0638072i
$699$	20001.3			1.08228
$700$	−6510.79	−	3033.83i	−0.351550	−	0.163812i
$701$	−8280.23			−0.446134			−0.223067	−	0.974803i	$-0.571607\pi$
$701$	−8280.23			−0.446134			−0.223067	+	0.974803i	$0.571607\pi$
$702$	4750.60	−	703.291i	0.255413	−	0.0378120i
$703$	−5077.50			−0.272406
$704$	−157.174	−	129.443i	−0.00841437	−	0.00692978i
$705$		−	9766.72i		−	0.521753i
$706$	−31679.4	+	4689.90i	−1.68877	+	0.250009i
$707$	9565.61	−	10688.7i	0.508843	−	0.568585i
$708$	−36577.9	+	11072.9i	−1.94164	+	0.587773i
$709$	4270.33			0.226200			0.113100	−	0.993584i	$-0.463922\pi$
$709$	4270.33			0.226200			0.113100	+	0.993584i	$0.463922\pi$
$710$	1761.96	+	11901.7i	0.0931340	+	0.629102i
$711$		−	8362.07i		−	0.441072i
$712$	−14258.9	+	6728.92i	−0.750525	+	0.354181i
$713$			15676.1i			0.823388i
$714$	−27881.8	−	18388.3i	−1.46142	−	0.963816i
$715$		−	263.435i		−	0.0137789i
$716$	−6032.85	−	19928.8i	−0.314886	−	1.04019i
$717$		−	32398.1i		−	1.68749i
$718$	15168.6	−	2245.60i	0.788422	−	0.116720i
$719$	24383.1			1.26472			0.632362	−	0.774673i	$-0.282085\pi$
$719$	24383.1			1.26472			0.632362	+	0.774673i	$0.282085\pi$
$720$	9305.80	+	13961.8i	0.481676	+	0.722673i
$721$	398.268	+	356.421i	0.0205718	+	0.0184103i
$722$	−2674.52	−	18065.8i	−0.137860	−	0.931220i
$723$			38109.0i			1.96029i
$724$	5503.89	+	18181.4i	0.282528	+	0.933298i
$725$	−8523.96			−0.436651
$726$	−4160.79	−	28105.3i	−0.212702	−	1.43676i
$727$	−19046.5			−0.971660			−0.485830	−	0.874053i	$-0.661483\pi$
$727$	−19046.5			−0.971660			−0.485830	+	0.874053i	$0.661483\pi$
$728$	30417.5	+	9046.51i	1.54856	+	0.460558i
$729$	−23749.6			−1.20661
$730$	−601.282	−	4061.54i	−0.0304855	−	0.205924i
$731$	5840.42			0.295507
$732$	57.0199	+	188.359i	0.00287912	+	0.00951084i
$733$		−	29493.0i		−	1.48615i	−0.669208	−	0.743075i	$-0.733367\pi$
$733$		−	29493.0i		−	1.48615i	0.669208	−	0.743075i	$-0.266633\pi$
$734$	−4532.04	−	30613.1i	−0.227903	−	1.53944i
$735$	22507.9	−	2503.81i	1.12955	−	0.125652i
$736$	−16436.0	+	14853.8i	−0.823150	+	0.743911i
$737$	219.327			0.0109620
$738$	6831.90	−	1011.41i	0.340767	−	0.0504480i
$739$		−	4813.56i		−	0.239607i	−0.992798	−	0.119804i	$-0.961773\pi$
$739$		−	4813.56i		−	0.239607i	0.992798	−	0.119804i	$-0.0382265\pi$
$740$	−5133.76	−	16958.8i	−0.255028	−	0.842454i
$741$			11462.1i			0.568248i
$742$	−8188.25	+	12415.7i	−0.405121	+	0.614278i
$743$		−	17606.1i		−	0.869318i	−0.900595	−	0.434659i	$-0.856869\pi$
$743$		−	17606.1i		−	0.869318i	0.900595	−	0.434659i	$-0.143131\pi$
$744$	9336.46	+	19784.3i	0.460069	+	0.974905i
$745$		−	7375.74i		−	0.362720i
$746$	161.517	+	1091.01i	0.00792701	+	0.0535454i
$747$	18647.2			0.913339
$748$	−257.225	+	77.8671i	−0.0125736	+	0.00380629i
$749$	−641.167	+	716.446i	−0.0312787	+	0.0349511i
$750$	32047.9	−	4744.46i	1.56030	−	0.230991i
$751$			6572.41i			0.319348i	0.987170	+	0.159674i	$0.0510443\pi$
$751$			6572.41i			0.319348i	−0.987170	+	0.159674i	$0.948956\pi$
$752$	7877.63	−	5250.59i	0.382005	−	0.254614i
$753$	3613.68			0.174887
$754$	37253.0	−	5515.03i	1.79930	−	0.266373i
$755$	−18268.4			−0.880602
$756$	3011.15	+	1403.11i	0.144861	+	0.0675007i
$757$	−10562.7			−0.507146			−0.253573	−	0.967316i	$-0.581606\pi$
$757$	−10562.7			−0.507146			−0.253573	+	0.967316i	$0.581606\pi$
$758$	36169.8	−	5354.68i	1.73318	−	0.256584i
$759$	367.352			0.0175679
$760$	−3589.67	+	1694.01i	−0.171330	+	0.0808528i
$761$			15844.6i			0.754750i	0.926061	+	0.377375i	$0.123173\pi$
$761$			15844.6i			0.754750i	−0.926061	+	0.377375i	$0.876827\pi$
$762$	17851.2	−	2642.74i	0.848663	−	0.125638i
$763$	1824.42	+	1632.72i	0.0865640	+	0.0774684i
$764$	−746.473	−	2465.88i	−0.0353487	−	0.116770i
$765$	22146.5			1.04668
$766$	5377.13	+	36321.5i	0.253634	+	1.71325i
$767$		−	47928.1i		−	2.25630i
$768$	−11896.6	+	28535.5i	−0.558962	+	1.34074i
$769$		−	6030.08i		−	0.282770i	−0.989955	−	0.141385i	$-0.954844\pi$
$769$		−	6030.08i		−	0.282770i	0.989955	−	0.141385i	$-0.0451555\pi$
$770$	100.328	−	152.125i	0.00469553	−	0.00711975i
$771$		−	15718.0i		−	0.734201i
$772$	30243.9	−	9155.42i	1.40997	−	0.426828i
$773$		−	16990.3i		−	0.790556i	−0.918562	−	0.395278i	$-0.870648\pi$
$773$		−	16990.3i		−	0.790556i	0.918562	−	0.395278i	$-0.129352\pi$
$774$	−5797.68	+	858.304i	−0.269242	+	0.0398593i
$775$	6209.92			0.287828
$776$	33212.2	−	15673.2i	1.53640	−	0.725046i
$777$	−26374.5	−	23603.3i	−1.21774	−	1.08979i
$778$	5203.74	+	35150.3i	0.239799	+	1.61979i
$779$			1633.81i			0.0751443i
$780$	−38283.3	+	11589.1i	−1.75739	+	0.531996i
$781$	193.386			0.00886029
$782$	4282.17	+	28925.2i	0.195819	+	1.32272i
$783$	3942.22			0.179928
$784$	14119.8	+	16808.4i	0.643212	+	0.765688i
$785$	−1475.63			−0.0670923
$786$	−4579.85	−	30936.0i	−0.207835	−	1.40388i
$787$	−41103.6			−1.86173			−0.930867	−	0.365357i	$-0.880947\pi$
$787$	−41103.6			−1.86173			−0.930867	+	0.365357i	$0.880947\pi$
$788$	−20768.2	+	6286.96i	−0.938880	+	0.284218i
$789$			30987.8i			1.39822i
$790$	1010.95	+	6828.78i	0.0455292	+	0.307541i
$791$	4389.31	+	3928.12i	0.197302	+	0.176571i
$792$	243.899	−	115.099i	0.0109426	−	0.00516396i
$793$	−246.807			−0.0110522
$794$	−16436.2	+	2433.26i	−0.734633	+	0.108757i
$795$		−	18746.0i		−	0.836294i
$796$	−21661.1	+	6557.24i	−0.964518	+	0.291979i
$797$			6489.74i			0.288430i	0.989546	+	0.144215i	$0.0460656\pi$
$797$			6489.74i			0.288430i	−0.989546	+	0.144215i	$0.953934\pi$
$798$	−4365.28	+	6618.99i	−0.193646	+	0.293621i
$799$		−	12495.7i		−	0.553272i
$800$	5884.17	+	6510.93i	0.260046	+	0.287745i
$801$		−	20883.6i		−	0.921205i
$802$	1976.44	+	13350.4i	0.0870204	+	0.587806i
$803$	−65.9944			−0.00290024
$804$	−9648.70	−	31873.3i	−0.423238	−	1.39812i
$805$	−14774.3	−	13221.9i	−0.646864	−	0.578896i
$806$	−27139.7	+	4017.84i	−1.18605	+	0.175586i
$807$			45441.7i			1.98219i
$808$	−15848.8	+	7479.24i	−0.690049	+	0.325642i
$809$	−2747.19			−0.119390			−0.0596948	−	0.998217i	$-0.519013\pi$
$809$	−2747.19			−0.119390			−0.0596948	+	0.998217i	$0.519013\pi$
$810$	15663.3	−	2318.84i	0.679449	−	0.100587i
$811$	17346.1			0.751053			0.375526	−	0.926812i	$-0.377462\pi$
$811$	17346.1			0.751053			0.375526	+	0.926812i	$0.377462\pi$
$812$	23612.7	+	11002.8i	1.02050	+	0.475521i
$813$	818.765			0.0353202
$814$	−281.731	+	41.7082i	−0.0121310	+	0.00179591i
$815$	25218.8			1.08390
$816$	22631.8	+	33955.2i	0.970922	+	1.45670i
$817$		−	1386.48i		−	0.0593720i
$818$	−6292.01	+	931.486i	−0.268942	+	0.0398150i
$819$	−28030.6	+	31321.7i	−1.19593	+	1.33635i
$820$	−5456.91	+	1651.92i	−0.232395	+	0.0703505i
$821$	−1049.07			−0.0445956			−0.0222978	−	0.999751i	$-0.507098\pi$
$821$	−1049.07			−0.0445956			−0.0222978	+	0.999751i	$0.507098\pi$
$822$	−2337.96	−	15792.5i	−0.0992040	−	0.670104i
$823$			4120.54i			0.174524i	0.996185	+	0.0872618i	$0.0278117\pi$
$823$			4120.54i			0.174524i	−0.996185	+	0.0872618i	$0.972188\pi$
$824$	−278.681	−	590.537i	−0.0117820	−	0.0249664i
$825$		−	145.522i		−	0.00614114i
$826$	18253.1	−	27676.8i	0.768894	−	1.16586i
$827$		−	493.902i		−	0.0207674i	−0.999946	−	0.0103837i	$-0.996695\pi$
$827$		−	493.902i		−	0.0207674i	0.999946	−	0.0103837i	$-0.00330530\pi$
$828$	−8501.66	−	28084.2i	−0.356827	−	1.17874i
$829$			7903.16i			0.331108i	0.986201	+	0.165554i	$0.0529412\pi$
$829$			7903.16i			0.331108i	−0.986201	+	0.165554i	$0.947059\pi$
$830$	−15228.0	+	2254.39i	−0.636832	+	0.0942784i
$831$	8145.61			0.340034
$832$	−29928.7	−	24648.2i	−1.24710	−	1.02707i
$833$	28796.9	−	3203.40i	1.19778	−	0.133243i
$834$	−6656.71	−	44964.8i	−0.276383	−	1.86691i
$835$		−	17397.1i		−	0.721020i
$836$	18.4852	+	61.0638i	0.000764743	+	0.00252624i
$837$	−2872.01			−0.118603
$838$	−4276.10	−	28884.3i	−0.176272	−	1.19068i
$839$	−35079.5			−1.44348			−0.721739	−	0.692166i	$-0.756657\pi$
$839$	−35079.5			−1.44348			−0.721739	+	0.692166i	$0.756657\pi$
$840$	−26521.0	−	7887.62i	−1.08936	−	0.323987i
$841$	6524.86			0.267533
$842$	1344.16	+	9079.55i	0.0550153	+	0.371617i
$843$	−3642.80			−0.148831
$844$	11473.7	+	37902.0i	0.467939	+	1.54578i
$845$		−	30944.3i		−	1.25978i
$846$	1836.35	+	12404.2i	0.0746277	+	0.504096i
$847$	18366.6	+	16436.8i	0.745082	+	0.666794i
$848$	15120.2	−	10077.9i	0.612298	−	0.408108i
$849$	−18692.0			−0.755602
$850$	11458.4	−	1696.33i	0.462377	−	0.0684515i
$851$			30986.6i			1.24819i
$852$	−8507.49	−	28103.5i	−0.342091	−	1.13006i
$853$			34167.2i			1.37147i	0.727852	+	0.685734i	$0.240519\pi$
$853$			34167.2i			1.37147i	−0.727852	+	0.685734i	$0.759481\pi$
$854$	−142.522	−	93.9947i	−0.00571080	−	0.00376631i
$855$		−	5257.44i		−	0.210293i
$856$	1062.32	−	501.322i	0.0424175	−	0.0200173i
$857$		−	9678.21i		−	0.385766i	−0.981222	−	0.192883i	$-0.938216\pi$
$857$		−	9678.21i		−	0.385766i	0.981222	−	0.192883i	$-0.0617838\pi$
$858$	94.1535	+	635.989i	0.00374633	+	0.0253057i
$859$	−7458.37			−0.296247			−0.148124	−	0.988969i	$-0.547323\pi$
$859$	−7458.37			−0.296247			−0.148124	+	0.988969i	$0.547323\pi$
$860$	4630.83	−	1401.85i	0.183616	−	0.0555844i
$861$	−7594.96	+	8486.68i	−0.300622	+	0.335918i
$862$	26737.3	−	3958.26i	1.05647	−	0.156403i
$863$			2106.36i			0.0830839i	0.999137	+	0.0415420i	$0.0132270\pi$
$863$			2106.36i			0.0830839i	−0.999137	+	0.0415420i	$0.986773\pi$
$864$	−2721.35	−	3011.22i	−0.107155	−	0.118569i
$865$	22012.9			0.865274
$866$	−15833.2	+	2343.99i	−0.621287	+	0.0919770i
$867$	16777.7			0.657211
$868$	−17202.5	−	8015.83i	−0.672684	−	0.313450i
$869$	110.958			0.00433141
$870$	−32480.7	+	4808.54i	−1.26575	+	0.187385i
$871$	41763.7			1.62469
$872$	−1276.61	−	2705.18i	−0.0495772	−	0.105056i
$873$			48642.6i			1.88580i
$874$	6866.69	−	1016.56i	0.265754	−	0.0393430i
$875$	−18742.5	+	20943.0i	−0.724128	+	0.809147i
$876$	2903.25	+	9590.53i	0.111977	+	0.369902i
$877$	1942.72			0.0748015			0.0374007	−	0.999300i	$-0.488092\pi$
$877$	1942.72			0.0748015			0.0374007	+	0.999300i	$0.488092\pi$
$878$	−1379.22	−	9316.35i	−0.0530141	−	0.358100i
$879$		−	35035.6i		−	1.34439i
$880$	−185.262	+	123.481i	−0.00709679	+	0.00473015i
$881$			11938.8i			0.456561i	0.973595	+	0.228280i	$0.0733103\pi$
$881$			11938.8i			0.456561i	−0.973595	+	0.228280i	$0.926690\pi$
$882$	−28115.4	+	7411.93i	−1.07335	+	0.282962i
$883$			6631.93i			0.252754i	0.991982	+	0.126377i	$0.0403350\pi$
$883$			6631.93i			0.252754i	−0.991982	+	0.126377i	$0.959665\pi$
$884$	−48980.1	+	14827.3i	−1.86355	+	0.564134i
$885$			41788.3i			1.58723i
$886$	−18372.8	+	2719.95i	−0.696664	+	0.103136i
$887$	−26193.4			−0.991530			−0.495765	−	0.868457i	$-0.665112\pi$
$887$	−26193.4			−0.991530			−0.495765	+	0.868457i	$0.665112\pi$
$888$	18455.2	+	39107.2i	0.697426	+	1.47787i
$889$	−10439.9	+	11665.6i	−0.393861	+	0.440104i
$890$	2524.77	+	17054.3i	0.0950903	+	0.642316i
$891$		−	254.507i		−	0.00956938i
$892$	45624.7	−	13811.5i	1.71259	−	0.518435i
$893$	−2966.40			−0.111161
$894$	2636.14	+	17806.6i	0.0986194	+	0.666155i
$895$	−22767.6			−0.850322
$896$	−7895.70	−	25631.6i	−0.294394	−	0.955684i
$897$	69950.3			2.60376
$898$	−6277.97	−	42406.5i	−0.233295	−	1.57586i
$899$	−22521.5			−0.835523
$900$	−11125.3	+	3367.84i	−0.412046	+	0.124735i
$901$		−	23983.9i		−	0.886814i
$902$	13.4207	+	90.6540i	0.000495409	+	0.00334639i
$903$	6445.22	−	7201.95i	0.237523	−	0.265411i
$904$	−3071.35	−	6508.32i	−0.113000	−	0.239451i
$905$	20771.4			0.762943
$906$	44103.8	−	6529.25i	1.61727	−	0.239426i
$907$		−	19976.6i		−	0.731324i	−0.930748	−	0.365662i	$-0.880843\pi$
$907$		−	19976.6i		−	0.731324i	0.930748	−	0.365662i	$-0.119157\pi$
$908$	6258.13	−	1894.46i	0.228726	−	0.0692400i
$909$		−	23212.2i		−	0.846976i
$910$	19104.1	−	28967.3i	0.695929	−	1.05523i
$911$		−	33720.7i		−	1.22636i	−0.789942	−	0.613182i	$-0.789889\pi$
$911$		−	33720.7i		−	1.22636i	0.789942	−	0.613182i	$-0.210111\pi$
$912$	8060.78	−	5372.67i	0.292675	−	0.195073i
$913$			247.433i			0.00896917i
$914$	6864.71	+	46369.8i	0.248429	+	1.67809i
$915$	215.190			0.00777482
$916$	7175.85	+	23704.6i	0.258839	+	0.855045i
$917$	20216.5	+	18092.3i	0.728033	+	0.651536i
$918$	−5299.36	+	784.532i	−0.190528	+	0.0282063i
$919$		−	39693.8i		−	1.42479i	−0.701780	−	0.712393i	$-0.747611\pi$
$919$		−	39693.8i		−	1.42479i	0.701780	−	0.712393i	$-0.252389\pi$
$920$	10338.1	+	21906.8i	0.370474	+	0.785050i
$921$	11660.0			0.417166
$922$	−16293.7	+	2412.16i	−0.581999	+	0.0861608i
$923$	36824.0			1.31319
$924$	−187.842	+	403.120i	−0.00668782	+	0.0143525i
$925$	12275.0			0.436324
$926$	36238.8	−	5364.89i	1.28605	−	0.190390i
$927$	864.903			0.0306442
$928$	−21340.1	−	23613.2i	−0.754875	−	0.835282i
$929$		−	32215.1i		−	1.13772i	−0.822434	−	0.568860i	$-0.807385\pi$
$929$		−	32215.1i		−	1.13772i	0.822434	−	0.568860i	$-0.192615\pi$
$930$	23663.1	−	3503.14i	0.834346	−	0.123519i
$931$	−760.470	−	6836.23i	−0.0267705	−	0.240653i
$932$	20290.0	−	6142.20i	0.713113	−	0.215874i
$933$	−67156.5			−2.35649
$934$	−2982.21	−	20144.3i	−0.104476	−	0.705718i
$935$			293.866i			0.0102786i
$936$	46442.6	−	21916.8i	1.62182	−	0.765356i
$937$		−	28308.4i		−	0.986973i	−0.869753	−	0.493487i	$-0.835722\pi$
$937$		−	28308.4i		−	0.986973i	0.869753	−	0.493487i	$-0.164278\pi$
$938$	24117.1	+	15905.4i	0.839501	+	0.553657i
$939$			14800.1i			0.514357i
$940$	−2999.27	−	9907.72i	−0.104069	−	0.343781i
$941$			35128.7i			1.21696i	0.793568	+	0.608482i	$0.208221\pi$
$941$			35128.7i			1.21696i	−0.793568	+	0.608482i	$0.791779\pi$
$942$	3562.48	−	527.399i	0.123219	−	0.0182416i
$943$	9970.72			0.344318
$944$	−33705.6	+	22465.4i	−1.16210	+	0.774563i
$945$	2422.38	−	2706.78i	0.0833861	−	0.0931764i
$946$	−11.3890	−	76.9306i	−0.000391426	−	0.00264401i
$947$			49095.2i			1.68467i	0.538957	+	0.842333i	$0.318819\pi$
$947$			49095.2i			1.68467i	−0.538957	+	0.842333i	$0.681181\pi$
$948$	−4881.31	−	16124.8i	−0.167234	−	0.552436i
$949$	−12566.5			−0.429848
$950$	−402.700	−	2720.16i	−0.0137530	−	0.0928987i
$951$	31964.1			1.08991
$952$	−33931.2	−	10091.5i	−1.15517	−	0.343559i
$953$	−49122.8			−1.66972			−0.834860	−	0.550463i	$-0.814451\pi$
$953$	−49122.8			−1.66972			−0.834860	+	0.550463i	$0.814451\pi$
$954$	3524.65	+	23808.4i	0.119617	+	0.807992i
$955$	−2817.15			−0.0954562
$956$	−9949.15	−	32865.8i	−0.336588	−	1.11188i
$957$			527.767i			0.0178268i
$958$	−4351.30	−	29392.2i	−0.146748	−	0.991251i
$959$	10320.2	+	9235.87i	0.347506	+	0.310993i
$960$	26094.7	+	21490.7i	0.877295	+	0.722509i
$961$	−13383.5			−0.449246
$962$	−53646.4	+	7941.97i	−1.79795	+	0.266174i
$963$			1555.88i			0.0520639i
$964$	11702.9	+	38659.2i	0.391002	+	1.29163i
$965$		−	34552.0i		−	1.15261i
$966$	40393.9	+	26640.1i	1.34540	+	0.887300i
$967$			25958.2i			0.863247i	0.902054	+	0.431624i	$0.142059\pi$
$967$			25958.2i			0.863247i	−0.902054	+	0.431624i	$0.857941\pi$
$968$	−12851.7	−	27233.4i	−0.426726	−	0.904250i
$969$		−	12786.2i		−	0.423892i
$970$	−5880.76	−	39723.4i	−0.194660	−	1.31489i
$971$	−29381.4			−0.971055			−0.485528	−	0.874221i	$-0.661373\pi$
$971$	−29381.4			−0.971055			−0.485528	+	0.874221i	$0.661373\pi$
$972$	−41621.2	+	12599.6i	−1.37346	+	0.415773i
$973$	29384.2	+	26296.7i	0.968153	+	0.866426i
$974$	−40884.8	+	6052.70i	−1.34500	+	0.199118i
$975$		−	27710.0i		−	0.910186i
$976$	115.686	+	173.568i	0.00379409	+	0.00569238i
$977$	−31221.5			−1.02238			−0.511189	−	0.859468i	$-0.670795\pi$
$977$	−31221.5			−1.02238			−0.511189	+	0.859468i	$0.670795\pi$
$978$	−60883.6	+	9013.38i	−1.99064	+	0.294699i
$979$	277.109			0.00904641
$980$	22064.0	−	9451.93i	0.719192	−	0.308093i
$981$	3962.01			0.128947
$982$	−47432.6	+	7022.05i	−1.54138	+	0.228190i
$983$	19941.1			0.647021			0.323511	−	0.946225i	$-0.395137\pi$
$983$	19941.1			0.647021			0.323511	+	0.946225i	$0.395137\pi$
$984$	12583.7	−	5938.41i	0.407678	−	0.192388i
$985$			23726.6i			0.767506i
$986$	−41556.3	+	6152.10i	−1.34221	+	0.198705i
$987$	−15408.7	−	13789.6i	−0.496923	−	0.444710i
$988$	3519.91	+	11627.6i	0.113343	+	0.374416i
$989$	−8461.34			−0.272047
$990$	−43.1863	−	291.715i	−0.00138642	−	0.00936497i
$991$			12092.8i			0.387629i	0.981038	+	0.193815i	$0.0620861\pi$
$991$			12092.8i			0.387629i	−0.981038	+	0.193815i	$0.937914\pi$
$992$	15546.8	+	17202.8i	0.497593	+	0.550595i
$993$		−	74418.6i		−	2.37825i
$994$	21264.6	+	14024.2i	0.678545	+	0.447506i
$995$			24746.6i			0.788464i
$996$	35957.9	−	10885.2i	1.14394	−	0.346295i
$997$			13741.5i			0.436509i	0.975892	+	0.218254i	$0.0700362\pi$
$997$			13741.5i			0.436509i	−0.975892	+	0.218254i	$0.929964\pi$
$998$	49487.9	−	7326.32i	1.56965	−	0.232375i
$999$	−5677.02			−0.179793

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.4.d.b.27.7	yes	8
3.2	odd	2		252.4.b.d.55.1		8
4.3	odd	2	inner	28.4.d.b.27.6	yes	8
7.2	even	3		196.4.f.c.31.6		16
7.3	odd	6		196.4.f.c.19.1		16
7.4	even	3		196.4.f.c.19.2		16
7.5	odd	6		196.4.f.c.31.5		16
7.6	odd	2	inner	28.4.d.b.27.8	yes	8
8.3	odd	2		448.4.f.d.447.1		8
8.5	even	2		448.4.f.d.447.7		8
12.11	even	2		252.4.b.d.55.3		8
21.20	even	2		252.4.b.d.55.2		8
28.3	even	6		196.4.f.c.19.6		16
28.11	odd	6		196.4.f.c.19.5		16
28.19	even	6		196.4.f.c.31.2		16
28.23	odd	6		196.4.f.c.31.1		16
28.27	even	2	inner	28.4.d.b.27.5	✓	8
56.13	odd	2		448.4.f.d.447.2		8
56.27	even	2		448.4.f.d.447.8		8
84.83	odd	2		252.4.b.d.55.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.4.d.b.27.5	✓	8	28.27	even	2	inner
28.4.d.b.27.6	yes	8	4.3	odd	2	inner
28.4.d.b.27.7	yes	8	1.1	even	1	trivial
28.4.d.b.27.8	yes	8	7.6	odd	2	inner
196.4.f.c.19.1		16	7.3	odd	6
196.4.f.c.19.2		16	7.4	even	3
196.4.f.c.19.5		16	28.11	odd	6
196.4.f.c.19.6		16	28.3	even	6
196.4.f.c.31.1		16	28.23	odd	6
196.4.f.c.31.2		16	28.19	even	6
196.4.f.c.31.5		16	7.5	odd	6
196.4.f.c.31.6		16	7.2	even	3
252.4.b.d.55.1		8	3.2	odd	2
252.4.b.d.55.2		8	21.20	even	2
252.4.b.d.55.3		8	12.11	even	2
252.4.b.d.55.4		8	84.83	odd	2
448.4.f.d.447.1		8	8.3	odd	2
448.4.f.d.447.2		8	56.13	odd	2
448.4.f.d.447.7		8	8.5	even	2
448.4.f.d.447.8		8	56.27	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	28.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.414214 + 2.79793i) q^{2} -7.54788 q^{3} +(-7.65685 + 2.31788i) q^{4} +8.74756i q^{5} +(-3.12644 - 21.1185i) q^{6} +(13.8008 + 12.3507i) q^{7} +(-9.65685 - 20.4633i) q^{8} +29.9706 q^{9} +(-24.4751 + 3.62336i) q^{10} +0.397686i q^{11} +(57.7931 - 17.4951i) q^{12} +75.7263i q^{13} +(-28.8399 + 43.7294i) q^{14} -66.0256i q^{15} +(53.2548 - 35.4954i) q^{16} -84.4739i q^{17} +(12.4142 + 83.8556i) q^{18} -20.0536 q^{19} +(-20.2758 - 66.9788i) q^{20} +(-104.167 - 93.2214i) q^{21} +(-1.11270 + 0.164727i) q^{22} +122.382i q^{23} +(72.8888 + 154.454i) q^{24} +48.4802 q^{25} +(-211.877 + 31.3669i) q^{26} -22.4215 q^{27} +(-134.298 - 62.5788i) q^{28} -175.823 q^{29} +(184.735 - 27.3487i) q^{30} +128.092 q^{31} +(121.373 + 134.301i) q^{32} -3.00169i q^{33} +(236.352 - 34.9902i) q^{34} +(-108.038 + 120.723i) q^{35} +(-229.480 + 69.4683i) q^{36} +253.196 q^{37} +(-8.30649 - 56.1087i) q^{38} -571.574i q^{39} +(179.004 - 84.4739i) q^{40} -81.4722i q^{41} +(217.680 - 330.065i) q^{42} +69.1388i q^{43} +(-0.921790 - 3.04502i) q^{44} +262.169i q^{45} +(-342.416 + 50.6922i) q^{46} +147.923 q^{47} +(-401.961 + 267.915i) q^{48} +(37.9218 + 340.897i) q^{49} +(20.0812 + 135.644i) q^{50} +637.599i q^{51} +(-175.525 - 579.826i) q^{52} +283.921 q^{53} +(-9.28727 - 62.7337i) q^{54} -3.47878 q^{55} +(119.463 - 401.677i) q^{56} +151.362 q^{57} +(-72.8284 - 491.942i) q^{58} -632.911 q^{59} +(153.040 + 505.548i) q^{60} +3.25919i q^{61} +(53.0574 + 358.392i) q^{62} +(413.616 + 370.157i) q^{63} +(-325.490 + 395.222i) q^{64} -662.420 q^{65} +(8.39852 - 1.24334i) q^{66} -551.508i q^{67} +(195.801 + 646.804i) q^{68} -923.724i q^{69} +(-382.525 - 252.279i) q^{70} -486.278i q^{71} +(-289.421 - 613.296i) q^{72} +165.946i q^{73} +(104.877 + 708.425i) q^{74} -365.923 q^{75} +(153.548 - 46.4820i) q^{76} +(-4.91169 + 5.48837i) q^{77} +(1599.22 - 236.754i) q^{78} -279.010i q^{79} +(310.498 + 465.850i) q^{80} -639.971 q^{81} +(227.954 - 33.7469i) q^{82} +622.183 q^{83} +(1013.66 + 472.337i) q^{84} +738.940 q^{85} +(-193.446 + 28.6382i) q^{86} +1327.09 q^{87} +(8.13795 - 3.84039i) q^{88} -696.803i q^{89} +(-733.532 + 108.594i) q^{90} +(-935.271 + 1045.08i) q^{91} +(-283.667 - 937.060i) q^{92} -966.823 q^{93} +(61.2718 + 413.879i) q^{94} -175.420i q^{95} +(-916.106 - 1013.69i) q^{96} +1623.01i q^{97} +(-938.100 + 247.307i) q^{98} +11.9189i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 16 q^{4} - 32 q^{8} + 104 q^{9} - 152 q^{14} + 64 q^{16} + 88 q^{18} - 64 q^{21} + 240 q^{22} - 472 q^{25} - 48 q^{28} - 592 q^{29} + 256 q^{30} + 1152 q^{32} - 976 q^{36} + 1392 q^{37}+ \cdots - 3144 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 - 16 * q^4 - 32 * q^8 + 104 * q^9 - 152 * q^14 + 64 * q^16 + 88 * q^18 - 64 * q^21 + 240 * q^22 - 472 * q^25 - 48 * q^28 - 592 * q^29 + 256 * q^30 + 1152 * q^32 - 976 * q^36 + 1392 * q^37 - 1024 * q^42 - 1184 * q^44 - 816 * q^46 + 1480 * q^49 + 1688 * q^50 - 1168 * q^53 + 800 * q^56 - 192 * q^57 - 560 * q^58 + 2944 * q^60 - 3328 * q^64 + 448 * q^65 - 3200 * q^70 - 1184 * q^72 - 496 * q^74 + 368 * q^77 + 7680 * q^78 - 4984 * q^81 + 4480 * q^84 + 1024 * q^85 + 240 * q^86 + 3776 * q^88 - 3808 * q^92 - 2304 * q^93 - 3144 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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