LMFDB - Embedded newform 28.4.d.b.27.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [28,4,Mod(27,28)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			27.6
Root			$4.98105 - 1.39897i$ of defining polynomial
Character	$\chi$	$=$	28.27
Dual form			28.4.d.b.27.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.414214 - 2.79793i) q^{2} +7.54788 q^{3} +(-7.65685 - 2.31788i) q^{4} +8.74756i q^{5} +(3.12644 - 21.1185i) q^{6} +(-13.8008 - 12.3507i) q^{7} +(-9.65685 + 20.4633i) q^{8} +29.9706 q^{9} +O(q^{10})$	\(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} +(-40.2728 + 33.4978i) 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} +(77.0430 + 126.556i) 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} +(-303.975 + 252.837i) 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} +(386.007 - 163.140i) 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} +(-293.024 - 352.289i) 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} +(581.511 + 955.229i) 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} +(969.515 + 35.1017i) 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}+O(q^{10}) $ 8 * q - 8 * q^2 - 16 * q^4 - 32 * q^8 + 104 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$-0.241240\pi$
$3$	7.54788			1.45259			0.726296	+	0.687383i	$0.241240\pi$
$4$	−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	$-0.998265\pi$
$11$		−	0.397686i		−	0.0109006i	0.999985	−	0.00545031i	$-0.00173490\pi$
$12$	−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	$0.700660\pi$
$14$	−40.2728	+	33.4978i	−0.768812	+	0.639475i
$15$			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	$-0.461368\pi$
$19$	20.0536			0.242138			0.121069	+	0.992644i	$0.461368\pi$
$20$	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	$-0.812815\pi$
$23$		−	122.382i		−	1.10950i	0.832019	−	0.554748i	$-0.187185\pi$
$24$	−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
$28$	77.0430	+	126.556i	0.519991	+	0.854172i
$29$	−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	$-0.621007\pi$
$31$	−128.092			−0.742128			−0.371064	+	0.928607i	$0.621007\pi$
$32$	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	$-0.0495921\pi$
$42$	−303.975	+	252.837i	−1.11677	+	0.928896i
$43$		−	69.1388i		−	0.245199i	−0.992456	−	0.122600i	$-0.960877\pi$
$43$		−	69.1388i		−	0.245199i	0.992456	−	0.122600i	$-0.0391231\pi$
$44$	−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	$-0.573722\pi$
$47$	−147.923			−0.459081			−0.229541	+	0.973299i	$0.573722\pi$
$48$	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
$56$	386.007	−	163.140i	0.921113	−	0.389294i
$57$	151.362			0.351727
$58$	−72.8284	+	491.942i	−0.164877	+	1.11371i
$59$	632.911			1.39658			0.698288	−	0.715816i	$-0.253945\pi$
$59$	632.911			1.39658			0.698288	+	0.715816i	$0.253945\pi$
$60$	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	$0.167703\pi$
$67$			551.508i			1.00563i	−0.864393	+	0.502817i	$0.832297\pi$
$68$	−195.801	+	646.804i	−0.349181	+	1.15348i
$69$		−	923.724i		−	1.61164i
$70$	−293.024	−	352.289i	−0.500329	−	0.601522i
$71$			486.278i			0.812825i	0.913690	+	0.406412i	$0.133220\pi$
$71$			486.278i			0.812825i	−0.913690	+	0.406412i	$0.866780\pi$
$72$	−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	$0.0636646\pi$
$79$			279.010i			0.397355i	−0.980065	+	0.198677i	$0.936335\pi$
$80$	−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	$-0.634962\pi$
$83$	−622.183			−0.822813			−0.411406	+	0.911452i	$0.634962\pi$
$84$	581.511	+	955.229i	0.755335	+	1.24076i
$85$	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	$0.676938\pi$
$98$	969.515	+	35.1017i	0.999345	+	0.0361817i
$99$		−	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	$-0.504394\pi$
$103$	−28.8584			−0.0276068			−0.0138034	+	0.999905i	$0.504394\pi$
$104$	−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	$-0.992534\pi$
$107$		−	51.9136i		−	0.0469035i	0.999725	−	0.0234517i	$-0.00746561\pi$
$108$	−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
$112$	−296.565	−	1147.60i	−0.250203	−	0.968193i
$113$	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
$126$	−1207.00	+	1003.95i	−0.853397	+	0.709831i
$127$		−	845.289i		−	0.590608i	−0.955403	−	0.295304i	$-0.904579\pi$
$127$		−	845.289i		−	0.590608i	0.955403	−	0.295304i	$-0.0954209\pi$
$128$	−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	$-0.662456\pi$
$131$	−1464.88			−0.977001			−0.488501	+	0.872564i	$0.662456\pi$
$132$	−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	$-0.725071\pi$
$139$	−2129.17			−1.29924			−0.649618	+	0.760261i	$0.725071\pi$
$140$	−1107.05	+	673.938i	−0.668308	+	0.406844i
$141$	−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	$-0.809742\pi$
$151$		−	2088.40i		−	1.12551i	0.826625	−	0.562753i	$-0.190258\pi$
$152$	−193.655	+	410.363i	−0.103339	+	0.218979i
$153$		−	2531.73i		−	1.33777i
$154$	13.3216	+	16.0159i	0.00697068	+	0.00838052i
$155$		−	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	$0.243566\pi$
$163$			2882.96i			1.38534i	−0.721254	+	0.692670i	$0.756434\pi$
$164$	−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	$-0.347573\pi$
$167$	1988.79			0.921542			0.460771	+	0.887519i	$0.347573\pi$
$168$	2913.54	−	1231.36i	1.33800	−	0.565486i
$169$	−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	$-0.817136\pi$
$179$		−	2602.74i		−	1.08681i	0.839472	−	0.543403i	$-0.182864\pi$
$180$	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	$-0.162114\pi$
$182$	−2536.66	−	3049.71i	−1.03313	−	1.24209i
$183$			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	$-0.980570\pi$
$191$		−	322.049i		−	0.122004i	0.998138	−	0.0610018i	$-0.0194295\pi$
$192$	−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
$196$	499.798	−	2698.10i	0.182142	−	0.983272i
$197$	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	$-0.668092\pi$
$199$	−2828.98			−1.00774			−0.503872	+	0.863779i	$0.668092\pi$
$200$	−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
$210$	−2211.71	−	2659.03i	−0.726773	−	0.873766i
$211$			4950.07i			1.61506i	0.589828	+	0.807529i	$0.299196\pi$
$211$			4950.07i			1.61506i	−0.589828	+	0.807529i	$0.700804\pi$
$212$	−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	$-0.147411\pi$
$223$	5958.68			1.78934			0.894669	+	0.446729i	$0.147411\pi$
$224$	−3333.74	+	354.419i	−0.994396	+	0.105717i
$225$	1452.98			0.430513
$226$	131.740	−	889.879i	0.0387753	−	0.261920i
$227$	817.324			0.238977			0.119488	−	0.992836i	$-0.461875\pi$
$227$	817.324			0.238977			0.119488	+	0.992836i	$0.461875\pi$
$228$	−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
$238$	2829.69	+	3402.00i	0.770678	+	0.926550i
$239$		−	4292.34i		−	1.16171i	−0.814007	−	0.580855i	$-0.802718\pi$
$239$		−	4292.34i		−	1.16171i	0.814007	−	0.580855i	$-0.197282\pi$
$240$	−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	$-0.480827\pi$
$251$	478.767			0.120396			0.0601982	+	0.998186i	$0.480827\pi$
$252$	2309.02	+	3792.95i	0.577201	+	0.948148i
$253$	−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	$0.159829\pi$
$263$			4105.49i			0.962568i	−0.876565	+	0.481284i	$0.840171\pi$
$264$	61.4243	+	28.9869i	0.0143197	+	0.00675764i
$265$			2483.61i			0.575725i
$266$	−807.616	+	671.752i	−0.186158	+	0.154841i
$267$		−	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	$-0.496130\pi$
$271$	108.476			0.0243153			0.0121577	+	0.999926i	$0.496130\pi$
$272$	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
$280$	1427.08	+	3376.62i	0.304586	+	0.720684i
$281$	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	$-0.583751\pi$
$283$	−2476.45			−0.520175			−0.260088	+	0.965585i	$0.583751\pi$
$284$	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	$0.846860\pi$
$294$	7317.79	+	264.943i	1.45164	+	0.0525572i
$295$			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	$-0.454134\pi$
$307$	1544.80			0.287187			0.143594	+	0.989637i	$0.454134\pi$
$308$	50.3295	−	30.6389i	0.00931100	−	0.00566823i
$309$	−217.820			−0.0401014
$310$	−3135.06	−	464.123i	−0.574385	−	0.0850335i
$311$	−8897.39			−1.62227			−0.811133	−	0.584862i	$-0.801149\pi$
$311$	−8897.39			−1.62227			−0.811133	+	0.584862i	$0.801149\pi$
$312$	−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
$322$	4099.52	+	4928.66i	0.709495	+	0.852993i
$323$		−	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	$-0.694738\pi$
$331$		−	9859.53i		−	1.63725i	0.574330	−	0.818624i	$-0.305262\pi$
$332$	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
$336$	−2238.44	−	8661.92i	−0.363443	−	1.40639i
$337$	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	$-0.993664\pi$
$347$		−	257.299i		−	0.0398055i	0.999802	−	0.0199028i	$-0.00633567\pi$
$348$	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	$-0.0699048\pi$
$350$	−1952.44	+	1623.98i	−0.298177	+	0.248015i
$351$			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	$0.130472\pi$
$359$			5421.36i			0.797014i	−0.917165	+	0.398507i	$0.869528\pi$
$360$	−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
$364$	−9583.61	+	5834.18i	−1.37999	+	0.840094i
$365$	−1451.62			−0.208168
$366$	68.8291	+	10.1897i	0.00982994	+	0.00145525i
$367$	10941.3			1.55622			0.778109	−	0.628129i	$-0.216179\pi$
$367$	10941.3			1.55622			0.778109	+	0.628129i	$0.216179\pi$
$368$	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
$378$	−902.975	+	751.069i	−0.122868	+	0.102198i
$379$			12927.3i			1.75207i	0.482252	+	0.876033i	$0.339819\pi$
$379$			12927.3i			1.75207i	−0.482252	+	0.876033i	$0.660181\pi$
$380$	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	$-0.833292\pi$
$383$	−12981.5			−1.73192			−0.865960	+	0.500113i	$0.833292\pi$
$384$	−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
$392$	−7342.08	−	2515.99i	−0.945997	−	0.324175i
$393$	−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
$406$	7080.90	−	5889.69i	0.865565	−	0.719952i
$407$		−	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	$-0.294439\pi$
$419$	10323.4			1.20366			0.601829	+	0.798625i	$0.294439\pi$
$420$	−8355.92	+	5086.80i	−0.970779	+	0.590978i
$421$	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	$0.179309\pi$
$431$			9556.09i			1.06798i	−0.845490	+	0.533992i	$0.820691\pi$
$432$	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	$0.898321\pi$
$434$	5158.62	−	4290.79i	0.570557	−	0.474573i
$435$		−	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	$-0.442066\pi$
$439$	3329.73			0.362003			0.181001	+	0.983483i	$0.442066\pi$
$440$	−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	$-0.885458\pi$
$443$		−	6566.55i		−	0.704257i	0.935952	−	0.352129i	$-0.114542\pi$
$444$	−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
$448$	−389.238	+	9474.38i	−0.0410486	+	0.999157i
$449$	−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	$0.904956\pi$
$462$	100.550	+	120.886i	0.0101255	+	0.0121735i
$463$			12952.0i			1.30007i	0.759906	+	0.650033i	$0.225245\pi$
$463$			12952.0i			1.30007i	−0.759906	+	0.650033i	$0.774755\pi$
$464$	−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	$-0.383900\pi$
$467$	7199.70			0.713410			0.356705	+	0.934217i	$0.383900\pi$
$468$	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
$476$	10690.7	−	6508.12i	1.02942	−	0.626679i
$477$	8509.27			0.816798
$478$	−12009.7	−	1777.95i	−1.14918	−	0.170128i
$479$	10505.0			1.00205			0.501027	−	0.865431i	$-0.332956\pi$
$479$	10505.0			1.00205			0.501027	+	0.865431i	$0.332956\pi$
$480$	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	$-0.762053\pi$
$487$		−	14612.5i		−	1.35966i	0.733369	−	0.679831i	$-0.237947\pi$
$488$	−66.6937	−	31.4735i	−0.00618664	−	0.00291955i
$489$			21760.2i			2.01233i
$490$	−307.054	+	8480.89i	−0.0283087	+	0.781893i
$491$		−	16952.7i		−	1.55818i	−0.626913	−	0.779089i	$-0.715682\pi$
$491$		−	16952.7i		−	1.55818i	0.626913	−	0.779089i	$-0.284318\pi$
$492$	−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	$0.291680\pi$
$499$			17687.3i			1.58676i	−0.608727	+	0.793379i	$0.708320\pi$
$500$	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	$-0.719016\pi$
$503$	−14327.9			−1.27008			−0.635038	+	0.772481i	$0.719016\pi$
$504$	11568.8	−	4889.39i	1.02246	−	0.432125i
$505$	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
$518$	−10196.9	+	8481.50i	−0.864916	+	0.719413i
$519$		−	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	$-0.384362\pi$
$523$	8500.33			0.710695			0.355348	+	0.934734i	$0.384362\pi$
$524$	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
$532$	1544.99	+	2537.90i	0.125910	+	0.206827i
$533$	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
$546$	−19146.4	−	23018.9i	−1.50072	−	1.80424i
$547$			16381.3i			1.28046i	0.768182	+	0.640232i	$0.221162\pi$
$547$			16381.3i			1.28046i	−0.768182	+	0.640232i	$0.778838\pi$
$548$	−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
$560$	10038.7	−	2594.22i	0.757520	−	0.195760i
$561$	−253.564			−0.0190829
$562$	199.910	−	1350.35i	0.0150048	−	0.101355i
$563$	22890.4			1.71353			0.856764	−	0.515709i	$-0.172472\pi$
$563$	22890.4			1.71353			0.856764	+	0.515709i	$0.172472\pi$
$564$	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	$-0.857554\pi$
$571$		−	11808.4i		−	0.865439i	0.901529	−	0.432720i	$-0.142446\pi$
$572$	−230.588	−	69.8037i	−0.0168556	−	0.00510252i
$573$		−	2430.79i		−	0.177221i
$574$	2729.14	+	3281.11i	0.198453	+	0.238591i
$575$		−	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	$-0.562009\pi$
$587$	−5506.03			−0.387152			−0.193576	+	0.981085i	$0.562009\pi$
$588$	3772.42	−	20364.9i	0.264578	−	1.42829i
$589$	−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	$-0.874528\pi$
$599$		−	11260.6i		−	0.768107i	0.923311	−	0.384054i	$-0.125472\pi$
$600$	−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	$-0.330347\pi$
$602$	2316.00	+	2784.41i	0.156799	+	0.188512i
$603$			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	$-0.598092\pi$
$607$	−9071.99			−0.606624			−0.303312	+	0.952891i	$0.598092\pi$
$608$	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
$616$	−64.8784	−	153.510i	−0.00424355	−	0.0100407i
$617$	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	$-0.812835\pi$
$619$	−25628.2			−1.66411			−0.832054	+	0.554695i	$0.812835\pi$
$620$	−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
$630$	−8782.09	−	10558.3i	−0.555376	−	0.667702i
$631$			6093.01i			0.384404i	0.981355	+	0.192202i	$0.0615628\pi$
$631$			6093.01i			0.384404i	−0.981355	+	0.192202i	$0.938437\pi$
$632$	−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	$-0.655182\pi$
$643$	−15275.5			−0.936868			−0.468434	+	0.883499i	$0.655182\pi$
$644$	15488.1	−	9428.66i	0.947699	−	0.576928i
$645$	4564.93			0.278673
$646$	−4739.72	−	701.681i	−0.288672	−	0.0427357i
$647$	−10058.4			−0.611184			−0.305592	−	0.952163i	$-0.598854\pi$
$647$	−10058.4			−0.611184			−0.305592	+	0.952163i	$0.598854\pi$
$648$	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
$658$	5957.29	−	4955.10i	0.352947	−	0.293571i
$659$		−	15031.5i		−	0.888532i	−0.895895	−	0.444266i	$-0.853464\pi$
$659$		−	15031.5i		−	0.888532i	0.895895	−	0.444266i	$-0.146536\pi$
$660$	−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
$672$	−25162.7	+	2675.12i	−1.44445	+	0.153564i
$673$	−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	$0.206727\pi$
$683$			21589.2i			1.20950i	−0.796415	+	0.604751i	$0.793273\pi$
$684$	−4601.91	−	1393.09i	−0.257249	−	0.0778745i
$685$			6541.45i			0.364870i
$686$	−12946.5	−	12458.6i	−0.720554	−	0.693398i
$687$		−	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	$-0.420781\pi$
$691$	8948.20			0.492628			0.246314	+	0.969190i	$0.420781\pi$
$692$	−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
$700$	3735.06	+	6135.46i	0.201674	+	0.331284i
$701$	−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
$714$	21358.2	+	25677.9i	1.11948	+	1.34590i
$715$			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	$-0.717915\pi$
$719$	−24383.1			−1.26472			−0.632362	+	0.774673i	$0.717915\pi$
$720$	−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	$-0.338517\pi$
$727$	19046.5			0.971660			0.485830	+	0.874053i	$0.338517\pi$
$728$	12354.0	+	29230.9i	0.628941	+	1.48814i
$729$	−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	$0.0382265\pi$
$739$			4813.56i			0.239607i	−0.992798	+	0.119804i	$0.961773\pi$
$740$	5133.76	−	16958.8i	0.255028	−	0.842454i
$741$			11462.1i			0.568248i
$742$	−11434.3	+	9510.72i	−0.565723	+	0.470552i
$743$			17606.1i			0.869318i	0.900595	+	0.434659i	$0.143131\pi$
$743$			17606.1i			0.869318i	−0.900595	+	0.434659i	$0.856869\pi$
$744$	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	$-0.948956\pi$
$751$		−	6572.41i		−	0.319348i	0.987170	−	0.159674i	$-0.0510443\pi$
$752$	−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
$756$	1727.42	+	2837.57i	0.0831025	+	0.136510i
$757$	−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	$-0.0451555\pi$
$770$	−140.100	+	116.531i	−0.00655697	+	0.00545390i
$771$			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
$784$	−10080.8	+	19500.5i	−0.459218	+	0.888323i
$785$	−1475.63			−0.0670923
$786$	−4579.85	+	30936.0i	−0.207835	+	1.40388i
$787$	41103.6			1.86173			0.930867	−	0.365357i	$-0.119053\pi$
$787$	41103.6			1.86173			0.930867	+	0.365357i	$0.119053\pi$
$788$	−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	$0.953934\pi$
$798$	−6095.79	+	5070.31i	−0.270412	+	0.224921i
$799$			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	$-0.622538\pi$
$811$	−17346.1			−0.751053			−0.375526	+	0.926812i	$0.622538\pi$
$812$	−13546.0	−	22251.5i	−0.585431	−	0.961667i
$813$	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	$-0.972188\pi$
$823$		−	4120.54i		−	0.174524i	0.996185	−	0.0872618i	$-0.0278117\pi$
$824$	278.681	−	590.537i	0.0117820	−	0.0249664i
$825$		−	145.522i		−	0.00614114i
$826$	−25489.1	+	21201.1i	−1.07370	+	0.893077i
$827$			493.902i			0.0207674i	0.999946	+	0.0103837i	$0.00330530\pi$
$827$			493.902i			0.0207674i	−0.999946	+	0.0103837i	$0.996695\pi$
$828$	−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	$-0.243343\pi$
$839$	35079.5			1.44348			0.721739	+	0.692166i	$0.243343\pi$
$840$	10771.4	+	25486.3i	0.442439	+	1.04686i
$841$	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	$0.759481\pi$
$854$	−109.176	−	131.257i	−0.00437461	−	0.00525939i
$855$			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	$-0.452677\pi$
$859$	7458.37			0.296247			0.148124	+	0.988969i	$0.452677\pi$
$860$	−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	$-0.986773\pi$
$863$		−	2106.36i		−	0.0830839i	0.999137	−	0.0415420i	$-0.0132270\pi$
$864$	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
$868$	−9868.58	−	16210.8i	−0.385900	−	0.633905i
$869$	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	$0.926690\pi$
$882$	29056.9	+	1052.02i	1.10929	+	0.0401624i
$883$		−	6631.93i		−	0.252754i	−0.991982	−	0.126377i	$-0.959665\pi$
$883$		−	6631.93i		−	0.252754i	0.991982	−	0.126377i	$-0.0403350\pi$
$884$	−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	$-0.334888\pi$
$887$	26193.4			0.991530			0.495765	+	0.868457i	$0.334888\pi$
$888$	−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
$896$	26347.5	+	5013.48i	0.982373	+	0.186929i
$897$	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	$0.119157\pi$
$907$			19976.6i			0.731324i	−0.930748	+	0.365662i	$0.880843\pi$
$908$	−6258.13	−	1894.46i	−0.228726	−	0.0692400i
$909$		−	23212.2i		−	0.846976i
$910$	26677.5	−	22189.6i	0.971815	−	0.808328i
$911$			33720.7i			1.22636i	0.789942	+	0.613182i	$0.210111\pi$
$911$			33720.7i			1.22636i	−0.789942	+	0.613182i	$0.789889\pi$
$912$	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	$0.252389\pi$
$919$			39693.8i			1.42479i	−0.701780	+	0.712393i	$0.747611\pi$
$920$	−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
$924$	379.881	−	231.259i	0.0135251	−	0.00823361i
$925$	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	$-0.164278\pi$
$938$	−18474.3	−	22210.8i	−0.643078	−	0.773142i
$939$		−	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	$-0.681181\pi$
$947$		−	49095.2i		−	1.68467i	0.538957	−	0.842333i	$-0.318819\pi$
$948$	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
$952$	−13781.1	−	32607.5i	−0.469167	−	1.11010i
$953$	−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
$966$	30942.7	+	37201.0i	1.03061	+	1.23905i
$967$		−	25958.2i		−	0.863247i	−0.902054	−	0.431624i	$-0.857941\pi$
$967$		−	25958.2i		−	0.863247i	0.902054	−	0.431624i	$-0.142059\pi$
$968$	−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	$-0.338627\pi$
$971$	29381.4			0.971055			0.485528	+	0.874221i	$0.338627\pi$
$972$	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
$980$	23601.8	+	4372.02i	0.769317	+	0.142509i
$981$	3962.01			0.128947
$982$	−47432.6	−	7022.05i	−1.54138	−	0.228190i
$983$	−19941.1			−0.647021			−0.323511	−	0.946225i	$-0.604863\pi$
$983$	−19941.1			−0.647021			−0.323511	+	0.946225i	$0.604863\pi$
$984$	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	$-0.937914\pi$
$991$		−	12092.8i		−	0.387629i	0.981038	−	0.193815i	$-0.0620861\pi$
$992$	−15546.8	+	17202.8i	−0.497593	+	0.550595i
$993$		−	74418.6i		−	2.37825i
$994$	−16289.2	−	19583.8i	−0.519782	−	0.624909i
$995$		−	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.27.6	yes	8
3.2	odd	2		252.4.b.d.55.3		8
4.3	odd	2	inner	28.4.d.b.27.7	yes	8
7.2	even	3		196.4.f.c.31.1		16
7.3	odd	6		196.4.f.c.19.6		16
7.4	even	3		196.4.f.c.19.5		16
7.5	odd	6		196.4.f.c.31.2		16
7.6	odd	2	inner	28.4.d.b.27.5	✓	8
8.3	odd	2		448.4.f.d.447.7		8
8.5	even	2		448.4.f.d.447.1		8
12.11	even	2		252.4.b.d.55.1		8
21.20	even	2		252.4.b.d.55.4		8
28.3	even	6		196.4.f.c.19.1		16
28.11	odd	6		196.4.f.c.19.2		16
28.19	even	6		196.4.f.c.31.5		16
28.23	odd	6		196.4.f.c.31.6		16
28.27	even	2	inner	28.4.d.b.27.8	yes	8
56.13	odd	2		448.4.f.d.447.8		8
56.27	even	2		448.4.f.d.447.2		8
84.83	odd	2		252.4.b.d.55.2		8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.414214 - 2.79793i) q^{2} +7.54788 q^{3} +(-7.65685 - 2.31788i) q^{4} +8.74756i q^{5} +(3.12644 - 21.1185i) q^{6} +(-13.8008 - 12.3507i) q^{7} +(-9.65685 + 20.4633i) q^{8} +29.9706 q^{9} +O(q^{10})\)	\(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} +(-40.2728 + 33.4978i) 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} +(77.0430 + 126.556i) 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} +(-303.975 + 252.837i) 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} +(386.007 - 163.140i) 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} +(-293.024 - 352.289i) 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} +(581.511 + 955.229i) 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} +(969.515 + 35.1017i) q^{98} -11.9189i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 16 q^{4} - 32 q^{8} + 104 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 16 * q^4 - 32 * q^8 + 104 * q^9	\( 8 q - 8 q^{2} - 16 q^{4} - 32 q^{8} + 104 q^{9} - 152 q^{14} + 64 q^{16} + 88 q^{18} - 64 q^{21} + 240 q^{22} - 472 q^{25} - 48 q^{28} - 592 q^{29} + 256 q^{30} + 1152 q^{32} - 976 q^{36} + 1392 q^{37} - 1024 q^{42} - 1184 q^{44} - 816 q^{46} + 1480 q^{49} + 1688 q^{50} - 1168 q^{53} + 800 q^{56} - 192 q^{57} - 560 q^{58} + 2944 q^{60} - 3328 q^{64} + 448 q^{65} - 3200 q^{70} - 1184 q^{72} - 496 q^{74} + 368 q^{77} + 7680 q^{78} - 4984 q^{81} + 4480 q^{84} + 1024 q^{85} + 240 q^{86} + 3776 q^{88} - 3808 q^{92} - 2304 q^{93} - 3144 q^{98}+O(q^{100}) \) 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

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