LMFDB - Embedded newform 74.4.b.a.73.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,4,Mod(73,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("74.73");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	74.b (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:	$4.36614134042$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 212x^{8} + 15052x^{6} + 392769x^{4} + 2690496x^{2} + 2985984 $ x^10 + 212x^8 + 15052x^6 + 392769x^4 + 2690496x^2 + 2985984
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			73.6
Root			$-9.15606i$ of defining polynomial
Character	$\chi$	$=$	74.73
Dual form			74.4.b.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -8.15606 q^{3} -4.00000 q^{4} -6.18414i q^{5} -16.3121i q^{6} +23.1710 q^{7} -8.00000i q^{8} +39.5214 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} -8.15606 q^{3} -4.00000 q^{4} -6.18414i q^{5} -16.3121i q^{6} +23.1710 q^{7} -8.00000i q^{8} +39.5214 q^{9} +12.3683 q^{10} +13.1720 q^{11} +32.6243 q^{12} -30.8318i q^{13} +46.3419i q^{14} +50.4382i q^{15} +16.0000 q^{16} -87.4073i q^{17} +79.0427i q^{18} -93.7642i q^{19} +24.7365i q^{20} -188.984 q^{21} +26.3440i q^{22} +73.1586i q^{23} +65.2485i q^{24} +86.7565 q^{25} +61.6636 q^{26} -102.125 q^{27} -92.6838 q^{28} -199.813i q^{29} -100.876 q^{30} +125.466i q^{31} +32.0000i q^{32} -107.432 q^{33} +174.815 q^{34} -143.292i q^{35} -158.085 q^{36} +(77.2704 - 211.382i) q^{37} +187.528 q^{38} +251.466i q^{39} -49.4731 q^{40} -339.539 q^{41} -377.967i q^{42} +501.524i q^{43} -52.6880 q^{44} -244.406i q^{45} -146.317 q^{46} +282.743 q^{47} -130.497 q^{48} +193.893 q^{49} +173.513i q^{50} +712.900i q^{51} +123.327i q^{52} -205.198 q^{53} -204.250i q^{54} -81.4574i q^{55} -185.368i q^{56} +764.747i q^{57} +399.625 q^{58} -680.820i q^{59} -201.753i q^{60} -352.825i q^{61} -250.932 q^{62} +915.748 q^{63} -64.0000 q^{64} -190.668 q^{65} -214.863i q^{66} +739.362 q^{67} +349.629i q^{68} -596.686i q^{69} +286.585 q^{70} -188.184 q^{71} -316.171i q^{72} +1218.89 q^{73} +(422.764 + 154.541i) q^{74} -707.591 q^{75} +375.057i q^{76} +305.208 q^{77} -502.932 q^{78} -750.645i q^{79} -98.9462i q^{80} -234.138 q^{81} -679.079i q^{82} -982.987 q^{83} +755.935 q^{84} -540.539 q^{85} -1003.05 q^{86} +1629.68i q^{87} -105.376i q^{88} +1142.82i q^{89} +488.811 q^{90} -714.402i q^{91} -292.634i q^{92} -1023.31i q^{93} +565.485i q^{94} -579.850 q^{95} -260.994i q^{96} +273.010i q^{97} +387.786i q^{98} +520.576 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9}+O(q^{10}) $ 10 * q + 14 * q^3 - 40 * q^4 - 4 * q^7 + 172 * q^9	$ 10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9} + 76 q^{10} - 50 q^{11} - 56 q^{12} + 160 q^{16} - 312 q^{21} - 700 q^{25} + 492 q^{26} + 848 q^{27} + 16 q^{28} - 240 q^{30} - 508 q^{33} - 568 q^{34} - 688 q^{36} + 82 q^{37} + 336 q^{38} - 304 q^{40} - 1194 q^{41} + 200 q^{44} + 60 q^{46} + 464 q^{47} + 224 q^{48} + 2382 q^{49} - 692 q^{53} + 1108 q^{58} - 1700 q^{62} + 2300 q^{63} - 640 q^{64} + 604 q^{65} + 1114 q^{67} + 1880 q^{70} - 1460 q^{71} + 2082 q^{73} + 968 q^{74} - 5160 q^{75} - 6096 q^{77} + 1004 q^{78} + 4978 q^{81} - 1364 q^{83} + 1248 q^{84} + 104 q^{85} + 1400 q^{86} - 2600 q^{90} + 5084 q^{95} + 508 q^{99}+O(q^{100}) $ 10 * q + 14 * q^3 - 40 * q^4 - 4 * q^7 + 172 * q^9 + 76 * q^10 - 50 * q^11 - 56 * q^12 + 160 * q^16 - 312 * q^21 - 700 * q^25 + 492 * q^26 + 848 * q^27 + 16 * q^28 - 240 * q^30 - 508 * q^33 - 568 * q^34 - 688 * q^36 + 82 * q^37 + 336 * q^38 - 304 * q^40 - 1194 * q^41 + 200 * q^44 + 60 * q^46 + 464 * q^47 + 224 * q^48 + 2382 * q^49 - 692 * q^53 + 1108 * q^58 - 1700 * q^62 + 2300 * q^63 - 640 * q^64 + 604 * q^65 + 1114 * q^67 + 1880 * q^70 - 1460 * q^71 + 2082 * q^73 + 968 * q^74 - 5160 * q^75 - 6096 * q^77 + 1004 * q^78 + 4978 * q^81 - 1364 * q^83 + 1248 * q^84 + 104 * q^85 + 1400 * q^86 - 2600 * q^90 + 5084 * q^95 + 508 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$-1$

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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$	−8.15606			−1.56964			−0.784818	−	0.619727i	$-0.787243\pi$
$3$	−8.15606			−1.56964			−0.784818	+	0.619727i	$0.787243\pi$
$4$	−4.00000			−0.500000
$5$		−	6.18414i		−	0.553126i	−0.960996	−	0.276563i	$-0.910805\pi$
$5$		−	6.18414i		−	0.553126i	0.960996	−	0.276563i	$-0.0891954\pi$
$6$		−	16.3121i		−	1.10990i
$7$	23.1710			1.25111			0.625557	−	0.780179i	$-0.284872\pi$
$7$	23.1710			1.25111			0.625557	+	0.780179i	$0.284872\pi$
$8$		−	8.00000i		−	0.353553i
$9$	39.5214			1.46375
$10$	12.3683			0.391119
$11$	13.1720			0.361046			0.180523	−	0.983571i	$-0.442221\pi$
$11$	13.1720			0.361046			0.180523	+	0.983571i	$0.442221\pi$
$12$	32.6243			0.784818
$13$		−	30.8318i		−	0.657785i	−0.944367	−	0.328892i	$-0.893325\pi$
$13$		−	30.8318i		−	0.657785i	0.944367	−	0.328892i	$-0.106675\pi$
$14$			46.3419i			0.884671i
$15$			50.4382i			0.868206i
$16$	16.0000			0.250000
$17$		−	87.4073i		−	1.24702i	−0.781814	−	0.623511i	$-0.785705\pi$
$17$		−	87.4073i		−	1.24702i	0.781814	−	0.623511i	$-0.214295\pi$
$18$			79.0427i			1.03503i
$19$		−	93.7642i		−	1.13216i	−0.824351	−	0.566078i	$-0.808460\pi$
$19$		−	93.7642i		−	1.13216i	0.824351	−	0.566078i	$-0.191540\pi$
$20$			24.7365i			0.276563i
$21$	−188.984			−1.96379
$22$			26.3440i			0.255298i
$23$			73.1586i			0.663244i	0.943412	+	0.331622i	$0.107596\pi$
$23$			73.1586i			0.663244i	−0.943412	+	0.331622i	$0.892404\pi$
$24$			65.2485i			0.554950i
$25$	86.7565			0.694052
$26$	61.6636			0.465124
$27$	−102.125			−0.727925
$28$	−92.6838			−0.625557
$29$		−	199.813i		−	1.27946i	−0.768601	−	0.639729i	$-0.779047\pi$
$29$		−	199.813i		−	1.27946i	0.768601	−	0.639729i	$-0.220953\pi$
$30$	−100.876			−0.613914
$31$			125.466i			0.726915i	0.931611	+	0.363458i	$0.118404\pi$
$31$			125.466i			0.726915i	−0.931611	+	0.363458i	$0.881596\pi$
$32$			32.0000i			0.176777i
$33$	−107.432			−0.566711
$34$	174.815			0.881778
$35$		−	143.292i		−	0.692023i
$36$	−158.085			−0.731877
$37$	77.2704	−	211.382i	0.343329	−	0.939215i
$37$	77.2704	−	211.382i	0.343329	−	0.939215i
$38$	187.528			0.800556
$39$			251.466i			1.03248i
$40$	−49.4731			−0.195560
$41$	−339.539			−1.29334			−0.646672	−	0.762768i	$-0.723840\pi$
$41$	−339.539			−1.29334			−0.646672	+	0.762768i	$0.723840\pi$
$42$		−	377.967i		−	1.38861i
$43$			501.524i			1.77864i	0.457283	+	0.889321i	$0.348823\pi$
$43$			501.524i			1.77864i	−0.457283	+	0.889321i	$0.651177\pi$
$44$	−52.6880			−0.180523
$45$		−	244.406i		−	0.809641i
$46$	−146.317			−0.468985
$47$	282.743			0.877494			0.438747	−	0.898611i	$-0.355422\pi$
$47$	282.743			0.877494			0.438747	+	0.898611i	$0.355422\pi$
$48$	−130.497			−0.392409
$49$	193.893			0.565286
$50$			173.513i			0.490769i
$51$			712.900i			1.95737i
$52$			123.327i			0.328892i
$53$	−205.198			−0.531814			−0.265907	−	0.963999i	$-0.585671\pi$
$53$	−205.198			−0.531814			−0.265907	+	0.963999i	$0.585671\pi$
$54$		−	204.250i		−	0.514721i
$55$		−	81.4574i		−	0.199704i
$56$		−	185.368i		−	0.442335i
$57$			764.747i			1.77707i
$58$	399.625			0.904713
$59$		−	680.820i		−	1.50229i	−0.660137	−	0.751145i	$-0.729502\pi$
$59$		−	680.820i		−	1.50229i	0.660137	−	0.751145i	$-0.270498\pi$
$60$		−	201.753i		−	0.434103i
$61$		−	352.825i		−	0.740568i	−0.928919	−	0.370284i	$-0.879260\pi$
$61$		−	352.825i		−	0.740568i	0.928919	−	0.370284i	$-0.120740\pi$
$62$	−250.932			−0.514007
$63$	915.748			1.83132
$64$	−64.0000			−0.125000
$65$	−190.668			−0.363838
$66$		−	214.863i		−	0.400725i
$67$	739.362			1.34817			0.674085	−	0.738653i	$-0.264538\pi$
$67$	739.362			1.34817			0.674085	+	0.738653i	$0.264538\pi$
$68$			349.629i			0.623511i
$69$		−	596.686i		−	1.04105i
$70$	286.585			0.489334
$71$	−188.184			−0.314554			−0.157277	−	0.987555i	$-0.550272\pi$
$71$	−188.184			−0.314554			−0.157277	+	0.987555i	$0.550272\pi$
$72$		−	316.171i		−	0.517515i
$73$	1218.89			1.95425			0.977124	−	0.212669i	$-0.0682155\pi$
$73$	1218.89			1.95425			0.977124	+	0.212669i	$0.0682155\pi$
$74$	422.764	+	154.541i	0.664125	+	0.242770i
$75$	−707.591			−1.08941
$76$			375.057i			0.566078i
$77$	305.208			0.451710
$78$	−502.932			−0.730075
$79$		−	750.645i		−	1.06904i	−0.845156	−	0.534520i	$-0.820493\pi$
$79$		−	750.645i		−	1.06904i	0.845156	−	0.534520i	$-0.179507\pi$
$80$		−	98.9462i		−	0.138281i
$81$	−234.138			−0.321177
$82$		−	679.079i		−	0.914533i
$83$	−982.987			−1.29996			−0.649981	−	0.759951i	$-0.725223\pi$
$83$	−982.987			−1.29996			−0.649981	+	0.759951i	$0.725223\pi$
$84$	755.935			0.981896
$85$	−540.539			−0.689761
$86$	−1003.05			−1.25769
$87$			1629.68i			2.00828i
$88$		−	105.376i		−	0.127649i
$89$			1142.82i			1.36111i	0.732697	+	0.680555i	$0.238261\pi$
$89$			1142.82i			1.36111i	−0.732697	+	0.680555i	$0.761739\pi$
$90$	488.811			0.572502
$91$		−	714.402i		−	0.822964i
$92$		−	292.634i		−	0.331622i
$93$		−	1023.31i		−	1.14099i
$94$			565.485i			0.620482i
$95$	−579.850			−0.626225
$96$		−	260.994i		−	0.277475i
$97$			273.010i			0.285773i	0.989739	+	0.142886i	$0.0456384\pi$
$97$			273.010i			0.285773i	−0.989739	+	0.142886i	$0.954362\pi$
$98$			387.786i			0.399717i
$99$	520.576			0.528483
$100$	−347.026			−0.347026
$101$	−494.376			−0.487052			−0.243526	−	0.969894i	$-0.578304\pi$
$101$	−494.376			−0.487052			−0.243526	+	0.969894i	$0.578304\pi$
$102$	−1425.80			−1.38407
$103$		−	29.4638i		−	0.0281859i	−0.999901	−	0.0140930i	$-0.995514\pi$
$103$		−	29.4638i		−	0.0281859i	0.999901	−	0.0140930i	$-0.00448608\pi$
$104$	−246.654			−0.232562
$105$			1168.70i			1.08622i
$106$		−	410.396i		−	0.376049i
$107$	−995.991			−0.899870			−0.449935	−	0.893061i	$-0.648553\pi$
$107$	−995.991			−0.899870			−0.449935	+	0.893061i	$0.648553\pi$
$108$	408.500			0.363963
$109$			1520.44i			1.33607i	0.744131	+	0.668033i	$0.232864\pi$
$109$			1520.44i			1.33607i	−0.744131	+	0.668033i	$0.767136\pi$
$110$	162.915			0.141212
$111$	−630.222	+	1724.04i	−0.538901	+	1.47423i
$112$	370.735			0.312778
$113$			345.963i			0.288013i	0.989577	+	0.144006i	$0.0459986\pi$
$113$			345.963i			0.288013i	−0.989577	+	0.144006i	$0.954001\pi$
$114$	−1529.49			−1.25658
$115$	452.423			0.366858
$116$			799.251i			0.639729i
$117$		−	1218.52i		−	0.962836i
$118$	1361.64			1.06228
$119$		−	2025.31i		−	1.56017i
$120$	403.506			0.306957
$121$	−1157.50			−0.869646
$122$	705.651			0.523661
$123$	2769.30			2.03008
$124$		−	501.864i		−	0.363458i
$125$		−	1309.53i		−	0.937024i
$126$			1831.50i			1.29494i
$127$	−274.140			−0.191544			−0.0957718	−	0.995403i	$-0.530532\pi$
$127$	−274.140			−0.191544			−0.0957718	+	0.995403i	$0.530532\pi$
$128$		−	128.000i		−	0.0883883i
$129$		−	4090.46i		−	2.79182i
$130$		−	381.336i		−	0.257272i
$131$			2121.21i			1.41474i	0.706843	+	0.707371i	$0.250119\pi$
$131$			2121.21i			1.41474i	−0.706843	+	0.707371i	$0.749881\pi$
$132$	429.727			0.283355
$133$		−	2172.60i		−	1.41646i
$134$			1478.72i			0.953301i
$135$			631.556i			0.402634i
$136$	−699.259			−0.440889
$137$	2884.30			1.79870			0.899352	−	0.437225i	$-0.144039\pi$
$137$	2884.30			1.79870			0.899352	+	0.437225i	$0.144039\pi$
$138$	1193.37			0.736135
$139$	−600.553			−0.366462			−0.183231	−	0.983070i	$-0.558656\pi$
$139$	−600.553			−0.366462			−0.183231	+	0.983070i	$0.558656\pi$
$140$			573.169i			0.346012i
$141$	−2306.07			−1.37735
$142$		−	376.368i		−	0.222423i
$143$		−	406.116i		−	0.237491i
$144$	632.342			0.365939
$145$	−1235.67			−0.707701
$146$			2437.78i			1.38186i
$147$	−1581.40			−0.887292
$148$	−309.081	+	845.527i	−0.171664	+	0.469608i
$149$	−2645.27			−1.45442			−0.727210	−	0.686415i	$-0.759183\pi$
$149$	−2645.27			−1.45442			−0.727210	+	0.686415i	$0.759183\pi$
$150$		−	1415.18i		−	0.770328i
$151$	522.302			0.281485			0.140743	−	0.990046i	$-0.455051\pi$
$151$	522.302			0.281485			0.140743	+	0.990046i	$0.455051\pi$
$152$	−750.113			−0.400278
$153$		−	3454.46i		−	1.82534i
$154$			610.415i			0.319407i
$155$	775.900			0.402076
$156$		−	1005.86i		−	0.516241i
$157$	2035.42			1.03468			0.517338	−	0.855781i	$-0.326923\pi$
$157$	2035.42			1.03468			0.517338	+	0.855781i	$0.326923\pi$
$158$	1501.29			0.755925
$159$	1673.61			0.834754
$160$	197.892			0.0977798
$161$			1695.15i			0.829794i
$162$		−	468.276i		−	0.227107i
$163$			2639.80i			1.26850i	0.773130	+	0.634248i	$0.218690\pi$
$163$			2639.80i			1.26850i	−0.773130	+	0.634248i	$0.781310\pi$
$164$	1358.16			0.646672
$165$			664.372i			0.313462i
$166$		−	1965.97i		−	0.919212i
$167$		−	1398.92i		−	0.648215i	−0.946020	−	0.324108i	$-0.894936\pi$
$167$		−	1398.92i		−	0.648215i	0.946020	−	0.324108i	$-0.105064\pi$
$168$			1511.87i			0.694305i
$169$	1246.40			0.567319
$170$		−	1081.08i		−	0.487734i
$171$		−	3705.69i		−	1.65720i
$172$		−	2006.09i		−	0.889321i
$173$	2092.92			0.919781			0.459890	−	0.887976i	$-0.347889\pi$
$173$	2092.92			0.919781			0.459890	+	0.887976i	$0.347889\pi$
$174$	−3259.37			−1.42007
$175$	2010.23			0.868338
$176$	210.752			0.0902615
$177$			5552.81i			2.35805i
$178$	−2285.64			−0.962451
$179$		−	353.155i		−	0.147464i	−0.997278	−	0.0737319i	$-0.976509\pi$
$179$		−	353.155i		−	0.147464i	0.997278	−	0.0737319i	$-0.0234909\pi$
$180$			977.622i			0.404820i
$181$	4743.66			1.94803			0.974014	−	0.226486i	$-0.0727237\pi$
$181$	4743.66			1.94803			0.974014	+	0.226486i	$0.0727237\pi$
$182$	1428.80			0.581923
$183$			2877.67i			1.16242i
$184$	585.269			0.234492
$185$	−1307.21	−	477.850i	−0.519504	−	0.189904i
$186$	2046.62			0.806803
$187$		−	1151.33i		−	0.450233i
$188$	−1130.97			−0.438747
$189$	−2366.34			−0.910718
$190$		−	1159.70i		−	0.442808i
$191$			2194.63i			0.831403i	0.909501	+	0.415701i	$0.136464\pi$
$191$			2194.63i			0.831403i	−0.909501	+	0.415701i	$0.863536\pi$
$192$	521.988			0.196204
$193$			1296.70i			0.483618i	0.970324	+	0.241809i	$0.0777408\pi$
$193$			1296.70i			0.483618i	−0.970324	+	0.241809i	$0.922259\pi$
$194$	−546.020			−0.202072
$195$	1555.10			0.571093
$196$	−775.572			−0.282643
$197$	−544.940			−0.197083			−0.0985415	−	0.995133i	$-0.531418\pi$
$197$	−544.940			−0.197083			−0.0985415	+	0.995133i	$0.531418\pi$
$198$			1041.15i			0.373694i
$199$			2593.20i			0.923753i	0.886944	+	0.461877i	$0.152824\pi$
$199$			2593.20i			0.923753i	−0.886944	+	0.461877i	$0.847176\pi$
$200$		−	694.052i		−	0.245384i
$201$	−6030.28			−2.11614
$202$		−	988.752i		−	0.344398i
$203$		−	4629.85i		−	1.60075i
$204$		−	2851.60i		−	0.978686i
$205$			2099.76i			0.715382i
$206$	58.9275			0.0199305
$207$			2891.33i			0.970827i
$208$		−	493.309i		−	0.164446i
$209$		−	1235.06i		−	0.408761i
$210$	−2337.40			−0.768077
$211$	−716.919			−0.233909			−0.116954	−	0.993137i	$-0.537313\pi$
$211$	−716.919			−0.233909			−0.116954	+	0.993137i	$0.537313\pi$
$212$	820.793			0.265907
$213$	1534.84			0.493735
$214$		−	1991.98i		−	0.636304i
$215$	3101.49			0.983813
$216$			817.001i			0.257361i
$217$			2907.17i			0.909454i
$218$	−3040.87			−0.944742
$219$	−9941.34			−3.06746
$220$			325.830i			0.0998520i
$221$	−2694.93			−0.820273
$222$	−3448.09	−	1260.44i	−1.04243	−	0.381061i
$223$	−4983.88			−1.49662			−0.748308	−	0.663351i	$-0.769134\pi$
$223$	−4983.88			−1.49662			−0.748308	+	0.663351i	$0.769134\pi$
$224$			741.470i			0.221168i
$225$	3428.73			1.01592
$226$	−691.926			−0.203656
$227$		−	1006.33i		−	0.294239i	−0.989119	−	0.147120i	$-0.953000\pi$
$227$		−	1006.33i		−	0.294239i	0.989119	−	0.147120i	$-0.0470002\pi$
$228$		−	3058.99i		−	0.888536i
$229$	−192.382			−0.0555152			−0.0277576	−	0.999615i	$-0.508837\pi$
$229$	−192.382			−0.0555152			−0.0277576	+	0.999615i	$0.508837\pi$
$230$			904.845i			0.259408i
$231$	−2489.29			−0.709020
$232$	−1598.50			−0.452357
$233$	−238.782			−0.0671378			−0.0335689	−	0.999436i	$-0.510687\pi$
$233$	−238.782			−0.0671378			−0.0335689	+	0.999436i	$0.510687\pi$
$234$	2437.03			0.680828
$235$		−	1748.52i		−	0.485365i
$236$			2723.28i			0.751145i
$237$			6122.31i			1.67800i
$238$	4050.62			1.10320
$239$			2906.15i			0.786541i	0.919423	+	0.393271i	$0.128656\pi$
$239$			2906.15i			0.786541i	−0.919423	+	0.393271i	$0.871344\pi$
$240$			807.011i			0.217051i
$241$		−	5886.39i		−	1.57334i	−0.617371	−	0.786672i	$-0.711802\pi$
$241$		−	5886.39i		−	1.57334i	0.617371	−	0.786672i	$-0.288198\pi$
$242$		−	2315.00i		−	0.614932i
$243$	4667.02			1.23206
$244$			1411.30i			0.370284i
$245$		−	1199.06i		−	0.312674i
$246$			5538.61i			1.43548i
$247$	−2890.92			−0.744715
$248$	1003.73			0.257003
$249$	8017.30			2.04047
$250$	2619.06			0.662576
$251$		−	3453.68i		−	0.868503i	−0.900792	−	0.434252i	$-0.857013\pi$
$251$		−	3453.68i		−	0.868503i	0.900792	−	0.434252i	$-0.142987\pi$
$252$	−3662.99			−0.915662
$253$			963.645i			0.239462i
$254$		−	548.281i		−	0.135442i
$255$	4408.67			1.08267
$256$	256.000			0.0625000
$257$			1220.86i			0.296323i	0.988963	+	0.148162i	$0.0473356\pi$
$257$			1220.86i			0.296323i	−0.988963	+	0.148162i	$0.952664\pi$
$258$	8180.92			1.97412
$259$	1790.43	−	4897.92i	0.429544	−	1.17507i
$260$	762.672			0.181919
$261$		−	7896.87i		−	1.87281i
$262$	−4242.42			−1.00037
$263$	5581.38			1.30860			0.654301	−	0.756234i	$-0.272963\pi$
$263$	5581.38			1.30860			0.654301	+	0.756234i	$0.272963\pi$
$264$			859.453i			0.200362i
$265$			1268.97i			0.294160i
$266$	4345.21			1.00159
$267$		−	9320.93i		−	2.13645i
$268$	−2957.45			−0.674085
$269$	−1692.42			−0.383601			−0.191800	−	0.981434i	$-0.561433\pi$
$269$	−1692.42			−0.383601			−0.191800	+	0.981434i	$0.561433\pi$
$270$	−1263.11			−0.284706
$271$	−174.882			−0.0392005			−0.0196002	−	0.999808i	$-0.506239\pi$
$271$	−174.882			−0.0392005			−0.0196002	+	0.999808i	$0.506239\pi$
$272$		−	1398.52i		−	0.311756i
$273$			5826.71i			1.29175i
$274$			5768.60i			1.27188i
$275$	1142.76			0.250585
$276$			2386.74i			0.520526i
$277$			8293.21i			1.79888i	0.437040	+	0.899442i	$0.356027\pi$
$277$			8293.21i			1.79888i	−0.437040	+	0.899442i	$0.643973\pi$
$278$		−	1201.11i		−	0.259128i
$279$			4958.59i			1.06403i
$280$	−1146.34			−0.244667
$281$		−	1151.14i		−	0.244381i	−0.992507	−	0.122191i	$-0.961008\pi$
$281$		−	1151.14i		−	0.244381i	0.992507	−	0.122191i	$-0.0389919\pi$
$282$		−	4612.13i		−	0.973931i
$283$			704.117i			0.147899i	0.997262	+	0.0739495i	$0.0235604\pi$
$283$			704.117i			0.147899i	−0.997262	+	0.0739495i	$0.976440\pi$
$284$	752.736			0.157277
$285$	4729.30			0.982945
$286$	812.233			0.167931
$287$	−7867.45			−1.61812
$288$			1264.68i			0.258758i
$289$	−2727.04			−0.555066
$290$		−	2471.34i		−	0.500420i
$291$		−	2226.69i		−	0.448559i
$292$	−4875.56			−0.977124
$293$	7314.96			1.45851			0.729257	−	0.684240i	$-0.239866\pi$
$293$	7314.96			1.45851			0.729257	+	0.684240i	$0.239866\pi$
$294$		−	3162.81i		−	0.627410i
$295$	−4210.28			−0.830956
$296$	−1691.05	−	618.163i	−0.332063	−	0.121385i
$297$	−1345.19			−0.262815
$298$		−	5290.53i		−	1.02843i
$299$	2255.61			0.436272
$300$	2830.36			0.544704
$301$			11620.8i			2.22528i
$302$			1044.60i			0.199040i
$303$	4032.16			0.764494
$304$		−	1500.23i		−	0.283039i
$305$	−2181.92			−0.409627
$306$	6908.91			1.29071
$307$	−4880.36			−0.907287			−0.453643	−	0.891183i	$-0.649876\pi$
$307$	−4880.36			−0.907287			−0.453643	+	0.891183i	$0.649876\pi$
$308$	−1220.83			−0.225855
$309$			240.308i			0.0442416i
$310$			1551.80i			0.284311i
$311$		−	5522.07i		−	1.00684i	−0.864041	−	0.503421i	$-0.832074\pi$
$311$		−	5522.07i		−	1.00684i	0.864041	−	0.503421i	$-0.167926\pi$
$312$	2011.73			0.365038
$313$			4987.38i			0.900649i	0.892865	+	0.450325i	$0.148692\pi$
$313$			4987.38i			0.900649i	−0.892865	+	0.450325i	$0.851308\pi$
$314$			4070.84i			0.731626i
$315$		−	5663.11i		−	1.01295i
$316$			3002.58i			0.534520i
$317$	−3919.37			−0.694429			−0.347214	−	0.937786i	$-0.612872\pi$
$317$	−3919.37			−0.694429			−0.347214	+	0.937786i	$0.612872\pi$
$318$			3347.22i			0.590260i
$319$		−	2631.93i		−	0.461943i
$320$			395.785i			0.0691407i
$321$	8123.37			1.41247
$322$	−3390.31			−0.586753
$323$	−8195.68			−1.41183
$324$	936.552			0.160589
$325$		−	2674.86i		−	0.456537i
$326$	−5279.59			−0.896962
$327$		−	12400.8i		−	2.09714i
$328$			2716.31i			0.457266i
$329$	6551.41			1.09785
$330$	−1328.74			−0.221651
$331$		−	6773.07i		−	1.12472i	−0.826893	−	0.562359i	$-0.809894\pi$
$331$		−	6773.07i		−	1.12472i	0.826893	−	0.562359i	$-0.190106\pi$
$332$	3931.95			0.649981
$333$	3053.83	−	8354.10i	0.502549	−	1.37478i
$334$	2797.85			0.458357
$335$		−	4572.31i		−	0.745708i
$336$	−3023.74			−0.490948
$337$	−3205.45			−0.518136			−0.259068	−	0.965859i	$-0.583415\pi$
$337$	−3205.45			−0.518136			−0.259068	+	0.965859i	$0.583415\pi$
$338$			2492.80i			0.401155i
$339$		−	2821.70i		−	0.452075i
$340$	2162.16			0.344880
$341$			1652.64i			0.262450i
$342$	7411.38			1.17182
$343$	−3454.95			−0.543877
$344$	4012.19			0.628845
$345$	−3689.99			−0.575833
$346$			4185.85i			0.650383i
$347$			6033.98i			0.933490i	0.884392	+	0.466745i	$0.154573\pi$
$347$			6033.98i			0.933490i	−0.884392	+	0.466745i	$0.845427\pi$
$348$		−	6518.74i		−	1.00414i
$349$	−9296.62			−1.42589			−0.712947	−	0.701218i	$-0.752640\pi$
$349$	−9296.62			−1.42589			−0.712947	+	0.701218i	$0.752640\pi$
$350$			4020.46i			0.614007i
$351$			3148.70i			0.478818i
$352$			421.504i			0.0638245i
$353$		−	1664.10i		−	0.250909i	−0.992099	−	0.125455i	$-0.959961\pi$
$353$		−	1664.10i		−	0.250909i	0.992099	−	0.125455i	$-0.0400389\pi$
$354$	−11105.6			−1.66739
$355$			1163.76i			0.173988i
$356$		−	4571.29i		−	0.680555i
$357$			16518.6i			2.44889i
$358$	706.309			0.104273
$359$	7059.31			1.03782			0.518908	−	0.854830i	$-0.326339\pi$
$359$	7059.31			1.03782			0.518908	+	0.854830i	$0.326339\pi$
$360$	−1955.24			−0.286251
$361$	−1932.72			−0.281779
$362$			9487.31i			1.37746i
$363$	9440.63			1.36503
$364$			2857.61i			0.411482i
$365$		−	7537.77i		−	1.08095i
$366$	−5755.33			−0.821956
$367$	2614.70			0.371896			0.185948	−	0.982560i	$-0.440464\pi$
$367$	2614.70			0.371896			0.185948	+	0.982560i	$0.440464\pi$
$368$			1170.54i			0.165811i
$369$	−13419.1			−1.89314
$370$	955.701	−	2614.43i	0.134283	−	0.367345i
$371$	−4754.64			−0.665360
$372$			4093.24i			0.570496i
$373$	−1349.32			−0.187306			−0.0936529	−	0.995605i	$-0.529854\pi$
$373$	−1349.32			−0.187306			−0.0936529	+	0.995605i	$0.529854\pi$
$374$	2302.66			0.318363
$375$			10680.6i			1.47079i
$376$		−	2261.94i		−	0.310241i
$377$	−6160.58			−0.841608
$378$		−	4732.67i		−	0.643975i
$379$	−6653.93			−0.901819			−0.450910	−	0.892570i	$-0.648900\pi$
$379$	−6653.93			−0.901819			−0.450910	+	0.892570i	$0.648900\pi$
$380$	2319.40			0.313113
$381$	2235.91			0.300653
$382$	−4389.26			−0.587891
$383$			5893.28i			0.786246i	0.919486	+	0.393123i	$0.128605\pi$
$383$			5893.28i			0.786246i	−0.919486	+	0.393123i	$0.871395\pi$
$384$			1043.98i			0.138737i
$385$		−	1887.45i		−	0.249852i
$386$	−2593.39			−0.341970
$387$			19820.9i			2.60350i
$388$		−	1092.04i		−	0.142886i
$389$			4433.83i			0.577902i	0.957344	+	0.288951i	$0.0933065\pi$
$389$			4433.83i			0.577902i	−0.957344	+	0.288951i	$0.906693\pi$
$390$			3110.20i			0.403824i
$391$	6394.60			0.827081
$392$		−	1551.14i		−	0.199859i
$393$		−	17300.7i		−	2.22063i
$394$		−	1089.88i		−	0.139359i
$395$	−4642.09			−0.591313
$396$	−2082.30			−0.264241
$397$	2683.49			0.339246			0.169623	−	0.985509i	$-0.445745\pi$
$397$	2683.49			0.339246			0.169623	+	0.985509i	$0.445745\pi$
$398$	−5186.39			−0.653192
$399$			17719.9i			2.22332i
$400$	1388.10			0.173513
$401$		−	14755.2i		−	1.83751i	−0.394828	−	0.918755i	$-0.629196\pi$
$401$		−	14755.2i		−	1.83751i	0.394828	−	0.918755i	$-0.370804\pi$
$402$		−	12060.6i		−	1.49633i
$403$	3868.35			0.478154
$404$	1977.50			0.243526
$405$			1447.94i			0.177651i
$406$	9259.70			1.13190
$407$	1017.81	−	2784.32i	0.123958	−	0.339100i
$408$	5703.20			0.692035
$409$		−	4811.91i		−	0.581745i	−0.956762	−	0.290872i	$-0.906054\pi$
$409$		−	4811.91i		−	0.581745i	0.956762	−	0.290872i	$-0.0939455\pi$
$410$	−4199.51			−0.505852
$411$	−23524.5			−2.82331
$412$			117.855i			0.0140930i
$413$		−	15775.2i		−	1.87954i
$414$	−5782.66			−0.686478
$415$			6078.92i			0.719042i
$416$	986.618			0.116281
$417$	4898.15			0.575212
$418$	2470.12			0.289038
$419$	14024.7			1.63521			0.817603	−	0.575783i	$-0.195303\pi$
$419$	14024.7			1.63521			0.817603	+	0.575783i	$0.195303\pi$
$420$		−	4674.80i		−	0.543112i
$421$			13289.8i			1.53849i	0.638955	+	0.769244i	$0.279367\pi$
$421$			13289.8i			1.53849i	−0.638955	+	0.769244i	$0.720633\pi$
$422$		−	1433.84i		−	0.165398i
$423$	11174.4			1.28444
$424$			1641.59i			0.188025i
$425$		−	7583.15i		−	0.865498i
$426$			3069.68i			0.349123i
$427$		−	8175.30i		−	0.926535i
$428$	3983.97			0.449935
$429$			3312.31i			0.372774i
$430$			6202.98i			0.695661i
$431$			15692.9i			1.75383i	0.480647	+	0.876914i	$0.340402\pi$
$431$			15692.9i			1.75383i	−0.480647	+	0.876914i	$0.659598\pi$
$432$	−1634.00			−0.181981
$433$	1824.03			0.202442			0.101221	−	0.994864i	$-0.467725\pi$
$433$	1824.03			0.202442			0.101221	+	0.994864i	$0.467725\pi$
$434$	−5814.34			−0.643081
$435$	10078.2			1.11083
$436$		−	6081.74i		−	0.668033i
$437$	6859.65			0.750896
$438$		−	19882.7i		−	2.16902i
$439$			194.588i			0.0211553i	0.999944	+	0.0105776i	$0.00336703\pi$
$439$			194.588i			0.0211553i	−0.999944	+	0.0105776i	$0.996633\pi$
$440$	−651.659			−0.0706060
$441$	7662.92			0.827439
$442$		−	5389.85i		−	0.580020i
$443$	9249.99			0.992055			0.496028	−	0.868307i	$-0.334791\pi$
$443$	9249.99			0.992055			0.496028	+	0.868307i	$0.334791\pi$
$444$	2520.89	−	6896.18i	0.269451	−	0.737113i
$445$	7067.36			0.752866
$446$		−	9967.76i		−	1.05827i
$447$	21575.0			2.28291
$448$	−1482.94			−0.156389
$449$			14312.1i			1.50430i	0.658994	+	0.752149i	$0.270982\pi$
$449$			14312.1i			1.50430i	−0.658994	+	0.752149i	$0.729018\pi$
$450$			6857.47i			0.718365i
$451$	−4472.41			−0.466957
$452$		−	1383.85i		−	0.144006i
$453$	−4259.92			−0.441829
$454$	2012.66			0.208059
$455$	−4417.96			−0.455203
$456$	6117.97			0.628290
$457$		−	11946.8i		−	1.22286i	−0.791297	−	0.611432i	$-0.790594\pi$
$457$		−	11946.8i		−	1.22286i	0.791297	−	0.611432i	$-0.209406\pi$
$458$		−	384.765i		−	0.0392552i
$459$			8926.48i			0.907740i
$460$	−1809.69			−0.183429
$461$		−	3743.32i		−	0.378187i	−0.981959	−	0.189093i	$-0.939445\pi$
$461$		−	3743.32i		−	0.378187i	0.981959	−	0.189093i	$-0.0605549\pi$
$462$		−	4978.59i		−	0.501352i
$463$		−	5707.06i		−	0.572850i	−0.958103	−	0.286425i	$-0.907533\pi$
$463$		−	5707.06i		−	0.572850i	0.958103	−	0.286425i	$-0.0924670\pi$
$464$		−	3197.00i		−	0.319864i
$465$	−6328.29			−0.631112
$466$		−	477.563i		−	0.0474736i
$467$			4857.49i			0.481323i	0.970609	+	0.240662i	$0.0773644\pi$
$467$			4857.49i			0.481323i	−0.970609	+	0.240662i	$0.922636\pi$
$468$			4874.06i			0.481418i
$469$	17131.7			1.68671
$470$	3497.04			0.343205
$471$	−16601.0			−1.62406
$472$	−5446.56			−0.531140
$473$			6606.07i			0.642172i
$474$	−12244.6			−1.18653
$475$		−	8134.65i		−	0.785775i
$476$			8101.24i			0.780084i
$477$	−8109.71			−0.778445
$478$	−5812.30			−0.556169
$479$			16589.6i			1.58246i	0.611517	+	0.791231i	$0.290560\pi$
$479$			16589.6i			1.58246i	−0.611517	+	0.791231i	$0.709440\pi$
$480$	−1614.02			−0.153479
$481$	−6517.28	−	2382.38i	−0.617802	−	0.225837i
$482$	11772.8			1.11252
$483$		−	13825.8i		−	1.30247i
$484$	4629.99			0.434823
$485$	1688.33			0.158068
$486$			9334.05i			0.871195i
$487$		−	18955.9i		−	1.76381i	−0.471428	−	0.881904i	$-0.656261\pi$
$487$		−	18955.9i		−	1.76381i	0.471428	−	0.881904i	$-0.343739\pi$
$488$	−2822.60			−0.261830
$489$		−	21530.3i		−	1.99107i
$490$	2398.12			0.221094
$491$	−9236.04			−0.848913			−0.424457	−	0.905448i	$-0.639535\pi$
$491$	−9236.04			−0.848913			−0.424457	+	0.905448i	$0.639535\pi$
$492$	−11077.2			−1.01504
$493$	−17465.1			−1.59551
$494$		−	5781.84i		−	0.526593i
$495$		−	3219.31i		−	0.292318i
$496$			2007.46i			0.181729i
$497$	−4360.40			−0.393543
$498$			16034.6i			1.44283i
$499$			10617.7i			0.952533i	0.879301	+	0.476266i	$0.158010\pi$
$499$			10617.7i			0.952533i	−0.879301	+	0.476266i	$0.841990\pi$
$500$			5238.12i			0.468512i
$501$			11409.7i			1.01746i
$502$	6907.36			0.614124
$503$			15590.1i			1.38197i	0.722870	+	0.690984i	$0.242822\pi$
$503$			15590.1i			1.38197i	−0.722870	+	0.690984i	$0.757178\pi$
$504$		−	7325.98i		−	0.647471i
$505$			3057.29i			0.269401i
$506$	−1927.29			−0.169325
$507$	−10165.7			−0.890484
$508$	1096.56			0.0957718
$509$	13076.8			1.13874			0.569369	−	0.822082i	$-0.307188\pi$
$509$	13076.8			1.13874			0.569369	+	0.822082i	$0.307188\pi$
$510$			8817.34i			0.765565i
$511$	28242.8			2.44499
$512$			512.000i			0.0441942i
$513$			9575.68i			0.824126i
$514$	−2441.72			−0.209532
$515$	−182.208			−0.0155904
$516$			16361.8i			1.39591i
$517$	3724.28			0.316816
$518$	9795.84	+	3580.86i	0.830896	+	0.303733i
$519$	−17070.0			−1.44372
$520$			1525.34i			0.128636i
$521$	−11619.9			−0.977117			−0.488559	−	0.872531i	$-0.662477\pi$
$521$	−11619.9			−0.977117			−0.488559	+	0.872531i	$0.662477\pi$
$522$	15793.7			1.32428
$523$		−	9064.30i		−	0.757847i	−0.925428	−	0.378924i	$-0.876294\pi$
$523$		−	9064.30i		−	0.757847i	0.925428	−	0.378924i	$-0.123706\pi$
$524$		−	8484.85i		−	0.707371i
$525$	−16395.6			−1.36297
$526$			11162.8i			0.925322i
$527$	10966.7			0.906480
$528$	−1718.91			−0.141678
$529$	6814.82			0.560107
$530$	−2537.95			−0.208003
$531$		−	26906.9i		−	2.19899i
$532$			8690.42i			0.708228i
$533$			10468.6i			0.850742i
$534$	18641.9			1.51070
$535$			6159.35i			0.497742i
$536$		−	5914.90i		−	0.476650i
$537$			2880.35i			0.231464i
$538$		−	3384.84i		−	0.271247i
$539$	2553.96			0.204094
$540$		−	2526.22i		−	0.201317i
$541$		−	2547.53i		−	0.202453i	−0.994863	−	0.101226i	$-0.967723\pi$
$541$		−	2547.53i		−	0.202453i	0.994863	−	0.101226i	$-0.0322766\pi$
$542$		−	349.764i		−	0.0277189i
$543$	−38689.6			−3.05769
$544$	2797.03			0.220445
$545$	9402.58			0.739013
$546$	−11653.4			−0.913407
$547$		−	1619.83i		−	0.126616i	−0.997994	−	0.0633082i	$-0.979835\pi$
$547$		−	1619.83i		−	0.126616i	0.997994	−	0.0633082i	$-0.0201651\pi$
$548$	−11537.2			−0.899352
$549$		−	13944.1i		−	1.08401i
$550$			2285.51i			0.177190i
$551$	−18735.3			−1.44855
$552$	−4773.49			−0.368067
$553$		−	17393.1i		−	1.33749i
$554$	−16586.4			−1.27200
$555$	10661.7	+	3897.38i	0.815432	+	0.298080i
$556$	2402.21			0.183231
$557$		−	1382.35i		−	0.105156i	−0.998617	−	0.0525781i	$-0.983256\pi$
$557$		−	1382.35i		−	0.105156i	0.998617	−	0.0525781i	$-0.0167439\pi$
$558$	−9917.19			−0.752380
$559$	15462.9			1.16996
$560$		−	2292.68i		−	0.173006i
$561$			9390.31i			0.706701i
$562$	2302.27			0.172804
$563$			18027.4i			1.34949i	0.738049	+	0.674747i	$0.235747\pi$
$563$			18027.4i			1.34949i	−0.738049	+	0.674747i	$0.764253\pi$
$564$	9224.26			0.688673
$565$	2139.48			0.159307
$566$	−1408.23			−0.104580
$567$	−5425.20			−0.401829
$568$			1505.47i			0.111212i
$569$			4549.68i			0.335207i	0.985855	+	0.167603i	$0.0536028\pi$
$569$			4549.68i			0.335207i	−0.985855	+	0.167603i	$0.946397\pi$
$570$			9458.59i			0.695047i
$571$	3957.06			0.290014			0.145007	−	0.989431i	$-0.453680\pi$
$571$	3957.06			0.290014			0.145007	+	0.989431i	$0.453680\pi$
$572$			1624.47i			0.118745i
$573$		−	17899.6i		−	1.30500i
$574$		−	15734.9i		−	1.14418i
$575$			6346.98i			0.460326i
$576$	−2529.37			−0.182969
$577$			1633.01i			0.117822i	0.998263	+	0.0589110i	$0.0187628\pi$
$577$			1633.01i			0.117822i	−0.998263	+	0.0589110i	$0.981237\pi$
$578$		−	5454.08i		−	0.392491i
$579$		−	10575.9i		−	0.759104i
$580$	4942.67			0.353851
$581$	−22776.7			−1.62640
$582$	4453.38			0.317179
$583$	−2702.87			−0.192009
$584$		−	9751.11i		−	0.690931i
$585$	−7535.46			−0.532569
$586$			14629.9i			1.03132i
$587$		−	13453.2i		−	0.945947i	−0.881077	−	0.472974i	$-0.843181\pi$
$587$		−	13453.2i		−	0.945947i	0.881077	−	0.472974i	$-0.156819\pi$
$588$	6325.61			0.443646
$589$	11764.2			0.822982
$590$		−	8420.56i		−	0.587575i
$591$	4444.56			0.309348
$592$	1236.33	−	3382.11i	0.0858322	−	0.234804i
$593$	−12143.7			−0.840946			−0.420473	−	0.907305i	$-0.638136\pi$
$593$	−12143.7			−0.840946			−0.420473	+	0.907305i	$0.638136\pi$
$594$		−	2690.38i		−	0.185838i
$595$	−12524.8			−0.862969
$596$	10581.1			0.727210
$597$		−	21150.3i		−	1.44996i
$598$			4511.22i			0.308491i
$599$	20514.1			1.39931			0.699653	−	0.714483i	$-0.253338\pi$
$599$	20514.1			1.39931			0.699653	+	0.714483i	$0.253338\pi$
$600$			5660.73i			0.385164i
$601$	3417.83			0.231974			0.115987	−	0.993251i	$-0.462997\pi$
$601$	3417.83			0.231974			0.115987	+	0.993251i	$0.462997\pi$
$602$	−23241.6			−1.57351
$603$	29220.6			1.97339
$604$	−2089.21			−0.140743
$605$			7158.13i			0.481024i
$606$			8064.33i			0.540579i
$607$			23949.2i			1.60143i	0.599046	+	0.800714i	$0.295547\pi$
$607$			23949.2i			1.60143i	−0.599046	+	0.800714i	$0.704453\pi$
$608$	3000.45			0.200139
$609$			37761.3i			2.51259i
$610$		−	4363.84i		−	0.289650i
$611$		−	8717.46i		−	0.577203i
$612$			13817.8i			0.912668i
$613$	−370.341			−0.0244012			−0.0122006	−	0.999926i	$-0.503884\pi$
$613$	−370.341			−0.0244012			−0.0122006	+	0.999926i	$0.503884\pi$
$614$		−	9760.72i		−	0.641548i
$615$		−	17125.8i		−	1.12289i
$616$		−	2441.66i		−	0.159704i
$617$	7413.70			0.483735			0.241867	−	0.970309i	$-0.422240\pi$
$617$	7413.70			0.483735			0.241867	+	0.970309i	$0.422240\pi$
$618$	−480.617			−0.0312836
$619$	−13991.2			−0.908488			−0.454244	−	0.890877i	$-0.650090\pi$
$619$	−13991.2			−0.908488			−0.454244	+	0.890877i	$0.650090\pi$
$620$	−3103.60			−0.201038
$621$		−	7471.33i		−	0.482792i
$622$	11044.1			0.711945
$623$			26480.3i			1.70290i
$624$			4023.46i			0.258121i
$625$	2746.24			0.175759
$626$	−9974.76			−0.636855
$627$			10073.2i			0.641605i
$628$	−8141.68			−0.517338
$629$	−18476.3	−	6754.00i	−1.17122	−	0.428139i
$630$	11326.2			0.716266
$631$		−	22243.5i		−	1.40333i	−0.712507	−	0.701665i	$-0.752440\pi$
$631$		−	22243.5i		−	1.40333i	0.712507	−	0.701665i	$-0.247560\pi$
$632$	−6005.16			−0.377963
$633$	5847.24			0.367151
$634$		−	7838.74i		−	0.491035i
$635$			1695.32i			0.105948i
$636$	−6694.44			−0.417377
$637$		−	5978.07i		−	0.371836i
$638$	5263.86			0.326643
$639$	−7437.29			−0.460430
$640$	−791.569			−0.0488899
$641$	6095.14			0.375575			0.187787	−	0.982210i	$-0.439868\pi$
$641$	6095.14			0.375575			0.187787	+	0.982210i	$0.439868\pi$
$642$			16246.7i			0.998766i
$643$			23128.4i			1.41850i	0.704958	+	0.709249i	$0.250966\pi$
$643$			23128.4i			1.41850i	−0.704958	+	0.709249i	$0.749034\pi$
$644$		−	6780.62i		−	0.414897i
$645$	−25296.0			−1.54423
$646$		−	16391.4i		−	0.998311i
$647$		−	6085.23i		−	0.369760i	−0.982761	−	0.184880i	$-0.940810\pi$
$647$		−	6085.23i		−	0.369760i	0.982761	−	0.184880i	$-0.0591897\pi$
$648$			1873.10i			0.113553i
$649$		−	8967.75i		−	0.542396i
$650$	5349.72			0.322820
$651$		−	23711.1i		−	1.42751i
$652$		−	10559.2i		−	0.634248i
$653$		−	12349.9i		−	0.740107i	−0.929010	−	0.370053i	$-0.879339\pi$
$653$		−	12349.9i		−	0.740107i	0.929010	−	0.370053i	$-0.120661\pi$
$654$	24801.5			1.48290
$655$	13117.9			0.782530
$656$	−5432.63			−0.323336
$657$	48172.2			2.86054
$658$			13102.8i			0.776294i
$659$	5796.24			0.342624			0.171312	−	0.985217i	$-0.445199\pi$
$659$	5796.24			0.342624			0.171312	+	0.985217i	$0.445199\pi$
$660$		−	2657.49i		−	0.156731i
$661$			7964.80i			0.468676i	0.972155	+	0.234338i	$0.0752923\pi$
$661$			7964.80i			0.468676i	−0.972155	+	0.234338i	$0.924708\pi$
$662$	13546.1			0.795295
$663$	21980.0			1.28753
$664$			7863.89i			0.459606i
$665$	−13435.7			−0.783479
$666$	16708.2	+	6107.66i	0.972117	+	0.355356i
$667$	14618.0			0.848593
$668$			5595.69i			0.324108i
$669$	40648.9			2.34914
$670$	9144.63			0.527295
$671$		−	4647.42i		−	0.267379i
$672$		−	6047.48i		−	0.347153i
$673$	5282.85			0.302584			0.151292	−	0.988489i	$-0.451657\pi$
$673$	5282.85			0.302584			0.151292	+	0.988489i	$0.451657\pi$
$674$		−	6410.90i		−	0.366378i
$675$	−8860.01			−0.505218
$676$	−4985.60			−0.283660
$677$	247.530			0.0140522			0.00702610	−	0.999975i	$-0.497764\pi$
$677$	247.530			0.0140522			0.00702610	+	0.999975i	$0.497764\pi$
$678$	5643.39			0.319665
$679$			6325.90i			0.357535i
$680$			4324.31i			0.243867i
$681$			8207.67i			0.461848i
$682$	−3305.28			−0.185580
$683$		−	7820.33i		−	0.438121i	−0.975711	−	0.219060i	$-0.929701\pi$
$683$		−	7820.33i		−	0.438121i	0.975711	−	0.219060i	$-0.0702992\pi$
$684$			14822.8i			0.828600i
$685$		−	17836.9i		−	0.994910i
$686$		−	6909.90i		−	0.384579i
$687$	1569.08			0.0871387
$688$			8024.38i			0.444661i
$689$			6326.63i			0.349819i
$690$		−	7379.98i		−	0.407175i
$691$	−26608.2			−1.46487			−0.732433	−	0.680839i	$-0.761615\pi$
$691$	−26608.2			−1.46487			−0.732433	+	0.680839i	$0.761615\pi$
$692$	−8371.70			−0.459890
$693$	12062.2			0.661192
$694$	−12068.0			−0.660077
$695$			3713.90i			0.202700i
$696$	13037.5			0.710035
$697$			29678.2i			1.61283i
$698$		−	18593.2i		−	1.00826i
$699$	1947.52			0.105382
$700$	−8040.92			−0.434169
$701$			5061.08i			0.272688i	0.990662	+	0.136344i	$0.0435353\pi$
$701$			5061.08i			0.272688i	−0.990662	+	0.136344i	$0.956465\pi$
$702$	−6297.40			−0.338576
$703$	−19820.0	−	7245.19i	−1.06334	−	0.388702i
$704$	−843.008			−0.0451308
$705$			14261.0i			0.761846i
$706$	3328.19			0.177420
$707$	−11455.2			−0.609358
$708$		−	22211.2i		−	1.17902i
$709$			23585.7i			1.24934i	0.780889	+	0.624669i	$0.214766\pi$
$709$			23585.7i			1.24934i	−0.780889	+	0.624669i	$0.785234\pi$
$710$	−2327.51			−0.123028
$711$		−	29666.5i		−	1.56481i
$712$	9142.57			0.481225
$713$	−9178.92			−0.482123
$714$	−33037.1			−1.73163
$715$	−2511.48			−0.131362
$716$			1412.62i			0.0737319i
$717$		−	23702.8i		−	1.23458i
$718$			14118.6i			0.733847i
$719$	−1655.30			−0.0858587			−0.0429294	−	0.999078i	$-0.513669\pi$
$719$	−1655.30			−0.0858587			−0.0429294	+	0.999078i	$0.513669\pi$
$720$		−	3910.49i		−	0.202410i
$721$		−	682.703i		−	0.0352638i
$722$		−	3865.44i		−	0.199248i
$723$			48009.8i			2.46958i
$724$	−18974.6			−0.974014
$725$		−	17335.0i		−	0.888010i
$726$			18881.3i			0.965219i
$727$		−	9753.86i		−	0.497594i	−0.968556	−	0.248797i	$-0.919965\pi$
$727$		−	9753.86i		−	0.497594i	0.968556	−	0.248797i	$-0.0800352\pi$
$728$	−5715.22			−0.290962
$729$	−31742.8			−1.61270
$730$	15075.5			0.764344
$731$	43836.8			2.21801
$732$		−	11510.7i		−	0.581211i
$733$	−20229.0			−1.01934			−0.509670	−	0.860370i	$-0.670232\pi$
$733$	−20229.0			−1.01934			−0.509670	+	0.860370i	$0.670232\pi$
$734$			5229.39i			0.262971i
$735$			9779.61i			0.490784i
$736$	−2341.07			−0.117246
$737$	9738.87			0.486752
$738$		−	26838.1i		−	1.33865i
$739$	−1175.03			−0.0584900			−0.0292450	−	0.999572i	$-0.509310\pi$
$739$	−1175.03			−0.0584900			−0.0292450	+	0.999572i	$0.509310\pi$
$740$	5228.86	+	1911.40i	0.259752	+	0.0949521i
$741$	23578.5			1.16893
$742$		−	9509.27i		−	0.470480i
$743$	−38911.0			−1.92128			−0.960638	−	0.277804i	$-0.910393\pi$
$743$	−38911.0			−1.92128			−0.960638	+	0.277804i	$0.910393\pi$
$744$	−8186.48			−0.403402
$745$			16358.7i			0.804478i
$746$		−	2698.64i		−	0.132445i
$747$	−38849.0			−1.90282
$748$			4605.32i			0.225116i
$749$	−23078.1			−1.12584
$750$	−21361.2			−1.04000
$751$	17627.5			0.856505			0.428252	−	0.903659i	$-0.359129\pi$
$751$	17627.5			0.856505			0.428252	+	0.903659i	$0.359129\pi$
$752$	4523.88			0.219374
$753$			28168.4i			1.36323i
$754$		−	12321.2i		−	0.595107i
$755$		−	3229.98i		−	0.155697i
$756$	9465.34			0.455359
$757$		−	37731.2i		−	1.81158i	−0.423731	−	0.905788i	$-0.639280\pi$
$757$		−	37731.2i		−	1.81158i	0.423731	−	0.905788i	$-0.360720\pi$
$758$		−	13307.9i		−	0.637682i
$759$		−	7859.55i		−	0.375868i
$760$			4638.80i			0.221404i
$761$	39136.7			1.86426			0.932131	−	0.362122i	$-0.117948\pi$
$761$	39136.7			1.86426			0.932131	+	0.362122i	$0.117948\pi$
$762$			4471.81i			0.212594i
$763$			35229.9i			1.67157i
$764$		−	8778.53i		−	0.415701i
$765$	−21362.8			−1.00964
$766$	−11786.6			−0.555960
$767$	−20990.9			−0.988184
$768$	−2087.95			−0.0981022
$769$		−	34254.3i		−	1.60629i	−0.595781	−	0.803147i	$-0.703157\pi$
$769$		−	34254.3i		−	1.60629i	0.595781	−	0.803147i	$-0.296843\pi$
$770$	3774.89			0.176672
$771$		−	9957.40i		−	0.465119i
$772$		−	5186.79i		−	0.241809i
$773$	−1001.30			−0.0465903			−0.0232952	−	0.999729i	$-0.507416\pi$
$773$	−1001.30			−0.0465903			−0.0232952	+	0.999729i	$0.507416\pi$
$774$	−39641.8			−1.84095
$775$			10885.0i			0.504517i
$776$	2184.08			0.101036
$777$	−14602.8	+	39947.7i	−0.674227	+	1.84442i
$778$	−8867.66			−0.408639
$779$			31836.6i			1.46427i
$780$	−6220.40			−0.285546
$781$	−2478.76			−0.113568
$782$			12789.2i			0.584834i
$783$			20405.9i			0.931350i
$784$	3102.29			0.141321
$785$		−	12587.3i		−	0.572306i
$786$	34601.5			1.57022
$787$	36270.4			1.64282			0.821410	−	0.570338i	$-0.193188\pi$
$787$	36270.4			1.64282			0.821410	+	0.570338i	$0.193188\pi$
$788$	2179.76			0.0985415
$789$	−45522.1			−2.05403
$790$		−	9284.18i		−	0.418122i
$791$			8016.29i			0.360337i
$792$		−	4164.60i		−	0.186847i
$793$	−10878.2			−0.487135
$794$			5366.98i			0.239883i
$795$		−	10349.8i		−	0.461724i
$796$		−	10372.8i		−	0.461877i
$797$			5619.37i			0.249747i	0.992173	+	0.124874i	$0.0398525\pi$
$797$			5619.37i			0.249747i	−0.992173	+	0.124874i	$0.960147\pi$
$798$	−35439.8			−1.57212
$799$		−	24713.8i		−	1.09426i
$800$			2776.21i			0.122692i
$801$			45165.9i			1.99233i
$802$	29510.5			1.29932
$803$	16055.2			0.705574
$804$	24121.1			1.05807
$805$	10483.1			0.458981
$806$			7736.69i			0.338106i
$807$	13803.5			0.602113
$808$			3955.01i			0.172199i
$809$		−	17495.4i		−	0.760330i	−0.924919	−	0.380165i	$-0.875867\pi$
$809$		−	17495.4i		−	0.760330i	0.924919	−	0.380165i	$-0.124133\pi$
$810$	−2895.88			−0.125619
$811$	−6867.21			−0.297337			−0.148668	−	0.988887i	$-0.547499\pi$
$811$	−6867.21			−0.297337			−0.148668	+	0.988887i	$0.547499\pi$
$812$			18519.4i			0.800374i
$813$	1426.35			0.0615304
$814$	5568.64	+	2035.61i	0.239780	+	0.0876512i
$815$	16324.9			0.701638
$816$			11406.4i			0.489343i
$817$	47025.0			2.01370
$818$	9623.82			0.411356
$819$		−	28234.2i		−	1.20462i
$820$		−	8399.03i		−	0.357691i
$821$	23847.9			1.01376			0.506881	−	0.862016i	$-0.330798\pi$
$821$	23847.9			1.01376			0.506881	+	0.862016i	$0.330798\pi$
$822$		−	47049.1i		−	1.99638i
$823$	4521.32			0.191499			0.0957493	−	0.995405i	$-0.469475\pi$
$823$	4521.32			0.191499			0.0957493	+	0.995405i	$0.469475\pi$
$824$	−235.710			−0.00996523
$825$	−9320.39			−0.393327
$826$	31550.5			1.32903
$827$			44578.8i			1.87443i	0.348747	+	0.937217i	$0.386607\pi$
$827$			44578.8i			1.87443i	−0.348747	+	0.937217i	$0.613393\pi$
$828$		−	11565.3i		−	0.485413i
$829$			31666.3i			1.32668i	0.748320	+	0.663338i	$0.230861\pi$
$829$			31666.3i			1.32668i	−0.748320	+	0.663338i	$0.769139\pi$
$830$	−12157.8			−0.508440
$831$		−	67640.0i		−	2.82359i
$832$			1973.24i			0.0822231i
$833$		−	16947.7i		−	0.704924i
$834$			9796.30i			0.406736i
$835$	−8651.13			−0.358545
$836$			4940.25i			0.204380i
$837$		−	12813.2i		−	0.529140i
$838$			28049.4i			1.15626i
$839$	5041.87			0.207467			0.103733	−	0.994605i	$-0.466921\pi$
$839$	5041.87			0.207467			0.103733	+	0.994605i	$0.466921\pi$
$840$	9349.61			0.384038
$841$	−15536.1			−0.637012
$842$	−26579.5			−1.08787
$843$			9388.75i			0.383589i
$844$	2867.68			0.116954
$845$		−	7707.91i		−	0.313799i
$846$			22348.7i			0.908234i
$847$	−26820.3			−1.08803
$848$	−3283.17			−0.132953
$849$		−	5742.83i		−	0.232148i
$850$	15166.3			0.612000
$851$	15464.4	+	5652.99i	0.622929	+	0.227711i
$852$	−6139.36			−0.246867
$853$			35652.6i			1.43109i	0.698565	+	0.715546i	$0.253822\pi$
$853$			35652.6i			1.43109i	−0.698565	+	0.715546i	$0.746178\pi$
$854$	16350.6			0.655159
$855$	−22916.5			−0.916640
$856$			7967.93i			0.318152i
$857$		−	13124.5i		−	0.523132i	−0.965186	−	0.261566i	$-0.915761\pi$
$857$		−	13124.5i		−	0.523132i	0.965186	−	0.261566i	$-0.0842389\pi$
$858$	−6624.62			−0.263591
$859$		−	12845.8i		−	0.510238i	−0.966910	−	0.255119i	$-0.917885\pi$
$859$		−	12845.8i		−	0.510238i	0.966910	−	0.255119i	$-0.0821147\pi$
$860$	−12406.0			−0.491907
$861$	64167.4			2.53986
$862$	−31385.8			−1.24014
$863$	−1294.17			−0.0510475			−0.0255238	−	0.999674i	$-0.508125\pi$
$863$	−1294.17			−0.0510475			−0.0255238	+	0.999674i	$0.508125\pi$
$864$		−	3268.00i		−	0.128680i
$865$		−	12942.9i		−	0.508755i
$866$			3648.06i			0.143148i
$867$	22241.9			0.871251
$868$		−	11628.7i		−	0.454727i
$869$		−	9887.49i		−	0.385973i
$870$			20156.4i			0.785477i
$871$		−	22795.9i		−	0.886806i
$872$	12163.5			0.472371
$873$			10789.7i			0.418302i
$874$			13719.3i			0.530964i
$875$		−	30343.1i		−	1.17232i
$876$	39765.3			1.53373
$877$	−26941.3			−1.03734			−0.518668	−	0.854976i	$-0.673572\pi$
$877$	−26941.3			−1.03734			−0.518668	+	0.854976i	$0.673572\pi$
$878$	−389.176			−0.0149591
$879$	−59661.3			−2.28933
$880$		−	1303.32i		−	0.0499260i
$881$	−35912.5			−1.37335			−0.686676	−	0.726964i	$-0.740931\pi$
$881$	−35912.5			−1.37335			−0.686676	+	0.726964i	$0.740931\pi$
$882$			15325.8i			0.585088i
$883$		−	20654.6i		−	0.787184i	−0.919285	−	0.393592i	$-0.871232\pi$
$883$		−	20654.6i		−	0.787184i	0.919285	−	0.393592i	$-0.128768\pi$
$884$	10779.7			0.410136
$885$	34339.3			1.30430
$886$			18500.0i			0.701489i
$887$	−3934.54			−0.148939			−0.0744696	−	0.997223i	$-0.523726\pi$
$887$	−3934.54			−0.148939			−0.0744696	+	0.997223i	$0.523726\pi$
$888$	13792.4	+	5041.78i	0.521217	+	0.190530i
$889$	−6352.09			−0.239643
$890$			14134.7i			0.532356i
$891$	−3084.07			−0.115960
$892$	19935.5			0.748308
$893$		−	26511.1i		−	0.993461i
$894$			43149.9i			1.61426i
$895$	−2183.96			−0.0815660
$896$		−	2965.88i		−	0.110584i
$897$	−18396.9			−0.684788
$898$	−28624.2			−1.06370
$899$	25069.7			0.930058
$900$	−13714.9			−0.507961
$901$			17935.8i			0.663184i
$902$		−	8944.82i		−	0.330188i
$903$		−	94779.8i		−	3.49288i
$904$	2767.70			0.101828
$905$		−	29335.4i		−	1.07751i
$906$		−	8519.85i		−	0.312421i
$907$			3925.18i			0.143697i	0.997416	+	0.0718487i	$0.0228899\pi$
$907$			3925.18i			0.143697i	−0.997416	+	0.0718487i	$0.977110\pi$
$908$			4025.31i			0.147120i
$909$	−19538.4			−0.712925
$910$		−	8835.92i		−	0.321877i
$911$			4901.78i			0.178269i	0.996020	+	0.0891346i	$0.0284101\pi$
$911$			4901.78i			0.178269i	−0.996020	+	0.0891346i	$0.971590\pi$
$912$			12235.9i			0.444268i
$913$	−12947.9			−0.469346
$914$	23893.6			0.864695
$915$	17795.9			0.642966
$916$	769.530			0.0277576
$917$			49150.5i			1.77000i
$918$	−17853.0			−0.641869
$919$			4530.77i			0.162629i	0.996688	+	0.0813147i	$0.0259119\pi$
$919$			4530.77i			0.162629i	−0.996688	+	0.0813147i	$0.974088\pi$
$920$		−	3619.38i		−	0.129704i
$921$	39804.5			1.42411
$922$	7486.65			0.267418
$923$			5802.05i			0.206909i
$924$	9957.18			0.354510
$925$	6703.70	−	18338.7i	0.238288	−	0.651864i
$926$	11414.1			0.405066
$927$		−	1164.45i		−	0.0412573i
$928$	6394.00			0.226178
$929$	25789.1			0.910780			0.455390	−	0.890292i	$-0.349500\pi$
$929$	25789.1			0.910780			0.455390	+	0.890292i	$0.349500\pi$
$930$		−	12656.6i		−	0.446264i
$931$		−	18180.2i		−	0.639992i
$932$	955.126			0.0335689
$933$			45038.4i			1.58038i
$934$	−9714.98			−0.340347
$935$	−7119.98			−0.249035
$936$	−9748.12			−0.340414
$937$	−44504.4			−1.55165			−0.775824	−	0.630950i	$-0.782665\pi$
$937$	−44504.4			−1.55165			−0.775824	+	0.630950i	$0.782665\pi$
$938$			34263.4i			1.19269i
$939$		−	40677.4i		−	1.41369i
$940$			6994.07i			0.242682i
$941$	18475.5			0.640047			0.320023	−	0.947410i	$-0.396309\pi$
$941$	18475.5			0.640047			0.320023	+	0.947410i	$0.396309\pi$
$942$		−	33202.0i		−	1.14839i
$943$		−	24840.2i		−	0.857803i
$944$		−	10893.1i		−	0.375573i
$945$			14633.7i			0.503742i
$946$	−13212.1			−0.454084
$947$			8172.17i			0.280422i	0.990122	+	0.140211i	$0.0447781\pi$
$947$			8172.17i			0.280422i	−0.990122	+	0.140211i	$0.955222\pi$
$948$		−	24489.2i		−	0.839001i
$949$		−	37580.5i		−	1.28548i
$950$	16269.3			0.555627
$951$	31966.6			1.09000
$952$	−16202.5			−0.551602
$953$	10066.0			0.342150			0.171075	−	0.985258i	$-0.445276\pi$
$953$	10066.0			0.342150			0.171075	+	0.985258i	$0.445276\pi$
$954$		−	16219.4i		−	0.550444i
$955$	13571.9			0.459870
$956$		−	11624.6i		−	0.393271i
$957$			21466.2i			0.725082i
$958$	−33179.3			−1.11897
$959$	66832.0			2.25038
$960$		−	3228.05i		−	0.108526i
$961$	14049.3			0.471594
$962$	4764.77	−	13034.6i	0.159691	−	0.436852i
$963$	−39362.9			−1.31719
$964$			23545.6i			0.786672i
$965$	8018.95			0.267502
$966$	27651.6			0.920988
$967$			28443.7i			0.945903i	0.881089	+	0.472951i	$0.156811\pi$
$967$			28443.7i			0.945903i	−0.881089	+	0.472951i	$0.843189\pi$
$968$			9259.99i			0.307466i
$969$	66844.4			2.21605
$970$			3376.66i			0.111771i
$971$	−49750.5			−1.64425			−0.822126	−	0.569306i	$-0.807212\pi$
$971$	−49750.5			−1.64425			−0.822126	+	0.569306i	$0.807212\pi$
$972$	−18668.1			−0.616028
$973$	−13915.4			−0.458486
$974$	37911.8			1.24720
$975$			21816.3i			0.716596i
$976$		−	5645.21i		−	0.185142i
$977$		−	32343.9i		−	1.05913i	−0.848269	−	0.529566i	$-0.822355\pi$
$977$		−	32343.9i		−	1.05913i	0.848269	−	0.529566i	$-0.177645\pi$
$978$	43060.7			1.40790
$979$			15053.2i			0.491424i
$980$			4796.24i			0.156337i
$981$			60089.7i			1.95567i
$982$		−	18472.1i		−	0.600272i
$983$	9554.55			0.310013			0.155006	−	0.987913i	$-0.450460\pi$
$983$	9554.55			0.310013			0.155006	+	0.987913i	$0.450460\pi$
$984$		−	22154.4i		−	0.717741i
$985$			3369.98i			0.109012i
$986$		−	34930.2i		−	1.12820i
$987$	−53433.7			−1.72322
$988$	11563.7			0.372358
$989$	−36690.8			−1.17967
$990$	6438.62			0.206700
$991$		−	20139.1i		−	0.645550i	−0.946476	−	0.322775i	$-0.895384\pi$
$991$		−	20139.1i		−	0.645550i	0.946476	−	0.322775i	$-0.104616\pi$
$992$	−4014.92			−0.128502
$993$			55241.6i			1.76540i
$994$		−	8720.80i		−	0.278277i
$995$	16036.7			0.510952
$996$	−32069.2			−1.02023
$997$			49008.7i			1.55679i	0.627773	+	0.778396i	$0.283967\pi$
$997$			49008.7i			1.55679i	−0.627773	+	0.778396i	$0.716033\pi$
$998$	−21235.4			−0.673542
$999$	−7891.25	+	21587.4i	−0.249918	+	0.683679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.4.b.a.73.6	yes	10
3.2	odd	2		666.4.c.d.73.3		10
4.3	odd	2		592.4.g.d.369.9		10
37.36	even	2	inner	74.4.b.a.73.1	✓	10
111.110	odd	2		666.4.c.d.73.8		10
148.147	odd	2		592.4.g.d.369.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.4.b.a.73.1	✓	10	37.36	even	2	inner
74.4.b.a.73.6	yes	10	1.1	even	1	trivial
592.4.g.d.369.9		10	4.3	odd	2
592.4.g.d.369.10		10	148.147	odd	2
666.4.c.d.73.3		10	3.2	odd	2
666.4.c.d.73.8		10	111.110	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	74.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -8.15606 q^{3} -4.00000 q^{4} -6.18414i q^{5} -16.3121i q^{6} +23.1710 q^{7} -8.00000i q^{8} +39.5214 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} -8.15606 q^{3} -4.00000 q^{4} -6.18414i q^{5} -16.3121i q^{6} +23.1710 q^{7} -8.00000i q^{8} +39.5214 q^{9} +12.3683 q^{10} +13.1720 q^{11} +32.6243 q^{12} -30.8318i q^{13} +46.3419i q^{14} +50.4382i q^{15} +16.0000 q^{16} -87.4073i q^{17} +79.0427i q^{18} -93.7642i q^{19} +24.7365i q^{20} -188.984 q^{21} +26.3440i q^{22} +73.1586i q^{23} +65.2485i q^{24} +86.7565 q^{25} +61.6636 q^{26} -102.125 q^{27} -92.6838 q^{28} -199.813i q^{29} -100.876 q^{30} +125.466i q^{31} +32.0000i q^{32} -107.432 q^{33} +174.815 q^{34} -143.292i q^{35} -158.085 q^{36} +(77.2704 - 211.382i) q^{37} +187.528 q^{38} +251.466i q^{39} -49.4731 q^{40} -339.539 q^{41} -377.967i q^{42} +501.524i q^{43} -52.6880 q^{44} -244.406i q^{45} -146.317 q^{46} +282.743 q^{47} -130.497 q^{48} +193.893 q^{49} +173.513i q^{50} +712.900i q^{51} +123.327i q^{52} -205.198 q^{53} -204.250i q^{54} -81.4574i q^{55} -185.368i q^{56} +764.747i q^{57} +399.625 q^{58} -680.820i q^{59} -201.753i q^{60} -352.825i q^{61} -250.932 q^{62} +915.748 q^{63} -64.0000 q^{64} -190.668 q^{65} -214.863i q^{66} +739.362 q^{67} +349.629i q^{68} -596.686i q^{69} +286.585 q^{70} -188.184 q^{71} -316.171i q^{72} +1218.89 q^{73} +(422.764 + 154.541i) q^{74} -707.591 q^{75} +375.057i q^{76} +305.208 q^{77} -502.932 q^{78} -750.645i q^{79} -98.9462i q^{80} -234.138 q^{81} -679.079i q^{82} -982.987 q^{83} +755.935 q^{84} -540.539 q^{85} -1003.05 q^{86} +1629.68i q^{87} -105.376i q^{88} +1142.82i q^{89} +488.811 q^{90} -714.402i q^{91} -292.634i q^{92} -1023.31i q^{93} +565.485i q^{94} -579.850 q^{95} -260.994i q^{96} +273.010i q^{97} +387.786i q^{98} +520.576 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9}+O(q^{10}) \) 10 * q + 14 * q^3 - 40 * q^4 - 4 * q^7 + 172 * q^9	\( 10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9} + 76 q^{10} - 50 q^{11} - 56 q^{12} + 160 q^{16} - 312 q^{21} - 700 q^{25} + 492 q^{26} + 848 q^{27} + 16 q^{28} - 240 q^{30} - 508 q^{33} - 568 q^{34} - 688 q^{36} + 82 q^{37} + 336 q^{38} - 304 q^{40} - 1194 q^{41} + 200 q^{44} + 60 q^{46} + 464 q^{47} + 224 q^{48} + 2382 q^{49} - 692 q^{53} + 1108 q^{58} - 1700 q^{62} + 2300 q^{63} - 640 q^{64} + 604 q^{65} + 1114 q^{67} + 1880 q^{70} - 1460 q^{71} + 2082 q^{73} + 968 q^{74} - 5160 q^{75} - 6096 q^{77} + 1004 q^{78} + 4978 q^{81} - 1364 q^{83} + 1248 q^{84} + 104 q^{85} + 1400 q^{86} - 2600 q^{90} + 5084 q^{95} + 508 q^{99}+O(q^{100}) \) 10 * q + 14 * q^3 - 40 * q^4 - 4 * q^7 + 172 * q^9 + 76 * q^10 - 50 * q^11 - 56 * q^12 + 160 * q^16 - 312 * q^21 - 700 * q^25 + 492 * q^26 + 848 * q^27 + 16 * q^28 - 240 * q^30 - 508 * q^33 - 568 * q^34 - 688 * q^36 + 82 * q^37 + 336 * q^38 - 304 * q^40 - 1194 * q^41 + 200 * q^44 + 60 * q^46 + 464 * q^47 + 224 * q^48 + 2382 * q^49 - 692 * q^53 + 1108 * q^58 - 1700 * q^62 + 2300 * q^63 - 640 * q^64 + 604 * q^65 + 1114 * q^67 + 1880 * q^70 - 1460 * q^71 + 2082 * q^73 + 968 * q^74 - 5160 * q^75 - 6096 * q^77 + 1004 * q^78 + 4978 * q^81 - 1364 * q^83 + 1248 * q^84 + 104 * q^85 + 1400 * q^86 - 2600 * q^90 + 5084 * q^95 + 508 * q^99

Introduction

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