LMFDB - Embedded newform 169.4.e.b.23.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,4,Mod(23,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("169.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	169.e (of order $6$, degree $2$, not 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:	$9.97132279097$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	169.23
Dual form			169.4.e.b.147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.00000 - 1.73205i) q^{2} +(3.50000 + 6.06218i) q^{3} +(2.00000 - 3.46410i) q^{4} +13.8564i q^{5} +(21.0000 + 12.1244i) q^{6} +(-19.5000 - 11.2583i) q^{7} +13.8564i q^{8} +(-11.0000 + 19.0526i) q^{9} +(24.0000 + 41.5692i) q^{10} +(19.5000 - 11.2583i) q^{11} +28.0000 q^{12} -78.0000 q^{14} +(-84.0000 + 48.4974i) q^{15} +(40.0000 + 69.2820i) q^{16} +(-13.5000 + 23.3827i) q^{17} +76.2102i q^{18} +(76.5000 + 44.1673i) q^{19} +(48.0000 + 27.7128i) q^{20} -157.617i q^{21} +(39.0000 - 67.5500i) q^{22} +(-28.5000 - 49.3634i) q^{23} +(-84.0000 + 48.4974i) q^{24} -67.0000 q^{25} +35.0000 q^{27} +(-78.0000 + 45.0333i) q^{28} +(34.5000 + 59.7558i) q^{29} +(-168.000 + 290.985i) q^{30} -72.7461i q^{31} +(144.000 + 83.1384i) q^{32} +(136.500 + 78.8083i) q^{33} +93.5307i q^{34} +(156.000 - 270.200i) q^{35} +(44.0000 + 76.2102i) q^{36} +(34.5000 - 19.9186i) q^{37} +306.000 q^{38} -192.000 q^{40} +(340.500 - 196.588i) q^{41} +(-273.000 - 472.850i) q^{42} +(42.5000 - 73.6122i) q^{43} -90.0666i q^{44} +(-264.000 - 152.420i) q^{45} +(-171.000 - 98.7269i) q^{46} -342.946i q^{47} +(-280.000 + 484.974i) q^{48} +(82.0000 + 142.028i) q^{49} +(-201.000 + 116.047i) q^{50} -189.000 q^{51} +426.000 q^{53} +(105.000 - 60.6218i) q^{54} +(156.000 + 270.200i) q^{55} +(156.000 - 270.200i) q^{56} +618.342i q^{57} +(207.000 + 119.512i) q^{58} +(16.5000 + 9.52628i) q^{59} +387.979i q^{60} +(8.50000 - 14.7224i) q^{61} +(-126.000 - 218.238i) q^{62} +(429.000 - 247.683i) q^{63} -64.0000 q^{64} +546.000 q^{66} +(-142.500 + 82.2724i) q^{67} +(54.0000 + 93.5307i) q^{68} +(199.500 - 345.544i) q^{69} -1080.80i q^{70} +(-505.500 - 291.851i) q^{71} +(-264.000 - 152.420i) q^{72} +1004.59i q^{73} +(69.0000 - 119.512i) q^{74} +(-234.500 - 406.166i) q^{75} +(306.000 - 176.669i) q^{76} -507.000 q^{77} -1244.00 q^{79} +(-960.000 + 554.256i) q^{80} +(419.500 + 726.595i) q^{81} +(681.000 - 1179.53i) q^{82} -426.084i q^{83} +(-546.000 - 315.233i) q^{84} +(-324.000 - 187.061i) q^{85} -294.449i q^{86} +(-241.500 + 418.290i) q^{87} +(156.000 + 270.200i) q^{88} +(-265.500 + 153.286i) q^{89} -1056.00 q^{90} -228.000 q^{92} +(441.000 - 254.611i) q^{93} +(-594.000 - 1028.84i) q^{94} +(-612.000 + 1060.02i) q^{95} +1163.94i q^{96} +(-1069.50 - 617.476i) q^{97} +(492.000 + 284.056i) q^{98} +495.367i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{2} + 7 q^{3} + 4 q^{4} + 42 q^{6} - 39 q^{7} - 22 q^{9} + 48 q^{10} + 39 q^{11} + 56 q^{12} - 156 q^{14} - 168 q^{15} + 80 q^{16} - 27 q^{17} + 153 q^{19} + 96 q^{20} + 78 q^{22} - 57 q^{23}+ \cdots + 984 q^{98}+O(q^{100}) $ 2 * q + 6 * q^2 + 7 * q^3 + 4 * q^4 + 42 * q^6 - 39 * q^7 - 22 * q^9 + 48 * q^10 + 39 * q^11 + 56 * q^12 - 156 * q^14 - 168 * q^15 + 80 * q^16 - 27 * q^17 + 153 * q^19 + 96 * q^20 + 78 * q^22 - 57 * q^23 - 168 * q^24 - 134 * q^25 + 70 * q^27 - 156 * q^28 + 69 * q^29 - 336 * q^30 + 288 * q^32 + 273 * q^33 + 312 * q^35 + 88 * q^36 + 69 * q^37 + 612 * q^38 - 384 * q^40 + 681 * q^41 - 546 * q^42 + 85 * q^43 - 528 * q^45 - 342 * q^46 - 560 * q^48 + 164 * q^49 - 402 * q^50 - 378 * q^51 + 852 * q^53 + 210 * q^54 + 312 * q^55 + 312 * q^56 + 414 * q^58 + 33 * q^59 + 17 * q^61 - 252 * q^62 + 858 * q^63 - 128 * q^64 + 1092 * q^66 - 285 * q^67 + 108 * q^68 + 399 * q^69 - 1011 * q^71 - 528 * q^72 + 138 * q^74 - 469 * q^75 + 612 * q^76 - 1014 * q^77 - 2488 * q^79 - 1920 * q^80 + 839 * q^81 + 1362 * q^82 - 1092 * q^84 - 648 * q^85 - 483 * q^87 + 312 * q^88 - 531 * q^89 - 2112 * q^90 - 456 * q^92 + 882 * q^93 - 1188 * q^94 - 1224 * q^95 - 2139 * q^97 + 984 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	3.00000	−	1.73205i	1.06066	−	0.612372i	0.135045	−	0.990839i	$-0.456882\pi$
$2$	3.00000	−	1.73205i	1.06066	−	0.612372i	0.925615	+	0.378467i	$0.123549\pi$
$3$	3.50000	+	6.06218i	0.673575	+	1.16667i	0.976883	+	0.213774i	$0.0685756\pi$
$3$	3.50000	+	6.06218i	0.673575	+	1.16667i	−0.303308	+	0.952893i	$0.598091\pi$
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$			13.8564i			1.23935i	0.784857	+	0.619677i	$0.212737\pi$
$5$			13.8564i			1.23935i	−0.784857	+	0.619677i	$0.787263\pi$
$6$	21.0000	+	12.1244i	1.42887	+	0.824958i
$7$	−19.5000	−	11.2583i	−1.05290	−	0.607893i	−0.129441	−	0.991587i	$-0.541318\pi$
$7$	−19.5000	−	11.2583i	−1.05290	−	0.607893i	−0.923460	+	0.383694i	$0.874652\pi$
$8$			13.8564i			0.612372i
$9$	−11.0000	+	19.0526i	−0.407407	+	0.705650i
$10$	24.0000	+	41.5692i	0.758947	+	1.31453i
$11$	19.5000	−	11.2583i	0.534497	−	0.308592i	−0.208349	−	0.978055i	$-0.566809\pi$
$11$	19.5000	−	11.2583i	0.534497	−	0.308592i	0.742846	+	0.669462i	$0.233475\pi$
$12$	28.0000			0.673575
$13$		0			0
$13$		0			0
$14$	−78.0000			−1.48903
$15$	−84.0000	+	48.4974i	−1.44591	+	0.834799i
$16$	40.0000	+	69.2820i	0.625000	+	1.08253i
$17$	−13.5000	+	23.3827i	−0.192602	+	0.333596i	−0.946112	−	0.323840i	$-0.895026\pi$
$17$	−13.5000	+	23.3827i	−0.192602	+	0.333596i	0.753510	+	0.657437i	$0.228359\pi$
$18$			76.2102i			0.997940i
$19$	76.5000	+	44.1673i	0.923700	+	0.533299i	0.884814	−	0.465945i	$-0.154286\pi$
$19$	76.5000	+	44.1673i	0.923700	+	0.533299i	0.0388865	+	0.999244i	$0.487619\pi$
$20$	48.0000	+	27.7128i	0.536656	+	0.309839i
$21$		−	157.617i		−	1.63785i
$22$	39.0000	−	67.5500i	0.377947	−	0.654623i
$23$	−28.5000	−	49.3634i	−0.258377	−	0.447521i	0.707431	−	0.706783i	$-0.249854\pi$
$23$	−28.5000	−	49.3634i	−0.258377	−	0.447521i	−0.965807	+	0.259261i	$0.916521\pi$
$24$	−84.0000	+	48.4974i	−0.714435	+	0.412479i
$25$	−67.0000			−0.536000
$26$		0			0
$27$	35.0000			0.249472
$28$	−78.0000	+	45.0333i	−0.526451	+	0.303946i
$29$	34.5000	+	59.7558i	0.220913	+	0.382633i	0.955086	−	0.296330i	$-0.0957628\pi$
$29$	34.5000	+	59.7558i	0.220913	+	0.382633i	−0.734172	+	0.678963i	$0.762430\pi$
$30$	−168.000	+	290.985i	−1.02242	+	1.77088i
$31$		−	72.7461i		−	0.421471i	−0.977543	−	0.210735i	$-0.932414\pi$
$31$		−	72.7461i		−	0.421471i	0.977543	−	0.210735i	$-0.0675858\pi$
$32$	144.000	+	83.1384i	0.795495	+	0.459279i
$33$	136.500	+	78.8083i	0.720048	+	0.415720i
$34$			93.5307i			0.471776i
$35$	156.000	−	270.200i	0.753395	−	1.30492i
$36$	44.0000	+	76.2102i	0.203704	+	0.352825i
$37$	34.5000	−	19.9186i	0.153291	−	0.0885026i	−0.421393	−	0.906878i	$-0.638459\pi$
$37$	34.5000	−	19.9186i	0.153291	−	0.0885026i	0.574683	+	0.818376i	$0.305125\pi$
$38$	306.000			1.30631
$39$		0			0
$40$	−192.000			−0.758947
$41$	340.500	−	196.588i	1.29700	−	0.748826i	0.317118	−	0.948386i	$-0.397285\pi$
$41$	340.500	−	196.588i	1.29700	−	0.748826i	0.979886	+	0.199560i	$0.0639514\pi$
$42$	−273.000	−	472.850i	−1.00297	−	1.73720i
$43$	42.5000	−	73.6122i	0.150725	−	0.261064i	−0.780769	−	0.624820i	$-0.785172\pi$
$43$	42.5000	−	73.6122i	0.150725	−	0.261064i	0.931494	+	0.363756i	$0.118506\pi$
$44$		−	90.0666i		−	0.308592i
$45$	−264.000	−	152.420i	−0.874551	−	0.504922i
$46$	−171.000	−	98.7269i	−0.548099	−	0.316445i
$47$		−	342.946i		−	1.06434i	−0.846639	−	0.532168i	$-0.821377\pi$
$47$		−	342.946i		−	1.06434i	0.846639	−	0.532168i	$-0.178623\pi$
$48$	−280.000	+	484.974i	−0.841969	+	1.45833i
$49$	82.0000	+	142.028i	0.239067	+	0.414076i
$50$	−201.000	+	116.047i	−0.568514	+	0.328232i
$51$	−189.000			−0.518927
$52$		0			0
$53$	426.000			1.10407			0.552034	−	0.833822i	$-0.313852\pi$
$53$	426.000			1.10407			0.552034	+	0.833822i	$0.313852\pi$
$54$	105.000	−	60.6218i	0.264605	−	0.152770i
$55$	156.000	+	270.200i	0.382455	+	0.662432i
$56$	156.000	−	270.200i	0.372257	−	0.644768i
$57$			618.342i			1.43687i
$58$	207.000	+	119.512i	0.468628	+	0.270563i
$59$	16.5000	+	9.52628i	0.0364088	+	0.0210206i	0.518094	−	0.855324i	$-0.326642\pi$
$59$	16.5000	+	9.52628i	0.0364088	+	0.0210206i	−0.481685	+	0.876344i	$0.659975\pi$
$60$			387.979i			0.834799i
$61$	8.50000	−	14.7224i	0.0178412	−	0.0309019i	−0.856967	−	0.515371i	$-0.827654\pi$
$61$	8.50000	−	14.7224i	0.0178412	−	0.0309019i	0.874808	+	0.484469i	$0.160987\pi$
$62$	−126.000	−	218.238i	−0.258097	−	0.447037i
$63$	429.000	−	247.683i	0.857919	−	0.495320i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	546.000			1.01830
$67$	−142.500	+	82.2724i	−0.259838	+	0.150018i	−0.624261	−	0.781216i	$-0.714600\pi$
$67$	−142.500	+	82.2724i	−0.259838	+	0.150018i	0.364423	+	0.931234i	$0.381266\pi$
$68$	54.0000	+	93.5307i	0.0963009	+	0.166798i
$69$	199.500	−	345.544i	0.348072	−	0.602879i
$70$		−	1080.80i		−	1.84543i
$71$	−505.500	−	291.851i	−0.844955	−	0.487835i	0.0139904	−	0.999902i	$-0.495547\pi$
$71$	−505.500	−	291.851i	−0.844955	−	0.487835i	−0.858945	+	0.512067i	$0.828880\pi$
$72$	−264.000	−	152.420i	−0.432121	−	0.249485i
$73$			1004.59i			1.61066i	0.592826	+	0.805331i	$0.298012\pi$
$73$			1004.59i			1.61066i	−0.592826	+	0.805331i	$0.701988\pi$
$74$	69.0000	−	119.512i	0.108393	−	0.187742i
$75$	−234.500	−	406.166i	−0.361036	−	0.625333i
$76$	306.000	−	176.669i	0.461850	−	0.266649i
$77$	−507.000			−0.750364
$78$		0			0
$79$	−1244.00			−1.77166			−0.885829	−	0.464012i	$-0.846409\pi$
$79$	−1244.00			−1.77166			−0.885829	+	0.464012i	$0.846409\pi$
$80$	−960.000	+	554.256i	−1.34164	+	0.774597i
$81$	419.500	+	726.595i	0.575446	+	0.996701i
$82$	681.000	−	1179.53i	0.917120	−	1.58850i
$83$		−	426.084i		−	0.563480i	−0.959491	−	0.281740i	$-0.909088\pi$
$83$		−	426.084i		−	0.563480i	0.959491	−	0.281740i	$-0.0909116\pi$
$84$	−546.000	−	315.233i	−0.709208	−	0.409462i
$85$	−324.000	−	187.061i	−0.413444	−	0.238702i
$86$		−	294.449i		−	0.369200i
$87$	−241.500	+	418.290i	−0.297604	+	0.515465i
$88$	156.000	+	270.200i	0.188973	+	0.327311i
$89$	−265.500	+	153.286i	−0.316213	+	0.182566i	−0.649703	−	0.760188i	$-0.725107\pi$
$89$	−265.500	+	153.286i	−0.316213	+	0.182566i	0.333490	+	0.942753i	$0.391774\pi$
$90$	−1056.00			−1.23680
$91$		0			0
$92$	−228.000			−0.258377
$93$	441.000	−	254.611i	0.491716	−	0.283892i
$94$	−594.000	−	1028.84i	−0.651770	−	1.12890i
$95$	−612.000	+	1060.02i	−0.660946	+	1.14479i
$96$			1163.94i			1.23744i
$97$	−1069.50	−	617.476i	−1.11950	−	0.646342i	−0.178225	−	0.983990i	$-0.557035\pi$
$97$	−1069.50	−	617.476i	−1.11950	−	0.646342i	−0.941273	+	0.337647i	$0.890369\pi$
$98$	492.000	+	284.056i	0.507138	+	0.292796i
$99$			495.367i			0.502891i
$100$	−134.000	+	232.095i	−0.134000	+	0.232095i
$101$	−979.500	−	1696.54i	−0.964989	−	1.67141i	−0.709645	−	0.704560i	$-0.751144\pi$
$101$	−979.500	−	1696.54i	−0.964989	−	1.67141i	−0.255345	−	0.966850i	$-0.582189\pi$
$102$	−567.000	+	327.358i	−0.550406	+	0.317777i
$103$	1856.00			1.77551			0.887753	−	0.460320i	$-0.152265\pi$
$103$	1856.00			1.77551			0.887753	+	0.460320i	$0.152265\pi$
$104$		0			0
$105$	2184.00			2.02987
$106$	1278.00	−	737.854i	1.17104	−	0.676101i
$107$	127.500	+	220.836i	0.115195	+	0.199524i	0.917858	−	0.396909i	$-0.129917\pi$
$107$	127.500	+	220.836i	0.115195	+	0.199524i	−0.802663	+	0.596433i	$0.796584\pi$
$108$	70.0000	−	121.244i	0.0623681	−	0.108025i
$109$		−	609.682i		−	0.535752i	−0.963453	−	0.267876i	$-0.913678\pi$
$109$		−	609.682i		−	0.535752i	0.963453	−	0.267876i	$-0.0863217\pi$
$110$	936.000	+	540.400i	0.811310	+	0.468410i
$111$	241.500	+	139.430i	0.206506	+	0.119226i
$112$		−	1801.33i		−	1.51973i
$113$	−205.500	+	355.936i	−0.171078	+	0.296316i	−0.938797	−	0.344471i	$-0.888058\pi$
$113$	−205.500	+	355.936i	−0.171078	+	0.296316i	0.767719	+	0.640787i	$0.221392\pi$
$114$	1071.00	+	1855.03i	0.879898	+	1.52403i
$115$	684.000	−	394.908i	0.554638	−	0.320220i
$116$	276.000			0.220913
$117$		0			0
$118$	66.0000			0.0514898
$119$	526.500	−	303.975i	0.405581	−	0.234162i
$120$	−672.000	−	1163.94i	−0.511208	−	0.885438i
$121$	−412.000	+	713.605i	−0.309542	+	0.536142i
$122$		−	58.8897i		−	0.0437018i
$123$	2383.50	+	1376.11i	1.74726	+	1.00878i
$124$	−252.000	−	145.492i	−0.182502	−	0.105368i
$125$			803.672i			0.575061i
$126$	858.000	−	1486.10i	0.606641	−	1.05073i
$127$	1121.50	+	1942.49i	0.783599	+	1.35723i	0.929833	+	0.367983i	$0.119951\pi$
$127$	1121.50	+	1942.49i	0.783599	+	1.35723i	−0.146234	+	0.989250i	$0.546715\pi$
$128$	−1344.00	+	775.959i	−0.928078	+	0.535826i
$129$	595.000			0.406099
$130$		0			0
$131$	−372.000			−0.248105			−0.124053	−	0.992276i	$-0.539589\pi$
$131$	−372.000			−0.248105			−0.124053	+	0.992276i	$0.539589\pi$
$132$	546.000	−	315.233i	0.360024	−	0.207860i
$133$	−994.500	−	1722.52i	−0.648377	−	1.12302i
$134$	−285.000	+	493.634i	−0.183733	+	0.318235i
$135$			484.974i			0.309185i
$136$	−324.000	−	187.061i	−0.204285	−	0.117944i
$137$	1030.50	+	594.959i	0.642639	+	0.371028i	0.785630	−	0.618696i	$-0.212339\pi$
$137$	1030.50	+	594.959i	0.642639	+	0.371028i	−0.142991	+	0.989724i	$0.545672\pi$
$138$		−	1382.18i		−	0.852599i
$139$	1272.50	−	2204.03i	0.776490	−	1.34492i	−0.157464	−	0.987525i	$-0.550332\pi$
$139$	1272.50	−	2204.03i	0.776490	−	1.34492i	0.933953	−	0.357395i	$-0.116335\pi$
$140$	−624.000	−	1080.80i	−0.376697	−	0.652459i
$141$	2079.00	−	1200.31i	1.24173	−	0.716911i
$142$	−2022.00			−1.19495
$143$		0			0
$144$	−1760.00			−1.01852
$145$	−828.000	+	478.046i	−0.474218	+	0.273790i
$146$	1740.00	+	3013.77i	0.986325	+	1.70836i
$147$	−574.000	+	994.197i	−0.322059	+	0.557823i
$148$		−	159.349i		−	0.0885026i
$149$	−1129.50	−	652.117i	−0.621022	−	0.358547i	0.156245	−	0.987718i	$-0.450061\pi$
$149$	−1129.50	−	652.117i	−0.621022	−	0.358547i	−0.777267	+	0.629171i	$0.783394\pi$
$150$	−1407.00	−	812.332i	−0.765874	−	0.442177i
$151$		−	86.6025i		−	0.0466729i	−0.999728	−	0.0233365i	$-0.992571\pi$
$151$		−	86.6025i		−	0.0466729i	0.999728	−	0.0233365i	$-0.00742890\pi$
$152$	−612.000	+	1060.02i	−0.326577	+	0.565649i
$153$	−297.000	−	514.419i	−0.156935	−	0.271819i
$154$	−1521.00	+	878.150i	−0.795881	+	0.459502i
$155$	1008.00			0.522352
$156$		0			0
$157$	−1534.00			−0.779787			−0.389893	−	0.920860i	$-0.627488\pi$
$157$	−1534.00			−0.779787			−0.389893	+	0.920860i	$0.627488\pi$
$158$	−3732.00	+	2154.67i	−1.87913	+	1.08491i
$159$	1491.00	+	2582.49i	0.743673	+	1.28808i
$160$	−1152.00	+	1995.32i	−0.569210	+	0.985901i
$161$			1283.45i			0.628261i
$162$	2517.00	+	1453.19i	1.22070	+	0.704774i
$163$	1414.50	+	816.662i	0.679707	+	0.392429i	0.799745	−	0.600340i	$-0.204968\pi$
$163$	1414.50	+	816.662i	0.679707	+	0.392429i	−0.120038	+	0.992769i	$0.538302\pi$
$164$		−	1572.70i		−	0.748826i
$165$	−1092.00	+	1891.40i	−0.515225	+	0.892395i
$166$	−738.000	−	1278.25i	−0.345060	−	0.597661i
$167$	−1408.50	+	813.198i	−0.652653	+	0.376809i	−0.789472	−	0.613787i	$-0.789645\pi$
$167$	−1408.50	+	813.198i	−0.652653	+	0.376809i	0.136819	+	0.990596i	$0.456312\pi$
$168$	2184.00			1.00297
$169$		0			0
$170$	−1296.00			−0.584698
$171$	−1683.00	+	971.681i	−0.752645	+	0.434540i
$172$	−170.000	−	294.449i	−0.0753627	−	0.130532i
$173$	436.500	−	756.040i	0.191829	−	0.332258i	−0.754027	−	0.656843i	$-0.771891\pi$
$173$	436.500	−	756.040i	0.191829	−	0.332258i	0.945857	+	0.324585i	$0.105225\pi$
$174$			1673.16i			0.728977i
$175$	1306.50	+	754.308i	0.564355	+	0.325830i
$176$	1560.00	+	900.666i	0.668122	+	0.385740i
$177$			133.368i			0.0566359i
$178$	−531.000	+	919.719i	−0.223596	+	0.387280i
$179$	643.500	+	1114.57i	0.268701	+	0.465403i	0.968527	−	0.248910i	$-0.0800724\pi$
$179$	643.500	+	1114.57i	0.268701	+	0.465403i	−0.699826	+	0.714314i	$0.746739\pi$
$180$	−1056.00	+	609.682i	−0.437276	+	0.252461i
$181$	2.00000			0.000821319			0.000410660	−	1.00000i	$-0.499869\pi$
$181$	2.00000			0.000821319			0.000410660		1.00000i	$0.499869\pi$
$182$		0			0
$183$	119.000			0.0480696
$184$	684.000	−	394.908i	0.274050	−	0.158223i
$185$	276.000	+	478.046i	0.109686	+	0.189982i
$186$	882.000	−	1527.67i	0.347696	−	0.602226i
$187$			607.950i			0.237742i
$188$	−1188.00	−	685.892i	−0.460871	−	0.266084i
$189$	−682.500	−	394.042i	−0.262670	−	0.151652i
$190$			4240.06i			1.61898i
$191$	1420.50	−	2460.38i	0.538135	−	0.932077i	−0.460870	−	0.887468i	$-0.652462\pi$
$191$	1420.50	−	2460.38i	0.538135	−	0.932077i	0.999005	−	0.0446092i	$-0.0142043\pi$
$192$	−224.000	−	387.979i	−0.0841969	−	0.145833i
$193$	3676.50	−	2122.63i	1.37119	−	0.791659i	0.380115	−	0.924939i	$-0.375885\pi$
$193$	3676.50	−	2122.63i	1.37119	−	0.791659i	0.991078	+	0.133281i	$0.0425512\pi$
$194$	−4278.00			−1.58321
$195$		0			0
$196$	656.000			0.239067
$197$	−2383.50	+	1376.11i	−0.862017	+	0.497686i	−0.864687	−	0.502311i	$-0.832483\pi$
$197$	−2383.50	+	1376.11i	−0.862017	+	0.497686i	0.00267023	+	0.999996i	$0.499150\pi$
$198$	858.000	+	1486.10i	0.307957	+	0.533396i
$199$	842.500	−	1459.25i	0.300117	−	0.519818i	−0.676045	−	0.736860i	$-0.736308\pi$
$199$	842.500	−	1459.25i	0.300117	−	0.519818i	0.976162	+	0.217042i	$0.0696410\pi$
$200$		−	928.379i		−	0.328232i
$201$	−997.500	−	575.907i	−0.350041	−	0.202096i
$202$	−5877.00	−	3393.09i	−2.04705	−	1.18187i
$203$		−	1553.65i		−	0.537167i
$204$	−378.000	+	654.715i	−0.129732	+	0.224702i
$205$	2724.00	+	4718.11i	0.928061	+	1.60745i
$206$	5568.00	−	3214.69i	1.88321	−	1.08727i
$207$	1254.00			0.421058
$208$		0			0
$209$	1989.00			0.658287
$210$	6552.00	−	3782.80i	2.15300	−	1.24304i
$211$	−840.500	−	1455.79i	−0.274229	−	0.474979i	0.695711	−	0.718322i	$-0.255089\pi$
$211$	−840.500	−	1455.79i	−0.274229	−	0.474979i	−0.969940	+	0.243343i	$0.921756\pi$
$212$	852.000	−	1475.71i	0.276017	−	0.478075i
$213$		−	4085.91i		−	1.31437i
$214$	765.000	+	441.673i	0.244366	+	0.141085i
$215$	1020.00	+	588.897i	0.323551	+	0.186802i
$216$			484.974i			0.152770i
$217$	−819.000	+	1418.55i	−0.256209	+	0.443767i
$218$	−1056.00	−	1829.05i	−0.328080	−	0.568250i
$219$	−6090.00	+	3516.06i	−1.87911	+	1.08490i
$220$	1248.00			0.382455
$221$		0			0
$222$	966.000			0.292044
$223$	3547.50	−	2048.15i	1.06528	−	0.615042i	0.138394	−	0.990377i	$-0.455806\pi$
$223$	3547.50	−	2048.15i	1.06528	−	0.615042i	0.926889	+	0.375336i	$0.122473\pi$
$224$	−1872.00	−	3242.40i	−0.558385	−	0.967151i
$225$	737.000	−	1276.52i	0.218370	−	0.378229i
$226$			1423.75i			0.419054i
$227$	−379.500	−	219.104i	−0.110962	−	0.0640638i	0.443492	−	0.896278i	$-0.353739\pi$
$227$	−379.500	−	219.104i	−0.110962	−	0.0640638i	−0.554454	+	0.832215i	$0.687073\pi$
$228$	2142.00	+	1236.68i	0.622182	+	0.359217i
$229$			180.133i			0.0519805i	0.999662	+	0.0259903i	$0.00827389\pi$
$229$			180.133i			0.0519805i	−0.999662	+	0.0259903i	$0.991726\pi$
$230$	1368.00	−	2369.45i	0.392188	−	0.679290i
$231$	−1774.50	−	3073.52i	−0.505427	−	0.875424i
$232$	−828.000	+	478.046i	−0.234314	+	0.135281i
$233$	−5778.00			−1.62459			−0.812295	−	0.583247i	$-0.801782\pi$
$233$	−5778.00			−1.62459			−0.812295	+	0.583247i	$0.801782\pi$
$234$		0			0
$235$	4752.00			1.31909
$236$	66.0000	−	38.1051i	0.0182044	−	0.0105103i
$237$	−4354.00	−	7541.35i	−1.19334	−	2.06693i
$238$	1053.00	−	1823.85i	0.286789	−	0.496734i
$239$		−	1860.22i		−	0.503464i	−0.967797	−	0.251732i	$-0.919000\pi$
$239$		−	1860.22i		−	0.503464i	0.967797	−	0.251732i	$-0.0810001\pi$
$240$	−6720.00	−	3879.79i	−1.80739	−	1.04350i
$241$	−1783.50	−	1029.70i	−0.476703	−	0.275224i	0.242339	−	0.970192i	$-0.422085\pi$
$241$	−1783.50	−	1029.70i	−0.476703	−	0.275224i	−0.719041	+	0.694967i	$0.755419\pi$
$242$			2854.42i			0.758219i
$243$	−2464.00	+	4267.77i	−0.650476	+	1.12666i
$244$	−34.0000	−	58.8897i	−0.00892060	−	0.0154509i
$245$	−1968.00	+	1136.23i	−0.513187	+	0.296289i
$246$	9534.00			2.47100
$247$		0			0
$248$	1008.00			0.258097
$249$	2583.00	−	1491.30i	0.657393	−	0.379546i
$250$	1392.00	+	2411.01i	0.352151	+	0.609944i
$251$	−2245.50	+	3889.32i	−0.564680	+	0.978055i	0.432399	+	0.901682i	$0.357667\pi$
$251$	−2245.50	+	3889.32i	−0.564680	+	0.978055i	−0.997079	+	0.0763724i	$0.975666\pi$
$252$		−	1981.47i		−	0.495320i
$253$	−1111.50	−	641.725i	−0.276203	−	0.159466i
$254$	6729.00	+	3884.99i	1.66226	+	0.959708i
$255$		−	2618.86i		−	0.643135i
$256$	−2432.00	+	4212.35i	−0.593750	+	1.02841i
$257$	−2725.50	−	4720.70i	−0.661525	−	1.14580i	−0.980215	−	0.197936i	$-0.936576\pi$
$257$	−2725.50	−	4720.70i	−0.661525	−	1.14580i	0.318690	−	0.947859i	$-0.396757\pi$
$258$	1785.00	−	1030.57i	0.430734	−	0.248684i
$259$	−897.000			−0.215200
$260$		0			0
$261$	−1518.00			−0.360007
$262$	−1116.00	+	644.323i	−0.263155	+	0.151933i
$263$	391.500	+	678.098i	0.0917906	+	0.158986i	0.908265	−	0.418396i	$-0.137408\pi$
$263$	391.500	+	678.098i	0.0917906	+	0.158986i	−0.816474	+	0.577382i	$0.804074\pi$
$264$	−1092.00	+	1891.40i	−0.254576	+	0.440938i
$265$			5902.83i			1.36833i
$266$	−5967.00	−	3445.05i	−1.37541	−	0.794096i
$267$	−1858.50	−	1073.01i	−0.425986	−	0.245943i
$268$			658.179i			0.150018i
$269$	2542.50	−	4403.74i	0.576279	−	0.998144i	−0.419623	−	0.907699i	$-0.637838\pi$
$269$	2542.50	−	4403.74i	0.576279	−	0.998144i	0.995901	−	0.0904453i	$-0.0288290\pi$
$270$	840.000	+	1454.92i	0.189336	+	0.327940i
$271$	1147.50	−	662.509i	0.257216	−	0.148504i	−0.365848	−	0.930675i	$-0.619221\pi$
$271$	1147.50	−	662.509i	0.257216	−	0.148504i	0.623064	+	0.782171i	$0.285888\pi$
$272$	−2160.00			−0.481505
$273$		0			0
$274$	4122.00			0.908829
$275$	−1306.50	+	754.308i	−0.286491	+	0.165405i
$276$	−798.000	−	1382.18i	−0.174036	−	0.301439i
$277$	1710.50	−	2962.67i	0.371025	−	0.642635i	−0.618698	−	0.785629i	$-0.712340\pi$
$277$	1710.50	−	2962.67i	0.371025	−	0.642635i	0.989724	+	0.142994i	$0.0456730\pi$
$278$		−	8816.14i		−	1.90200i
$279$	1386.00	+	800.207i	0.297411	+	0.171710i
$280$	3744.00	+	2161.60i	0.799096	+	0.461358i
$281$			810.600i			0.172087i	0.996291	+	0.0860433i	$0.0274223\pi$
$281$			810.600i			0.172087i	−0.996291	+	0.0860433i	$0.972578\pi$
$282$	4158.00	−	7201.87i	0.878033	−	1.52080i
$283$	−3588.50	−	6215.46i	−0.753760	−	1.30555i	−0.945988	−	0.324201i	$-0.894905\pi$
$283$	−3588.50	−	6215.46i	−0.753760	−	1.30555i	0.192228	−	0.981350i	$-0.438429\pi$
$284$	−2022.00	+	1167.40i	−0.422478	+	0.243918i
$285$	−8568.00			−1.78079
$286$		0			0
$287$	−8853.00			−1.82082
$288$	−3168.00	+	1829.05i	−0.648181	+	0.374228i
$289$	2092.00	+	3623.45i	0.425809	+	0.737523i
$290$	−1656.00	+	2868.28i	−0.335323	+	0.580796i
$291$		−	8644.67i		−	1.74144i
$292$	3480.00	+	2009.18i	0.697437	+	0.402665i
$293$	−8065.50	−	4656.62i	−1.60816	−	0.928473i	−0.989781	−	0.142595i	$-0.954456\pi$
$293$	−8065.50	−	4656.62i	−1.60816	−	0.928473i	−0.618381	−	0.785878i	$-0.712211\pi$
$294$			3976.79i			0.788881i
$295$	−132.000	+	228.631i	−0.0260520	+	0.0451234i
$296$	276.000	+	478.046i	0.0541965	+	0.0938712i
$297$	682.500	−	394.042i	0.133342	−	0.0769852i
$298$	−4518.00			−0.878257
$299$		0			0
$300$	−1876.00			−0.361036
$301$	−1657.50	+	956.958i	−0.317398	+	0.183250i
$302$	−150.000	−	259.808i	−0.0285812	−	0.0495041i
$303$	6856.50	−	11875.8i	1.29999	−	2.25164i
$304$			7066.77i			1.33325i
$305$	204.000	+	117.779i	0.0382984	+	0.0221116i
$306$	−1782.00	−	1028.84i	−0.332909	−	0.192205i
$307$		−	4777.00i		−	0.888070i	−0.896009	−	0.444035i	$-0.853547\pi$
$307$		−	4777.00i		−	0.888070i	0.896009	−	0.444035i	$-0.146453\pi$
$308$	−1014.00	+	1756.30i	−0.187591	+	0.324917i
$309$	6496.00	+	11251.4i	1.19594	+	2.07142i
$310$	3024.00	−	1745.91i	0.554038	−	0.319874i
$311$	6192.00			1.12899			0.564495	−	0.825436i	$-0.309071\pi$
$311$	6192.00			1.12899			0.564495	+	0.825436i	$0.309071\pi$
$312$		0			0
$313$	−770.000			−0.139051			−0.0695255	−	0.997580i	$-0.522149\pi$
$313$	−770.000			−0.139051			−0.0695255	+	0.997580i	$0.522149\pi$
$314$	−4602.00	+	2656.97i	−0.827089	+	0.477520i
$315$	3432.00	+	5944.40i	0.613877	+	1.06327i
$316$	−2488.00	+	4309.34i	−0.442914	+	0.767150i
$317$			8057.50i			1.42762i	0.700341	+	0.713808i	$0.253031\pi$
$317$			8057.50i			1.42762i	−0.700341	+	0.713808i	$0.746969\pi$
$318$	8946.00	+	5164.98i	1.57757	+	0.910810i
$319$	1345.50	+	776.825i	0.236155	+	0.136344i
$320$		−	886.810i		−	0.154919i
$321$	−892.500	+	1545.86i	−0.155185	+	0.268789i
$322$	2223.00	+	3850.35i	0.384730	+	0.666371i
$323$	−2065.50	+	1192.52i	−0.355813	+	0.205429i
$324$	3356.00			0.575446
$325$		0			0
$326$	5658.00			0.961250
$327$	3696.00	−	2133.89i	0.625044	−	0.360869i
$328$	2724.00	+	4718.11i	0.458560	+	0.794250i
$329$	−3861.00	+	6687.45i	−0.647002	+	1.12064i
$330$			7565.60i			1.26204i
$331$	4570.50	+	2638.78i	0.758965	+	0.438189i	0.828924	−	0.559361i	$-0.188954\pi$
$331$	4570.50	+	2638.78i	0.758965	+	0.438189i	−0.0699590	+	0.997550i	$0.522287\pi$
$332$	−1476.00	−	852.169i	−0.243994	−	0.140870i
$333$			876.418i			0.144226i
$334$	−2817.00	+	4879.19i	−0.461495	+	0.799333i
$335$	−1140.00	−	1974.54i	−0.185925	−	0.322031i
$336$	10920.0	−	6304.66i	1.77302	−	1.02365i
$337$	8278.00			1.33808			0.669038	−	0.743228i	$-0.266706\pi$
$337$	8278.00			1.33808			0.669038	+	0.743228i	$0.266706\pi$
$338$		0			0
$339$	−2877.00			−0.460936
$340$	−1296.00	+	748.246i	−0.206722	+	0.119351i
$341$	−819.000	−	1418.55i	−0.130063	−	0.225275i
$342$	−3366.00	+	5830.08i	−0.532200	+	0.921798i
$343$			4030.48i			0.634477i
$344$	1020.00	+	588.897i	0.159868	+	0.0923000i
$345$	4788.00	+	2764.35i	0.747180	+	0.431385i
$346$		−	3024.16i		−	0.469884i
$347$	−3433.50	+	5947.00i	−0.531181	+	0.920033i	0.468156	+	0.883646i	$0.344918\pi$
$347$	−3433.50	+	5947.00i	−0.531181	+	0.920033i	−0.999338	+	0.0363875i	$0.988415\pi$
$348$	966.000	+	1673.16i	0.148802	+	0.257732i
$349$	−10525.5	+	6076.90i	−1.61438	+	0.932060i	−0.626036	+	0.779794i	$0.715324\pi$
$349$	−10525.5	+	6076.90i	−1.61438	+	0.932060i	−0.988340	+	0.152266i	$0.951343\pi$
$350$	5226.00			0.798118
$351$		0			0
$352$	3744.00			0.566920
$353$	−5029.50	+	2903.78i	−0.758338	+	0.437827i	−0.828699	−	0.559695i	$-0.810918\pi$
$353$	−5029.50	+	2903.78i	−0.758338	+	0.437827i	0.0703608	+	0.997522i	$0.477585\pi$
$354$	231.000	+	400.104i	0.0346822	+	0.0600714i
$355$	4044.00	−	7004.41i	0.604601	−	1.04720i
$356$			1226.29i			0.182566i
$357$	3685.50	+	2127.82i	0.546379	+	0.315452i
$358$	3861.00	+	2229.15i	0.570001	+	0.329090i
$359$			1340.61i			0.197088i	0.995133	+	0.0985439i	$0.0314185\pi$
$359$			1340.61i			0.197088i	−0.995133	+	0.0985439i	$0.968581\pi$
$360$	2112.00	−	3658.09i	0.309200	−	0.535551i
$361$	472.000	+	817.528i	0.0688147	+	0.119191i
$362$	6.00000	−	3.46410i	0.000871141	−	0.000502953i
$363$	−5768.00			−0.833999
$364$		0			0
$365$	−13920.0			−1.99618
$366$	357.000	−	206.114i	0.0509855	−	0.0294365i
$367$	−1832.50	−	3173.98i	−0.260642	−	0.451446i	0.705770	−	0.708441i	$-0.250601\pi$
$367$	−1832.50	−	3173.98i	−0.260642	−	0.451446i	−0.966413	+	0.256995i	$0.917268\pi$
$368$	2280.00	−	3949.08i	0.322971	−	0.559402i
$369$			8649.86i			1.22031i
$370$	1656.00	+	956.092i	0.232679	+	0.134337i
$371$	−8307.00	−	4796.05i	−1.16247	−	0.671155i
$372$		−	2036.89i		−	0.283892i
$373$	−2685.50	+	4651.42i	−0.372788	+	0.645688i	−0.989993	−	0.141114i	$-0.954931\pi$
$373$	−2685.50	+	4651.42i	−0.372788	+	0.645688i	0.617205	+	0.786802i	$0.288265\pi$
$374$	1053.00	+	1823.85i	0.145586	+	0.252163i
$375$	−4872.00	+	2812.85i	−0.670904	+	0.387347i
$376$	4752.00			0.651770
$377$		0			0
$378$	−2730.00			−0.371471
$379$	9967.50	−	5754.74i	1.35091	−	0.779950i	0.362536	−	0.931970i	$-0.381911\pi$
$379$	9967.50	−	5754.74i	1.35091	−	0.779950i	0.988377	+	0.152020i	$0.0485778\pi$
$380$	2448.00	+	4240.06i	0.330473	+	0.572396i
$381$	−7850.50	+	13597.5i	−1.05563	+	1.82840i
$382$		−	9841.51i		−	1.31816i
$383$	−2095.50	−	1209.84i	−0.279569	−	0.161409i	0.353659	−	0.935374i	$-0.384937\pi$
$383$	−2095.50	−	1209.84i	−0.279569	−	0.161409i	−0.633228	+	0.773965i	$0.718271\pi$
$384$	−9408.00	−	5431.71i	−1.25026	−	0.721838i
$385$		−	7025.20i		−	0.929967i
$386$	7353.00	−	12735.8i	0.969580	−	1.67936i
$387$	935.000	+	1619.47i	0.122813	+	0.212719i
$388$	−4278.00	+	2469.90i	−0.559749	+	0.323171i
$389$	−9858.00			−1.28489			−0.642443	−	0.766334i	$-0.722079\pi$
$389$	−9858.00			−1.28489			−0.642443	+	0.766334i	$0.722079\pi$
$390$		0			0
$391$	1539.00			0.199055
$392$	−1968.00	+	1136.23i	−0.253569	+	0.146398i
$393$	−1302.00	−	2255.13i	−0.167118	−	0.289456i
$394$	−4767.00	+	8256.69i	−0.609538	+	1.05575i
$395$		−	17237.4i		−	2.19571i
$396$	1716.00	+	990.733i	0.217758	+	0.125723i
$397$	7552.50	+	4360.44i	0.954784	+	0.551245i	0.894564	−	0.446941i	$-0.147486\pi$
$397$	7552.50	+	4360.44i	0.954784	+	0.551245i	0.0602200	+	0.998185i	$0.480820\pi$
$398$		−	5837.01i		−	0.735133i
$399$	6961.50	−	12057.7i	0.873461	−	1.51288i
$400$	−2680.00	−	4641.90i	−0.335000	−	0.580237i
$401$	6568.50	−	3792.33i	0.817993	−	0.472269i	−0.0317308	−	0.999496i	$-0.510102\pi$
$401$	6568.50	−	3792.33i	0.817993	−	0.472269i	0.849724	+	0.527228i	$0.176769\pi$
$402$	−3990.00			−0.495033
$403$		0			0
$404$	−7836.00			−0.964989
$405$	−10068.0	+	5812.76i	−1.23527	+	0.713181i
$406$	−2691.00	−	4660.95i	−0.328946	−	0.569751i
$407$	448.500	−	776.825i	0.0546224	−	0.0946088i
$408$		−	2618.86i		−	0.317777i
$409$	−3727.50	−	2152.07i	−0.450643	−	0.260179i	0.257459	−	0.966289i	$-0.417115\pi$
$409$	−3727.50	−	2152.07i	−0.450643	−	0.260179i	−0.708102	+	0.706110i	$0.750448\pi$
$410$	16344.0	+	9436.21i	1.96871	+	1.13664i
$411$			8329.43i			0.999661i
$412$	3712.00	−	6429.37i	0.443876	−	0.768817i
$413$	−214.500	−	371.525i	−0.0255565	−	0.0442652i
$414$	3762.00	−	2171.99i	0.446600	−	0.257844i
$415$	5904.00			0.698352
$416$		0			0
$417$	17815.0			2.09210
$418$	5967.00	−	3445.05i	0.698219	−	0.403117i
$419$	−2698.50	−	4673.94i	−0.314631	−	0.544957i	0.664728	−	0.747085i	$-0.268547\pi$
$419$	−2698.50	−	4673.94i	−0.314631	−	0.544957i	−0.979359	+	0.202129i	$0.935214\pi$
$420$	4368.00	−	7565.60i	0.507468	−	0.878960i
$421$			7260.76i			0.840541i	0.907399	+	0.420270i	$0.138065\pi$
$421$			7260.76i			0.840541i	−0.907399	+	0.420270i	$0.861935\pi$
$422$	−5043.00	−	2911.58i	−0.581728	−	0.335861i
$423$	6534.00	+	3772.41i	0.751050	+	0.433619i
$424$			5902.83i			0.676101i
$425$	904.500	−	1566.64i	0.103235	−	0.178808i
$426$	−7077.00	−	12257.7i	−0.804887	−	1.39410i
$427$	−331.500	+	191.392i	−0.0375700	+	0.0216911i
$428$	1020.00			0.115195
$429$		0			0
$430$	4080.00			0.457570
$431$	421.500	−	243.353i	0.0471066	−	0.0271970i	−0.476262	−	0.879304i	$-0.658009\pi$
$431$	421.500	−	243.353i	0.0471066	−	0.0271970i	0.523368	+	0.852107i	$0.324675\pi$
$432$	1400.00	+	2424.87i	0.155920	+	0.270062i
$433$	−6069.50	+	10512.7i	−0.673629	+	1.16676i	0.303238	+	0.952915i	$0.401932\pi$
$433$	−6069.50	+	10512.7i	−0.673629	+	1.16676i	−0.976867	+	0.213846i	$0.931401\pi$
$434$			5674.20i			0.627581i
$435$	−5796.00	−	3346.32i	−0.638844	−	0.368836i
$436$	−2112.00	−	1219.36i	−0.231987	−	0.133938i
$437$		−	5035.07i		−	0.551167i
$438$	−12180.0	+	21096.4i	−1.32873	+	2.30142i
$439$	−230.500	−	399.238i	−0.0250596	−	0.0434045i	0.853224	−	0.521545i	$-0.174644\pi$
$439$	−230.500	−	399.238i	−0.0250596	−	0.0434045i	−0.878283	+	0.478141i	$0.841311\pi$
$440$	−3744.00	+	2161.60i	−0.405655	+	0.234205i
$441$	−3608.00			−0.389591
$442$		0			0
$443$	12156.0			1.30372			0.651861	−	0.758338i	$-0.273988\pi$
$443$	12156.0			1.30372			0.651861	+	0.758338i	$0.273988\pi$
$444$	966.000	−	557.720i	0.103253	−	0.0596131i
$445$	−2124.00	−	3678.88i	−0.226263	−	0.391900i
$446$	7095.00	−	12288.9i	0.753269	−	1.30470i
$447$		−	9129.64i		−	0.966034i
$448$	1248.00	+	720.533i	0.131613	+	0.0759866i
$449$	256.500	+	148.090i	0.0269599	+	0.0155653i	0.513419	−	0.858138i	$-0.328379\pi$
$449$	256.500	+	148.090i	0.0269599	+	0.0155653i	−0.486459	+	0.873703i	$0.661712\pi$
$450$		−	5106.09i		−	0.534896i
$451$	4426.50	−	7666.92i	0.462164	−	0.800491i
$452$	822.000	+	1423.75i	0.0855390	+	0.148158i
$453$	525.000	−	303.109i	0.0544518	−	0.0314377i
$454$	−1518.00			−0.156924
$455$		0			0
$456$	−8568.00			−0.879898
$457$	−529.500	+	305.707i	−0.0541990	+	0.0312918i	−0.526855	−	0.849955i	$-0.676629\pi$
$457$	−529.500	+	305.707i	−0.0541990	+	0.0312918i	0.472656	+	0.881247i	$0.343295\pi$
$458$	312.000	+	540.400i	0.0318314	+	0.0551337i
$459$	−472.500	+	818.394i	−0.0480488	+	0.0832230i
$460$		−	3159.26i		−	0.320220i
$461$	11368.5	+	6563.61i	1.14855	+	0.663119i	0.948535	−	0.316673i	$-0.102566\pi$
$461$	11368.5	+	6563.61i	1.14855	+	0.663119i	0.200020	+	0.979792i	$0.435899\pi$
$462$	−10647.0	−	6147.05i	−1.07217	−	0.619019i
$463$		−	834.848i		−	0.0837985i	−0.999122	−	0.0418992i	$-0.986659\pi$
$463$		−	834.848i		−	0.0837985i	0.999122	−	0.0418992i	$-0.0133408\pi$
$464$	−2760.00	+	4780.46i	−0.276142	+	0.478292i
$465$	3528.00	+	6110.68i	0.351843	+	0.609410i
$466$	−17334.0	+	10007.8i	−1.72314	+	0.994854i
$467$	14496.0			1.43639			0.718196	−	0.695841i	$-0.244968\pi$
$467$	14496.0			1.43639			0.718196	+	0.695841i	$0.244968\pi$
$468$		0			0
$469$	3705.00			0.364778
$470$	14256.0	−	8230.71i	1.39911	−	0.807775i
$471$	−5369.00	−	9299.38i	−0.525245	−	0.909751i
$472$	−132.000	+	228.631i	−0.0128724	+	0.0222957i
$473$		−	1913.92i		−	0.186051i
$474$	−26124.0	−	15082.7i	−2.53147	−	1.46154i
$475$	−5125.50	−	2959.21i	−0.495103	−	0.285848i
$476$		−	2431.80i		−	0.234162i
$477$	−4686.00	+	8116.39i	−0.449805	+	0.779086i
$478$	−3222.00	−	5580.67i	−0.308307	−	0.534004i
$479$	7705.50	−	4448.77i	0.735017	−	0.424362i	−0.0852376	−	0.996361i	$-0.527165\pi$
$479$	7705.50	−	4448.77i	0.735017	−	0.424362i	0.820255	+	0.571998i	$0.193832\pi$
$480$	−16128.0			−1.53362
$481$		0			0
$482$	−7134.00			−0.674159
$483$	−7780.50	+	4492.07i	−0.732971	+	0.423181i
$484$	1648.00	+	2854.42i	0.154771	+	0.268071i
$485$	8556.00	−	14819.4i	0.801047	−	1.38745i
$486$			17071.1i			1.59333i
$487$	−4117.50	−	2377.24i	−0.383125	−	0.221197i	0.296052	−	0.955172i	$-0.404330\pi$
$487$	−4117.50	−	2377.24i	−0.383125	−	0.221197i	−0.679177	+	0.733975i	$0.737663\pi$
$488$	204.000	+	117.779i	0.0189235	+	0.0109255i
$489$			11433.3i			1.05732i
$490$	−3936.00	+	6817.35i	−0.362878	+	0.628524i
$491$	817.500	+	1415.95i	0.0751390	+	0.130145i	0.901147	−	0.433514i	$-0.142727\pi$
$491$	817.500	+	1415.95i	0.0751390	+	0.130145i	−0.826008	+	0.563659i	$0.809393\pi$
$492$	9534.00	−	5504.46i	0.873630	−	0.504390i
$493$	−1863.00			−0.170193
$494$		0			0
$495$	−6864.00			−0.623260
$496$	5040.00	−	2909.85i	0.456255	−	0.263419i
$497$	6571.50	+	11382.2i	0.593103	+	1.02728i
$498$	5166.00	−	8947.77i	0.464847	−	0.805139i
$499$		−	14434.9i		−	1.29498i	−0.762074	−	0.647490i	$-0.775819\pi$
$499$		−	14434.9i		−	1.29498i	0.762074	−	0.647490i	$-0.224181\pi$
$500$	2784.00	+	1607.34i	0.249009	+	0.143765i
$501$	−9859.50	−	5692.38i	−0.879222	−	0.507619i
$502$			15557.3i			1.38318i
$503$	−6343.50	+	10987.3i	−0.562312	+	0.973952i	0.434983	+	0.900439i	$0.356754\pi$
$503$	−6343.50	+	10987.3i	−0.562312	+	0.973952i	−0.997294	+	0.0735133i	$0.976579\pi$
$504$	3432.00	+	5944.40i	0.303320	+	0.525366i
$505$	23508.0	−	13572.4i	2.07147	−	1.19596i
$506$	−4446.00			−0.390610
$507$		0			0
$508$	8972.00			0.783599
$509$	4978.50	−	2874.34i	0.433533	−	0.250300i	−0.267318	−	0.963608i	$-0.586137\pi$
$509$	4978.50	−	2874.34i	0.433533	−	0.250300i	0.700850	+	0.713308i	$0.252804\pi$
$510$	−4536.00	−	7856.58i	−0.393838	−	0.682148i
$511$	11310.0	−	19589.5i	0.979109	−	1.69587i
$512$			4434.05i			0.382733i
$513$	2677.50	+	1545.86i	0.230438	+	0.133043i
$514$	−16353.0	−	9441.41i	−1.40331	−	0.810200i
$515$			25717.5i			2.20048i
$516$	1190.00	−	2061.14i	0.101525	−	0.175846i
$517$	−3861.00	−	6687.45i	−0.328446	−	0.568885i
$518$	−2691.00	+	1553.65i	−0.228254	+	0.131783i
$519$	6111.00			0.516846
$520$		0			0
$521$	6054.00			0.509080			0.254540	−	0.967062i	$-0.418076\pi$
$521$	6054.00			0.509080			0.254540	+	0.967062i	$0.418076\pi$
$522$	−4554.00	+	2629.25i	−0.381845	+	0.220458i
$523$	7401.50	+	12819.8i	0.618824	+	1.07183i	0.989701	+	0.143153i	$0.0457240\pi$
$523$	7401.50	+	12819.8i	0.618824	+	1.07183i	−0.370877	+	0.928682i	$0.620943\pi$
$524$	−744.000	+	1288.65i	−0.0620263	+	0.107433i
$525$			10560.3i			0.877885i
$526$	2349.00	+	1356.20i	0.194717	+	0.112420i
$527$	1701.00	+	982.073i	0.140601	+	0.0811760i
$528$			12609.3i			1.03930i
$529$	4459.00	−	7723.21i	0.366483	−	0.634767i
$530$	10224.0	+	17708.5i	0.837929	+	1.45133i
$531$	−363.000	+	209.578i	−0.0296664	+	0.0171279i
$532$	−7956.00			−0.648377
$533$		0			0
$534$	−7434.00			−0.602436
$535$	−3060.00	+	1766.69i	−0.247281	+	0.142768i
$536$	−1140.00	−	1974.54i	−0.0918666	−	0.159118i
$537$	−4504.50	+	7802.02i	−0.361980	+	0.626969i
$538$		−	17615.0i		−	1.41159i
$539$	3198.00	+	1846.37i	0.255561	+	0.147548i
$540$	1680.00	+	969.948i	0.133881	+	0.0772962i
$541$		−	21470.5i		−	1.70626i	−0.521695	−	0.853132i	$-0.674700\pi$
$541$		−	21470.5i		−	1.70626i	0.521695	−	0.853132i	$-0.325300\pi$
$542$	2295.00	−	3975.06i	0.181880	−	0.315025i
$543$	7.00000	+	12.1244i	0.000553221	+	0.000958206i
$544$	−3888.00	+	2244.74i	−0.306428	+	0.176916i
$545$	8448.00			0.663986
$546$		0			0
$547$	−13516.0			−1.05649			−0.528247	−	0.849091i	$-0.677151\pi$
$547$	−13516.0			−1.05649			−0.528247	+	0.849091i	$0.677151\pi$
$548$	4122.00	−	2379.84i	0.321320	−	0.185514i
$549$	187.000	+	323.894i	0.0145373	+	0.0251793i
$550$	−2613.00	+	4525.85i	−0.202579	+	0.350878i
$551$			6095.09i			0.471251i
$552$	4788.00	+	2764.35i	0.369186	+	0.213150i
$553$	24258.0	+	14005.4i	1.86538	+	1.07698i
$554$		−	11850.7i		−	0.908822i
$555$	−1932.00	+	3346.32i	−0.147764	+	0.255934i
$556$	−5090.00	−	8816.14i	−0.388245	−	0.672460i
$557$	−2503.50	+	1445.40i	−0.190443	+	0.109952i	−0.592190	−	0.805798i	$-0.701736\pi$
$557$	−2503.50	+	1445.40i	−0.190443	+	0.109952i	0.401747	+	0.915751i	$0.368403\pi$
$558$	5544.00			0.420603
$559$		0			0
$560$	24960.0			1.88349
$561$	−3685.50	+	2127.82i	−0.277365	+	0.160137i
$562$	1404.00	+	2431.80i	0.105381	+	0.182525i
$563$	−5791.50	+	10031.2i	−0.433539	+	0.750912i	−0.997175	−	0.0751113i	$-0.976069\pi$
$563$	−5791.50	+	10031.2i	−0.433539	+	0.750912i	0.563636	+	0.826023i	$0.309402\pi$
$564$		−	9602.49i		−	0.716911i
$565$	−4932.00	−	2847.49i	−0.367240	−	0.212026i
$566$	−21531.0	−	12430.9i	−1.59897	−	0.923164i
$567$		−	18891.5i		−	1.39924i
$568$	4044.00	−	7004.41i	0.298737	−	0.517427i
$569$	−6439.50	−	11153.5i	−0.474443	−	0.821759i	0.525129	−	0.851023i	$-0.324017\pi$
$569$	−6439.50	−	11153.5i	−0.474443	−	0.821759i	−0.999572	+	0.0292638i	$0.990684\pi$
$570$	−25704.0	+	14840.2i	−1.88881	+	1.09051i
$571$	−11636.0			−0.852805			−0.426402	−	0.904534i	$-0.640219\pi$
$571$	−11636.0			−0.852805			−0.426402	+	0.904534i	$0.640219\pi$
$572$		0			0
$573$	19887.0			1.44990
$574$	−26559.0	+	15333.8i	−1.93127	+	1.11502i
$575$	1909.50	+	3307.35i	0.138490	+	0.239871i
$576$	704.000	−	1219.36i	0.0509259	−	0.0882063i
$577$			12311.4i			0.888269i	0.895960	+	0.444134i	$0.146489\pi$
$577$			12311.4i			0.888269i	−0.895960	+	0.444134i	$0.853511\pi$
$578$	12552.0	+	7246.90i	0.903277	+	0.521507i
$579$	25735.5	+	14858.4i	1.84720	+	1.06648i
$580$			3824.37i			0.273790i
$581$	−4797.00	+	8308.65i	−0.342535	+	0.593289i
$582$	−14973.0	−	25934.0i	−1.06641	−	1.84708i
$583$	8307.00	−	4796.05i	0.590121	−	0.340707i
$584$	−13920.0			−0.986325
$585$		0			0
$586$	−32262.0			−2.27428
$587$	13549.5	−	7822.81i	0.952722	−	0.550054i	0.0587964	−	0.998270i	$-0.481274\pi$
$587$	13549.5	−	7822.81i	0.952722	−	0.550054i	0.893925	+	0.448216i	$0.147940\pi$
$588$	2296.00	+	3976.79i	0.161030	+	0.278912i
$589$	3213.00	−	5565.08i	0.224770	−	0.389313i
$590$			914.523i			0.0638141i
$591$	−16684.5	−	9632.80i	−1.16127	−	0.670458i
$592$	2760.00	+	1593.49i	0.191614	+	0.110628i
$593$			25821.4i			1.78813i	0.447942	+	0.894063i	$0.352157\pi$
$593$			25821.4i			1.78813i	−0.447942	+	0.894063i	$0.647843\pi$
$594$	1365.00	−	2364.25i	0.0942873	−	0.163310i
$595$	4212.00	+	7295.40i	0.290210	+	0.502659i
$596$	−4518.00	+	2608.47i	−0.310511	+	0.179274i
$597$	11795.0			0.808605
$598$		0			0
$599$	1668.00			0.113777			0.0568887	−	0.998381i	$-0.481882\pi$
$599$	1668.00			0.113777			0.0568887	+	0.998381i	$0.481882\pi$
$600$	5628.00	−	3249.33i	0.382937	−	0.221089i
$601$	−6849.50	−	11863.7i	−0.464887	−	0.805207i	0.534310	−	0.845289i	$-0.320572\pi$
$601$	−6849.50	−	11863.7i	−0.464887	−	0.805207i	−0.999196	+	0.0400813i	$0.987238\pi$
$602$	−3315.00	+	5741.75i	−0.224434	+	0.388731i
$603$		−	3619.99i		−	0.244473i
$604$	−300.000	−	173.205i	−0.0202100	−	0.0116682i
$605$	−9888.00	−	5708.84i	−0.664470	−	0.383632i
$606$		−	47503.2i		−	3.18430i
$607$	11586.5	−	20068.4i	0.774764	−	1.34193i	−0.160164	−	0.987090i	$-0.551202\pi$
$607$	11586.5	−	20068.4i	0.774764	−	1.34193i	0.934927	−	0.354839i	$-0.115464\pi$
$608$	7344.00	+	12720.2i	0.489866	+	0.848473i
$609$	9418.50	−	5437.77i	0.626694	−	0.361822i
$610$	816.000			0.0541621
$611$		0			0
$612$	−2376.00			−0.156935
$613$	−14389.5	+	8307.78i	−0.948102	+	0.547387i	−0.892491	−	0.451066i	$-0.851044\pi$
$613$	−14389.5	+	8307.78i	−0.948102	+	0.547387i	−0.0556111	+	0.998453i	$0.517711\pi$
$614$	−8274.00	−	14331.0i	−0.543830	−	0.941941i
$615$	−19068.0	+	33026.7i	−1.25024	+	2.16547i
$616$		−	7025.20i		−	0.459502i
$617$	−24589.5	−	14196.8i	−1.60443	−	0.926321i	−0.990585	−	0.136897i	$-0.956287\pi$
$617$	−24589.5	−	14196.8i	−1.60443	−	0.926321i	−0.613849	−	0.789423i	$-0.710380\pi$
$618$	38976.0	+	22502.8i	2.53697	+	1.46472i
$619$		−	6245.78i		−	0.405556i	−0.979225	−	0.202778i	$-0.935003\pi$
$619$		−	6245.78i		−	0.405556i	0.979225	−	0.202778i	$-0.0649969\pi$
$620$	2016.00	−	3491.81i	0.130588	−	0.226185i
$621$	−997.500	−	1727.72i	−0.0644578	−	0.111644i
$622$	18576.0	−	10724.9i	1.19748	−	0.691363i
$623$	6903.00			0.443921
$624$		0			0
$625$	−19511.0			−1.24870
$626$	−2310.00	+	1333.68i	−0.147486	+	0.0851510i
$627$	6961.50	+	12057.7i	0.443406	+	0.768002i
$628$	−3068.00	+	5313.93i	−0.194947	+	0.337658i
$629$			1075.60i			0.0681830i
$630$	20592.0	+	11888.8i	1.30223	+	0.751843i
$631$	−19381.5	−	11189.9i	−1.22277	−	0.705964i	−0.257259	−	0.966342i	$-0.582819\pi$
$631$	−19381.5	−	11189.9i	−1.22277	−	0.705964i	−0.965507	+	0.260378i	$0.916153\pi$
$632$		−	17237.4i		−	1.08491i
$633$	5883.50	−	10190.5i	0.369428	−	0.639869i
$634$	13956.0	+	24172.5i	0.874233	+	1.51422i
$635$	−26916.0	+	15540.0i	−1.68209	+	0.971157i
$636$	11928.0			0.743673
$637$		0			0
$638$	5382.00			0.333974
$639$	11121.0	−	6420.71i	0.688482	−	0.397495i
$640$	−10752.0	−	18623.0i	−0.664078	−	1.15022i
$641$	−9913.50	+	17170.7i	−0.610858	+	1.05804i	0.380239	+	0.924888i	$0.375842\pi$
$641$	−9913.50	+	17170.7i	−0.610858	+	1.05804i	−0.991096	+	0.133148i	$0.957491\pi$
$642$			6183.42i			0.380125i
$643$	7318.50	+	4225.34i	0.448855	+	0.259146i	0.707346	−	0.706867i	$-0.249892\pi$
$643$	7318.50	+	4225.34i	0.448855	+	0.259146i	−0.258492	+	0.966013i	$0.583225\pi$
$644$	4446.00	+	2566.90i	0.272045	+	0.157065i
$645$			8244.56i			0.503301i
$646$	−4131.00	+	7155.10i	−0.251598	+	0.435780i
$647$	−1474.50	−	2553.91i	−0.0895959	−	0.155185i	0.817744	−	0.575581i	$-0.195224\pi$
$647$	−1474.50	−	2553.91i	−0.0895959	−	0.155185i	−0.907340	+	0.420397i	$0.861891\pi$
$648$	−10068.0	+	5812.76i	−0.610352	+	0.352387i
$649$	429.000			0.0259472
$650$		0			0
$651$	−11466.0			−0.690304
$652$	5658.00	−	3266.65i	0.339853	−	0.196214i
$653$	−6019.50	−	10426.1i	−0.360737	−	0.624815i	0.627345	−	0.778741i	$-0.284141\pi$
$653$	−6019.50	−	10426.1i	−0.360737	−	0.624815i	−0.988082	+	0.153926i	$0.950808\pi$
$654$	7392.00	−	12803.3i	0.441973	−	0.765519i
$655$		−	5154.58i		−	0.307490i
$656$	27240.0	+	15727.0i	1.62126	+	0.936032i
$657$	−19140.0	−	11050.5i	−1.13656	−	0.656196i
$658$			26749.8i			1.58483i
$659$	−1681.50	+	2912.44i	−0.0993960	+	0.172159i	−0.911435	−	0.411445i	$-0.865024\pi$
$659$	−1681.50	+	2912.44i	−0.0993960	+	0.172159i	0.812039	+	0.583603i	$0.198358\pi$
$660$	4368.00	+	7565.60i	0.257612	+	0.446198i
$661$	−8797.50	+	5079.24i	−0.517675	+	0.298880i	−0.735983	−	0.677000i	$-0.763280\pi$
$661$	−8797.50	+	5079.24i	−0.517675	+	0.298880i	0.218308	+	0.975880i	$0.429946\pi$
$662$	18282.0			1.07334
$663$		0			0
$664$	5904.00			0.345060
$665$	23868.0	−	13780.2i	1.39182	−	0.803569i
$666$	1518.00	+	2629.25i	0.0883203	+	0.152975i
$667$	1966.50	−	3406.08i	0.114158	−	0.197727i
$668$			6505.58i			0.376809i
$669$	24832.5	+	14337.1i	1.43510	+	0.828554i
$670$	−6840.00	−	3949.08i	−0.394406	−	0.227711i
$671$		−	382.783i		−	0.0220226i
$672$	13104.0	−	22696.8i	0.752229	−	1.30290i
$673$	9084.50	+	15734.8i	0.520329	+	0.901237i	0.999721	+	0.0236358i	$0.00752419\pi$
$673$	9084.50	+	15734.8i	0.520329	+	0.901237i	−0.479391	+	0.877601i	$0.659142\pi$
$674$	24834.0	−	14337.9i	1.41924	−	0.819400i
$675$	−2345.00			−0.133717
$676$		0			0
$677$	9042.00			0.513312			0.256656	−	0.966503i	$-0.417379\pi$
$677$	9042.00			0.513312			0.256656	+	0.966503i	$0.417379\pi$
$678$	−8631.00	+	4983.11i	−0.488896	+	0.282264i
$679$	13903.5	+	24081.6i	0.785813	+	1.36107i
$680$	2592.00	−	4489.48i	0.146175	−	0.253182i
$681$		−	3067.46i		−	0.172607i
$682$	−4914.00	−	2837.10i	−0.275904	−	0.159293i
$683$	10792.5	+	6231.05i	0.604632	+	0.349084i	0.770862	−	0.637003i	$-0.219826\pi$
$683$	10792.5	+	6231.05i	0.604632	+	0.349084i	−0.166230	+	0.986087i	$0.553159\pi$
$684$			7773.44i			0.434540i
$685$	−8244.00	+	14279.0i	−0.459835	+	0.796458i
$686$	6981.00	+	12091.4i	0.388536	+	0.672964i
$687$	−1092.00	+	630.466i	−0.0606440	+	0.0350128i
$688$	6800.00			0.376813
$689$		0			0
$690$	19152.0			1.05667
$691$	3739.50	−	2159.00i	0.205872	−	0.118860i	−0.393520	−	0.919316i	$-0.628743\pi$
$691$	3739.50	−	2159.00i	0.205872	−	0.118860i	0.599391	+	0.800456i	$0.295409\pi$
$692$	−1746.00	−	3024.16i	−0.0959147	−	0.166129i
$693$	5577.00	−	9659.65i	0.305704	−	0.529494i
$694$			23788.0i			1.30112i
$695$	30540.0	+	17632.3i	1.66683	+	0.962346i
$696$	−5796.00	−	3346.32i	−0.315656	−	0.182244i
$697$			10615.7i			0.576901i
$698$	−21051.0	+	36461.4i	−1.14154	+	1.97720i
$699$	−20223.0	−	35027.3i	−1.09428	−	1.89535i
$700$	5226.00	−	3017.23i	0.282177	−	0.162915i
$701$	−18270.0			−0.984377			−0.492189	−	0.870489i	$-0.663803\pi$
$701$	−18270.0			−0.984377			−0.492189	+	0.870489i	$0.663803\pi$
$702$		0			0
$703$	3519.00			0.188793
$704$	−1248.00	+	720.533i	−0.0668122	+	0.0385740i
$705$	16632.0	+	28807.5i	0.888507	+	1.53894i
$706$	−10059.0	+	17422.7i	−0.536226	+	0.928770i
$707$			44110.1i			2.34644i
$708$	462.000	+	266.736i	0.0245240	+	0.0141590i
$709$	−1411.50	−	814.930i	−0.0747673	−	0.0431669i	0.462150	−	0.886802i	$-0.347078\pi$
$709$	−1411.50	−	814.930i	−0.0747673	−	0.0431669i	−0.536918	+	0.843635i	$0.680411\pi$
$710$		−	28017.7i		−	1.48096i
$711$	13684.0	−	23701.4i	0.721786	−	1.25017i
$712$	−2124.00	−	3678.88i	−0.111798	−	0.193640i
$713$	−3591.00	+	2073.26i	−0.188617	+	0.108898i
$714$	14742.0			0.772697
$715$		0			0
$716$	5148.00			0.268701
$717$	11277.0	−	6510.78i	0.587374	−	0.339121i
$718$	2322.00	+	4021.82i	0.120691	+	0.209043i
$719$	−4915.50	+	8513.90i	−0.254961	+	0.441606i	−0.964885	−	0.262673i	$-0.915396\pi$
$719$	−4915.50	+	8513.90i	−0.254961	+	0.441606i	0.709924	+	0.704279i	$0.248729\pi$
$720$		−	24387.3i		−	1.26231i
$721$	−36192.0	−	20895.5i	−1.86943	−	1.07932i
$722$	2832.00	+	1635.06i	0.145978	+	0.0842804i
$723$		−	14415.9i		−	0.741537i
$724$	4.00000	−	6.92820i	0.000205330	−	0.000355642i
$725$	−2311.50	−	4003.64i	−0.118410	−	0.205091i
$726$	−17304.0	+	9990.47i	−0.884589	+	0.510718i
$727$	−15464.0			−0.788897			−0.394448	−	0.918918i	$-0.629064\pi$
$727$	−15464.0			−0.788897			−0.394448	+	0.918918i	$0.629064\pi$
$728$		0			0
$729$	−11843.0			−0.601687
$730$	−41760.0	+	24110.1i	−2.11727	+	1.22241i
$731$	1147.50	+	1987.53i	0.0580599	+	0.100563i
$732$	238.000	−	412.228i	0.0120174	−	0.0208147i
$733$		−	12616.3i		−	0.635733i	−0.948136	−	0.317866i	$-0.897034\pi$
$733$		−	12616.3i		−	0.635733i	0.948136	−	0.317866i	$-0.102966\pi$
$734$	−10995.0	−	6347.97i	−0.552906	−	0.319220i
$735$	−13776.0	−	7953.58i	−0.691341	−	0.399146i
$736$		−	9477.78i		−	0.474668i
$737$	−1852.50	+	3208.62i	−0.0925885	+	0.160368i
$738$	14982.0	+	25949.6i	0.747283	+	1.29433i
$739$	14101.5	−	8141.50i	0.701938	−	0.405264i	−0.106131	−	0.994352i	$-0.533846\pi$
$739$	14101.5	−	8141.50i	0.701938	−	0.405264i	0.808069	+	0.589088i	$0.200513\pi$
$740$	2208.00			0.109686
$741$		0			0
$742$	−33228.0			−1.64399
$743$	−9358.50	+	5403.13i	−0.462086	+	0.266786i	−0.712921	−	0.701244i	$-0.752628\pi$
$743$	−9358.50	+	5403.13i	−0.462086	+	0.266786i	0.250835	+	0.968030i	$0.419295\pi$
$744$	3528.00	+	6110.68i	0.173848	+	0.301113i
$745$	9036.00	−	15650.8i	0.444367	−	0.769666i
$746$			18605.7i			0.913140i
$747$	8118.00	+	4686.93i	0.397620	+	0.229566i
$748$	2106.00	+	1215.90i	0.102945	+	0.0594354i
$749$		−	5741.75i		−	0.280105i
$750$	−9744.00	+	16877.1i	−0.474401	+	0.821686i
$751$	6807.50	+	11790.9i	0.330771	+	0.572913i	0.982663	−	0.185399i	$-0.0593578\pi$
$751$	6807.50	+	11790.9i	0.330771	+	0.572913i	−0.651892	+	0.758312i	$0.726024\pi$
$752$	23760.0	−	13717.8i	1.15218	−	0.665210i
$753$	−31437.0			−1.52142
$754$		0			0
$755$	1200.00			0.0578443
$756$	−2730.00	+	1576.17i	−0.131335	+	0.0758262i
$757$	−2775.50	−	4807.31i	−0.133259	−	0.230812i	0.791672	−	0.610947i	$-0.209211\pi$
$757$	−2775.50	−	4807.31i	−0.133259	−	0.230812i	−0.924931	+	0.380135i	$0.875878\pi$
$758$	19935.0	−	34528.4i	0.955240	−	1.65452i
$759$		−	8984.15i		−	0.429649i
$760$	−14688.0	−	8480.12i	−0.701039	−	0.404745i
$761$	−8731.50	−	5041.13i	−0.415922	−	0.240133i	0.277409	−	0.960752i	$-0.410524\pi$
$761$	−8731.50	−	5041.13i	−0.415922	−	0.240133i	−0.693331	+	0.720619i	$0.743858\pi$
$762$			54389.9i			2.58574i
$763$	−6864.00	+	11888.8i	−0.325680	+	0.564093i
$764$	−5682.00	−	9841.51i	−0.269067	−	0.466039i
$765$	7128.00	−	4115.35i	0.336880	−	0.194498i
$766$	−8382.00			−0.395371
$767$		0			0
$768$	−34048.0			−1.59974
$769$	−25771.5	+	14879.2i	−1.20851	+	0.697733i	−0.962434	−	0.271517i	$-0.912475\pi$
$769$	−25771.5	+	14879.2i	−1.20851	+	0.697733i	−0.246076	+	0.969250i	$0.579141\pi$
$770$	−12168.0	−	21075.6i	−0.569486	−	0.986379i
$771$	19078.5	−	33044.9i	0.891174	−	1.54356i
$772$		−	16981.0i		−	0.791659i
$773$	−24019.5	−	13867.7i	−1.11762	−	0.645259i	−0.176829	−	0.984242i	$-0.556584\pi$
$773$	−24019.5	−	13867.7i	−1.11762	−	0.645259i	−0.940793	+	0.338983i	$0.889917\pi$
$774$	5610.00	+	3238.94i	0.260526	+	0.150415i
$775$			4873.99i			0.225908i
$776$	8556.00	−	14819.4i	0.395802	−	0.685550i
$777$	−3139.50	−	5437.77i	−0.144954	−	0.251067i
$778$	−29574.0	+	17074.6i	−1.36283	+	0.786828i
$779$	34731.0			1.59739
$780$		0			0
$781$	−13143.0			−0.602168
$782$	4617.00	−	2665.63i	0.211130	−	0.121896i
$783$	1207.50	+	2091.45i	0.0551118	+	0.0954564i
$784$	−6560.00	+	11362.3i	−0.298834	+	0.517595i
$785$		−	21255.7i		−	0.966432i
$786$	−7812.00	−	4510.26i	−0.354510	−	0.204676i
$787$	27322.5	+	15774.7i	1.23754	+	0.714493i	0.968590	−	0.248662i	$-0.0799910\pi$
$787$	27322.5	+	15774.7i	1.23754	+	0.714493i	0.268947	+	0.963155i	$0.413324\pi$
$788$			11008.9i			0.497686i
$789$	−2740.50	+	4746.69i	−0.123656	+	0.214178i
$790$	−29856.0	−	51712.1i	−1.34459	−	2.32890i
$791$	8014.50	−	4627.17i	0.360256	−	0.207994i
$792$	−6864.00			−0.307957
$793$		0			0
$794$	30210.0			1.35027
$795$	−35784.0	+	20659.9i	−1.59639	+	0.921674i
$796$	−3370.00	−	5837.01i	−0.150058	−	0.259909i
$797$	−727.500	+	1260.07i	−0.0323330	+	0.0560023i	−0.881739	−	0.471737i	$-0.843627\pi$
$797$	−727.500	+	1260.07i	−0.0323330	+	0.0560023i	0.849406	+	0.527740i	$0.176960\pi$
$798$		−	48230.7i		−	2.13953i
$799$	8019.00	+	4629.77i	0.355059	+	0.204993i
$800$	−9648.00	−	5570.28i	−0.426385	−	0.246174i
$801$		−	6744.61i		−	0.297514i
$802$	13137.0	−	22754.0i	0.578408	−	1.00183i
$803$	11310.0	+	19589.5i	0.497038	+	0.860894i
$804$	−3990.00	+	2303.63i	−0.175020	+	0.101048i
$805$	−17784.0			−0.778638
$806$		0			0
$807$	35595.0			1.55267
$808$	23508.0	−	13572.4i	1.02353	−	0.590933i
$809$	−829.500	−	1436.74i	−0.0360490	−	0.0624388i	0.847438	−	0.530894i	$-0.178144\pi$
$809$	−829.500	−	1436.74i	−0.0360490	−	0.0624388i	−0.883487	+	0.468456i	$0.844811\pi$
$810$	−20136.0	+	34876.6i	−0.873465	+	1.51289i
$811$			4402.87i			0.190636i	0.995447	+	0.0953180i	$0.0303868\pi$
$811$			4402.87i			0.190636i	−0.995447	+	0.0953180i	$0.969613\pi$
$812$	−5382.00	−	3107.30i	−0.232600	−	0.134292i
$813$	8032.50	+	4637.57i	0.346509	+	0.200057i
$814$		−	3107.30i		−	0.133797i
$815$	−11316.0	+	19599.9i	−0.486359	+	0.842398i
$816$	−7560.00	−	13094.3i	−0.324330	−	0.561755i
$817$	6502.50	−	3754.22i	0.278450	−	0.160763i
$818$	−14910.0			−0.637306
$819$		0			0
$820$	21792.0			0.928061
$821$	24856.5	−	14350.9i	1.05664	−	0.610049i	0.132136	−	0.991232i	$-0.457816\pi$
$821$	24856.5	−	14350.9i	1.05664	−	0.610049i	0.924500	+	0.381183i	$0.124483\pi$
$822$	14427.0	+	24988.3i	0.612165	+	1.06030i
$823$	−7889.50	+	13665.0i	−0.334156	+	0.578776i	−0.983322	−	0.181871i	$-0.941785\pi$
$823$	−7889.50	+	13665.0i	−0.334156	+	0.578776i	0.649166	+	0.760647i	$0.275118\pi$
$824$			25717.5i			1.08727i
$825$	−9145.50	−	5280.16i	−0.385946	−	0.222826i
$826$	−1287.00	−	743.050i	−0.0542136	−	0.0313003i
$827$		−	7354.29i		−	0.309231i	−0.987975	−	0.154615i	$-0.950586\pi$
$827$		−	7354.29i		−	0.309231i	0.987975	−	0.154615i	$-0.0494138\pi$
$828$	2508.00	−	4343.98i	0.105265	−	0.182324i
$829$	−8685.50	−	15043.7i	−0.363884	−	0.630266i	0.624712	−	0.780855i	$-0.285216\pi$
$829$	−8685.50	−	15043.7i	−0.363884	−	0.630266i	−0.988596	+	0.150589i	$0.951883\pi$
$830$	17712.0	−	10226.0i	0.740714	−	0.427651i
$831$	23947.0			0.999654
$832$		0			0
$833$	−4428.00			−0.184179
$834$	53445.0	−	30856.5i	2.21900	−	1.28114i
$835$	−11268.0	−	19516.7i	−0.467000	−	0.808868i
$836$	3978.00	−	6890.10i	0.164572	−	0.285047i
$837$		−	2546.11i		−	0.105145i
$838$	−16191.0	−	9347.88i	−0.667433	−	0.385343i
$839$	−25525.5	−	14737.2i	−1.05034	−	0.606416i	−0.127598	−	0.991826i	$-0.540727\pi$
$839$	−25525.5	−	14737.2i	−1.05034	−	0.606416i	−0.922745	+	0.385410i	$0.874060\pi$
$840$			30262.4i			1.24304i
$841$	9814.00	−	16998.3i	0.402395	−	0.696968i
$842$	12576.0	+	21782.3i	0.514724	+	0.891528i
$843$	−4914.00	+	2837.10i	−0.200768	+	0.115913i
$844$	−6724.00			−0.274229
$845$		0			0
$846$	26136.0			1.06214
$847$	16068.0	−	9276.86i	0.651834	−	0.376336i
$848$	17040.0	+	29514.1i	0.690042	+	1.19519i
$849$	25119.5	−	43508.3i	1.01543	−	1.75877i
$850$		−	6266.56i		−	0.252872i
$851$	−1966.50	−	1135.36i	−0.0792136	−	0.0457340i
$852$	−14154.0	−	8171.82i	−0.569141	−	0.328594i
$853$			2909.85i			0.116801i	0.998293	+	0.0584005i	$0.0186000\pi$
$853$			2909.85i			0.116801i	−0.998293	+	0.0584005i	$0.981400\pi$
$854$	−663.000	+	1148.35i	−0.0265660	+	0.0460137i
$855$	−13464.0	−	23320.3i	−0.538549	−	0.932794i
$856$	−3060.00	+	1766.69i	−0.122183	+	0.0705424i
$857$	−5346.00			−0.213087			−0.106544	−	0.994308i	$-0.533978\pi$
$857$	−5346.00			−0.213087			−0.106544	+	0.994308i	$0.533978\pi$
$858$		0			0
$859$	24244.0			0.962974			0.481487	−	0.876453i	$-0.340097\pi$
$859$	24244.0			0.962974			0.481487	+	0.876453i	$0.340097\pi$
$860$	4080.00	−	2355.59i	0.161775	−	0.0934011i
$861$	−30985.5	−	53668.5i	−1.22646	−	2.12429i
$862$	843.000	−	1460.12i	0.0333094	−	0.0576936i
$863$			32780.8i			1.29301i	0.762908	+	0.646507i	$0.223771\pi$
$863$			32780.8i			1.29301i	−0.762908	+	0.646507i	$0.776229\pi$
$864$	5040.00	+	2909.85i	0.198454	+	0.114577i
$865$	10476.0	+	6048.32i	0.411786	+	0.237745i
$866$			42050.7i			1.65005i
$867$	−14644.0	+	25364.2i	−0.573629	+	0.993555i
$868$	3276.00	+	5674.20i	0.128104	+	0.221883i
$869$	−24258.0	+	14005.4i	−0.946946	+	0.546720i
$870$	−23184.0			−0.903461
$871$		0			0
$872$	8448.00			0.328080
$873$	23529.0	−	13584.5i	0.912183	−	0.526649i
$874$	−8721.00	−	15105.2i	−0.337520	−	0.584601i
$875$	9048.00	−	15671.6i	0.349575	−	0.605482i
$876$			28128.5i			1.08490i
$877$	3934.50	+	2271.58i	0.151492	+	0.0874640i	0.573830	−	0.818974i	$-0.305457\pi$
$877$	3934.50	+	2271.58i	0.151492	+	0.0874640i	−0.422338	+	0.906439i	$0.638790\pi$
$878$	−1383.00	−	798.475i	−0.0531594	−	0.0306916i
$879$		−	65192.7i		−	2.50159i
$880$	−12480.0	+	21616.0i	−0.478069	+	0.828040i
$881$	10258.5	+	17768.2i	0.392302	+	0.679486i	0.992753	−	0.120175i	$-0.0383456\pi$
$881$	10258.5	+	17768.2i	0.392302	+	0.679486i	−0.600451	+	0.799661i	$0.705012\pi$
$882$	−10824.0	+	6249.24i	−0.413223	+	0.238575i
$883$	−23852.0			−0.909042			−0.454521	−	0.890736i	$-0.650189\pi$
$883$	−23852.0			−0.909042			−0.454521	+	0.890736i	$0.650189\pi$
$884$		0			0
$885$	−1848.00			−0.0701919
$886$	36468.0	−	21054.8i	1.38281	−	0.798364i
$887$	−19378.5	−	33564.5i	−0.733558	−	1.27056i	−0.955353	−	0.295467i	$-0.904525\pi$
$887$	−19378.5	−	33564.5i	−0.733558	−	1.27056i	0.221794	−	0.975093i	$-0.428809\pi$
$888$	−1932.00	+	3346.32i	−0.0730109	+	0.126459i
$889$		−	50504.9i		−	1.90538i
$890$	−12744.0	−	7357.75i	−0.479977	−	0.277115i
$891$	16360.5	+	9445.74i	0.615149	+	0.355156i
$892$		−	16385.2i		−	0.615042i
$893$	15147.0	−	26235.4i	0.567609	−	0.983128i
$894$	−15813.0	−	27388.9i	−0.591573	−	1.02463i
$895$	−15444.0	+	8916.60i	−0.576800	+	0.333016i
$896$	34944.0			1.30290
$897$		0			0
$898$	1026.00			0.0381270
$899$	4347.00	−	2509.74i	0.161269	−	0.0931085i
$900$	−2948.00	−	5106.09i	−0.109185	−	0.189114i
$901$	−5751.00	+	9961.02i	−0.212645	+	0.368313i
$902$		−	30667.7i		−	1.13206i
$903$	−11602.5	−	6698.71i	−0.427583	−	0.246865i
$904$	−4932.00	−	2847.49i	−0.181456	−	0.104763i
$905$			27.7128i			0.00101791i
$906$	1050.00	−	1818.65i	0.0385032	−	0.0666895i
$907$	19535.5	+	33836.5i	0.715177	+	1.23872i	0.962891	+	0.269890i	$0.0869873\pi$
$907$	19535.5	+	33836.5i	0.715177	+	1.23872i	−0.247714	+	0.968833i	$0.579679\pi$
$908$	−1518.00	+	876.418i	−0.0554808	+	0.0320319i
$909$	43098.0			1.57257
$910$		0			0
$911$	−53040.0			−1.92897			−0.964486	−	0.264134i	$-0.914914\pi$
$911$	−53040.0			−1.92897			−0.964486	+	0.264134i	$0.914914\pi$
$912$	−42840.0	+	24733.7i	−1.55545	+	0.898042i
$913$	−4797.00	−	8308.65i	−0.173886	−	0.301179i
$914$	−1059.00	+	1834.24i	−0.0383245	+	0.0663800i
$915$			1648.91i			0.0595753i
$916$	624.000	+	360.267i	0.0225082	+	0.0129951i
$917$	7254.00	+	4188.10i	0.261230	+	0.150821i
$918$			3273.58i			0.117695i
$919$	−183.500	+	317.831i	−0.00658662	+	0.0114084i	−0.869300	−	0.494285i	$-0.835430\pi$
$919$	−183.500	+	317.831i	−0.00658662	+	0.0114084i	0.862713	+	0.505693i	$0.168763\pi$
$920$	5472.00	+	9477.78i	0.196094	+	0.339645i
$921$	28959.0	−	16719.5i	1.03608	−	0.598182i
$922$	45474.0			1.62430
$923$		0			0
$924$	−14196.0			−0.505427
$925$	−2311.50	+	1334.55i	−0.0821639	+	0.0474374i
$926$	−1446.00	−	2504.55i	−0.0513159	−	0.0888817i
$927$	−20416.0	+	35361.5i	−0.723354	+	1.25289i
$928$			11473.1i			0.405844i
$929$	25924.5	+	14967.5i	0.915560	+	0.528599i	0.882216	−	0.470845i	$-0.156051\pi$
$929$	25924.5	+	14967.5i	0.915560	+	0.528599i	0.0333441	+	0.999444i	$0.489384\pi$
$930$	21168.0	+	12221.4i	0.746372	+	0.430918i
$931$			14486.9i			0.509976i
$932$	−11556.0	+	20015.6i	−0.406147	+	0.703468i
$933$	21672.0	+	37537.0i	0.760460	+	1.31716i
$934$	43488.0	−	25107.8i	1.52352	−	0.879607i
$935$	−8424.00			−0.294646
$936$		0			0
$937$	42166.0			1.47012			0.735060	−	0.678002i	$-0.237154\pi$
$937$	42166.0			1.47012			0.735060	+	0.678002i	$0.237154\pi$
$938$	11115.0	−	6417.25i	0.386906	−	0.223380i
$939$	−2695.00	−	4667.88i	−0.0936613	−	0.162226i
$940$	9504.00	−	16461.4i	0.329773	−	0.571183i
$941$		−	35022.1i		−	1.21327i	−0.794981	−	0.606635i	$-0.792519\pi$
$941$		−	35022.1i		−	1.21327i	0.794981	−	0.606635i	$-0.207481\pi$
$942$	−32214.0	−	18598.8i	−1.11421	−	0.643291i
$943$	−19408.5	−	11205.5i	−0.670231	−	0.386958i
$944$			1524.20i			0.0525515i
$945$	5460.00	−	9457.00i	0.187951	−	0.325541i
$946$	−3315.00	−	5741.75i	−0.113932	−	0.197337i
$947$	2251.50	−	1299.90i	0.0772586	−	0.0446053i	−0.460873	−	0.887466i	$-0.652464\pi$
$947$	2251.50	−	1299.90i	0.0772586	−	0.0446053i	0.538132	+	0.842861i	$0.319130\pi$
$948$	−34832.0			−1.19334
$949$		0			0
$950$	−20502.0			−0.700182
$951$	−48846.0	+	28201.3i	−1.66555	+	0.961607i
$952$	4212.00	+	7295.40i	0.143395	+	0.248367i
$953$	−5311.50	+	9199.79i	−0.180542	+	0.312708i	−0.942065	−	0.335430i	$-0.891118\pi$
$953$	−5311.50	+	9199.79i	−0.180542	+	0.312708i	0.761523	+	0.648137i	$0.224452\pi$
$954$			32465.6i			1.10179i
$955$	34092.0	+	19683.0i	1.15517	+	0.666940i
$956$	−6444.00	−	3720.45i	−0.218006	−	0.125866i
$957$			10875.5i			0.367353i
$958$	15411.0	−	26692.6i	0.519736	−	0.900209i
$959$	−13396.5	−	23203.4i	−0.451090	−	0.781311i
$960$	5376.00	−	3103.84i	0.180739	−	0.104350i
$961$	24499.0			0.822362
$962$		0			0
$963$	−5610.00			−0.187726
$964$	−7134.00	+	4118.82i	−0.238351	+	0.137612i
$965$	29412.0	+	50943.1i	0.981146	+	1.69939i
$966$	−15561.0	+	26952.4i	−0.518289	+	0.897703i
$967$			20199.2i			0.671729i	0.941910	+	0.335864i	$0.109028\pi$
$967$			20199.2i			0.671729i	−0.941910	+	0.335864i	$0.890972\pi$
$968$	−9888.00	−	5708.84i	−0.328319	−	0.189555i
$969$	−14458.5	−	8347.62i	−0.479333	−	0.276743i
$970$		−	59277.7i		−	1.96216i
$971$	1162.50	−	2013.51i	0.0384206	−	0.0665464i	−0.846176	−	0.532904i	$-0.821101\pi$
$971$	1162.50	−	2013.51i	0.0384206	−	0.0665464i	0.884596	+	0.466358i	$0.154434\pi$
$972$	9856.00	+	17071.1i	0.325238	+	0.563329i
$973$	−49627.5	+	28652.5i	−1.63513	+	0.944045i
$974$	−16470.0			−0.541820
$975$		0			0
$976$	1360.00			0.0446030
$977$	−28525.5	+	16469.2i	−0.934096	+	0.539300i	−0.888105	−	0.459641i	$-0.847978\pi$
$977$	−28525.5	+	16469.2i	−0.934096	+	0.539300i	−0.0459912	+	0.998942i	$0.514645\pi$
$978$	19803.0	+	34299.8i	0.647475	+	1.12146i
$979$	−3451.50	+	5978.17i	−0.112677	+	0.195162i
$980$			9089.80i			0.296289i
$981$	11616.0	+	6706.50i	0.378053	+	0.218269i
$982$	4905.00	+	2831.90i	0.159394	+	0.0920261i
$983$			42702.0i			1.38554i	0.721161	+	0.692768i	$0.243609\pi$
$983$			42702.0i			1.38554i	−0.721161	+	0.692768i	$0.756391\pi$
$984$	−19068.0	+	33026.7i	−0.617750	+	1.06997i
$985$	−19068.0	−	33026.7i	−0.616809	−	1.06834i
$986$	−5589.00	+	3226.81i	−0.180517	+	0.104222i
$987$	−54054.0			−1.74322
$988$		0			0
$989$	−4845.00			−0.155776
$990$	−20592.0	+	11888.8i	−0.661067	+	0.381667i
$991$	2421.50	+	4194.16i	0.0776201	+	0.134442i	0.902223	−	0.431271i	$-0.141935\pi$
$991$	2421.50	+	4194.16i	0.0776201	+	0.134442i	−0.824603	+	0.565712i	$0.808601\pi$
$992$	6048.00	−	10475.4i	0.193573	−	0.335278i
$993$			36942.9i			1.18061i
$994$	39429.0	+	22764.3i	1.25816	+	0.726400i
$995$	20220.0	+	11674.0i	0.644238	+	0.371951i
$996$		−	11930.4i		−	0.379546i
$997$	−5471.50	+	9476.92i	−0.173806	+	0.301040i	−0.939747	−	0.341870i	$-0.888940\pi$
$997$	−5471.50	+	9476.92i	−0.173806	+	0.301040i	0.765942	+	0.642910i	$0.222273\pi$
$998$	−25002.0	−	43304.7i	−0.793011	−	1.37353i
$999$	1207.50	−	697.150i	0.0382419	−	0.0220789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.4.e.b.23.1		2
13.2	odd	12		169.4.a.h.1.2		2
13.3	even	3		169.4.b.b.168.2		2
13.4	even	6	inner	169.4.e.b.147.1		2
13.5	odd	4		169.4.c.i.146.1		4
13.6	odd	12		169.4.c.i.22.1		4
13.7	odd	12		169.4.c.i.22.2		4
13.8	odd	4		169.4.c.i.146.2		4
13.9	even	3		13.4.e.a.4.1	✓	2
13.10	even	6		169.4.b.b.168.1		2
13.11	odd	12		169.4.a.h.1.1		2
13.12	even	2		13.4.e.a.10.1	yes	2
39.2	even	12		1521.4.a.q.1.1		2
39.11	even	12		1521.4.a.q.1.2		2
39.35	odd	6		117.4.q.c.82.1		2
39.38	odd	2		117.4.q.c.10.1		2
52.35	odd	6		208.4.w.a.17.1		2
52.51	odd	2		208.4.w.a.49.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.e.a.4.1	✓	2	13.9	even	3
13.4.e.a.10.1	yes	2	13.12	even	2
117.4.q.c.10.1		2	39.38	odd	2
117.4.q.c.82.1		2	39.35	odd	6
169.4.a.h.1.1		2	13.11	odd	12
169.4.a.h.1.2		2	13.2	odd	12
169.4.b.b.168.1		2	13.10	even	6
169.4.b.b.168.2		2	13.3	even	3
169.4.c.i.22.1		4	13.6	odd	12
169.4.c.i.22.2		4	13.7	odd	12
169.4.c.i.146.1		4	13.5	odd	4
169.4.c.i.146.2		4	13.8	odd	4
169.4.e.b.23.1		2	1.1	even	1	trivial
169.4.e.b.147.1		2	13.4	even	6	inner
208.4.w.a.17.1		2	52.35	odd	6
208.4.w.a.49.1		2	52.51	odd	2
1521.4.a.q.1.1		2	39.2	even	12
1521.4.a.q.1.2		2	39.11	even	12

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	169.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.00000 - 1.73205i) q^{2} +(3.50000 + 6.06218i) q^{3} +(2.00000 - 3.46410i) q^{4} +13.8564i q^{5} +(21.0000 + 12.1244i) q^{6} +(-19.5000 - 11.2583i) q^{7} +13.8564i q^{8} +(-11.0000 + 19.0526i) q^{9} +(24.0000 + 41.5692i) q^{10} +(19.5000 - 11.2583i) q^{11} +28.0000 q^{12} -78.0000 q^{14} +(-84.0000 + 48.4974i) q^{15} +(40.0000 + 69.2820i) q^{16} +(-13.5000 + 23.3827i) q^{17} +76.2102i q^{18} +(76.5000 + 44.1673i) q^{19} +(48.0000 + 27.7128i) q^{20} -157.617i q^{21} +(39.0000 - 67.5500i) q^{22} +(-28.5000 - 49.3634i) q^{23} +(-84.0000 + 48.4974i) q^{24} -67.0000 q^{25} +35.0000 q^{27} +(-78.0000 + 45.0333i) q^{28} +(34.5000 + 59.7558i) q^{29} +(-168.000 + 290.985i) q^{30} -72.7461i q^{31} +(144.000 + 83.1384i) q^{32} +(136.500 + 78.8083i) q^{33} +93.5307i q^{34} +(156.000 - 270.200i) q^{35} +(44.0000 + 76.2102i) q^{36} +(34.5000 - 19.9186i) q^{37} +306.000 q^{38} -192.000 q^{40} +(340.500 - 196.588i) q^{41} +(-273.000 - 472.850i) q^{42} +(42.5000 - 73.6122i) q^{43} -90.0666i q^{44} +(-264.000 - 152.420i) q^{45} +(-171.000 - 98.7269i) q^{46} -342.946i q^{47} +(-280.000 + 484.974i) q^{48} +(82.0000 + 142.028i) q^{49} +(-201.000 + 116.047i) q^{50} -189.000 q^{51} +426.000 q^{53} +(105.000 - 60.6218i) q^{54} +(156.000 + 270.200i) q^{55} +(156.000 - 270.200i) q^{56} +618.342i q^{57} +(207.000 + 119.512i) q^{58} +(16.5000 + 9.52628i) q^{59} +387.979i q^{60} +(8.50000 - 14.7224i) q^{61} +(-126.000 - 218.238i) q^{62} +(429.000 - 247.683i) q^{63} -64.0000 q^{64} +546.000 q^{66} +(-142.500 + 82.2724i) q^{67} +(54.0000 + 93.5307i) q^{68} +(199.500 - 345.544i) q^{69} -1080.80i q^{70} +(-505.500 - 291.851i) q^{71} +(-264.000 - 152.420i) q^{72} +1004.59i q^{73} +(69.0000 - 119.512i) q^{74} +(-234.500 - 406.166i) q^{75} +(306.000 - 176.669i) q^{76} -507.000 q^{77} -1244.00 q^{79} +(-960.000 + 554.256i) q^{80} +(419.500 + 726.595i) q^{81} +(681.000 - 1179.53i) q^{82} -426.084i q^{83} +(-546.000 - 315.233i) q^{84} +(-324.000 - 187.061i) q^{85} -294.449i q^{86} +(-241.500 + 418.290i) q^{87} +(156.000 + 270.200i) q^{88} +(-265.500 + 153.286i) q^{89} -1056.00 q^{90} -228.000 q^{92} +(441.000 - 254.611i) q^{93} +(-594.000 - 1028.84i) q^{94} +(-612.000 + 1060.02i) q^{95} +1163.94i q^{96} +(-1069.50 - 617.476i) q^{97} +(492.000 + 284.056i) q^{98} +495.367i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{2} + 7 q^{3} + 4 q^{4} + 42 q^{6} - 39 q^{7} - 22 q^{9} + 48 q^{10} + 39 q^{11} + 56 q^{12} - 156 q^{14} - 168 q^{15} + 80 q^{16} - 27 q^{17} + 153 q^{19} + 96 q^{20} + 78 q^{22} - 57 q^{23}+ \cdots + 984 q^{98}+O(q^{100}) \) 2 * q + 6 * q^2 + 7 * q^3 + 4 * q^4 + 42 * q^6 - 39 * q^7 - 22 * q^9 + 48 * q^10 + 39 * q^11 + 56 * q^12 - 156 * q^14 - 168 * q^15 + 80 * q^16 - 27 * q^17 + 153 * q^19 + 96 * q^20 + 78 * q^22 - 57 * q^23 - 168 * q^24 - 134 * q^25 + 70 * q^27 - 156 * q^28 + 69 * q^29 - 336 * q^30 + 288 * q^32 + 273 * q^33 + 312 * q^35 + 88 * q^36 + 69 * q^37 + 612 * q^38 - 384 * q^40 + 681 * q^41 - 546 * q^42 + 85 * q^43 - 528 * q^45 - 342 * q^46 - 560 * q^48 + 164 * q^49 - 402 * q^50 - 378 * q^51 + 852 * q^53 + 210 * q^54 + 312 * q^55 + 312 * q^56 + 414 * q^58 + 33 * q^59 + 17 * q^61 - 252 * q^62 + 858 * q^63 - 128 * q^64 + 1092 * q^66 - 285 * q^67 + 108 * q^68 + 399 * q^69 - 1011 * q^71 - 528 * q^72 + 138 * q^74 - 469 * q^75 + 612 * q^76 - 1014 * q^77 - 2488 * q^79 - 1920 * q^80 + 839 * q^81 + 1362 * q^82 - 1092 * q^84 - 648 * q^85 - 483 * q^87 + 312 * q^88 - 531 * q^89 - 2112 * q^90 - 456 * q^92 + 882 * q^93 - 1188 * q^94 - 1224 * q^95 - 2139 * q^97 + 984 * q^98

Introduction

L-functions

Modular forms

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