LMFDB - Embedded newform 177.4.e.b.4.6

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.e (of order $29$, degree $28$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$420$
Relative dimension:	$15$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			4.6
Character	$\chi$	$=$	177.4
Dual form			177.4.e.b.133.6

$q$-expansion

$f(q)$	$=$	$q+(-1.68795 - 0.183576i) q^{2} +(1.94216 - 2.28649i) q^{3} +(-4.99749 - 1.10003i) q^{4} +(3.49616 + 2.65771i) q^{5} +(-3.69801 + 3.50294i) q^{6} +(0.0781424 - 0.196123i) q^{7} +(21.1058 + 7.11136i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})$	\(q+(-1.68795 - 0.183576i) q^{2} +(1.94216 - 2.28649i) q^{3} +(-4.99749 - 1.10003i) q^{4} +(3.49616 + 2.65771i) q^{5} +(-3.69801 + 3.50294i) q^{6} +(0.0781424 - 0.196123i) q^{7} +(21.1058 + 7.11136i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(-5.41345 - 5.12789i) q^{10} +(21.6921 - 10.0358i) q^{11} +(-12.2211 + 9.29026i) q^{12} +(0.213949 - 1.30503i) q^{13} +(-0.167904 + 0.316700i) q^{14} +(12.8669 - 2.83222i) q^{15} +(2.83344 + 1.31089i) q^{16} +(-48.2163 - 121.014i) q^{17} +(0.827303 + 15.2587i) q^{18} +(-10.2176 - 15.0698i) q^{19} +(-14.5485 - 17.1278i) q^{20} +(-0.296667 - 0.559573i) q^{21} +(-38.4576 + 12.9579i) q^{22} +(-2.72912 + 50.3356i) q^{23} +(57.2508 - 34.4466i) q^{24} +(-28.2813 - 101.860i) q^{25} +(-0.600708 + 2.16355i) q^{26} +(-23.1351 - 13.9200i) q^{27} +(-0.606257 + 0.894163i) q^{28} +(-294.685 + 32.0489i) q^{29} +(-22.2386 + 2.41860i) q^{30} +(86.2936 - 127.273i) q^{31} +(-157.211 - 94.5906i) q^{32} +(19.1827 - 69.0900i) q^{33} +(59.1715 + 213.117i) q^{34} +(0.794436 - 0.477996i) q^{35} +(-2.49332 + 45.9866i) q^{36} +(358.654 - 120.845i) q^{37} +(14.4803 + 27.3127i) q^{38} +(-2.56842 - 3.02377i) q^{39} +(54.8891 + 80.9554i) q^{40} +(-23.3284 - 430.267i) q^{41} +(0.398035 + 0.998992i) q^{42} +(-394.172 - 182.363i) q^{43} +(-119.446 + 26.2920i) q^{44} +(18.5137 - 34.9206i) q^{45} +(13.8470 - 84.4630i) q^{46} +(278.874 - 211.995i) q^{47} +(8.50032 - 3.93267i) q^{48} +(248.984 + 235.850i) q^{49} +(29.0384 + 177.127i) q^{50} +(-370.340 - 124.782i) q^{51} +(-2.50479 + 6.28654i) q^{52} +(-298.990 + 283.219i) q^{53} +(36.4956 + 27.7432i) q^{54} +(102.511 + 22.5645i) q^{55} +(3.04395 - 3.58362i) q^{56} +(-54.3010 - 5.90559i) q^{57} +503.297 q^{58} +(-274.031 - 360.952i) q^{59} -67.4178 q^{60} +(404.753 + 44.0195i) q^{61} +(-169.024 + 198.990i) q^{62} +(-1.85563 - 0.408455i) q^{63} +(228.116 + 173.409i) q^{64} +(4.21640 - 3.99399i) q^{65} +(-45.0627 + 113.099i) q^{66} +(452.704 + 152.534i) q^{67} +(107.842 + 657.805i) q^{68} +(109.791 + 104.000i) q^{69} +(-1.42872 + 0.660994i) q^{70} +(107.998 - 82.0977i) q^{71} +(32.4283 - 197.804i) q^{72} +(-256.061 + 482.982i) q^{73} +(-627.575 + 138.140i) q^{74} +(-287.829 - 133.164i) q^{75} +(34.4850 + 86.5508i) q^{76} +(-0.273182 - 5.03855i) q^{77} +(3.78027 + 5.57548i) q^{78} +(582.663 + 685.964i) q^{79} +(6.42219 + 12.1135i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(-39.6093 + 730.551i) q^{82} +(-343.843 + 206.884i) q^{83} +(0.867042 + 3.12280i) q^{84} +(153.048 - 551.228i) q^{85} +(631.865 + 380.181i) q^{86} +(-499.046 + 736.037i) q^{87} +(529.197 - 57.5537i) q^{88} +(941.349 - 102.378i) q^{89} +(-37.6609 + 55.5456i) q^{90} +(-0.239228 - 0.143939i) q^{91} +(69.0095 - 248.550i) q^{92} +(-123.413 - 444.494i) q^{93} +(-509.643 + 306.642i) q^{94} +(4.32889 - 79.8417i) q^{95} +(-521.608 + 175.750i) q^{96} +(523.064 + 986.603i) q^{97} +(-376.976 - 443.811i) q^{98} +(-120.717 - 178.045i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420q + 2q^{2} - 45q^{3} - 56q^{4} - 14q^{5} + 6q^{6} + 6q^{7} + 66q^{8} - 135q^{9} + O(q^{10}) $	\( 420q + 2q^{2} - 45q^{3} - 56q^{4} - 14q^{5} + 6q^{6} + 6q^{7} + 66q^{8} - 135q^{9} - 754q^{10} + 64q^{11} - 168q^{12} + 90q^{13} + 1024q^{14} - 42q^{15} - 172q^{16} + 96q^{17} + 18q^{18} + 16q^{19} - 178q^{20} - 243q^{21} - 604q^{22} + 48q^{23} + 198q^{24} - 173q^{25} + 156q^{26} - 405q^{27} + 84q^{28} - 50q^{29} + 174q^{30} + 222q^{31} - 45q^{32} + 192q^{33} - 64q^{34} - 132q^{35} - 504q^{36} + 30q^{37} - 108q^{38} + 270q^{39} + 6984q^{40} + 400q^{41} + 114q^{42} + 1220q^{43} + 1180q^{44} - 126q^{45} + 4938q^{46} + 370q^{47} - 516q^{48} + 771q^{49} + 1048q^{50} + 288q^{51} - 1964q^{52} - 822q^{53} + 54q^{54} - 2342q^{55} - 13824q^{56} + 48q^{57} - 13150q^{58} - 3423q^{59} - 534q^{60} - 2182q^{61} + 845q^{62} + 54q^{63} - 8018q^{64} + 4140q^{65} - 1812q^{66} + 506q^{67} + 4826q^{68} - 3684q^{69} + 6882q^{70} + 5874q^{71} + 594q^{72} + 206q^{73} + 11124q^{74} - 867q^{75} + 16940q^{76} + 9940q^{77} + 468q^{78} - 1762q^{79} - 28954q^{80} - 1215q^{81} + 3770q^{82} - 1216q^{83} - 8013q^{84} - 420q^{85} - 2256q^{86} + 5940q^{87} + 13458q^{88} - 1580q^{89} + 522q^{90} - 12204q^{91} + 4562q^{92} + 666q^{93} + 176q^{94} - 28456q^{95} + 2040q^{96} + 2574q^{97} + 50690q^{98} + 576q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{1}{29}\right)$	$1$

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 $

$2$	−1.68795	−	0.183576i	−0.596780	−	0.0649038i	−0.195256	−	0.980752i	$-0.562554\pi$
$2$	−1.68795	−	0.183576i	−0.596780	−	0.0649038i	−0.401524	+	0.915848i	$0.631519\pi$
$3$	1.94216	−	2.28649i	0.373769	−	0.440034i
$3$	1.94216	−	2.28649i	0.373769	−	0.440034i
$4$	−4.99749	−	1.10003i	−0.624686	−	0.137504i
$5$	3.49616	+	2.65771i	0.312706	+	0.237713i	0.749741	−	0.661732i	$-0.230178\pi$
$5$	3.49616	+	2.65771i	0.312706	+	0.237713i	−0.437035	+	0.899445i	$0.643971\pi$
$6$	−3.69801	+	3.50294i	−0.251618	+	0.238345i
$7$	0.0781424	−	0.196123i	0.00421930	−	0.0105896i	−0.926852	−	0.375427i	$-0.877496\pi$
$7$	0.0781424	−	0.196123i	0.00421930	−	0.0105896i	0.931071	+	0.364837i	$0.118875\pi$
$8$	21.1058	+	7.11136i	0.932752	+	0.314281i
$9$	−1.45604	−	8.88144i	−0.0539273	−	0.328942i
$10$	−5.41345	−	5.12789i	−0.171188	−	0.162158i
$11$	21.6921	−	10.0358i	0.594584	−	0.275084i	−0.0994310	−	0.995044i	$-0.531702\pi$
$11$	21.6921	−	10.0358i	0.594584	−	0.275084i	0.694015	+	0.719961i	$0.255840\pi$
$12$	−12.2211	+	9.29026i	−0.293995	+	0.223489i
$13$	0.213949	−	1.30503i	0.00456453	−	0.0278424i	−0.984446	−	0.175687i	$-0.943785\pi$
$13$	0.213949	−	1.30503i	0.00456453	−	0.0278424i	0.989011	+	0.147845i	$0.0472336\pi$
$14$	−0.167904	+	0.316700i	−0.00320530	+	0.00604584i
$15$	12.8669	−	2.83222i	0.221481	−	0.0487518i
$16$	2.83344	+	1.31089i	0.0442725	+	0.0204826i
$17$	−48.2163	−	121.014i	−0.687893	−	1.72648i	−0.687187	−	0.726481i	$-0.741155\pi$
$17$	−48.2163	−	121.014i	−0.687893	−	1.72648i	−0.000705979	−	1.00000i	$-0.500225\pi$
$18$	0.827303	+	15.2587i	0.0108332	+	0.199806i
$19$	−10.2176	−	15.0698i	−0.123372	−	0.181960i	0.760987	−	0.648767i	$-0.224715\pi$
$19$	−10.2176	−	15.0698i	−0.123372	−	0.181960i	−0.884360	+	0.466806i	$0.845405\pi$
$20$	−14.5485	−	17.1278i	−0.162657	−	0.191494i
$21$	−0.296667	−	0.559573i	−0.00308276	−	0.00581471i
$22$	−38.4576	+	12.9579i	−0.372690	+	0.125574i
$23$	−2.72912	+	50.3356i	−0.0247418	+	0.456335i	0.959745	+	0.280874i	$0.0906243\pi$
$23$	−2.72912	+	50.3356i	−0.0247418	+	0.456335i	−0.984486	+	0.175461i	$0.943858\pi$
$24$	57.2508	−	34.4466i	0.486928	−	0.292975i
$25$	−28.2813	−	101.860i	−0.226251	−	0.814882i
$26$	−0.600708	+	2.16355i	−0.00453110	+	0.0163195i
$27$	−23.1351	−	13.9200i	−0.164902	−	0.0992184i
$28$	−0.606257	+	0.894163i	−0.00409185	+	0.00603503i
$29$	−294.685	+	32.0489i	−1.88695	+	0.205218i	−0.977551	−	0.210700i	$-0.932426\pi$
$29$	−294.685	+	32.0489i	−1.88695	+	0.205218i	−0.909402	+	0.415918i	$0.863460\pi$
$30$	−22.2386	+	2.41860i	−0.135340	+	0.0147191i
$31$	86.2936	−	127.273i	0.499961	−	0.737387i	−0.491056	−	0.871128i	$-0.663389\pi$
$31$	86.2936	−	127.273i	0.499961	−	0.737387i	0.991016	+	0.133741i	$0.0426991\pi$
$32$	−157.211	−	94.5906i	−0.868475	−	0.522544i
$33$	19.1827	−	69.0900i	0.101190	−	0.364455i
$34$	59.1715	+	213.117i	0.298466	+	1.07498i
$35$	0.794436	−	0.477996i	0.00383669	−	0.00230846i
$36$	−2.49332	+	45.9866i	−0.0115432	+	0.212901i
$37$	358.654	−	120.845i	1.59358	−	0.536939i	0.623938	−	0.781474i	$-0.285532\pi$
$37$	358.654	−	120.845i	1.59358	−	0.536939i	0.969641	+	0.244534i	$0.0786350\pi$
$38$	14.4803	+	27.3127i	0.0618162	+	0.116598i
$39$	−2.56842	−	3.02377i	−0.0105455	−	0.0124152i
$40$	54.8891	+	80.9554i	0.216968	+	0.320004i
$41$	−23.3284	−	430.267i	−0.0888605	−	1.63894i	−0.614993	−	0.788533i	$-0.710841\pi$
$41$	−23.3284	−	430.267i	−0.0888605	−	1.63894i	0.526132	−	0.850403i	$-0.323642\pi$
$42$	0.398035	+	0.998992i	0.00146234	+	0.00367019i
$43$	−394.172	−	182.363i	−1.39792	−	0.646748i	−0.431126	−	0.902292i	$-0.641883\pi$
$43$	−394.172	−	182.363i	−1.39792	−	0.646748i	−0.966797	+	0.255544i	$0.917745\pi$
$44$	−119.446	+	26.2920i	−0.409254	+	0.0900835i
$45$	18.5137	−	34.9206i	0.0613304	−	0.115681i
$46$	13.8470	−	84.4630i	0.0443832	−	0.270726i
$47$	278.874	−	211.995i	0.865489	−	0.657928i	−0.0752105	−	0.997168i	$-0.523963\pi$
$47$	278.874	−	211.995i	0.865489	−	0.657928i	0.940700	+	0.339240i	$0.110170\pi$
$48$	8.50032	−	3.93267i	0.0255607	−	0.0118257i
$49$	248.984	+	235.850i	0.725901	+	0.687610i
$50$	29.0384	+	177.127i	0.0821331	+	0.500990i
$51$	−370.340	−	124.782i	−1.01682	−	0.342608i
$52$	−2.50479	+	6.28654i	−0.00667984	+	0.0167651i
$53$	−298.990	+	283.219i	−0.774896	+	0.734020i	−0.969027	−	0.246956i	$-0.920570\pi$
$53$	−298.990	+	283.219i	−0.774896	+	0.734020i	0.194131	+	0.980976i	$0.437811\pi$
$54$	36.4956	+	27.7432i	0.0919708	+	0.0699144i
$55$	102.511	+	22.5645i	0.251321	+	0.0553199i
$56$	3.04395	−	3.58362i	0.00726367	−	0.00855145i
$57$	−54.3010	−	5.90559i	−0.126182	−	0.0137231i
$58$	503.297			1.13942
$59$	−274.031	−	360.952i	−0.604674	−	0.796473i
$59$	−274.031	−	360.952i	−0.604674	−	0.796473i
$60$	−67.4178			−0.145060
$61$	404.753	+	44.0195i	0.849561	+	0.0923954i	0.522533	−	0.852619i	$-0.324987\pi$
$61$	404.753	+	44.0195i	0.849561	+	0.0923954i	0.327029	+	0.945014i	$0.393953\pi$
$62$	−169.024	+	198.990i	−0.346226	+	0.407609i
$63$	−1.85563	−	0.408455i	−0.00371091	−	0.000816834i
$64$	228.116	+	173.409i	0.445539	+	0.338690i
$65$	4.21640	−	3.99399i	0.00804585	−	0.00762143i
$66$	−45.0627	+	113.099i	−0.0840430	+	0.210932i
$67$	452.704	+	152.534i	0.825471	+	0.278133i	0.700162	−	0.713984i	$-0.253111\pi$
$67$	452.704	+	152.534i	0.825471	+	0.278133i	0.125309	+	0.992118i	$0.460008\pi$
$68$	107.842	+	657.805i	0.192319	+	1.17310i
$69$	109.791	+	104.000i	0.191555	+	0.181451i
$70$	−1.42872	+	0.660994i	−0.00243949	+	0.00112863i
$71$	107.998	−	82.0977i	0.180521	−	0.137228i	−0.511012	−	0.859574i	$-0.670729\pi$
$71$	107.998	−	82.0977i	0.180521	−	0.137228i	0.691532	+	0.722346i	$0.256936\pi$
$72$	32.4283	−	197.804i	0.0530793	−	0.323770i
$73$	−256.061	+	482.982i	−0.410543	+	0.774366i	−0.999427	−	0.0338516i	$-0.989223\pi$
$73$	−256.061	+	482.982i	−0.410543	+	0.774366i	0.588884	+	0.808218i	$0.299567\pi$
$74$	−627.575	+	138.140i	−0.985866	+	0.217006i
$75$	−287.829	−	133.164i	−0.443141	−	0.205019i
$76$	34.4850	+	86.5508i	0.0520487	+	0.130632i
$77$	−0.273182	−	5.03855i	−0.000404311	−	0.00745709i
$78$	3.78027	+	5.57548i	0.00548758	+	0.00809357i
$79$	582.663	+	685.964i	0.829807	+	0.976924i	0.999964	−	0.00849274i	$-0.00270336\pi$
$79$	582.663	+	685.964i	0.829807	+	0.976924i	−0.170157	+	0.985417i	$0.554427\pi$
$80$	6.42219	+	12.1135i	0.00897528	+	0.0169292i
$81$	−76.7599	+	25.8634i	−0.105295	+	0.0354779i
$82$	−39.6093	+	730.551i	−0.0533429	+	0.983852i
$83$	−343.843	+	206.884i	−0.454720	+	0.273596i	−0.724433	−	0.689345i	$-0.757899\pi$
$83$	−343.843	+	206.884i	−0.454720	+	0.273596i	0.269714	+	0.962941i	$0.413071\pi$
$84$	0.867042	+	3.12280i	0.00112622	+	0.00405626i
$85$	153.048	−	551.228i	0.195298	−	0.703401i
$86$	631.865	+	380.181i	0.792277	+	0.476697i
$87$	−499.046	+	736.037i	−0.614981	+	0.907028i
$88$	529.197	−	57.5537i	0.641053	−	0.0697187i
$89$	941.349	−	102.378i	1.12116	−	0.121933i	0.471287	−	0.881980i	$-0.343790\pi$
$89$	941.349	−	102.378i	1.12116	−	0.121933i	0.649868	+	0.760047i	$0.274824\pi$
$90$	−37.6609	+	55.5456i	−0.0441089	+	0.0650558i
$91$	−0.239228	−	0.143939i	−0.000275582	−	0.000165812i
$92$	69.0095	−	248.550i	0.0782036	−	0.281664i
$93$	−123.413	−	444.494i	−0.137606	−	0.495612i
$94$	−509.643	+	306.642i	−0.559209	+	0.336465i
$95$	4.32889	−	79.8417i	0.00467510	−	0.0862272i
$96$	−521.608	+	175.750i	−0.554546	+	0.186848i
$97$	523.064	+	986.603i	0.547516	+	1.03273i	0.990670	+	0.136280i	$0.0435147\pi$
$97$	523.064	+	986.603i	0.547516	+	1.03273i	−0.443154	+	0.896445i	$0.646141\pi$
$98$	−376.976	−	443.811i	−0.388575	−	0.457466i
$99$	−120.717	−	178.045i	−0.122551	−	0.180749i
$100$	29.2864	+	540.156i	0.0292864	+	0.540156i
$101$	636.740	+	1598.10i	0.627307	+	1.57442i	0.806904	+	0.590682i	$0.201141\pi$
$101$	636.740	+	1598.10i	0.627307	+	1.57442i	−0.179597	+	0.983740i	$0.557479\pi$
$102$	602.209	+	278.611i	0.584584	+	0.270457i
$103$	−123.345	+	27.1503i	−0.117995	+	0.0259728i	−0.273576	−	0.961851i	$-0.588206\pi$
$103$	−123.345	+	27.1503i	−0.117995	+	0.0259728i	0.155580	+	0.987823i	$0.450275\pi$
$104$	13.7961	−	26.0222i	0.0130079	−	0.0245355i
$105$	0.449989	−	2.74481i	0.000418233	−	0.00255111i
$106$	556.672	−	423.171i	0.510083	−	0.387755i
$107$	−581.887	+	269.210i	−0.525730	+	0.243229i	−0.664757	−	0.747060i	$-0.731465\pi$
$107$	−581.887	+	269.210i	−0.525730	+	0.243229i	0.139026	+	0.990289i	$0.455603\pi$
$108$	100.305	+	95.0142i	0.0893693	+	0.0846551i
$109$	−294.224	−	1794.68i	−0.258546	−	1.57706i	−0.722608	−	0.691258i	$-0.757057\pi$
$109$	−294.224	−	1794.68i	−0.258546	−	1.57706i	0.464062	−	0.885803i	$-0.346391\pi$
$110$	−168.892	−	56.9063i	−0.146393	−	0.0493255i
$111$	420.254	−	1054.76i	0.359358	−	0.901921i
$112$	0.478507	−	0.453266i	0.000403702	−	0.000382407i
$113$	−910.437	−	692.096i	−0.757936	−	0.576168i	0.153238	−	0.988189i	$-0.451030\pi$
$113$	−910.437	−	692.096i	−0.757936	−	0.576168i	−0.911174	+	0.412022i	$0.864823\pi$
$114$	90.5733	+	19.9367i	0.0744120	+	0.0163793i
$115$	−143.319	+	168.728i	−0.116214	+	0.136817i
$116$	1507.94	+	163.998i	1.20697	+	0.131266i
$117$	−11.9021			−0.00940469
$118$	396.288	+	659.574i	0.309163	+	0.514565i
$119$	−27.5013			−0.0211852
$120$	291.707	+	31.7250i	0.221909	+	0.0241340i
$121$	−491.841	+	579.040i	−0.369527	+	0.435041i
$122$	−675.121	−	148.605i	−0.501005	−	0.110279i
$123$	−1029.11	−	782.306i	−0.754402	−	0.573481i
$124$	−571.256	+	541.122i	−0.413712	+	0.391889i
$125$	375.028	−	941.250i	0.268348	−	0.673504i
$126$	3.05723	+	1.03010i	0.00216158	+	0.000728322i
$127$	−411.833	−	2512.07i	−0.287750	−	1.75520i	−0.595147	−	0.803617i	$-0.702906\pi$
$127$	−411.833	−	2512.07i	−0.287750	−	1.75520i	0.307397	−	0.951581i	$-0.400542\pi$
$128$	712.394	+	674.815i	0.491932	+	0.465983i
$129$	−1182.52	+	547.090i	−0.807091	+	0.373400i
$130$	−7.85027	+	5.96762i	−0.00529626	+	0.00402612i
$131$	345.141	−	2105.27i	0.230192	−	1.40411i	−0.578407	−	0.815748i	$-0.696326\pi$
$131$	345.141	−	2105.27i	0.230192	−	1.40411i	0.808599	−	0.588360i	$-0.200226\pi$
$132$	−171.867	+	324.175i	−0.113326	+	0.213756i
$133$	−3.75396	+	0.826308i	−0.00244744	+	0.000538722i
$134$	−736.139	−	340.574i	−0.474573	−	0.219561i
$135$	−43.8889	−	110.153i	−0.0279804	−	0.0702255i
$136$	−157.069	−	2896.97i	−0.0990337	−	1.82657i
$137$	−564.382	−	832.402i	−0.351959	−	0.519101i	0.609961	−	0.792432i	$-0.291185\pi$
$137$	−564.382	−	832.402i	−0.351959	−	0.519101i	−0.961920	+	0.273330i	$0.911875\pi$
$138$	−166.230	−	195.702i	−0.102540	−	0.120719i
$139$	−185.631	−	350.136i	−0.113273	−	0.213656i	0.820393	−	0.571800i	$-0.193755\pi$
$139$	−185.631	−	350.136i	−0.113273	−	0.213656i	−0.933666	+	0.358144i	$0.883410\pi$
$140$	−4.49600	+	1.51488i	−0.00271415	+	0.000914503i
$141$	56.8952	−	1049.37i	0.0339818	−	0.626758i
$142$	−197.366	+	118.751i	−0.116638	+	0.0701786i
$143$	−8.45610	−	30.4561i	−0.00494500	−	0.0178103i
$144$	7.51698	−	27.0737i	0.00435011	−	0.0156677i
$145$	−1115.44	−	671.139i	−0.638844	−	0.384380i
$146$	520.881	−	768.242i	0.295263	−	0.435481i
$147$	1022.84	−	111.240i	0.573891	−	0.0624144i
$148$	−1925.31	+	209.390i	−1.06932	+	0.116295i
$149$	−36.5605	+	53.9228i	−0.0201017	+	0.0296478i	−0.837607	−	0.546273i	$-0.816046\pi$
$149$	−36.5605	+	53.9228i	−0.0201017	+	0.0296478i	0.817505	+	0.575921i	$0.195356\pi$
$150$	461.395	+	277.612i	0.251152	+	0.151113i
$151$	−237.972	+	857.099i	−0.128251	+	0.461919i	−0.999586	−	0.0287699i	$-0.990841\pi$
$151$	−237.972	+	857.099i	−0.128251	+	0.461919i	0.871335	+	0.490689i	$0.163255\pi$
$152$	−108.483	−	390.720i	−0.0578890	−	0.208497i
$153$	−1004.57	+	604.431i	−0.530816	+	0.319381i
$154$	−0.463837	+	8.55496i	−0.000242708	+	0.00447648i
$155$	639.952	−	215.625i	0.331627	−	0.111738i
$156$	9.50940	+	17.9366i	0.00488052	+	0.00920564i
$157$	1662.95	+	1957.78i	0.845338	+	0.995209i	0.999974	+	0.00723765i	$0.00230383\pi$
$157$	1662.95	+	1957.78i	0.845338	+	0.995209i	−0.154635	+	0.987972i	$0.549420\pi$
$158$	−857.580	−	1264.84i	−0.431806	−	0.636867i
$159$	66.8889	+	1233.69i	0.0333625	+	0.615334i
$160$	−298.239	−	748.524i	−0.147362	−	0.369850i
$161$	9.65870	+	4.46859i	0.00472803	+	0.00218742i
$162$	134.315	−	29.5649i	0.0651405	−	0.0143385i
$163$	503.273	−	949.273i	0.241836	−	0.456152i	−0.732648	−	0.680608i	$-0.761716\pi$
$163$	503.273	−	949.273i	0.241836	−	0.456152i	0.974484	+	0.224456i	$0.0720605\pi$
$164$	−356.723	+	2175.92i	−0.169850	+	1.03604i
$165$	250.687	−	190.567i	0.118278	−	0.0899130i
$166$	618.369	−	286.088i	0.289125	−	0.133764i
$167$	1056.89	+	1001.14i	0.489728	+	0.463895i	0.892267	−	0.451508i	$-0.149114\pi$
$167$	1056.89	+	1001.14i	0.489728	+	0.463895i	−0.402539	+	0.915403i	$0.631872\pi$
$168$	−2.28206	−	13.9199i	−0.00104800	−	0.00639253i
$169$	2080.34	+	700.947i	0.946899	+	0.319047i
$170$	−359.529	+	902.350i	−0.162204	+	0.407101i
$171$	−118.964	+	112.689i	−0.0532013	+	0.0503950i
$172$	1769.27	+	1344.96i	0.784333	+	0.596234i
$173$	486.205	+	107.022i	0.213673	+	0.0470330i	0.320517	−	0.947243i	$-0.396143\pi$
$173$	486.205	+	107.022i	0.213673	+	0.0470330i	−0.106844	+	0.994276i	$0.534074\pi$
$174$	977.482	−	1150.78i	0.425878	−	0.501382i
$175$	−22.1871	−	2.41299i	−0.00958392	−	0.00104231i
$176$	74.6192			0.0319582
$177$	−1357.52	−	74.4587i	−0.576484	−	0.0316195i
$178$	−1607.74			−0.676997
$179$	−1203.15	−	130.851i	−0.502391	−	0.0546383i	−0.146585	−	0.989198i	$-0.546828\pi$
$179$	−1203.15	−	130.851i	−0.502391	−	0.0546383i	−0.355806	+	0.934560i	$0.615794\pi$
$180$	−130.936	+	154.150i	−0.0542189	+	0.0638314i
$181$	−1781.34	−	392.102i	−0.731523	−	0.161020i	−0.166437	−	0.986052i	$-0.553226\pi$
$181$	−1781.34	−	392.102i	−0.731523	−	0.161020i	−0.565086	+	0.825032i	$0.691157\pi$
$182$	0.377382	+	0.286878i	0.000153700	+	0.000116840i
$183$	886.744	−	839.968i	0.358197	−	0.339302i
$184$	−415.555	+	1042.96i	−0.166495	+	0.417871i
$185$	1575.08	+	530.707i	0.625959	+	0.210910i
$186$	126.717	+	772.940i	0.0499535	+	0.304703i
$187$	−2260.39	−	2141.16i	−0.883937	−	0.837309i
$188$	−1626.87	+	752.671i	−0.631127	+	0.291990i
$189$	−4.53786	+	3.44959i	−0.00174646	+	0.00132762i
$190$	−21.9639	+	133.974i	−0.00838648	+	0.0511553i
$191$	−1718.23	+	3240.92i	−0.650925	+	1.22777i	0.309940	+	0.950756i	$0.399691\pi$
$191$	−1718.23	+	3240.92i	−0.650925	+	1.22777i	−0.960865	+	0.277018i	$0.910654\pi$
$192$	839.536	−	184.796i	0.315564	−	0.0694609i
$193$	1710.08	+	791.169i	0.637795	+	0.295075i	0.712013	−	0.702167i	$-0.247784\pi$
$193$	1710.08	+	791.169i	0.637795	+	0.295075i	−0.0742175	+	0.997242i	$0.523646\pi$
$194$	−701.789	−	1761.36i	−0.259719	−	0.651846i
$195$	−0.943276	−	17.3977i	−0.000346407	−	0.00638910i
$196$	−984.853	−	1452.55i	−0.358911	−	0.529355i
$197$	322.092	+	379.196i	0.116488	+	0.137140i	0.817315	−	0.576191i	$-0.195461\pi$
$197$	322.092	+	379.196i	0.116488	+	0.137140i	−0.700827	+	0.713331i	$0.747186\pi$
$198$	171.080	+	322.691i	0.0614047	+	0.115822i
$199$	−1102.61	+	371.512i	−0.392773	+	0.132341i	−0.508757	−	0.860910i	$-0.669895\pi$
$199$	−1102.61	+	371.512i	−0.392773	+	0.132341i	0.115983	+	0.993251i	$0.462998\pi$
$200$	127.465	−	2350.96i	0.0450657	−	0.831188i
$201$	1227.99	−	738.856i	0.430923	−	0.259278i
$202$	−781.414	−	2814.40i	−0.272179	−	0.980299i
$203$	−16.7419	+	60.2988i	−0.00578842	+	0.0208480i
$204$	1713.51	+	1030.98i	0.588086	+	0.353840i
$205$	1061.96	−	1566.28i	0.361809	−	0.533628i
$206$	213.184	−	23.1852i	0.0721031	−	0.00784168i
$207$	451.026	−	49.0521i	0.151442	−	0.0164703i
$208$	2.31697	−	3.41727i	0.000772369	−	0.00113916i
$209$	−372.879	−	224.354i	−0.123409	−	0.0742530i
$210$	−1.26344	+	4.55049i	−0.000415169	+	0.00149530i
$211$	1270.74	+	4576.78i	0.414602	+	1.49326i	0.816375	+	0.577523i	$0.195980\pi$
$211$	1270.74	+	4576.78i	0.414602	+	1.49326i	−0.401773	+	0.915740i	$0.631606\pi$
$212$	1805.75	−	1086.48i	0.584997	−	0.351981i
$213$	22.0334	−	406.382i	0.00708781	−	0.130727i
$214$	1031.62	−	347.592i	0.329532	−	0.111032i
$215$	−893.419	−	1685.17i	−0.283398	−	0.534546i
$216$	−389.295	−	458.313i	−0.122630	−	0.144372i
$217$	−18.2180	−	26.8696i	−0.00569917	−	0.00840565i
$218$	167.174	+	3083.35i	0.0519380	+	0.957939i
$219$	607.020	+	1523.51i	0.187300	+	0.470087i
$220$	−487.478	−	225.532i	−0.149390	−	0.0691152i
$221$	−168.243	+	37.0331i	−0.0512093	+	0.0112720i
$222$	−902.995	+	1703.23i	−0.272996	+	0.514925i
$223$	218.737	−	1334.23i	0.0656847	−	0.400659i	−0.933436	−	0.358743i	$-0.883206\pi$
$223$	218.737	−	1334.23i	0.0656847	−	0.400659i	0.999121	−	0.0419160i	$-0.0133462\pi$
$224$	−30.8362	+	23.4411i	−0.00919790	+	0.00699206i
$225$	−863.486	+	399.491i	−0.255848	+	0.118368i
$226$	1409.72	+	1335.36i	0.414926	+	0.393038i
$227$	−152.216	−	928.475i	−0.0445062	−	0.271476i	0.955193	−	0.295982i	$-0.0956469\pi$
$227$	−152.216	−	928.475i	−0.0445062	−	0.271476i	−0.999700	+	0.0245063i	$0.992199\pi$
$228$	264.873	+	89.2459i	0.0769369	+	0.0259231i
$229$	−1133.06	+	2843.76i	−0.326963	+	0.820614i	0.669973	+	0.742386i	$0.266306\pi$
$229$	−1133.06	+	2843.76i	−0.326963	+	0.820614i	−0.996935	+	0.0782288i	$0.975074\pi$
$230$	272.889	−	258.495i	0.0782339	−	0.0741071i
$231$	−12.0511	−	9.16103i	−0.00343249	−	0.00260931i
$232$	−6447.46	−	1419.19i	−1.82455	−	0.401615i
$233$	3314.23	−	3901.81i	0.931855	−	1.09706i	−0.0632260	−	0.997999i	$-0.520139\pi$
$233$	3314.23	−	3901.81i	0.931855	−	1.09706i	0.995081	−	0.0990652i	$-0.0315852\pi$
$234$	20.0901	+	2.18493i	0.00561253	+	0.000610400i
$235$	1538.41			0.427042
$236$	972.407	+	2105.30i	0.268213	+	0.580691i
$237$	2700.07			0.740036
$238$	46.4208	+	5.04857i	0.0126429	+	0.00137500i
$239$	−996.031	+	1172.62i	−0.269573	+	0.317366i	−0.880246	−	0.474517i	$-0.842623\pi$
$239$	−996.031	+	1172.62i	−0.269573	+	0.317366i	0.610674	+	0.791882i	$0.290899\pi$
$240$	40.1703	+	8.84216i	0.0108041	+	0.00237816i
$241$	−344.466	−	261.856i	−0.0920705	−	0.0699902i	0.558126	−	0.829756i	$-0.311520\pi$
$241$	−344.466	−	261.856i	−0.0920705	−	0.0699902i	−0.650197	+	0.759766i	$0.725314\pi$
$242$	936.500	−	887.100i	0.248762	−	0.235640i
$243$	−89.9436	+	225.741i	−0.0237444	+	0.0595939i
$244$	−1974.32	−	665.227i	−0.518005	−	0.174536i
$245$	243.666	+	1486.30i	0.0635398	+	0.387576i
$246$	1593.47	+	1509.41i	0.412991	+	0.391206i
$247$	−21.8526	+	10.1101i	−0.00562935	+	0.00260441i
$248$	2726.38	−	2072.54i	0.698086	−	0.530671i
$249$	−194.762	+	1187.99i	−0.0495684	+	0.302354i
$250$	−805.819	+	1519.94i	−0.203858	+	0.384517i
$251$	1066.68	−	234.793i	0.268239	−	0.0590438i	−0.0788142	−	0.996889i	$-0.525113\pi$
$251$	1066.68	−	234.793i	0.268239	−	0.0590438i	0.347053	+	0.937845i	$0.387182\pi$
$252$	8.82418	+	4.08250i	0.00220584	+	0.00102053i
$253$	445.960	+	1119.28i	0.110819	+	0.278135i
$254$	233.999	+	4315.85i	0.0578046	+	1.06614i
$255$	−963.133	−	1420.52i	−0.236524	−	0.348847i
$256$	−2562.65	−	3016.98i	−0.625646	−	0.736567i
$257$	1762.32	+	3324.09i	0.427745	+	0.806813i	0.999911	−	0.0133250i	$-0.00424160\pi$
$257$	1762.32	+	3324.09i	0.427745	+	0.806813i	−0.572166	+	0.820138i	$0.693897\pi$
$258$	2096.46	−	706.380i	0.505891	−	0.170455i
$259$	4.32573	−	79.7834i	0.00103779	−	0.0191409i
$260$	−25.4649	+	15.3217i	−0.00607411	+	0.00365467i
$261$	713.713	+	2570.56i	0.169263	+	0.609631i
$262$	−969.057	+	3490.23i	−0.228506	+	0.823004i
$263$	103.892	+	62.5100i	0.0243585	+	0.0146560i	0.527681	−	0.849443i	$-0.323062\pi$
$263$	103.892	+	62.5100i	0.0243585	+	0.0146560i	−0.503323	+	0.864099i	$0.667889\pi$
$264$	896.190	−	1321.78i	0.208927	−	0.308144i
$265$	−1798.03	+	195.548i	−0.416800	+	0.0453298i
$266$	6.48818	−	0.705632i	0.00149555	−	0.000162651i
$267$	1594.16	−	2351.22i	0.365398	−	0.538922i
$268$	−2094.59	−	1260.27i	−0.477416	−	0.287252i
$269$	−716.832	+	2581.80i	−0.162476	+	0.585185i	0.836813	+	0.547488i	$0.184416\pi$
$269$	−716.832	+	2581.80i	−0.162476	+	0.585185i	−0.999289	+	0.0376970i	$0.987998\pi$
$270$	53.8609	+	193.989i	0.0121403	+	0.0437253i
$271$	7170.56	−	4314.38i	1.60731	−	0.967085i	0.624818	−	0.780770i	$-0.285173\pi$
$271$	7170.56	−	4314.38i	1.60731	−	0.967085i	0.982490	−	0.186315i	$-0.0596546\pi$
$272$	22.0177	−	406.092i	0.00490815	−	0.0905255i
$273$	−0.793733	+	0.267440i	−0.000175967	+	5.92901e-5i
$274$	799.840	+	1508.66i	0.176351	+	0.332633i
$275$	−1635.74	−	1925.74i	−0.358686	−	0.422278i
$276$	−434.278	−	640.512i	−0.0947118	−	0.139689i
$277$	38.0340	+	701.496i	0.00824998	+	0.152162i	0.999756	+	0.0220994i	$0.00703503\pi$
$277$	38.0340	+	701.496i	0.00824998	+	0.152162i	−0.991506	+	0.130062i	$0.958482\pi$
$278$	249.059	+	625.090i	0.0537322	+	0.134858i
$279$	−1256.02	−	581.096i	−0.269519	−	0.124693i
$280$	20.1664	−	4.43895i	0.00430418	−	0.000947422i
$281$	−2919.75	+	5507.23i	−0.619850	+	1.16916i	0.352540	+	0.935797i	$0.385318\pi$
$281$	−2919.75	+	5507.23i	−0.619850	+	1.16916i	−0.972390	+	0.233364i	$0.925027\pi$
$282$	−288.675	+	1760.84i	−0.0609587	+	0.371831i
$283$	−3974.98	+	3021.70i	−0.834940	+	0.634705i	−0.932760	−	0.360499i	$-0.882606\pi$
$283$	−3974.98	+	3021.70i	−0.834940	+	0.634705i	0.0978194	+	0.995204i	$0.468813\pi$
$284$	−630.027	+	291.482i	−0.131638	+	0.0609023i
$285$	−174.150	−	164.963i	−0.0361955	−	0.0342862i
$286$	8.68247	+	52.9607i	0.00179512	+	0.0109498i
$287$	−86.2080	−	29.0469i	−0.0177307	−	0.00597415i
$288$	−611.195	+	1533.98i	−0.125052	+	0.313857i
$289$	−8752.72	+	8291.02i	−1.78154	+	1.68757i
$290$	1759.60	+	1337.62i	0.356302	+	0.270854i
$291$	3271.73	+	720.162i	0.659079	+	0.145074i
$292$	1810.96	−	2132.02i	0.362939	−	0.427285i
$293$	−5397.84	−	587.051i	−1.07626	−	0.117051i	−0.447223	−	0.894423i	$-0.647587\pi$
$293$	−5397.84	−	587.051i	−1.07626	−	0.117051i	−0.629041	+	0.777372i	$0.716552\pi$
$294$	−1746.91			−0.346538
$295$	1.25114	−	1990.24i	0.000246930	−	0.392801i
$296$	8429.04			1.65516
$297$	−641.549	−	69.7727i	−0.125342	−	0.0136317i
$298$	71.6113	−	84.3073i	0.0139206	−	0.0163886i
$299$	65.1058	+	14.3309i	0.0125925	+	0.00277182i
$300$	1291.94	+	982.105i	0.248633	+	0.189006i
$301$	−66.5672	+	63.0558i	−0.0127471	+	0.0120747i
$302$	559.028	−	1403.05i	0.106518	−	0.267340i
$303$	4890.68	+	1647.86i	0.927268	+	0.312433i
$304$	−9.19606	−	56.0935i	−0.00173497	−	0.0105828i
$305$	1298.09	+	1229.61i	0.243699	+	0.230844i
$306$	1806.63	−	835.834i	0.337510	−	0.156149i
$307$	7451.01	−	5664.11i	1.38518	−	1.05299i	0.394198	−	0.919026i	$-0.371022\pi$
$307$	7451.01	−	5664.11i	1.38518	−	1.05299i	0.990986	−	0.133964i	$-0.0427707\pi$
$308$	−4.17733	+	25.4806i	−0.000772810	+	0.00471393i
$309$	−177.477	+	334.756i	−0.0326741	+	0.0616299i
$310$	−1119.79	+	246.484i	−0.205161	+	0.0451593i
$311$	−1242.10	−	574.656i	−0.226472	−	0.104777i	0.303372	−	0.952872i	$-0.401888\pi$
$311$	−1242.10	−	574.656i	−0.226472	−	0.104777i	−0.529844	+	0.848095i	$0.677750\pi$
$312$	−32.7052	−	82.0840i	−0.00593452	−	0.0148945i
$313$	−142.113	−	2621.11i	−0.0256635	−	0.473336i	−0.982913	−	0.184072i	$-0.941072\pi$
$313$	−142.113	−	2621.11i	−0.0256635	−	0.473336i	0.957249	−	0.289264i	$-0.0934106\pi$
$314$	−2447.58	−	3609.91i	−0.439888	−	0.648787i
$315$	−5.40202	−	6.35975i	−0.000966252	−	0.00113756i
$316$	−2157.27	−	4069.05i	−0.384038	−	0.724373i
$317$	2888.41	−	973.219i	0.511764	−	0.172433i	−0.0515592	−	0.998670i	$-0.516419\pi$
$317$	2888.41	−	973.219i	0.511764	−	0.172433i	0.563323	+	0.826236i	$0.309523\pi$
$318$	113.571	−	2094.69i	0.0200275	−	0.369385i
$319$	−6070.71	+	3652.62i	−1.06550	+	0.641090i
$320$	336.658	+	1212.53i	0.0588118	+	0.211821i
$321$	−514.573	+	1853.32i	−0.0894725	+	0.322251i
$322$	−15.4831	−	9.31586i	−0.00267962	−	0.00161227i
$323$	−1331.00	+	1963.08i	−0.229284	+	0.338169i
$324$	412.057	−	44.8140i	0.0706546	−	0.00768415i
$325$	−138.982	+	15.1152i	−0.0237210	+	0.00257981i
$326$	−1023.76	+	1509.94i	−0.173929	+	0.256526i
$327$	−4674.95	−	2812.82i	−0.790597	−	0.475687i
$328$	2567.42	−	9247.00i	0.432201	−	1.55665i
$329$	−19.7851	−	71.2594i	−0.00331546	−	0.0119412i
$330$	−458.130	+	275.648i	−0.0764220	+	0.0459816i
$331$	−164.100	+	3026.64i	−0.0272499	+	0.502596i	0.952770	+	0.303694i	$0.0982201\pi$
$331$	−164.100	+	3026.64i	−0.0272499	+	0.502596i	−0.980020	+	0.198901i	$0.936263\pi$
$332$	1945.93	−	655.661i	0.321678	−	0.108386i
$333$	−1595.49	−	3009.41i	−0.262559	−	0.495240i
$334$	−1600.19	−	1883.89i	−0.262151	−	0.308628i
$335$	1177.33	+	1736.44i	0.192014	+	0.283199i
$336$	−0.107050	−	1.97441i	−1.73811e−5	−	0.000320575i
$337$	2938.27	+	7374.50i	0.474949	+	1.19203i	0.950049	+	0.312100i	$0.101032\pi$
$337$	2938.27	+	7374.50i	0.474949	+	1.19203i	−0.475100	+	0.879932i	$0.657588\pi$
$338$	−3382.83	−	1565.06i	−0.544383	−	0.251858i
$339$	−3350.68	+	737.541i	−0.536826	+	0.118164i
$340$	−1371.22	+	2586.40i	−0.218721	+	0.412551i
$341$	594.594	−	3626.86i	0.0944254	−	0.575969i
$342$	221.493	−	168.374i	0.0350203	−	0.0266218i
$343$	131.432	−	60.8070i	0.0206900	−	0.00957222i
$344$	−7022.45	−	6652.02i	−1.10065	−	1.04260i
$345$	107.446	+	655.393i	0.0167673	+	0.102276i
$346$	−801.043	−	269.903i	−0.124463	−	0.0419366i
$347$	1994.26	−	5005.21i	0.308523	−	0.774334i	−0.690191	−	0.723628i	$-0.742473\pi$
$347$	1994.26	−	5005.21i	0.308523	−	0.774334i	0.998714	−	0.0507066i	$-0.0161473\pi$
$348$	3303.64	−	3129.37i	0.508890	−	0.482046i
$349$	4462.25	+	3392.11i	0.684409	+	0.520274i	0.888615	−	0.458654i	$-0.151668\pi$
$349$	4462.25	+	3392.11i	0.684409	+	0.520274i	−0.204206	+	0.978928i	$0.565461\pi$
$350$	37.0077	+	8.14601i	0.00565184	+	0.00124406i
$351$	−23.1158	+	27.2140i	−0.00351518	+	0.00413839i
$352$	−4359.53	−	474.128i	−0.660125	−	0.0717929i
$353$	6749.49			1.01768			0.508838	−	0.860863i	$-0.330075\pi$
$353$	6749.49			1.01768			0.508838	+	0.860863i	$0.330075\pi$
$354$	2277.76	+	374.890i	0.341982	+	0.0562859i
$355$	595.769			0.0890708
$356$	−4817.00	−	523.881i	−0.717137	−	0.0779933i
$357$	−53.4119	+	62.8814i	−0.00791837	+	0.00932223i
$358$	2006.84	+	441.739i	0.296271	+	0.0652141i
$359$	−6732.93	−	5118.24i	−0.989834	−	0.752452i	−0.0209021	−	0.999782i	$-0.506654\pi$
$359$	−6732.93	−	5118.24i	−0.989834	−	0.752452i	−0.968931	+	0.247330i	$0.920447\pi$
$360$	639.080	−	605.369i	0.0935624	−	0.0886270i
$361$	2416.08	−	6063.90i	0.352249	−	0.884079i
$362$	2934.83	+	988.858i	0.426108	+	0.143572i
$363$	368.734	+	2249.17i	0.0533154	+	0.325210i
$364$	1.03720	+	0.982491i	0.000149352	+	0.000141474i
$365$	−2178.85	+	1008.04i	−0.312456	+	0.144557i
$366$	−1650.98	+	1255.04i	−0.235787	+	0.179240i
$367$	35.1001	−	214.101i	0.00499240	−	0.0304523i	−0.984213	−	0.176989i	$-0.943364\pi$
$367$	35.1001	−	214.101i	0.00499240	−	0.0304523i	0.989205	+	0.146537i	$0.0468126\pi$
$368$	−73.7172	+	139.045i	−0.0104423	+	0.0196963i
$369$	−3787.42	+	833.674i	−0.534323	+	0.117613i
$370$	−2561.24	−	1184.95i	−0.359871	−	0.166494i
$371$	32.1818	+	80.7702i	0.00450349	+	0.0113029i
$372$	127.799	+	2357.11i	0.0178120	+	0.328523i
$373$	3698.84	+	5455.38i	0.513455	+	0.757290i	0.992728	−	0.120376i	$-0.0384100\pi$
$373$	3698.84	+	5455.38i	0.513455	+	0.757290i	−0.479273	+	0.877666i	$0.659100\pi$
$374$	3422.36	+	4029.12i	0.473172	+	0.557061i
$375$	−1423.79	−	2685.55i	−0.196065	−	0.369817i
$376$	7393.43	−	2491.13i	1.01406	−	0.341677i
$377$	−21.2228	+	391.431i	−0.00289928	+	0.0534740i
$378$	8.29293	−	4.98969i	0.00112842	−	0.000678947i
$379$	−787.528	−	2836.42i	−0.106735	−	0.384425i	0.890816	−	0.454364i	$-0.150133\pi$
$379$	−787.528	−	2836.42i	−0.106735	−	0.384425i	−0.997551	+	0.0699389i	$0.977720\pi$
$380$	−109.462	+	394.246i	−0.0147771	+	0.0532221i
$381$	−6543.66	−	3937.19i	−0.879900	−	0.529418i
$382$	3495.24	−	5155.09i	0.468146	−	0.690464i
$383$	11330.3	−	1232.24i	1.51162	−	0.164398i	0.685572	−	0.728005i	$-0.259552\pi$
$383$	11330.3	−	1232.24i	1.51162	−	0.164398i	0.826043	+	0.563607i	$0.190587\pi$
$384$	2926.54	−	318.280i	0.388917	−	0.0422973i
$385$	12.4359	−	18.3416i	0.00164621	−	0.00242798i
$386$	−2741.29	−	1649.38i	−0.361472	−	0.217491i
$387$	−1045.72	+	3766.34i	−0.137356	+	0.494713i
$388$	−1528.71	−	5505.93i	−0.200022	−	0.720415i
$389$	−5563.64	+	3347.53i	−0.725162	+	0.436315i	−0.829703	−	0.558205i	$-0.811490\pi$
$389$	−5563.64	+	3347.53i	−0.725162	+	0.436315i	0.104541	+	0.994521i	$0.466663\pi$
$390$	−1.60159	+	29.5396i	−0.000207948	+	0.00383537i
$391$	6222.89	−	2096.74i	0.804873	−	0.271193i
$392$	3577.78	+	6748.41i	0.460983	+	0.869506i
$393$	−4143.35	−	4877.93i	−0.531817	−	0.626104i
$394$	−474.064	−	699.193i	−0.0606168	−	0.0894031i
$395$	213.989	+	3946.79i	0.0272581	+	0.502746i
$396$	407.429	+	1022.57i	0.0517022	+	0.129763i
$397$	1402.23	+	648.743i	0.177270	+	0.0820138i	0.506517	−	0.862230i	$-0.330933\pi$
$397$	1402.23	+	648.743i	0.177270	+	0.0820138i	−0.329247	+	0.944244i	$0.606795\pi$
$398$	1929.35	−	424.682i	0.242989	−	0.0534859i
$399$	−5.40144	+	10.1882i	−0.000677719	+	0.00127831i
$400$	53.3939	−	325.688i	0.00667424	−	0.0407111i
$401$	−5287.53	+	4019.48i	−0.658471	+	0.500557i	−0.880231	−	0.474545i	$-0.842613\pi$
$401$	−5287.53	+	4019.48i	−0.658471	+	0.500557i	0.221761	+	0.975101i	$0.428820\pi$
$402$	−2208.42	+	1021.72i	−0.273995	+	0.126763i
$403$	−147.634	−	139.846i	−0.0182485	−	0.0172859i
$404$	−1424.15	−	8686.91i	−0.175381	−	1.06978i
$405$	−337.102	−	113.583i	−0.0413599	−	0.0139358i
$406$	39.3288	−	98.7080i	0.00480753	−	0.0120660i
$407$	6567.20	−	6220.78i	0.799813	−	0.757623i
$408$	−6928.94	−	5267.24i	−0.840769	−	0.639136i
$409$	−8275.01	−	1821.47i	−1.00042	−	0.220210i	−0.315579	−	0.948899i	$-0.602199\pi$
$409$	−8275.01	−	1821.47i	−1.00042	−	0.220210i	−0.684844	+	0.728689i	$0.740130\pi$
$410$	−2080.07	+	2448.85i	−0.250555	+	0.294976i
$411$	−2999.40	−	326.204i	−0.359974	−	0.0391495i
$412$	646.281			0.0772815
$413$	−92.2043	+	25.5380i	−0.0109857	+	0.00304272i
$414$	−770.315			−0.0914466
$415$	−1751.97	−	190.538i	−0.207231	−	0.0225377i
$416$	−157.079	+	184.928i	−0.0185131	+	0.0217953i
$417$	−1161.11	−	255.579i	−0.136354	−	0.0300138i
$418$	588.215	+	447.150i	0.0688291	+	0.0523225i
$419$	11077.3	−	10493.0i	1.29156	−	1.22343i	0.331560	−	0.943434i	$-0.392425\pi$
$419$	11077.3	−	10493.0i	1.29156	−	1.22343i	0.960001	−	0.279997i	$-0.0903335\pi$
$420$	−5.26819	+	13.2222i	−0.000612051	+	0.00153613i
$421$	1404.40	+	473.198i	0.162580	+	0.0547797i	0.399415	−	0.916770i	$-0.369213\pi$
$421$	1404.40	+	473.198i	0.162580	+	0.0547797i	−0.236834	+	0.971550i	$0.576110\pi$
$422$	−1304.75	−	7958.64i	−0.150508	−	0.918059i
$423$	−2288.87	−	2168.13i	−0.263094	−	0.249216i
$424$	−8324.48	+	3851.32i	−0.953473	+	0.441124i
$425$	−10962.9	+	8333.76i	−1.25124	+	0.951169i
$426$	−111.793	+	681.908i	−0.0127145	+	0.0775552i
$427$	40.2616	−	75.9414i	0.00456298	−	0.00860670i
$428$	3204.11	−	705.279i	0.361861	−	0.0796517i
$429$	−86.0606	−	39.8159i	−0.00968542	−	0.00448095i
$430$	1198.69	+	3008.49i	0.134433	+	0.337400i
$431$	−934.275	−	17231.7i	−0.104414	−	1.92580i	−0.316573	−	0.948568i	$-0.602532\pi$
$431$	−934.275	−	17231.7i	−0.104414	−	1.92580i	0.212159	−	0.977235i	$-0.431951\pi$
$432$	−47.3045	−	69.7690i	−0.00526838	−	0.00777028i
$433$	7928.51	+	9334.17i	0.879954	+	1.03596i	0.999072	+	0.0430817i	$0.0137176\pi$
$433$	7928.51	+	9334.17i	0.879954	+	1.03596i	−0.119118	+	0.992880i	$0.538007\pi$
$434$	25.8185	+	48.6989i	0.00285560	+	0.00538623i
$435$	−3700.92	+	1246.98i	−0.407920	+	0.137444i
$436$	−503.829	+	9292.57i	−0.0553418	+	1.02072i
$437$	786.432	−	473.181i	0.0860873	−	0.0517970i
$438$	−744.941	−	2683.04i	−0.0812664	−	0.292695i
$439$	−1046.85	+	3770.43i	−0.113812	+	0.409915i	−0.998406	−	0.0564486i	$-0.982022\pi$
$439$	−1046.85	+	3770.43i	−0.113812	+	0.409915i	0.884593	+	0.466363i	$0.154436\pi$
$440$	2003.12	+	1205.24i	0.217034	+	0.130585i
$441$	1732.16	−	2554.74i	0.187038	−	0.275860i
$442$	290.784	−	31.6247i	0.0312923	−	0.00340324i
$443$	−9532.33	+	1036.70i	−1.02234	+	0.111186i	−0.603900	−	0.797060i	$-0.706387\pi$
$443$	−9532.33	+	1036.70i	−1.02234	+	0.111186i	−0.418436	+	0.908246i	$0.637422\pi$
$444$	−3260.48	+	4808.85i	−0.348504	+	0.514004i
$445$	3563.20	+	2143.90i	0.379577	+	0.228384i
$446$	−614.149	+	2211.97i	−0.0652036	+	0.234842i
$447$	52.2873	+	188.322i	0.00553267	+	0.0199269i
$448$	51.8351	−	31.1881i	0.00546647	−	0.00328906i
$449$	−530.713	+	9788.42i	−0.0557815	+	1.02883i	0.827940	+	0.560816i	$0.189513\pi$
$449$	−530.713	+	9788.42i	−0.0557815	+	1.02883i	−0.883722	+	0.468013i	$0.844970\pi$
$450$	1530.86	−	515.806i	0.160367	−	0.0540341i
$451$	−4824.13	−	9099.28i	−0.503680	−	0.950041i
$452$	3788.57	+	4460.25i	0.394247	+	0.464143i
$453$	1497.57	+	2208.74i	0.155324	+	0.229086i
$454$	86.4871	+	1595.16i	0.00894062	+	0.164900i
$455$	−0.453832	−	1.13903i	−4.67604e−5	−	0.000117360i
$456$	−1104.07	−	510.796i	−0.113383	−	0.0524566i
$457$	14048.0	−	3092.21i	1.43794	−	0.316515i	0.573482	−	0.819218i	$-0.305592\pi$
$457$	14048.0	−	3092.21i	1.43794	−	0.316515i	0.864459	+	0.502703i	$0.167661\pi$
$458$	2434.59	−	4592.12i	0.248386	−	0.468505i
$459$	−569.016	+	3470.84i	−0.0578636	+	0.352952i
$460$	901.841	−	685.562i	0.0914099	−	0.0694880i
$461$	−4944.23	+	2287.45i	−0.499514	+	0.231100i	−0.653434	−	0.756984i	$-0.726672\pi$
$461$	−4944.23	+	2287.45i	−0.499514	+	0.231100i	0.153920	+	0.988083i	$0.450810\pi$
$462$	18.6600	+	17.6756i	0.00187909	+	0.00177997i
$463$	−1833.35	−	11182.9i	−0.184023	−	1.12249i	−0.903695	−	0.428178i	$-0.859156\pi$
$463$	−1833.35	−	11182.9i	−0.184023	−	1.12249i	0.719671	−	0.694315i	$-0.244292\pi$
$464$	−876.985	−	295.491i	−0.0877435	−	0.0295642i
$465$	749.865	−	1882.02i	0.0747831	−	0.187691i
$466$	−6310.52	+	5977.65i	−0.627316	+	0.594226i
$467$	−7764.03	−	5902.06i	−0.769329	−	0.584829i	0.145175	−	0.989406i	$-0.453626\pi$
$467$	−7764.03	−	5902.06i	−0.769329	−	0.584829i	−0.914504	+	0.404577i	$0.867419\pi$
$468$	59.4806	+	13.0927i	0.00587498	+	0.00129318i
$469$	65.2907	−	76.8661i	0.00642824	−	0.00756791i
$470$	−2596.76	−	282.414i	−0.254850	−	0.0277166i
$471$	7706.16			0.753887
$472$	−3216.77	−	9566.89i	−0.313694	−	0.932949i
$473$	−10380.6			−1.00909
$474$	−4557.59	−	495.667i	−0.441639	−	0.0480311i
$475$	−1246.05	+	1466.96i	−0.120363	+	0.141702i
$476$	137.438	+	30.2523i	0.0132341	+	0.00291305i
$477$	2950.73	+	2243.09i	0.283238	+	0.215312i
$478$	1896.51	−	1796.47i	0.181474	−	0.171901i
$479$	−5867.46	+	14726.2i	−0.559689	+	1.40471i	0.328179	+	0.944616i	$0.393565\pi$
$479$	−5867.46	+	14726.2i	−0.559689	+	1.40471i	−0.887868	+	0.460098i	$0.847814\pi$
$480$	−2290.72	−	771.833i	−0.217826	−	0.0733941i
$481$	−80.9726	−	493.911i	−0.00767574	−	0.0468199i
$482$	533.371	+	505.236i	0.0504033	+	0.0477445i
$483$	28.9761	−	13.4058i	0.00272973	−	0.00126291i
$484$	3094.93	−	2352.71i	0.290659	−	0.220953i
$485$	−793.391	+	4839.47i	−0.0742805	+	0.453091i
$486$	193.261	−	364.529i	0.0180380	−	0.0340234i
$487$	15410.8	−	3392.17i	1.43394	−	0.315635i	0.571006	−	0.820946i	$-0.306553\pi$
$487$	15410.8	−	3392.17i	1.43394	−	0.315635i	0.862937	+	0.505312i	$0.168622\pi$
$488$	8229.57	+	3807.40i	0.763392	+	0.353183i
$489$	−1193.06	−	2994.36i	−0.110332	−	0.276912i
$490$	−138.448	−	2553.53i	−0.0127642	−	0.235422i
$491$	1952.30	+	2879.42i	0.179442	+	0.264657i	0.906763	−	0.421640i	$-0.138545\pi$
$491$	1952.30	+	2879.42i	0.179442	+	0.264657i	−0.727321	+	0.686297i	$0.759235\pi$
$492$	4282.39	+	5041.62i	0.392408	+	0.461979i
$493$	18087.0	+	34115.7i	1.65233	+	3.11662i
$494$	38.7421	−	13.0537i	0.00352852	−	0.00118890i
$495$	51.1445	−	943.304i	0.00464399	−	0.0856533i
$496$	411.349	−	247.500i	0.0372381	−	0.0224054i
$497$	−7.66203	−	27.5961i	−0.000691527	−	0.00249065i
$498$	546.835	−	1969.52i	0.0492053	−	0.177222i
$499$	15270.7	+	9188.10i	1.36996	+	0.824280i	0.994718	−	0.102645i	$-0.0327306\pi$
$499$	15270.7	+	9188.10i	1.36996	+	0.824280i	0.375246	+	0.926925i	$0.377558\pi$
$500$	−2909.60	+	4291.34i	−0.260243	+	0.383830i
$501$	4341.73	−	472.192i	0.387174	−	0.0421078i
$502$	−1843.60	+	200.503i	−0.163912	+	0.0178265i
$503$	5724.26	−	8442.65i	0.507420	−	0.748388i	−0.484564	−	0.874756i	$-0.661022\pi$
$503$	5724.26	−	8442.65i	0.507420	−	0.748388i	0.991983	+	0.126368i	$0.0403319\pi$
$504$	−36.2598	−	21.8168i	−0.00320464	−	0.00192817i
$505$	−2021.14	+	7279.47i	−0.178098	+	0.641450i
$506$	−547.287	−	1971.15i	−0.0480827	−	0.173178i
$507$	5643.05	−	3395.31i	0.494313	−	0.297418i
$508$	−705.223	+	13007.1i	−0.0615929	+	1.13601i
$509$	717.065	−	241.607i	0.0624427	−	0.0210394i	−0.287907	−	0.957658i	$-0.592959\pi$
$509$	717.065	−	241.607i	0.0624427	−	0.0210394i	0.350350	+	0.936619i	$0.386063\pi$
$510$	1364.95	+	2574.57i	0.118512	+	0.223537i
$511$	74.7145	+	87.9607i	0.00646805	+	0.00761478i
$512$	−633.612	−	934.507i	−0.0546913	−	0.0806636i
$513$	26.6142	+	490.870i	0.00229054	+	0.0422465i
$514$	−2364.49	−	5934.41i	−0.202905	−	0.509252i
$515$	−503.391	−	232.893i	−0.0430719	−	0.0199272i
$516$	6511.43	−	1433.27i	0.555523	−	0.122280i
$517$	3921.83	−	7397.36i	0.333621	−	0.629276i
$518$	−21.9479	+	133.876i	−0.00186165	+	0.0113556i
$519$	1188.99	−	903.847i	0.100560	−	0.0764441i
$520$	117.393	−	54.3118i	0.00990005	−	0.00458025i
$521$	3664.16	+	3470.88i	0.308119	+	0.291866i	0.826097	−	0.563528i	$-0.190556\pi$
$521$	3664.16	+	3470.88i	0.308119	+	0.291866i	−0.517978	+	0.855394i	$0.673315\pi$
$522$	−732.819	−	4470.00i	−0.0614456	−	0.374802i
$523$	3583.92	+	1207.56i	0.299644	+	0.100962i	0.465108	−	0.885254i	$-0.346016\pi$
$523$	3583.92	+	1207.56i	0.299644	+	0.100962i	−0.165464	+	0.986216i	$0.552912\pi$
$524$	−4040.70	+	10141.4i	−0.336868	+	0.845475i
$525$	−48.6081	+	46.0440i	−0.00404082	+	0.00382767i
$526$	−163.890	−	124.586i	−0.0135854	−	0.0103274i
$527$	−19562.6	−	4306.06i	−1.61700	−	0.355929i
$528$	144.922	−	170.616i	0.0119450	−	0.0140627i
$529$	9569.45	+	1040.74i	0.786509	+	0.0855380i
$530$	3070.88			0.251680
$531$	−2806.77	+	2959.35i	−0.229385	+	0.241854i
$532$	19.6693			0.00160296
$533$	−566.504	−	61.6110i	−0.0460375	−	0.00500688i
$534$	−3122.49	+	3676.08i	−0.253040	+	0.297902i
$535$	−2749.85	−	605.288i	−0.222218	−	0.0489138i
$536$	8469.93	+	6438.67i	0.682547	+	0.518859i
$537$	−2635.90	+	2496.86i	−0.211821	+	0.200647i
$538$	1683.93	−	4226.35i	0.134943	−	0.338682i
$539$	7767.95	+	2617.33i	0.620760	+	0.209158i
$540$	98.1629	+	598.767i	0.00782270	+	0.0477163i
$541$	7453.41	+	7060.24i	0.592324	+	0.561079i	0.924038	−	0.382301i	$-0.124868\pi$
$541$	7453.41	+	7060.24i	0.592324	+	0.561079i	−0.331714	+	0.943380i	$0.607627\pi$
$542$	−12895.6	+	5966.12i	−1.02198	+	0.472817i
$543$	−4356.17	+	3311.48i	−0.344275	+	0.261711i
$544$	−3866.64	+	23585.5i	−0.304744	+	1.85886i
$545$	3741.10	−	7056.46i	0.294039	−	0.554616i
$546$	1.38888	−	0.305715i	0.000108862	−	2.39623e-5i
$547$	−19258.4	−	8909.87i	−1.50535	−	0.696451i	−0.518058	−	0.855346i	$-0.673345\pi$
$547$	−19258.4	−	8909.87i	−1.50535	−	0.696451i	−0.987295	+	0.158895i	$0.949207\pi$
$548$	1904.83	+	4780.76i	0.148486	+	0.372671i
$549$	−198.379	−	3658.88i	−0.0154218	−	0.284439i
$550$	2407.52	+	3550.83i	0.186649	+	0.275287i
$551$	3493.94	+	4113.38i	0.270139	+	0.318032i
$552$	1577.65	+	2975.76i	0.121647	+	0.229451i
$553$	180.064	−	60.6706i	0.0138465	−	0.00466542i
$554$	64.5781	−	1191.07i	0.00495245	−	0.0913427i
$555$	4272.52	−	2570.69i	0.326771	−	0.196612i
$556$	542.526	+	1954.00i	0.0413817	+	0.149043i
$557$	−40.0226	+	144.149i	−0.00304455	+	0.0109655i	−0.965057	−	0.262041i	$-0.915604\pi$
$557$	−40.0226	+	144.149i	−0.00304455	+	0.0109655i	0.962012	+	0.273007i	$0.0880181\pi$
$558$	2013.42	+	1211.44i	0.152751	+	0.0919071i
$559$	−322.323	+	475.391i	−0.0243879	+	0.0359694i
$560$	2.87759	−	0.312956i	0.000217143	−	2.36157e-5i
$561$	−9285.76	+	1009.89i	−0.698833	+	0.0760027i
$562$	5939.39	−	8759.94i	0.445797	−	0.657501i
$563$	−15334.2	−	9226.28i	−1.14789	−	0.690660i	−0.191134	−	0.981564i	$-0.561216\pi$
$563$	−15334.2	−	9226.28i	−1.14789	−	0.690660i	−0.956752	+	0.290904i	$0.906044\pi$
$564$	−1438.67	+	5181.63i	−0.107410	+	0.386855i
$565$	−1343.64	−	4839.36i	−0.100048	−	0.360342i
$566$	7264.28	−	4370.77i	0.539471	−	0.324589i
$567$	−0.925801	+	17.0754i	−6.85714e−5	+	0.00126473i
$568$	2863.20	−	964.724i	0.211509	−	0.0712657i
$569$	−1323.91	−	2497.16i	−0.0975418	−	0.183983i	0.829939	−	0.557854i	$-0.188375\pi$
$569$	−1323.91	−	2497.16i	−0.0975418	−	0.183983i	−0.927481	+	0.373871i	$0.878030\pi$
$570$	263.673	+	310.419i	0.0193755	+	0.0228106i
$571$	−3969.88	−	5855.13i	−0.290953	−	0.429124i	0.653918	−	0.756565i	$-0.273124\pi$
$571$	−3969.88	−	5855.13i	−0.290953	−	0.429124i	−0.944871	+	0.327441i	$0.893814\pi$
$572$	8.75661	+	161.506i	0.000640091	+	0.0118058i
$573$	4073.25	+	10223.1i	0.296968	+	0.745333i
$574$	140.183	+	64.8553i	0.0101936	+	0.00471604i
$575$	5204.38	−	1145.57i	0.377457	−	0.0830845i
$576$	1207.98	−	2278.49i	0.0873827	−	0.164821i
$577$	2247.88	−	13711.5i	0.162185	−	0.989283i	−0.772814	−	0.634632i	$-0.781152\pi$
$577$	2247.88	−	13711.5i	0.162185	−	0.989283i	0.934999	−	0.354651i	$-0.115400\pi$
$578$	16296.2	−	12388.0i	1.17272	−	0.891478i
$579$	5130.25	−	2373.51i	0.368231	−	0.170362i
$580$	4836.14	+	4581.03i	0.346224	+	0.327960i
$581$	13.7058	+	83.6019i	0.000978682	+	0.00596970i
$582$	−5390.31	−	1816.21i	−0.383910	−	0.129354i
$583$	−3643.40	+	9144.23i	−0.258823	+	0.649598i
$584$	−8839.01	+	8372.75i	−0.626303	+	0.593265i
$585$	−41.6116	−	31.6323i	−0.00294090	−	0.00223562i
$586$	9003.52	+	1981.82i	0.634696	+	0.139707i
$587$	1102.45	−	1297.91i	0.0775181	−	0.0912613i	−0.722036	−	0.691856i	$-0.756793\pi$
$587$	1102.45	−	1297.91i	0.0775181	−	0.0912613i	0.799554	+	0.600594i	$0.205069\pi$
$588$	−5233.98	−	569.229i	−0.367084	−	0.0399228i
$589$	−2799.70			−0.195856
$590$	−367.471	+	3359.19i	−0.0256416	+	0.234400i
$591$	1492.58			0.103886
$592$	1174.64	+	127.750i	0.0815497	+	0.00886906i
$593$	10484.0	−	12342.7i	0.726011	−	0.854726i	−0.268067	−	0.963400i	$-0.586385\pi$
$593$	10484.0	−	12342.7i	0.726011	−	0.854726i	0.994077	+	0.108674i	$0.0346606\pi$
$594$	1070.09	+	235.545i	0.0739166	+	0.0162703i
$595$	−96.1489	−	73.0905i	−0.00662474	−	0.00503600i
$596$	242.028	−	229.261i	0.0166340	−	0.0157565i
$597$	−1291.98	+	3242.64i	−0.0885719	+	0.222299i
$598$	−107.264	−	36.1416i	−0.00733507	−	0.00247147i
$599$	4004.96	+	24429.2i	0.273186	+	1.66636i	0.665401	+	0.746486i	$0.268261\pi$
$599$	4004.96	+	24429.2i	0.273186	+	1.66636i	−0.392215	+	0.919874i	$0.628291\pi$
$600$	−5127.87	−	4857.38i	−0.348907	−	0.330503i
$601$	−20964.7	+	9699.32i	−1.42291	+	0.658309i	−0.972155	−	0.234338i	$-0.924708\pi$
$601$	−20964.7	+	9699.32i	−1.42291	+	0.658309i	−0.450756	+	0.892647i	$0.648846\pi$
$602$	123.938	−	94.2149i	0.00839090	−	0.00637859i
$603$	695.564	−	4242.75i	0.0469744	−	0.286531i
$604$	2132.10	−	4021.57i	0.143632	−	0.270919i
$605$	−3258.47	+	717.244i	−0.218968	+	0.0481986i
$606$	−7952.71	−	3679.32i	−0.533097	−	0.246637i
$607$	3669.73	+	9210.32i	0.245387	+	0.615874i	0.999148	−	0.0412746i	$-0.0131418\pi$
$607$	3669.73	+	9210.32i	0.245387	+	0.615874i	−0.753761	+	0.657148i	$0.771763\pi$
$608$	180.852	+	3335.62i	0.0120634	+	0.222495i
$609$	105.357	+	155.390i	0.00701031	+	0.0103394i
$610$	−1965.38	−	2313.82i	−0.130452	−	0.153580i
$611$	−216.995	−	409.297i	−0.0143677	−	0.0271004i
$612$	5685.23	−	1915.58i	0.375510	−	0.126524i
$613$	2.08218	−	38.4036i	0.000137192	−	0.00253036i	−0.998464	−	0.0554040i	$-0.982355\pi$
$613$	2.08218	−	38.4036i	0.000137192	−	0.00253036i	0.998601	+	0.0528737i	$0.0168381\pi$
$614$	−13616.7	+	8192.91i	−0.894994	+	0.538500i
$615$	−1518.77	−	5470.13i	−0.0995820	−	0.358662i
$616$	30.0652	−	108.285i	0.00196650	−	0.00708267i
$617$	4434.07	+	2667.89i	0.289317	+	0.174076i	0.652812	−	0.757520i	$-0.273589\pi$
$617$	4434.07	+	2667.89i	0.289317	+	0.174076i	−0.363495	+	0.931596i	$0.618417\pi$
$618$	361.025	−	532.472i	0.0234993	−	0.0346588i
$619$	−7262.01	+	789.791i	−0.471543	+	0.0512833i	−0.340806	−	0.940134i	$-0.610700\pi$
$619$	−7262.01	+	789.791i	−0.471543	+	0.0512833i	−0.130737	+	0.991417i	$0.541734\pi$
$620$	−3435.35	+	373.617i	−0.222527	+	0.0242013i
$621$	763.808	−	1126.53i	0.0493568	−	0.0727958i
$622$	1991.11	+	1198.01i	0.128354	+	0.0772279i
$623$	53.4807	−	192.620i	0.00343926	−	0.0123871i
$624$	−3.31362	−	11.9346i	−0.000212582	−	0.000765651i
$625$	−7509.94	+	4518.58i	−0.480636	+	0.289189i
$626$	−241.293	+	4450.39i	−0.0154058	+	0.284143i
$627$	−1237.17	+	416.852i	−0.0788005	+	0.0265510i
$628$	−6156.97	−	11613.3i	−0.391226	−	0.737931i
$629$	−31916.9	−	37575.5i	−2.02323	−	2.38193i
$630$	7.95085	+	11.7266i	0.000502808	+	0.000741587i
$631$	−1202.98	−	22187.7i	−0.0758954	−	1.39981i	−0.750130	−	0.661291i	$-0.770009\pi$
$631$	−1202.98	−	22187.7i	−0.0758954	−	1.39981i	0.674234	−	0.738518i	$-0.264474\pi$
$632$	7419.41	+	18621.3i	0.466975	+	1.17202i
$633$	12932.7	+	5983.31i	0.812052	+	0.375695i
$634$	−5054.15	+	1112.50i	−0.316602	+	0.0696895i
$635$	5236.52	−	9877.12i	0.327252	−	0.617263i
$636$	1022.82	−	6238.95i	0.0637698	−	0.388978i
$637$	361.062	−	274.473i	0.0224581	−	0.0170722i
$638$	10917.6	−	5051.01i	0.677478	−	0.313435i
$639$	−886.395	−	839.638i	−0.0548752	−	0.0519805i
$640$	697.178	+	4252.60i	0.0430599	+	0.262654i
$641$	−7938.33	−	2674.73i	−0.489150	−	0.164814i	0.0639093	−	0.997956i	$-0.479643\pi$
$641$	−7938.33	−	2674.73i	−0.489150	−	0.164814i	−0.553059	+	0.833142i	$0.686540\pi$
$642$	1208.80	−	3033.86i	0.0743107	−	0.186506i
$643$	16144.8	−	15293.2i	0.990185	−	0.937953i	−0.00789014	−	0.999969i	$-0.502512\pi$
$643$	16144.8	−	15293.2i	0.990185	−	0.937953i	0.998075	+	0.0620158i	$0.0197529\pi$
$644$	−43.3537	−	32.9566i	−0.00265275	−	0.00201657i
$645$	−5588.27	−	1230.07i	−0.341144	−	0.0750915i
$646$	2607.03	−	3069.24i	0.158781	−	0.186931i
$647$	−9826.69	−	1068.72i	−0.597105	−	0.0649391i	−0.195424	−	0.980719i	$-0.562608\pi$
$647$	−9826.69	−	1068.72i	−0.597105	−	0.0649391i	−0.401681	+	0.915780i	$0.631574\pi$
$648$	−1804.00			−0.109364
$649$	−9566.76	−	5079.68i	−0.578626	−	0.307234i
$650$	237.369			0.0143237
$651$	−96.8193	−	10.5297i	−0.00582895	−	0.000633937i
$652$	−3559.33	+	4190.37i	−0.213795	+	0.251698i
$653$	−17486.6	−	3849.10i	−1.04794	−	0.230669i	−0.342559	−	0.939496i	$-0.611294\pi$
$653$	−17486.6	−	3849.10i	−1.04794	−	0.230669i	−0.705382	+	0.708827i	$0.749225\pi$
$654$	7374.72	+	5606.11i	0.440939	+	0.335193i
$655$	6801.86	−	6443.06i	0.405757	−	0.384353i
$656$	497.932	−	1249.72i	0.0296357	−	0.0743799i
$657$	4662.41	+	1570.95i	0.276861	+	0.0932854i
$658$	20.3147	+	123.914i	0.00120357	+	0.00734146i
$659$	5615.48	+	5319.27i	0.331940	+	0.314430i	0.835458	−	0.549555i	$-0.185203\pi$
$659$	5615.48	+	5319.27i	0.331940	+	0.314430i	−0.503518	+	0.863985i	$0.667961\pi$
$660$	−1462.44	+	676.595i	−0.0862503	+	0.0399037i
$661$	8822.62	−	6706.78i	0.519153	−	0.394650i	−0.312524	−	0.949910i	$-0.601174\pi$
$661$	8822.62	−	6706.78i	0.519153	−	0.394650i	0.831677	+	0.555260i	$0.187381\pi$
$662$	832.609	−	5078.69i	0.0488826	−	0.298171i
$663$	−242.079	+	456.609i	−0.0141803	+	0.0267470i
$664$	−8728.30	+	1921.24i	−0.510126	+	0.112287i
$665$	−15.3205	−	7.08802i	−0.000893389	−	0.000413326i
$666$	2140.65	+	5372.63i	0.124547	+	0.312590i
$667$	−808.972	−	14920.6i	−0.0469618	−	0.866160i
$668$	−4180.51	−	6165.79i	−0.242139	−	0.357128i
$669$	−2625.89	−	3091.43i	−0.151753	−	0.178657i
$670$	−1668.51	−	3147.15i	−0.0962093	−	0.181470i
$671$	9221.72	−	3107.16i	0.530552	−	0.178764i
$672$	−6.29112	+	116.033i	−0.000361138	+	0.00666081i
$673$	9529.59	−	5733.76i	0.545823	−	0.328411i	−0.215793	−	0.976439i	$-0.569234\pi$
$673$	9529.59	−	5733.76i	0.545823	−	0.328411i	0.761616	+	0.648028i	$0.224406\pi$
$674$	−3605.87	−	12987.2i	−0.206073	−	0.742207i
$675$	−763.596	+	2750.23i	−0.0435420	+	0.156824i
$676$	−9625.40	−	5791.41i	−0.547644	−	0.329507i
$677$	13242.1	−	19530.6i	0.751748	−	1.10875i	−0.238731	−	0.971086i	$-0.576731\pi$
$677$	13242.1	−	19530.6i	0.751748	−	1.10875i	0.990480	−	0.137660i	$-0.0439582\pi$
$678$	5791.18	−	629.829i	0.328037	−	0.0356761i
$679$	234.369	−	25.4891i	0.0132463	−	0.00144062i
$680$	7150.17	−	10545.7i	0.403230	−	0.594720i
$681$	−2418.57	−	1455.21i	−0.136094	−	0.0818849i
$682$	−1669.45	+	6012.81i	−0.0937338	+	0.337599i
$683$	−3716.75	−	13386.5i	−0.208225	−	0.749958i	−0.991704	−	0.128540i	$-0.958971\pi$
$683$	−3716.75	−	13386.5i	−0.208225	−	0.749958i	0.783479	−	0.621418i	$-0.213443\pi$
$684$	718.484	−	432.298i	0.0401636	−	0.0241657i
$685$	239.113	−	4410.17i	0.0133373	−	0.245991i
$686$	−233.014	+	78.5114i	−0.0129687	+	0.00436965i
$687$	4301.63	+	8113.74i	0.238890	+	0.450595i
$688$	−877.805	−	1033.43i	−0.0486424	−	0.0572663i
$689$	305.641	+	450.787i	0.0168998	+	0.0249254i
$690$	−61.0497	−	1126.00i	−0.00336829	−	0.0621245i
$691$	−6743.37	−	16924.6i	−0.371245	−	0.931754i	−0.989336	−	0.145648i	$-0.953473\pi$
$691$	−6743.37	−	16924.6i	−0.371245	−	0.931754i	0.618092	−	0.786106i	$-0.287906\pi$
$692$	−2312.08	−	1069.68i	−0.127012	−	0.0587618i
$693$	−44.3518	+	9.76256i	−0.00243115	+	0.000535136i
$694$	−4285.04	+	8082.45i	−0.234378	+	0.442083i
$695$	281.567	−	1717.48i	0.0153676	−	0.0937380i
$696$	−15767.0	+	11985.7i	−0.858685	+	0.652756i
$697$	−50943.4	+	23568.9i	−2.76846	+	1.28083i
$698$	−6909.34	−	6544.87i	−0.374674	−	0.354910i
$699$	−2484.68	−	15155.9i	−0.134448	−	0.820097i
$700$	108.225	+	36.4654i	0.00584362	+	0.00196894i
$701$	283.023	−	710.334i	0.0152491	−	0.0382724i	−0.921155	−	0.389196i	$-0.872753\pi$
$701$	283.023	−	710.334i	0.0152491	−	0.0382724i	0.936404	+	0.350923i	$0.114132\pi$
$702$	44.0141	−	41.6923i	0.00236639	−	0.00224156i
$703$	−5485.68	−	4170.11i	−0.294305	−	0.223725i
$704$	6688.63	+	1472.28i	0.358079	+	0.0788191i
$705$	2987.84	−	3517.55i	0.159615	−	0.187913i
$706$	−11392.8	−	1239.04i	−0.607329	−	0.0660510i
$707$	363.180			0.0193193
$708$	6702.30	+	1865.42i	0.355774	+	0.0990210i
$709$	15591.6			0.825889			0.412945	−	0.910756i	$-0.364500\pi$
$709$	15591.6			0.825889			0.412945	+	0.910756i	$0.364500\pi$
$710$	−1005.63	−	109.369i	−0.0531557	−	0.00578103i
$711$	5243.97	−	6173.68i	0.276602	−	0.325641i
$712$	20595.9	+	4533.51i	1.08408	+	0.238624i
$713$	6170.88	+	4690.98i	0.324125	+	0.246394i
$714$	101.700	−	96.3355i	0.00533058	−	0.00504939i
$715$	51.3797	−	128.953i	0.00268740	−	0.00674486i
$716$	5868.81	+	1977.43i	0.306324	+	0.103212i
$717$	746.725	+	4554.82i	0.0388939	+	0.237243i
$718$	10425.3	+	9875.33i	0.541876	+	0.513292i
$719$	15882.9	−	7348.21i	0.823828	−	0.381143i	0.0377627	−	0.999287i	$-0.487977\pi$
$719$	15882.9	−	7348.21i	0.823828	−	0.381143i	0.786065	+	0.618143i	$0.212115\pi$
$720$	98.2347	−	74.6760i	0.00508471	−	0.00386529i
$721$	−4.31369	+	26.3123i	−0.000222816	+	0.00135912i
$722$	−5191.40	+	9792.02i	−0.267595	+	0.504739i
$723$	−1267.74	+	279.050i	−0.0652112	+	0.0143541i
$724$	8470.89	+	3919.05i	0.434831	+	0.201174i
$725$	11598.6	+	29110.3i	0.594153	+	1.49121i
$726$	−209.510	−	3864.18i	−0.0107103	−	0.197539i
$727$	−16485.4	−	24314.2i	−0.841004	−	1.24039i	−0.968615	−	0.248564i	$-0.920041\pi$
$727$	−16485.4	−	24314.2i	−0.841004	−	1.24039i	0.127611	−	0.991824i	$-0.459269\pi$
$728$	−4.02549	−	4.73918i	−0.000204938	−	0.000241271i
$729$	341.470	+	644.080i	0.0173485	+	0.0327227i
$730$	3862.85	−	1301.54i	0.195850	−	0.0659895i
$731$	−3062.97	+	56493.2i	−0.154977	+	2.85838i
$732$	−5355.48	+	3222.29i	−0.270416	+	0.162704i
$733$	−7778.04	−	28014.0i	−0.391935	−	1.41162i	−0.851909	−	0.523690i	$-0.824555\pi$
$733$	−7778.04	−	28014.0i	−0.391935	−	1.41162i	0.459974	−	0.887933i	$-0.347859\pi$
$734$	−98.5510	+	354.949i	−0.00495583	+	0.0178493i
$735$	3871.64	+	2329.49i	0.194296	+	0.116904i
$736$	5190.32	−	7655.15i	0.259943	−	0.383387i
$737$	11350.9	−	1234.49i	0.567322	−	0.0616999i
$738$	6546.02	−	711.922i	0.326507	−	0.0355098i
$739$	−16037.1	+	23653.0i	−0.798289	+	1.17739i	0.182670	+	0.983174i	$0.441526\pi$
$739$	−16037.1	+	23653.0i	−0.798289	+	1.17739i	−0.980959	+	0.194214i	$0.937784\pi$
$740$	−7287.67	−	4384.84i	−0.362027	−	0.217824i
$741$	−19.3247	+	69.6012i	−0.000958042	+	0.00345056i
$742$	−39.4938	−	142.244i	−0.00195399	−	0.00703765i
$743$	30944.0	−	18618.4i	1.52790	−	0.919304i	0.530461	−	0.847709i	$-0.322019\pi$
$743$	30944.0	−	18618.4i	1.52790	−	0.919304i	0.997434	−	0.0715947i	$-0.0228088\pi$
$744$	556.228	−	10259.0i	0.0274090	−	0.505530i
$745$	−271.133	+	91.3552i	−0.0133336	+	0.00449261i
$746$	−5241.98	−	9887.43i	−0.257269	−	0.485261i
$747$	2338.07	+	2752.59i	0.114519	+	0.134822i
$748$	8940.95	+	13186.9i	0.437050	+	0.644600i
$749$	7.32805	+	135.158i	0.000357492	+	0.00659354i
$750$	1910.28	+	4794.45i	0.0930050	+	0.233425i
$751$	−32722.8	−	15139.2i	−1.58998	−	0.735602i	−0.592432	−	0.805621i	$-0.701832\pi$
$751$	−32722.8	−	15139.2i	−1.58998	−	0.735602i	−0.997546	+	0.0700187i	$0.977694\pi$
$752$	1068.08	−	235.101i	0.0517935	−	0.0114006i
$753$	1534.80	−	2894.94i	0.0742780	−	0.140103i
$754$	107.680	−	656.819i	0.00520090	−	0.0317241i
$755$	−3109.91	+	2364.09i	−0.149909	+	0.113958i
$756$	26.4725	−	12.2475i	0.00127354	−	0.000589203i
$757$	−149.229	−	141.357i	−0.00716487	−	0.00678692i	0.684109	−	0.729380i	$-0.260191\pi$
$757$	−149.229	−	141.357i	−0.00716487	−	0.00678692i	−0.691274	+	0.722593i	$0.742950\pi$
$758$	808.610	+	4932.30i	0.0387468	+	0.236345i
$759$	3425.33	+	1154.13i	0.163810	+	0.0551940i
$760$	659.148	−	1654.34i	0.0314603	−	0.0789593i
$761$	2483.62	−	2352.61i	0.118306	−	0.112066i	−0.626260	−	0.779614i	$-0.715415\pi$
$761$	2483.62	−	2352.61i	0.118306	−	0.112066i	0.744566	+	0.667549i	$0.232656\pi$
$762$	10322.6	+	7847.03i	0.490746	+	0.373055i
$763$	−374.970	−	82.5371i	−0.0177914	−	0.00391618i
$764$	12151.9	−	14306.4i	0.575447	−	0.677469i
$765$	−5118.55	−	556.675i	−0.241910	−	0.0263093i
$766$	−19351.1			−0.912772
$767$	−529.683	+	280.394i	−0.0249358	+	0.0132000i
$768$	−11875.3			−0.557962
$769$	−2107.94	−	229.253i	−0.0988483	−	0.0107504i	0.0585611	−	0.998284i	$-0.481349\pi$
$769$	−2107.94	−	229.253i	−0.0988483	−	0.0107504i	−0.157409	+	0.987533i	$0.550314\pi$
$770$	−24.3582	+	28.6767i	−0.00114001	+	0.00134213i

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68795 - 0.183576i) q^{2} +(1.94216 - 2.28649i) q^{3} +(-4.99749 - 1.10003i) q^{4} +(3.49616 + 2.65771i) q^{5} +(-3.69801 + 3.50294i) q^{6} +(0.0781424 - 0.196123i) q^{7} +(21.1058 + 7.11136i) q^{8} +(-1.45604 - 8.88144i) q^{9} +O(q^{10})\)	\(q+(-1.68795 - 0.183576i) q^{2} +(1.94216 - 2.28649i) q^{3} +(-4.99749 - 1.10003i) q^{4} +(3.49616 + 2.65771i) q^{5} +(-3.69801 + 3.50294i) q^{6} +(0.0781424 - 0.196123i) q^{7} +(21.1058 + 7.11136i) q^{8} +(-1.45604 - 8.88144i) q^{9} +(-5.41345 - 5.12789i) q^{10} +(21.6921 - 10.0358i) q^{11} +(-12.2211 + 9.29026i) q^{12} +(0.213949 - 1.30503i) q^{13} +(-0.167904 + 0.316700i) q^{14} +(12.8669 - 2.83222i) q^{15} +(2.83344 + 1.31089i) q^{16} +(-48.2163 - 121.014i) q^{17} +(0.827303 + 15.2587i) q^{18} +(-10.2176 - 15.0698i) q^{19} +(-14.5485 - 17.1278i) q^{20} +(-0.296667 - 0.559573i) q^{21} +(-38.4576 + 12.9579i) q^{22} +(-2.72912 + 50.3356i) q^{23} +(57.2508 - 34.4466i) q^{24} +(-28.2813 - 101.860i) q^{25} +(-0.600708 + 2.16355i) q^{26} +(-23.1351 - 13.9200i) q^{27} +(-0.606257 + 0.894163i) q^{28} +(-294.685 + 32.0489i) q^{29} +(-22.2386 + 2.41860i) q^{30} +(86.2936 - 127.273i) q^{31} +(-157.211 - 94.5906i) q^{32} +(19.1827 - 69.0900i) q^{33} +(59.1715 + 213.117i) q^{34} +(0.794436 - 0.477996i) q^{35} +(-2.49332 + 45.9866i) q^{36} +(358.654 - 120.845i) q^{37} +(14.4803 + 27.3127i) q^{38} +(-2.56842 - 3.02377i) q^{39} +(54.8891 + 80.9554i) q^{40} +(-23.3284 - 430.267i) q^{41} +(0.398035 + 0.998992i) q^{42} +(-394.172 - 182.363i) q^{43} +(-119.446 + 26.2920i) q^{44} +(18.5137 - 34.9206i) q^{45} +(13.8470 - 84.4630i) q^{46} +(278.874 - 211.995i) q^{47} +(8.50032 - 3.93267i) q^{48} +(248.984 + 235.850i) q^{49} +(29.0384 + 177.127i) q^{50} +(-370.340 - 124.782i) q^{51} +(-2.50479 + 6.28654i) q^{52} +(-298.990 + 283.219i) q^{53} +(36.4956 + 27.7432i) q^{54} +(102.511 + 22.5645i) q^{55} +(3.04395 - 3.58362i) q^{56} +(-54.3010 - 5.90559i) q^{57} +503.297 q^{58} +(-274.031 - 360.952i) q^{59} -67.4178 q^{60} +(404.753 + 44.0195i) q^{61} +(-169.024 + 198.990i) q^{62} +(-1.85563 - 0.408455i) q^{63} +(228.116 + 173.409i) q^{64} +(4.21640 - 3.99399i) q^{65} +(-45.0627 + 113.099i) q^{66} +(452.704 + 152.534i) q^{67} +(107.842 + 657.805i) q^{68} +(109.791 + 104.000i) q^{69} +(-1.42872 + 0.660994i) q^{70} +(107.998 - 82.0977i) q^{71} +(32.4283 - 197.804i) q^{72} +(-256.061 + 482.982i) q^{73} +(-627.575 + 138.140i) q^{74} +(-287.829 - 133.164i) q^{75} +(34.4850 + 86.5508i) q^{76} +(-0.273182 - 5.03855i) q^{77} +(3.78027 + 5.57548i) q^{78} +(582.663 + 685.964i) q^{79} +(6.42219 + 12.1135i) q^{80} +(-76.7599 + 25.8634i) q^{81} +(-39.6093 + 730.551i) q^{82} +(-343.843 + 206.884i) q^{83} +(0.867042 + 3.12280i) q^{84} +(153.048 - 551.228i) q^{85} +(631.865 + 380.181i) q^{86} +(-499.046 + 736.037i) q^{87} +(529.197 - 57.5537i) q^{88} +(941.349 - 102.378i) q^{89} +(-37.6609 + 55.5456i) q^{90} +(-0.239228 - 0.143939i) q^{91} +(69.0095 - 248.550i) q^{92} +(-123.413 - 444.494i) q^{93} +(-509.643 + 306.642i) q^{94} +(4.32889 - 79.8417i) q^{95} +(-521.608 + 175.750i) q^{96} +(523.064 + 986.603i) q^{97} +(-376.976 - 443.811i) q^{98} +(-120.717 - 178.045i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420q + 2q^{2} - 45q^{3} - 56q^{4} - 14q^{5} + 6q^{6} + 6q^{7} + 66q^{8} - 135q^{9} + O(q^{10}) \)	\( 420q + 2q^{2} - 45q^{3} - 56q^{4} - 14q^{5} + 6q^{6} + 6q^{7} + 66q^{8} - 135q^{9} - 754q^{10} + 64q^{11} - 168q^{12} + 90q^{13} + 1024q^{14} - 42q^{15} - 172q^{16} + 96q^{17} + 18q^{18} + 16q^{19} - 178q^{20} - 243q^{21} - 604q^{22} + 48q^{23} + 198q^{24} - 173q^{25} + 156q^{26} - 405q^{27} + 84q^{28} - 50q^{29} + 174q^{30} + 222q^{31} - 45q^{32} + 192q^{33} - 64q^{34} - 132q^{35} - 504q^{36} + 30q^{37} - 108q^{38} + 270q^{39} + 6984q^{40} + 400q^{41} + 114q^{42} + 1220q^{43} + 1180q^{44} - 126q^{45} + 4938q^{46} + 370q^{47} - 516q^{48} + 771q^{49} + 1048q^{50} + 288q^{51} - 1964q^{52} - 822q^{53} + 54q^{54} - 2342q^{55} - 13824q^{56} + 48q^{57} - 13150q^{58} - 3423q^{59} - 534q^{60} - 2182q^{61} + 845q^{62} + 54q^{63} - 8018q^{64} + 4140q^{65} - 1812q^{66} + 506q^{67} + 4826q^{68} - 3684q^{69} + 6882q^{70} + 5874q^{71} + 594q^{72} + 206q^{73} + 11124q^{74} - 867q^{75} + 16940q^{76} + 9940q^{77} + 468q^{78} - 1762q^{79} - 28954q^{80} - 1215q^{81} + 3770q^{82} - 1216q^{83} - 8013q^{84} - 420q^{85} - 2256q^{86} + 5940q^{87} + 13458q^{88} - 1580q^{89} + 522q^{90} - 12204q^{91} + 4562q^{92} + 666q^{93} + 176q^{94} - 28456q^{95} + 2040q^{96} + 2574q^{97} + 50690q^{98} + 576q^{99} + O(q^{100}) \)

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