LMFDB - Embedded newform 74.5.d.a.31.2

Newspace parameters

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	74.d (of order $4$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.64937726820$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
Defining polynomial:	$ x^{14} + 727 x^{12} + 198453 x^{10} + 24875201 x^{8} + 1392846203 x^{6} + 29089700589 x^{4} + 220261242916 x^{2} + 446074380544 $ x^14 + 727x^12 + 198453x^10 + 24875201x^8 + 1392846203x^6 + 29089700589x^4 + 220261242916x^2 + 446074380544
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.2
Root			$-9.51876i$ of defining polynomial
Character	$\chi$	$=$	74.31
Dual form			74.5.d.a.43.6

$q$-expansion

$f(q)$	$=$	$q+(-2.00000 - 2.00000i) q^{2} -10.5188i q^{3} +8.00000i q^{4} +(30.2483 - 30.2483i) q^{5} +(-21.0375 + 21.0375i) q^{6} +69.0478 q^{7} +(16.0000 - 16.0000i) q^{8} -29.6443 q^{9} +O(q^{10})$	\(q+(-2.00000 - 2.00000i) q^{2} -10.5188i q^{3} +8.00000i q^{4} +(30.2483 - 30.2483i) q^{5} +(-21.0375 + 21.0375i) q^{6} +69.0478 q^{7} +(16.0000 - 16.0000i) q^{8} -29.6443 q^{9} -120.993 q^{10} +10.9953i q^{11} +84.1501 q^{12} +(80.0125 - 80.0125i) q^{13} +(-138.096 - 138.096i) q^{14} +(-318.174 - 318.174i) q^{15} -64.0000 q^{16} +(-345.037 + 345.037i) q^{17} +(59.2886 + 59.2886i) q^{18} +(121.486 - 121.486i) q^{19} +(241.986 + 241.986i) q^{20} -726.297i q^{21} +(21.9906 - 21.9906i) q^{22} +(-590.441 + 590.441i) q^{23} +(-168.300 - 168.300i) q^{24} -1204.92i q^{25} -320.050 q^{26} -540.198i q^{27} +552.382i q^{28} +(49.9544 + 49.9544i) q^{29} +1272.70i q^{30} +(947.769 + 947.769i) q^{31} +(128.000 + 128.000i) q^{32} +115.657 q^{33} +1380.15 q^{34} +(2088.58 - 2088.58i) q^{35} -237.155i q^{36} +(-917.114 + 1016.40i) q^{37} -485.944 q^{38} +(-841.632 - 841.632i) q^{39} -967.945i q^{40} +3127.67i q^{41} +(-1452.59 + 1452.59i) q^{42} +(522.294 - 522.294i) q^{43} -87.9624 q^{44} +(-896.689 + 896.689i) q^{45} +2361.76 q^{46} +315.367 q^{47} +673.201i q^{48} +2366.59 q^{49} +(-2409.83 + 2409.83i) q^{50} +(3629.36 + 3629.36i) q^{51} +(640.100 + 640.100i) q^{52} -3942.78 q^{53} +(-1080.40 + 1080.40i) q^{54} +(332.589 + 332.589i) q^{55} +(1104.76 - 1104.76i) q^{56} +(-1277.88 - 1277.88i) q^{57} -199.818i q^{58} +(3550.97 - 3550.97i) q^{59} +(2545.39 - 2545.39i) q^{60} +(-519.449 - 519.449i) q^{61} -3791.08i q^{62} -2046.87 q^{63} -512.000i q^{64} -4840.48i q^{65} +(-231.314 - 231.314i) q^{66} -3736.40i q^{67} +(-2760.30 - 2760.30i) q^{68} +(6210.71 + 6210.71i) q^{69} -8354.30 q^{70} -1195.01 q^{71} +(-474.309 + 474.309i) q^{72} -1212.04i q^{73} +(3867.02 - 198.567i) q^{74} -12674.2 q^{75} +(971.887 + 971.887i) q^{76} +759.201i q^{77} +3366.53i q^{78} +(-1838.99 + 1838.99i) q^{79} +(-1935.89 + 1935.89i) q^{80} -8083.40 q^{81} +(6255.34 - 6255.34i) q^{82} -1530.34 q^{83} +5810.37 q^{84} +20873.6i q^{85} -2089.17 q^{86} +(525.459 - 525.459i) q^{87} +(175.925 + 175.925i) q^{88} +(-5115.00 - 5115.00i) q^{89} +3586.76 q^{90} +(5524.68 - 5524.68i) q^{91} +(-4723.53 - 4723.53i) q^{92} +(9969.36 - 9969.36i) q^{93} +(-630.735 - 630.735i) q^{94} -7349.48i q^{95} +(1346.40 - 1346.40i) q^{96} +(-4016.43 + 4016.43i) q^{97} +(-4733.19 - 4733.19i) q^{98} -325.948i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9}+O(q^{10}) $ 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98}+O(q^{100}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9 + 48 * q^10 + 160 * q^12 - 56 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 - 348 * q^17 + 692 * q^18 - 184 * q^19 - 96 * q^20 - 320 * q^22 - 502 * q^23 - 320 * q^24 + 224 * q^26 - 474 * q^29 - 630 * q^31 + 1792 * q^32 + 632 * q^33 + 1392 * q^34 + 1826 * q^35 - 2544 * q^37 + 736 * q^38 - 798 * q^39 - 224 * q^42 + 1936 * q^43 + 1280 * q^44 + 6162 * q^45 + 2008 * q^46 + 5716 * q^47 + 7862 * q^49 - 1372 * q^50 - 2422 * q^51 - 448 * q^52 - 20228 * q^53 - 656 * q^54 + 14006 * q^55 + 768 * q^56 - 2270 * q^57 - 4502 * q^59 + 3024 * q^60 - 11906 * q^61 - 2588 * q^63 - 1264 * q^66 - 2784 * q^68 + 21440 * q^69 - 7304 * q^70 - 11224 * q^71 - 5536 * q^72 + 4924 * q^74 - 18652 * q^75 - 1472 * q^76 + 20488 * q^79 + 768 * q^80 - 1706 * q^81 + 9808 * q^82 - 20224 * q^83 + 896 * q^84 - 7744 * q^86 + 19636 * q^87 - 2560 * q^88 + 13864 * q^89 - 24648 * q^90 - 6070 * q^91 - 4016 * q^92 - 13800 * q^93 - 11432 * q^94 + 2560 * q^96 + 16622 * q^97 - 15724 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$3$		−	10.5188i		−	1.16875i	−0.811483	−	0.584376i	$-0.801340\pi$
$3$		−	10.5188i		−	1.16875i	0.811483	−	0.584376i	$-0.198660\pi$
$4$			8.00000i			0.500000i
$5$	30.2483	−	30.2483i	1.20993	−	1.20993i	0.238882	−	0.971049i	$-0.423219\pi$
$5$	30.2483	−	30.2483i	1.20993	−	1.20993i	0.971049	−	0.238882i	$-0.0767810\pi$
$6$	−21.0375	+	21.0375i	−0.584376	+	0.584376i
$7$	69.0478			1.40914			0.704569	−	0.709636i	$-0.251140\pi$
$7$	69.0478			1.40914			0.704569	+	0.709636i	$0.251140\pi$
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$	−29.6443			−0.365979
$10$	−120.993			−1.20993
$11$			10.9953i			0.0908702i	0.998967	+	0.0454351i	$0.0144674\pi$
$11$			10.9953i			0.0908702i	−0.998967	+	0.0454351i	$0.985533\pi$
$12$	84.1501			0.584376
$13$	80.0125	−	80.0125i	0.473447	−	0.473447i	−0.429582	−	0.903028i	$-0.641339\pi$
$13$	80.0125	−	80.0125i	0.473447	−	0.473447i	0.903028	+	0.429582i	$0.141339\pi$
$14$	−138.096	−	138.096i	−0.704569	−	0.704569i
$15$	−318.174	−	318.174i	−1.41411	−	1.41411i
$16$	−64.0000			−0.250000
$17$	−345.037	+	345.037i	−1.19390	+	1.19390i	−0.217938	+	0.975963i	$0.569933\pi$
$17$	−345.037	+	345.037i	−1.19390	+	1.19390i	−0.975963	+	0.217938i	$0.930067\pi$
$18$	59.2886	+	59.2886i	0.182990	+	0.182990i
$19$	121.486	−	121.486i	0.336526	−	0.336526i	−0.518532	−	0.855058i	$-0.673521\pi$
$19$	121.486	−	121.486i	0.336526	−	0.336526i	0.855058	+	0.518532i	$0.173521\pi$
$20$	241.986	+	241.986i	0.604965	+	0.604965i
$21$		−	726.297i		−	1.64693i
$22$	21.9906	−	21.9906i	0.0454351	−	0.0454351i
$23$	−590.441	+	590.441i	−1.11615	+	1.11615i	−0.123844	+	0.992302i	$0.539522\pi$
$23$	−590.441	+	590.441i	−1.11615	+	1.11615i	−0.992302	+	0.123844i	$0.960478\pi$
$24$	−168.300	−	168.300i	−0.292188	−	0.292188i
$25$		−	1204.92i		−	1.92786i
$26$	−320.050			−0.473447
$27$		−	540.198i		−	0.741012i
$28$			552.382i			0.704569i
$29$	49.9544	+	49.9544i	0.0593989	+	0.0593989i	0.736182	−	0.676783i	$-0.236627\pi$
$29$	49.9544	+	49.9544i	0.0593989	+	0.0593989i	−0.676783	+	0.736182i	$0.736627\pi$
$30$			1272.70i			1.41411i
$31$	947.769	+	947.769i	0.986232	+	0.986232i	0.999907	−	0.0136744i	$-0.00435284\pi$
$31$	947.769	+	947.769i	0.986232	+	0.986232i	−0.0136744	+	0.999907i	$0.504353\pi$
$32$	128.000	+	128.000i	0.125000	+	0.125000i
$33$	115.657			0.106205
$34$	1380.15			1.19390
$35$	2088.58	−	2088.58i	1.70496	−	1.70496i
$36$		−	237.155i		−	0.182990i
$37$	−917.114	+	1016.40i	−0.669915	+	0.742438i
$37$	−917.114	+	1016.40i	−0.669915	+	0.742438i
$38$	−485.944			−0.336526
$39$	−841.632	−	841.632i	−0.553341	−	0.553341i
$40$		−	967.945i		−	0.604965i
$41$			3127.67i			1.86060i	0.366799	+	0.930300i	$0.380454\pi$
$41$			3127.67i			1.86060i	−0.366799	+	0.930300i	$0.619546\pi$
$42$	−1452.59	+	1452.59i	−0.823466	+	0.823466i
$43$	522.294	−	522.294i	0.282474	−	0.282474i	−0.551621	−	0.834095i	$-0.685991\pi$
$43$	522.294	−	522.294i	0.282474	−	0.282474i	0.834095	+	0.551621i	$0.185991\pi$
$44$	−87.9624			−0.0454351
$45$	−896.689	+	896.689i	−0.442810	+	0.442810i
$46$	2361.76			1.11615
$47$	315.367			0.142765			0.0713824	−	0.997449i	$-0.477259\pi$
$47$	315.367			0.142765			0.0713824	+	0.997449i	$0.477259\pi$
$48$			673.201i			0.292188i
$49$	2366.59			0.985670
$50$	−2409.83	+	2409.83i	−0.963932	+	0.963932i
$51$	3629.36	+	3629.36i	1.39537	+	1.39537i
$52$	640.100	+	640.100i	0.236723	+	0.236723i
$53$	−3942.78			−1.40362			−0.701811	−	0.712363i	$-0.747625\pi$
$53$	−3942.78			−1.40362			−0.701811	+	0.712363i	$0.747625\pi$
$54$	−1080.40	+	1080.40i	−0.370506	+	0.370506i
$55$	332.589	+	332.589i	0.109947	+	0.109947i
$56$	1104.76	−	1104.76i	0.352284	−	0.352284i
$57$	−1277.88	−	1277.88i	−0.393315	−	0.393315i
$58$		−	199.818i		−	0.0593989i
$59$	3550.97	−	3550.97i	1.02010	−	1.02010i	0.0203075	−	0.999794i	$-0.493535\pi$
$59$	3550.97	−	3550.97i	1.02010	−	1.02010i	0.999794	−	0.0203075i	$-0.00646453\pi$
$60$	2545.39	−	2545.39i	0.707054	−	0.707054i
$61$	−519.449	−	519.449i	−0.139599	−	0.139599i	0.633854	−	0.773453i	$-0.281472\pi$
$61$	−519.449	−	519.449i	−0.139599	−	0.139599i	−0.773453	+	0.633854i	$0.781472\pi$
$62$		−	3791.08i		−	0.986232i
$63$	−2046.87			−0.515715
$64$		−	512.000i		−	0.125000i
$65$		−	4840.48i		−	1.14568i
$66$	−231.314	−	231.314i	−0.0531023	−	0.0531023i
$67$		−	3736.40i		−	0.832345i	−0.909286	−	0.416173i	$-0.863371\pi$
$67$		−	3736.40i		−	0.832345i	0.909286	−	0.416173i	$-0.136629\pi$
$68$	−2760.30	−	2760.30i	−0.596950	−	0.596950i
$69$	6210.71	+	6210.71i	1.30450	+	1.30450i
$70$	−8354.30			−1.70496
$71$	−1195.01			−0.237058			−0.118529	−	0.992951i	$-0.537818\pi$
$71$	−1195.01			−0.237058			−0.118529	+	0.992951i	$0.537818\pi$
$72$	−474.309	+	474.309i	−0.0914948	+	0.0914948i
$73$		−	1212.04i		−	0.227442i	−0.993513	−	0.113721i	$-0.963723\pi$
$73$		−	1212.04i		−	0.227442i	0.993513	−	0.113721i	$-0.0362770\pi$
$74$	3867.02	−	198.567i	0.706176	−	0.0362614i
$75$	−12674.2			−2.25319
$76$	971.887	+	971.887i	0.168263	+	0.168263i
$77$			759.201i			0.128049i
$78$			3366.53i			0.553341i
$79$	−1838.99	+	1838.99i	−0.294663	+	0.294663i	−0.838919	−	0.544256i	$-0.816812\pi$
$79$	−1838.99	+	1838.99i	−0.294663	+	0.294663i	0.544256	+	0.838919i	$0.316812\pi$
$80$	−1935.89	+	1935.89i	−0.302483	+	0.302483i
$81$	−8083.40			−1.23204
$82$	6255.34	−	6255.34i	0.930300	−	0.930300i
$83$	−1530.34			−0.222143			−0.111071	−	0.993812i	$-0.535428\pi$
$83$	−1530.34			−0.222143			−0.111071	+	0.993812i	$0.535428\pi$
$84$	5810.37			0.823466
$85$			20873.6i			2.88907i
$86$	−2089.17			−0.282474
$87$	525.459	−	525.459i	0.0694225	−	0.0694225i
$88$	175.925	+	175.925i	0.0227176	+	0.0227176i
$89$	−5115.00	−	5115.00i	−0.645752	−	0.645752i	0.306212	−	0.951963i	$-0.400938\pi$
$89$	−5115.00	−	5115.00i	−0.645752	−	0.645752i	−0.951963	+	0.306212i	$0.900938\pi$
$90$	3586.76			0.442810
$91$	5524.68	−	5524.68i	0.667151	−	0.667151i
$92$	−4723.53	−	4723.53i	−0.558073	−	0.558073i
$93$	9969.36	−	9969.36i	1.15266	−	1.15266i
$94$	−630.735	−	630.735i	−0.0713824	−	0.0713824i
$95$		−	7349.48i		−	0.814346i
$96$	1346.40	−	1346.40i	0.146094	−	0.146094i
$97$	−4016.43	+	4016.43i	−0.426871	+	0.426871i	−0.887561	−	0.460690i	$-0.847602\pi$
$97$	−4016.43	+	4016.43i	−0.426871	+	0.426871i	0.460690	+	0.887561i	$0.347602\pi$
$98$	−4733.19	−	4733.19i	−0.492835	−	0.492835i
$99$		−	325.948i		−	0.0332566i
$100$	9639.32			0.963932
$101$		−	1115.89i		−	0.109390i	−0.998503	−	0.0546952i	$-0.982581\pi$
$101$		−	1115.89i		−	0.109390i	0.998503	−	0.0546952i	$-0.0174187\pi$
$102$		−	14517.5i		−	1.39537i
$103$	12833.7	+	12833.7i	1.20970	+	1.20970i	0.971123	+	0.238578i	$0.0766813\pi$
$103$	12833.7	+	12833.7i	1.20970	+	1.20970i	0.238578	+	0.971123i	$0.423319\pi$
$104$		−	2560.40i		−	0.236723i
$105$	−21969.2	−	21969.2i	−1.99267	−	1.99267i
$106$	7885.55	+	7885.55i	0.701811	+	0.701811i
$107$	11472.8			1.00208			0.501038	−	0.865425i	$-0.332952\pi$
$107$	11472.8			1.00208			0.501038	+	0.865425i	$0.332952\pi$
$108$	4321.58			0.370506
$109$	528.108	−	528.108i	0.0444498	−	0.0444498i	−0.684533	−	0.728982i	$-0.739994\pi$
$109$	528.108	−	528.108i	0.0444498	−	0.0444498i	0.728982	+	0.684533i	$0.239994\pi$
$110$		−	1330.35i		−	0.109947i
$111$	10691.2	+	9646.90i	0.867725	+	0.782964i
$112$	−4419.06			−0.352284
$113$	3930.94	+	3930.94i	0.307850	+	0.307850i	0.844075	−	0.536225i	$-0.180150\pi$
$113$	3930.94	+	3930.94i	0.307850	+	0.307850i	−0.536225	+	0.844075i	$0.680150\pi$
$114$			5111.52i			0.393315i
$115$			35719.6i			2.70092i
$116$	−399.636	+	399.636i	−0.0296994	+	0.0296994i
$117$	−2371.92	+	2371.92i	−0.173272	+	0.173272i
$118$	−14203.9			−1.02010
$119$	−23824.0	+	23824.0i	−1.68237	+	1.68237i
$120$	−10181.6			−0.707054
$121$	14520.1			0.991743
$122$			2077.80i			0.139599i
$123$	32899.2			2.17458
$124$	−7582.15	+	7582.15i	−0.493116	+	0.493116i
$125$	−17541.4	−	17541.4i	−1.12265	−	1.12265i
$126$	4093.75	+	4093.75i	0.257858	+	0.257858i
$127$	15432.9			0.956842			0.478421	−	0.878131i	$-0.341209\pi$
$127$	15432.9			0.956842			0.478421	+	0.878131i	$0.341209\pi$
$128$	−1024.00	+	1024.00i	−0.0625000	+	0.0625000i
$129$	−5493.88	−	5493.88i	−0.330141	−	0.330141i
$130$	−9680.95	+	9680.95i	−0.572838	+	0.572838i
$131$	13940.0	+	13940.0i	0.812306	+	0.812306i	0.984979	−	0.172673i	$-0.0552404\pi$
$131$	13940.0	+	13940.0i	0.812306	+	0.812306i	−0.172673	+	0.984979i	$0.555240\pi$
$132$			925.255i			0.0531023i
$133$	8388.33	−	8388.33i	0.474212	−	0.474212i
$134$	−7472.79	+	7472.79i	−0.416173	+	0.416173i
$135$	−16340.1	−	16340.1i	−0.896574	−	0.896574i
$136$			11041.2i			0.596950i
$137$	−33823.3			−1.80208			−0.901042	−	0.433731i	$-0.857197\pi$
$137$	−33823.3			−1.80208			−0.901042	+	0.433731i	$0.857197\pi$
$138$		−	24842.8i		−	1.30450i
$139$		−	16424.1i		−	0.850066i	−0.905178	−	0.425033i	$-0.860263\pi$
$139$		−	16424.1i		−	0.850066i	0.905178	−	0.425033i	$-0.139737\pi$
$140$	16708.6	+	16708.6i	0.852480	+	0.852480i
$141$		−	3317.27i		−	0.166856i
$142$	2390.02	+	2390.02i	0.118529	+	0.118529i
$143$	879.761	+	879.761i	0.0430222	+	0.0430222i
$144$	1897.24			0.0914948
$145$	3022.07			0.143737
$146$	−2424.08	+	2424.08i	−0.113721	+	0.113721i
$147$		−	24893.6i		−	1.15200i
$148$	−8131.18	−	7336.91i	−0.371219	−	0.334958i
$149$	21406.1			0.964197			0.482099	−	0.876117i	$-0.339875\pi$
$149$	21406.1			0.964197			0.482099	+	0.876117i	$0.339875\pi$
$150$	25348.4	+	25348.4i	1.12660	+	1.12660i
$151$		−	11689.7i		−	0.512685i	−0.966586	−	0.256342i	$-0.917483\pi$
$151$		−	11689.7i		−	0.512685i	0.966586	−	0.256342i	$-0.0825175\pi$
$152$		−	3887.55i		−	0.168263i
$153$	10228.4	−	10228.4i	0.436943	−	0.436943i
$154$	1518.40	−	1518.40i	0.0640243	−	0.0640243i
$155$	57336.7			2.38655
$156$	6733.06	−	6733.06i	0.276671	−	0.276671i
$157$	−24556.9			−0.996265			−0.498132	−	0.867101i	$-0.665981\pi$
$157$	−24556.9			−0.996265			−0.498132	+	0.867101i	$0.665981\pi$
$158$	7355.96			0.294663
$159$			41473.1i			1.64049i
$160$	7743.56			0.302483
$161$	−40768.6	+	40768.6i	−1.57280	+	1.57280i
$162$	16166.8	+	16166.8i	0.616019	+	0.616019i
$163$	−9561.68	−	9561.68i	−0.359881	−	0.359881i	0.503888	−	0.863769i	$-0.331902\pi$
$163$	−9561.68	−	9561.68i	−0.359881	−	0.359881i	−0.863769	+	0.503888i	$0.831902\pi$
$164$	−25021.4			−0.930300
$165$	3498.42	−	3498.42i	0.128500	−	0.128500i
$166$	3060.68	+	3060.68i	0.111071	+	0.111071i
$167$	−14826.8	+	14826.8i	−0.531635	+	0.531635i	−0.921059	−	0.389423i	$-0.872674\pi$
$167$	−14826.8	+	14826.8i	−0.531635	+	0.531635i	0.389423	+	0.921059i	$0.372674\pi$
$168$	−11620.7	−	11620.7i	−0.411733	−	0.411733i
$169$			15757.0i			0.551697i
$170$	41747.1	−	41747.1i	1.44454	−	1.44454i
$171$	−3601.37	+	3601.37i	−0.123162	+	0.123162i
$172$	4178.35	+	4178.35i	0.141237	+	0.141237i
$173$		−	52583.7i		−	1.75695i	−0.477791	−	0.878473i	$-0.658562\pi$
$173$		−	52583.7i		−	1.75695i	0.477791	−	0.878473i	$-0.341438\pi$
$174$	−2101.84			−0.0694225
$175$		−	83196.7i		−	2.71663i
$176$		−	703.699i		−	0.0227176i
$177$	−37351.8	−	37351.8i	−1.19224	−	1.19224i
$178$			20460.0i			0.645752i
$179$	−6643.45	−	6643.45i	−0.207342	−	0.207342i	0.595795	−	0.803137i	$-0.296837\pi$
$179$	−6643.45	−	6643.45i	−0.207342	−	0.207342i	−0.803137	+	0.595795i	$0.796837\pi$
$180$	−7173.51	−	7173.51i	−0.221405	−	0.221405i
$181$	−5056.88			−0.154357			−0.0771783	−	0.997017i	$-0.524591\pi$
$181$	−5056.88			−0.154357			−0.0771783	+	0.997017i	$0.524591\pi$
$182$	−22098.7			−0.667151
$183$	−5463.96	+	5463.96i	−0.163157	+	0.163157i
$184$			18894.1i			0.558073i
$185$	3003.16	+	58485.4i	0.0877475	+	1.70885i
$186$	−39877.4			−1.15266
$187$	−3793.79	−	3793.79i	−0.108490	−	0.108490i
$188$			2522.94i			0.0713824i
$189$		−	37299.5i		−	1.04419i
$190$	−14699.0	+	14699.0i	−0.407173	+	0.407173i
$191$	38695.9	−	38695.9i	1.06071	−	1.06071i	0.0626796	−	0.998034i	$-0.480035\pi$
$191$	38695.9	−	38695.9i	1.06071	−	1.06071i	0.998034	−	0.0626796i	$-0.0199646\pi$
$192$	−5385.61			−0.146094
$193$	42591.4	−	42591.4i	1.14342	−	1.14342i	0.155605	−	0.987819i	$-0.450267\pi$
$193$	42591.4	−	42591.4i	1.14342	−	1.14342i	0.987819	−	0.155605i	$-0.0497326\pi$
$194$	16065.7			0.426871
$195$	−50915.8			−1.33901
$196$			18932.7i			0.492835i
$197$	−38271.7			−0.986154			−0.493077	−	0.869986i	$-0.664128\pi$
$197$	−38271.7			−0.986154			−0.493077	+	0.869986i	$0.664128\pi$
$198$	−651.896	+	651.896i	−0.0166283	+	0.0166283i
$199$	−2855.95	−	2855.95i	−0.0721181	−	0.0721181i	0.670128	−	0.742246i	$-0.266239\pi$
$199$	−2855.95	−	2855.95i	−0.0721181	−	0.0721181i	−0.742246	+	0.670128i	$0.766239\pi$
$200$	−19278.6	−	19278.6i	−0.481966	−	0.481966i
$201$	−39302.3			−0.972804
$202$	−2231.78	+	2231.78i	−0.0546952	+	0.0546952i
$203$	3449.24	+	3449.24i	0.0837012	+	0.0837012i
$204$	−29034.9	+	29034.9i	−0.697686	+	0.697686i
$205$	94606.6	+	94606.6i	2.25120	+	2.25120i
$206$		−	51334.9i		−	1.20970i
$207$	17503.2	−	17503.2i	0.408486	−	0.408486i
$208$	−5120.80	+	5120.80i	−0.118362	+	0.118362i
$209$	1335.77	+	1335.77i	0.0305802	+	0.0305802i
$210$			87876.9i			1.99267i
$211$	−70101.5			−1.57457			−0.787285	−	0.616589i	$-0.788514\pi$
$211$	−70101.5			−1.57457			−0.787285	+	0.616589i	$0.788514\pi$
$212$		−	31542.2i		−	0.701811i
$213$			12570.0i			0.277062i
$214$	−22945.5	−	22945.5i	−0.501038	−	0.501038i
$215$		−	31596.9i		−	0.683547i
$216$	−8643.17	−	8643.17i	−0.185253	−	0.185253i
$217$	65441.3	+	65441.3i	1.38974	+	1.38974i
$218$	−2112.43			−0.0444498
$219$	−12749.1			−0.265823
$220$	−2660.71	+	2660.71i	−0.0549733	+	0.0549733i
$221$			55214.6i			1.13050i
$222$	−2088.68	−	40676.3i	−0.0423805	−	0.825344i
$223$	24775.0			0.498201			0.249101	−	0.968478i	$-0.419865\pi$
$223$	24775.0			0.498201			0.249101	+	0.968478i	$0.419865\pi$
$224$	8838.11	+	8838.11i	0.176142	+	0.176142i
$225$			35718.9i			0.705559i
$226$		−	15723.8i		−	0.307850i
$227$	−14116.9	+	14116.9i	−0.273960	+	0.273960i	−0.830692	−	0.556732i	$-0.812055\pi$
$227$	−14116.9	+	14116.9i	−0.273960	+	0.273960i	0.556732	+	0.830692i	$0.312055\pi$
$228$	10223.0	−	10223.0i	0.196658	−	0.196658i
$229$	14224.9			0.271255			0.135628	−	0.990760i	$-0.456695\pi$
$229$	14224.9			0.271255			0.135628	+	0.990760i	$0.456695\pi$
$230$	71439.3	−	71439.3i	1.35046	−	1.35046i
$231$	7985.85			0.149657
$232$	1598.54			0.0296994
$233$		−	49309.5i		−	0.908277i	−0.890931	−	0.454139i	$-0.849947\pi$
$233$		−	49309.5i		−	0.908277i	0.890931	−	0.454139i	$-0.150053\pi$
$234$	9487.66			0.173272
$235$	9539.32	−	9539.32i	0.172735	−	0.172735i
$236$	28407.8	+	28407.8i	0.510051	+	0.510051i
$237$	19343.9	+	19343.9i	0.344388	+	0.344388i
$238$	95296.2			1.68237
$239$	−38382.7	+	38382.7i	−0.671954	+	0.671954i	−0.958166	−	0.286212i	$-0.907604\pi$
$239$	−38382.7	+	38382.7i	−0.671954	+	0.671954i	0.286212	+	0.958166i	$0.407604\pi$
$240$	20363.2	+	20363.2i	0.353527	+	0.353527i
$241$	−36762.8	+	36762.8i	−0.632957	+	0.632957i	−0.948809	−	0.315851i	$-0.897710\pi$
$241$	−36762.8	+	36762.8i	−0.632957	+	0.632957i	0.315851	+	0.948809i	$0.397710\pi$
$242$	−29040.2	−	29040.2i	−0.495871	−	0.495871i
$243$			41271.3i			0.698934i
$244$	4155.59	−	4155.59i	0.0697996	−	0.0697996i
$245$	71585.3	−	71585.3i	1.19259	−	1.19259i
$246$	−65798.4	−	65798.4i	−1.08729	−	1.08729i
$247$		−	19440.8i		−	0.318654i
$248$	30328.6			0.493116
$249$			16097.3i			0.259630i
$250$			70165.8i			1.12265i
$251$	77326.3	+	77326.3i	1.22738	+	1.22738i	0.964951	+	0.262430i	$0.0845240\pi$
$251$	77326.3	+	77326.3i	1.22738	+	1.22738i	0.262430	+	0.964951i	$0.415476\pi$
$252$		−	16375.0i		−	0.257858i
$253$	−6492.07	−	6492.07i	−0.101424	−	0.101424i
$254$	−30865.8	−	30865.8i	−0.478421	−	0.478421i
$255$	219564.			3.37661
$256$	4096.00			0.0625000
$257$	−54239.9	+	54239.9i	−0.821206	+	0.821206i	−0.986281	−	0.165075i	$-0.947213\pi$
$257$	−54239.9	+	54239.9i	−0.821206	+	0.821206i	0.165075	+	0.986281i	$0.447213\pi$
$258$			21975.5i			0.330141i
$259$	−63324.6	+	70180.0i	−0.944003	+	1.04620i
$260$	38723.8			0.572838
$261$	−1480.87	−	1480.87i	−0.0217388	−	0.0217388i
$262$		−	55759.9i		−	0.812306i
$263$		−	112716.i		−	1.62957i	−0.579762	−	0.814786i	$-0.696855\pi$
$263$		−	112716.i		−	1.62957i	0.579762	−	0.814786i	$-0.303145\pi$
$264$	1850.51	−	1850.51i	0.0265512	−	0.0265512i
$265$	−119262.	+	119262.i	−1.69829	+	1.69829i
$266$	−33553.3			−0.474212
$267$	−53803.4	+	53803.4i	−0.754723	+	0.754723i
$268$	29891.2			0.416173
$269$	−4250.50			−0.0587402			−0.0293701	−	0.999569i	$-0.509350\pi$
$269$	−4250.50			−0.0587402			−0.0293701	+	0.999569i	$0.509350\pi$
$270$			65360.2i			0.896574i
$271$	−77055.1			−1.04921			−0.524605	−	0.851346i	$-0.675787\pi$
$271$	−77055.1			−1.04921			−0.524605	+	0.851346i	$0.675787\pi$
$272$	22082.4	−	22082.4i	0.298475	−	0.298475i
$273$	−58112.8	−	58112.8i	−0.779734	−	0.779734i
$274$	67646.6	+	67646.6i	0.901042	+	0.901042i
$275$	13248.4			0.175185
$276$	−49685.6	+	49685.6i	−0.652248	+	0.652248i
$277$	41531.0	+	41531.0i	0.541269	+	0.541269i	0.923901	−	0.382632i	$-0.124982\pi$
$277$	41531.0	+	41531.0i	0.541269	+	0.541269i	−0.382632	+	0.923901i	$0.624982\pi$
$278$	−32848.2	+	32848.2i	−0.425033	+	0.425033i
$279$	−28096.0	−	28096.0i	−0.360940	−	0.360940i
$280$		−	66834.4i		−	0.852480i
$281$	93101.9	−	93101.9i	1.17909	−	1.17909i	0.199110	−	0.979977i	$-0.436195\pi$
$281$	93101.9	−	93101.9i	1.17909	−	1.17909i	0.979977	−	0.199110i	$-0.0638051\pi$
$282$	−6634.55	+	6634.55i	−0.0834282	+	0.0834282i
$283$	−44952.4	−	44952.4i	−0.561281	−	0.561281i	0.368390	−	0.929671i	$-0.379909\pi$
$283$	−44952.4	−	44952.4i	−0.561281	−	0.561281i	−0.929671	+	0.368390i	$0.879909\pi$
$284$		−	9560.09i		−	0.118529i
$285$	−77307.4			−0.951768
$286$		−	3519.04i		−	0.0430222i
$287$			215959.i			2.62184i
$288$	−3794.47	−	3794.47i	−0.0457474	−	0.0457474i
$289$		−	154580.i		−	1.85080i
$290$	−6044.14	−	6044.14i	−0.0718685	−	0.0718685i
$291$	42247.9	+	42247.9i	0.498906	+	0.498906i
$292$	9696.30			0.113721
$293$	−54120.6			−0.630416			−0.315208	−	0.949023i	$-0.602074\pi$
$293$	−54120.6			−0.630416			−0.315208	+	0.949023i	$0.602074\pi$
$294$	−49787.2	+	49787.2i	−0.576001	+	0.576001i
$295$		−	214822.i		−	2.46850i
$296$	1588.54	+	30936.2i	0.0181307	+	0.353088i
$297$	5939.64			0.0673360
$298$	−42812.3	−	42812.3i	−0.482099	−	0.482099i
$299$			94485.3i			1.05687i
$300$		−	101394.i		−	1.12660i
$301$	36063.2	−	36063.2i	0.398044	−	0.398044i
$302$	−23379.5	+	23379.5i	−0.256342	+	0.256342i
$303$	−11737.8			−0.127850
$304$	−7775.10	+	7775.10i	−0.0841315	+	0.0841315i
$305$	−31424.9			−0.337811
$306$	−40913.6			−0.436943
$307$		−	2227.91i		−	0.0236385i	−0.999930	−	0.0118193i	$-0.996238\pi$
$307$		−	2227.91i		−	0.0236385i	0.999930	−	0.0118193i	$-0.00376228\pi$
$308$	−6073.60			−0.0640243
$309$	134995.	−	134995.i	1.41384	−	1.41384i
$310$	−114673.	−	114673.i	−1.19327	−	1.19327i
$311$	−39146.1	−	39146.1i	−0.404732	−	0.404732i	0.475165	−	0.879897i	$-0.342389\pi$
$311$	−39146.1	−	39146.1i	−0.404732	−	0.404732i	−0.879897	+	0.475165i	$0.842389\pi$
$312$	−26932.2			−0.276671
$313$	37424.8	−	37424.8i	0.382007	−	0.382007i	−0.489818	−	0.871825i	$-0.662937\pi$
$313$	37424.8	−	37424.8i	0.382007	−	0.382007i	0.871825	+	0.489818i	$0.162937\pi$
$314$	49113.9	+	49113.9i	0.498132	+	0.498132i
$315$	−61914.4	+	61914.4i	−0.623980	+	0.623980i
$316$	−14711.9	−	14711.9i	−0.147331	−	0.147331i
$317$			152147.i			1.51407i	0.653376	+	0.757034i	$0.273352\pi$
$317$			152147.i			1.51407i	−0.653376	+	0.757034i	$0.726648\pi$
$318$	82946.2	−	82946.2i	0.820243	−	0.820243i
$319$	−549.264	+	549.264i	−0.00539759	+	0.00539759i
$320$	−15487.1	−	15487.1i	−0.151241	−	0.151241i
$321$		−	120679.i		−	1.17118i
$322$	163074.			1.57280
$323$			83834.3i			0.803557i
$324$		−	64667.2i		−	0.616019i
$325$	−96408.3	−	96408.3i	−0.912741	−	0.912741i
$326$			38246.7i			0.359881i
$327$	−5555.05	−	5555.05i	−0.0519508	−	0.0519508i
$328$	50042.7	+	50042.7i	0.465150	+	0.465150i
$329$	21775.4			0.201175
$330$	−13993.7			−0.128500
$331$	−81389.5	+	81389.5i	−0.742869	+	0.742869i	−0.973129	−	0.230260i	$-0.926042\pi$
$331$	−81389.5	+	81389.5i	−0.742869	+	0.742869i	0.230260	+	0.973129i	$0.426042\pi$
$332$		−	12242.7i		−	0.111071i
$333$	27187.2	−	30130.4i	0.245175	−	0.271717i
$334$	59307.1			0.531635
$335$	−113020.	−	113020.i	−1.00708	−	1.00708i
$336$			46483.0i			0.411733i
$337$		−	120061.i		−	1.05716i	−0.848883	−	0.528580i	$-0.822725\pi$
$337$		−	120061.i		−	1.05716i	0.848883	−	0.528580i	$-0.177275\pi$
$338$	31514.0	−	31514.0i	0.275848	−	0.275848i
$339$	41348.6	−	41348.6i	0.359800	−	0.359800i
$340$	−166988.			−1.44454
$341$	−10421.0	+	10421.0i	−0.0896191	+	0.0896191i
$342$	14405.5			0.123162
$343$	−2375.75			−0.0201936
$344$		−	16713.4i		−	0.141237i
$345$	375726.			3.15670
$346$	−105167.	+	105167.i	−0.878473	+	0.878473i
$347$	−124619.	−	124619.i	−1.03497	−	1.03497i	−0.999366	−	0.0355998i	$-0.988666\pi$
$347$	−124619.	−	124619.i	−1.03497	−	1.03497i	−0.0355998	−	0.999366i	$-0.511334\pi$
$348$	4203.67	+	4203.67i	0.0347112	+	0.0347112i
$349$	−117331.			−0.963303			−0.481652	−	0.876363i	$-0.659963\pi$
$349$	−117331.			−0.963303			−0.481652	+	0.876363i	$0.659963\pi$
$350$	−166393.	+	166393.i	−1.35831	+	1.35831i
$351$	−43222.6	−	43222.6i	−0.350830	−	0.350830i
$352$	−1407.40	+	1407.40i	−0.0113588	+	0.0113588i
$353$	48307.3	+	48307.3i	0.387671	+	0.387671i	0.873856	−	0.486185i	$-0.161612\pi$
$353$	48307.3	+	48307.3i	0.387671	+	0.387671i	−0.486185	+	0.873856i	$0.661612\pi$
$354$			149407.i			1.19224i
$355$	−36147.0	+	36147.0i	−0.286824	+	0.286824i
$356$	40920.0	−	40920.0i	0.322876	−	0.322876i
$357$	250599.	+	250599.i	1.96627	+	1.96627i
$358$			26573.8i			0.207342i
$359$	219239.			1.70110			0.850549	−	0.525895i	$-0.176270\pi$
$359$	219239.			1.70110			0.850549	+	0.525895i	$0.176270\pi$
$360$			28694.1i			0.221405i
$361$			100803.i			0.773500i
$362$	10113.8	+	10113.8i	0.0771783	+	0.0771783i
$363$		−	152733.i		−	1.15910i
$364$	44197.5	+	44197.5i	0.333576	+	0.333576i
$365$	−36662.1	−	36662.1i	−0.275189	−	0.275189i
$366$	21855.8			0.163157
$367$	66951.0			0.497078			0.248539	−	0.968622i	$-0.420050\pi$
$367$	66951.0			0.497078			0.248539	+	0.968622i	$0.420050\pi$
$368$	37788.2	−	37788.2i	0.279036	−	0.279036i
$369$		−	92717.6i		−	0.680941i
$370$	110964.	−	122977.i	0.810551	−	0.898298i
$371$	−272240.			−1.97790
$372$	79754.8	+	79754.8i	0.576330	+	0.576330i
$373$			133716.i			0.961094i	0.876969	+	0.480547i	$0.159562\pi$
$373$			133716.i			0.961094i	−0.876969	+	0.480547i	$0.840438\pi$
$374$			15175.1i			0.108490i
$375$	−184514.	+	184514.i	−1.31210	+	1.31210i
$376$	5045.88	−	5045.88i	0.0356912	−	0.0356912i
$377$	7993.96			0.0562444
$378$	−74598.9	+	74598.9i	−0.522094	+	0.522094i
$379$	156448.			1.08916			0.544580	−	0.838709i	$-0.316689\pi$
$379$	156448.			1.08916			0.544580	+	0.838709i	$0.316689\pi$
$380$	58795.8			0.407173
$381$		−	162335.i		−	1.11831i
$382$	−154784.			−1.06071
$383$	−26425.8	+	26425.8i	−0.180149	+	0.180149i	−0.791421	−	0.611272i	$-0.790658\pi$
$383$	−26425.8	+	26425.8i	−0.180149	+	0.180149i	0.611272	+	0.791421i	$0.290658\pi$
$384$	10771.2	+	10771.2i	0.0730469	+	0.0730469i
$385$	22964.5	+	22964.5i	0.154930	+	0.154930i
$386$	−170366.			−1.14342
$387$	−15483.0	+	15483.0i	−0.103379	+	0.103379i
$388$	−32131.5	−	32131.5i	−0.213436	−	0.213436i
$389$	−124197.	+	124197.i	−0.820754	+	0.820754i	−0.986216	−	0.165462i	$-0.947088\pi$
$389$	−124197.	+	124197.i	−0.820754	+	0.820754i	0.165462	+	0.986216i	$0.447088\pi$
$390$	101832.	+	101832.i	0.669505	+	0.669505i
$391$		−	407448.i		−	2.66513i
$392$	37865.5	−	37865.5i	0.246417	−	0.246417i
$393$	146631.	−	146631.i	0.949384	−	0.949384i
$394$	76543.3	+	76543.3i	0.493077	+	0.493077i
$395$			111253.i			0.713043i
$396$	2607.58			0.0166283
$397$		−	216499.i		−	1.37365i	−0.726824	−	0.686823i	$-0.759005\pi$
$397$		−	216499.i		−	1.37365i	0.726824	−	0.686823i	$-0.240995\pi$
$398$			11423.8i			0.0721181i
$399$	−88234.8	−	88234.8i	−0.554235	−	0.554235i
$400$			77114.6i			0.481966i
$401$	161025.	+	161025.i	1.00139	+	1.00139i	0.999999	+	0.00139254i	$0.000443259\pi$
$401$	161025.	+	161025.i	1.00139	+	1.00139i	0.00139254	+	0.999999i	$0.499557\pi$
$402$	78604.5	+	78604.5i	0.486402	+	0.486402i
$403$	151667.			0.933856
$404$	8927.14			0.0546952
$405$	−244509.	+	244509.i	−1.49068	+	1.49068i
$406$		−	13797.0i		−	0.0837012i
$407$	−11175.6	−	10083.9i	−0.0674655	−	0.0608753i
$408$	116140.			0.697686
$409$	9905.97	+	9905.97i	0.0592175	+	0.0592175i	0.736095	−	0.676878i	$-0.236667\pi$
$409$	9905.97	+	9905.97i	0.0592175	+	0.0592175i	−0.676878	+	0.736095i	$0.736667\pi$
$410$		−	378426.i		−	2.25120i
$411$			355779.i			2.10619i
$412$	−102670.	+	102670.i	−0.604851	+	0.604851i
$413$	245187.	−	245187.i	1.43746	−	1.43746i
$414$	−70012.9			−0.408486
$415$	−46290.2	+	46290.2i	−0.268777	+	0.268777i
$416$	20483.2			0.118362
$417$	−172761.			−0.993515
$418$		−	5343.09i		−	0.0305802i
$419$	−282949.			−1.61168			−0.805842	−	0.592131i	$-0.798287\pi$
$419$	−282949.			−1.61168			−0.805842	+	0.592131i	$0.798287\pi$
$420$	175754.	−	175754.i	0.996337	−	0.996337i
$421$	40193.9	+	40193.9i	0.226775	+	0.226775i	0.811344	−	0.584569i	$-0.198736\pi$
$421$	40193.9	+	40193.9i	0.226775	+	0.226775i	−0.584569	+	0.811344i	$0.698736\pi$
$422$	140203.	+	140203.i	0.787285	+	0.787285i
$423$	−9348.85			−0.0522489
$424$	−63084.4	+	63084.4i	−0.350906	+	0.350906i
$425$	415741.	+	415741.i	2.30168	+	2.30168i
$426$	25140.1	−	25140.1i	0.138531	−	0.138531i
$427$	−35866.8	−	35866.8i	−0.196715	−	0.196715i
$428$			91782.1i			0.501038i
$429$	9253.99	−	9253.99i	0.0502822	−	0.0502822i
$430$	−63193.9	+	63193.9i	−0.341773	+	0.341773i
$431$	−17448.6	−	17448.6i	−0.0939305	−	0.0939305i	0.658580	−	0.752511i	$-0.271157\pi$
$431$	−17448.6	−	17448.6i	−0.0939305	−	0.0939305i	−0.752511	+	0.658580i	$0.771157\pi$
$432$			34572.7i			0.185253i
$433$	169891.			0.906138			0.453069	−	0.891476i	$-0.350329\pi$
$433$	169891.			0.906138			0.453069	+	0.891476i	$0.350329\pi$
$434$		−	261765.i		−	1.38974i
$435$		−	31788.4i		−	0.167993i
$436$	4224.87	+	4224.87i	0.0222249	+	0.0222249i
$437$			143460.i			0.751224i
$438$	25498.3	+	25498.3i	0.132911	+	0.132911i
$439$	158221.	+	158221.i	0.820985	+	0.820985i	0.986249	−	0.165265i	$-0.0528478\pi$
$439$	158221.	+	158221.i	0.820985	+	0.820985i	−0.165265	+	0.986249i	$0.552848\pi$
$440$	10642.8			0.0549733
$441$	−70156.0			−0.360735
$442$	110429.	−	110429.i	0.565248	−	0.565248i
$443$		−	173144.i		−	0.882266i	−0.897442	−	0.441133i	$-0.854577\pi$
$443$		−	173144.i		−	0.882266i	0.897442	−	0.441133i	$-0.145423\pi$
$444$	−77175.2	+	85529.9i	−0.391482	+	0.433862i
$445$	−309440.			−1.56263
$446$	−49550.1	−	49550.1i	−0.249101	−	0.249101i
$447$		−	225166.i		−	1.12691i
$448$		−	35352.5i		−	0.176142i
$449$	−246154.	+	246154.i	−1.22099	+	1.22099i	−0.253716	+	0.967279i	$0.581653\pi$
$449$	−246154.	+	246154.i	−1.22099	+	1.22099i	−0.967279	+	0.253716i	$0.918347\pi$
$450$	71437.8	−	71437.8i	0.352779	−	0.352779i
$451$	−34389.6			−0.169073
$452$	−31447.5	+	31447.5i	−0.153925	+	0.153925i
$453$	−122961.			−0.599201
$454$	56467.6			0.273960
$455$		−	334224.i		−	1.61441i
$456$	−40892.2			−0.196658
$457$	−146814.	+	146814.i	−0.702965	+	0.702965i	−0.965046	−	0.262081i	$-0.915591\pi$
$457$	−146814.	+	146814.i	−0.702965	+	0.702965i	0.262081	+	0.965046i	$0.415591\pi$
$458$	−28449.8	−	28449.8i	−0.135628	−	0.135628i
$459$	186388.	+	186388.i	0.884695	+	0.884695i
$460$	−285757.			−1.35046
$461$	55295.6	−	55295.6i	0.260189	−	0.260189i	−0.564942	−	0.825131i	$-0.691101\pi$
$461$	55295.6	−	55295.6i	0.260189	−	0.260189i	0.825131	+	0.564942i	$0.191101\pi$
$462$	−15971.7	−	15971.7i	−0.0748285	−	0.0748285i
$463$	123996.	−	123996.i	0.578425	−	0.578425i	−0.356044	−	0.934469i	$-0.615875\pi$
$463$	123996.	−	123996.i	0.578425	−	0.578425i	0.934469	+	0.356044i	$0.115875\pi$
$464$	−3197.08	−	3197.08i	−0.0148497	−	0.0148497i
$465$		−	603111.i		−	2.78928i
$466$	−98618.9	+	98618.9i	−0.454139	+	0.454139i
$467$	−36279.1	+	36279.1i	−0.166350	+	0.166350i	−0.785373	−	0.619023i	$-0.787529\pi$
$467$	−36279.1	+	36279.1i	−0.166350	+	0.166350i	0.619023	+	0.785373i	$0.287529\pi$
$468$	−18975.3	−	18975.3i	−0.0866358	−	0.0866358i
$469$		−	257990.i		−	1.17289i
$470$	−38157.3			−0.172735
$471$			258308.i			1.16439i
$472$		−	113631.i		−	0.510051i
$473$	5742.77	+	5742.77i	0.0256684	+	0.0256684i
$474$		−	77375.6i		−	0.344388i
$475$	−146380.	−	146380.i	−0.648777	−	0.648777i
$476$	−190592.	−	190592.i	−0.841185	−	0.841185i
$477$	116881.			0.513697
$478$	153531.			0.671954
$479$	2.68921	−	2.68921i	1.17207e−5	−	1.17207e-5i	−0.707101	−	0.707113i	$-0.749997\pi$
$479$	2.68921	−	2.68921i	1.17207e−5	−	1.17207e-5i	0.707113	+	0.707101i	$0.249997\pi$
$480$		−	81452.6i		−	0.353527i
$481$	7943.93	+	154705.i	0.0343356	+	0.668674i
$482$	147051.			0.632957
$483$	428835.	+	428835.i	1.83821	+	1.83821i
$484$			116161.i			0.495871i
$485$			242980.i			1.03297i
$486$	82542.7	−	82542.7i	0.349467	−	0.349467i
$487$	−94175.6	+	94175.6i	−0.397082	+	0.397082i	−0.877203	−	0.480120i	$-0.840593\pi$
$487$	−94175.6	+	94175.6i	−0.397082	+	0.397082i	0.480120	+	0.877203i	$0.340593\pi$
$488$	−16622.4			−0.0697996
$489$	−100577.	+	100577.i	−0.420612	+	0.420612i
$490$	−286341.			−1.19259
$491$	−93918.8			−0.389573			−0.194787	−	0.980846i	$-0.562401\pi$
$491$	−93918.8			−0.389573			−0.194787	+	0.980846i	$0.562401\pi$
$492$			263194.i			1.08729i
$493$	−34472.3			−0.141833
$494$	−38881.6	+	38881.6i	−0.159327	+	0.159327i
$495$	−9859.36	−	9859.36i	−0.0402382	−	0.0402382i
$496$	−60657.2	−	60657.2i	−0.246558	−	0.246558i
$497$	−82512.8			−0.334048
$498$	32194.6	−	32194.6i	0.129815	−	0.129815i
$499$	26209.4	+	26209.4i	0.105258	+	0.105258i	0.757775	−	0.652516i	$-0.226287\pi$
$499$	26209.4	+	26209.4i	0.105258	+	0.105258i	−0.652516	+	0.757775i	$0.726287\pi$
$500$	140332.	−	140332.i	0.561326	−	0.561326i
$501$	155959.	+	155959.i	0.621350	+	0.621350i
$502$		−	309305.i		−	1.22738i
$503$	85511.3	−	85511.3i	0.337977	−	0.337977i	−0.517628	−	0.855606i	$-0.673185\pi$
$503$	85511.3	−	85511.3i	0.337977	−	0.337977i	0.855606	+	0.517628i	$0.173185\pi$
$504$	−32750.0	+	32750.0i	−0.128929	+	0.128929i
$505$	−33753.8	−	33753.8i	−0.132355	−	0.132355i
$506$			25968.3i			0.101424i
$507$	165744.			0.644796
$508$			123463.i			0.478421i
$509$		−	151332.i		−	0.584112i	−0.956401	−	0.292056i	$-0.905661\pi$
$509$		−	151332.i		−	0.584112i	0.956401	−	0.292056i	$-0.0943394\pi$
$510$	−439128.	−	439128.i	−1.68830	−	1.68830i
$511$		−	83688.5i		−	0.320497i
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$	−65626.5	−	65626.5i	−0.249370	−	0.249370i
$514$	216959.			0.821206
$515$	776396.			2.92731
$516$	43951.0	−	43951.0i	0.165071	−	0.165071i
$517$			3467.56i			0.0129731i
$518$	267009.	−	13710.6i	0.995100	−	0.0510972i
$519$	−553115.			−2.05343
$520$	−77447.6	−	77447.6i	−0.286419	−	0.286419i
$521$		−	196551.i		−	0.724102i	−0.932158	−	0.362051i	$-0.882077\pi$
$521$		−	196551.i		−	0.724102i	0.932158	−	0.362051i	$-0.117923\pi$
$522$			5923.46i			0.0217388i
$523$	245504.	−	245504.i	0.897542	−	0.897542i	−0.0976765	−	0.995218i	$-0.531141\pi$
$523$	245504.	−	245504.i	0.897542	−	0.897542i	0.995218	+	0.0976765i	$0.0311410\pi$
$524$	−111520.	+	111520.i	−0.406153	+	0.406153i
$525$	−875126.			−3.17506
$526$	−225432.	+	225432.i	−0.814786	+	0.814786i
$527$	−654031.			−2.35493
$528$	−7402.04			−0.0265512
$529$		−	417400.i		−	1.49156i
$530$	477049.			1.69829
$531$	−105266.	+	105266.i	−0.373336	+	0.373336i
$532$	67106.6	+	67106.6i	0.237106	+	0.237106i
$533$	250253.	+	250253.i	0.880895	+	0.880895i
$534$	215214.			0.754723
$535$	347031.	−	347031.i	1.21244	−	1.21244i
$536$	−59782.4	−	59782.4i	−0.208086	−	0.208086i
$537$	−69880.8	+	69880.8i	−0.242331	+	0.242331i
$538$	8501.00	+	8501.00i	0.0293701	+	0.0293701i
$539$			26021.4i			0.0895680i
$540$	130720.	−	130720.i	0.448287	−	0.448287i
$541$	−210674.	+	210674.i	−0.719807	+	0.719807i	−0.968566	−	0.248758i	$-0.919978\pi$
$541$	−210674.	+	210674.i	−0.719807	+	0.719807i	0.248758	+	0.968566i	$0.419978\pi$
$542$	154110.	+	154110.i	0.524605	+	0.524605i
$543$			53192.1i			0.180404i
$544$	−88329.5			−0.298475
$545$		−	31948.7i		−	0.107562i
$546$			232451.i			0.779734i
$547$	−23718.7	−	23718.7i	−0.0792713	−	0.0792713i	0.666359	−	0.745631i	$-0.267852\pi$
$547$	−23718.7	−	23718.7i	−0.0792713	−	0.0792713i	−0.745631	+	0.666359i	$0.767852\pi$
$548$		−	270587.i		−	0.901042i
$549$	15398.7	+	15398.7i	0.0510904	+	0.0510904i
$550$	−26496.8	−	26496.8i	−0.0875927	−	0.0875927i
$551$	12137.5			0.0399785
$552$	198743.			0.652248
$553$	−126978.	+	126978.i	−0.415221	+	0.415221i
$554$		−	166124.i		−	0.541269i
$555$	615193.	−	31589.5i	1.99722	−	0.102555i
$556$	131393.			0.425033
$557$	−105334.	−	105334.i	−0.339513	−	0.339513i	0.516671	−	0.856184i	$-0.327171\pi$
$557$	−105334.	−	105334.i	−0.339513	−	0.339513i	−0.856184	+	0.516671i	$0.827171\pi$
$558$			112384.i			0.360940i
$559$		−	83580.0i		−	0.267472i
$560$	−133669.	+	133669.i	−0.426240	+	0.426240i
$561$	−39905.9	+	39905.9i	−0.126798	+	0.126798i
$562$	−372408.			−1.17909
$563$	−248718.	+	248718.i	−0.784675	+	0.784675i	−0.980616	−	0.195940i	$-0.937224\pi$
$563$	−248718.	+	248718.i	−0.784675	+	0.784675i	0.195940	+	0.980616i	$0.437224\pi$
$564$	26538.2			0.0834282
$565$	237808.			0.744955
$566$			179810.i			0.561281i
$567$	−558141.			−1.73611
$568$	−19120.2	+	19120.2i	−0.0592646	+	0.0592646i
$569$	420587.	+	420587.i	1.29907	+	1.29907i	0.929010	+	0.370055i	$0.120661\pi$
$569$	420587.	+	420587.i	1.29907	+	1.29907i	0.370055	+	0.929010i	$0.379339\pi$
$570$	154615.	+	154615.i	0.475884	+	0.475884i
$571$	−496254.			−1.52206			−0.761030	−	0.648717i	$-0.775306\pi$
$571$	−496254.			−1.52206			−0.761030	+	0.648717i	$0.775306\pi$
$572$	−7038.09	+	7038.09i	−0.0215111	+	0.0215111i
$573$	−407033.	−	407033.i	−1.23971	−	1.23971i
$574$	431917.	−	431917.i	1.31092	−	1.31092i
$575$	711431.	+	711431.i	2.15178	+	2.15178i
$576$			15177.9i			0.0457474i
$577$	−101034.	+	101034.i	−0.303469	+	0.303469i	−0.842369	−	0.538901i	$-0.818840\pi$
$577$	−101034.	+	101034.i	−0.303469	+	0.303469i	0.538901	+	0.842369i	$0.318840\pi$
$578$	−309161.	+	309161.i	−0.925398	+	0.925398i
$579$	−448009.	−	448009.i	−1.33638	−	1.33638i
$580$			24176.6i			0.0718685i
$581$	−105667.			−0.313030
$582$		−	168992.i		−	0.498906i
$583$		−	43352.0i		−	0.127547i
$584$	−19392.6	−	19392.6i	−0.0568605	−	0.0568605i
$585$			143493.i			0.419293i
$586$	108241.	+	108241.i	0.315208	+	0.315208i
$587$	−315193.	−	315193.i	−0.914746	−	0.914746i	0.0818952	−	0.996641i	$-0.473903\pi$
$587$	−315193.	−	315193.i	−0.914746	−	0.914746i	−0.996641	+	0.0818952i	$0.973903\pi$
$588$	199149.			0.576001
$589$	230281.			0.663786
$590$	−429643.	+	429643.i	−1.23425	+	1.23425i
$591$			402570.i			1.15257i
$592$	58695.3	−	65049.4i	0.167479	−	0.185609i
$593$	549407.			1.56237			0.781186	−	0.624298i	$-0.214615\pi$
$593$	549407.			1.56237			0.781186	+	0.624298i	$0.214615\pi$
$594$	−11879.3	−	11879.3i	−0.0336680	−	0.0336680i
$595$			1.44127e6i			4.07110i
$596$			171249.i			0.482099i
$597$	−30041.0	+	30041.0i	−0.0842881	+	0.0842881i
$598$	188971.	−	188971.i	0.528435	−	0.528435i
$599$	172763.			0.481501			0.240750	−	0.970587i	$-0.422606\pi$
$599$	172763.			0.481501			0.240750	+	0.970587i	$0.422606\pi$
$600$	−202787.	+	202787.i	−0.563299	+	0.563299i
$601$	190910.			0.528543			0.264272	−	0.964448i	$-0.414868\pi$
$601$	190910.			0.528543			0.264272	+	0.964448i	$0.414868\pi$
$602$	−144253.			−0.398044
$603$			110763.i			0.304621i
$604$	93517.8			0.256342
$605$	439208.	−	439208.i	1.19994	−	1.19994i
$606$	23475.6	+	23475.6i	0.0639251	+	0.0639251i
$607$	201474.	+	201474.i	0.546816	+	0.546816i	0.925519	−	0.378702i	$-0.123630\pi$
$607$	201474.	+	201474.i	0.546816	+	0.546816i	−0.378702	+	0.925519i	$0.623630\pi$
$608$	31100.4			0.0841315
$609$	36281.8	−	36281.8i	0.0978259	−	0.0978259i
$610$	62849.7	+	62849.7i	0.168905	+	0.168905i
$611$	25233.3	−	25233.3i	0.0675915	−	0.0675915i
$612$	81827.2	+	81827.2i	0.218471	+	0.218471i
$613$		−	171480.i		−	0.456344i	−0.973621	−	0.228172i	$-0.926725\pi$
$613$		−	171480.i		−	0.456344i	0.973621	−	0.228172i	$-0.0732749\pi$
$614$	−4455.82	+	4455.82i	−0.0118193	+	0.0118193i
$615$	995144.	−	995144.i	2.63109	−	2.63109i
$616$	12147.2	+	12147.2i	0.0320122	+	0.0320122i
$617$		−	75449.0i		−	0.198191i	−0.995078	−	0.0990953i	$-0.968405\pi$
$617$		−	75449.0i		−	0.198191i	0.995078	−	0.0990953i	$-0.0315949\pi$
$618$	−539979.			−1.41384
$619$			40455.4i			0.105583i	0.998606	+	0.0527917i	$0.0168119\pi$
$619$			40455.4i			0.105583i	−0.998606	+	0.0527917i	$0.983188\pi$
$620$			458694.i			1.19327i
$621$	318955.	+	318955.i	0.827078	+	0.827078i
$622$			156584.i			0.404732i
$623$	−353179.	−	353179.i	−0.909953	−	0.909953i
$624$	53864.4	+	53864.4i	0.138335	+	0.138335i
$625$	−308124.			−0.788798
$626$	−149699.			−0.382007
$627$	14050.7	−	14050.7i	0.0357406	−	0.0357406i
$628$		−	196455.i		−	0.498132i
$629$	−34256.5	−	667133.i	−0.0865849	−	1.68621i
$630$	247658.			0.623980
$631$	35252.8	+	35252.8i	0.0885391	+	0.0885391i	0.749989	−	0.661450i	$-0.230059\pi$
$631$	35252.8	+	35252.8i	0.0885391	+	0.0885391i	−0.661450	+	0.749989i	$0.730059\pi$
$632$			58847.7i			0.147331i
$633$			737380.i			1.84028i
$634$	304294.	−	304294.i	0.757034	−	0.757034i
$635$	466819.	−	466819.i	1.15771	−	1.15771i
$636$	−331785.			−0.820243
$637$	189357.	−	189357.i	0.466662	−	0.466662i
$638$	2197.06			0.00539759
$639$	35425.3			0.0867584
$640$			61948.5i			0.151241i
$641$	30042.1			0.0731164			0.0365582	−	0.999332i	$-0.488361\pi$
$641$	30042.1			0.0731164			0.0365582	+	0.999332i	$0.488361\pi$
$642$	−241359.	+	241359.i	−0.585589	+	0.585589i
$643$	288466.	+	288466.i	0.697706	+	0.697706i	0.963915	−	0.266209i	$-0.0857713\pi$
$643$	288466.	+	288466.i	0.697706	+	0.697706i	−0.266209	+	0.963915i	$0.585771\pi$
$644$	−326149.	−	326149.i	−0.786401	−	0.786401i
$645$	−332361.			−0.798896
$646$	167669.	−	167669.i	0.401779	−	0.401779i
$647$	−398994.	−	398994.i	−0.953142	−	0.953142i	0.0458081	−	0.998950i	$-0.485414\pi$
$647$	−398994.	−	398994.i	−0.953142	−	0.953142i	−0.998950	+	0.0458081i	$0.985414\pi$
$648$	−129334.	+	129334.i	−0.308010	+	0.308010i
$649$	39044.0	+	39044.0i	0.0926968	+	0.0926968i
$650$			385633.i			0.912741i
$651$	688362.	−	688362.i	1.62426	−	1.62426i
$652$	76493.5	−	76493.5i	0.179941	−	0.179941i
$653$	−187012.	−	187012.i	−0.438575	−	0.438575i	0.452957	−	0.891532i	$-0.350369\pi$
$653$	−187012.	−	187012.i	−0.438575	−	0.438575i	−0.891532	+	0.452957i	$0.850369\pi$
$654$			22220.2i			0.0519508i
$655$	843321.			1.96567
$656$		−	200171.i		−	0.465150i
$657$			35930.0i			0.0832390i
$658$	−43550.8	−	43550.8i	−0.100588	−	0.100588i
$659$		−	199346.i		−	0.459024i	−0.973306	−	0.229512i	$-0.926287\pi$
$659$		−	199346.i		−	0.459024i	0.973306	−	0.229512i	$-0.0737131\pi$
$660$	27987.4	+	27987.4i	0.0642501	+	0.0642501i
$661$	−43738.2	−	43738.2i	−0.100106	−	0.100106i	0.655280	−	0.755386i	$-0.272551\pi$
$661$	−43738.2	−	43738.2i	−0.100106	−	0.100106i	−0.755386	+	0.655280i	$0.772551\pi$
$662$	325558.			0.742869
$663$	580789.			1.32127
$664$	−24485.5	+	24485.5i	−0.0555357	+	0.0555357i
$665$		−	507465.i		−	1.14753i
$666$	−114635.	+	5886.39i	−0.258446	+	0.0132709i
$667$	−58990.3			−0.132596
$668$	−118614.	−	118614.i	−0.265818	−	0.265818i
$669$		−	260603.i		−	0.582273i
$670$			452078.i			1.00708i
$671$	5711.50	−	5711.50i	0.0126854	−	0.0126854i
$672$	92966.0	−	92966.0i	0.205866	−	0.205866i
$673$	−725075.			−1.60086			−0.800429	−	0.599427i	$-0.795395\pi$
$673$	−725075.			−1.60086			−0.800429	+	0.599427i	$0.795395\pi$
$674$	−240121.	+	240121.i	−0.528580	+	0.528580i
$675$	−650893.			−1.42857
$676$	−126056.			−0.275848
$677$		−	661665.i		−	1.44365i	−0.692078	−	0.721823i	$-0.743304\pi$
$677$		−	661665.i		−	1.44365i	0.692078	−	0.721823i	$-0.256696\pi$
$678$	−165394.			−0.359800
$679$	−277326.	+	277326.i	−0.601521	+	0.601521i
$680$	333977.	+	333977.i	0.722268	+	0.722268i
$681$	148492.	+	148492.i	0.320192	+	0.320192i
$682$	41684.0			0.0896191
$683$	−529677.	+	529677.i	−1.13545	+	1.13545i	−0.146198	+	0.989255i	$0.546704\pi$
$683$	−529677.	+	529677.i	−1.13545	+	1.13545i	−0.989255	+	0.146198i	$0.953296\pi$
$684$	−28810.9	−	28810.9i	−0.0615808	−	0.0615808i
$685$	−1.02310e6	+	1.02310e6i	−2.18040	+	2.18040i
$686$	4751.51	+	4751.51i	0.0100968	+	0.0100968i
$687$		−	149628.i		−	0.317030i
$688$	−33426.8	+	33426.8i	−0.0706184	+	0.0706184i
$689$	−315471.	+	315471.i	−0.664540	+	0.664540i
$690$	−751452.	−	751452.i	−1.57835	−	1.57835i
$691$			580294.i			1.21532i	0.794196	+	0.607662i	$0.207892\pi$
$691$			580294.i			1.21532i	−0.794196	+	0.607662i	$0.792108\pi$
$692$	420669.			0.878473
$693$		−	22506.0i		−	0.0468632i
$694$			498477.i			1.03497i
$695$	−496801.	−	496801.i	−1.02852	−	1.02852i
$696$		−	16814.7i		−	0.0347112i
$697$	−1.07916e6	−	1.07916e6i	−2.22137	−	2.22137i
$698$	234663.	+	234663.i	0.481652	+	0.481652i
$699$	−518675.			−1.06155
$700$	665574.			1.35831
$701$	−235973.	+	235973.i	−0.480205	+	0.480205i	−0.905197	−	0.424992i	$-0.860277\pi$
$701$	−235973.	+	235973.i	−0.480205	+	0.480205i	0.424992	+	0.905197i	$0.360277\pi$
$702$			172890.i			0.350830i
$703$	12061.6	+	234894.i	0.0244058	+	0.475294i
$704$	5629.59			0.0113588
$705$	−100342.	−	100342.i	−0.201885	−	0.201885i
$706$		−	193229.i		−	0.387671i
$707$		−	77049.8i		−	0.154146i
$708$	298815.	−	298815.i	0.596122	−	0.596122i
$709$	263351.	−	263351.i	0.523892	−	0.523892i	−0.394852	−	0.918745i	$-0.629204\pi$
$709$	263351.	−	263351.i	0.523892	−	0.523892i	0.918745	+	0.394852i	$0.129204\pi$
$710$	144588.			0.286824
$711$	54515.6	−	54515.6i	0.107840	−	0.107840i
$712$	−163680.			−0.322876
$713$	−1.11920e6			−2.20156
$714$		−	1.00240e6i		−	1.96627i
$715$	53222.5			0.104108
$716$	53147.6	−	53147.6i	0.103671	−	0.103671i
$717$	403738.	+	403738.i	0.785347	+	0.785347i
$718$	−438479.	−	438479.i	−0.850549	−	0.850549i
$719$	64557.5			0.124879			0.0624394	−	0.998049i	$-0.480112\pi$
$719$	64557.5			0.124879			0.0624394	+	0.998049i	$0.480112\pi$
$720$	57388.1	−	57388.1i	0.110702	−	0.110702i
$721$	886140.	+	886140.i	1.70464	+	1.70464i
$722$	201607.	−	201607.i	0.386750	−	0.386750i
$723$	386699.	+	386699.i	0.739769	+	0.739769i
$724$		−	40455.0i		−	0.0771783i
$725$	60190.9	−	60190.9i	0.114513	−	0.114513i
$726$	−305467.	+	305467.i	−0.579550	+	0.579550i
$727$	164676.	+	164676.i	0.311575	+	0.311575i	0.845520	−	0.533944i	$-0.179291\pi$
$727$	164676.	+	164676.i	0.311575	+	0.311575i	−0.533944	+	0.845520i	$0.679291\pi$
$728$		−	176790.i		−	0.333576i
$729$	−220632.			−0.415159
$730$			146648.i			0.275189i
$731$			360421.i			0.674491i
$732$	−43711.7	−	43711.7i	−0.0815784	−	0.0815784i
$733$		−	274893.i		−	0.511630i	−0.966726	−	0.255815i	$-0.917656\pi$
$733$		−	274893.i		−	0.511630i	0.966726	−	0.255815i	$-0.0823437\pi$
$734$	−133902.	−	133902.i	−0.248539	−	0.248539i
$735$	−752989.	−	752989.i	−1.39384	−	1.39384i
$736$	−151153.			−0.279036
$737$	41082.8			0.0756354
$738$	−185435.	+	185435.i	−0.340471	+	0.340471i
$739$			308699.i			0.565257i	0.959229	+	0.282629i	$0.0912064\pi$
$739$			308699.i			0.565257i	−0.959229	+	0.282629i	$0.908794\pi$
$740$	−467883.	+	24025.3i	−0.854425	+	0.0438737i
$741$	−204493.			−0.372427
$742$	544480.	+	544480.i	0.988949	+	0.988949i
$743$			61344.7i			0.111122i	0.998455	+	0.0555609i	$0.0176947\pi$
$743$			61344.7i			0.111122i	−0.998455	+	0.0555609i	$0.982305\pi$
$744$		−	319019.i		−	0.576330i
$745$	647499.	−	647499.i	1.16661	−	1.16661i
$746$	267432.	−	267432.i	0.480547	−	0.480547i
$747$	45365.9			0.0812997
$748$	30350.3	−	30350.3i	0.0542450	−	0.0542450i
$749$	792169.			1.41206
$750$	738057.			1.31210
$751$			685483.i			1.21539i	0.794169	+	0.607697i	$0.207906\pi$
$751$			685483.i			1.21539i	−0.794169	+	0.607697i	$0.792094\pi$
$752$	−20183.5			−0.0356912
$753$	813376.	−	813376.i	1.43450	−	1.43450i
$754$	−15987.9	−	15987.9i	−0.0281222	−	0.0281222i
$755$	−353594.	−	353594.i	−0.620313	−	0.620313i
$756$	298396.			0.522094
$757$	−68334.1	+	68334.1i	−0.119246	+	0.119246i	−0.764212	−	0.644965i	$-0.776872\pi$
$757$	−68334.1	+	68334.1i	−0.119246	+	0.119246i	0.644965	+	0.764212i	$0.276872\pi$
$758$	−312896.	−	312896.i	−0.544580	−	0.544580i
$759$	−68288.6	+	68288.6i	−0.118540	+	0.118540i
$760$	−117592.	−	117592.i	−0.203587	−	0.203587i
$761$		−	1.05937e6i		−	1.82928i	−0.404273	−	0.914639i	$-0.632475\pi$
$761$		−	1.05937e6i		−	1.82928i	0.404273	−	0.914639i	$-0.367525\pi$
$762$	−324670.	+	324670.i	−0.559155	+	0.559155i
$763$	36464.7	−	36464.7i	0.0626359	−	0.0626359i
$764$	309567.	+	309567.i	0.530357	+	0.530357i
$765$		−	618782.i		−	1.05734i
$766$	105703.			0.180149
$767$		−	568244.i		−	0.965927i
$768$		−	43084.8i		−	0.0730469i
$769$	−240561.	−	240561.i	−0.406793	−	0.406793i	0.473826	−	0.880619i	$-0.342873\pi$
$769$	−240561.	−	240561.i	−0.406793	−	0.406793i	−0.880619	+	0.473826i	$0.842873\pi$
$770$		−	91858.0i		−	0.154930i
$771$	570536.	+	570536.i	0.959786	+	0.959786i
$772$	340731.	+	340731.i	0.571712	+	0.571712i
$773$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	74.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} -10.5188i q^{3} +8.00000i q^{4} +(30.2483 - 30.2483i) q^{5} +(-21.0375 + 21.0375i) q^{6} +69.0478 q^{7} +(16.0000 - 16.0000i) q^{8} -29.6443 q^{9} +O(q^{10})\)	\(q+(-2.00000 - 2.00000i) q^{2} -10.5188i q^{3} +8.00000i q^{4} +(30.2483 - 30.2483i) q^{5} +(-21.0375 + 21.0375i) q^{6} +69.0478 q^{7} +(16.0000 - 16.0000i) q^{8} -29.6443 q^{9} -120.993 q^{10} +10.9953i q^{11} +84.1501 q^{12} +(80.0125 - 80.0125i) q^{13} +(-138.096 - 138.096i) q^{14} +(-318.174 - 318.174i) q^{15} -64.0000 q^{16} +(-345.037 + 345.037i) q^{17} +(59.2886 + 59.2886i) q^{18} +(121.486 - 121.486i) q^{19} +(241.986 + 241.986i) q^{20} -726.297i q^{21} +(21.9906 - 21.9906i) q^{22} +(-590.441 + 590.441i) q^{23} +(-168.300 - 168.300i) q^{24} -1204.92i q^{25} -320.050 q^{26} -540.198i q^{27} +552.382i q^{28} +(49.9544 + 49.9544i) q^{29} +1272.70i q^{30} +(947.769 + 947.769i) q^{31} +(128.000 + 128.000i) q^{32} +115.657 q^{33} +1380.15 q^{34} +(2088.58 - 2088.58i) q^{35} -237.155i q^{36} +(-917.114 + 1016.40i) q^{37} -485.944 q^{38} +(-841.632 - 841.632i) q^{39} -967.945i q^{40} +3127.67i q^{41} +(-1452.59 + 1452.59i) q^{42} +(522.294 - 522.294i) q^{43} -87.9624 q^{44} +(-896.689 + 896.689i) q^{45} +2361.76 q^{46} +315.367 q^{47} +673.201i q^{48} +2366.59 q^{49} +(-2409.83 + 2409.83i) q^{50} +(3629.36 + 3629.36i) q^{51} +(640.100 + 640.100i) q^{52} -3942.78 q^{53} +(-1080.40 + 1080.40i) q^{54} +(332.589 + 332.589i) q^{55} +(1104.76 - 1104.76i) q^{56} +(-1277.88 - 1277.88i) q^{57} -199.818i q^{58} +(3550.97 - 3550.97i) q^{59} +(2545.39 - 2545.39i) q^{60} +(-519.449 - 519.449i) q^{61} -3791.08i q^{62} -2046.87 q^{63} -512.000i q^{64} -4840.48i q^{65} +(-231.314 - 231.314i) q^{66} -3736.40i q^{67} +(-2760.30 - 2760.30i) q^{68} +(6210.71 + 6210.71i) q^{69} -8354.30 q^{70} -1195.01 q^{71} +(-474.309 + 474.309i) q^{72} -1212.04i q^{73} +(3867.02 - 198.567i) q^{74} -12674.2 q^{75} +(971.887 + 971.887i) q^{76} +759.201i q^{77} +3366.53i q^{78} +(-1838.99 + 1838.99i) q^{79} +(-1935.89 + 1935.89i) q^{80} -8083.40 q^{81} +(6255.34 - 6255.34i) q^{82} -1530.34 q^{83} +5810.37 q^{84} +20873.6i q^{85} -2089.17 q^{86} +(525.459 - 525.459i) q^{87} +(175.925 + 175.925i) q^{88} +(-5115.00 - 5115.00i) q^{89} +3586.76 q^{90} +(5524.68 - 5524.68i) q^{91} +(-4723.53 - 4723.53i) q^{92} +(9969.36 - 9969.36i) q^{93} +(-630.735 - 630.735i) q^{94} -7349.48i q^{95} +(1346.40 - 1346.40i) q^{96} +(-4016.43 + 4016.43i) q^{97} +(-4733.19 - 4733.19i) q^{98} -325.948i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9}+O(q^{10}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9	\( 14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98}+O(q^{100}) \) 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9 + 48 * q^10 + 160 * q^12 - 56 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 - 348 * q^17 + 692 * q^18 - 184 * q^19 - 96 * q^20 - 320 * q^22 - 502 * q^23 - 320 * q^24 + 224 * q^26 - 474 * q^29 - 630 * q^31 + 1792 * q^32 + 632 * q^33 + 1392 * q^34 + 1826 * q^35 - 2544 * q^37 + 736 * q^38 - 798 * q^39 - 224 * q^42 + 1936 * q^43 + 1280 * q^44 + 6162 * q^45 + 2008 * q^46 + 5716 * q^47 + 7862 * q^49 - 1372 * q^50 - 2422 * q^51 - 448 * q^52 - 20228 * q^53 - 656 * q^54 + 14006 * q^55 + 768 * q^56 - 2270 * q^57 - 4502 * q^59 + 3024 * q^60 - 11906 * q^61 - 2588 * q^63 - 1264 * q^66 - 2784 * q^68 + 21440 * q^69 - 7304 * q^70 - 11224 * q^71 - 5536 * q^72 + 4924 * q^74 - 18652 * q^75 - 1472 * q^76 + 20488 * q^79 + 768 * q^80 - 1706 * q^81 + 9808 * q^82 - 20224 * q^83 + 896 * q^84 - 7744 * q^86 + 19636 * q^87 - 2560 * q^88 + 13864 * q^89 - 24648 * q^90 - 6070 * q^91 - 4016 * q^92 - 13800 * q^93 - 11432 * q^94 + 2560 * q^96 + 16622 * q^97 - 15724 * q^98

Introduction

L-functions

Modular forms

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