LMFDB - Embedded newform 49.4.e.a.8.9

Newspace parameters

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	49.e (of order $7$, degree $6$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.89109359028$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			8.9
Character	$\chi$	$=$	49.8
Dual form			49.4.e.a.43.9

$q$-expansion

$f(q)$	$=$	$q+(0.777062 + 0.974405i) q^{2} +(-0.189548 + 0.0912813i) q^{3} +(1.43453 - 6.28508i) q^{4} +(7.66912 - 3.69325i) q^{5} +(-0.236235 - 0.113765i) q^{6} +(18.3768 + 2.30053i) q^{7} +(16.2220 - 7.81211i) q^{8} +(-16.8066 + 21.0748i) q^{9} +O(q^{10})$	\(q+(0.777062 + 0.974405i) q^{2} +(-0.189548 + 0.0912813i) q^{3} +(1.43453 - 6.28508i) q^{4} +(7.66912 - 3.69325i) q^{5} +(-0.236235 - 0.113765i) q^{6} +(18.3768 + 2.30053i) q^{7} +(16.2220 - 7.81211i) q^{8} +(-16.8066 + 21.0748i) q^{9} +(9.55811 + 4.60294i) q^{10} +(2.58443 + 3.24077i) q^{11} +(0.301799 + 1.32227i) q^{12} +(-11.7770 - 14.7678i) q^{13} +(12.0383 + 19.6941i) q^{14} +(-1.11654 + 1.40009i) q^{15} +(-26.2486 - 12.6407i) q^{16} +(-4.87109 - 21.3416i) q^{17} -33.5952 q^{18} -46.4772 q^{19} +(-12.2108 - 53.4991i) q^{20} +(-3.69328 + 1.24140i) q^{21} +(-1.14956 + 5.03655i) q^{22} +(-18.3535 + 80.4119i) q^{23} +(-2.36174 + 2.96153i) q^{24} +(-32.7609 + 41.0809i) q^{25} +(5.23843 - 22.9511i) q^{26} +(2.52590 - 11.0667i) q^{27} +(40.8211 - 112.200i) q^{28} +(44.6635 + 195.683i) q^{29} -2.23188 q^{30} -276.703 q^{31} +(-40.1317 - 175.829i) q^{32} +(-0.785693 - 0.378370i) q^{33} +(17.0102 - 21.3302i) q^{34} +(149.431 - 50.2272i) q^{35} +(108.347 + 135.863i) q^{36} +(48.3784 + 211.960i) q^{37} +(-36.1157 - 45.2876i) q^{38} +(3.58032 + 1.72419i) q^{39} +(95.5565 - 119.824i) q^{40} +(386.663 - 186.207i) q^{41} +(-4.07953 - 2.63410i) q^{42} +(188.263 + 90.6627i) q^{43} +(24.0759 - 11.5943i) q^{44} +(-51.0573 + 223.697i) q^{45} +(-92.6155 + 44.6013i) q^{46} +(-258.855 - 324.593i) q^{47} +6.12922 q^{48} +(332.415 + 84.5528i) q^{49} -65.4867 q^{50} +(2.87139 + 3.60061i) q^{51} +(-109.711 + 52.8343i) q^{52} +(39.2802 - 172.098i) q^{53} +(12.7462 - 6.13826i) q^{54} +(31.7893 + 15.3089i) q^{55} +(316.081 - 106.243i) q^{56} +(8.80964 - 4.24250i) q^{57} +(-155.969 + 195.578i) q^{58} +(149.792 + 72.1360i) q^{59} +(7.19800 + 9.02601i) q^{60} +(-72.4363 - 317.364i) q^{61} +(-215.015 - 269.621i) q^{62} +(-357.336 + 348.625i) q^{63} +(-5.17349 + 6.48736i) q^{64} +(-144.860 - 69.7611i) q^{65} +(-0.241847 - 1.05960i) q^{66} -809.291 q^{67} -141.121 q^{68} +(-3.86124 - 16.9172i) q^{69} +(165.058 + 106.576i) q^{70} +(44.7834 - 196.209i) q^{71} +(-107.998 + 473.172i) q^{72} +(-391.210 + 490.561i) q^{73} +(-168.941 + 211.846i) q^{74} +(2.45983 - 10.7772i) q^{75} +(-66.6729 + 292.113i) q^{76} +(40.0381 + 65.5006i) q^{77} +(1.10207 + 4.82849i) q^{78} +69.4560 q^{79} -247.989 q^{80} +(-161.420 - 707.229i) q^{81} +(481.902 + 232.072i) q^{82} +(441.287 - 553.356i) q^{83} +(2.50419 + 24.9934i) q^{84} +(-116.177 - 145.681i) q^{85} +(57.9498 + 253.895i) q^{86} +(-26.3281 - 33.0144i) q^{87} +(67.2419 + 32.3820i) q^{88} +(537.947 - 674.565i) q^{89} +(-257.646 + 124.076i) q^{90} +(-182.449 - 298.479i) q^{91} +(479.067 + 230.706i) q^{92} +(52.4484 - 25.2578i) q^{93} +(115.139 - 504.458i) q^{94} +(-356.440 + 171.652i) q^{95} +(23.6567 + 29.6646i) q^{96} +1059.44 q^{97} +(175.918 + 389.610i) q^{98} -111.734 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9}+O(q^{10}) $ 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19} + 553 q^{20} - 21 q^{21} - 605 q^{22} + 149 q^{23} + 653 q^{24} - 370 q^{25} - 511 q^{26} - 65 q^{27} + 70 q^{28} - 187 q^{29} + 84 q^{30} + 1276 q^{31} + 1399 q^{32} - 23 q^{33} - 765 q^{34} - 805 q^{35} - 1691 q^{36} - 1531 q^{37} - 1041 q^{38} - 1351 q^{39} - 1759 q^{40} - 301 q^{41} + 3395 q^{42} - 257 q^{43} - 883 q^{44} + 3105 q^{45} + 1593 q^{46} + 733 q^{47} - 1948 q^{48} + 1288 q^{49} + 6148 q^{50} + 1197 q^{51} - 1099 q^{52} - 285 q^{53} + 660 q^{54} + 2641 q^{55} - 1988 q^{56} - 2352 q^{57} + 1173 q^{58} - 3603 q^{59} - 175 q^{60} - 2613 q^{61} - 1927 q^{62} - 3066 q^{63} + 1589 q^{64} - 371 q^{65} - 2175 q^{66} + 352 q^{67} + 6076 q^{68} + 5549 q^{69} - 6293 q^{70} - 2623 q^{71} + 6220 q^{72} + 2039 q^{73} - 2411 q^{74} - 3903 q^{75} + 4130 q^{76} + 1029 q^{77} - 3759 q^{78} + 44 q^{79} - 1608 q^{80} + 1394 q^{81} - 10920 q^{82} - 553 q^{83} - 7798 q^{84} + 497 q^{85} - 2985 q^{86} - 4273 q^{87} - 2197 q^{88} - 3957 q^{89} - 2958 q^{90} + 14119 q^{91} - 9136 q^{92} + 6272 q^{93} + 14912 q^{94} + 5866 q^{95} + 21882 q^{96} - 1540 q^{97} - 2303 q^{98} + 10768 q^{99}+O(q^{100}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	0.777062	+	0.974405i	0.274733	+	0.344504i	0.899987	−	0.435917i	$-0.143576\pi$
$2$	0.777062	+	0.974405i	0.274733	+	0.344504i	−0.625254	+	0.780421i	$0.715005\pi$
$3$	−0.189548	+	0.0912813i	−0.0364784	+	0.0175671i	−0.452034	−	0.892001i	$-0.649301\pi$
$3$	−0.189548	+	0.0912813i	−0.0364784	+	0.0175671i	0.415556	+	0.909568i	$0.363587\pi$
$4$	1.43453	−	6.28508i	0.179316	−	0.785635i
$5$	7.66912	−	3.69325i	0.685947	−	0.330335i	−0.0582431	−	0.998302i	$-0.518550\pi$
$5$	7.66912	−	3.69325i	0.685947	−	0.330335i	0.744190	+	0.667968i	$0.232836\pi$
$6$	−0.236235	−	0.113765i	−0.0160738	−	0.00774071i
$7$	18.3768	+	2.30053i	0.992255	+	0.124217i
$7$	18.3768	+	2.30053i	0.992255	+	0.124217i
$8$	16.2220	−	7.81211i	0.716919	−	0.345250i
$9$	−16.8066	+	21.0748i	−0.622468	+	0.780550i
$10$	9.55811	+	4.60294i	0.302254	+	0.145558i
$11$	2.58443	+	3.24077i	0.0708394	+	0.0888299i	0.815989	−	0.578068i	$-0.196193\pi$
$11$	2.58443	+	3.24077i	0.0708394	+	0.0888299i	−0.745149	+	0.666898i	$0.767622\pi$
$12$	0.301799	+	1.32227i	0.00726015	+	0.0318088i
$13$	−11.7770	−	14.7678i	−0.251257	−	0.315066i	0.640168	−	0.768235i	$-0.278865\pi$
$13$	−11.7770	−	14.7678i	−0.251257	−	0.315066i	−0.891425	+	0.453169i	$0.850293\pi$
$14$	12.0383	+	19.6941i	0.229812	+	0.375962i
$15$	−1.11654	+	1.40009i	−0.0192193	+	0.0241002i
$16$	−26.2486	−	12.6407i	−0.410135	−	0.197510i
$17$	−4.87109	−	21.3416i	−0.0694948	−	0.304477i	0.928221	−	0.372030i	$-0.121338\pi$
$17$	−4.87109	−	21.3416i	−0.0694948	−	0.304477i	−0.997716	+	0.0675529i	$0.978481\pi$
$18$	−33.5952			−0.439915
$19$	−46.4772			−0.561190			−0.280595	−	0.959826i	$-0.590532\pi$
$19$	−46.4772			−0.561190			−0.280595	+	0.959826i	$0.590532\pi$
$20$	−12.2108	−	53.4991i	−0.136521	−	0.598138i
$21$	−3.69328	+	1.24140i	−0.0383780	+	0.0128998i
$22$	−1.14956	+	5.03655i	−0.0111403	+	0.0488089i
$23$	−18.3535	+	80.4119i	−0.166390	+	0.729002i	0.821030	+	0.570884i	$0.193400\pi$
$23$	−18.3535	+	80.4119i	−0.166390	+	0.729002i	−0.987420	+	0.158117i	$0.949458\pi$
$24$	−2.36174	+	2.96153i	−0.0200870	+	0.0251884i
$25$	−32.7609	+	41.0809i	−0.262087	+	0.328647i
$26$	5.23843	−	22.9511i	0.0395131	−	0.173118i
$27$	2.52590	−	11.0667i	0.0180041	−	0.0788811i
$28$	40.8211	−	112.200i	0.275516	−	0.757276i
$29$	44.6635	+	195.683i	0.285993	+	1.25302i	0.889971	+	0.456017i	$0.150724\pi$
$29$	44.6635	+	195.683i	0.285993	+	1.25302i	−0.603978	+	0.797001i	$0.706419\pi$
$30$	−2.23188			−0.0135828
$31$	−276.703			−1.60314			−0.801570	−	0.597901i	$-0.796002\pi$
$31$	−276.703			−1.60314			−0.801570	+	0.597901i	$0.796002\pi$
$32$	−40.1317	−	175.829i	−0.221699	−	0.971325i
$33$	−0.785693	−	0.378370i	−0.00414459	−	0.00199593i
$34$	17.0102	−	21.3302i	0.0858010	−	0.107591i
$35$	149.431	−	50.2272i	0.721668	−	0.242570i
$36$	108.347	+	135.863i	0.501609	+	0.628997i
$37$	48.3784	+	211.960i	0.214956	+	0.941782i	0.961144	+	0.276047i	$0.0890247\pi$
$37$	48.3784	+	211.960i	0.214956	+	0.941782i	−0.746188	+	0.665735i	$0.768118\pi$
$38$	−36.1157	−	45.2876i	−0.154177	−	0.193332i
$39$	3.58032	+	1.72419i	0.0147003	+	0.00707928i
$40$	95.5565	−	119.824i	0.377720	−	0.473646i
$41$	386.663	−	186.207i	1.47284	−	0.709284i	0.486453	−	0.873707i	$-0.338291\pi$
$41$	386.663	−	186.207i	1.47284	−	0.709284i	0.986390	+	0.164423i	$0.0525762\pi$
$42$	−4.07953	−	2.63410i	−0.0149877	−	0.00967739i
$43$	188.263	+	90.6627i	0.667670	+	0.321533i	0.736835	−	0.676072i	$-0.236319\pi$
$43$	188.263	+	90.6627i	0.667670	+	0.321533i	−0.0691650	+	0.997605i	$0.522034\pi$
$44$	24.0759	−	11.5943i	0.0824905	−	0.0397253i
$45$	−51.0573	+	223.697i	−0.169137	+	0.741039i
$46$	−92.6155	+	44.6013i	−0.296857	+	0.142959i
$47$	−258.855	−	324.593i	−0.803358	−	1.00738i	−0.999640	−	0.0268314i	$-0.991458\pi$
$47$	−258.855	−	324.593i	−0.803358	−	1.00738i	0.196282	−	0.980547i	$-0.437113\pi$
$48$	6.12922			0.0184308
$49$	332.415	+	84.5528i	0.969140	+	0.246510i
$50$	−65.4867			−0.185224
$51$	2.87139	+	3.60061i	0.00788383	+	0.00988601i
$52$	−109.711	+	52.8343i	−0.292582	+	0.140900i
$53$	39.2802	−	172.098i	0.101803	−	0.446028i	−0.898177	−	0.439635i	$-0.855108\pi$
$53$	39.2802	−	172.098i	0.101803	−	0.446028i	0.999980	−	0.00639292i	$-0.00203494\pi$
$54$	12.7462	−	6.13826i	0.0321212	−	0.0154687i
$55$	31.7893	+	15.3089i	0.0779357	+	0.0375319i
$56$	316.081	−	106.243i	0.754252	−	0.253522i
$57$	8.80964	−	4.24250i	0.0204713	−	0.00985847i
$58$	−155.969	+	195.578i	−0.353098	+	0.442771i
$59$	149.792	+	72.1360i	0.330530	+	0.159175i	0.591787	−	0.806095i	$-0.298423\pi$
$59$	149.792	+	72.1360i	0.330530	+	0.159175i	−0.261257	+	0.965269i	$0.584137\pi$
$60$	7.19800	+	9.02601i	0.0154876	+	0.0194209i
$61$	−72.4363	−	317.364i	−0.152041	−	0.666136i	−0.992290	−	0.123936i	$-0.960448\pi$
$61$	−72.4363	−	317.364i	−0.152041	−	0.666136i	0.840249	−	0.542201i	$-0.182409\pi$
$62$	−215.015	−	269.621i	−0.440435	−	0.552288i
$63$	−357.336	+	348.625i	−0.714604	+	0.697184i
$64$	−5.17349	+	6.48736i	−0.0101045	+	0.0126706i
$65$	−144.860	−	69.7611i	−0.276427	−	0.133120i
$66$	−0.241847	−	1.05960i	−0.000451050	−	0.00197618i
$67$	−809.291			−1.47568			−0.737841	−	0.674975i	$-0.764154\pi$
$67$	−809.291			−1.47568			−0.737841	+	0.674975i	$0.764154\pi$
$68$	−141.121			−0.251669
$69$	−3.86124	−	16.9172i	−0.00673680	−	0.0295158i
$70$	165.058	+	106.576i	0.281832	+	0.181975i
$71$	44.7834	−	196.209i	0.0748565	−	0.327968i	−0.923610	−	0.383334i	$-0.874776\pi$
$71$	44.7834	−	196.209i	0.0748565	−	0.327968i	0.998466	+	0.0553667i	$0.0176328\pi$
$72$	−107.998	+	473.172i	−0.176774	+	0.774498i
$73$	−391.210	+	490.561i	−0.627228	+	0.786519i	−0.989341	−	0.145615i	$-0.953484\pi$
$73$	−391.210	+	490.561i	−0.627228	+	0.786519i	0.362113	+	0.932134i	$0.382055\pi$
$74$	−168.941	+	211.846i	−0.265392	+	0.332792i
$75$	2.45983	−	10.7772i	0.00378716	−	0.0165926i
$76$	−66.6729	+	292.113i	−0.100630	+	0.440890i
$77$	40.0381	+	65.5006i	0.0592566	+	0.0969413i
$78$	1.10207	+	4.82849i	0.00159981	+	0.00700921i
$79$	69.4560			0.0989167			0.0494583	−	0.998776i	$-0.484250\pi$
$79$	69.4560			0.0989167			0.0494583	+	0.998776i	$0.484250\pi$
$80$	−247.989			−0.346575
$81$	−161.420	−	707.229i	−0.221427	−	0.970136i
$82$	481.902	+	232.072i	0.648989	+	0.312537i
$83$	441.287	−	553.356i	0.583585	−	0.731792i	−0.399135	−	0.916892i	$-0.630690\pi$
$83$	441.287	−	553.356i	0.583585	−	0.731792i	0.982720	+	0.185100i	$0.0592610\pi$
$84$	2.50419	+	24.9934i	0.00325273	+	0.0324643i
$85$	−116.177	−	145.681i	−0.148249	−	0.185898i
$86$	57.9498	+	253.895i	0.0726615	+	0.318351i
$87$	−26.3281	−	33.0144i	−0.0324445	−	0.0406841i
$88$	67.2419	+	32.3820i	0.0814546	+	0.0392265i
$89$	537.947	−	674.565i	0.640700	−	0.803413i	−0.350390	−	0.936604i	$-0.613951\pi$
$89$	537.947	−	674.565i	0.640700	−	0.803413i	0.991090	+	0.133191i	$0.0425225\pi$
$90$	−257.646	+	124.076i	−0.301758	+	0.145319i
$91$	−182.449	−	298.479i	−0.210175	−	0.343837i
$92$	479.067	+	230.706i	0.542893	+	0.261443i
$93$	52.4484	−	25.2578i	0.0584801	−	0.0281625i
$94$	115.139	−	504.458i	0.126337	−	0.553520i
$95$	−356.440	+	171.652i	−0.384947	+	0.185380i
$96$	23.6567	+	29.6646i	0.0251506	+	0.0315378i
$97$	1059.44			1.10896			0.554481	−	0.832196i	$-0.312917\pi$
$97$	1059.44			1.10896			0.554481	+	0.832196i	$0.312917\pi$
$98$	175.918	+	389.610i	0.181331	+	0.401597i
$99$	−111.734			−0.113431
$100$	211.200	+	264.837i	0.211200	+	0.264837i
$101$	889.783	−	428.497i	0.876601	−	0.422149i	0.0592190	−	0.998245i	$-0.481139\pi$
$101$	889.783	−	428.497i	0.876601	−	0.422149i	0.817382	+	0.576096i	$0.195425\pi$
$102$	−1.27720	+	5.59580i	−0.00123982	+	0.00543202i
$103$	−766.990	+	369.363i	−0.733726	+	0.353344i	−0.763148	−	0.646223i	$-0.776347\pi$
$103$	−766.990	+	369.363i	−0.733726	+	0.353344i	0.0294226	+	0.999567i	$0.490633\pi$
$104$	−306.414	−	147.561i	−0.288908	−	0.139131i
$105$	−23.7394	+	23.1607i	−0.0220641	+	0.0215262i
$106$	198.216	−	95.4559i	0.181627	−	0.0874669i
$107$	1011.63	−	1268.54i	0.914000	−	1.14612i	−0.0748488	−	0.997195i	$-0.523847\pi$
$107$	1011.63	−	1268.54i	0.914000	−	1.14612i	0.988849	−	0.148925i	$-0.0475812\pi$
$108$	−65.9317	−	31.7510i	−0.0587433	−	0.0282893i
$109$	743.116	+	931.838i	0.653006	+	0.818843i	0.992562	−	0.121743i	$-0.0388482\pi$
$109$	743.116	+	931.838i	0.653006	+	0.818843i	−0.339556	+	0.940586i	$0.610277\pi$
$110$	9.78516	+	42.8716i	0.00848162	+	0.0371604i
$111$	−28.5179	−	35.7604i	−0.0243856	−	0.0305786i
$112$	−453.286	−	292.681i	−0.382424	−	0.246926i
$113$	−918.631	+	1151.93i	−0.764757	+	0.958975i	−0.999916	−	0.0129823i	$-0.995867\pi$
$113$	−918.631	+	1151.93i	−0.764757	+	0.958975i	0.235159	+	0.971957i	$0.424439\pi$
$114$	10.9795	+	5.28747i	0.00902043	+	0.00434401i
$115$	156.226	+	684.473i	0.126680	+	0.555021i
$116$	1293.96			1.03570
$117$	509.161			0.402325
$118$	46.1079	+	202.012i	0.0359710	+	0.157599i
$119$	−40.4180	−	403.397i	−0.0311354	−	0.310751i
$120$	−7.17481	+	31.4349i	−0.00545806	+	0.0239133i
$121$	292.352	−	1280.88i	0.219648	−	0.962343i
$122$	252.954	−	317.194i	0.187716	−	0.235388i
$123$	−56.2937	+	70.5901i	−0.0412670	+	0.0517471i
$124$	−396.938	+	1739.10i	−0.287469	+	1.25948i
$125$	−336.290	+	1473.38i	−0.240629	+	1.05427i
$126$	−617.373	−	77.2868i	−0.436508	−	0.0546449i
$127$	−412.014	−	1805.15i	−0.287877	−	1.26127i	−0.887432	−	0.460938i	$-0.847513\pi$
$127$	−412.014	−	1805.15i	−0.287877	−	1.26127i	0.599556	−	0.800333i	$-0.295344\pi$
$128$	−1453.14			−1.00345
$129$	−43.9606			−0.0300040
$130$	−44.5900	−	195.361i	−0.0300831	−	0.131802i
$131$	−959.091	−	461.874i	−0.639665	−	0.308047i	0.0857928	−	0.996313i	$-0.472658\pi$
$131$	−959.091	−	461.874i	−0.639665	−	0.308047i	−0.725458	+	0.688266i	$0.758372\pi$
$132$	−3.50518	+	4.39536i	−0.00231127	+	0.00289824i
$133$	−854.104	−	106.922i	−0.556843	−	0.0697093i
$134$	−628.869	−	788.577i	−0.405418	−	0.508378i
$135$	−21.5007	−	94.2008i	−0.0137073	−	0.0600556i
$136$	−245.742	−	308.151i	−0.154943	−	0.194292i
$137$	1426.58	+	687.006i	0.889643	+	0.428430i	0.822137	−	0.569289i	$-0.192782\pi$
$137$	1426.58	+	687.006i	0.889643	+	0.428430i	0.0675060	+	0.997719i	$0.478496\pi$
$138$	13.4838	−	16.9081i	0.00831750	−	0.0104298i
$139$	−2822.28	+	1359.14i	−1.72218	+	0.829358i	−0.733433	+	0.679762i	$0.762083\pi$
$139$	−2822.28	+	1359.14i	−1.72218	+	0.829358i	−0.988747	+	0.149597i	$0.952202\pi$
$140$	−101.320	−	1011.24i	−0.0611649	−	0.610464i
$141$	78.6945	+	37.8973i	0.0470020	+	0.0226349i
$142$	225.986	−	108.829i	0.133552	−	0.0643151i
$143$	17.4225	−	76.3328i	0.0101884	−	0.0446383i
$144$	707.551	−	340.739i	0.409462	−	0.197187i
$145$	1065.24	+	1335.77i	0.610091	+	0.765030i
$146$	−781.999			−0.443279
$147$	−70.7266	+	14.3165i	−0.0396832	+	0.00803268i
$148$	1401.58			0.778442
$149$	−16.6867	−	20.9245i	−0.00917469	−	0.0115047i	0.777223	−	0.629225i	$-0.216628\pi$
$149$	−16.6867	−	20.9245i	−0.00917469	−	0.0115047i	−0.786398	+	0.617721i	$0.788056\pi$
$150$	12.4128	−	5.97771i	0.00675669	−	0.00325385i
$151$	128.306	−	562.147i	0.0691486	−	0.302960i	−0.928514	−	0.371298i	$-0.878913\pi$
$151$	128.306	−	562.147i	0.0691486	−	0.302960i	0.997662	+	0.0683387i	$0.0217698\pi$
$152$	−753.954	+	363.085i	−0.402327	+	0.193751i
$153$	531.638	+	256.023i	0.280918	+	0.135283i
$154$	−32.7120	+	89.9113i	−0.0171169	+	0.0470471i
$155$	−2122.07	+	1021.94i	−1.09967	+	0.529573i
$156$	15.9728	−	20.0292i	0.00819772	−	0.0102796i
$157$	1576.92	+	759.404i	0.801603	+	0.386032i	0.789389	−	0.613894i	$-0.210398\pi$
$157$	1576.92	+	759.404i	0.801603	+	0.386032i	0.0122146	+	0.999925i	$0.496112\pi$
$158$	53.9716	+	67.6783i	0.0271756	+	0.0340772i
$159$	8.26385	+	36.2063i	0.00412180	+	0.0180588i
$160$	−957.155	−	1200.23i	−0.472936	−	0.593043i
$161$	−522.269	+	1435.49i	−0.255656	+	0.702687i
$162$	563.694	−	706.849i	0.273382	−	0.342811i
$163$	−1671.09	−	804.754i	−0.803005	−	0.386707i	−0.0130831	−	0.999914i	$-0.504165\pi$
$163$	−1671.09	−	804.754i	−0.803005	−	0.386707i	−0.789922	+	0.613208i	$0.789879\pi$
$164$	−615.647	−	2697.32i	−0.293134	−	1.28430i
$165$	−7.42299			−0.00350230
$166$	882.100			0.412435
$167$	364.776	+	1598.19i	0.169025	+	0.740549i	0.986389	+	0.164427i	$0.0525775\pi$
$167$	364.776	+	1598.19i	0.169025	+	0.740549i	−0.817364	+	0.576122i	$0.804565\pi$
$168$	−50.2144	+	48.9903i	−0.0230603	+	0.0224981i
$169$	409.486	−	1794.08i	0.186384	−	0.816603i
$170$	51.6759	−	226.407i	0.0233139	−	0.102145i
$171$	781.125	−	979.500i	0.349323	−	0.438037i
$172$	839.890	−	1053.19i	0.372332	−	0.466889i
$173$	−327.191	+	1433.52i	−0.143791	+	0.629990i	0.850743	+	0.525581i	$0.176152\pi$
$173$	−327.191	+	1433.52i	−0.143791	+	0.629990i	−0.994534	+	0.104409i	$0.966705\pi$
$174$	11.7108	−	51.3084i	0.00510227	−	0.0223545i
$175$	−696.549	+	679.569i	−0.300881	+	0.293546i
$176$	−26.8721	−	117.735i	−0.0115089	−	0.0504237i
$177$	−34.9773			−0.0148534
$178$	1075.32			0.452800
$179$	710.873	+	3114.54i	0.296833	+	1.30051i	0.874813	+	0.484461i	$0.160984\pi$
$179$	710.873	+	3114.54i	0.296833	+	1.30051i	−0.577980	+	0.816051i	$0.696159\pi$
$180$	1332.71	+	641.799i	0.551857	+	0.265760i
$181$	2134.95	−	2677.14i	0.876737	−	1.09939i	−0.117594	−	0.993062i	$-0.537518\pi$
$181$	2134.95	−	2677.14i	0.876737	−	1.09939i	0.994331	−	0.106331i	$-0.0339104\pi$
$182$	149.065	−	409.716i	0.0607113	−	0.166869i
$183$	42.6995	+	53.5435i	0.0172483	+	0.0216287i
$184$	330.456	+	1447.82i	0.132400	+	0.580081i
$185$	1153.84	+	1446.87i	0.458552	+	0.575006i
$186$	65.3670	+	31.4791i	0.0257685	+	0.0124094i
$187$	56.5743	−	70.9419i	0.0221236	−	0.0277422i
$188$	−2411.43	+	1161.28i	−0.935487	+	0.450507i
$189$	71.8774	−	197.560i	0.0276630	−	0.0760337i
$190$	−444.234	−	213.932i	−0.169622	−	0.0816855i
$191$	2267.15	−	1091.80i	0.858874	−	0.413612i	0.0480101	−	0.998847i	$-0.484712\pi$
$191$	2267.15	−	1091.80i	0.858874	−	0.413612i	0.810864	+	0.585235i	$0.198998\pi$
$192$	0.388449	−	1.70191i	0.000146010	−	0.000639711i
$193$	−1264.46	+	608.932i	−0.471595	+	0.227108i	−0.654558	−	0.756012i	$-0.727145\pi$
$193$	−1264.46	+	608.932i	−0.471595	+	0.227108i	0.182963	+	0.983120i	$0.441431\pi$
$194$	823.247	+	1032.32i	0.304668	+	0.382042i
$195$	33.8258			0.0124221
$196$	1008.28	−	1967.96i	0.367449	−	0.717187i
$197$	−1587.00			−0.573956			−0.286978	−	0.957937i	$-0.592651\pi$
$197$	−1587.00			−0.573956			−0.286978	+	0.957937i	$0.592651\pi$
$198$	−86.8244	−	108.874i	−0.0311633	−	0.0390776i
$199$	2899.11	−	1396.14i	1.03273	−	0.497335i	0.160808	−	0.986986i	$-0.448590\pi$
$199$	2899.11	−	1396.14i	1.03273	−	0.497335i	0.871919	+	0.489651i	$0.162876\pi$
$200$	−210.520	+	922.347i	−0.0744299	+	0.326099i
$201$	153.399	−	73.8731i	0.0538306	−	0.0259234i
$202$	1108.95	+	534.040i	0.386263	+	0.186014i
$203$	370.597	+	3698.79i	0.128132	+	1.27884i
$204$	26.7492	−	12.8818i	0.00918049	−	0.00442109i
$205$	2277.65	−	2856.09i	0.775991	−	0.973062i
$206$	−955.907	−	460.341i	−0.323307	−	0.155696i
$207$	−1386.21	−	1738.25i	−0.465450	−	0.583656i
$208$	122.454	+	536.504i	0.0408203	+	0.178846i
$209$	−120.117	−	150.622i	−0.0397544	−	0.0498504i
$210$	−41.0148	−	5.13450i	−0.0134776	−	0.00168721i
$211$	874.334	−	1096.38i	0.285268	−	0.357715i	−0.618464	−	0.785813i	$-0.712245\pi$
$211$	874.334	−	1096.38i	0.285268	−	0.357715i	0.903732	+	0.428098i	$0.140816\pi$
$212$	−1025.30	−	493.759i	−0.332160	−	0.159960i
$213$	9.42162	+	41.2788i	0.00303079	+	0.0132788i
$214$	2022.17			0.645948
$215$	1778.65			0.564200
$216$	−45.4791	−	199.257i	−0.0143262	−	0.0627672i
$217$	−5084.92	−	636.564i	−1.59072	−	0.199137i
$218$	−330.540	+	1448.19i	−0.102693	+	0.449926i
$219$	29.3738	−	128.695i	0.00906345	−	0.0397095i
$220$	141.820	−	177.837i	0.0434615	−	0.0544989i
$221$	−257.803	+	323.275i	−0.0784693	+	0.0983974i
$222$	12.6849	−	55.5760i	0.00383492	−	0.0168019i
$223$	29.0554	−	127.300i	0.00872508	−	0.0382271i	−0.970378	−	0.241592i	$-0.922331\pi$
$223$	29.0554	−	127.300i	0.00872508	−	0.0382271i	0.979103	+	0.203365i	$0.0651877\pi$
$224$	−332.995	−	3323.50i	−0.0993265	−	0.991341i
$225$	−315.173	−	1380.86i	−0.0933845	−	0.409144i
$226$	−1836.28			−0.540474
$227$	−4046.40			−1.18312			−0.591562	−	0.806259i	$-0.701489\pi$
$227$	−4046.40			−1.18312			−0.591562	+	0.806259i	$0.701489\pi$
$228$	−14.0268	−	61.4553i	−0.00407432	−	0.0178508i
$229$	−4657.91	−	2243.13i	−1.34412	−	0.647293i	−0.383082	−	0.923714i	$-0.625137\pi$
$229$	−4657.91	−	2243.13i	−1.34412	−	0.647293i	−0.961037	+	0.276421i	$0.910852\pi$
$230$	−545.556	+	684.105i	−0.156404	+	0.196124i
$231$	−13.5681	−	8.76075i	−0.00386457	−	0.00249530i
$232$	2253.23	+	2825.47i	0.637638	+	0.799573i
$233$	1190.56	+	5216.18i	0.334748	+	1.46662i	0.809820	+	0.586678i	$0.199565\pi$
$233$	1190.56	+	5216.18i	0.334748	+	1.46662i	−0.475073	+	0.879947i	$0.657578\pi$
$234$	395.650	+	496.129i	0.110532	+	0.138602i
$235$	−3183.99	−	1533.33i	−0.883833	−	0.425632i
$236$	668.261	−	837.973i	0.184322	−	0.231133i
$237$	−13.1652	+	6.34004i	−0.00360833	+	0.00173768i
$238$	361.665	−	352.848i	0.0985011	−	0.0960998i
$239$	−1278.15	−	615.524i	−0.345927	−	0.166590i	0.252850	−	0.967506i	$-0.418632\pi$
$239$	−1278.15	−	615.524i	−0.345927	−	0.166590i	−0.598777	+	0.800916i	$0.704346\pi$
$240$	47.0057	−	22.6368i	0.0126425	−	0.00608832i
$241$	−1060.04	+	4644.33i	−0.283332	+	1.24136i	0.610160	+	0.792278i	$0.291105\pi$
$241$	−1060.04	+	4644.33i	−0.283332	+	1.24136i	−0.893492	+	0.449080i	$0.851752\pi$
$242$	1475.27	−	710.452i	0.391876	−	0.188717i
$243$	286.244	+	358.939i	0.0755661	+	0.0947569i
$244$	−2098.57			−0.550603
$245$	2861.61	−	579.248i	0.746210	−	0.151048i
$246$	−112.527			−0.0291645
$247$	547.361	+	686.369i	0.141003	+	0.176812i
$248$	−4488.68	+	2161.64i	−1.14932	+	0.553484i
$249$	−33.1338	+	145.169i	−0.00843280	+	0.0369465i
$250$	−1696.99	+	817.227i	−0.429308	+	0.206744i
$251$	6654.27	+	3204.53i	1.67336	+	0.805849i	0.997638	+	0.0686956i	$0.0218837\pi$
$251$	6654.27	+	3204.53i	1.67336	+	0.805849i	0.675725	+	0.737154i	$0.263831\pi$
$252$	1678.52	+	2745.99i	0.419592	+	0.686434i
$253$	−308.030	+	148.339i	−0.0765441	+	0.0368617i
$254$	1438.79	−	1804.18i	0.355424	−	0.445687i
$255$	35.3190	+	17.0088i	0.00867359	+	0.00417698i
$256$	−1087.79	−	1364.05i	−0.265575	−	0.333020i
$257$	−1640.45	−	7187.28i	−0.398165	−	1.74447i	−0.634613	−	0.772830i	$-0.718840\pi$
$257$	−1640.45	−	7187.28i	−0.398165	−	1.74447i	0.236448	−	0.971644i	$-0.424017\pi$
$258$	−34.1601	−	42.8354i	−0.00824308	−	0.0103365i
$259$	401.422	+	4006.44i	0.0963055	+	0.961189i
$260$	−646.260	+	810.385i	−0.154151	+	0.193300i
$261$	−4874.64	−	2347.50i	−1.15606	−	0.556731i
$262$	−295.221	−	1293.45i	−0.0696137	−	0.304998i
$263$	−2202.52			−0.516401			−0.258201	−	0.966091i	$-0.583130\pi$
$263$	−2202.52			−0.516401			−0.258201	+	0.966091i	$0.583130\pi$
$264$	−15.7014			−0.00366043
$265$	−334.357	−	1464.91i	−0.0775070	−	0.339580i
$266$	−559.506	−	915.328i	−0.128968	−	0.210986i
$267$	−40.3915	+	176.967i	−0.00925812	+	0.0405625i
$268$	−1160.95	+	5086.46i	−0.264613	+	1.15935i
$269$	−513.275	+	643.626i	−0.116338	+	0.145883i	−0.836590	−	0.547829i	$-0.815455\pi$
$269$	−513.275	+	643.626i	−0.116338	+	0.145883i	0.720253	+	0.693712i	$0.244026\pi$
$270$	75.0823	−	94.1502i	0.0169236	−	0.0212215i
$271$	1137.11	−	4982.00i	0.254887	−	1.11673i	−0.671751	−	0.740777i	$-0.734457\pi$
$271$	1137.11	−	4982.00i	0.254887	−	1.11673i	0.926638	−	0.375956i	$-0.122686\pi$
$272$	−141.913	+	621.762i	−0.0316351	+	0.138602i
$273$	61.8284	+	39.9218i	0.0137071	+	0.00885047i
$274$	439.121	+	1923.91i	0.0968185	+	0.424189i
$275$	−217.802			−0.0477598
$276$	−111.865			−0.0243967
$277$	211.636	+	927.240i	0.0459061	+	0.201128i	0.992681	−	0.120770i	$-0.0385364\pi$
$277$	211.636	+	927.240i	0.0459061	+	0.201128i	−0.946774	+	0.321898i	$0.895679\pi$
$278$	−3517.44	−	1693.91i	−0.758857	−	0.365446i
$279$	4650.45	−	5831.48i	0.997903	−	1.25133i
$280$	2031.68	−	1982.16i	0.433630	−	0.423059i
$281$	432.533	+	542.379i	0.0918247	+	0.115145i	0.825621	−	0.564225i	$-0.190825\pi$
$281$	432.533	+	542.379i	0.0918247	+	0.115145i	−0.733797	+	0.679369i	$0.762253\pi$
$282$	24.2232	+	106.129i	0.00511515	+	0.0224109i
$283$	1015.73	+	1273.69i	0.213353	+	0.267537i	0.876980	−	0.480528i	$-0.159555\pi$
$283$	1015.73	+	1273.69i	0.213353	+	0.267537i	−0.663626	+	0.748064i	$0.730983\pi$
$284$	−1168.95	−	562.934i	−0.244240	−	0.117620i
$285$	51.8936	−	65.0725i	0.0107857	−	0.0135248i
$286$	87.9174	−	42.3388i	0.0181771	−	0.00875365i
$287$	7534.00	−	2532.36i	1.54954	−	0.520838i
$288$	4380.04	+	2109.32i	0.896168	+	0.431572i
$289$	3994.72	−	1923.76i	0.813092	−	0.391565i
$290$	−473.821	+	2075.95i	−0.0959440	+	0.420358i
$291$	−200.813	+	96.7066i	−0.0404532	+	0.0194813i
$292$	2522.02	+	3162.51i	0.505445	+	0.633807i
$293$	2804.83			0.559248			0.279624	−	0.960110i	$-0.409790\pi$
$293$	2804.83			0.559248			0.279624	+	0.960110i	$0.409790\pi$
$294$	−68.9090	−	57.7915i	−0.0136696	−	0.0114642i
$295$	1415.19			0.279307
$296$	2440.65	+	3060.48i	0.479256	+	0.600968i
$297$	42.3927	−	20.4152i	0.00828239	−	0.00398859i
$298$	7.42230	−	32.5192i	0.00144283	−	0.00632144i
$299$	1403.66	−	675.967i	0.271491	−	0.130743i
$300$	−64.2071	−	30.9205i	−0.0123567	−	0.00595065i
$301$	3251.10	+	2099.20i	0.622560	+	0.401979i
$302$	647.461	−	311.801i	0.123368	−	0.0594110i
$303$	−129.542	+	162.441i	−0.0245611	+	0.0307987i
$304$	1219.96	+	587.503i	0.230163	+	0.110841i
$305$	−1727.63	−	2166.38i	−0.324340	−	0.406710i
$306$	163.645	+	716.976i	0.0305718	+	0.133944i
$307$	−4980.14	−	6244.90i	−0.925836	−	1.16096i	−0.986657	−	0.162813i	$-0.947943\pi$
$307$	−4980.14	−	6244.90i	−0.925836	−	1.16096i	0.0608211	−	0.998149i	$-0.480628\pi$
$308$	469.112	−	157.680i	0.0867861	−	0.0291709i
$309$	111.665	−	140.024i	0.0205579	−	0.0257788i
$310$	−2644.76	−	1273.65i	−0.484555	−	0.233350i
$311$	−628.340	−	2752.94i	−0.114566	−	0.501945i	−0.999354	−	0.0359509i	$-0.988554\pi$
$311$	−628.340	−	2752.94i	−0.114566	−	0.501945i	0.884788	−	0.465994i	$-0.154303\pi$
$312$	71.5497			0.0129830
$313$	3639.11			0.657171			0.328585	−	0.944474i	$-0.393428\pi$
$313$	3639.11			0.657171			0.328585	+	0.944474i	$0.393428\pi$
$314$	485.396	+	2126.66i	0.0872372	+	0.382211i
$315$	−1452.89	+	3993.38i	−0.259877	+	0.714290i
$316$	99.6367	−	436.537i	0.0177373	−	0.0777124i
$317$	−745.396	+	3265.79i	−0.132068	+	0.578628i	0.864977	+	0.501811i	$0.167333\pi$
$317$	−745.396	+	3265.79i	−0.132068	+	0.578628i	−0.997045	+	0.0768168i	$0.975524\pi$
$318$	−28.8580	+	36.1868i	−0.00508893	+	0.00638131i
$319$	−518.735	+	650.474i	−0.0910458	+	0.114168i
$320$	−15.7167	+	68.8594i	−0.00274559	+	0.0120292i
$321$	−75.9577	+	332.792i	−0.0132073	+	0.0578650i
$322$	−1804.59	+	606.565i	−0.312316	+	0.104977i
$323$	226.395	+	991.899i	0.0389998	+	0.170869i
$324$	−4676.55			−0.801878
$325$	992.501			0.169397
$326$	−514.383	−	2253.66i	−0.0873897	−	0.382879i
$327$	−225.915	−	108.795i	−0.0382053	−	0.0183987i
$328$	4817.78	−	6041.30i	0.811028	−	1.01700i
$329$	−4010.19	−	6560.50i	−0.672002	−	1.09937i
$330$	−5.76812	−	7.23300i	−0.000962196	−	0.00120656i
$331$	2610.61	+	11437.8i	0.433511	+	1.89933i	0.437248	+	0.899341i	$0.355953\pi$
$331$	2610.61	+	11437.8i	0.433511	+	1.89933i	−0.00373758	+	0.999993i	$0.501190\pi$
$332$	−2844.85	−	3567.33i	−0.470275	−	0.589706i
$333$	−5280.09	−	2542.76i	−0.868911	−	0.418445i
$334$	−1273.83	+	1597.33i	−0.208685	+	0.261683i
$335$	−6206.55	+	2988.92i	−1.01224	+	0.487469i
$336$	112.636	+	14.1004i	0.0182880	+	0.00228941i
$337$	1992.46	+	959.519i	0.322066	+	0.155099i	0.587930	−	0.808912i	$-0.299943\pi$
$337$	1992.46	+	959.519i	0.322066	+	0.155099i	−0.265864	+	0.964011i	$0.585657\pi$
$338$	2066.35	−	995.102i	0.332529	−	0.160137i
$339$	68.9749	−	302.199i	0.0110507	−	0.0484164i
$340$	−1082.28	+	521.198i	−0.172632	+	0.0831350i
$341$	−715.119	−	896.731i	−0.113566	−	0.142407i
$342$	1561.41			0.246876
$343$	5914.22	+	2318.54i	0.931014	+	0.364984i
$344$	3762.27			0.589675
$345$	−92.0919	−	115.480i	−0.0143712	−	0.0180209i
$346$	−1651.07	+	795.114i	−0.256538	+	0.123542i
$347$	−922.316	+	4040.93i	−0.142687	+	0.625154i	0.852117	+	0.523351i	$0.175318\pi$
$347$	−922.316	+	4040.93i	−0.142687	+	0.625154i	−0.994805	+	0.101803i	$0.967539\pi$
$348$	−245.266	+	118.114i	−0.0377806	+	0.0181942i
$349$	−115.471	−	55.6078i	−0.0177106	−	0.00852898i	0.425007	−	0.905190i	$-0.360271\pi$
$349$	−115.471	−	55.6078i	−0.0177106	−	0.00852898i	−0.442718	+	0.896661i	$0.645986\pi$
$350$	−1203.44	−	150.654i	−0.183790	−	0.0230080i
$351$	−193.179	+	93.0301i	−0.0293764	+	0.0141469i
$352$	466.102	−	584.474i	0.0705777	−	0.0885016i
$353$	−7903.61	−	3806.18i	−1.19169	−	0.573888i	−0.270395	−	0.962750i	$-0.587154\pi$
$353$	−7903.61	−	3806.18i	−1.19169	−	0.573888i	−0.921296	+	0.388861i	$0.872869\pi$
$354$	−27.1796	−	34.0821i	−0.00408073	−	0.00511707i
$355$	−381.200	−	1670.15i	−0.0569915	−	0.249696i
$356$	−3467.99	−	4348.72i	−0.516301	−	0.647421i
$357$	44.4838	+	72.7736i	0.00659476	+	0.0107888i
$358$	−2482.43	+	3112.87i	−0.366482	+	0.459553i
$359$	−1050.36	−	505.827i	−0.154418	−	0.0743636i	0.355079	−	0.934836i	$-0.384454\pi$
$359$	−1050.36	−	505.827i	−0.154418	−	0.0743636i	−0.509496	+	0.860473i	$0.670168\pi$
$360$	919.291	+	4027.68i	0.134586	+	0.589659i
$361$	−4698.87			−0.685066
$362$	4267.60			0.619614
$363$	61.5056	+	269.474i	0.00889313	+	0.0389633i
$364$	−2137.70	+	718.531i	−0.307818	+	0.103465i
$365$	−1188.47	+	5207.01i	−0.170431	+	0.746706i
$366$	−18.9929	+	83.2132i	−0.00271250	+	0.0118842i
$367$	−442.098	+	554.374i	−0.0628811	+	0.0788504i	−0.812277	−	0.583271i	$-0.801772\pi$
$367$	−442.098	+	554.374i	−0.0628811	+	0.0788504i	0.749396	+	0.662122i	$0.230344\pi$
$368$	1498.21	−	1878.70i	0.212228	−	0.266125i
$369$	−2574.21	+	11278.4i	−0.363166	+	1.59113i
$370$	−513.232	+	2248.61i	−0.0721126	+	0.315946i
$371$	1117.76	−	3072.25i	0.156419	−	0.429928i
$372$	−83.5087	−	365.875i	−0.0116390	−	0.0509940i
$373$	−10232.3			−1.42039			−0.710196	−	0.704004i	$-0.751393\pi$
$373$	−10232.3			−1.42039			−0.710196	+	0.704004i	$0.751393\pi$
$374$	113.088			0.0156354
$375$	−70.7493	−	309.973i	−0.00974261	−	0.0426852i
$376$	−6734.90	−	3243.36i	−0.923740	−	0.444850i
$377$	2363.82	−	2964.14i	0.322926	−	0.404936i
$378$	248.357	−	83.4787i	0.0337939	−	0.0113589i
$379$	−891.862	−	1118.36i	−0.120876	−	0.151573i	0.717712	−	0.696340i	$-0.245190\pi$
$379$	−891.862	−	1118.36i	−0.120876	−	0.151573i	−0.838587	+	0.544767i	$0.816618\pi$
$380$	567.525	+	2486.49i	0.0766143	+	0.335669i
$381$	242.873	+	304.553i	0.0326582	+	0.0409520i
$382$	2825.57	+	1360.72i	0.378452	+	0.182253i
$383$	7720.69	−	9681.43i	1.03005	−	1.29164i	0.0743691	−	0.997231i	$-0.476306\pi$
$383$	7720.69	−	9681.43i	1.03005	−	1.29164i	0.955679	−	0.294409i	$-0.0951229\pi$
$384$	275.440	−	132.645i	0.0366041	−	0.0176276i
$385$	548.967	+	354.461i	0.0726700	+	0.0469221i
$386$	−1575.91	−	758.918i	−0.207802	−	0.100072i
$387$	−5074.77	+	2443.88i	−0.666576	+	0.321006i
$388$	1519.79	−	6658.64i	0.198855	−	0.871240i
$389$	6064.35	−	2920.44i	0.790423	−	0.380648i	0.00529882	−	0.999986i	$-0.498313\pi$
$389$	6064.35	−	2920.44i	0.790423	−	0.380648i	0.785124	+	0.619338i	$0.212599\pi$
$390$	26.2847	+	32.9600i	0.00341277	+	0.00427948i
$391$	1805.52			0.233527
$392$	6052.98	−	1225.25i	0.779902	−	0.157868i
$393$	223.954			0.0287455
$394$	−1233.20	−	1546.38i	−0.157685	−	0.197730i
$395$	532.667	−	256.519i	0.0678516	−	0.0326756i
$396$	−160.286	+	702.258i	−0.0203401	+	0.0891157i
$397$	−10947.6	+	5272.08i	−1.38399	+	0.666494i	−0.969846	−	0.243718i	$-0.921633\pi$
$397$	−10947.6	+	5272.08i	−1.38399	+	0.666494i	−0.414143	+	0.910212i	$0.635919\pi$
$398$	3613.19	+	1740.02i	0.455058	+	0.219144i
$399$	171.653	−	57.6968i	0.0215374	−	0.00723923i
$400$	1379.22	−	664.197i	0.172402	−	0.0830246i
$401$	9919.07	−	12438.1i	1.23525	−	1.54895i	0.510636	−	0.859797i	$-0.329410\pi$
$401$	9919.07	−	12438.1i	1.23525	−	1.54895i	0.724613	−	0.689157i	$-0.242019\pi$
$402$	191.183	+	92.0689i	0.0237197	+	0.0114228i
$403$	3258.72	+	4086.31i	0.402800	+	0.505096i
$404$	−1416.72	−	6207.04i	−0.174466	−	0.764386i
$405$	−3849.93	−	4827.66i	−0.472357	−	0.592317i
$406$	−3316.14	+	3235.30i	−0.405363	+	0.395481i
$407$	−561.882	+	704.577i	−0.0684310	+	0.0858098i
$408$	74.7082	+	35.9776i	0.00906521	+	0.00436558i
$409$	1822.05	+	7982.90i	0.220280	+	0.965108i	0.957268	+	0.289203i	$0.0933901\pi$
$409$	1822.05	+	7982.90i	0.220280	+	0.965108i	−0.736988	+	0.675905i	$0.763753\pi$
$410$	4552.86			0.548414
$411$	−333.116			−0.0399791
$412$	1221.21	+	5350.45i	0.146030	+	0.639801i
$413$	2586.75	+	1670.23i	0.308197	+	0.198999i
$414$	616.590	−	2701.46i	0.0731974	−	0.320699i
$415$	1340.60	−	5873.54i	0.158572	−	0.694749i
$416$	−2123.98	+	2663.39i	−0.250329	+	0.313902i
$417$	410.893	−	515.243i	0.0482530	−	0.0605074i
$418$	53.4284	−	234.085i	0.00625184	−	0.0273911i
$419$	−3083.42	+	13509.4i	−0.359511	+	1.57512i	0.394904	+	0.918723i	$0.370778\pi$
$419$	−3083.42	+	13509.4i	−0.359511	+	1.57512i	−0.754415	+	0.656398i	$0.772079\pi$
$420$	111.512	+	182.428i	0.0129553	+	0.0211943i
$421$	1042.61	+	4567.98i	0.120698	+	0.528812i	0.998738	+	0.0502246i	$0.0159937\pi$
$421$	1042.61	+	4567.98i	0.120698	+	0.528812i	−0.878040	+	0.478587i	$0.841149\pi$
$422$	1747.73			0.201607
$423$	11191.2			1.28637
$424$	−707.244	−	3098.64i	−0.0810066	−	0.354913i
$425$	1036.31	+	499.063i	0.118279	+	0.0569602i
$426$	−32.9011	+	41.2566i	−0.00374193	+	0.00469223i
$427$	−601.043	−	5998.79i	−0.0681183	−	0.679863i
$428$	−6521.69	−	8177.94i	−0.736537	−	0.923588i
$429$	3.66537	+	16.0590i	0.000412508	+	0.00180731i
$430$	1382.12	+	1733.13i	0.155004	+	0.194369i
$431$	9609.19	+	4627.54i	1.07392	+	0.517171i	0.885367	−	0.464892i	$-0.153907\pi$
$431$	9609.19	+	4627.54i	1.07392	+	0.517171i	0.188550	+	0.982064i	$0.439621\pi$
$432$	−206.192	+	258.557i	−0.0229639	+	0.0287959i
$433$	−5665.85	+	2728.53i	−0.628830	+	0.302829i	−0.721022	−	0.692913i	$-0.756327\pi$
$433$	−5665.85	+	2728.53i	−0.628830	+	0.302829i	0.0921912	+	0.995741i	$0.470613\pi$
$434$	−3331.03	−	5449.42i	−0.368421	−	0.602720i
$435$	−323.844	−	155.955i	−0.0356945	−	0.0171896i
$436$	6922.70	−	3333.80i	0.760406	−	0.366192i
$437$	853.019	−	3737.32i	0.0933763	−	0.409108i
$438$	148.226	−	71.3819i	0.0161701	−	0.00778712i
$439$	9590.40	+	12026.0i	1.04265	+	1.30745i	0.950170	+	0.311732i	$0.100909\pi$
$439$	9590.40	+	12026.0i	1.04265	+	1.30745i	0.0924837	+	0.995714i	$0.470519\pi$
$440$	635.281			0.0688314
$441$	−7368.72	+	5584.55i	−0.795672	+	0.603018i
$442$	−515.330			−0.0554564
$443$	6152.54	+	7715.04i	0.659855	+	0.827432i	0.993328	−	0.115328i	$-0.0367918\pi$
$443$	6152.54	+	7715.04i	0.659855	+	0.827432i	−0.333472	+	0.942760i	$0.608220\pi$
$444$	−265.667	+	127.938i	−0.0283963	+	0.0136750i
$445$	1634.25	−	7160.10i	0.174091	−	0.762744i
$446$	146.620	−	70.6083i	0.0155665	−	0.00749641i
$447$	5.07294	+	2.44300i	0.000536782	+	0.000258501i
$448$	−109.997	+	107.315i	−0.0116001	+	0.0113173i
$449$	3971.57	−	1912.61i	0.417438	−	0.201028i	−0.213362	−	0.976973i	$-0.568441\pi$
$449$	3971.57	−	1912.61i	0.417438	−	0.201028i	0.630800	+	0.775946i	$0.282727\pi$
$450$	1100.61	−	1380.12i	0.115296	−	0.144577i
$451$	1602.75	+	771.846i	0.167341	+	0.0805871i
$452$	5922.15	+	7426.14i	0.616271	+	0.772779i
$453$	26.9934	+	118.266i	0.00279969	+	0.0122662i
$454$	−3144.30	−	3942.83i	−0.325043	−	0.407591i
$455$	−2501.59	−	1615.24i	−0.257750	−	0.166426i
$456$	109.767	−	137.644i	0.0112726	−	0.0141354i
$457$	−11938.3	−	5749.20i	−1.22200	−	0.588482i	−0.292129	−	0.956379i	$-0.594364\pi$
$457$	−11938.3	−	5749.20i	−1.22200	−	0.588482i	−0.929867	+	0.367897i	$0.880078\pi$
$458$	−1433.77	−	6281.74i	−0.146278	−	0.640887i
$459$	−248.485			−0.0252686
$460$	4526.08			0.458760
$461$	3723.25	+	16312.6i	0.376158	+	1.64806i	0.709100	+	0.705108i	$0.249102\pi$
$461$	3723.25	+	16312.6i	0.376158	+	1.64806i	−0.332941	+	0.942947i	$0.608041\pi$
$462$	−2.00673	−	20.0284i	−0.000202082	−	0.00201690i
$463$	2779.92	−	12179.6i	0.279036	−	1.22254i	−0.619979	−	0.784619i	$-0.712859\pi$
$463$	2779.92	−	12179.6i	0.279036	−	1.22254i	0.899015	−	0.437918i	$-0.144284\pi$
$464$	1301.22	−	5701.00i	0.130188	−	0.570393i
$465$	308.950	−	387.411i	0.0308112	−	0.0386360i
$466$	−4157.54	+	5213.38i	−0.413292	+	0.518252i
$467$	−2383.24	+	10441.7i	−0.236152	+	1.03465i	0.708277	+	0.705935i	$0.249473\pi$
$467$	−2383.24	+	10441.7i	−0.236152	+	1.03465i	−0.944429	+	0.328716i	$0.893384\pi$
$468$	730.406	−	3200.12i	0.0721432	−	0.316080i
$469$	−14872.2	−	1861.80i	−1.46425	−	0.183305i
$470$	−980.075	−	4293.99i	−0.0961862	−	0.421419i
$471$	−368.220			−0.0360227
$472$	2993.46			0.291918
$473$	192.735	+	844.428i	0.0187357	+	0.0820863i
$474$	−16.4080	−	7.90165i	−0.00158996	−	0.000765685i
$475$	1522.64	−	1909.33i	0.147081	−	0.184433i
$476$	−2593.36	−	324.654i	−0.249720	−	0.0312616i
$477$	2966.77	+	3720.21i	0.284778	+	0.357100i
$478$	−393.431	−	1723.73i	−0.0376467	−	0.164941i
$479$	−1701.95	−	2134.18i	−0.162347	−	0.203577i	0.694004	−	0.719971i	$-0.255845\pi$
$479$	−1701.95	−	2134.18i	−0.162347	−	0.203577i	−0.856351	+	0.516395i	$0.827274\pi$
$480$	290.985	+	140.131i	0.0276700	+	0.0133252i
$481$	2560.44	−	3210.69i	0.242715	−	0.304355i
$482$	−5349.17	+	2576.02i	−0.505493	+	0.243433i
$483$	−32.0388	−	319.767i	−0.00301825	−	0.0301241i
$484$	−7631.03	−	3674.91i	−0.716663	−	0.345127i
$485$	8124.94	−	3912.77i	0.760690	−	0.366329i
$486$	−127.322	+	557.835i	−0.0118836	+	0.0520657i
$487$	1596.84	−	768.997i	0.148583	−	0.0715536i	−0.358115	−	0.933678i	$-0.616580\pi$
$487$	1596.84	−	768.997i	0.148583	−	0.0715536i	0.506697	+	0.862124i	$0.330866\pi$
$488$	−3654.35	−	4582.41i	−0.338985	−	0.425073i
$489$	390.210			0.0360857
$490$	2788.07	+	2338.25i	0.257045	+	0.215574i
$491$	−20216.2			−1.85814			−0.929068	−	0.369909i	$-0.879389\pi$
$491$	−20216.2			−1.85814			−0.929068	+	0.369909i	$0.879389\pi$
$492$	362.909	+	455.074i	0.0332545	+	0.0416998i
$493$	3958.64	−	1906.38i	0.361640	−	0.174156i
$494$	−243.468	+	1066.70i	−0.0221743	+	0.0971522i
$495$	−856.903	+	412.663i	−0.0778079	+	0.0374703i
$496$	7263.07	+	3497.71i	0.657503	+	0.316637i
$497$	1274.36	−	3502.67i	0.115016	−	0.316129i
$498$	−167.200	+	80.5192i	−0.0150450	+	0.00724528i
$499$	871.661	−	1093.03i	0.0781982	−	0.0980574i	−0.741194	−	0.671291i	$-0.765740\pi$
$499$	871.661	−	1093.03i	0.0781982	−	0.0980574i	0.819392	+	0.573234i	$0.194311\pi$
$500$	8777.91	+	4227.22i	0.785120	+	0.378094i
$501$	−215.027	−	269.636i	−0.0191751	−	0.0240448i
$502$	2048.27	+	8974.07i	0.182109	+	0.797873i
$503$	−10825.3	−	13574.5i	−0.959598	−	1.20330i	−0.979077	−	0.203488i	$-0.934772\pi$
$503$	−10825.3	−	13574.5i	−0.959598	−	1.20330i	0.0194794	−	0.999810i	$-0.493799\pi$
$504$	−3073.21	+	8446.94i	−0.271611	+	0.746541i
$505$	5241.30	−	6572.39i	0.461851	−	0.579143i
$506$	−383.900	−	184.877i	−0.0337282	−	0.0162426i
$507$	86.1485	+	377.441i	0.00754633	+	0.0330626i
$508$	−11936.6			−1.04252
$509$	−3614.55			−0.314759			−0.157379	−	0.987538i	$-0.550305\pi$
$509$	−3614.55			−0.314759			−0.157379	+	0.987538i	$0.550305\pi$
$510$	10.8717	+	47.6319i	0.000943933	+	0.00413564i
$511$	−8317.74	+	8114.97i	−0.720069	+	0.702515i
$512$	−2102.99	+	9213.78i	−0.181523	+	0.795304i
$513$	−117.397	+	514.350i	−0.0101037	+	0.0442673i
$514$	5728.58	−	7183.42i	0.491590	−	0.616434i
$515$	−4517.99	+	5665.38i	−0.386575	+	0.484750i
$516$	−63.0627	+	276.296i	−0.00538019	+	0.0235722i
$517$	382.941	−	1677.78i	0.0325759	−	0.142724i
$518$	−3591.96	+	3504.40i	−0.304675	+	0.297248i
$519$	−68.8350	−	301.586i	−0.00582181	−	0.0255070i
$520$	−2894.91			−0.244135
$521$	−10816.8			−0.909579			−0.454790	−	0.890599i	$-0.650286\pi$
$521$	−10816.8			−0.909579			−0.454790	+	0.890599i	$0.650286\pi$
$522$	−1500.48	−	6574.03i	−0.125813	−	0.551221i
$523$	12308.6	+	5927.51i	1.02910	+	0.495587i	0.870714	−	0.491791i	$-0.163657\pi$
$523$	12308.6	+	5927.51i	1.02910	+	0.495587i	0.158384	+	0.987378i	$0.449372\pi$
$524$	−4278.75	+	5365.39i	−0.356714	+	0.447306i
$525$	69.9973	−	192.392i	0.00581892	−	0.0159937i
$526$	−1711.50	−	2146.15i	−0.141872	−	0.177902i
$527$	1347.84	+	5905.29i	0.111410	+	0.488119i
$528$	15.8405	+	19.8634i	0.00130562	+	0.00163720i
$529$	4832.86	+	2327.38i	0.397211	+	0.191287i
$530$	1167.60	−	1464.13i	0.0956931	−	0.119995i
$531$	−4037.75	+	1944.48i	−0.329988	+	0.158914i
$532$	−1897.25	+	5214.73i	−0.154617	+	0.424976i
$533$	−7303.59	−	3517.22i	−0.593534	−	0.285831i
$534$	−203.824	+	98.1563i	−0.0165174	+	0.00795438i
$535$	3073.26	−	13464.8i	0.248352	−	1.08810i
$536$	−13128.3	+	6322.27i	−1.05794	+	0.509479i
$537$	−419.043	−	525.464i	−0.0336742	−	0.0422261i
$538$	−1026.00			−0.0822192
$539$	585.086	+	1295.80i	0.0467559	+	0.103551i
$540$	−622.902			−0.0496397
$541$	−6939.25	−	8701.55i	−0.551464	−	0.691513i	0.425491	−	0.904963i	$-0.360102\pi$
$541$	−6939.25	−	8701.55i	−0.551464	−	0.691513i	−0.976954	+	0.213449i	$0.931530\pi$
$542$	5738.08	−	2763.31i	0.454745	−	0.218994i
$543$	−160.301	+	702.326i	−0.0126688	+	0.0555059i
$544$	−3556.98	+	1712.95i	−0.280339	+	0.135004i
$545$	9140.57	+	4401.86i	0.718420	+	0.345973i
$546$	9.14448	+	91.2676i	0.000716754	+	0.00715365i
$547$	4834.37	−	2328.11i	0.377884	−	0.181980i	−0.235293	−	0.971924i	$-0.575605\pi$
$547$	4834.37	−	2328.11i	0.377884	−	0.181980i	0.613178	+	0.789945i	$0.289891\pi$
$548$	6364.36	−	7980.65i	0.496116	−	0.622110i
$549$	7905.81	+	3807.24i	0.614593	+	0.295973i
$550$	−169.245	−	212.227i	−0.0131212	−	0.0164534i
$551$	−2075.83	−	9094.83i	−0.160496	−	0.703181i
$552$	−194.796	−	244.267i	−0.0150201	−	0.0188346i
$553$	1276.38	+	159.786i	0.0981506	+	0.0122871i
$554$	−739.052	+	926.742i	−0.0566775	+	0.0710713i
$555$	−350.780	−	168.927i	−0.0268284	−	0.0129199i
$556$	4493.66	+	19688.0i	0.342758	+	1.50172i
$557$	19698.8			1.49850			0.749251	−	0.662286i	$-0.230414\pi$
$557$	19698.8			1.49850			0.749251	+	0.662286i	$0.230414\pi$
$558$	9295.90			0.705245
$559$	−878.274	−	3847.97i	−0.0664527	−	0.291148i
$560$	−4557.25	−	570.506i	−0.343891	−	0.0430505i
$561$	−4.24785	+	18.6110i	−0.000319687	+	0.00140064i
$562$	−192.392	+	842.924i	−0.0144405	+	0.0632680i
$563$	568.763	−	713.206i	0.0425764	−	0.0533891i	−0.760087	−	0.649821i	$-0.774844\pi$
$563$	568.763	−	713.206i	0.0425764	−	0.0533891i	0.802664	+	0.596432i	$0.203415\pi$
$564$	351.077	−	440.237i	0.0262110	−	0.0328676i
$565$	−2790.73	+	12227.0i	−0.207800	+	0.910432i
$566$	−451.800	+	1979.47i	−0.0335523	+	0.147002i
$567$	−1339.39	−	13368.0i	−0.0992050	−	0.990127i
$568$	−806.329	−	3532.76i	−0.0595648	−	0.260970i
$569$	3777.51			0.278315			0.139158	−	0.990270i	$-0.455561\pi$
$569$	3777.51			0.278315			0.139158	+	0.990270i	$0.455561\pi$
$570$	103.731			0.00762251
$571$	−557.494	−	2442.54i	−0.0408589	−	0.179014i	0.950381	−	0.311088i	$-0.100693\pi$
$571$	−557.494	−	2442.54i	−0.0408589	−	0.179014i	−0.991240	+	0.132074i	$0.957836\pi$
$572$	−454.765	−	219.003i	−0.0332424	−	0.0160087i
$573$	−330.071	+	413.896i	−0.0240644	+	0.0301758i
$574$	8321.93	+	5373.37i	0.605141	+	0.390732i
$575$	−2702.12	−	3388.35i	−0.195976	−	0.245746i
$576$	−49.7710	−	218.061i	−0.00360034	−	0.0157741i
$577$	−5498.56	−	6894.98i	−0.396721	−	0.497473i	0.542848	−	0.839831i	$-0.317346\pi$
$577$	−5498.56	−	6894.98i	−0.396721	−	0.497473i	−0.939570	+	0.342358i	$0.888774\pi$
$578$	4978.66	+	2397.60i	0.358279	+	0.172538i
$579$	184.091	−	230.843i	0.0132134	−	0.0165691i
$580$	9923.52	−	4778.91i	0.710434	−	0.342127i
$581$	9382.46	−	9153.73i	0.669966	−	0.653633i
$582$	−250.276	−	120.526i	−0.0178252	−	0.00858416i
$583$	659.246	−	317.476i	0.0468322	−	0.0225532i
$584$	−2513.89	+	11014.1i	−0.178126	+	0.780420i
$585$	3904.82	−	1880.46i	0.275973	−	0.132902i
$586$	2179.52	+	2733.04i	0.153644	+	0.192663i
$587$	−24302.6			−1.70882			−0.854409	−	0.519601i	$-0.826080\pi$
$587$	−24302.6			−1.70882			−0.854409	+	0.519601i	$0.826080\pi$
$588$	−11.4789	+	465.059i	−0.000805075	+	0.0326169i
$589$	12860.4			0.899666
$590$	1099.69	+	1378.97i	0.0767347	+	0.0962223i
$591$	300.813	−	144.864i	0.0209370	−	0.0100827i
$592$	1409.44	−	6175.18i	0.0978511	−	0.428714i
$593$	−6269.51	+	3019.24i	−0.434162	+	0.209081i	−0.638182	−	0.769885i	$-0.720313\pi$
$593$	−6269.51	+	3019.24i	−0.434162	+	0.209081i	0.204020	+	0.978967i	$0.434599\pi$
$594$	52.8344	+	25.4437i	0.00364953	+	0.00175752i
$595$	−1799.82	−	2944.43i	−0.124009	−	0.202874i
$596$	−155.450	+	74.8606i	−0.0106837	+	0.00514498i
$597$	−422.078	+	529.269i	−0.0289355	+	0.0362840i
$598$	1749.39	+	842.464i	0.119629	+	0.0576102i
$599$	4613.53	+	5785.18i	0.314697	+	0.394618i	0.913873	−	0.405999i	$-0.133076\pi$
$599$	4613.53	+	5785.18i	0.314697	+	0.394618i	−0.599176	+	0.800617i	$0.704505\pi$
$600$	−44.2895	−	194.045i	−0.00301352	−	0.0132031i
$601$	11656.9	+	14617.3i	0.791175	+	0.992103i	0.999900	+	0.0141283i	$0.00449731\pi$
$601$	11656.9	+	14617.3i	0.791175	+	0.992103i	−0.208725	+	0.977974i	$0.566931\pi$
$602$	480.841	+	4799.09i	0.0325542	+	0.324911i
$603$	13601.5	−	17055.7i	0.918564	−	1.15184i
$604$	−3349.08	−	1612.83i	−0.225616	−	0.108651i
$605$	−2488.53	−	10902.9i	−0.167228	−	0.732674i
$606$	−258.946			−0.0173580
$607$	−5906.40			−0.394948			−0.197474	−	0.980308i	$-0.563274\pi$
$607$	−5906.40			−0.394948			−0.197474	+	0.980308i	$0.563274\pi$
$608$	1865.21	+	8172.03i	0.124415	+	0.545098i
$609$	−407.876	−	667.268i	−0.0271395	−	0.0443991i
$610$	768.455	−	3366.82i	0.0510063	−	0.223473i
$611$	−1745.02	+	7645.45i	−0.115542	+	0.506222i
$612$	2371.78	−	2974.11i	0.156656	−	0.196440i
$613$	16803.7	−	21071.1i	1.10717	−	1.38834i	0.193880	−	0.981025i	$-0.437893\pi$
$613$	16803.7	−	21071.1i	1.10717	−	1.38834i	0.913286	−	0.407318i	$-0.133536\pi$
$614$	2215.18	−	9705.34i	0.145598	−	0.637908i
$615$	−171.016	+	749.271i	−0.0112131	+	0.0491277i
$616$	1161.20	+	749.770i	0.0759512	+	0.0490407i
$617$	6281.36	+	27520.4i	0.409851	+	1.79567i	0.584889	+	0.811113i	$0.301138\pi$
$617$	6281.36	+	27520.4i	0.409851	+	1.79567i	−0.175038	+	0.984562i	$0.556005\pi$
$618$	223.210			0.0145289
$619$	−6231.29			−0.404615			−0.202307	−	0.979322i	$-0.564844\pi$
$619$	−6231.29			−0.404615			−0.202307	+	0.979322i	$0.564844\pi$
$620$	3378.77	+	14803.4i	0.218863	+	0.958900i
$621$	843.536	+	406.226i	0.0545088	+	0.0262500i
$622$	2194.22	−	2751.46i	0.141447	−	0.177369i
$623$	11437.6	−	11158.8i	0.735535	−	0.717604i
$624$	−72.1836	−	90.5154i	−0.00463086	−	0.00580691i
$625$	1401.00	+	6138.17i	0.0896639	+	0.392843i
$626$	2827.81	+	3545.96i	0.180546	+	0.226398i
$627$	36.5168	+	17.5856i	0.00232590	+	0.00112010i
$628$	7035.04	−	8821.67i	0.447020	−	0.560546i
$629$	4287.91	−	2064.95i	0.271812	−	0.130898i
$630$	−5020.15	+	1687.39i	−0.317472	+	0.106710i
$631$	−4804.20	−	2313.58i	−0.303094	−	0.145962i	0.276155	−	0.961113i	$-0.410940\pi$
$631$	−4804.20	−	2313.58i	−0.303094	−	0.145962i	−0.579249	+	0.815151i	$0.696654\pi$
$632$	1126.72	−	542.598i	0.0709152	−	0.0341510i
$633$	−65.6489	+	287.626i	−0.00412213	+	0.0180602i
$634$	−3761.42	+	1811.40i	−0.235623	+	0.113470i
$635$	−9826.68	−	12322.3i	−0.614110	−	0.770069i
$636$	239.414			0.0149267
$637$	−2666.18	−	5904.83i	−0.165836	−	0.367281i
$638$	−1036.91			−0.0643445
$639$	3382.41	+	4241.41i	0.209399	+	0.262579i
$640$	−11144.3	+	5366.83i	−0.688311	+	0.331473i
$641$	1092.93	−	4788.46i	0.0673452	−	0.295059i	−0.930028	−	0.367488i	$-0.880218\pi$
$641$	1092.93	−	4788.46i	0.0673452	−	0.295059i	0.997374	+	0.0724291i	$0.0230751\pi$
$642$	−383.298	+	184.587i	−0.0235632	+	0.0113474i
$643$	−6487.50	−	3124.21i	−0.397888	−	0.191613i	0.224230	−	0.974536i	$-0.428013\pi$
$643$	−6487.50	−	3124.21i	−0.397888	−	0.191613i	−0.622118	+	0.782923i	$0.713728\pi$
$644$	8272.97	+	5341.76i	0.506212	+	0.326855i
$645$	−337.139	+	162.358i	−0.0205811	+	0.00991136i
$646$	−790.589	+	991.367i	−0.0481506	+	0.0603790i
$647$	−20620.8	−	9930.45i	−1.25299	−	0.603410i	−0.314681	−	0.949198i	$-0.601897\pi$
$647$	−20620.8	−	9930.45i	−1.25299	−	0.603410i	−0.938313	+	0.345788i	$0.887612\pi$
$648$	−8143.52	−	10211.7i	−0.493685	−	0.619061i
$649$	153.350	+	671.871i	0.00927507	+	0.0406367i
$650$	771.234	+	967.097i	0.0465389	+	0.0583579i
$651$	1021.94	−	343.499i	0.0615254	−	0.0206802i
$652$	−7455.17	+	9348.48i	−0.447802	+	0.561526i
$653$	−3912.93	−	1884.37i	−0.234494	−	0.112927i	0.312947	−	0.949771i	$-0.398684\pi$
$653$	−3912.93	−	1884.37i	−0.234494	−	0.112927i	−0.547441	+	0.836844i	$0.684398\pi$
$654$	−69.5397	−	304.673i	−0.00415782	−	0.0182166i
$655$	−9061.20			−0.540535
$656$	−12503.1			−0.744155
$657$	−3763.59	−	16489.4i	−0.223488	−	0.979165i
$658$	3276.41	−	9005.45i	0.194115	−	0.533540i
$659$	−5897.70	+	25839.5i	−0.348622	+	1.52741i	0.431691	+	0.902021i	$0.357917\pi$
$659$	−5897.70	+	25839.5i	−0.348622	+	1.52741i	−0.780313	+	0.625389i	$0.784940\pi$
$660$	−10.6485	+	46.6541i	−0.000628018	+	0.00275153i
$661$	−17153.2	+	21509.5i	−1.00935	+	1.26569i	−0.0455835	+	0.998961i	$0.514515\pi$
$661$	−17153.2	+	21509.5i	−1.00935	+	1.26569i	−0.963771	+	0.266730i	$0.914057\pi$
$662$	−9116.46	+	11431.7i	−0.535229	+	0.671155i
$663$	19.3570	−	84.8086i	0.00113388	−	0.00496786i
$664$	2835.68	−	12423.9i	0.165732	−	0.726118i
$665$	−6945.12	+	2334.42i	−0.404993	+	0.136128i
$666$	−1625.28	−	7120.83i	−0.0945622	−	0.414304i
$667$	−16555.0			−0.961039
$668$	10568.0			0.612110
$669$	6.11273	+	26.7816i	0.000353261	+	0.00154774i
$670$	−7735.29	−	3725.12i	−0.446030	−	0.214797i
$671$	841.297	−	1054.95i	0.0484023	−	0.0606945i
$672$	366.491	+	599.564i	0.0210383	+	0.0344177i
$673$	20905.4	+	26214.5i	1.19739	+	1.50148i	0.816986	+	0.576657i	$0.195643\pi$
$673$	20905.4	+	26214.5i	1.19739	+	1.50148i	0.380403	+	0.924821i	$0.375785\pi$
$674$	613.306	+	2687.07i	0.0350500	+	0.153564i
$675$	371.879	+	466.322i	0.0212054	+	0.0265907i
$676$	−10688.5	−	5147.30i	−0.608130	−	0.292860i
$677$	−10391.1	+	13030.1i	−0.589902	+	0.739714i	−0.983766	−	0.179455i	$-0.942567\pi$
$677$	−10391.1	+	13030.1i	−0.589902	+	0.739714i	0.393864	+	0.919169i	$0.371138\pi$
$678$	348.061	−	167.618i	0.0197157	−	0.00949456i
$679$	19469.1	+	2437.26i	1.10037	+	0.137752i
$680$	−3022.71	−	1455.66i	−0.170464	−	0.0820911i
$681$	766.986	−	369.361i	0.0431585	−	0.0207841i
$682$	318.087	−	1393.63i	0.0178595	−	0.0782476i
$683$	−11070.5	+	5331.25i	−0.620204	+	0.298674i	−0.717476	−	0.696583i	$-0.754703\pi$
$683$	−11070.5	+	5331.25i	−0.620204	+	0.298674i	0.0972720	+	0.995258i	$0.468988\pi$
$684$	−5035.69	−	6314.56i	−0.281498	−	0.352987i
$685$	13477.9			0.751773
$686$	2336.51	+	7564.49i	0.130041	+	0.421011i
$687$	1087.65			0.0604024
$688$	−3795.61	−	4759.54i	−0.210329	−	0.263744i
$689$	−3004.12	+	1446.71i	−0.166107	+	0.0799929i
$690$	40.9627	−	179.470i	0.00226004	−	0.00990187i
$691$	14542.9	−	7003.51i	0.800636	−	0.385566i	0.0116152	−	0.999933i	$-0.496303\pi$
$691$	14542.9	−	7003.51i	0.800636	−	0.385566i	0.789021	+	0.614367i	$0.210588\pi$
$692$	8540.40	+	4112.84i	0.469158	+	0.225935i
$693$	−2053.32	−	257.048i	−0.112553	−	0.0140901i
$694$	−4654.20	+	2241.34i	−0.254569	+	0.122594i
$695$	−16624.8	+	20846.8i	−0.907359	+	1.13779i
$696$	−685.007	−	329.882i	−0.0373062	−	0.0179657i
$697$	−5857.42	−	7344.98i	−0.318315	−	0.399155i
$698$	−35.5434	−	155.726i	−0.00192742	−	0.00844457i
$699$	−701.808	−	880.039i	−0.0379754	−	0.0476196i
$700$	3271.92	+	5352.73i	0.176667	+	0.289020i
$701$	−3101.59	+	3889.27i	−0.167112	+	0.209552i	−0.858335	−	0.513090i	$-0.828501\pi$
$701$	−3101.59	+	3889.27i	−0.167112	+	0.209552i	0.691223	+	0.722641i	$0.257072\pi$
$702$	−240.761	−	115.944i	−0.0129444	−	0.00623367i
$703$	−2248.49	−	9851.29i	−0.120631	−	0.528519i
$704$	−34.3945			−0.00184133
$705$	743.482			0.0397180
$706$	−2432.84	−	10659.0i	−0.129690	−	0.568208i
$707$	17337.1	−	5827.44i	0.922250	−	0.309991i
$708$	−50.1760	+	219.835i	−0.00266346	+	0.0116694i
$709$	−4820.24	+	21118.8i	−0.255328	+	1.11867i	0.670853	+	0.741590i	$0.265928\pi$
$709$	−4820.24	+	21118.8i	−0.255328	+	1.11867i	−0.926182	+	0.377077i	$0.876929\pi$
$710$	1331.18	−	1669.25i	0.0703639	−	0.0882336i
$711$	−1167.32	+	1463.78i	−0.0615724	+	0.0772094i
$712$	3456.82	−	15145.3i	0.181952	−	0.797183i
$713$	5078.47	−	22250.2i	0.266746	−	1.16869i
$714$	−36.3443	+	99.8947i	−0.00190497	+	0.00523595i
$715$	−148.302	−	649.752i	−0.00775687	−	0.0339851i
$716$	20594.9			1.07495
$717$	298.456			0.0155454
$718$	−323.315	−	1416.54i	−0.0168050	−	0.0736276i
$719$	−1728.73	−	832.510i	−0.0896670	−	0.0431814i	0.388513	−	0.921443i	$-0.372989\pi$
$719$	−1728.73	−	832.510i	−0.0896670	−	0.0431814i	−0.478180	+	0.878262i	$0.658703\pi$
$720$	4167.86	−	5226.33i	0.215732	−	0.270519i
$721$	−14944.6	+	5023.23i	−0.771934	+	0.259466i
$722$	−3651.31	−	4578.60i	−0.188210	−	0.236008i
$723$	−223.013	−	977.082i	−0.0114715	−	0.0502601i
$724$	−13763.4	−	17258.7i	−0.706508	−	0.885934i
$725$	−9502.07	−	4575.96i	−0.486756	−	0.234409i
$726$	−214.783	+	269.329i	−0.0109798	+	0.0137682i
$727$	−9340.22	+	4498.01i	−0.476492	+	0.229466i	−0.656685	−	0.754165i	$-0.728042\pi$
$727$	−9340.22	+	4498.01i	−0.476492	+	0.229466i	0.180193	+	0.983631i	$0.442328\pi$
$728$	−5291.45	−	3416.62i	−0.269388	−	0.173940i
$729$	17559.6	+	8456.25i	0.892119	+	0.429622i
$730$	−5997.25	+	2888.12i	−0.304066	+	0.146430i
$731$	1017.84	−	4459.46i	0.0514997	−	0.225635i
$732$	397.779	−	191.560i	0.0200851	−	0.00967250i
$733$	4310.92	+	5405.72i	0.217227	+	0.272394i	0.878491	−	0.477759i	$-0.158551\pi$
$733$	4310.92	+	5405.72i	0.217227	+	0.272394i	−0.661264	+	0.750154i	$0.729980\pi$
$734$	−883.722			−0.0444398
$735$	−489.536	+	371.006i	−0.0245671	+	0.0186187i
$736$	14875.3			0.744986
$737$	−2091.55	−	2622.73i	−0.104536	−	0.131085i
$738$	−12990.0	+	6255.66i	−0.647925	+	0.312024i
$739$	−293.572	+	1286.22i	−0.0146133	+	0.0640251i	−0.981709	−	0.190388i	$-0.939025\pi$
$739$	−293.572	+	1286.22i	−0.0146133	+	0.0640251i	0.967096	+	0.254413i	$0.0818824\pi$
$740$	10748.9	−	5176.40i	0.533970	−	0.257146i
$741$	−166.403	−	80.1357i	−0.00824964	−	0.00397282i
$742$	3862.18	−	1298.17i	0.191085	−	0.0642283i
$743$	4519.07	−	2176.27i	0.223134	−	0.107456i	−0.318977	−	0.947762i	$-0.603339\pi$
$743$	4519.07	−	2176.27i	0.223134	−	0.107456i	0.542111	+	0.840307i	$0.317625\pi$
$744$	653.502	−	819.466i	0.0322023	−	0.0403805i
$745$	−205.252	−	98.8441i	−0.0100938	−	0.00486090i
$746$	−7951.09	−	9970.35i	−0.390228	−	0.489330i
$747$	4245.35	+	18600.1i	0.207938	+	0.911034i
$748$	−364.718	−	457.342i	−0.0178281	−	0.0223557i
$749$	21508.9	−	20984.5i	1.04929	−	1.02371i
$750$	247.062	−	309.807i	0.0120286	−	0.0150834i
$751$	25318.1	+	12192.5i	1.23019	+	0.592426i	0.932130	−	0.362123i	$-0.117948\pi$
$751$	25318.1	+	12192.5i	1.23019	+	0.592426i	0.298055	+	0.954549i	$0.403662\pi$
$752$	2691.50	+	11792.2i	0.130517	+	0.571833i
$753$	−1553.81			−0.0751981
$754$	4725.11			0.228221
$755$	−1092.16	−	4785.05i	−0.0526458	−	0.230657i
$756$	−1138.57	−	735.160i	−0.0547743	−	0.0353671i
$757$	3575.83	−	15666.7i	0.171685	−	0.752202i	−0.813620	−	0.581398i	$-0.802506\pi$
$757$	3575.83	−	15666.7i	0.171685	−	0.752202i	0.985305	−	0.170805i	$-0.0546367\pi$
$758$	396.703	−	1738.07i	0.0190091	−	0.0832843i
$759$	44.8457	−	56.2347i	0.00214466	−	0.00268931i
$760$	−4441.20	+	5569.09i	−0.211973	+	0.265805i
$761$	2302.07	−	10086.0i	0.109658	−	0.480445i	−0.890040	−	0.455883i	$-0.849324\pi$
$761$	2302.07	−	10086.0i	0.109658	−	0.480445i	0.999698	−	0.0245622i	$-0.00781917\pi$
$762$	−108.031	+	473.313i	−0.00513587	+	0.0225017i
$763$	11512.4	+	18833.8i	0.546234	+	0.893616i
$764$	−3609.76	−	15815.4i	−0.170938	−	0.748928i
$765$	5022.76			0.237383
$766$	15433.1			0.727963
$767$	−698.801	−	3061.65i	−0.0328973	−	0.144133i
$768$	330.701	+	159.257i	0.0155380	+	0.00748269i
$769$	−1168.47	+	1465.21i	−0.0547934	+	0.0687087i	−0.808473	−	0.588533i	$-0.799706\pi$
$769$	−1168.47	+	1465.21i	−0.0547934	+	0.0687087i	0.753680	+	0.657242i	$0.228277\pi$

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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.777062 + 0.974405i) q^{2} +(-0.189548 + 0.0912813i) q^{3} +(1.43453 - 6.28508i) q^{4} +(7.66912 - 3.69325i) q^{5} +(-0.236235 - 0.113765i) q^{6} +(18.3768 + 2.30053i) q^{7} +(16.2220 - 7.81211i) q^{8} +(-16.8066 + 21.0748i) q^{9} +O(q^{10})\)	\(q+(0.777062 + 0.974405i) q^{2} +(-0.189548 + 0.0912813i) q^{3} +(1.43453 - 6.28508i) q^{4} +(7.66912 - 3.69325i) q^{5} +(-0.236235 - 0.113765i) q^{6} +(18.3768 + 2.30053i) q^{7} +(16.2220 - 7.81211i) q^{8} +(-16.8066 + 21.0748i) q^{9} +(9.55811 + 4.60294i) q^{10} +(2.58443 + 3.24077i) q^{11} +(0.301799 + 1.32227i) q^{12} +(-11.7770 - 14.7678i) q^{13} +(12.0383 + 19.6941i) q^{14} +(-1.11654 + 1.40009i) q^{15} +(-26.2486 - 12.6407i) q^{16} +(-4.87109 - 21.3416i) q^{17} -33.5952 q^{18} -46.4772 q^{19} +(-12.2108 - 53.4991i) q^{20} +(-3.69328 + 1.24140i) q^{21} +(-1.14956 + 5.03655i) q^{22} +(-18.3535 + 80.4119i) q^{23} +(-2.36174 + 2.96153i) q^{24} +(-32.7609 + 41.0809i) q^{25} +(5.23843 - 22.9511i) q^{26} +(2.52590 - 11.0667i) q^{27} +(40.8211 - 112.200i) q^{28} +(44.6635 + 195.683i) q^{29} -2.23188 q^{30} -276.703 q^{31} +(-40.1317 - 175.829i) q^{32} +(-0.785693 - 0.378370i) q^{33} +(17.0102 - 21.3302i) q^{34} +(149.431 - 50.2272i) q^{35} +(108.347 + 135.863i) q^{36} +(48.3784 + 211.960i) q^{37} +(-36.1157 - 45.2876i) q^{38} +(3.58032 + 1.72419i) q^{39} +(95.5565 - 119.824i) q^{40} +(386.663 - 186.207i) q^{41} +(-4.07953 - 2.63410i) q^{42} +(188.263 + 90.6627i) q^{43} +(24.0759 - 11.5943i) q^{44} +(-51.0573 + 223.697i) q^{45} +(-92.6155 + 44.6013i) q^{46} +(-258.855 - 324.593i) q^{47} +6.12922 q^{48} +(332.415 + 84.5528i) q^{49} -65.4867 q^{50} +(2.87139 + 3.60061i) q^{51} +(-109.711 + 52.8343i) q^{52} +(39.2802 - 172.098i) q^{53} +(12.7462 - 6.13826i) q^{54} +(31.7893 + 15.3089i) q^{55} +(316.081 - 106.243i) q^{56} +(8.80964 - 4.24250i) q^{57} +(-155.969 + 195.578i) q^{58} +(149.792 + 72.1360i) q^{59} +(7.19800 + 9.02601i) q^{60} +(-72.4363 - 317.364i) q^{61} +(-215.015 - 269.621i) q^{62} +(-357.336 + 348.625i) q^{63} +(-5.17349 + 6.48736i) q^{64} +(-144.860 - 69.7611i) q^{65} +(-0.241847 - 1.05960i) q^{66} -809.291 q^{67} -141.121 q^{68} +(-3.86124 - 16.9172i) q^{69} +(165.058 + 106.576i) q^{70} +(44.7834 - 196.209i) q^{71} +(-107.998 + 473.172i) q^{72} +(-391.210 + 490.561i) q^{73} +(-168.941 + 211.846i) q^{74} +(2.45983 - 10.7772i) q^{75} +(-66.6729 + 292.113i) q^{76} +(40.0381 + 65.5006i) q^{77} +(1.10207 + 4.82849i) q^{78} +69.4560 q^{79} -247.989 q^{80} +(-161.420 - 707.229i) q^{81} +(481.902 + 232.072i) q^{82} +(441.287 - 553.356i) q^{83} +(2.50419 + 24.9934i) q^{84} +(-116.177 - 145.681i) q^{85} +(57.9498 + 253.895i) q^{86} +(-26.3281 - 33.0144i) q^{87} +(67.2419 + 32.3820i) q^{88} +(537.947 - 674.565i) q^{89} +(-257.646 + 124.076i) q^{90} +(-182.449 - 298.479i) q^{91} +(479.067 + 230.706i) q^{92} +(52.4484 - 25.2578i) q^{93} +(115.139 - 504.458i) q^{94} +(-356.440 + 171.652i) q^{95} +(23.6567 + 29.6646i) q^{96} +1059.44 q^{97} +(175.918 + 389.610i) q^{98} -111.734 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9}+O(q^{10}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9	\( 78 q - 5 q^{2} - 5 q^{3} - 53 q^{4} - 23 q^{5} + 19 q^{6} - 31 q^{8} - 174 q^{9} + 9 q^{10} - 103 q^{11} + 364 q^{12} - 35 q^{13} + 161 q^{14} - 245 q^{15} - 205 q^{16} - 285 q^{17} + 16 q^{18} + 628 q^{19} + 553 q^{20} - 21 q^{21} - 605 q^{22} + 149 q^{23} + 653 q^{24} - 370 q^{25} - 511 q^{26} - 65 q^{27} + 70 q^{28} - 187 q^{29} + 84 q^{30} + 1276 q^{31} + 1399 q^{32} - 23 q^{33} - 765 q^{34} - 805 q^{35} - 1691 q^{36} - 1531 q^{37} - 1041 q^{38} - 1351 q^{39} - 1759 q^{40} - 301 q^{41} + 3395 q^{42} - 257 q^{43} - 883 q^{44} + 3105 q^{45} + 1593 q^{46} + 733 q^{47} - 1948 q^{48} + 1288 q^{49} + 6148 q^{50} + 1197 q^{51} - 1099 q^{52} - 285 q^{53} + 660 q^{54} + 2641 q^{55} - 1988 q^{56} - 2352 q^{57} + 1173 q^{58} - 3603 q^{59} - 175 q^{60} - 2613 q^{61} - 1927 q^{62} - 3066 q^{63} + 1589 q^{64} - 371 q^{65} - 2175 q^{66} + 352 q^{67} + 6076 q^{68} + 5549 q^{69} - 6293 q^{70} - 2623 q^{71} + 6220 q^{72} + 2039 q^{73} - 2411 q^{74} - 3903 q^{75} + 4130 q^{76} + 1029 q^{77} - 3759 q^{78} + 44 q^{79} - 1608 q^{80} + 1394 q^{81} - 10920 q^{82} - 553 q^{83} - 7798 q^{84} + 497 q^{85} - 2985 q^{86} - 4273 q^{87} - 2197 q^{88} - 3957 q^{89} - 2958 q^{90} + 14119 q^{91} - 9136 q^{92} + 6272 q^{93} + 14912 q^{94} + 5866 q^{95} + 21882 q^{96} - 1540 q^{97} - 2303 q^{98} + 10768 q^{99}+O(q^{100}) \) 78 * q - 5 * q^2 - 5 * q^3 - 53 * q^4 - 23 * q^5 + 19 * q^6 - 31 * q^8 - 174 * q^9 + 9 * q^10 - 103 * q^11 + 364 * q^12 - 35 * q^13 + 161 * q^14 - 245 * q^15 - 205 * q^16 - 285 * q^17 + 16 * q^18 + 628 * q^19 + 553 * q^20 - 21 * q^21 - 605 * q^22 + 149 * q^23 + 653 * q^24 - 370 * q^25 - 511 * q^26 - 65 * q^27 + 70 * q^28 - 187 * q^29 + 84 * q^30 + 1276 * q^31 + 1399 * q^32 - 23 * q^33 - 765 * q^34 - 805 * q^35 - 1691 * q^36 - 1531 * q^37 - 1041 * q^38 - 1351 * q^39 - 1759 * q^40 - 301 * q^41 + 3395 * q^42 - 257 * q^43 - 883 * q^44 + 3105 * q^45 + 1593 * q^46 + 733 * q^47 - 1948 * q^48 + 1288 * q^49 + 6148 * q^50 + 1197 * q^51 - 1099 * q^52 - 285 * q^53 + 660 * q^54 + 2641 * q^55 - 1988 * q^56 - 2352 * q^57 + 1173 * q^58 - 3603 * q^59 - 175 * q^60 - 2613 * q^61 - 1927 * q^62 - 3066 * q^63 + 1589 * q^64 - 371 * q^65 - 2175 * q^66 + 352 * q^67 + 6076 * q^68 + 5549 * q^69 - 6293 * q^70 - 2623 * q^71 + 6220 * q^72 + 2039 * q^73 - 2411 * q^74 - 3903 * q^75 + 4130 * q^76 + 1029 * q^77 - 3759 * q^78 + 44 * q^79 - 1608 * q^80 + 1394 * q^81 - 10920 * q^82 - 553 * q^83 - 7798 * q^84 + 497 * q^85 - 2985 * q^86 - 4273 * q^87 - 2197 * q^88 - 3957 * q^89 - 2958 * q^90 + 14119 * q^91 - 9136 * q^92 + 6272 * q^93 + 14912 * q^94 + 5866 * q^95 + 21882 * q^96 - 1540 * q^97 - 2303 * q^98 + 10768 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more