LMFDB - Embedded newform 45.4.l.a.2.5

Newspace parameters

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.l (of order $12$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			2.5
Character	$\chi$	$=$	45.2
Dual form			45.4.l.a.23.5

$q$-expansion

$f(q)$	$=$	$q+(-0.748271 - 2.79258i) q^{2} +(-0.352314 - 5.18419i) q^{3} +(-0.310415 + 0.179218i) q^{4} +(11.0394 - 1.76941i) q^{5} +(-14.2137 + 4.86305i) q^{6} +(-18.7862 + 5.03374i) q^{7} +(-15.6218 - 15.6218i) q^{8} +(-26.7517 + 3.65293i) q^{9} +O(q^{10})$	\(q+(-0.748271 - 2.79258i) q^{2} +(-0.352314 - 5.18419i) q^{3} +(-0.310415 + 0.179218i) q^{4} +(11.0394 - 1.76941i) q^{5} +(-14.2137 + 4.86305i) q^{6} +(-18.7862 + 5.03374i) q^{7} +(-15.6218 - 15.6218i) q^{8} +(-26.7517 + 3.65293i) q^{9} +(-13.2017 - 29.5046i) q^{10} +(49.0377 + 28.3119i) q^{11} +(1.03846 + 1.54611i) q^{12} +(2.30137 + 0.616650i) q^{13} +(28.1143 + 48.6954i) q^{14} +(-13.0623 - 56.6072i) q^{15} +(-33.3695 + 57.7977i) q^{16} +(92.5976 - 92.5976i) q^{17} +(30.2187 + 71.9731i) q^{18} -21.7774i q^{19} +(-3.10969 + 2.52772i) q^{20} +(32.7146 + 95.6178i) q^{21} +(42.3700 - 158.127i) q^{22} +(-26.4989 + 98.8952i) q^{23} +(-75.4824 + 86.4900i) q^{24} +(118.738 - 39.0667i) q^{25} -6.88818i q^{26} +(28.3625 + 137.399i) q^{27} +(4.92937 - 4.92937i) q^{28} +(40.6009 - 70.3228i) q^{29} +(-148.306 + 78.8352i) q^{30} +(4.26447 + 7.38628i) q^{31} +(15.6566 + 4.19518i) q^{32} +(129.498 - 264.196i) q^{33} +(-327.875 - 189.298i) q^{34} +(-198.482 + 88.8102i) q^{35} +(7.64946 - 5.92832i) q^{36} +(8.92697 + 8.92697i) q^{37} +(-60.8153 + 16.2954i) q^{38} +(2.38603 - 12.1480i) q^{39} +(-200.097 - 144.814i) q^{40} +(-28.1572 + 16.2566i) q^{41} +(242.541 - 162.906i) q^{42} +(114.874 + 428.714i) q^{43} -20.2960 q^{44} +(-288.861 + 87.6612i) q^{45} +296.002 q^{46} +(-37.5556 - 140.159i) q^{47} +(311.391 + 152.631i) q^{48} +(30.5356 - 17.6297i) q^{49} +(-197.945 - 302.354i) q^{50} +(-512.667 - 447.420i) q^{51} +(-0.824893 + 0.221029i) q^{52} +(-82.9808 - 82.9808i) q^{53} +(362.476 - 182.017i) q^{54} +(591.444 + 225.780i) q^{55} +(372.109 + 214.837i) q^{56} +(-112.898 + 7.67250i) q^{57} +(-226.763 - 60.7609i) q^{58} +(129.436 + 224.189i) q^{59} +(14.1998 + 15.2307i) q^{60} +(-282.613 + 489.500i) q^{61} +(17.4358 - 17.4358i) q^{62} +(484.175 - 203.286i) q^{63} +487.051i q^{64} +(26.4969 + 2.73539i) q^{65} +(-834.688 - 163.944i) q^{66} +(-116.526 + 434.879i) q^{67} +(-12.1485 + 45.3388i) q^{68} +(522.028 + 102.533i) q^{69} +(396.528 + 487.824i) q^{70} -16.2978i q^{71} +(474.974 + 360.844i) q^{72} +(59.2407 - 59.2407i) q^{73} +(18.2495 - 31.6091i) q^{74} +(-244.362 - 601.799i) q^{75} +(3.90290 + 6.76003i) q^{76} +(-1063.75 - 285.030i) q^{77} +(-35.7097 + 2.42681i) q^{78} +(-472.049 - 272.538i) q^{79} +(-266.113 + 697.098i) q^{80} +(702.312 - 195.445i) q^{81} +(66.4671 + 66.4671i) q^{82} +(-972.735 + 260.644i) q^{83} +(-27.2915 - 23.8181i) q^{84} +(858.382 - 1186.07i) q^{85} +(1111.26 - 641.588i) q^{86} +(-378.871 - 185.707i) q^{87} +(-323.773 - 1208.34i) q^{88} +844.831 q^{89} +(460.947 + 741.074i) q^{90} -46.3380 q^{91} +(-9.49816 - 35.4476i) q^{92} +(36.7895 - 24.7101i) q^{93} +(-363.305 + 209.754i) q^{94} +(-38.5333 - 240.410i) q^{95} +(16.2326 - 82.6450i) q^{96} +(393.261 - 105.374i) q^{97} +(-72.0814 - 72.0814i) q^{98} +(-1415.27 - 578.262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.748271	−	2.79258i	−0.264554	−	0.987328i	−0.962523	−	0.271200i	$-0.912580\pi$
$2$	−0.748271	−	2.79258i	−0.264554	−	0.987328i	0.697969	−	0.716128i	$-0.254087\pi$
$3$	−0.352314	−	5.18419i	−0.0678029	−	0.997699i
$3$	−0.352314	−	5.18419i	−0.0678029	−	0.997699i
$4$	−0.310415	+	0.179218i	−0.0388018	+	0.0224022i
$5$	11.0394	−	1.76941i	0.987397	−	0.158261i
$5$	11.0394	−	1.76941i	0.987397	−	0.158261i
$6$	−14.2137	+	4.86305i	−0.967118	+	0.330889i
$7$	−18.7862	+	5.03374i	−1.01436	+	0.271797i	−0.727450	−	0.686161i	$-0.759294\pi$
$7$	−18.7862	+	5.03374i	−1.01436	+	0.271797i	−0.286909	+	0.957958i	$0.592628\pi$
$8$	−15.6218	−	15.6218i	−0.690390	−	0.690390i
$9$	−26.7517	+	3.65293i	−0.990806	+	0.135294i
$10$	−13.2017	−	29.5046i	−0.417475	−	0.933016i
$11$	49.0377	+	28.3119i	1.34413	+	0.776033i	0.987410	−	0.158179i	$-0.0505623\pi$
$11$	49.0377	+	28.3119i	1.34413	+	0.776033i	0.356718	+	0.934212i	$0.383896\pi$
$12$	1.03846	+	1.54611i	0.0249816	+	0.0371936i
$13$	2.30137	+	0.616650i	0.0490988	+	0.0131560i	0.283285	−	0.959036i	$-0.408576\pi$
$13$	2.30137	+	0.616650i	0.0490988	+	0.0131560i	−0.234186	+	0.972192i	$0.575242\pi$
$14$	28.1143	+	48.6954i	0.536705	+	0.929600i
$15$	−13.0623	−	56.6072i	−0.224845	−	0.974394i
$16$	−33.3695	+	57.7977i	−0.521399	+	0.903089i
$17$	92.5976	−	92.5976i	1.32107	−	1.32107i	0.408161	−	0.912910i	$-0.366170\pi$
$17$	92.5976	−	92.5976i	1.32107	−	1.32107i	0.912910	−	0.408161i	$-0.133830\pi$
$18$	30.2187	+	71.9731i	0.395700	+	0.942457i
$19$		−	21.7774i		−	0.262952i	−0.991319	−	0.131476i	$-0.958028\pi$
$19$		−	21.7774i		−	0.262952i	0.991319	−	0.131476i	$-0.0419716\pi$
$20$	−3.10969	+	2.52772i	−0.0347674	+	0.0282607i
$21$	32.7146	+	95.6178i	0.339948	+	0.993596i
$22$	42.3700	−	158.127i	0.410605	−	1.53240i
$23$	−26.4989	+	98.8952i	−0.240235	+	0.896569i	0.735484	+	0.677542i	$0.236955\pi$
$23$	−26.4989	+	98.8952i	−0.240235	+	0.896569i	−0.975719	+	0.219027i	$0.929712\pi$
$24$	−75.4824	+	86.4900i	−0.641991	+	0.735612i
$25$	118.738	−	39.0667i	0.949907	−	0.312533i
$26$		−	6.88818i		−	0.0519571i
$27$	28.3625	+	137.399i	0.202162	+	0.979352i
$28$	4.92937	−	4.92937i	0.0332701	−	0.0332701i
$29$	40.6009	−	70.3228i	0.259979	−	0.450297i	−0.706257	−	0.707956i	$-0.749618\pi$
$29$	40.6009	−	70.3228i	0.259979	−	0.450297i	0.966236	+	0.257659i	$0.0829510\pi$
$30$	−148.306	+	78.8352i	−0.902563	+	0.479776i
$31$	4.26447	+	7.38628i	0.0247071	+	0.0427940i	0.878115	−	0.478450i	$-0.158801\pi$
$31$	4.26447	+	7.38628i	0.0247071	+	0.0427940i	−0.853407	+	0.521244i	$0.825468\pi$
$32$	15.6566	+	4.19518i	0.0864914	+	0.0231753i
$33$	129.498	−	264.196i	0.683111	−	1.39365i
$34$	−327.875	−	189.298i	−1.65382	−	0.954836i
$35$	−198.482	+	88.8102i	−0.958560	+	0.428905i
$36$	7.64946	−	5.92832i	0.0354142	−	0.0274459i
$37$	8.92697	+	8.92697i	0.0396645	+	0.0396645i	0.726661	−	0.686996i	$-0.241071\pi$
$37$	8.92697	+	8.92697i	0.0396645	+	0.0396645i	−0.686996	+	0.726661i	$0.741071\pi$
$38$	−60.8153	+	16.2954i	−0.259619	+	0.0695648i
$39$	2.38603	−	12.1480i	0.00979667	−	0.0498778i
$40$	−200.097	−	144.814i	−0.790952	−	0.572428i
$41$	−28.1572	+	16.2566i	−0.107254	+	0.0619232i	−0.552668	−	0.833402i	$-0.686390\pi$
$41$	−28.1572	+	16.2566i	−0.107254	+	0.0619232i	0.445413	+	0.895325i	$0.353057\pi$
$42$	242.541	−	162.906i	0.891070	−	0.598499i
$43$	114.874	+	428.714i	0.407396	+	1.52042i	0.799593	+	0.600543i	$0.205049\pi$
$43$	114.874	+	428.714i	0.407396	+	1.52042i	−0.392196	+	0.919882i	$0.628285\pi$
$44$	−20.2960			−0.0695395
$45$	−288.861	+	87.6612i	−0.956907	+	0.290395i
$46$	296.002			0.948762
$47$	−37.5556	−	140.159i	−0.116554	−	0.434986i	0.882844	−	0.469666i	$-0.155626\pi$
$47$	−37.5556	−	140.159i	−0.116554	−	0.434986i	−0.999398	+	0.0346799i	$0.988959\pi$
$48$	311.391	+	152.631i	0.936363	+	0.458967i
$49$	30.5356	−	17.6297i	0.0890251	−	0.0513987i
$50$	−197.945	−	302.354i	−0.559874	−	0.855187i
$51$	−512.667	−	447.420i	−1.40760	−	1.22846i
$52$	−0.824893	+	0.221029i	−0.00219985	+	0.000589447i
$53$	−82.9808	−	82.9808i	−0.215062	−	0.215062i	0.591352	−	0.806414i	$-0.298595\pi$
$53$	−82.9808	−	82.9808i	−0.215062	−	0.215062i	−0.806414	+	0.591352i	$0.798595\pi$
$54$	362.476	−	182.017i	0.913459	−	0.458691i
$55$	591.444	+	225.780i	1.45000	+	0.553530i
$56$	372.109	+	214.837i	0.887950	+	0.512658i
$57$	−112.898	+	7.67250i	−0.262347	+	0.0178289i
$58$	−226.763	−	60.7609i	−0.513369	−	0.137557i
$59$	129.436	+	224.189i	0.285612	+	0.494695i	0.972757	−	0.231825i	$-0.0744698\pi$
$59$	129.436	+	224.189i	0.285612	+	0.494695i	−0.687145	+	0.726520i	$0.741136\pi$
$60$	14.1998	+	15.2307i	0.0305530	+	0.0327712i
$61$	−282.613	+	489.500i	−0.593195	+	1.02744i	0.400604	+	0.916251i	$0.368800\pi$
$61$	−282.613	+	489.500i	−0.593195	+	1.02744i	−0.993799	+	0.111192i	$0.964533\pi$
$62$	17.4358	−	17.4358i	0.0357153	−	0.0357153i
$63$	484.175	−	203.286i	0.968260	−	0.406534i
$64$			487.051i			0.951271i
$65$	26.4969	+	2.73539i	0.0505621	+	0.00521975i
$66$	−834.688	−	163.944i	−1.55671	−	0.305759i
$67$	−116.526	+	434.879i	−0.212476	+	0.792970i	0.774564	+	0.632495i	$0.217969\pi$
$67$	−116.526	+	434.879i	−0.212476	+	0.792970i	−0.987040	+	0.160475i	$0.948698\pi$
$68$	−12.1485	+	45.3388i	−0.0216650	+	0.0808549i
$69$	522.028	+	102.533i	0.910794	+	0.178892i
$70$	396.528	+	487.824i	0.677060	+	0.832945i
$71$		−	16.2978i		−	0.0272422i	−0.999907	−	0.0136211i	$-0.995664\pi$
$71$		−	16.2978i		−	0.0272422i	0.999907	−	0.0136211i	$-0.00433587\pi$
$72$	474.974	+	360.844i	0.777448	+	0.590637i
$73$	59.2407	−	59.2407i	0.0949809	−	0.0949809i	−0.658020	−	0.753001i	$-0.728606\pi$
$73$	59.2407	−	59.2407i	0.0949809	−	0.0949809i	0.753001	+	0.658020i	$0.228606\pi$
$74$	18.2495	−	31.6091i	0.0286684	−	0.0496552i
$75$	−244.362	−	601.799i	−0.376220	−	0.926530i
$76$	3.90290	+	6.76003i	0.00589071	+	0.0102030i
$77$	−1063.75	−	285.030i	−1.57435	−	0.421846i
$78$	−35.7097	+	2.42681i	−0.0518375	+	0.00352284i
$79$	−472.049	−	272.538i	−0.672274	−	0.388138i	0.124663	−	0.992199i	$-0.460215\pi$
$79$	−472.049	−	272.538i	−0.672274	−	0.388138i	−0.796938	+	0.604061i	$0.793548\pi$
$80$	−266.113	+	697.098i	−0.371904	+	0.974224i
$81$	702.312	−	195.445i	0.963391	−	0.268100i
$82$	66.4671	+	66.4671i	0.0895129	+	0.0895129i
$83$	−972.735	+	260.644i	−1.28640	+	0.344691i	−0.836294	−	0.548282i	$-0.815282\pi$
$83$	−972.735	+	260.644i	−1.28640	+	0.344691i	−0.450110	+	0.892973i	$0.648615\pi$
$84$	−27.2915	−	23.8181i	−0.0354494	−	0.0309377i
$85$	858.382	−	1186.07i	1.09535	−	1.51350i
$86$	1111.26	−	641.588i	1.39338	−	0.804467i
$87$	−378.871	−	185.707i	−0.466888	−	0.228849i
$88$	−323.773	−	1208.34i	−0.392208	−	1.46374i
$89$	844.831			1.00620			0.503101	−	0.864228i	$-0.332192\pi$
$89$	844.831			1.00620			0.503101	+	0.864228i	$0.332192\pi$
$90$	460.947	+	741.074i	0.539868	+	0.867956i
$91$	−46.3380			−0.0533796
$92$	−9.49816	−	35.4476i	−0.0107636	−	0.0401703i
$93$	36.7895	−	24.7101i	0.0410203	−	0.0275518i
$94$	−363.305	+	209.754i	−0.398639	+	0.230154i
$95$	−38.5333	−	240.410i	−0.0416150	−	0.259638i
$96$	16.2326	−	82.6450i	0.0172576	−	0.0878637i
$97$	393.261	−	105.374i	0.411645	−	0.110300i	−0.0470524	−	0.998892i	$-0.514983\pi$
$97$	393.261	−	105.374i	0.411645	−	0.110300i	0.458698	+	0.888592i	$0.348316\pi$
$98$	−72.0814	−	72.0814i	−0.0742992	−	0.0742992i
$99$	−1415.27	−	578.262i	−1.43676	−	0.587046i
$100$	−29.8567	+	33.4069i	−0.0298567	+	0.0334069i
$101$	−398.138	−	229.865i	−0.392240	−	0.226460i	0.290890	−	0.956756i	$-0.406049\pi$
$101$	−398.138	−	229.865i	−0.392240	−	0.226460i	−0.683130	+	0.730297i	$0.739382\pi$
$102$	−865.845	+	1766.46i	−0.840504	+	1.71476i
$103$	−1343.92	−	360.103i	−1.28564	−	0.344485i	−0.449635	−	0.893212i	$-0.648446\pi$
$103$	−1343.92	−	360.103i	−1.28564	−	0.344485i	−0.836001	+	0.548727i	$0.815113\pi$
$104$	−26.3182	−	45.5845i	−0.0248146	−	0.0429801i
$105$	530.338	+	997.681i	0.492911	+	0.927273i
$106$	−169.639	+	293.823i	−0.155441	+	0.269232i
$107$	−319.287	+	319.287i	−0.288473	+	0.288473i	−0.836476	−	0.548003i	$-0.815388\pi$
$107$	−319.287	+	319.287i	−0.288473	+	0.288473i	0.548003	+	0.836476i	$0.315388\pi$
$108$	−33.4286	−	37.5677i	−0.0297839	−	0.0334718i
$109$		−	1126.24i		−	0.989672i	−0.868986	−	0.494836i	$-0.835228\pi$
$109$		−	1126.24i		−	0.989672i	0.868986	−	0.494836i	$-0.164772\pi$
$110$	187.949	−	1820.60i	0.162911	−	1.57807i
$111$	43.1341	−	49.4243i	0.0368838	−	0.0422625i
$112$	335.947	−	1253.77i	0.283429	−	1.05777i
$113$	−390.853	+	1458.69i	−0.325384	+	1.21435i	0.588541	+	0.808467i	$0.299703\pi$
$113$	−390.853	+	1458.69i	−0.325384	+	1.21435i	−0.913925	+	0.405883i	$0.866964\pi$
$114$	105.905	+	309.537i	0.0870077	+	0.254305i
$115$	−117.546	+	1138.64i	−0.0953153	+	0.923289i
$116$			29.1056i			0.0232965i
$117$	−63.8182	−	8.08972i	−0.0504273	−	0.00639226i
$118$	529.215	−	529.215i	0.412866	−	0.412866i
$119$	−1273.44	+	2205.67i	−0.980977	+	1.69910i
$120$	−680.247	+	1088.36i	−0.517482	+	0.827944i
$121$	937.629	+	1624.02i	0.704455	+	1.22015i
$122$	1578.44	+	422.942i	1.17136	+	0.313864i
$123$	94.1974	+	140.245i	0.0690528	+	0.102809i
$124$	−2.64751	−	1.52854i	−0.00191736	−	0.00110699i
$125$	1241.68	−	641.371i	0.888474	−	0.458928i
$126$	−929.988	−	1199.99i	−0.657539	−	0.848440i
$127$	−638.135	−	638.135i	−0.445869	−	0.445869i	0.448110	−	0.893979i	$-0.352097\pi$
$127$	−638.135	−	638.135i	−0.445869	−	0.445869i	−0.893979	+	0.448110i	$0.852097\pi$
$128$	1485.38	−	398.007i	1.02571	−	0.274837i
$129$	2182.06	−	746.569i	1.48930	−	0.509548i
$130$	−12.1880	−	76.0417i	−0.00822279	−	0.0513023i
$131$	2261.94	−	1305.93i	1.50860	−	0.870992i	0.508653	−	0.860972i	$-0.330144\pi$
$131$	2261.94	−	1305.93i	1.50860	−	0.870992i	0.999950	−	0.0100207i	$-0.00318975\pi$
$132$	7.15058	+	105.218i	0.00471498	+	0.0693795i
$133$	109.622	+	409.115i	0.0714694	+	0.266727i
$134$	1301.63			0.839132
$135$	556.223	+	1466.63i	0.354608	+	0.935015i
$136$	−2893.07			−1.82411
$137$	252.432	+	942.088i	0.157421	+	0.587504i	0.998886	+	0.0471916i	$0.0150271\pi$
$137$	252.432	+	942.088i	0.157421	+	0.587504i	−0.841465	+	0.540312i	$0.818306\pi$
$138$	−104.286	−	1534.53i	−0.0643288	−	0.946579i
$139$	1106.34	−	638.748i	0.675099	−	0.389769i	−0.122907	−	0.992418i	$-0.539222\pi$
$139$	1106.34	−	638.748i	0.675099	−	0.389769i	0.798006	+	0.602649i	$0.205888\pi$
$140$	45.6954	−	63.1396i	0.0275855	−	0.0381162i
$141$	−713.382	+	244.075i	−0.426082	+	0.145779i
$142$	−45.5131	+	12.1952i	−0.0268970	+	0.00720703i
$143$	95.3952	+	95.3952i	0.0557856	+	0.0557856i
$144$	681.562	−	1668.09i	0.394422	−	0.965327i
$145$	323.781	−	848.164i	0.185438	−	0.485767i
$146$	−209.763	−	121.107i	−0.118905	−	0.0686497i
$147$	−102.154	−	152.091i	−0.0573165	−	0.0853352i
$148$	−4.37094	−	1.17119i	−0.00242763	−	0.000650480i
$149$	−69.6092	−	120.567i	−0.0382725	−	0.0662900i	0.846255	−	0.532779i	$-0.178852\pi$
$149$	−69.6092	−	120.567i	−0.0382725	−	0.0662900i	−0.884527	+	0.466489i	$0.845519\pi$
$150$	−1497.73	+	1132.71i	−0.815258	+	0.616570i
$151$	706.994	−	1224.55i	0.381022	−	0.659950i	−0.610186	−	0.792258i	$-0.708905\pi$
$151$	706.994	−	1224.55i	0.381022	−	0.659950i	0.991209	+	0.132308i	$0.0422388\pi$
$152$	−340.201	+	340.201i	−0.181539	+	0.181539i
$153$	−2138.89	+	2815.40i	−1.13019	+	1.48766i
$154$			3183.88i			1.66600i
$155$	60.1467	+	73.9947i	0.0311684	+	0.0383445i
$156$	1.43648	+	4.19853i	0.000737247	+	0.00215482i
$157$	−614.674	+	2293.99i	−0.312461	+	1.16612i	0.613870	+	0.789407i	$0.289612\pi$
$157$	−614.674	+	2293.99i	−0.312461	+	1.16612i	−0.926330	+	0.376712i	$0.877055\pi$
$158$	−407.864	+	1522.17i	−0.205367	+	0.766438i
$159$	−400.953	+	459.424i	−0.199985	+	0.229149i
$160$	180.263	+	18.6094i	0.0890691	+	0.00919500i
$161$		−	1991.25i		−	0.974738i
$162$	−1071.32	−	1815.02i	−0.519571	−	0.880256i
$163$	940.543	−	940.543i	0.451957	−	0.451957i	−0.444046	−	0.896004i	$-0.646457\pi$
$163$	940.543	−	940.543i	0.451957	−	0.451957i	0.896004	+	0.444046i	$0.146457\pi$
$164$	5.82694	−	10.0926i	0.00277444	−	0.00480547i
$165$	962.112	−	3145.71i	0.453941	−	1.48420i
$166$	1455.74	+	2521.41i	0.680646	+	1.17891i
$167$	−3634.62	−	973.893i	−1.68416	−	0.451270i	−0.715290	−	0.698828i	$-0.753705\pi$
$167$	−3634.62	−	973.893i	−1.68416	−	0.451270i	−0.968873	+	0.247558i	$0.920372\pi$
$168$	982.659	−	2004.78i	0.451273	−	0.920666i
$169$	−1897.74	−	1095.66i	−0.863788	−	0.498708i
$170$	−3954.50	−	1509.60i	−1.78409	−	0.681066i
$171$	79.5514	+	582.584i	0.0355757	+	0.260534i
$172$	−112.492	−	112.492i	−0.0498686	−	0.0498686i
$173$	4215.81	−	1129.62i	1.85273	−	0.496437i	0.853052	−	0.521826i	$-0.174749\pi$
$173$	4215.81	−	1129.62i	1.85273	−	0.496437i	0.999678	+	0.0253882i	$0.00808217\pi$
$174$	−235.105	+	1196.99i	−0.102432	+	0.521515i
$175$	−2033.99	+	1331.61i	−0.878601	+	0.575202i
$176$	−3272.73	+	1889.51i	−1.40165	+	0.809245i
$177$	1116.64	−	750.006i	0.474191	−	0.318497i
$178$	−632.163	−	2359.26i	−0.266194	−	0.993451i
$179$	−2857.68			−1.19326			−0.596628	−	0.802518i	$-0.703493\pi$
$179$	−2857.68			−1.19326			−0.596628	+	0.802518i	$0.703493\pi$
$180$	73.9561	−	78.9803i	0.0306242	−	0.0327047i
$181$	−1459.11			−0.599199			−0.299599	−	0.954065i	$-0.596853\pi$
$181$	−1459.11			−0.599199			−0.299599	+	0.954065i	$0.596853\pi$
$182$	34.6734	+	129.403i	0.0141218	+	0.0527031i
$183$	2637.23	+	1292.66i	1.06530	+	0.522166i
$184$	1958.88	−	1130.96i	0.784838	−	0.453127i
$185$	114.344	+	82.7532i	0.0454419	+	0.0328872i
$186$	−96.5336	−	84.2478i	−0.0380548	−	0.0332116i
$187$	7162.38	−	1919.15i	2.80088	−	0.750495i
$188$	36.7768	+	36.7768i	0.0142672	+	0.0142672i
$189$	−1224.46	−	2438.44i	−0.471249	−	0.938468i
$190$	−642.533	+	287.499i	−0.245338	+	0.109776i
$191$	610.123	+	352.255i	0.231136	+	0.133446i	0.611096	−	0.791557i	$-0.290729\pi$
$191$	610.123	+	352.255i	0.231136	+	0.133446i	−0.379960	+	0.925003i	$0.624062\pi$
$192$	2524.96	−	171.595i	0.949081	−	0.0644989i
$193$	−1480.98	−	396.828i	−0.552349	−	0.148001i	−0.0281599	−	0.999603i	$-0.508965\pi$
$193$	−1480.98	−	396.828i	−0.552349	−	0.148001i	−0.524189	+	0.851602i	$0.675631\pi$
$194$	−588.531	−	1019.37i	−0.217804	−	0.377248i
$195$	4.84558	−	138.329i	0.00177948	−	0.0507997i
$196$	−6.31913	+	10.9451i	−0.00230289	+	0.00398872i
$197$	989.475	−	989.475i	0.357854	−	0.357854i	−0.505168	−	0.863021i	$-0.668569\pi$
$197$	989.475	−	989.475i	0.357854	−	0.357854i	0.863021	+	0.505168i	$0.168569\pi$
$198$	−555.844	+	4384.94i	−0.199506	+	1.57386i
$199$			2035.66i			0.725146i	0.931955	+	0.362573i	$0.118102\pi$
$199$			2035.66i			0.725146i	−0.931955	+	0.362573i	$0.881898\pi$
$200$	−2465.19	−	1244.61i	−0.871577	−	0.440037i
$201$	2295.55	+	450.877i	0.805551	+	0.158221i
$202$	−344.003	+	1283.84i	−0.119822	+	0.447180i
$203$	−408.749	+	1525.47i	−0.141323	+	0.527424i
$204$	239.325	+	47.0066i	0.0821378	+	0.0161330i
$205$	−282.075	+	229.285i	−0.0961024	+	0.0781169i
$206$			4022.47i			1.36048i
$207$	347.634	−	2742.42i	0.116726	−	0.920828i
$208$	−112.436	+	112.436i	−0.0374811	+	0.0374811i
$209$	616.560	−	1067.91i	0.204059	−	0.353441i
$210$	2389.27	−	2227.55i	0.785121	−	0.731978i
$211$	−688.380	−	1192.31i	−0.224597	−	0.389014i	0.731601	−	0.681733i	$-0.238773\pi$
$211$	−688.380	−	1192.31i	−0.224597	−	0.389014i	−0.956199	+	0.292719i	$0.905440\pi$
$212$	40.6301	+	10.8868i	0.0131627	+	0.00352693i
$213$	−84.4912	+	5.74196i	−0.0271795	+	0.00184710i
$214$	1130.55	+	652.723i	0.361134	+	0.208501i
$215$	2026.71	+	4529.50i	0.642886	+	1.43679i
$216$	1703.35	−	2589.49i	0.536565	−	0.815706i
$217$	−117.294	−	117.294i	−0.0366932	−	0.0366932i
$218$	−3145.12	+	842.733i	−0.977131	+	0.261821i
$219$	−327.987	−	286.244i	−0.101202	−	0.0883223i
$220$	−224.057	+	35.9120i	−0.0686631	+	0.0110054i
$221$	270.201	−	156.001i	0.0822430	−	0.0474830i
$222$	−170.297	−	83.4728i	−0.0514847	−	0.0252357i
$223$	1017.06	+	3795.71i	0.305413	+	1.13982i	0.932589	+	0.360940i	$0.117544\pi$
$223$	1017.06	+	3795.71i	0.305413	+	1.13982i	−0.627176	+	0.778878i	$0.715789\pi$
$224$	−315.246			−0.0940323
$225$	−3033.75	+	1478.84i	−0.898889	+	0.438176i
$226$	4365.96			1.28504
$227$	−233.869	−	872.812i	−0.0683809	−	0.255201i	0.923270	−	0.384151i	$-0.125506\pi$
$227$	−233.869	−	872.812i	−0.0683809	−	0.255201i	−0.991651	+	0.128950i	$0.958839\pi$
$228$	33.6703	−	22.6151i	0.00978012	−	0.00656895i
$229$	−3128.15	+	1806.04i	−0.902682	+	0.521164i	−0.878069	−	0.478533i	$-0.841169\pi$
$229$	−3128.15	+	1806.04i	−0.902682	+	0.521164i	−0.0246126	+	0.999697i	$0.507835\pi$
$230$	3267.69	−	523.749i	0.936805	−	0.150152i
$231$	−1102.88	+	5615.09i	−0.314130	+	1.59933i
$232$	−1732.82	+	464.308i	−0.490368	+	0.131394i
$233$	−2992.27	−	2992.27i	−0.841332	−	0.841332i	0.147700	−	0.989032i	$-0.452813\pi$
$233$	−2992.27	−	2992.27i	−0.841332	−	0.841332i	−0.989032	+	0.147700i	$0.952813\pi$
$234$	25.1621	+	184.271i	0.00702947	+	0.0514794i
$235$	−662.592	−	1480.83i	−0.183927	−	0.411058i
$236$	−80.3575	−	46.3945i	−0.0221645	−	0.0127967i
$237$	−1246.58	+	2543.21i	−0.341662	+	0.697044i
$238$	7112.39	+	1905.76i	1.93709	+	0.519042i
$239$	−1931.06	−	3344.69i	−0.522635	−	0.905230i	−0.999653	−	0.0263367i	$-0.991616\pi$
$239$	−1931.06	−	3344.69i	−0.522635	−	0.905230i	0.477018	−	0.878893i	$-0.341718\pi$
$240$	3707.65	+	1133.98i	0.997199	+	0.304993i
$241$	858.250	−	1486.53i	0.229397	−	0.397328i	−0.728232	−	0.685330i	$-0.759658\pi$
$241$	858.250	−	1486.53i	0.229397	−	0.397328i	0.957630	+	0.288003i	$0.0929912\pi$
$242$	3833.62	−	3833.62i	1.01832	−	1.01832i
$243$	−1260.66	−	3572.07i	−0.332803	−	0.942996i
$244$		−	202.597i		−	0.0531556i
$245$	305.902	−	248.653i	0.0797687	−	0.0648401i
$246$	321.161	−	367.996i	0.0832377	−	0.0953762i
$247$	13.4290	−	50.1178i	0.00345939	−	0.0129106i
$248$	48.7681	−	182.005i	0.0124870	−	0.0466021i
$249$	1693.94	+	4951.02i	0.431120	+	1.26007i
$250$	−2720.20	−	2987.58i	−0.688161	−	0.755803i
$251$			2285.88i			0.574836i	0.957805	+	0.287418i	$0.0927968\pi$
$251$			2285.88i			0.574836i	−0.957805	+	0.287418i	$0.907203\pi$
$252$	−113.863	+	149.876i	−0.0284630	+	0.0374655i
$253$	−4099.36	+	4099.36i	−1.01867	+	1.01867i
$254$	−1304.55	+	2259.54i	−0.322262	+	0.558175i
$255$	−6451.23	−	4032.15i	−1.58428	−	0.990208i
$256$	−274.734	−	475.854i	−0.0670738	−	0.116175i
$257$	3690.98	+	988.996i	0.895865	+	0.240046i	0.677239	−	0.735763i	$-0.263176\pi$
$257$	3690.98	+	988.996i	0.895865	+	0.240046i	0.218625	+	0.975809i	$0.429843\pi$
$258$	−3717.63	−	5534.96i	−0.897091	−	1.33563i
$259$	−212.640	−	122.768i	−0.0510147	−	0.0294533i
$260$	−8.71526	+	3.89962i	−0.00207884	+	0.000930169i
$261$	−829.260	+	2029.57i	−0.196666	+	0.481330i
$262$	−5339.48	−	5339.48i	−1.25906	−	1.25906i
$263$	4764.50	−	1276.64i	1.11708	−	0.299320i	0.347378	−	0.937725i	$-0.387072\pi$
$263$	4764.50	−	1276.64i	1.11708	−	0.299320i	0.769701	+	0.638405i	$0.220405\pi$
$264$	−6150.18	+	2104.21i	−1.43378	+	0.490551i
$265$	−1062.89	−	769.234i	−0.246388	−	0.178316i
$266$	1060.46	−	612.257i	0.244440	−	0.141127i
$267$	−297.646	−	4379.77i	−0.0682234	−	1.00389i
$268$	−41.7669	−	155.876i	−0.00951986	−	0.0355286i
$269$	6569.52			1.48904			0.744518	−	0.667602i	$-0.232679\pi$
$269$	6569.52			1.48904			0.744518	+	0.667602i	$0.232679\pi$
$270$	3679.47	−	2650.73i	0.829354	−	0.597475i
$271$	−1603.65			−0.359465			−0.179733	−	0.983715i	$-0.557523\pi$
$271$	−1603.65			−0.359465			−0.179733	+	0.983715i	$0.557523\pi$
$272$	2261.99	+	8441.86i	0.504240	+	1.88185i
$273$	16.3255	+	240.225i	0.00361929	+	0.0532567i
$274$	2441.97	−	1409.87i	0.538412	−	0.310852i
$275$	6928.70	+	1445.97i	1.51933	+	0.317074i
$276$	−180.421	+	61.7290i	−0.0393481	+	0.0134625i
$277$	−8497.59	+	2276.92i	−1.84322	+	0.493888i	−0.999106	−	0.0422830i	$-0.986537\pi$
$277$	−8497.59	+	2276.92i	−1.84322	+	0.493888i	−0.844109	+	0.536171i	$0.819870\pi$
$278$	−2611.60	−	2611.60i	−0.563430	−	0.563430i
$279$	−141.064	−	182.018i	−0.0302697	−	0.0390578i
$280$	4488.01	+	1713.27i	0.957893	+	0.365669i
$281$	−5805.61	−	3351.87i	−1.23250	−	0.711586i	−0.264953	−	0.964261i	$-0.585356\pi$
$281$	−5805.61	−	3351.87i	−1.23250	−	0.711586i	−0.967551	+	0.252675i	$0.918690\pi$
$282$	1215.40	+	1809.54i	0.256653	+	0.382116i
$283$	−1103.65	−	295.723i	−0.231821	−	0.0621163i	0.141038	−	0.990004i	$-0.454956\pi$
$283$	−1103.65	−	295.723i	−0.231821	−	0.0621163i	−0.372859	+	0.927888i	$0.621623\pi$
$284$	2.92087	+	5.05909i	0.000610287	+	0.00105705i
$285$	−1232.76	+	284.464i	−0.256219	+	0.0591235i
$286$	195.018	−	337.781i	0.0403204	−	0.0698370i
$287$	447.135	−	447.135i	0.0919636	−	0.0919636i
$288$	−434.167	−	55.0358i	−0.0888316	−	0.0112605i
$289$		−	12235.6i		−	2.49046i
$290$	−2610.85	−	269.529i	−0.528669	−	0.0545769i
$291$	−684.830	−	2001.62i	−0.137957	−	0.403219i
$292$	−7.77218	+	29.0062i	−0.00155765	+	0.00581322i
$293$	1628.20	−	6076.51i	0.324642	−	1.21158i	−0.590029	−	0.807382i	$-0.700884\pi$
$293$	1628.20	−	6076.51i	0.324642	−	1.21158i	0.914671	−	0.404199i	$-0.132450\pi$
$294$	−348.289	+	399.080i	−0.0690905	+	0.0791660i
$295$	1825.58	+	2245.90i	0.360303	+	0.443259i
$296$		−	278.910i		−	0.0547679i
$297$	−2499.20	+	7540.74i	−0.488278	+	1.47326i
$298$	−284.606	+	284.606i	−0.0553248	+	0.0553248i
$299$	−121.967	+	211.254i	−0.0235905	+	0.0408599i
$300$	183.707	+	143.013i	0.0353544	+	0.0275229i
$301$	−4316.07	−	7475.65i	−0.826492	−	1.43153i
$302$	−3948.68	−	1058.05i	−0.752388	−	0.201602i
$303$	−1051.40	+	2145.01i	−0.199344	+	0.406692i
$304$	1258.68	+	726.702i	0.237469	+	0.137103i
$305$	−2253.76	+	5903.86i	−0.423115	+	1.10837i
$306$	9462.71	+	3866.36i	1.76780	+	0.722304i
$307$	4998.67	+	4998.67i	0.929281	+	0.929281i	0.997659	−	0.0683782i	$-0.0217824\pi$
$307$	4998.67	+	4998.67i	0.929281	+	0.929281i	−0.0683782	+	0.997659i	$0.521782\pi$
$308$	381.285	−	102.165i	0.0705380	−	0.0189006i
$309$	−1393.36	+	7094.02i	−0.256523	+	1.30603i
$310$	161.630	−	223.333i	0.0296129	−	0.0409176i
$311$	−2626.45	+	1516.38i	−0.478882	+	0.276483i	−0.719950	−	0.694025i	$-0.755835\pi$
$311$	−2626.45	+	1516.38i	−0.478882	+	0.276483i	0.241068	+	0.970508i	$0.422502\pi$
$312$	−227.047	+	152.499i	−0.0411987	+	0.0276717i
$313$	1115.49	+	4163.08i	0.201442	+	0.751793i	0.990505	+	0.137480i	$0.0439002\pi$
$313$	1115.49	+	4163.08i	0.201442	+	0.751793i	−0.789062	+	0.614313i	$0.789433\pi$
$314$	6866.12			1.23400
$315$	4985.33	−	3100.87i	0.891719	−	0.554649i
$316$	195.375			0.0347806
$317$	−1248.69	−	4660.18i	−0.221241	−	0.825684i	−0.983876	−	0.178854i	$-0.942761\pi$
$317$	−1248.69	−	4660.18i	−0.221241	−	0.825684i	0.762634	−	0.646830i	$-0.223906\pi$
$318$	1583.00	+	775.922i	0.279152	+	0.136829i
$319$	3981.95	−	2298.98i	0.698891	−	0.403505i
$320$	861.794	+	5376.76i	0.150549	+	0.939282i
$321$	1767.74	+	1542.76i	0.307369	+	0.268250i
$322$	−5560.74	+	1490.00i	−0.962385	+	0.257870i
$323$	−2016.54	−	2016.54i	−0.347378	−	0.347378i
$324$	−182.981	+	186.536i	−0.0313753	+	0.0319849i
$325$	297.351	−	16.6868i	0.0507510	−	0.00284805i
$326$	−3330.33	−	1922.77i	−0.565797	−	0.326663i
$327$	−5838.65	+	396.791i	−0.987395	+	0.0671027i
$328$	693.821	+	185.909i	0.116798	+	0.0312960i
$329$	1411.05	+	2444.01i	0.236455	+	0.409553i
$330$	−9504.57	−	332.939i	−1.58548	−	0.0555385i
$331$	5632.10	−	9755.08i	0.935251	−	1.61990i	0.161065	−	0.986944i	$-0.448507\pi$
$331$	5632.10	−	9755.08i	0.935251	−	1.61990i	0.774186	−	0.632958i	$-0.218160\pi$
$332$	255.239	−	255.239i	0.0421930	−	0.0421930i
$333$	−271.422	−	206.202i	−0.0446661	−	0.0339334i
$334$			10878.7i			1.78221i
$335$	−516.895	+	5007.00i	−0.0843015	+	0.816603i
$336$	−6618.16	−	1299.89i	−1.07455	−	0.211057i
$337$	−612.060	+	2284.24i	−0.0989348	+	0.369230i	−0.997587	−	0.0694329i	$-0.977881\pi$
$337$	−612.060	+	2284.24i	−0.0989348	+	0.369230i	0.898652	+	0.438663i	$0.144548\pi$
$338$	−1639.70	+	6119.46i	−0.263870	+	0.984777i
$339$	7699.81	+	1512.34i	1.23362	+	0.242299i
$340$	−53.8894	+	522.010i	−0.00859578	+	0.0832646i
$341$			482.941i			0.0766942i
$342$	1567.39	−	658.085i	0.247821	−	0.104050i
$343$	4232.18	−	4232.18i	0.666229	−	0.666229i
$344$	4902.73	−	8491.79i	0.768424	−	1.33095i
$345$	5944.32	+	208.226i	0.927627	+	0.0324942i
$346$	−6309.14	−	10927.7i	−0.980293	−	1.69792i
$347$	−994.834	−	266.565i	−0.153906	−	0.0412391i	0.181043	−	0.983475i	$-0.442053\pi$
$347$	−994.834	−	266.565i	−0.153906	−	0.0412391i	−0.334950	+	0.942236i	$0.608719\pi$
$348$	150.889	−	10.2543i	0.0232429	−	0.00157957i
$349$	4729.47	+	2730.56i	0.725394	+	0.418807i	0.816735	−	0.577013i	$-0.195782\pi$
$349$	4729.47	+	2730.56i	0.725394	+	0.418807i	−0.0913406	+	0.995820i	$0.529115\pi$
$350$	5240.61	+	4683.68i	0.800350	+	0.715295i
$351$	−19.4546	+	333.696i	−0.00295843	+	0.0507447i
$352$	648.991	+	648.991i	0.0982708	+	0.0982708i
$353$	−643.090	+	172.316i	−0.0969638	+	0.0259814i	−0.306975	−	0.951718i	$-0.599317\pi$
$353$	−643.090	+	172.316i	−0.0969638	+	0.0259814i	0.210011	+	0.977699i	$0.432650\pi$
$354$	−2930.00	−	2557.10i	−0.439909	−	0.383922i
$355$	−28.8376	−	179.919i	−0.00431139	−	0.0268989i
$356$	−262.248	+	151.409i	−0.0390425	+	0.0225412i
$357$	11883.3	+	5824.69i	1.76171	+	0.863516i
$358$	2138.31	+	7980.30i	0.315680	+	1.17813i
$359$	−6703.88			−0.985563			−0.492781	−	0.870153i	$-0.664020\pi$
$359$	−6703.88			−0.985563			−0.492781	+	0.870153i	$0.664020\pi$
$360$	5881.93	+	3143.09i	0.861125	+	0.460154i
$361$	6384.74			0.930856
$362$	1091.81	+	4074.69i	0.158520	+	0.591605i
$363$	8088.90	−	5433.02i	1.16958	−	0.785563i
$364$	14.3840	−	8.30460i	0.00207122	−	0.00119582i
$365$	549.163	−	758.806i	0.0787521	−	0.108816i
$366$	1636.51	−	8331.95i	0.233720	−	1.18994i
$367$	−3154.29	+	845.191i	−0.448645	+	0.120214i	−0.476065	−	0.879410i	$-0.657937\pi$
$367$	−3154.29	+	845.191i	−0.448645	+	0.120214i	0.0274202	+	0.999624i	$0.491271\pi$
$368$	−4831.66	−	4831.66i	−0.684423	−	0.684423i
$369$	693.871	−	537.748i	0.0978901	−	0.0758646i
$370$	145.535	−	381.238i	0.0204487	−	0.0535665i
$371$	1976.60	+	1141.19i	0.276603	+	0.159697i
$372$	−6.99149	+	14.2637i	−0.000974440	+	0.00198801i
$373$	−4082.74	−	1093.97i	−0.566747	−	0.151859i	−0.0359425	−	0.999354i	$-0.511443\pi$
$373$	−4082.74	−	1093.97i	−0.566747	−	0.151859i	−0.530804	+	0.847495i	$0.678110\pi$
$374$	−10718.8	−	18565.5i	−1.48197	−	2.56684i
$375$	−3762.45	−	6211.14i	−0.518113	−	0.855312i
$376$	−1602.85	+	2776.22i	−0.219842	+	0.380778i
$377$	136.802	−	136.802i	0.0186888	−	0.0186888i
$378$	−5893.32	+	5244.01i	−0.801904	+	0.713553i
$379$		−	2005.61i		−	0.271824i	−0.990721	−	0.135912i	$-0.956604\pi$
$379$		−	2005.61i		−	0.271824i	0.990721	−	0.135912i	$-0.0433965\pi$
$380$	55.0472	+	67.7211i	0.00743121	+	0.00914215i
$381$	−3083.39	+	3533.04i	−0.414612	+	0.475074i
$382$	527.164	−	1967.40i	0.0706074	−	0.263511i
$383$	303.630	−	1133.16i	0.0405085	−	0.151180i	−0.942709	−	0.333615i	$-0.891731\pi$
$383$	303.630	−	1133.16i	0.0405085	−	0.151180i	0.983218	+	0.182435i	$0.0583980\pi$
$384$	−2586.67	−	7560.29i	−0.343751	−	1.00471i
$385$	−12247.5	−	1264.36i	−1.62127	−	0.167371i
$386$			4432.70i			0.584504i
$387$	−4639.13	−	11049.2i	−0.609355	−	1.45133i
$388$	−103.189	+	103.189i	−0.0135016	+	0.0135016i
$389$	−5874.10	+	10174.2i	−0.765627	+	1.32610i	0.174288	+	0.984695i	$0.444238\pi$
$389$	−5874.10	+	10174.2i	−0.765627	+	1.32610i	−0.939915	+	0.341410i	$0.889096\pi$
$390$	−389.921	+	89.9758i	−0.0506267	+	0.0116823i
$391$	6703.72	+	11611.2i	0.867064	+	1.50180i
$392$	−752.427	−	201.612i	−0.0969472	−	0.0259769i
$393$	−7567.13	−	11266.3i	−0.971276	−	1.44608i
$394$	−3503.59	−	2022.80i	−0.447990	−	0.258647i
$395$	−5693.39	−	2173.41i	−0.725229	−	0.276851i
$396$	542.954	−	74.1400i	0.0689001	−	0.00940826i
$397$	10419.9	+	10419.9i	1.31728	+	1.31728i	0.915919	+	0.401363i	$0.131463\pi$
$397$	10419.9	+	10419.9i	1.31728	+	1.31728i	0.401363	+	0.915919i	$0.368537\pi$
$398$	5684.75	−	1523.22i	0.715957	−	0.191840i
$399$	2082.31	−	712.439i	0.261268	−	0.0893898i
$400$	−1704.28	+	8166.44i	−0.213035	+	1.02080i
$401$	−4827.90	+	2787.39i	−0.601231	+	0.347121i	−0.769526	−	0.638616i	$-0.779507\pi$
$401$	−4827.90	+	2787.39i	−0.601231	+	0.347121i	0.168295	+	0.985737i	$0.446174\pi$
$402$	−458.583	−	6747.90i	−0.0568956	−	0.837201i
$403$	5.25937	+	19.6282i	0.000650093	+	0.00242618i
$404$	164.784			0.0202928
$405$	7407.31	−	3400.28i	0.908820	−	0.417188i
$406$	4565.86			0.558128
$407$	185.018	+	690.498i	0.0225332	+	0.0840951i
$408$	1019.27	+	14998.2i	0.123680	+	1.81991i
$409$	−8856.21	+	5113.13i	−1.07069	+	0.618162i	−0.928369	−	0.371659i	$-0.878789\pi$
$409$	−8856.21	+	5113.13i	−1.07069	+	0.618162i	−0.142318	+	0.989821i	$0.545456\pi$
$410$	851.367	+	616.151i	0.102551	+	0.0742184i
$411$	4795.03	−	1640.57i	0.575478	−	0.196893i
$412$	481.710	−	129.074i	0.0576023	−	0.0154345i
$413$	−3560.12	−	3560.12i	−0.424169	−	0.424169i
$414$	−7918.56	+	1081.27i	−0.940039	+	0.128362i
$415$	−10277.3	+	4598.53i	−1.21564	+	0.543935i
$416$	33.4447	+	19.3093i	0.00394173	+	0.00227576i
$417$	−3701.17	−	5510.46i	−0.434646	−	0.647118i
$418$	−3443.59	−	922.708i	−0.402947	−	0.107969i
$419$	4387.14	+	7598.75i	0.511517	+	0.885974i	0.999911	+	0.0133505i	$0.00424974\pi$
$419$	4387.14	+	7598.75i	0.511517	+	0.885974i	−0.488394	+	0.872623i	$0.662417\pi$
$420$	−343.427	−	214.649i	−0.0398989	−	0.0249376i
$421$	−6005.42	+	10401.7i	−0.695217	+	1.20415i	0.274891	+	0.961475i	$0.411358\pi$
$421$	−6005.42	+	10401.7i	−0.695217	+	1.20415i	−0.970108	+	0.242675i	$0.921975\pi$
$422$	−2814.53	+	2814.53i	−0.324666	+	0.324666i
$423$	1516.67	+	3612.32i	0.174333	+	0.415217i
$424$			2592.61i			0.296954i
$425$	7377.40	−	14612.4i	0.842016	−	1.66777i
$426$	79.2572	+	231.652i	0.00901414	+	0.0263464i
$427$	2845.20	−	10618.4i	0.322457	−	1.20342i
$428$	41.8894	−	156.333i	0.00473084	−	0.0176557i
$429$	460.938	−	528.156i	0.0518748	−	0.0594397i
$430$	11132.5	−	9049.05i	1.24850	−	1.01485i
$431$			4099.38i			0.458145i	0.973409	+	0.229072i	$0.0735692\pi$
$431$			4099.38i			0.458145i	−0.973409	+	0.229072i	$0.926431\pi$
$432$	−8887.80	−	2945.66i	−0.989849	−	0.328063i
$433$	4324.33	−	4324.33i	0.479940	−	0.479940i	−0.425172	−	0.905112i	$-0.639787\pi$
$433$	4324.33	−	4324.33i	0.479940	−	0.479940i	0.905112	+	0.425172i	$0.139787\pi$
$434$	−239.785	+	415.320i	−0.0265209	+	0.0459355i
$435$	−4511.12	−	1379.72i	−0.497222	−	0.152075i
$436$	201.843	+	349.602i	0.0221709	+	0.0384011i
$437$	2153.68	+	577.078i	0.235754	+	0.0631702i
$438$	−553.938	+	1130.12i	−0.0604296	+	0.123286i
$439$	10469.7	+	6044.67i	1.13825	+	0.657167i	0.945996	−	0.324179i	$-0.105088\pi$
$439$	10469.7	+	6044.67i	1.13825	+	0.657167i	0.192251	+	0.981346i	$0.438421\pi$
$440$	−5712.31	−	12766.5i	−0.618918	−	1.38322i
$441$	−752.481	+	583.171i	−0.0812526	+	0.0629706i
$442$	−637.829	−	637.829i	−0.0686390	−	0.0686390i
$443$	8924.79	−	2391.39i	0.957177	−	0.256475i	0.253772	−	0.967264i	$-0.418329\pi$
$443$	8924.79	−	2391.39i	0.957177	−	0.256475i	0.703405	+	0.710789i	$0.251662\pi$
$444$	−4.53173	+	23.0724i	−0.000484383	+	0.00246614i
$445$	9326.46	−	1494.86i	0.993521	−	0.159243i
$446$	9838.80	−	5680.43i	1.04458	−	0.603086i
$447$	−600.517	+	403.345i	−0.0635424	+	0.0426791i
$448$	−2451.69	−	9149.82i	−0.258552	−	0.964930i
$449$	702.553			0.0738431			0.0369215	−	0.999318i	$-0.488245\pi$
$449$	702.553			0.0738431			0.0369215	+	0.999318i	$0.488245\pi$
$450$	6399.86	+	7365.43i	0.670428	+	0.771577i
$451$	−1841.02			−0.192218
$452$	−140.096	−	522.845i	−0.0145787	−	0.0544083i
$453$	−6597.39	−	3233.77i	−0.684266	−	0.335399i
$454$	−2262.40	+	1306.20i	−0.233876	+	0.135029i
$455$	−511.545	+	81.9910i	−0.0527068	+	0.00844791i
$456$	1883.53	+	1643.81i	0.193430	+	0.168813i
$457$	4386.55	−	1175.37i	0.449002	−	0.120310i	−0.0272303	−	0.999629i	$-0.508669\pi$
$457$	4386.55	−	1175.37i	0.449002	−	0.120310i	0.476232	+	0.879319i	$0.342002\pi$
$458$	7384.22	+	7384.22i	0.753367	+	0.753367i
$459$	15349.1	+	10096.5i	1.56086	+	1.02672i
$460$	−167.576	−	374.515i	−0.0169853	−	0.0379606i
$461$	−7776.73	−	4489.90i	−0.785680	−	0.453613i	0.0527593	−	0.998607i	$-0.483198\pi$
$461$	−7776.73	−	4489.90i	−0.785680	−	0.453613i	−0.838440	+	0.544995i	$0.816532\pi$
$462$	16505.9	−	1121.73i	1.66217	−	0.112960i
$463$	6607.21	+	1770.40i	0.663204	+	0.177705i	0.574691	−	0.818370i	$-0.305122\pi$
$463$	6607.21	+	1770.40i	0.663204	+	0.177705i	0.0885123	+	0.996075i	$0.471789\pi$
$464$	2709.66	+	4693.27i	0.271106	+	0.469569i
$465$	362.413	−	337.882i	0.0361430	−	0.0336965i
$466$	−6117.14	+	10595.2i	−0.608093	+	1.05325i
$467$	1646.02	−	1646.02i	0.163102	−	0.163102i	−0.620837	−	0.783939i	$-0.713207\pi$
$467$	1646.02	−	1646.02i	0.163102	−	0.163102i	0.783939	+	0.620837i	$0.213207\pi$
$468$	21.2599	−	8.92620i	0.00209987	−	0.000881653i
$469$		−	8756.28i		−	0.862106i
$470$	−3639.54	+	2958.40i	−0.357190	+	0.290343i
$471$	12109.1	+	2378.38i	1.18462	+	0.232675i
$472$	1480.22	−	5524.25i	0.144349	−	0.538716i
$473$	−6504.58	+	24275.4i	−0.632306	+	2.35980i
$474$	8034.92	+	1578.16i	0.778599	+	0.152927i
$475$	−850.771	−	2585.81i	−0.0821811	−	0.249780i
$476$		−	912.895i		−	0.0879044i
$477$	2523.00	+	1916.76i	0.242181	+	0.183988i
$478$	−7895.37	+	7895.37i	−0.755494	+	0.755494i
$479$	−7066.68	+	12239.8i	−0.674081	+	1.16754i	0.302656	+	0.953100i	$0.402127\pi$
$479$	−7066.68	+	12239.8i	−0.674081	+	1.16754i	−0.976737	+	0.214442i	$0.931207\pi$
$480$	32.9653	−	941.076i	0.00313470	−	0.0894876i
$481$	15.0394	+	26.0491i	0.00142565	+	0.00246930i
$482$	−4793.47	−	1284.41i	−0.452980	−	0.121376i
$483$	−10323.0	+	701.547i	−0.972494	+	0.0660901i
$484$	−582.107	−	336.080i	−0.0546682	−	0.0315627i
$485$	4154.93	−	1859.11i	0.389001	−	0.174057i
$486$	−9031.98	+	6193.36i	−0.843002	+	0.578059i
$487$	−6660.19	−	6660.19i	−0.619717	−	0.619717i	0.325742	−	0.945459i	$-0.394386\pi$
$487$	−6660.19	−	6660.19i	−0.619717	−	0.619717i	−0.945459	+	0.325742i	$0.894386\pi$
$488$	12061.8	−	3231.94i	1.11887	−	0.299801i
$489$	−5207.33	−	4544.59i	−0.481561	−	0.420273i
$490$	−923.280	−	668.197i	−0.0851215	−	0.0616042i
$491$	−4778.58	+	2758.92i	−0.439215	+	0.253581i	−0.703264	−	0.710928i	$-0.748275\pi$
$491$	−4778.58	+	2758.92i	−0.439215	+	0.253581i	0.264050	+	0.964509i	$0.414942\pi$
$492$	−54.3747	−	26.6522i	−0.00498252	−	0.00244223i
$493$	−2752.18	−	10271.3i	−0.251424	−	0.938325i
$494$	−150.007			−0.0136622
$495$	−16646.9	−	3879.50i	−1.51156	−	0.352264i
$496$	−569.213			−0.0515291
$497$	82.0392	+	306.174i	0.00740435	+	0.0276334i
$498$	12558.6	−	8435.16i	1.13005	−	0.759013i
$499$	−4628.28	+	2672.14i	−0.415211	+	0.239722i	−0.693026	−	0.720913i	$-0.743723\pi$
$499$	−4628.28	+	2672.14i	−0.415211	+	0.239722i	0.277816	+	0.960634i	$0.410390\pi$
$500$	−270.490	+	421.622i	−0.0241934	+	0.0377110i
$501$	−3768.32	+	19185.7i	−0.336040	+	1.71088i
$502$	6383.52	−	1710.46i	0.567551	−	0.152075i
$503$	3380.78	+	3380.78i	0.299685	+	0.299685i	0.840890	−	0.541205i	$-0.182032\pi$
$503$	3380.78	+	3380.78i	0.299685	+	0.299685i	−0.541205	+	0.840890i	$0.682032\pi$
$504$	−10739.4	−	4387.98i	−0.949145	−	0.387810i
$505$	−4801.95	−	1833.11i	−0.423136	−	0.161529i
$506$	14515.2	+	8380.37i	1.27526	+	0.736271i
$507$	−5011.52	+	10224.3i	−0.438993	+	0.895614i
$508$	312.452	+	83.7212i	0.0272890	+	0.00731206i
$509$	−6234.51	−	10798.5i	−0.542908	−	0.940344i	−0.998735	−	0.0502756i	$-0.983990\pi$
$509$	−6234.51	−	10798.5i	−0.542908	−	0.940344i	0.455828	−	0.890068i	$-0.349343\pi$
$510$	−6432.85	+	21032.7i	−0.558532	+	1.82617i
$511$	−814.705	+	1411.11i	−0.0705292	+	0.122160i
$512$	7575.72	−	7575.72i	0.653911	−	0.653911i
$513$	2992.20	−	617.663i	0.257522	−	0.0531588i
$514$		−	11047.4i		−	0.948017i
$515$	−15473.3	−	1597.38i	−1.32395	−	0.136678i
$516$	−543.546	+	622.811i	−0.0463726	+	0.0531351i
$517$	2126.54	−	7936.35i	0.180900	−	0.675127i
$518$	−183.727	+	685.678i	−0.0155840	+	0.0581602i
$519$	−7341.48	−	21457.6i	−0.620916	−	1.81481i
$520$	−371.197	−	456.660i	−0.0313039	−	0.0385113i
$521$		−	16543.1i		−	1.39111i	−0.718473	−	0.695555i	$-0.755159\pi$
$521$		−	16543.1i		−	1.39111i	0.718473	−	0.695555i	$-0.244841\pi$
$522$	6288.26	+	797.112i	0.527260	+	0.0668365i
$523$	−937.744	+	937.744i	−0.0784029	+	0.0784029i	−0.745221	−	0.666818i	$-0.767656\pi$
$523$	−937.744	+	937.744i	−0.0784029	+	0.0784029i	0.666818	+	0.745221i	$0.267656\pi$
$524$	−468.094	+	810.762i	−0.0390244	+	0.0675922i
$525$	7619.94	+	10075.5i	0.633450	+	0.837579i
$526$	−7130.27	−	12350.0i	−0.591054	−	1.02374i
$527$	1078.83	+	289.072i	0.0891738	+	0.0238940i
$528$	10948.6	+	16300.7i	0.902419	+	1.34356i
$529$	1458.85	+	842.270i	0.119903	+	0.0692258i
$530$	−1352.82	+	3543.80i	−0.110873	+	0.290439i
$531$	−4281.58	−	5524.64i	−0.349915	−	0.451505i
$532$	−107.349	−	107.349i	−0.00874843	−	0.00874843i
$533$	−74.8247	+	20.0492i	−0.00608071	+	0.00162932i
$534$	−12008.2	+	4108.46i	−0.973116	+	0.332941i
$535$	−2959.80	+	4089.70i	−0.239184	+	0.330492i
$536$	8613.91	−	4973.24i	0.694150	−	0.400768i
$537$	1006.80	+	14814.7i	0.0809062	+	1.19051i
$538$	−4915.78	−	18345.9i	−0.393930	−	1.47017i
$539$	1996.53			0.159548
$540$	−435.505	−	355.577i	−0.0347059	−	0.0283363i
$541$	−946.946			−0.0752540			−0.0376270	−	0.999292i	$-0.511980\pi$
$541$	−946.946			−0.0752540			−0.0376270	+	0.999292i	$0.511980\pi$
$542$	1199.97	+	4478.34i	0.0950979	+	0.354910i
$543$	514.066	+	7564.32i	0.0406274	+	0.597820i
$544$	1838.23	−	1061.30i	0.144878	−	0.0836451i
$545$	−1992.79	−	12433.1i	−0.156627	−	0.977200i
$546$	658.633	−	225.344i	0.0516243	−	0.0176627i
$547$	11253.3	−	3015.33i	0.879631	−	0.235697i	0.209383	−	0.977834i	$-0.432854\pi$
$547$	11253.3	−	3015.33i	0.879631	−	0.235697i	0.670248	+	0.742137i	$0.266188\pi$
$548$	−247.198	−	247.198i	−0.0192696	−	0.0192696i
$549$	5772.28	−	14127.3i	0.448734	−	1.09825i
$550$	−1146.55	−	20431.0i	−0.0888890	−	1.58396i
$551$	−1531.45	−	884.183i	−0.118406	−	0.0683620i
$552$	−6553.25	−	9756.74i	−0.505298	−	0.752309i
$553$	10239.9	+	2743.77i	0.787422	+	0.210989i
$554$	12717.0	+	22026.5i	0.975259	+	1.68920i
$555$	388.724	−	621.938i	0.0297305	−	0.0475672i
$556$	−228.950	+	396.553i	−0.0174634	+	0.0302475i
$557$	1609.11	−	1609.11i	0.122406	−	0.122406i	−0.643250	−	0.765656i	$-0.722414\pi$
$557$	1609.11	−	1609.11i	0.122406	−	0.122406i	0.765656	+	0.643250i	$0.222414\pi$
$558$	−402.747	+	530.131i	−0.0305549	+	0.0402190i
$559$			1057.46i			0.0800107i
$560$	1490.23	−	14435.4i	0.112453	−	1.08930i
$561$	−12472.7	−	36455.0i	−0.938676	−	2.74355i
$562$	−5016.21	+	18720.8i	−0.376506	+	1.40514i
$563$	4701.86	−	17547.6i	0.351971	−	1.31357i	−0.532282	−	0.846567i	$-0.678665\pi$
$563$	4701.86	−	17547.6i	0.351971	−	1.31357i	0.884253	−	0.467008i	$-0.154668\pi$
$564$	177.701	−	203.615i	0.0132670	−	0.0152017i
$565$	−1733.79	+	16794.6i	−0.129099	+	1.25054i
$566$			3303.33i			0.245317i
$567$	−12210.0	+	7206.92i	−0.904356	+	0.533796i
$568$	−254.601	+	254.601i	−0.0188078	+	0.0188078i
$569$	149.738	−	259.354i	0.0110322	−	0.0191084i	−0.860457	−	0.509524i	$-0.829822\pi$
$569$	149.738	−	259.354i	0.0110322	−	0.0191084i	0.871489	+	0.490415i	$0.163155\pi$
$570$	1716.83	+	3229.73i	0.126158	+	0.237330i
$571$	10802.7	+	18710.8i	0.791732	+	1.37132i	0.924894	+	0.380226i	$0.124154\pi$
$571$	10802.7	+	18710.8i	0.791732	+	1.37132i	−0.133162	+	0.991094i	$0.542513\pi$
$572$	−46.7086	−	12.5155i	−0.00341431	−	0.000914861i
$573$	1611.20	−	3287.10i	0.117468	−	0.239652i
$574$	−1583.24	−	914.085i	−0.115128	−	0.0664689i
$575$	717.070	+	12777.9i	0.0520068	+	0.926738i
$576$	−1779.16	−	13029.5i	−0.128701	−	0.942524i
$577$	−6073.88	−	6073.88i	−0.438231	−	0.438231i	0.453186	−	0.891416i	$-0.350288\pi$
$577$	−6073.88	−	6073.88i	−0.438231	−	0.438231i	−0.891416	+	0.453186i	$0.850288\pi$
$578$	−34169.0	+	9155.55i	−2.45890	+	0.658859i
$579$	−1535.46	+	7817.50i	−0.110210	+	0.561113i
$580$	51.4999	+	321.310i	0.00368693	+	0.0230029i
$581$	16962.0	−	9793.00i	1.21119	−	0.699281i
$582$	−5077.24	+	3410.20i	−0.361613	+	0.242882i
$583$	−1719.84	−	6418.53i	−0.122176	−	0.455966i
$584$	−1850.89			−0.131148
$585$	−718.831	+	23.6148i	−0.0508034	+	0.00166898i
$586$	−18187.5			−1.28211
$587$	−2913.25	−	10872.4i	−0.204843	−	0.764484i	−0.989497	−	0.144551i	$-0.953826\pi$
$587$	−2913.25	−	10872.4i	−0.204843	−	0.764484i	0.784654	−	0.619933i	$-0.212840\pi$
$588$	58.9676	+	28.9035i	0.00413569	+	0.00202714i
$589$	160.854	−	92.8691i	0.0112528	−	0.00649678i
$590$	4905.83	−	6778.63i	0.342322	−	0.473003i
$591$	−5478.24	−	4781.02i	−0.381294	−	0.332767i
$592$	−813.847	+	218.070i	−0.0565015	+	0.0151395i
$593$	19651.0	+	19651.0i	1.36082	+	1.36082i	0.872870	+	0.487953i	$0.162256\pi$
$593$	19651.0	+	19651.0i	1.36082	+	1.36082i	0.487953	+	0.872870i	$0.337744\pi$
$594$	22928.2	+	1336.72i	1.58377	+	0.0923341i
$595$	−10155.4	+	26602.6i	−0.699712	+	1.83294i
$596$	43.2154	+	24.9504i	0.00297009	+	0.00171478i
$597$	10553.3	−	717.192i	0.723478	−	0.0491670i
$598$	681.209	+	182.529i	0.0465831	+	0.0124819i
$599$	1419.69	+	2458.97i	0.0968396	+	0.167731i	0.910375	−	0.413784i	$-0.135793\pi$
$599$	1419.69	+	2458.97i	0.0968396	+	0.167731i	−0.813535	+	0.581516i	$0.802460\pi$
$600$	−5583.79	+	13218.5i	−0.379929	+	0.899407i
$601$	−254.777	+	441.286i	−0.0172921	+	0.0299508i	−0.874542	−	0.484950i	$-0.838838\pi$
$601$	−254.777	+	441.286i	−0.0172921	+	0.0299508i	0.857250	+	0.514901i	$0.172171\pi$
$602$	−17646.8	+	17646.8i	−1.19473	+	1.19473i
$603$	1528.68	−	12059.4i	0.103238	−	0.814425i
$604$			506.824i			0.0341430i
$605$	13224.5	+	16269.2i	0.888679	+	1.09329i
$606$	6776.85	+	1331.06i	0.454275	+	0.0892257i
$607$	−885.947	+	3306.40i	−0.0592413	+	0.221092i	−0.989200	−	0.146573i	$-0.953176\pi$
$607$	−885.947	+	3306.40i	−0.0592413	+	0.221092i	0.929959	+	0.367664i	$0.119842\pi$
$608$	91.3602	−	340.961i	0.00609399	−	0.0227431i
$609$	8052.35	+	1581.59i	0.535793	+	0.105237i
$610$	18173.5	+	1876.13i	1.20627	+	0.124528i
$611$		−	345.717i		−	0.0228907i
$612$	159.374	−	1257.27i	0.0105266	−	0.0830426i
$613$	−6435.77	+	6435.77i	−0.424043	+	0.424043i	−0.886593	−	0.462550i	$-0.846934\pi$
$613$	−6435.77	+	6435.77i	−0.424043	+	0.424043i	0.462550	+	0.886593i	$0.346934\pi$
$614$	10218.9	−	17699.6i	0.671660	−	1.16335i
$615$	1288.04	+	1381.55i	0.0844532	+	0.0905847i
$616$	12164.9	+	21070.2i	0.795679	+	1.37816i
$617$	2076.34	+	556.352i	0.135478	+	0.0363013i	0.325921	−	0.945397i	$-0.394326\pi$
$617$	2076.34	+	556.352i	0.135478	+	0.0363013i	−0.190443	+	0.981698i	$0.560992\pi$
$618$	20853.3	−	1417.17i	1.35735	−	0.0922444i
$619$	−16359.4	−	9445.11i	−1.06226	−	0.613297i	−0.136205	−	0.990681i	$-0.543491\pi$
$619$	−16359.4	−	9445.11i	−1.06226	−	0.613297i	−0.926057	+	0.377383i	$0.876824\pi$
$620$	−31.9316	−	12.1897i	−0.00206839	−	0.000789595i
$621$	−14339.7	−	836.011i	−0.926623	−	0.0540225i
$622$	6199.92	+	6199.92i	0.399669	+	0.399669i
$623$	−15871.2	+	4252.66i	−1.02065	+	0.273482i
$624$	622.505	+	543.279i	0.0399361	+	0.0348535i
$625$	12572.6	−	9277.42i	0.804646	−	0.593755i
$626$	10791.1	−	6230.22i	0.688974	−	0.397779i
$627$	−5753.50	−	2820.13i	−0.366463	−	0.179625i
$628$	−220.321	−	822.250i	−0.0139996	−	0.0522474i
$629$	1653.23			0.104799
$630$	−12389.8	−	11601.7i	−0.783527	−	0.733684i
$631$	865.068			0.0545766			0.0272883	−	0.999628i	$-0.491313\pi$
$631$	865.068			0.0545766			0.0272883	+	0.999628i	$0.491313\pi$
$632$	3116.72	+	11631.8i	0.196165	+	0.732099i
$633$	−5938.64	+	3988.77i	−0.372891	+	0.250457i
$634$	−12079.6	+	6974.16i	−0.756691	+	0.436876i
$635$	−8173.78	−	5915.53i	−0.510813	−	0.369686i
$636$	42.1247	−	214.470i	0.00262634	−	0.0133715i
$637$	81.1450	−	21.7427i	0.00504723	−	0.00135240i
$638$	−9399.66	−	9399.66i	−0.583286	−	0.583286i
$639$	59.5349	+	435.996i	0.00368570	+	0.0269917i
$640$	15693.5	−	7022.03i	0.969284	−	0.433703i
$641$	6830.18	+	3943.41i	0.420867	+	0.242988i	0.695448	−	0.718576i	$-0.255206\pi$
$641$	6830.18	+	3943.41i	0.420867	+	0.242988i	−0.274581	+	0.961564i	$0.588539\pi$
$642$	2985.53	−	6090.95i	0.183535	−	0.374440i
$643$	−6866.75	−	1839.94i	−0.421148	−	0.112846i	0.0420200	−	0.999117i	$-0.486621\pi$
$643$	−6866.75	−	1839.94i	−0.421148	−	0.112846i	−0.463168	+	0.886270i	$0.653287\pi$
$644$	356.868	+	618.114i	0.0218363	+	0.0378216i
$645$	22767.8	−	12102.7i	1.38989	−	0.738825i
$646$	−4122.43	+	7140.26i	−0.251076	+	0.434876i
$647$	1933.74	−	1933.74i	0.117501	−	0.117501i	−0.645911	−	0.763412i	$-0.723522\pi$
$647$	1933.74	−	1933.74i	0.117501	−	0.117501i	0.763412	+	0.645911i	$0.223522\pi$
$648$	−14024.5	−	7918.16i	−0.850210	−	0.480023i
$649$			14658.3i			0.886578i
$650$	−269.098	−	817.892i	−0.0162383	−	0.0493544i
$651$	−566.749	+	649.398i	−0.0341208	+	0.0390966i
$652$	−123.396	+	460.521i	−0.00741191	+	0.0276616i
$653$	−1669.93	+	6232.28i	−0.100076	+	0.373488i	−0.997740	−	0.0671918i	$-0.978596\pi$
$653$	−1669.93	+	6232.28i	−0.100076	+	0.373488i	0.897664	+	0.440680i	$0.145263\pi$
$654$	5476.96	+	16008.0i	0.327471	+	0.957130i
$655$	22659.9	−	18419.1i	1.35175	−	1.09877i
$656$		−	2169.90i		−	0.129147i
$657$	−1368.39	+	1801.20i	−0.0812572	+	0.106958i
$658$	5769.26	−	5769.26i	0.341807	−	0.341807i
$659$	3849.42	−	6667.40i	0.227545	−	0.394120i	−0.729535	−	0.683944i	$-0.760263\pi$
$659$	3849.42	−	6667.40i	0.227545	−	0.394120i	0.957080	+	0.289824i	$0.0935968\pi$
$660$	265.113	+	1148.90i	0.0156356	+	0.0677589i
$661$	−1130.78	−	1958.57i	−0.0665392	−	0.115249i	0.830837	−	0.556517i	$-0.187862\pi$
$661$	−1130.78	−	1958.57i	−0.0665392	−	0.115249i	−0.897376	+	0.441267i	$0.854529\pi$
$662$	−31456.2	−	8428.67i	−1.84680	−	0.494848i
$663$	−903.934	−	1345.81i	−0.0529501	−	0.0788343i
$664$	19267.5	+	11124.1i	1.12609	+	0.650150i
$665$	1934.06	+	4322.43i	0.112781	+	0.252055i
$666$	−372.741	+	912.263i	−0.0216868	+	0.0530773i
$667$	5878.71	+	5878.71i	0.341266	+	0.341266i
$668$	1302.78	−	349.078i	0.0754581	−	0.0202189i
$669$	19319.4	−	6609.90i	1.11649	−	0.381993i
$670$	14369.3	−	2303.12i	0.828557	−	0.132802i
$671$	−27717.4	+	16002.6i	−1.59466	+	0.920678i
$672$	111.066	+	1634.29i	0.00637566	+	0.0938159i
$673$	2233.43	+	8335.28i	0.127923	+	0.477417i	0.999927	−	0.0120828i	$-0.00384618\pi$
$673$	2233.43	+	8335.28i	0.127923	+	0.477417i	−0.872004	+	0.489499i	$0.837180\pi$
$674$	6836.92			0.390724
$675$	8735.45	+	15206.5i	0.498115	+	0.867111i
$676$	785.449			0.0446887
$677$	−3462.76	−	12923.2i	−0.196580	−	0.733646i	−0.991852	−	0.127394i	$-0.959339\pi$
$677$	−3462.76	−	12923.2i	−0.196580	−	0.733646i	0.795272	−	0.606252i	$-0.207328\pi$
$678$	−1538.19	−	22634.0i	−0.0871297	−	1.28209i
$679$	−6857.45	+	3959.15i	−0.387577	+	0.223768i
$680$	−31937.9	+	5119.04i	−1.80112	+	0.288686i
$681$	−4442.43	+	1519.93i	−0.249977	+	0.0855269i
$682$	1348.65	−	361.371i	0.0757223	−	0.0202897i
$683$	−14959.7	−	14959.7i	−0.838091	−	0.838091i	0.150516	−	0.988608i	$-0.451906\pi$
$683$	−14959.7	−	14959.7i	−0.838091	−	0.838091i	−0.988608	+	0.150516i	$0.951906\pi$
$684$	−129.103	−	166.586i	−0.00721695	−	0.00931222i
$685$	4453.65	+	9953.46i	0.248416	+	0.555186i
$686$	−14985.6	−	8651.91i	−0.834039	−	0.481533i
$687$	10465.0	+	15580.7i	0.581169	+	0.865268i
$688$	−28611.9	−	7666.54i	−1.58549	−	0.424832i
$689$	−139.799	−	242.139i	−0.00772994	−	0.0133886i
$690$	−3866.47	−	16755.8i	−0.213325	−	0.924469i
$691$	14446.2	−	25021.6i	0.795311	−	1.37752i	−0.127331	−	0.991860i	$-0.540641\pi$
$691$	14446.2	−	25021.6i	0.795311	−	1.37752i	0.922642	−	0.385658i	$-0.126026\pi$
$692$	−1106.20	+	1106.20i	−0.0607680	+	0.0607680i
$693$	29498.3	+	3739.26i	1.61695	+	0.204968i
$694$			2977.62i			0.162866i
$695$	11083.2	−	9008.99i	0.604906	−	0.491699i
$696$	3017.56	+	8819.71i	0.164340	+	0.480331i
$697$	−1101.97	+	4112.61i	−0.0598854	+	0.223495i
$698$	4086.39	−	15250.6i	0.221594	−	0.826999i
$699$	−14458.3	+	16566.7i	−0.782351	+	0.896440i
$700$	392.731	−	777.879i	0.0212055	−	0.0420015i
$701$		−	4479.63i		−	0.241360i	−0.992691	−	0.120680i	$-0.961493\pi$
$701$		−	4479.63i		−	0.241360i	0.992691	−	0.120680i	$-0.0385075\pi$
$702$	946.432	−	195.366i	0.0508843	−	0.0105037i
$703$	194.406	−	194.406i	0.0104298	−	0.0104298i
$704$	−13789.3	+	23883.8i	−0.738217	+	1.27863i
$705$	−7443.46	+	3956.72i	−0.397641	+	0.211374i
$706$	962.411	+	1666.94i	0.0513043	+	0.0888616i
$707$	8636.58	+	2314.17i	0.459423	+	0.123102i
$708$	−212.207	+	432.935i	−0.0112644	+	0.0229812i
$709$	−25712.6	−	14845.2i	−1.36200	−	0.786351i	−0.372110	−	0.928188i	$-0.621366\pi$
$709$	−25712.6	−	14845.2i	−1.36200	−	0.786351i	−0.989890	+	0.141837i	$0.954699\pi$
$710$	−480.861	+	215.160i	−0.0254174	+	0.0113730i
$711$	13623.7	+	5566.50i	0.718606	+	0.293615i
$712$	−13197.7	−	13197.7i	−0.694672	−	0.694672i
$713$	−843.471	+	226.007i	−0.0443033	+	0.0118710i
$714$	7374.03	−	37543.5i	0.386507	−	1.96783i
$715$	1221.90	+	884.316i	0.0639113	+	0.0462539i
$716$	887.064	−	512.147i	0.0463005	−	0.0267316i
$717$	−16659.2	+	11189.4i	−0.867711	+	0.582809i
$718$	5016.31	+	18721.1i	0.260734	+	0.973073i
$719$	−17740.3			−0.920171			−0.460085	−	0.887875i	$-0.652181\pi$
$719$	−17740.3			−0.920171			−0.460085	+	0.887875i	$0.652181\pi$
$720$	4572.52	−	19620.7i	0.236678	−	1.01558i
$721$	27059.8			1.39773
$722$	−4777.52	−	17829.9i	−0.246261	−	0.919060i
$723$	−8008.85	−	3925.61i	−0.411967	−	0.201929i
$724$	452.930	−	261.499i	0.0232500	−	0.0134234i
$725$	2073.61	−	9936.16i	0.106223	−	0.508992i
$726$	−21224.8	−	18523.6i	−1.08502	−	0.946934i
$727$	−29265.6	+	7841.69i	−1.49299	+	0.400044i	−0.910744	−	0.412972i	$-0.864491\pi$
$727$	−29265.6	+	7841.69i	−1.49299	+	0.400044i	−0.582242	+	0.813016i	$0.697824\pi$
$728$	723.881	+	723.881i	0.0368527	+	0.0368527i
$729$	−18074.1	+	7793.98i	−0.918261	+	0.395975i
$730$	−2529.95	−	965.792i	−0.128271	−	0.0489665i
$731$	50334.8	+	29060.8i	2.54679	+	1.47039i
$732$	−1050.30	+	71.3779i	−0.0530333	+	0.00360410i
$733$	−24440.0	−	6548.68i	−1.23153	−	0.329988i	−0.416355	−	0.909202i	$-0.636693\pi$
$733$	−24440.0	−	6548.68i	−1.23153	−	0.329988i	−0.815175	+	0.579214i	$0.803359\pi$
$734$	4720.53	+	8176.20i	0.237381	+	0.411157i
$735$	−1396.84	−	1498.25i	−0.0700994	−	0.0751888i
$736$	−829.766	+	1437.20i	−0.0415565	+	0.0719780i
$737$	−18026.4	+	18026.4i	−0.900965	+	0.900965i
$738$	−2020.91	−	1535.31i	−0.100800	−	0.0765794i
$739$		−	27310.7i		−	1.35946i	−0.733463	−	0.679730i	$-0.762097\pi$
$739$		−	27310.7i		−	1.35946i	0.733463	−	0.679730i	$-0.237903\pi$
$740$	−50.3250	−	5.19527i	−0.00249998	−	0.000258084i
$741$	−264.552	−	51.9615i	−0.0131155	−	0.00257605i
$742$	1707.84	−	6373.73i	0.0844968	−	0.315346i
$743$	−2660.70	+	9929.86i	−0.131375	+	0.490298i	−0.999987	−	0.00519568i	$-0.998346\pi$
$743$	−2660.70	+	9929.86i	−0.131375	+	0.490298i	0.868612	+	0.495494i	$0.165013\pi$
$744$	−960.731	−	188.700i	−0.0473416	−	0.00929851i
$745$	−981.779	−	1207.82i	−0.0482813	−	0.0593975i
$746$			12220.0i			0.599739i
$747$	25070.2	−	10526.0i	1.22794	−	0.515564i
$748$	−1879.36	+	1879.36i	−0.0918666	+	0.0918666i
$749$	4390.98	−	7605.39i	0.214209	−	0.371021i
$750$	−14529.8	+	15154.6i	−0.707405	+	0.737823i
$751$	−12313.5	−	21327.6i	−0.598302	−	1.03629i	−0.993072	−	0.117509i	$-0.962509\pi$
$751$	−12313.5	−	21327.6i	−0.598302	−	1.03629i	0.394770	−	0.918780i	$-0.370824\pi$
$752$	9354.09	+	2506.42i	0.453602	+	0.121542i
$753$	11850.5	−	805.350i	0.573513	−	0.0389755i
$754$	−484.396	−	279.666i	−0.0233961	−	0.0135078i
$755$	5638.08	−	14769.3i	0.271776	−	0.711934i
$756$	817.101	+	537.483i	0.0393091	+	0.0258572i
$757$	3491.44	+	3491.44i	0.167633	+	0.167633i	0.785938	−	0.618305i	$-0.212180\pi$
$757$	3491.44	+	3491.44i	0.167633	+	0.167633i	−0.618305	+	0.785938i	$0.712180\pi$
$758$	−5600.84	+	1500.74i	−0.268380	+	0.0719121i
$759$	22696.1	+	19807.6i	1.08540	+	0.947260i
$760$	−3153.68	+	4357.59i	−0.150521	+	0.207982i
$761$	1927.71	−	1112.96i	0.0918256	−	0.0530155i	−0.453384	−	0.891315i	$-0.649783\pi$
$761$	1927.71	−	1112.96i	0.0918256	−	0.0530155i	0.545210	+	0.838300i	$0.316450\pi$
$762$	12173.5	+	5966.96i	0.578741	+	0.283675i
$763$	5669.21	+	21157.8i	0.268990	+	1.00388i
$764$	−252.521			−0.0119580
$765$	−18630.6	+	34865.0i	−0.880510	+	1.64777i
$766$	−3391.65			−0.159981
$767$	159.633	+	595.759i	0.00751502	+	0.0280464i
$768$	−2370.13	+	1591.93i	−0.111360	+	0.0747965i
$769$	28584.4	−	16503.2i	1.34042	−	0.773890i	0.353548	−	0.935416i	$-0.384975\pi$
$769$	28584.4	−	16503.2i	1.34042	−	0.773890i	0.986868	+	0.161526i

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.748271 - 2.79258i) q^{2} +(-0.352314 - 5.18419i) q^{3} +(-0.310415 + 0.179218i) q^{4} +(11.0394 - 1.76941i) q^{5} +(-14.2137 + 4.86305i) q^{6} +(-18.7862 + 5.03374i) q^{7} +(-15.6218 - 15.6218i) q^{8} +(-26.7517 + 3.65293i) q^{9} +O(q^{10})\)	\(q+(-0.748271 - 2.79258i) q^{2} +(-0.352314 - 5.18419i) q^{3} +(-0.310415 + 0.179218i) q^{4} +(11.0394 - 1.76941i) q^{5} +(-14.2137 + 4.86305i) q^{6} +(-18.7862 + 5.03374i) q^{7} +(-15.6218 - 15.6218i) q^{8} +(-26.7517 + 3.65293i) q^{9} +(-13.2017 - 29.5046i) q^{10} +(49.0377 + 28.3119i) q^{11} +(1.03846 + 1.54611i) q^{12} +(2.30137 + 0.616650i) q^{13} +(28.1143 + 48.6954i) q^{14} +(-13.0623 - 56.6072i) q^{15} +(-33.3695 + 57.7977i) q^{16} +(92.5976 - 92.5976i) q^{17} +(30.2187 + 71.9731i) q^{18} -21.7774i q^{19} +(-3.10969 + 2.52772i) q^{20} +(32.7146 + 95.6178i) q^{21} +(42.3700 - 158.127i) q^{22} +(-26.4989 + 98.8952i) q^{23} +(-75.4824 + 86.4900i) q^{24} +(118.738 - 39.0667i) q^{25} -6.88818i q^{26} +(28.3625 + 137.399i) q^{27} +(4.92937 - 4.92937i) q^{28} +(40.6009 - 70.3228i) q^{29} +(-148.306 + 78.8352i) q^{30} +(4.26447 + 7.38628i) q^{31} +(15.6566 + 4.19518i) q^{32} +(129.498 - 264.196i) q^{33} +(-327.875 - 189.298i) q^{34} +(-198.482 + 88.8102i) q^{35} +(7.64946 - 5.92832i) q^{36} +(8.92697 + 8.92697i) q^{37} +(-60.8153 + 16.2954i) q^{38} +(2.38603 - 12.1480i) q^{39} +(-200.097 - 144.814i) q^{40} +(-28.1572 + 16.2566i) q^{41} +(242.541 - 162.906i) q^{42} +(114.874 + 428.714i) q^{43} -20.2960 q^{44} +(-288.861 + 87.6612i) q^{45} +296.002 q^{46} +(-37.5556 - 140.159i) q^{47} +(311.391 + 152.631i) q^{48} +(30.5356 - 17.6297i) q^{49} +(-197.945 - 302.354i) q^{50} +(-512.667 - 447.420i) q^{51} +(-0.824893 + 0.221029i) q^{52} +(-82.9808 - 82.9808i) q^{53} +(362.476 - 182.017i) q^{54} +(591.444 + 225.780i) q^{55} +(372.109 + 214.837i) q^{56} +(-112.898 + 7.67250i) q^{57} +(-226.763 - 60.7609i) q^{58} +(129.436 + 224.189i) q^{59} +(14.1998 + 15.2307i) q^{60} +(-282.613 + 489.500i) q^{61} +(17.4358 - 17.4358i) q^{62} +(484.175 - 203.286i) q^{63} +487.051i q^{64} +(26.4969 + 2.73539i) q^{65} +(-834.688 - 163.944i) q^{66} +(-116.526 + 434.879i) q^{67} +(-12.1485 + 45.3388i) q^{68} +(522.028 + 102.533i) q^{69} +(396.528 + 487.824i) q^{70} -16.2978i q^{71} +(474.974 + 360.844i) q^{72} +(59.2407 - 59.2407i) q^{73} +(18.2495 - 31.6091i) q^{74} +(-244.362 - 601.799i) q^{75} +(3.90290 + 6.76003i) q^{76} +(-1063.75 - 285.030i) q^{77} +(-35.7097 + 2.42681i) q^{78} +(-472.049 - 272.538i) q^{79} +(-266.113 + 697.098i) q^{80} +(702.312 - 195.445i) q^{81} +(66.4671 + 66.4671i) q^{82} +(-972.735 + 260.644i) q^{83} +(-27.2915 - 23.8181i) q^{84} +(858.382 - 1186.07i) q^{85} +(1111.26 - 641.588i) q^{86} +(-378.871 - 185.707i) q^{87} +(-323.773 - 1208.34i) q^{88} +844.831 q^{89} +(460.947 + 741.074i) q^{90} -46.3380 q^{91} +(-9.49816 - 35.4476i) q^{92} +(36.7895 - 24.7101i) q^{93} +(-363.305 + 209.754i) q^{94} +(-38.5333 - 240.410i) q^{95} +(16.2326 - 82.6450i) q^{96} +(393.261 - 105.374i) q^{97} +(-72.0814 - 72.0814i) q^{98} +(-1415.27 - 578.262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

Introduction

L-functions

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