LMFDB - Embedded newform 177.10.a.b.1.1

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$91.1613430010$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-44.6602 q^{2} -81.0000 q^{3} +1482.53 q^{4} -714.289 q^{5} +3617.48 q^{6} -10082.7 q^{7} -43344.2 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-44.6602 q^{2} -81.0000 q^{3} +1482.53 q^{4} -714.289 q^{5} +3617.48 q^{6} -10082.7 q^{7} -43344.2 q^{8} +6561.00 q^{9} +31900.3 q^{10} -16906.1 q^{11} -120085. q^{12} -19313.4 q^{13} +450296. q^{14} +57857.4 q^{15} +1.17670e6 q^{16} +336949. q^{17} -293016. q^{18} -788177. q^{19} -1.05896e6 q^{20} +816700. q^{21} +755028. q^{22} +124126. q^{23} +3.51088e6 q^{24} -1.44292e6 q^{25} +862542. q^{26} -531441. q^{27} -1.49480e7 q^{28} +4.52185e6 q^{29} -2.58392e6 q^{30} -5.79823e6 q^{31} -3.03596e7 q^{32} +1.36939e6 q^{33} -1.50482e7 q^{34} +7.20198e6 q^{35} +9.72690e6 q^{36} +3.64731e6 q^{37} +3.52001e7 q^{38} +1.56439e6 q^{39} +3.09603e7 q^{40} +1.96043e7 q^{41} -3.64740e7 q^{42} -3.00271e6 q^{43} -2.50638e7 q^{44} -4.68645e6 q^{45} -5.54351e6 q^{46} -3.78665e7 q^{47} -9.53129e7 q^{48} +6.13075e7 q^{49} +6.44409e7 q^{50} -2.72929e7 q^{51} -2.86328e7 q^{52} +8.32101e7 q^{53} +2.37343e7 q^{54} +1.20758e7 q^{55} +4.37027e8 q^{56} +6.38424e7 q^{57} -2.01947e8 q^{58} -1.21174e7 q^{59} +8.57756e7 q^{60} +1.36610e8 q^{61} +2.58950e8 q^{62} -6.61527e7 q^{63} +7.53392e8 q^{64} +1.37954e7 q^{65} -6.11572e7 q^{66} -4.31228e7 q^{67} +4.99539e8 q^{68} -1.00542e7 q^{69} -3.21642e8 q^{70} +2.79479e8 q^{71} -2.84381e8 q^{72} -1.26714e8 q^{73} -1.62890e8 q^{74} +1.16876e8 q^{75} -1.16850e9 q^{76} +1.70459e8 q^{77} -6.98659e7 q^{78} +5.15802e8 q^{79} -8.40506e8 q^{80} +4.30467e7 q^{81} -8.75532e8 q^{82} -4.95727e8 q^{83} +1.21078e9 q^{84} -2.40679e8 q^{85} +1.34102e8 q^{86} -3.66270e8 q^{87} +7.32779e8 q^{88} +3.38658e8 q^{89} +2.09298e8 q^{90} +1.94732e8 q^{91} +1.84021e8 q^{92} +4.69656e8 q^{93} +1.69112e9 q^{94} +5.62987e8 q^{95} +2.45912e9 q^{96} +1.18214e9 q^{97} -2.73801e9 q^{98} -1.10921e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) $	\( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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 $

$2$	−44.6602	−1.97372	−0.986860	−	0.161577i	$-0.948342\pi$
$2$	−44.6602	−1.97372	−0.986860	+	0.161577i	$0.948342\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	1482.53	2.89557
$5$	−714.289	−0.511104	−0.255552	−	0.966795i	$-0.582257\pi$
$5$	−714.289	−0.511104	−0.255552	+	0.966795i	$0.582257\pi$
$6$	3617.48	1.13953
$7$	−10082.7	−1.58722	−0.793609	−	0.608429i	$-0.791800\pi$
$7$	−10082.7	−1.58722	−0.793609	+	0.608429i	$0.791800\pi$
$8$	−43344.2	−3.74133
$9$	6561.00	0.333333
$10$	31900.3	1.00878
$11$	−16906.1	−0.348157	−0.174078	−	0.984732i	$-0.555695\pi$
$11$	−16906.1	−0.348157	−0.174078	+	0.984732i	$0.555695\pi$
$12$	−120085.	−1.67176
$13$	−19313.4	−0.187549	−0.0937745	−	0.995593i	$-0.529893\pi$
$13$	−19313.4	−0.187549	−0.0937745	+	0.995593i	$0.529893\pi$
$14$	450296.	3.13272
$15$	57857.4	0.295086
$16$	1.17670e6	4.48877
$17$	336949.	0.978463	0.489232	−	0.872154i	$-0.337277\pi$
$17$	336949.	0.978463	0.489232	+	0.872154i	$0.337277\pi$
$18$	−293016.	−0.657907
$19$	−788177.	−1.38750	−0.693750	−	0.720216i	$-0.744043\pi$
$19$	−788177.	−1.38750	−0.693750	+	0.720216i	$0.744043\pi$
$20$	−1.05896e6	−1.47994
$21$	816700.	0.916380
$22$	755028.	0.687164
$23$	124126.	0.0924887	0.0462444	−	0.998930i	$-0.485275\pi$
$23$	124126.	0.0924887	0.0462444	+	0.998930i	$0.485275\pi$
$24$	3.51088e6	2.16006
$25$	−1.44292e6	−0.738773
$26$	862542.	0.370169
$27$	−531441.	−0.192450
$28$	−1.49480e7	−4.59590
$29$	4.52185e6	1.18720	0.593602	−	0.804759i	$-0.297706\pi$
$29$	4.52185e6	1.18720	0.593602	+	0.804759i	$0.297706\pi$
$30$	−2.58392e6	−0.582417
$31$	−5.79823e6	−1.12763	−0.563816	−	0.825900i	$-0.690667\pi$
$31$	−5.79823e6	−1.12763	−0.563816	+	0.825900i	$0.690667\pi$
$32$	−3.03596e7	−5.11824
$33$	1.36939e6	0.201009
$34$	−1.50482e7	−1.93121
$35$	7.20198e6	0.811233
$36$	9.72690e6	0.965191
$37$	3.64731e6	0.319937	0.159969	−	0.987122i	$-0.448861\pi$
$37$	3.64731e6	0.319937	0.159969	+	0.987122i	$0.448861\pi$
$38$	3.52001e7	2.73854
$39$	1.56439e6	0.108281
$40$	3.09603e7	1.91221
$41$	1.96043e7	1.08349	0.541744	−	0.840544i	$-0.317764\pi$
$41$	1.96043e7	1.08349	0.541744	+	0.840544i	$0.317764\pi$
$42$	−3.64740e7	−1.80868
$43$	−3.00271e6	−0.133938	−0.0669692	−	0.997755i	$-0.521333\pi$
$43$	−3.00271e6	−0.133938	−0.0669692	+	0.997755i	$0.521333\pi$
$44$	−2.50638e7	−1.00811
$45$	−4.68645e6	−0.170368
$46$	−5.54351e6	−0.182547
$47$	−3.78665e7	−1.13192	−0.565958	−	0.824434i	$-0.691494\pi$
$47$	−3.78665e7	−1.13192	−0.565958	+	0.824434i	$0.691494\pi$
$48$	−9.53129e7	−2.59159
$49$	6.13075e7	1.51926
$50$	6.44409e7	1.45813
$51$	−2.72929e7	−0.564916
$52$	−2.86328e7	−0.543062
$53$	8.32101e7	1.44855	0.724277	−	0.689509i	$-0.242174\pi$
$53$	8.32101e7	1.44855	0.724277	+	0.689509i	$0.242174\pi$
$54$	2.37343e7	0.379843
$55$	1.20758e7	0.177944
$56$	4.37027e8	5.93830
$57$	6.38424e7	0.801073
$58$	−2.01947e8	−2.34321
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	8.57756e7	0.854443
$61$	1.36610e8	1.26328	0.631639	−	0.775263i	$-0.282383\pi$
$61$	1.36610e8	1.26328	0.631639	+	0.775263i	$0.282383\pi$
$62$	2.58950e8	2.22563
$63$	−6.61527e7	−0.529072
$64$	7.53392e8	5.61321
$65$	1.37954e7	0.0958570
$66$	−6.11572e7	−0.396735
$67$	−4.31228e7	−0.261439	−0.130720	−	0.991419i	$-0.541729\pi$
$67$	−4.31228e7	−0.261439	−0.130720	+	0.991419i	$0.541729\pi$
$68$	4.99539e8	2.83321
$69$	−1.00542e7	−0.0533984
$70$	−3.21642e8	−1.60115
$71$	2.79479e8	1.30523	0.652613	−	0.757691i	$-0.273673\pi$
$71$	2.79479e8	1.30523	0.652613	+	0.757691i	$0.273673\pi$
$72$	−2.84381e8	−1.24711
$73$	−1.26714e8	−0.522241	−0.261120	−	0.965306i	$-0.584092\pi$
$73$	−1.26714e8	−0.522241	−0.261120	+	0.965306i	$0.584092\pi$
$74$	−1.62890e8	−0.631467
$75$	1.16876e8	0.426531
$76$	−1.16850e9	−4.01760
$77$	1.70459e8	0.552601
$78$	−6.98659e7	−0.213717
$79$	5.15802e8	1.48991	0.744957	−	0.667112i	$-0.232470\pi$
$79$	5.15802e8	1.48991	0.744957	+	0.667112i	$0.232470\pi$
$80$	−8.40506e8	−2.29423
$81$	4.30467e7	0.111111
$82$	−8.75532e8	−2.13850
$83$	−4.95727e8	−1.14655	−0.573273	−	0.819365i	$-0.694326\pi$
$83$	−4.95727e8	−1.14655	−0.573273	+	0.819365i	$0.694326\pi$
$84$	1.21078e9	2.65344
$85$	−2.40679e8	−0.500096
$86$	1.34102e8	0.264357
$87$	−3.66270e8	−0.685432
$88$	7.32779e8	1.30257
$89$	3.38658e8	0.572145	0.286073	−	0.958208i	$-0.407650\pi$
$89$	3.38658e8	0.572145	0.286073	+	0.958208i	$0.407650\pi$
$90$	2.09298e8	0.336259
$91$	1.94732e8	0.297681
$92$	1.84021e8	0.267808
$93$	4.69656e8	0.651039
$94$	1.69112e9	2.23409
$95$	5.62987e8	0.709156
$96$	2.45912e9	2.95502
$97$	1.18214e9	1.35580	0.677898	−	0.735156i	$-0.262891\pi$
$97$	1.18214e9	1.35580	0.677898	+	0.735156i	$0.262891\pi$
$98$	−2.73801e9	−2.99859
$99$	−1.10921e8	−0.116052
$100$	−2.13917e9	−2.13917
$101$	−1.65119e9	−1.57889	−0.789444	−	0.613823i	$-0.789631\pi$
$101$	−1.65119e9	−1.57889	−0.789444	+	0.613823i	$0.789631\pi$
$102$	1.21891e9	1.11499
$103$	−1.01347e9	−0.887243	−0.443621	−	0.896214i	$-0.646307\pi$
$103$	−1.01347e9	−0.887243	−0.443621	+	0.896214i	$0.646307\pi$
$104$	8.37126e8	0.701683
$105$	−5.83360e8	−0.468365
$106$	−3.71618e9	−2.85904
$107$	1.81281e9	1.33698	0.668491	−	0.743721i	$-0.266941\pi$
$107$	1.81281e9	1.33698	0.668491	+	0.743721i	$0.266941\pi$
$108$	−7.87879e8	−0.557253
$109$	2.21832e9	1.50523	0.752617	−	0.658458i	$-0.228791\pi$
$109$	2.21832e9	1.50523	0.752617	+	0.658458i	$0.228791\pi$
$110$	−5.39308e8	−0.351212
$111$	−2.95432e8	−0.184716
$112$	−1.18644e10	−7.12464
$113$	3.03819e9	1.75292	0.876459	−	0.481477i	$-0.159899\pi$
$113$	3.03819e9	1.75292	0.876459	+	0.481477i	$0.159899\pi$
$114$	−2.85121e9	−1.58109
$115$	−8.86621e7	−0.0472713
$116$	6.70379e9	3.43763
$117$	−1.26716e8	−0.0625163
$118$	5.41164e8	0.256957
$119$	−3.39736e9	−1.55303
$120$	−2.50778e9	−1.10401
$121$	−2.07213e9	−0.878787
$122$	−6.10103e9	−2.49336
$123$	−1.58795e9	−0.625552
$124$	−8.59606e9	−3.26514
$125$	2.42576e9	0.888694
$126$	2.95439e9	1.04424
$127$	−3.83014e8	−0.130647	−0.0653233	−	0.997864i	$-0.520808\pi$
$127$	−3.83014e8	−0.130647	−0.0653233	+	0.997864i	$0.520808\pi$
$128$	−1.81025e10	−5.96066
$129$	2.43219e8	0.0773294
$130$	−6.16105e8	−0.189195
$131$	4.36924e9	1.29624	0.648120	−	0.761539i	$-0.275556\pi$
$131$	4.36924e9	1.29624	0.648120	+	0.761539i	$0.275556\pi$
$132$	2.03017e9	0.582035
$133$	7.94697e9	2.20226
$134$	1.92587e9	0.516008
$135$	3.79603e8	0.0983620
$136$	−1.46048e10	−3.66075
$137$	3.55561e8	0.0862327	0.0431163	−	0.999070i	$-0.486271\pi$
$137$	3.55561e8	0.0862327	0.0431163	+	0.999070i	$0.486271\pi$
$138$	4.49024e8	0.105393
$139$	−4.32519e9	−0.982739	−0.491369	−	0.870951i	$-0.663504\pi$
$139$	−4.32519e9	−0.982739	−0.491369	+	0.870951i	$0.663504\pi$
$140$	1.06772e10	2.34898
$141$	3.06718e9	0.653512
$142$	−1.24816e10	−2.57615
$143$	3.26514e8	0.0652965
$144$	7.72035e9	1.49626
$145$	−3.22991e9	−0.606784
$146$	5.65906e9	1.03076
$147$	−4.96591e9	−0.877144
$148$	5.40726e9	0.926402
$149$	6.02336e9	1.00115	0.500577	−	0.865692i	$-0.333121\pi$
$149$	6.02336e9	1.00115	0.500577	+	0.865692i	$0.333121\pi$
$150$	−5.21971e9	−0.841852
$151$	4.61177e9	0.721890	0.360945	−	0.932587i	$-0.382454\pi$
$151$	4.61177e9	0.721890	0.360945	+	0.932587i	$0.382454\pi$
$152$	3.41629e10	5.19109
$153$	2.21073e9	0.326154
$154$	−7.61273e9	−1.09068
$155$	4.14161e9	0.576337
$156$	2.31926e9	0.313537
$157$	−1.23953e10	−1.62821	−0.814103	−	0.580721i	$-0.802771\pi$
$157$	−1.23953e10	−1.62821	−0.814103	+	0.580721i	$0.802771\pi$
$158$	−2.30358e10	−2.94067
$159$	−6.74002e9	−0.836323
$160$	2.16855e10	2.61595
$161$	−1.25153e9	−0.146800
$162$	−1.92247e9	−0.219302
$163$	−6.68175e9	−0.741389	−0.370694	−	0.928755i	$-0.620880\pi$
$163$	−6.68175e9	−0.741389	−0.370694	+	0.928755i	$0.620880\pi$
$164$	2.90640e10	3.13732
$165$	−9.78141e8	−0.102736
$166$	2.21393e10	2.26296
$167$	−7.15932e9	−0.712275	−0.356138	−	0.934434i	$-0.615907\pi$
$167$	−7.15932e9	−0.712275	−0.356138	+	0.934434i	$0.615907\pi$
$168$	−3.53992e10	−3.42848
$169$	−1.02315e10	−0.964825
$170$	1.07488e10	0.987050
$171$	−5.17123e9	−0.462500
$172$	−4.45161e9	−0.387828
$173$	−1.96798e10	−1.67037	−0.835184	−	0.549970i	$-0.814639\pi$
$173$	−1.96798e10	−1.67037	−0.835184	+	0.549970i	$0.814639\pi$
$174$	1.63577e10	1.35285
$175$	1.45485e10	1.17259
$176$	−1.98934e10	−1.56279
$177$	9.81506e8	0.0751646
$178$	−1.51245e10	−1.12925
$179$	7.58491e9	0.552220	0.276110	−	0.961126i	$-0.410955\pi$
$179$	7.58491e9	0.552220	0.276110	+	0.961126i	$0.410955\pi$
$180$	−6.94782e9	−0.493313
$181$	6.65611e9	0.460964	0.230482	−	0.973077i	$-0.425970\pi$
$181$	6.65611e9	0.460964	0.230482	+	0.973077i	$0.425970\pi$
$182$	−8.69677e9	−0.587539
$183$	−1.10654e10	−0.729353
$184$	−5.38016e9	−0.346031
$185$	−2.60524e9	−0.163521
$186$	−2.09749e10	−1.28497
$187$	−5.69648e9	−0.340659
$188$	−5.61383e10	−3.27755
$189$	5.35837e9	0.305460
$190$	−2.51431e10	−1.39968
$191$	−3.30386e9	−0.179627	−0.0898136	−	0.995959i	$-0.528627\pi$
$191$	−3.30386e9	−0.179627	−0.0898136	+	0.995959i	$0.528627\pi$
$192$	−6.10247e10	−3.24079
$193$	−6.10928e8	−0.0316944	−0.0158472	−	0.999874i	$-0.505045\pi$
$193$	−6.10928e8	−0.0316944	−0.0158472	+	0.999874i	$0.505045\pi$
$194$	−5.27944e10	−2.67596
$195$	−1.11743e9	−0.0553431
$196$	9.08904e10	4.39912
$197$	−1.35254e10	−0.639812	−0.319906	−	0.947449i	$-0.603651\pi$
$197$	−1.35254e10	−0.639812	−0.319906	+	0.947449i	$0.603651\pi$
$198$	4.95374e9	0.229055
$199$	2.83709e10	1.28243	0.641217	−	0.767360i	$-0.278430\pi$
$199$	2.83709e10	1.28243	0.641217	+	0.767360i	$0.278430\pi$
$200$	6.25420e10	2.76399
$201$	3.49295e9	0.150942
$202$	7.37425e10	3.11628
$203$	−4.55925e10	−1.88435
$204$	−4.04626e10	−1.63576
$205$	−1.40031e10	−0.553775
$206$	4.52617e10	1.75117
$207$	8.14393e8	0.0308296
$208$	−2.27262e10	−0.841863
$209$	1.33250e10	0.483067
$210$	2.60530e10	0.924422
$211$	−7.15753e9	−0.248595	−0.124297	−	0.992245i	$-0.539668\pi$
$211$	−7.15753e9	−0.248595	−0.124297	+	0.992245i	$0.539668\pi$
$212$	1.23362e11	4.19439
$213$	−2.26378e10	−0.753573
$214$	−8.09604e10	−2.63883
$215$	2.14480e9	0.0684564
$216$	2.30349e10	0.720019
$217$	5.84619e10	1.78980
$218$	−9.90704e10	−2.97091
$219$	1.02638e10	0.301516
$220$	1.79028e10	0.515251
$221$	−6.50766e9	−0.183510
$222$	1.31941e10	0.364578
$223$	−3.19386e10	−0.864856	−0.432428	−	0.901668i	$-0.642343\pi$
$223$	−3.19386e10	−0.864856	−0.432428	+	0.901668i	$0.642343\pi$
$224$	3.06107e11	8.12376
$225$	−9.46697e9	−0.246258
$226$	−1.35686e11	−3.45977
$227$	−2.57665e10	−0.644080	−0.322040	−	0.946726i	$-0.604369\pi$
$227$	−2.57665e10	−0.644080	−0.322040	+	0.946726i	$0.604369\pi$
$228$	9.46484e10	2.31956
$229$	5.02517e10	1.20751	0.603756	−	0.797169i	$-0.293670\pi$
$229$	5.02517e10	1.20751	0.603756	+	0.797169i	$0.293670\pi$
$230$	3.95967e9	0.0933004
$231$	−1.38072e10	−0.319044
$232$	−1.95996e11	−4.44172
$233$	7.38541e9	0.164162	0.0820811	−	0.996626i	$-0.473843\pi$
$233$	7.38541e9	0.164162	0.0820811	+	0.996626i	$0.473843\pi$
$234$	5.65914e9	0.123390
$235$	2.70476e10	0.578527
$236$	−1.79644e10	−0.376971
$237$	−4.17800e10	−0.860203
$238$	1.51727e11	3.06525
$239$	−6.16374e10	−1.22195	−0.610976	−	0.791649i	$-0.709223\pi$
$239$	−6.16374e10	−1.22195	−0.610976	+	0.791649i	$0.709223\pi$
$240$	6.80810e10	1.32457
$241$	9.05914e9	0.172986	0.0864929	−	0.996252i	$-0.472434\pi$
$241$	9.05914e9	0.172986	0.0864929	+	0.996252i	$0.472434\pi$
$242$	9.25419e10	1.73448
$243$	−3.48678e9	−0.0641500
$244$	2.02529e11	3.65791
$245$	−4.37913e10	−0.776499
$246$	7.09181e10	1.23466
$247$	1.52224e10	0.260224
$248$	2.51319e11	4.21884
$249$	4.01539e10	0.661958
$250$	−1.08335e11	−1.75403
$251$	2.81470e10	0.447611	0.223806	−	0.974634i	$-0.428152\pi$
$251$	2.81470e10	0.447611	0.223806	+	0.974634i	$0.428152\pi$
$252$	−9.80735e10	−1.53197
$253$	−2.09849e9	−0.0322006
$254$	1.71055e10	0.257860
$255$	1.94950e10	0.288731
$256$	4.22726e11	6.15147
$257$	−1.40914e9	−0.0201491	−0.0100745	−	0.999949i	$-0.503207\pi$
$257$	−1.40914e9	−0.0201491	−0.0100745	+	0.999949i	$0.503207\pi$
$258$	−1.08622e10	−0.152627
$259$	−3.67748e10	−0.507810
$260$	2.04521e10	0.277561
$261$	2.96679e10	0.395734
$262$	−1.95131e11	−2.55841
$263$	7.83402e9	0.100968	0.0504840	−	0.998725i	$-0.483924\pi$
$263$	7.83402e9	0.100968	0.0504840	+	0.998725i	$0.483924\pi$
$264$	−5.93551e10	−0.752039
$265$	−5.94361e10	−0.740362
$266$	−3.54913e11	−4.34665
$267$	−2.74313e10	−0.330328
$268$	−6.39310e10	−0.757016
$269$	−1.12060e11	−1.30486	−0.652431	−	0.757848i	$-0.726251\pi$
$269$	−1.12060e11	−1.30486	−0.652431	+	0.757848i	$0.726251\pi$
$270$	−1.69531e10	−0.194139
$271$	−1.03942e11	−1.17066	−0.585330	−	0.810795i	$-0.699035\pi$
$271$	−1.03942e11	−1.17066	−0.585330	+	0.810795i	$0.699035\pi$
$272$	3.96489e11	4.39209
$273$	−1.57733e10	−0.171866
$274$	−1.58794e10	−0.170199
$275$	2.43940e10	0.257209
$276$	−1.49057e10	−0.154619
$277$	8.37465e9	0.0854688	0.0427344	−	0.999086i	$-0.486393\pi$
$277$	8.37465e9	0.0854688	0.0427344	+	0.999086i	$0.486393\pi$
$278$	1.93164e11	1.93965
$279$	−3.80422e10	−0.375878
$280$	−3.12164e11	−3.03509
$281$	2.73924e10	0.262091	0.131045	−	0.991376i	$-0.458167\pi$
$281$	2.73924e10	0.262091	0.131045	+	0.991376i	$0.458167\pi$
$282$	−1.36981e11	−1.28985
$283$	4.96575e10	0.460199	0.230100	−	0.973167i	$-0.426095\pi$
$283$	4.96575e10	0.460199	0.230100	+	0.973167i	$0.426095\pi$
$284$	4.14336e11	3.77938
$285$	−4.56019e10	−0.409431
$286$	−1.45822e10	−0.128877
$287$	−1.97665e11	−1.71973
$288$	−1.99189e11	−1.70608
$289$	−5.05298e9	−0.0426095
$290$	1.44248e11	1.19762
$291$	−9.57530e10	−0.782769
$292$	−1.87857e11	−1.51219
$293$	−2.07884e11	−1.64785	−0.823924	−	0.566700i	$-0.808220\pi$
$293$	−2.07884e11	−1.64785	−0.823924	+	0.566700i	$0.808220\pi$
$294$	2.21779e11	1.73124
$295$	8.65530e9	0.0665401
$296$	−1.58090e11	−1.19699
$297$	8.98457e9	0.0670028
$298$	−2.69004e11	−1.97600
$299$	−2.39731e9	−0.0173462
$300$	1.73273e11	1.23505
$301$	3.02754e10	0.212589
$302$	−2.05962e11	−1.42481
$303$	1.33747e11	0.911571
$304$	−9.27450e11	−6.22816
$305$	−9.75792e10	−0.645666
$306$	−9.87314e10	−0.643738
$307$	−1.03771e11	−0.666735	−0.333368	−	0.942797i	$-0.608185\pi$
$307$	−1.03771e11	−0.666735	−0.333368	+	0.942797i	$0.608185\pi$
$308$	2.52711e11	1.60010
$309$	8.20909e10	0.512250
$310$	−1.84965e11	−1.13753
$311$	−3.62366e10	−0.219647	−0.109824	−	0.993951i	$-0.535029\pi$
$311$	−3.62366e10	−0.219647	−0.109824	+	0.993951i	$0.535029\pi$
$312$	−6.78072e10	−0.405117
$313$	−3.00938e10	−0.177226	−0.0886131	−	0.996066i	$-0.528243\pi$
$313$	−3.00938e10	−0.177226	−0.0886131	+	0.996066i	$0.528243\pi$
$314$	5.53577e11	3.21362
$315$	4.72522e10	0.270411
$316$	7.64694e11	4.31415
$317$	2.82988e11	1.57399	0.786993	−	0.616962i	$-0.211637\pi$
$317$	2.82988e11	1.57399	0.786993	+	0.616962i	$0.211637\pi$
$318$	3.01011e11	1.65067
$319$	−7.64466e10	−0.413333
$320$	−5.38140e11	−2.86893
$321$	−1.46838e11	−0.771906
$322$	5.58936e10	0.289741
$323$	−2.65576e11	−1.35762
$324$	6.38182e10	0.321730
$325$	2.78677e10	0.138556
$326$	2.98408e11	1.46329
$327$	−1.79684e11	−0.869047
$328$	−8.49733e11	−4.05368
$329$	3.81797e11	1.79660
$330$	4.36840e10	0.202773
$331$	−1.25712e11	−0.575638	−0.287819	−	0.957685i	$-0.592930\pi$
$331$	−1.25712e11	−0.575638	−0.287819	+	0.957685i	$0.592930\pi$
$332$	−7.34932e11	−3.31990
$333$	2.39300e10	0.106646
$334$	3.19737e11	1.40583
$335$	3.08022e10	0.133623
$336$	9.61013e11	4.11342
$337$	−4.20323e11	−1.77520	−0.887602	−	0.460612i	$-0.847630\pi$
$337$	−4.20323e11	−1.77520	−0.887602	+	0.460612i	$0.847630\pi$
$338$	4.56940e11	1.90430
$339$	−2.46093e11	−1.01205
$340$	−3.56815e11	−1.44807
$341$	9.80251e10	0.392593
$342$	2.30948e11	0.912845
$343$	−2.11273e11	−0.824175
$344$	1.30150e11	0.501108
$345$	7.18163e9	0.0272921
$346$	8.78902e11	3.29684
$347$	−1.58534e11	−0.587001	−0.293500	−	0.955959i	$-0.594820\pi$
$347$	−1.58534e11	−0.587001	−0.293500	+	0.955959i	$0.594820\pi$
$348$	−5.43007e11	−1.98472
$349$	−4.32565e10	−0.156076	−0.0780382	−	0.996950i	$-0.524866\pi$
$349$	−4.32565e10	−0.156076	−0.0780382	+	0.996950i	$0.524866\pi$
$350$	−6.49739e11	−2.31437
$351$	1.02640e10	0.0360938
$352$	5.13260e11	1.78195
$353$	−5.07910e11	−1.74101	−0.870504	−	0.492161i	$-0.836207\pi$
$353$	−5.07910e11	−1.74101	−0.870504	+	0.492161i	$0.836207\pi$
$354$	−4.38343e10	−0.148354
$355$	−1.99629e11	−0.667107
$356$	5.02071e11	1.65669
$357$	2.75187e11	0.896644
$358$	−3.38744e11	−1.08993
$359$	5.31759e11	1.68962	0.844811	−	0.535065i	$-0.179713\pi$
$359$	5.31759e11	1.68962	0.844811	+	0.535065i	$0.179713\pi$
$360$	2.03130e11	0.637403
$361$	2.98536e11	0.925154
$362$	−2.97263e11	−0.909814
$363$	1.67843e11	0.507368
$364$	2.88697e11	0.861957
$365$	9.05103e10	0.266919
$366$	4.94184e11	1.43954
$367$	2.26219e11	0.650928	0.325464	−	0.945555i	$-0.394480\pi$
$367$	2.26219e11	0.650928	0.325464	+	0.945555i	$0.394480\pi$
$368$	1.46060e11	0.415160
$369$	1.28624e11	0.361163
$370$	1.16350e11	0.322745
$371$	−8.38984e11	−2.29917
$372$	6.96281e11	1.88513
$373$	−4.91064e11	−1.31356	−0.656778	−	0.754084i	$-0.728081\pi$
$373$	−4.91064e11	−1.31356	−0.656778	+	0.754084i	$0.728081\pi$
$374$	2.54406e11	0.672365
$375$	−1.96486e11	−0.513087
$376$	1.64129e12	4.23487
$377$	−8.73325e10	−0.222659
$378$	−2.39306e11	−0.602893
$379$	−1.07690e11	−0.268101	−0.134050	−	0.990975i	$-0.542798\pi$
$379$	−1.07690e11	−0.268101	−0.134050	+	0.990975i	$0.542798\pi$
$380$	8.34646e11	2.05341
$381$	3.10241e10	0.0754288
$382$	1.47551e11	0.354534
$383$	4.65577e11	1.10560	0.552799	−	0.833315i	$-0.313560\pi$
$383$	4.65577e11	1.10560	0.552799	+	0.833315i	$0.313560\pi$
$384$	1.46630e12	3.44139
$385$	−1.21757e11	−0.282436
$386$	2.72842e10	0.0625558
$387$	−1.97008e10	−0.0446461
$388$	1.75255e12	3.92581
$389$	6.17970e11	1.36834	0.684171	−	0.729322i	$-0.260164\pi$
$389$	6.17970e11	1.36834	0.684171	+	0.729322i	$0.260164\pi$
$390$	4.99045e10	0.109232
$391$	4.18243e10	0.0904968
$392$	−2.65733e12	−5.68404
$393$	−3.53908e11	−0.748384
$394$	6.04047e11	1.26281
$395$	−3.68432e11	−0.761501
$396$	−1.64443e11	−0.336038
$397$	7.25731e11	1.46628	0.733142	−	0.680075i	$-0.238053\pi$
$397$	7.25731e11	1.46628	0.733142	+	0.680075i	$0.238053\pi$
$398$	−1.26705e12	−2.53117
$399$	−6.43704e11	−1.27148
$400$	−1.69788e12	−3.31618
$401$	−3.42697e11	−0.661852	−0.330926	−	0.943657i	$-0.607361\pi$
$401$	−3.42697e11	−0.661852	−0.330926	+	0.943657i	$0.607361\pi$
$402$	−1.55996e11	−0.297917
$403$	1.11984e11	0.211486
$404$	−2.44795e12	−4.57178
$405$	−3.07478e10	−0.0567893
$406$	2.03617e12	3.71918
$407$	−6.16616e10	−0.111388
$408$	1.18299e12	2.11354
$409$	3.28076e11	0.579721	0.289860	−	0.957069i	$-0.406391\pi$
$409$	3.28076e11	0.579721	0.289860	+	0.957069i	$0.406391\pi$
$410$	6.25383e11	1.09300
$411$	−2.88005e10	−0.0497865
$412$	−1.50250e12	−2.56908
$413$	1.22176e11	0.206638
$414$	−3.63710e10	−0.0608490
$415$	3.54093e11	0.586004
$416$	5.86348e11	0.959921
$417$	3.50340e11	0.567385
$418$	−5.95096e11	−0.953440
$419$	−9.17573e11	−1.45438	−0.727189	−	0.686437i	$-0.759174\pi$
$419$	−9.17573e11	−1.45438	−0.727189	+	0.686437i	$0.759174\pi$
$420$	−8.64851e11	−1.35619
$421$	−6.07549e11	−0.942566	−0.471283	−	0.881982i	$-0.656209\pi$
$421$	−6.07549e11	−0.942566	−0.471283	+	0.881982i	$0.656209\pi$
$422$	3.19657e11	0.490656
$423$	−2.48442e11	−0.377306
$424$	−3.60668e12	−5.41952
$425$	−4.86190e11	−0.722862
$426$	1.01101e12	1.48734
$427$	−1.37740e12	−2.00510
$428$	2.68755e12	3.87132
$429$	−2.64476e10	−0.0376989
$430$	−9.57873e10	−0.135114
$431$	7.76828e11	1.08437	0.542185	−	0.840259i	$-0.317597\pi$
$431$	7.76828e11	1.08437	0.542185	+	0.840259i	$0.317597\pi$
$432$	−6.25348e11	−0.863863
$433$	−3.38772e11	−0.463140	−0.231570	−	0.972818i	$-0.574386\pi$
$433$	−3.38772e11	−0.463140	−0.231570	+	0.972818i	$0.574386\pi$
$434$	−2.61092e12	−3.53256
$435$	2.61623e11	0.350327
$436$	3.28873e12	4.35851
$437$	−9.78336e10	−0.128328
$438$	−4.58384e11	−0.595108
$439$	−1.32693e12	−1.70513	−0.852566	−	0.522619i	$-0.824955\pi$
$439$	−1.32693e12	−1.70513	−0.852566	+	0.522619i	$0.824955\pi$
$440$	−5.23416e11	−0.665748
$441$	4.02239e11	0.506419
$442$	2.90633e11	0.362197
$443$	5.39539e11	0.665589	0.332795	−	0.942999i	$-0.392008\pi$
$443$	5.39539e11	0.665589	0.332795	+	0.942999i	$0.392008\pi$
$444$	−4.37988e11	−0.534858
$445$	−2.41900e11	−0.292426
$446$	1.42638e12	1.70698
$447$	−4.87892e11	−0.578016
$448$	−7.59623e12	−8.90938
$449$	−4.12062e11	−0.478470	−0.239235	−	0.970962i	$-0.576897\pi$
$449$	−4.12062e11	−0.478470	−0.239235	+	0.970962i	$0.576897\pi$
$450$	4.22797e11	0.486044
$451$	−3.31431e11	−0.377224
$452$	4.50421e12	5.07570
$453$	−3.73553e11	−0.416783
$454$	1.15074e12	1.27123
$455$	−1.39095e11	−0.152146
$456$	−2.76719e12	−2.99708
$457$	1.04050e12	1.11589	0.557944	−	0.829879i	$-0.311590\pi$
$457$	1.04050e12	1.11589	0.557944	+	0.829879i	$0.311590\pi$
$458$	−2.24425e12	−2.38329
$459$	−1.79069e11	−0.188305
$460$	−1.31445e11	−0.136878
$461$	−3.43691e11	−0.354417	−0.177208	−	0.984173i	$-0.556707\pi$
$461$	−3.43691e11	−0.354417	−0.177208	+	0.984173i	$0.556707\pi$
$462$	6.16631e11	0.629704
$463$	1.60518e12	1.62334	0.811668	−	0.584119i	$-0.198560\pi$
$463$	1.60518e12	1.62334	0.811668	+	0.584119i	$0.198560\pi$
$464$	5.32087e12	5.32908
$465$	−3.35471e11	−0.332749
$466$	−3.29834e11	−0.324010
$467$	1.49305e12	1.45261	0.726305	−	0.687373i	$-0.241236\pi$
$467$	1.49305e12	1.45261	0.726305	+	0.687373i	$0.241236\pi$
$468$	−1.87860e11	−0.181021
$469$	4.34795e11	0.414961
$470$	−1.20795e12	−1.14185
$471$	1.00402e12	0.940045
$472$	5.25217e11	0.487080
$473$	5.07639e10	0.0466316
$474$	1.86590e12	1.69780
$475$	1.13727e12	1.02505
$476$	−5.03671e12	−4.49692
$477$	5.45942e11	0.482852
$478$	2.75274e12	2.41179
$479$	−4.99884e11	−0.433870	−0.216935	−	0.976186i	$-0.569606\pi$
$479$	−4.99884e11	−0.433870	−0.216935	+	0.976186i	$0.569606\pi$
$480$	−1.75653e12	−1.51032
$481$	−7.04422e10	−0.0600040
$482$	−4.04583e11	−0.341426
$483$	1.01374e11	0.0847548
$484$	−3.07201e12	−2.54459
$485$	−8.44387e11	−0.692953
$486$	1.55720e11	0.126614
$487$	1.80213e12	1.45180	0.725899	−	0.687802i	$-0.241424\pi$
$487$	1.80213e12	1.45180	0.725899	+	0.687802i	$0.241424\pi$
$488$	−5.92125e12	−4.72634
$489$	5.41222e11	0.428041
$490$	1.95573e12	1.53259
$491$	2.17553e12	1.68926	0.844632	−	0.535347i	$-0.179819\pi$
$491$	2.17553e12	1.68926	0.844632	+	0.535347i	$0.179819\pi$
$492$	−2.35419e12	−1.81133
$493$	1.52363e12	1.16163
$494$	−6.79836e11	−0.513610
$495$	7.92294e10	0.0593148
$496$	−6.82279e12	−5.06168
$497$	−2.81790e12	−2.07168
$498$	−1.79328e12	−1.30652
$499$	2.29747e12	1.65882	0.829408	−	0.558643i	$-0.188678\pi$
$499$	2.29747e12	1.65882	0.829408	+	0.558643i	$0.188678\pi$
$500$	3.59626e12	2.57328
$501$	5.79905e11	0.411232
$502$	−1.25705e12	−0.883459
$503$	−7.81795e11	−0.544549	−0.272275	−	0.962220i	$-0.587776\pi$
$503$	−7.81795e11	−0.544549	−0.272275	+	0.962220i	$0.587776\pi$
$504$	2.86733e12	1.97943
$505$	1.17943e12	0.806976
$506$	9.37188e10	0.0635550
$507$	8.28751e11	0.557042
$508$	−5.67831e11	−0.378297
$509$	−3.00641e11	−0.198526	−0.0992631	−	0.995061i	$-0.531649\pi$
$509$	−3.00641e11	−0.198526	−0.0992631	+	0.995061i	$0.531649\pi$
$510$	−8.70652e11	−0.569874
$511$	1.27762e12	0.828910
$512$	−9.61052e12	−6.18062
$513$	4.18870e11	0.267024
$514$	6.29325e10	0.0397687
$515$	7.23909e11	0.453473
$516$	3.60581e11	0.223913
$517$	6.40172e11	0.394085
$518$	1.64237e12	1.00228
$519$	1.59406e12	0.964388
$520$	−5.97950e11	−0.358633
$521$	−2.82772e11	−0.168138	−0.0840690	−	0.996460i	$-0.526792\pi$
$521$	−2.82772e11	−0.168138	−0.0840690	+	0.996460i	$0.526792\pi$
$522$	−1.32497e12	−0.781069
$523$	2.40276e12	1.40428	0.702139	−	0.712040i	$-0.252229\pi$
$523$	2.40276e12	1.40428	0.702139	+	0.712040i	$0.252229\pi$
$524$	6.47754e12	3.75335
$525$	−1.17843e12	−0.676997
$526$	−3.49869e11	−0.199283
$527$	−1.95371e12	−1.10335
$528$	1.61137e12	0.902280
$529$	−1.78575e12	−0.991446
$530$	2.65443e12	1.46127
$531$	−7.95020e10	−0.0433963
$532$	1.17816e13	6.37681
$533$	−3.78627e11	−0.203207
$534$	1.22509e12	0.651975
$535$	−1.29487e12	−0.683336
$536$	1.86912e12	0.978130
$537$	−6.14378e11	−0.318824
$538$	5.00461e12	2.57543
$539$	−1.03647e12	−0.528940
$540$	5.62773e11	0.284814
$541$	−1.63631e12	−0.821253	−0.410627	−	0.911804i	$-0.634690\pi$
$541$	−1.63631e12	−0.821253	−0.410627	+	0.911804i	$0.634690\pi$
$542$	4.64208e12	2.31055
$543$	−5.39145e11	−0.266138
$544$	−1.02296e13	−5.00801
$545$	−1.58452e12	−0.769331
$546$	7.04438e11	0.339216
$547$	−2.05554e12	−0.981709	−0.490854	−	0.871242i	$-0.663315\pi$
$547$	−2.05554e12	−0.981709	−0.490854	+	0.871242i	$0.663315\pi$
$548$	5.27131e11	0.249693
$549$	8.96299e11	0.421092
$550$	−1.08944e12	−0.507658
$551$	−3.56402e12	−1.64724
$552$	4.35793e11	0.199781
$553$	−5.20069e12	−2.36482
$554$	−3.74014e11	−0.168692
$555$	2.11024e11	0.0944091
$556$	−6.41223e12	−2.84559
$557$	1.75217e12	0.771309	0.385654	−	0.922643i	$-0.373976\pi$
$557$	1.75217e12	0.771309	0.385654	+	0.922643i	$0.373976\pi$
$558$	1.69897e12	0.741877
$559$	5.79926e10	0.0251200
$560$	8.47459e12	3.64143
$561$	4.61415e11	0.196679
$562$	−1.22335e12	−0.517294
$563$	1.47516e12	0.618802	0.309401	−	0.950932i	$-0.399872\pi$
$563$	1.47516e12	0.618802	0.309401	+	0.950932i	$0.399872\pi$
$564$	4.54720e12	1.89229
$565$	−2.17014e12	−0.895923
$566$	−2.21771e12	−0.908304
$567$	−4.34028e11	−0.176357
$568$	−1.21138e13	−4.88328
$569$	−2.61095e12	−1.04422	−0.522111	−	0.852878i	$-0.674855\pi$
$569$	−2.61095e12	−1.04422	−0.522111	+	0.852878i	$0.674855\pi$
$570$	2.03659e12	0.808103
$571$	−1.13826e12	−0.448104	−0.224052	−	0.974577i	$-0.571928\pi$
$571$	−1.13826e12	−0.448104	−0.224052	+	0.974577i	$0.571928\pi$
$572$	4.84068e11	0.189071
$573$	2.67613e11	0.103708
$574$	8.82774e12	3.39427
$575$	−1.79104e11	−0.0683282
$576$	4.94300e12	1.87107
$577$	5.82770e11	0.218880	0.109440	−	0.993993i	$-0.465094\pi$
$577$	5.82770e11	0.218880	0.109440	+	0.993993i	$0.465094\pi$
$578$	2.25667e11	0.0840993
$579$	4.94851e10	0.0182987
$580$	−4.78845e12	−1.75699
$581$	4.99827e12	1.81982
$582$	4.27635e12	1.54497
$583$	−1.40675e12	−0.504324
$584$	5.49231e12	1.95388
$585$	9.05116e10	0.0319523
$586$	9.28415e12	3.25239
$587$	−5.08815e11	−0.176884	−0.0884420	−	0.996081i	$-0.528189\pi$
$587$	−5.08815e11	−0.176884	−0.0884420	+	0.996081i	$0.528189\pi$
$588$	−7.36213e12	−2.53983
$589$	4.57003e12	1.56459
$590$	−3.86547e11	−0.131331
$591$	1.09556e12	0.369395
$592$	4.29180e12	1.43612
$593$	8.59531e11	0.285440	0.142720	−	0.989763i	$-0.454415\pi$
$593$	8.59531e11	0.285440	0.142720	+	0.989763i	$0.454415\pi$
$594$	−4.01253e11	−0.132245
$595$	2.42670e12	0.793762
$596$	8.92983e12	2.89891
$597$	−2.29805e12	−0.740414
$598$	1.07064e11	0.0342365
$599$	−3.76859e12	−1.19607	−0.598037	−	0.801469i	$-0.704052\pi$
$599$	−3.76859e12	−1.19607	−0.598037	+	0.801469i	$0.704052\pi$
$600$	−5.06590e12	−1.59579
$601$	−4.46763e12	−1.39683	−0.698413	−	0.715695i	$-0.746110\pi$
$601$	−4.46763e12	−1.39683	−0.698413	+	0.715695i	$0.746110\pi$
$602$	−1.35211e12	−0.419592
$603$	−2.82929e11	−0.0871464
$604$	6.83709e12	2.09028
$605$	1.48010e12	0.449151
$606$	−5.97315e12	−1.79919
$607$	5.11907e12	1.53053	0.765265	−	0.643715i	$-0.222608\pi$
$607$	5.11907e12	1.53053	0.765265	+	0.643715i	$0.222608\pi$
$608$	2.39287e13	7.10155
$609$	3.69299e12	1.08793
$610$	4.35790e12	1.27436
$611$	7.31332e11	0.212290
$612$	3.27747e12	0.944404
$613$	−4.88066e12	−1.39607	−0.698034	−	0.716065i	$-0.745941\pi$
$613$	−4.88066e12	−1.39607	−0.698034	+	0.716065i	$0.745941\pi$
$614$	4.63444e12	1.31595
$615$	1.13425e12	0.319722
$616$	−7.38840e12	−2.06746
$617$	7.01368e11	0.194833	0.0974165	−	0.995244i	$-0.468942\pi$
$617$	7.01368e11	0.194833	0.0974165	+	0.995244i	$0.468942\pi$
$618$	−3.66620e12	−1.01104
$619$	−2.21391e12	−0.606111	−0.303055	−	0.952973i	$-0.598007\pi$
$619$	−2.21391e12	−0.606111	−0.303055	+	0.952973i	$0.598007\pi$
$620$	6.14008e12	1.66883
$621$	−6.59658e10	−0.0177995
$622$	1.61834e12	0.433523
$623$	−3.41459e12	−0.908118
$624$	1.84082e12	0.486050
$625$	1.08550e12	0.284558
$626$	1.34400e12	0.349795
$627$	−1.07932e12	−0.278899
$628$	−1.83765e13	−4.71459
$629$	1.22896e12	0.313047
$630$	−2.11029e12	−0.533716
$631$	−1.22716e12	−0.308155	−0.154078	−	0.988059i	$-0.549241\pi$
$631$	−1.22716e12	−0.308155	−0.154078	+	0.988059i	$0.549241\pi$
$632$	−2.23570e13	−5.57426
$633$	5.79760e11	0.143526
$634$	−1.26383e13	−3.10661
$635$	2.73583e11	0.0667740
$636$	−9.99230e12	−2.42163
$637$	−1.18406e12	−0.284935
$638$	3.41412e12	0.815804
$639$	1.83366e12	0.435076
$640$	1.29304e13	3.04652
$641$	6.87504e12	1.60847	0.804237	−	0.594309i	$-0.202574\pi$
$641$	6.87504e12	1.60847	0.804237	+	0.594309i	$0.202574\pi$
$642$	6.55780e12	1.52353
$643$	6.49891e12	1.49931	0.749655	−	0.661829i	$-0.230220\pi$
$643$	6.49891e12	1.49931	0.749655	+	0.661829i	$0.230220\pi$
$644$	−1.85544e12	−0.425069
$645$	−1.73729e11	−0.0395233
$646$	1.18607e13	2.67956
$647$	−3.42884e12	−0.769268	−0.384634	−	0.923069i	$-0.625672\pi$
$647$	−3.42884e12	−0.769268	−0.384634	+	0.923069i	$0.625672\pi$
$648$	−1.86583e12	−0.415703
$649$	2.04857e11	0.0453262
$650$	−1.24458e12	−0.273471
$651$	−4.73541e12	−1.03334
$652$	−9.90591e12	−2.14674
$653$	−3.38071e12	−0.727609	−0.363805	−	0.931475i	$-0.618522\pi$
$653$	−3.38071e12	−0.727609	−0.363805	+	0.931475i	$0.618522\pi$
$654$	8.02470e12	1.71526
$655$	−3.12090e12	−0.662513
$656$	2.30684e13	4.86352
$657$	−8.31369e11	−0.174080
$658$	−1.70511e13	−3.54598
$659$	−7.25128e12	−1.49772	−0.748859	−	0.662729i	$-0.769398\pi$
$659$	−7.25128e12	−1.49772	−0.748859	+	0.662729i	$0.769398\pi$
$660$	−1.45013e12	−0.297480
$661$	9.13436e12	1.86111	0.930554	−	0.366154i	$-0.119326\pi$
$661$	9.13436e12	1.86111	0.930554	+	0.366154i	$0.119326\pi$
$662$	5.61430e12	1.13615
$663$	5.27120e11	0.105949
$664$	2.14869e13	4.28960
$665$	−5.67643e12	−1.12558
$666$	−1.06872e12	−0.210489
$667$	5.61281e11	0.109803
$668$	−1.06139e13	−2.06244
$669$	2.58703e12	0.499325
$670$	−1.37563e12	−0.263734
$671$	−2.30954e12	−0.439819
$672$	−2.47946e13	−4.69025
$673$	5.01704e12	0.942713	0.471357	−	0.881943i	$-0.343764\pi$
$673$	5.01704e12	0.942713	0.471357	+	0.881943i	$0.343764\pi$
$674$	1.87717e13	3.50376
$675$	7.66825e11	0.142177
$676$	−1.51685e13	−2.79372
$677$	1.26871e12	0.232120	0.116060	−	0.993242i	$-0.462973\pi$
$677$	1.26871e12	0.232120	0.116060	+	0.993242i	$0.462973\pi$
$678$	1.09906e13	1.99750
$679$	−1.19191e13	−2.15194
$680$	1.04321e13	1.87103
$681$	2.08709e12	0.371860
$682$	−4.37782e12	−0.774869
$683$	7.93026e12	1.39442	0.697211	−	0.716866i	$-0.254424\pi$
$683$	7.93026e12	1.39442	0.697211	+	0.716866i	$0.254424\pi$
$684$	−7.66652e12	−1.33920
$685$	−2.53974e11	−0.0440739
$686$	9.43547e12	1.62669
$687$	−4.07039e12	−0.697157
$688$	−3.53330e12	−0.601218
$689$	−1.60707e12	−0.271675
$690$	−3.20733e11	−0.0538670
$691$	1.01252e13	1.68947	0.844736	−	0.535183i	$-0.179757\pi$
$691$	1.01252e13	1.68947	0.844736	+	0.535183i	$0.179757\pi$
$692$	−2.91759e13	−4.83667
$693$	1.11838e12	0.184200
$694$	7.08014e12	1.15858
$695$	3.08943e12	0.502282
$696$	1.58757e13	2.56443
$697$	6.60566e12	1.06015
$698$	1.93184e12	0.308051
$699$	−5.98219e11	−0.0947791
$700$	2.15686e13	3.39533
$701$	−7.69928e12	−1.20426	−0.602128	−	0.798399i	$-0.705680\pi$
$701$	−7.69928e12	−1.20426	−0.602128	+	0.798399i	$0.705680\pi$
$702$	−4.58390e11	−0.0712391
$703$	−2.87473e12	−0.443913
$704$	−1.27369e13	−1.95428
$705$	−2.19086e12	−0.334013
$706$	2.26834e13	3.43626
$707$	1.66485e13	2.50604
$708$	1.45512e12	0.217645
$709$	3.84430e12	0.571359	0.285679	−	0.958325i	$-0.407781\pi$
$709$	3.84430e12	0.571359	0.285679	+	0.958325i	$0.407781\pi$
$710$	8.91545e12	1.31668
$711$	3.38418e12	0.496638
$712$	−1.46789e13	−2.14058
$713$	−7.19713e11	−0.104293
$714$	−1.22899e13	−1.76973
$715$	−2.33226e11	−0.0333733
$716$	1.12449e13	1.59899
$717$	4.99263e12	0.705494
$718$	−2.37484e13	−3.33484
$719$	−4.05595e12	−0.565995	−0.282997	−	0.959121i	$-0.591329\pi$
$719$	−4.05595e12	−0.565995	−0.282997	+	0.959121i	$0.591329\pi$
$720$	−5.51456e12	−0.764742
$721$	1.02185e13	1.40825
$722$	−1.33327e13	−1.82599
$723$	−7.33790e11	−0.0998734
$724$	9.86790e12	1.33475
$725$	−6.52465e12	−0.877073
$726$	−7.49589e12	−1.00140
$727$	−6.97886e12	−0.926573	−0.463287	−	0.886209i	$-0.653330\pi$
$727$	−6.97886e12	−0.926573	−0.463287	+	0.886209i	$0.653330\pi$
$728$	−8.44050e12	−1.11372
$729$	2.82430e11	0.0370370
$730$	−4.04221e12	−0.526824
$731$	−1.01176e12	−0.131054
$732$	−1.64048e13	−2.11190
$733$	−2.31364e12	−0.296024	−0.148012	−	0.988986i	$-0.547287\pi$
$733$	−2.31364e12	−0.296024	−0.148012	+	0.988986i	$0.547287\pi$
$734$	−1.01030e13	−1.28475
$735$	3.54710e12	0.448312
$736$	−3.76842e12	−0.473379
$737$	7.29037e11	0.0910219
$738$	−5.74437e12	−0.712834
$739$	−8.89103e12	−1.09661	−0.548305	−	0.836278i	$-0.684727\pi$
$739$	−8.89103e12	−1.09661	−0.548305	+	0.836278i	$0.684727\pi$
$740$	−3.86235e12	−0.473488
$741$	−1.23302e12	−0.150240
$742$	3.74692e13	4.53792
$743$	−6.42980e12	−0.774012	−0.387006	−	0.922077i	$-0.626491\pi$
$743$	−6.42980e12	−0.774012	−0.387006	+	0.922077i	$0.626491\pi$
$744$	−2.03569e13	−2.43575
$745$	−4.30242e12	−0.511693
$746$	2.19310e13	2.59259
$747$	−3.25247e12	−0.382182
$748$	−8.44522e12	−0.986402
$749$	−1.82780e13	−2.12208
$750$	8.77511e12	1.01269
$751$	5.87435e12	0.673877	0.336938	−	0.941527i	$-0.390609\pi$
$751$	5.87435e12	0.673877	0.336938	+	0.941527i	$0.390609\pi$
$752$	−4.45576e13	−5.08091
$753$	−2.27991e12	−0.258428
$754$	3.90029e12	0.439466
$755$	−3.29413e12	−0.368961
$756$	7.94396e12	0.884482
$757$	2.51325e12	0.278167	0.139083	−	0.990281i	$-0.455584\pi$
$757$	2.51325e12	0.278167	0.139083	+	0.990281i	$0.455584\pi$
$758$	4.80945e12	0.529156
$759$	1.69977e11	0.0185910
$760$	−2.44022e13	−2.65319
$761$	−4.65254e12	−0.502874	−0.251437	−	0.967874i	$-0.580903\pi$
$761$	−4.65254e12	−0.502874	−0.251437	+	0.967874i	$0.580903\pi$
$762$	−1.38554e12	−0.148875
$763$	−2.23666e13	−2.38913
$764$	−4.89809e12	−0.520124
$765$	−1.57910e12	−0.166699
$766$	−2.07928e13	−2.18214
$767$	2.34028e11	0.0244168
$768$	−3.42408e13	−3.55155
$769$	−1.90426e13	−1.96362	−0.981812	−	0.189857i	$-0.939198\pi$
$769$	−1.90426e13	−1.96362	−0.981812	+	0.189857i	$0.939198\pi$
$770$	5.43769e12	0.557450
$771$	1.14140e11	0.0116331
$772$	−9.05720e11	−0.0917733
$773$	1.38070e13	1.39089	0.695445	−	0.718579i	$-0.255207\pi$
$773$	1.38070e13	1.39089	0.695445	+	0.718579i	$0.255207\pi$
$774$	8.79840e11	0.0881190
$775$	8.36635e12	0.833064
$776$	−5.12387e13	−5.07248
$777$	2.97876e12	0.293184
$778$	−2.75987e13	−2.70072
$779$	−1.54517e13	−1.50334
$780$	−1.65662e12	−0.160250
$781$	−4.72488e12	−0.454424
$782$	−1.86788e12	−0.178615
$783$	−2.40310e12	−0.228477
$784$	7.21408e13	6.81959
$785$	8.85384e12	0.832182
$786$	1.58056e13	1.47710
$787$	1.23088e13	1.14375	0.571874	−	0.820342i	$-0.306217\pi$
$787$	1.23088e13	1.14375	0.571874	+	0.820342i	$0.306217\pi$
$788$	−2.00518e13	−1.85262
$789$	−6.34556e11	−0.0582939
$790$	1.64542e13	1.50299
$791$	−3.06332e13	−2.78226
$792$	4.80776e12	0.434190
$793$	−2.63841e12	−0.236926
$794$	−3.24113e13	−2.89403
$795$	4.81433e12	0.427448
$796$	4.20609e13	3.71338
$797$	−1.82300e13	−1.60038	−0.800191	−	0.599745i	$-0.795269\pi$
$797$	−1.82300e13	−1.60038	−0.800191	+	0.599745i	$0.795269\pi$
$798$	2.87480e13	2.50954
$799$	−1.27591e13	−1.10754
$800$	4.38063e13	3.78122
$801$	2.22193e12	0.190715
$802$	1.53049e13	1.30631
$803$	2.14223e12	0.181822
$804$	5.17841e12	0.437064
$805$	8.93955e11	0.0750299
$806$	−5.00122e12	−0.417415
$807$	9.07685e12	0.753363
$808$	7.15696e13	5.90714
$809$	−7.40819e12	−0.608056	−0.304028	−	0.952663i	$-0.598332\pi$
$809$	−7.40819e12	−0.608056	−0.304028	+	0.952663i	$0.598332\pi$
$810$	1.37320e12	0.112086
$811$	1.07341e13	0.871310	0.435655	−	0.900114i	$-0.356517\pi$
$811$	1.07341e13	0.871310	0.435655	+	0.900114i	$0.356517\pi$
$812$	−6.75924e13	−5.45627
$813$	8.41933e12	0.675880
$814$	2.75382e12	0.219850
$815$	4.77270e12	0.378927
$816$	−3.21156e13	−2.53578
$817$	2.36667e12	0.185839
$818$	−1.46519e13	−1.14421
$819$	1.27764e12	0.0992270
$820$	−2.07601e13	−1.60349
$821$	−1.58404e13	−1.21680	−0.608402	−	0.793629i	$-0.708189\pi$
$821$	−1.58404e13	−1.21680	−0.608402	+	0.793629i	$0.708189\pi$
$822$	1.28623e12	0.0982646
$823$	1.15449e13	0.877181	0.438591	−	0.898687i	$-0.355478\pi$
$823$	1.15449e13	0.877181	0.438591	+	0.898687i	$0.355478\pi$
$824$	4.39279e13	3.31947
$825$	−1.97591e12	−0.148500
$826$	−5.45640e12	−0.407846
$827$	−2.22688e13	−1.65547	−0.827737	−	0.561116i	$-0.810372\pi$
$827$	−2.22688e13	−1.65547	−0.827737	+	0.561116i	$0.810372\pi$
$828$	1.20736e12	0.0892692
$829$	−2.43527e13	−1.79082	−0.895410	−	0.445243i	$-0.853117\pi$
$829$	−2.43527e13	−1.79082	−0.895410	+	0.445243i	$0.853117\pi$
$830$	−1.58138e13	−1.15661
$831$	−6.78347e11	−0.0493455
$832$	−1.45506e13	−1.05275
$833$	2.06575e13	1.48654
$834$	−1.56463e13	−1.11986
$835$	5.11383e12	0.364047
$836$	1.97547e13	1.39876
$837$	3.08142e12	0.217013
$838$	4.09790e13	2.87054
$839$	−1.29695e13	−0.903638	−0.451819	−	0.892110i	$-0.649225\pi$
$839$	−1.29695e13	−0.903638	−0.451819	+	0.892110i	$0.649225\pi$
$840$	2.52853e13	1.75231
$841$	5.93997e12	0.409451
$842$	2.71332e13	1.86036
$843$	−2.21878e12	−0.151318
$844$	−1.06113e13	−0.719824
$845$	7.30824e12	0.493126
$846$	1.10955e13	0.744696
$847$	2.08927e13	1.39483
$848$	9.79136e13	6.50222
$849$	−4.02226e12	−0.265696
$850$	2.17133e13	1.42673
$851$	4.52728e11	0.0295906
$852$	−3.35612e13	−2.18203
$853$	−1.28073e13	−0.828298	−0.414149	−	0.910209i	$-0.635921\pi$
$853$	−1.28073e13	−0.828298	−0.414149	+	0.910209i	$0.635921\pi$
$854$	6.15150e13	3.95750
$855$	3.69376e12	0.236385
$856$	−7.85748e13	−5.00209
$857$	4.05538e12	0.256814	0.128407	−	0.991722i	$-0.459014\pi$
$857$	4.05538e12	0.256814	0.128407	+	0.991722i	$0.459014\pi$
$858$	1.18116e12	0.0744072
$859$	2.20178e13	1.37976	0.689881	−	0.723923i	$-0.257663\pi$
$859$	2.20178e13	1.37976	0.689881	+	0.723923i	$0.257663\pi$
$860$	3.17974e12	0.198221
$861$	1.60108e13	0.992887
$862$	−3.46933e13	−2.14024
$863$	4.04656e12	0.248334	0.124167	−	0.992261i	$-0.460374\pi$
$863$	4.04656e12	0.248334	0.124167	+	0.992261i	$0.460374\pi$
$864$	1.61343e13	0.985005
$865$	1.40570e13	0.853732
$866$	1.51296e13	0.914108
$867$	4.09291e11	0.0246006
$868$	8.66717e13	5.18249
$869$	−8.72018e12	−0.518724
$870$	−1.16841e13	−0.691448
$871$	8.32851e11	0.0490327
$872$	−9.61511e13	−5.63158
$873$	7.75599e12	0.451932
$874$	4.36927e12	0.253284
$875$	−2.44582e13	−1.41055
$876$	1.52164e13	0.873061
$877$	−3.26723e13	−1.86501	−0.932504	−	0.361158i	$-0.882381\pi$
$877$	−3.26723e13	−1.86501	−0.932504	+	0.361158i	$0.882381\pi$
$878$	5.92610e13	3.36545
$879$	1.68386e13	0.951386
$880$	1.42096e13	0.798751
$881$	1.87901e13	1.05084	0.525421	−	0.850842i	$-0.323908\pi$
$881$	1.87901e13	1.05084	0.525421	+	0.850842i	$0.323908\pi$
$882$	−1.79641e13	−0.999530
$883$	1.77166e13	0.980746	0.490373	−	0.871513i	$-0.336861\pi$
$883$	1.77166e13	0.980746	0.490373	+	0.871513i	$0.336861\pi$
$884$	−9.64781e12	−0.531366
$885$	−7.01079e11	−0.0384169
$886$	−2.40959e13	−1.31369
$887$	7.96820e11	0.0432219	0.0216110	−	0.999766i	$-0.493120\pi$
$887$	7.96820e11	0.0432219	0.0216110	+	0.999766i	$0.493120\pi$
$888$	1.28053e13	0.691083
$889$	3.86182e12	0.207364
$890$	1.08033e13	0.577166
$891$	−7.27750e11	−0.0386841
$892$	−4.73500e13	−2.50425
$893$	2.98455e13	1.57053
$894$	2.17894e13	1.14084
$895$	−5.41782e12	−0.282242
$896$	1.82523e14	9.46086
$897$	1.94182e11	0.0100148
$898$	1.84028e13	0.944365
$899$	−2.62187e13	−1.33873
$900$	−1.40351e13	−0.713057
$901$	2.80376e13	1.41736
$902$	1.48018e13	0.744534
$903$	−2.45231e12	−0.122738
$904$	−1.31688e14	−6.55824
$905$	−4.75439e12	−0.235600
$906$	1.66829e13	0.822614
$907$	−3.02533e13	−1.48436	−0.742180	−	0.670200i	$-0.766208\pi$
$907$	−3.02533e13	−1.48436	−0.742180	+	0.670200i	$0.766208\pi$
$908$	−3.81997e13	−1.86498
$909$	−1.08335e13	−0.526296
$910$	6.21201e12	0.300293
$911$	−2.80501e13	−1.34928	−0.674639	−	0.738148i	$-0.735701\pi$
$911$	−2.80501e13	−1.34928	−0.674639	+	0.738148i	$0.735701\pi$
$912$	7.51235e13	3.59583
$913$	8.38079e12	0.399178
$914$	−4.64691e13	−2.20245
$915$	7.90391e12	0.372775
$916$	7.44998e13	3.49644
$917$	−4.40538e13	−2.05741
$918$	7.99724e12	0.371662
$919$	−3.79031e13	−1.75289	−0.876445	−	0.481503i	$-0.840091\pi$
$919$	−3.79031e13	−1.75289	−0.876445	+	0.481503i	$0.840091\pi$
$920$	3.84299e12	0.176858
$921$	8.40545e12	0.384940
$922$	1.53493e13	0.699519
$923$	−5.39770e12	−0.244794
$924$	−2.04696e13	−0.923815
$925$	−5.26276e12	−0.236361
$926$	−7.16875e13	−3.20401
$927$	−6.64936e12	−0.295748
$928$	−1.37281e14	−6.07639
$929$	1.77369e12	0.0781281	0.0390640	−	0.999237i	$-0.487562\pi$
$929$	1.77369e12	0.0781281	0.0390640	+	0.999237i	$0.487562\pi$
$930$	1.49822e13	0.656753
$931$	−4.83212e13	−2.10797
$932$	1.09491e13	0.475344
$933$	2.93517e12	0.126814
$934$	−6.66800e13	−2.86704
$935$	4.06894e12	0.174112
$936$	5.49238e12	0.233894
$937$	8.40273e11	0.0356117	0.0178058	−	0.999841i	$-0.494332\pi$
$937$	8.40273e11	0.0356117	0.0178058	+	0.999841i	$0.494332\pi$
$938$	−1.94180e13	−0.819017
$939$	2.43760e12	0.102322
$940$	4.00990e13	1.67517
$941$	2.44547e13	1.01674	0.508370	−	0.861139i	$-0.330248\pi$
$941$	2.44547e13	1.01674	0.508370	+	0.861139i	$0.330248\pi$
$942$	−4.48398e13	−1.85539
$943$	2.43341e12	0.100210
$944$	−1.42585e13	−0.584387
$945$	−3.82743e12	−0.156122
$946$	−2.26713e12	−0.0920377
$947$	2.87343e13	1.16098	0.580491	−	0.814266i	$-0.302861\pi$
$947$	2.87343e13	1.16098	0.580491	+	0.814266i	$0.302861\pi$
$948$	−6.19402e13	−2.49078
$949$	2.44728e12	0.0979458
$950$	−5.07908e13	−2.02316
$951$	−2.29220e13	−0.908742
$952$	1.47256e14	5.81041
$953$	4.58606e13	1.80103	0.900516	−	0.434822i	$-0.143189\pi$
$953$	4.58606e13	1.80103	0.900516	+	0.434822i	$0.143189\pi$
$954$	−2.43819e13	−0.953014
$955$	2.35992e12	0.0918082
$956$	−9.13795e13	−3.53825
$957$	6.19218e12	0.238638
$958$	2.23249e13	0.856338
$959$	−3.58502e12	−0.136870
$960$	4.35893e13	1.65638
$961$	7.17982e12	0.271555
$962$	3.14596e12	0.118431
$963$	1.18938e13	0.445660
$964$	1.34305e13	0.500893
$965$	4.36379e11	0.0161991
$966$	−4.52738e12	−0.167282
$967$	−6.54729e12	−0.240792	−0.120396	−	0.992726i	$-0.538416\pi$
$967$	−6.54729e12	−0.240792	−0.120396	+	0.992726i	$0.538416\pi$
$968$	8.98149e13	3.28783
$969$	2.15116e13	0.783820
$970$	3.77105e13	1.36770
$971$	−7.61211e12	−0.274801	−0.137401	−	0.990516i	$-0.543875\pi$
$971$	−7.61211e12	−0.274801	−0.137401	+	0.990516i	$0.543875\pi$
$972$	−5.16927e12	−0.185751
$973$	4.36096e13	1.55982
$974$	−8.04835e13	−2.86544
$975$	−2.25728e12	−0.0799954
$976$	1.60750e14	5.67055
$977$	−8.95339e12	−0.314385	−0.157192	−	0.987568i	$-0.550244\pi$
$977$	−8.95339e12	−0.314385	−0.157192	+	0.987568i	$0.550244\pi$
$978$	−2.41711e13	−0.844833
$979$	−5.72537e12	−0.199196
$980$	−6.49221e13	−2.24841
$981$	1.45544e13	0.501745
$982$	−9.71594e13	−3.33414
$983$	4.12416e13	1.40878	0.704392	−	0.709811i	$-0.251220\pi$
$983$	4.12416e13	1.40878	0.704392	+	0.709811i	$0.251220\pi$
$984$	6.88283e13	2.34040
$985$	9.66105e12	0.327010
$986$	−6.80458e13	−2.29274
$987$	−3.09255e13	−1.03727
$988$	2.25677e13	0.753498
$989$	−3.72715e11	−0.0123878
$990$	−3.53840e12	−0.117071
$991$	−1.53502e13	−0.505572	−0.252786	−	0.967522i	$-0.581347\pi$
$991$	−1.53502e13	−0.505572	−0.252786	+	0.967522i	$0.581347\pi$
$992$	1.76032e14	5.77149
$993$	1.01826e13	0.332345
$994$	1.25848e14	4.08891
$995$	−2.02651e13	−0.655457
$996$	5.95295e13	1.91675
$997$	−3.08890e13	−0.990092	−0.495046	−	0.868867i	$-0.664849\pi$
$997$	−3.08890e13	−0.990092	−0.495046	+	0.868867i	$0.664849\pi$
$998$	−1.02606e14	−3.27404
$999$	−1.93833e12	−0.0615720

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.1	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.1	✓	21	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-44.6602 q^{2} -81.0000 q^{3} +1482.53 q^{4} -714.289 q^{5} +3617.48 q^{6} -10082.7 q^{7} -43344.2 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-44.6602 q^{2} -81.0000 q^{3} +1482.53 q^{4} -714.289 q^{5} +3617.48 q^{6} -10082.7 q^{7} -43344.2 q^{8} +6561.00 q^{9} +31900.3 q^{10} -16906.1 q^{11} -120085. q^{12} -19313.4 q^{13} +450296. q^{14} +57857.4 q^{15} +1.17670e6 q^{16} +336949. q^{17} -293016. q^{18} -788177. q^{19} -1.05896e6 q^{20} +816700. q^{21} +755028. q^{22} +124126. q^{23} +3.51088e6 q^{24} -1.44292e6 q^{25} +862542. q^{26} -531441. q^{27} -1.49480e7 q^{28} +4.52185e6 q^{29} -2.58392e6 q^{30} -5.79823e6 q^{31} -3.03596e7 q^{32} +1.36939e6 q^{33} -1.50482e7 q^{34} +7.20198e6 q^{35} +9.72690e6 q^{36} +3.64731e6 q^{37} +3.52001e7 q^{38} +1.56439e6 q^{39} +3.09603e7 q^{40} +1.96043e7 q^{41} -3.64740e7 q^{42} -3.00271e6 q^{43} -2.50638e7 q^{44} -4.68645e6 q^{45} -5.54351e6 q^{46} -3.78665e7 q^{47} -9.53129e7 q^{48} +6.13075e7 q^{49} +6.44409e7 q^{50} -2.72929e7 q^{51} -2.86328e7 q^{52} +8.32101e7 q^{53} +2.37343e7 q^{54} +1.20758e7 q^{55} +4.37027e8 q^{56} +6.38424e7 q^{57} -2.01947e8 q^{58} -1.21174e7 q^{59} +8.57756e7 q^{60} +1.36610e8 q^{61} +2.58950e8 q^{62} -6.61527e7 q^{63} +7.53392e8 q^{64} +1.37954e7 q^{65} -6.11572e7 q^{66} -4.31228e7 q^{67} +4.99539e8 q^{68} -1.00542e7 q^{69} -3.21642e8 q^{70} +2.79479e8 q^{71} -2.84381e8 q^{72} -1.26714e8 q^{73} -1.62890e8 q^{74} +1.16876e8 q^{75} -1.16850e9 q^{76} +1.70459e8 q^{77} -6.98659e7 q^{78} +5.15802e8 q^{79} -8.40506e8 q^{80} +4.30467e7 q^{81} -8.75532e8 q^{82} -4.95727e8 q^{83} +1.21078e9 q^{84} -2.40679e8 q^{85} +1.34102e8 q^{86} -3.66270e8 q^{87} +7.32779e8 q^{88} +3.38658e8 q^{89} +2.09298e8 q^{90} +1.94732e8 q^{91} +1.84021e8 q^{92} +4.69656e8 q^{93} +1.69112e9 q^{94} +5.62987e8 q^{95} +2.45912e9 q^{96} +1.18214e9 q^{97} -2.73801e9 q^{98} -1.10921e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) \)	\( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

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