LMFDB - Embedded newform 177.12.a.c.1.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,Mod(1,177)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$135.996742959$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+77.0530 q^{2} -243.000 q^{3} +3889.17 q^{4} +2375.88 q^{5} -18723.9 q^{6} +42674.5 q^{7} +141868. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+77.0530 q^{2} -243.000 q^{3} +3889.17 q^{4} +2375.88 q^{5} -18723.9 q^{6} +42674.5 q^{7} +141868. q^{8} +59049.0 q^{9} +183068. q^{10} -732469. q^{11} -945069. q^{12} +2.06909e6 q^{13} +3.28820e6 q^{14} -577338. q^{15} +2.96633e6 q^{16} +3.22018e6 q^{17} +4.54991e6 q^{18} +7.79943e6 q^{19} +9.24019e6 q^{20} -1.03699e7 q^{21} -5.64390e7 q^{22} +1.03216e7 q^{23} -3.44739e7 q^{24} -4.31833e7 q^{25} +1.59430e8 q^{26} -1.43489e7 q^{27} +1.65969e8 q^{28} +1.21516e8 q^{29} -4.44856e7 q^{30} -4.95083e7 q^{31} -6.19808e7 q^{32} +1.77990e8 q^{33} +2.48125e8 q^{34} +1.01389e8 q^{35} +2.29652e8 q^{36} +5.42012e8 q^{37} +6.00970e8 q^{38} -5.02788e8 q^{39} +3.37060e8 q^{40} -1.04682e9 q^{41} -7.99033e8 q^{42} -8.93436e7 q^{43} -2.84870e9 q^{44} +1.40293e8 q^{45} +7.95311e8 q^{46} +2.62334e9 q^{47} -7.20818e8 q^{48} -1.56210e8 q^{49} -3.32741e9 q^{50} -7.82504e8 q^{51} +8.04704e9 q^{52} +5.24521e9 q^{53} -1.10563e9 q^{54} -1.74026e9 q^{55} +6.05415e9 q^{56} -1.89526e9 q^{57} +9.36320e9 q^{58} -7.14924e8 q^{59} -2.24537e9 q^{60} -4.55782e8 q^{61} -3.81477e9 q^{62} +2.51989e9 q^{63} -1.08508e10 q^{64} +4.91590e9 q^{65} +1.37147e10 q^{66} +1.20932e10 q^{67} +1.25238e10 q^{68} -2.50815e9 q^{69} +7.81236e9 q^{70} +6.37545e9 q^{71} +8.37716e9 q^{72} -6.24653e8 q^{73} +4.17637e10 q^{74} +1.04936e10 q^{75} +3.03333e10 q^{76} -3.12578e10 q^{77} -3.87414e10 q^{78} +6.22898e9 q^{79} +7.04763e9 q^{80} +3.48678e9 q^{81} -8.06607e10 q^{82} -3.66198e10 q^{83} -4.03304e10 q^{84} +7.65075e9 q^{85} -6.88420e9 q^{86} -2.95285e10 q^{87} -1.03914e11 q^{88} -9.06105e10 q^{89} +1.08100e10 q^{90} +8.82974e10 q^{91} +4.01425e10 q^{92} +1.20305e10 q^{93} +2.02136e11 q^{94} +1.85305e10 q^{95} +1.50613e10 q^{96} -3.76534e10 q^{97} -1.20365e10 q^{98} -4.32516e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9} + 140249 q^{10} + 256992 q^{11} - 6352506 q^{12} + 2436978 q^{13} + 5233061 q^{14} + 593406 q^{15} + 28295194 q^{16} - 4565351 q^{17} - 2716254 q^{18} + 33607699 q^{19} - 19208463 q^{20} - 41332599 q^{21} + 79735622 q^{22} + 43966161 q^{23} + 4699863 q^{24} + 406675819 q^{25} + 42605404 q^{26} - 387420489 q^{27} + 635747682 q^{28} - 107217773 q^{29} - 34080507 q^{30} + 570926627 q^{31} + 526569236 q^{32} - 62449056 q^{33} + 129790240 q^{34} + 134356079 q^{35} + 1543658958 q^{36} - 107121371 q^{37} + 208302581 q^{38} - 592185654 q^{39} - 958762162 q^{40} - 1935967559 q^{41} - 1271633823 q^{42} + 1725943824 q^{43} + 196885756 q^{44} - 144197658 q^{45} - 13265966407 q^{46} + 1801256065 q^{47} - 6875732142 q^{48} + 10484289252 q^{49} - 10067682271 q^{50} + 1109380293 q^{51} - 882697024 q^{52} - 6214238922 q^{53} + 660049722 q^{54} + 4460552366 q^{55} + 28328012310 q^{56} - 8166670857 q^{57} + 12220116750 q^{58} - 19302956073 q^{59} + 4667656509 q^{60} + 13167821039 q^{61} - 1162130230 q^{62} + 10043821557 q^{63} - 5337557395 q^{64} - 16849896006 q^{65} - 19375756146 q^{66} - 16856763152 q^{67} - 36171071977 q^{68} - 10683777123 q^{69} - 120177261588 q^{70} - 5198545690 q^{71} - 1142066709 q^{72} - 25075321857 q^{73} - 182979651978 q^{74} - 98822224017 q^{75} - 3501293988 q^{76} - 42787697701 q^{77} - 10353113172 q^{78} + 6850314702 q^{79} - 261464428159 q^{80} + 94143178827 q^{81} - 148881516273 q^{82} + 30908370899 q^{83} - 154486686726 q^{84} - 49419624969 q^{85} - 220725475224 q^{86} + 26053918839 q^{87} - 53091280787 q^{88} + 28988060121 q^{89} + 8281563201 q^{90} + 97120614047 q^{91} + 45374597708 q^{92} - 138735170361 q^{93} + 208966927220 q^{94} - 125253904969 q^{95} - 127956324348 q^{96} + 367722840268 q^{97} - 48265639912 q^{98} + 15175120608 q^{99}+O(q^{100}) \) 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9 + 140249 * q^10 + 256992 * q^11 - 6352506 * q^12 + 2436978 * q^13 + 5233061 * q^14 + 593406 * q^15 + 28295194 * q^16 - 4565351 * q^17 - 2716254 * q^18 + 33607699 * q^19 - 19208463 * q^20 - 41332599 * q^21 + 79735622 * q^22 + 43966161 * q^23 + 4699863 * q^24 + 406675819 * q^25 + 42605404 * q^26 - 387420489 * q^27 + 635747682 * q^28 - 107217773 * q^29 - 34080507 * q^30 + 570926627 * q^31 + 526569236 * q^32 - 62449056 * q^33 + 129790240 * q^34 + 134356079 * q^35 + 1543658958 * q^36 - 107121371 * q^37 + 208302581 * q^38 - 592185654 * q^39 - 958762162 * q^40 - 1935967559 * q^41 - 1271633823 * q^42 + 1725943824 * q^43 + 196885756 * q^44 - 144197658 * q^45 - 13265966407 * q^46 + 1801256065 * q^47 - 6875732142 * q^48 + 10484289252 * q^49 - 10067682271 * q^50 + 1109380293 * q^51 - 882697024 * q^52 - 6214238922 * q^53 + 660049722 * q^54 + 4460552366 * q^55 + 28328012310 * q^56 - 8166670857 * q^57 + 12220116750 * q^58 - 19302956073 * q^59 + 4667656509 * q^60 + 13167821039 * q^61 - 1162130230 * q^62 + 10043821557 * q^63 - 5337557395 * q^64 - 16849896006 * q^65 - 19375756146 * q^66 - 16856763152 * q^67 - 36171071977 * q^68 - 10683777123 * q^69 - 120177261588 * q^70 - 5198545690 * q^71 - 1142066709 * q^72 - 25075321857 * q^73 - 182979651978 * q^74 - 98822224017 * q^75 - 3501293988 * q^76 - 42787697701 * q^77 - 10353113172 * q^78 + 6850314702 * q^79 - 261464428159 * q^80 + 94143178827 * q^81 - 148881516273 * q^82 + 30908370899 * q^83 - 154486686726 * q^84 - 49419624969 * q^85 - 220725475224 * q^86 + 26053918839 * q^87 - 53091280787 * q^88 + 28988060121 * q^89 + 8281563201 * q^90 + 97120614047 * q^91 + 45374597708 * q^92 - 138735170361 * q^93 + 208966927220 * q^94 - 125253904969 * q^95 - 127956324348 * q^96 + 367722840268 * q^97 - 48265639912 * q^98 + 15175120608 * q^99

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 $

$2$	77.0530	1.70265	0.851324	−	0.524640i	$-0.175800\pi$
$2$	77.0530	1.70265	0.851324	+	0.524640i	$0.175800\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	3889.17	1.89901
$5$	2375.88	0.340008	0.170004	−	0.985443i	$-0.445622\pi$
$5$	2375.88	0.340008	0.170004	+	0.985443i	$0.445622\pi$
$6$	−18723.9	−0.983024
$7$	42674.5	0.959687	0.479844	−	0.877354i	$-0.340693\pi$
$7$	42674.5	0.959687	0.479844	+	0.877354i	$0.340693\pi$
$8$	141868.	1.53070
$9$	59049.0	0.333333
$10$	183068.	0.578913
$11$	−732469.	−1.37129	−0.685645	−	0.727936i	$-0.740480\pi$
$11$	−732469.	−1.37129	−0.685645	+	0.727936i	$0.740480\pi$
$12$	−945069.	−1.09639
$13$	2.06909e6	1.54558	0.772788	−	0.634664i	$-0.218861\pi$
$13$	2.06909e6	1.54558	0.772788	+	0.634664i	$0.218861\pi$
$14$	3.28820e6	1.63401
$15$	−577338.	−0.196303
$16$	2.96633e6	0.707228
$17$	3.22018e6	0.550062	0.275031	−	0.961435i	$-0.411312\pi$
$17$	3.22018e6	0.550062	0.275031	+	0.961435i	$0.411312\pi$
$18$	4.54991e6	0.567549
$19$	7.79943e6	0.722633	0.361317	−	0.932443i	$-0.382327\pi$
$19$	7.79943e6	0.722633	0.361317	+	0.932443i	$0.382327\pi$
$20$	9.24019e6	0.645678
$21$	−1.03699e7	−0.554076
$22$	−5.64390e7	−2.33482
$23$	1.03216e7	0.334383	0.167192	−	0.985924i	$-0.446530\pi$
$23$	1.03216e7	0.334383	0.167192	+	0.985924i	$0.446530\pi$
$24$	−3.44739e7	−0.883748
$25$	−4.31833e7	−0.884395
$26$	1.59430e8	2.63157
$27$	−1.43489e7	−0.192450
$28$	1.65969e8	1.82245
$29$	1.21516e8	1.10013	0.550067	−	0.835120i	$-0.314602\pi$
$29$	1.21516e8	1.10013	0.550067	+	0.835120i	$0.314602\pi$
$30$	−4.44856e7	−0.334236
$31$	−4.95083e7	−0.310591	−0.155295	−	0.987868i	$-0.549633\pi$
$31$	−4.95083e7	−0.310591	−0.155295	+	0.987868i	$0.549633\pi$
$32$	−6.19808e7	−0.326537
$33$	1.77990e8	0.791715
$34$	2.48125e8	0.936561
$35$	1.01389e8	0.326301
$36$	2.29652e8	0.633003
$37$	5.42012e8	1.28499	0.642495	−	0.766290i	$-0.277899\pi$
$37$	5.42012e8	1.28499	0.642495	+	0.766290i	$0.277899\pi$
$38$	6.00970e8	1.23039
$39$	−5.02788e8	−0.892339
$40$	3.37060e8	0.520449
$41$	−1.04682e9	−1.41111	−0.705555	−	0.708655i	$-0.749302\pi$
$41$	−1.04682e9	−1.41111	−0.705555	+	0.708655i	$0.749302\pi$
$42$	−7.99033e8	−0.943396
$43$	−8.93436e7	−0.0926802	−0.0463401	−	0.998926i	$-0.514756\pi$
$43$	−8.93436e7	−0.0926802	−0.0463401	+	0.998926i	$0.514756\pi$
$44$	−2.84870e9	−2.60409
$45$	1.40293e8	0.113336
$46$	7.95311e8	0.569336
$47$	2.62334e9	1.66846	0.834232	−	0.551414i	$-0.185912\pi$
$47$	2.62334e9	1.66846	0.834232	+	0.551414i	$0.185912\pi$
$48$	−7.20818e8	−0.408318
$49$	−1.56210e8	−0.0790006
$50$	−3.32741e9	−1.50581
$51$	−7.82504e8	−0.317578
$52$	8.04704e9	2.93506
$53$	5.24521e9	1.72284	0.861422	−	0.507890i	$-0.169574\pi$
$53$	5.24521e9	1.72284	0.861422	+	0.507890i	$0.169574\pi$
$54$	−1.10563e9	−0.327675
$55$	−1.74026e9	−0.466249
$56$	6.05415e9	1.46899
$57$	−1.89526e9	−0.417212
$58$	9.36320e9	1.87314
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	−2.24537e9	−0.372782
$61$	−4.55782e8	−0.0690944	−0.0345472	−	0.999403i	$-0.510999\pi$
$61$	−4.55782e8	−0.0690944	−0.0345472	+	0.999403i	$0.510999\pi$
$62$	−3.81477e9	−0.528827
$63$	2.51989e9	0.319896
$64$	−1.08508e10	−1.26321
$65$	4.91590e9	0.525508
$66$	1.37147e10	1.34801
$67$	1.20932e10	1.09429	0.547143	−	0.837039i	$-0.315715\pi$
$67$	1.20932e10	1.09429	0.547143	+	0.837039i	$0.315715\pi$
$68$	1.25238e10	1.04457
$69$	−2.50815e9	−0.193056
$70$	7.81236e9	0.555576
$71$	6.37545e9	0.419363	0.209681	−	0.977770i	$-0.432757\pi$
$71$	6.37545e9	0.419363	0.209681	+	0.977770i	$0.432757\pi$
$72$	8.37716e9	0.510232
$73$	−6.24653e8	−0.0352666	−0.0176333	−	0.999845i	$-0.505613\pi$
$73$	−6.24653e8	−0.0352666	−0.0176333	+	0.999845i	$0.505613\pi$
$74$	4.17637e10	2.18789
$75$	1.04936e10	0.510606
$76$	3.03333e10	1.37229
$77$	−3.12578e10	−1.31601
$78$	−3.87414e10	−1.51934
$79$	6.22898e9	0.227755	0.113878	−	0.993495i	$-0.463673\pi$
$79$	6.22898e9	0.227755	0.113878	+	0.993495i	$0.463673\pi$
$80$	7.04763e9	0.240463
$81$	3.48678e9	0.111111
$82$	−8.06607e10	−2.40262
$83$	−3.66198e10	−1.02044	−0.510218	−	0.860045i	$-0.670435\pi$
$83$	−3.66198e10	−1.02044	−0.510218	+	0.860045i	$0.670435\pi$
$84$	−4.03304e10	−1.05219
$85$	7.65075e9	0.187025
$86$	−6.88420e9	−0.157802
$87$	−2.95285e10	−0.635163
$88$	−1.03914e11	−2.09903
$89$	−9.06105e10	−1.72002	−0.860010	−	0.510277i	$-0.829543\pi$
$89$	−9.06105e10	−1.72002	−0.860010	+	0.510277i	$0.829543\pi$
$90$	1.08100e10	0.192971
$91$	8.82974e10	1.48327
$92$	4.01425e10	0.634997
$93$	1.20305e10	0.179320
$94$	2.02136e11	2.84081
$95$	1.85305e10	0.245701
$96$	1.50613e10	0.188526
$97$	−3.76534e10	−0.445204	−0.222602	−	0.974909i	$-0.571455\pi$
$97$	−3.76534e10	−0.445204	−0.222602	+	0.974909i	$0.571455\pi$
$98$	−1.20365e10	−0.134510
$99$	−4.32516e10	−0.457097
$100$	−1.67947e11	−1.67947
$101$	1.77528e11	1.68073	0.840367	−	0.542018i	$-0.182340\pi$
$101$	1.77528e11	1.68073	0.840367	+	0.542018i	$0.182340\pi$
$102$	−6.02943e10	−0.540724
$103$	1.51486e11	1.28756	0.643779	−	0.765212i	$-0.277366\pi$
$103$	1.51486e11	1.28756	0.643779	+	0.765212i	$0.277366\pi$
$104$	2.93537e11	2.36581
$105$	−2.46376e10	−0.188390
$106$	4.04160e11	2.93340
$107$	3.17315e10	0.218716	0.109358	−	0.994002i	$-0.465121\pi$
$107$	3.17315e10	0.218716	0.109358	+	0.994002i	$0.465121\pi$
$108$	−5.58054e10	−0.365465
$109$	1.81417e11	1.12936	0.564681	−	0.825309i	$-0.308999\pi$
$109$	1.81417e11	1.12936	0.564681	+	0.825309i	$0.308999\pi$
$110$	−1.34092e11	−0.793858
$111$	−1.31709e11	−0.741889
$112$	1.26587e11	0.678717
$113$	3.32494e11	1.69767	0.848833	−	0.528661i	$-0.177306\pi$
$113$	3.32494e11	1.69767	0.848833	+	0.528661i	$0.177306\pi$
$114$	−1.46036e11	−0.710366
$115$	2.45229e10	0.113693
$116$	4.72598e11	2.08917
$117$	1.22178e11	0.515192
$118$	−5.50871e10	−0.221666
$119$	1.37420e11	0.527887
$120$	−8.19057e10	−0.300481
$121$	2.51199e11	0.880438
$122$	−3.51194e10	−0.117643
$123$	2.54377e11	0.814705
$124$	−1.92546e11	−0.589815
$125$	−2.18608e11	−0.640709
$126$	1.94165e11	0.544670
$127$	4.36614e11	1.17267	0.586337	−	0.810067i	$-0.300569\pi$
$127$	4.36614e11	1.17267	0.586337	+	0.810067i	$0.300569\pi$
$128$	−7.09154e11	−1.82426
$129$	2.17105e10	0.0535089
$130$	3.78785e11	0.894755
$131$	3.86989e11	0.876409	0.438204	−	0.898875i	$-0.355615\pi$
$131$	3.86989e11	0.876409	0.438204	+	0.898875i	$0.355615\pi$
$132$	6.92233e11	1.50347
$133$	3.32837e11	0.693502
$134$	9.31820e11	1.86318
$135$	−3.40912e10	−0.0654345
$136$	4.56840e11	0.841978
$137$	−7.95555e11	−1.40834	−0.704169	−	0.710032i	$-0.748680\pi$
$137$	−7.95555e11	−1.40834	−0.704169	+	0.710032i	$0.748680\pi$
$138$	−1.93261e11	−0.328707
$139$	8.45523e11	1.38212	0.691058	−	0.722800i	$-0.257145\pi$
$139$	8.45523e11	1.38212	0.691058	+	0.722800i	$0.257145\pi$
$140$	3.94321e11	0.619649
$141$	−6.37472e11	−0.963288
$142$	4.91248e11	0.714027
$143$	−1.51554e12	−2.11943
$144$	1.75159e11	0.235743
$145$	2.88708e11	0.374054
$146$	−4.81314e10	−0.0600465
$147$	3.79590e10	0.0456110
$148$	2.10798e12	2.44021
$149$	−7.04304e11	−0.785662	−0.392831	−	0.919611i	$-0.628504\pi$
$149$	−7.04304e11	−0.785662	−0.392831	+	0.919611i	$0.628504\pi$
$150$	8.08560e11	0.869381
$151$	2.44834e11	0.253804	0.126902	−	0.991915i	$-0.459497\pi$
$151$	2.44834e11	0.253804	0.126902	+	0.991915i	$0.459497\pi$
$152$	1.10649e12	1.10613
$153$	1.90149e11	0.183354
$154$	−2.40851e12	−2.24070
$155$	−1.17626e11	−0.105603
$156$	−1.95543e12	−1.69456
$157$	8.00083e11	0.669402	0.334701	−	0.942324i	$-0.391365\pi$
$157$	8.00083e11	0.669402	0.334701	+	0.942324i	$0.391365\pi$
$158$	4.79962e11	0.387787
$159$	−1.27459e12	−0.994685
$160$	−1.47259e11	−0.111025
$161$	4.40470e11	0.320903
$162$	2.68667e11	0.189183
$163$	5.34959e11	0.364157	0.182079	−	0.983284i	$-0.441717\pi$
$163$	5.34959e11	0.364157	0.182079	+	0.983284i	$0.441717\pi$
$164$	−4.07126e12	−2.67971
$165$	4.22882e11	0.269189
$166$	−2.82166e12	−1.73744
$167$	6.18995e11	0.368762	0.184381	−	0.982855i	$-0.440972\pi$
$167$	6.18995e11	0.368762	0.184381	+	0.982855i	$0.440972\pi$
$168$	−1.47116e12	−0.848122
$169$	2.48896e12	1.38881
$170$	5.89514e11	0.318438
$171$	4.60548e11	0.240878
$172$	−3.47473e11	−0.176001
$173$	−3.64535e12	−1.78848	−0.894242	−	0.447583i	$-0.852285\pi$
$173$	−3.64535e12	−1.78848	−0.894242	+	0.447583i	$0.852285\pi$
$174$	−2.27526e12	−1.08146
$175$	−1.84283e12	−0.848742
$176$	−2.17274e12	−0.969814
$177$	1.73727e11	0.0751646
$178$	−6.98182e12	−2.92859
$179$	−8.82844e11	−0.359081	−0.179541	−	0.983751i	$-0.557461\pi$
$179$	−8.82844e11	−0.359081	−0.179541	+	0.983751i	$0.557461\pi$
$180$	5.45624e11	0.215226
$181$	1.46190e12	0.559352	0.279676	−	0.960094i	$-0.409773\pi$
$181$	1.46190e12	0.559352	0.279676	+	0.960094i	$0.409773\pi$
$182$	6.80358e12	2.52549
$183$	1.10755e11	0.0398917
$184$	1.46430e12	0.511839
$185$	1.28775e12	0.436906
$186$	9.26988e11	0.305318
$187$	−2.35868e12	−0.754294
$188$	1.02026e13	3.16843
$189$	−6.12333e11	−0.184692
$190$	1.42783e12	0.418342
$191$	−1.86760e12	−0.531618	−0.265809	−	0.964026i	$-0.585639\pi$
$191$	−1.86760e12	−0.531618	−0.265809	+	0.964026i	$0.585639\pi$
$192$	2.63676e12	0.729312
$193$	−6.02799e12	−1.62034	−0.810172	−	0.586192i	$-0.800626\pi$
$193$	−6.02799e12	−1.62034	−0.810172	+	0.586192i	$0.800626\pi$
$194$	−2.90131e12	−0.758026
$195$	−1.19456e12	−0.303402
$196$	−6.07528e11	−0.150023
$197$	−5.24462e11	−0.125936	−0.0629680	−	0.998016i	$-0.520057\pi$
$197$	−5.24462e11	−0.125936	−0.0629680	+	0.998016i	$0.520057\pi$
$198$	−3.33266e12	−0.778275
$199$	2.41836e12	0.549324	0.274662	−	0.961541i	$-0.411434\pi$
$199$	2.41836e12	0.549324	0.274662	+	0.961541i	$0.411434\pi$
$200$	−6.12633e12	−1.35374
$201$	−2.93866e12	−0.631787
$202$	1.36791e13	2.86170
$203$	5.18565e12	1.05578
$204$	−3.04329e12	−0.603084
$205$	−2.48711e12	−0.479788
$206$	1.16724e13	2.19226
$207$	6.09481e11	0.111461
$208$	6.13759e12	1.09307
$209$	−5.71284e12	−0.990940
$210$	−1.89840e12	−0.320762
$211$	−3.30462e12	−0.543962	−0.271981	−	0.962303i	$-0.587679\pi$
$211$	−3.30462e12	−0.543962	−0.271981	+	0.962303i	$0.587679\pi$
$212$	2.03995e13	3.27170
$213$	−1.54923e12	−0.242119
$214$	2.44501e12	0.372396
$215$	−2.12269e11	−0.0315120
$216$	−2.03565e12	−0.294583
$217$	−2.11274e12	−0.298070
$218$	1.39788e13	1.92290
$219$	1.51791e11	0.0203612
$220$	−6.76815e12	−0.885412
$221$	6.66284e12	0.850162
$222$	−1.01486e13	−1.26318
$223$	−1.53856e13	−1.86827	−0.934133	−	0.356924i	$-0.883825\pi$
$223$	−1.53856e13	−1.86827	−0.934133	+	0.356924i	$0.883825\pi$
$224$	−2.64500e12	−0.313373
$225$	−2.54993e12	−0.294798
$226$	2.56197e13	2.89053
$227$	−4.76918e12	−0.525172	−0.262586	−	0.964909i	$-0.584575\pi$
$227$	−4.76918e12	−0.525172	−0.262586	+	0.964909i	$0.584575\pi$
$228$	−7.37099e12	−0.792290
$229$	−1.33708e13	−1.40302	−0.701509	−	0.712660i	$-0.747490\pi$
$229$	−1.33708e13	−1.40302	−0.701509	+	0.712660i	$0.747490\pi$
$230$	1.88956e12	0.193579
$231$	7.59564e12	0.759799
$232$	1.72393e13	1.68397
$233$	−1.84437e13	−1.75950	−0.879750	−	0.475436i	$-0.842290\pi$
$233$	−1.84437e13	−1.75950	−0.879750	+	0.475436i	$0.842290\pi$
$234$	9.41415e12	0.877191
$235$	6.23273e12	0.567290
$236$	−2.78046e12	−0.247230
$237$	−1.51364e12	−0.131494
$238$	1.05886e13	0.898806
$239$	1.32861e13	1.10207	0.551035	−	0.834482i	$-0.314233\pi$
$239$	1.32861e13	1.10207	0.551035	+	0.834482i	$0.314233\pi$
$240$	−1.71257e12	−0.138831
$241$	1.95983e12	0.155283	0.0776415	−	0.996981i	$-0.475261\pi$
$241$	1.95983e12	0.155283	0.0776415	+	0.996981i	$0.475261\pi$
$242$	1.93557e13	1.49907
$243$	−8.47289e11	−0.0641500
$244$	−1.77261e12	−0.131211
$245$	−3.71136e11	−0.0268608
$246$	1.96005e13	1.38715
$247$	1.61377e13	1.11688
$248$	−7.02364e12	−0.475421
$249$	8.89860e12	0.589149
$250$	−1.68444e13	−1.09090
$251$	9.88980e12	0.626588	0.313294	−	0.949656i	$-0.398567\pi$
$251$	9.88980e12	0.626588	0.313294	+	0.949656i	$0.398567\pi$
$252$	9.80028e12	0.607485
$253$	−7.56026e12	−0.458536
$254$	3.36425e13	1.99665
$255$	−1.85913e12	−0.107979
$256$	−3.24200e13	−1.84286
$257$	−6.74155e12	−0.375083	−0.187542	−	0.982257i	$-0.560052\pi$
$257$	−6.74155e12	−0.375083	−0.187542	+	0.982257i	$0.560052\pi$
$258$	1.67286e12	0.0911069
$259$	2.31301e13	1.23319
$260$	1.91188e13	0.997944
$261$	7.17542e12	0.366711
$262$	2.98187e13	1.49222
$263$	2.50030e13	1.22528	0.612641	−	0.790362i	$-0.290107\pi$
$263$	2.50030e13	1.22528	0.612641	+	0.790362i	$0.290107\pi$
$264$	2.52511e13	1.21188
$265$	1.24620e13	0.585780
$266$	2.56461e13	1.18079
$267$	2.20184e13	0.993054
$268$	4.70327e13	2.07806
$269$	−3.56217e13	−1.54197	−0.770987	−	0.636851i	$-0.780236\pi$
$269$	−3.56217e13	−1.54197	−0.770987	+	0.636851i	$0.780236\pi$
$270$	−2.62683e12	−0.111412
$271$	−2.05382e13	−0.853555	−0.426777	−	0.904357i	$-0.640351\pi$
$271$	−2.05382e13	−0.853555	−0.426777	+	0.904357i	$0.640351\pi$
$272$	9.55212e12	0.389019
$273$	−2.14563e13	−0.856366
$274$	−6.12999e13	−2.39790
$275$	3.16305e13	1.21276
$276$	−9.75463e12	−0.366615
$277$	−3.66345e13	−1.34974	−0.674872	−	0.737935i	$-0.735801\pi$
$277$	−3.66345e13	−1.34974	−0.674872	+	0.737935i	$0.735801\pi$
$278$	6.51502e13	2.35326
$279$	−2.92342e12	−0.103530
$280$	1.43839e13	0.499468
$281$	−3.90849e13	−1.33084	−0.665418	−	0.746471i	$-0.731747\pi$
$281$	−3.90849e13	−1.33084	−0.665418	+	0.746471i	$0.731747\pi$
$282$	−4.91192e13	−1.64014
$283$	4.31109e13	1.41176	0.705882	−	0.708330i	$-0.250551\pi$
$283$	4.31109e13	1.41176	0.705882	+	0.708330i	$0.250551\pi$
$284$	2.47952e13	0.796374
$285$	−4.50290e12	−0.141855
$286$	−1.16777e14	−3.60865
$287$	−4.46726e13	−1.35422
$288$	−3.65991e12	−0.108846
$289$	−2.39023e13	−0.697432
$290$	2.22458e13	0.636882
$291$	9.14977e12	0.257039
$292$	−2.42938e12	−0.0669715
$293$	−3.77230e13	−1.02055	−0.510276	−	0.860011i	$-0.670457\pi$
$293$	−3.77230e13	−1.02055	−0.510276	+	0.860011i	$0.670457\pi$
$294$	2.92486e12	0.0776595
$295$	−1.69857e12	−0.0442652
$296$	7.68941e13	1.96693
$297$	1.05101e13	0.263905
$298$	−5.42688e13	−1.33771
$299$	2.13563e13	0.516815
$300$	4.08112e13	0.969645
$301$	−3.81270e12	−0.0889440
$302$	1.88652e13	0.432138
$303$	−4.31393e13	−0.970372
$304$	2.31357e13	0.511066
$305$	−1.08288e12	−0.0234926
$306$	1.46515e13	0.312187
$307$	−3.58818e12	−0.0750954	−0.0375477	−	0.999295i	$-0.511955\pi$
$307$	−3.58818e12	−0.0750954	−0.0375477	+	0.999295i	$0.511955\pi$
$308$	−1.21567e14	−2.49912
$309$	−3.68110e13	−0.743371
$310$	−9.06341e12	−0.179805
$311$	1.99749e13	0.389316	0.194658	−	0.980871i	$-0.437640\pi$
$311$	1.99749e13	0.389316	0.194658	+	0.980871i	$0.437640\pi$
$312$	−7.13295e13	−1.36590
$313$	−3.09733e13	−0.582765	−0.291383	−	0.956607i	$-0.594115\pi$
$313$	−3.09733e13	−0.582765	−0.291383	+	0.956607i	$0.594115\pi$
$314$	6.16488e13	1.13976
$315$	5.98694e12	0.108767
$316$	2.42256e13	0.432509
$317$	9.64172e13	1.69172	0.845860	−	0.533405i	$-0.179088\pi$
$317$	9.64172e13	1.69172	0.845860	+	0.533405i	$0.179088\pi$
$318$	−9.82108e13	−1.69360
$319$	−8.90069e13	−1.50860
$320$	−2.57803e13	−0.429499
$321$	−7.71076e12	−0.126276
$322$	3.39395e13	0.546385
$323$	2.51156e13	0.397493
$324$	1.35607e13	0.211001
$325$	−8.93501e13	−1.36690
$326$	4.12202e13	0.620031
$327$	−4.40844e13	−0.652037
$328$	−1.48510e14	−2.15998
$329$	1.11950e14	1.60120
$330$	3.25843e13	0.458334
$331$	−4.66348e13	−0.645144	−0.322572	−	0.946545i	$-0.604547\pi$
$331$	−4.66348e13	−0.645144	−0.322572	+	0.946545i	$0.604547\pi$
$332$	−1.42420e14	−1.93782
$333$	3.20053e13	0.428330
$334$	4.76954e13	0.627872
$335$	2.87320e13	0.372066
$336$	−3.07606e13	−0.391858
$337$	3.71059e13	0.465027	0.232514	−	0.972593i	$-0.425305\pi$
$337$	3.71059e13	0.465027	0.232514	+	0.972593i	$0.425305\pi$
$338$	1.91782e14	2.36465
$339$	−8.07960e13	−0.980148
$340$	2.97551e13	0.355163
$341$	3.62633e13	0.425910
$342$	3.54867e13	0.410130
$343$	−9.10477e13	−1.03550
$344$	−1.26750e13	−0.141865
$345$	−5.95905e12	−0.0656406
$346$	−2.80885e14	−3.04516
$347$	6.27308e12	0.0669374	0.0334687	−	0.999440i	$-0.489345\pi$
$347$	6.27308e12	0.0669374	0.0334687	+	0.999440i	$0.489345\pi$
$348$	−1.14841e14	−1.20618
$349$	1.11153e14	1.14917	0.574583	−	0.818446i	$-0.305164\pi$
$349$	1.11153e14	1.14917	0.574583	+	0.818446i	$0.305164\pi$
$350$	−1.41996e14	−1.44511
$351$	−2.96892e13	−0.297446
$352$	4.53990e13	0.447777
$353$	−4.37056e13	−0.424401	−0.212201	−	0.977226i	$-0.568063\pi$
$353$	−4.37056e13	−0.424401	−0.212201	+	0.977226i	$0.568063\pi$
$354$	1.33862e13	0.127979
$355$	1.51473e13	0.142587
$356$	−3.52400e14	−3.26634
$357$	−3.33930e13	−0.304776
$358$	−6.80258e13	−0.611388
$359$	−1.52753e14	−1.35198	−0.675988	−	0.736912i	$-0.736283\pi$
$359$	−1.52753e14	−1.35198	−0.675988	+	0.736912i	$0.736283\pi$
$360$	1.99031e13	0.173483
$361$	−5.56592e13	−0.477801
$362$	1.12644e14	0.952380
$363$	−6.10414e13	−0.508321
$364$	3.43404e14	2.81674
$365$	−1.48410e12	−0.0119909
$366$	8.53400e12	0.0679214
$367$	8.70365e13	0.682399	0.341199	−	0.939991i	$-0.389167\pi$
$367$	8.70365e13	0.682399	0.341199	+	0.939991i	$0.389167\pi$
$368$	3.06173e13	0.236485
$369$	−6.18137e13	−0.470370
$370$	9.92254e13	0.743898
$371$	2.23837e14	1.65339
$372$	4.67888e13	0.340530
$373$	−1.28593e14	−0.922184	−0.461092	−	0.887352i	$-0.652542\pi$
$373$	−1.28593e14	−0.922184	−0.461092	+	0.887352i	$0.652542\pi$
$374$	−1.81744e14	−1.28430
$375$	5.31217e13	0.369913
$376$	3.72168e14	2.55391
$377$	2.51428e14	1.70034
$378$	−4.71821e13	−0.314465
$379$	−5.54019e13	−0.363923	−0.181961	−	0.983306i	$-0.558245\pi$
$379$	−5.54019e13	−0.363923	−0.181961	+	0.983306i	$0.558245\pi$
$380$	7.20682e13	0.466588
$381$	−1.06097e14	−0.677044
$382$	−1.43904e14	−0.905158
$383$	−2.35468e14	−1.45995	−0.729975	−	0.683474i	$-0.760468\pi$
$383$	−2.35468e14	−1.45995	−0.729975	+	0.683474i	$0.760468\pi$
$384$	1.72324e14	1.05323
$385$	−7.42646e13	−0.447453
$386$	−4.64475e14	−2.75888
$387$	−5.27565e12	−0.0308934
$388$	−1.46440e14	−0.845448
$389$	−4.34876e13	−0.247538	−0.123769	−	0.992311i	$-0.539498\pi$
$389$	−4.34876e13	−0.247538	−0.123769	+	0.992311i	$0.539498\pi$
$390$	−9.20447e13	−0.516587
$391$	3.32375e13	0.183931
$392$	−2.21612e13	−0.120926
$393$	−9.40384e13	−0.505995
$394$	−4.04114e13	−0.214425
$395$	1.47993e13	0.0774385
$396$	−1.68213e14	−0.868031
$397$	5.00931e13	0.254936	0.127468	−	0.991843i	$-0.459315\pi$
$397$	5.00931e13	0.254936	0.127468	+	0.991843i	$0.459315\pi$
$398$	1.86342e14	0.935305
$399$	−8.08794e13	−0.400393
$400$	−1.28096e14	−0.625468
$401$	−4.46932e13	−0.215252	−0.107626	−	0.994191i	$-0.534325\pi$
$401$	−4.46932e13	−0.215252	−0.107626	+	0.994191i	$0.534325\pi$
$402$	−2.26432e14	−1.07571
$403$	−1.02437e14	−0.480042
$404$	6.90436e14	3.19173
$405$	8.28417e12	0.0377786
$406$	3.99570e14	1.79763
$407$	−3.97007e14	−1.76209
$408$	−1.11012e14	−0.486116
$409$	−2.02690e14	−0.875698	−0.437849	−	0.899049i	$-0.644260\pi$
$409$	−2.02690e14	−0.875698	−0.437849	+	0.899049i	$0.644260\pi$
$410$	−1.91640e14	−0.816910
$411$	1.93320e14	0.813105
$412$	5.89153e14	2.44508
$413$	−3.05091e13	−0.124941
$414$	4.69623e13	0.189779
$415$	−8.70040e13	−0.346956
$416$	−1.28244e14	−0.504688
$417$	−2.05462e14	−0.797965
$418$	−4.40192e14	−1.68722
$419$	−4.68030e14	−1.77050	−0.885252	−	0.465111i	$-0.846014\pi$
$419$	−4.68030e14	−1.77050	−0.885252	+	0.465111i	$0.846014\pi$
$420$	−9.58199e13	−0.357754
$421$	3.96010e14	1.45933	0.729667	−	0.683803i	$-0.239675\pi$
$421$	3.96010e14	1.45933	0.729667	+	0.683803i	$0.239675\pi$
$422$	−2.54631e14	−0.926176
$423$	1.54906e14	0.556154
$424$	7.44127e14	2.63715
$425$	−1.39058e14	−0.486472
$426$	−1.19373e14	−0.412244
$427$	−1.94503e13	−0.0663090
$428$	1.23409e14	0.415343
$429$	3.68277e14	1.22366
$430$	−1.63560e13	−0.0536538
$431$	−4.43621e14	−1.43677	−0.718384	−	0.695647i	$-0.755118\pi$
$431$	−4.43621e14	−1.43677	−0.718384	+	0.695647i	$0.755118\pi$
$432$	−4.25636e13	−0.136106
$433$	1.38761e13	0.0438110	0.0219055	−	0.999760i	$-0.493027\pi$
$433$	1.38761e13	0.0438110	0.0219055	+	0.999760i	$0.493027\pi$
$434$	−1.62793e14	−0.507509
$435$	−7.01560e13	−0.215960
$436$	7.05563e14	2.14467
$437$	8.05026e13	0.241636
$438$	1.16959e13	0.0346679
$439$	2.82390e14	0.826599	0.413300	−	0.910595i	$-0.364376\pi$
$439$	2.82390e14	0.826599	0.413300	+	0.910595i	$0.364376\pi$
$440$	−2.46886e14	−0.713686
$441$	−9.22405e12	−0.0263335
$442$	5.13392e14	1.44753
$443$	−4.37060e14	−1.21708	−0.608542	−	0.793522i	$-0.708245\pi$
$443$	−4.37060e14	−1.21708	−0.608542	+	0.793522i	$0.708245\pi$
$444$	−5.12239e14	−1.40885
$445$	−2.15279e14	−0.584820
$446$	−1.18551e15	−3.18100
$447$	1.71146e14	0.453602
$448$	−4.63055e14	−1.21228
$449$	4.37829e14	1.13227	0.566134	−	0.824313i	$-0.308438\pi$
$449$	4.37829e14	1.13227	0.566134	+	0.824313i	$0.308438\pi$
$450$	−1.96480e14	−0.501938
$451$	7.66763e14	1.93504
$452$	1.29313e15	3.22388
$453$	−5.94946e13	−0.146534
$454$	−3.67480e14	−0.894183
$455$	2.09784e14	0.504323
$456$	−2.68877e14	−0.638626
$457$	−5.70437e14	−1.33865	−0.669327	−	0.742968i	$-0.733417\pi$
$457$	−5.70437e14	−1.33865	−0.669327	+	0.742968i	$0.733417\pi$
$458$	−1.03026e15	−2.38885
$459$	−4.62061e13	−0.105859
$460$	9.53736e13	0.215904
$461$	5.69806e14	1.27459	0.637297	−	0.770618i	$-0.280053\pi$
$461$	5.69806e14	1.27459	0.637297	+	0.770618i	$0.280053\pi$
$462$	5.85267e14	1.29367
$463$	5.57595e14	1.21793	0.608966	−	0.793196i	$-0.291584\pi$
$463$	5.57595e14	1.21793	0.608966	+	0.793196i	$0.291584\pi$
$464$	3.60457e14	0.778045
$465$	2.85830e13	0.0609701
$466$	−1.42114e15	−2.99581
$467$	−3.01658e14	−0.628452	−0.314226	−	0.949348i	$-0.601745\pi$
$467$	−3.01658e14	−0.628452	−0.314226	+	0.949348i	$0.601745\pi$
$468$	4.75170e14	0.978355
$469$	5.16073e14	1.05017
$470$	4.80251e14	0.965895
$471$	−1.94420e14	−0.386479
$472$	−1.01425e14	−0.199280
$473$	6.54414e13	0.127091
$474$	−1.16631e14	−0.223889
$475$	−3.36805e14	−0.639093
$476$	5.34449e14	1.00246
$477$	3.09725e14	0.574281
$478$	1.02374e15	1.87644
$479$	−2.92239e14	−0.529533	−0.264767	−	0.964313i	$-0.585295\pi$
$479$	−2.92239e14	−0.529533	−0.264767	+	0.964313i	$0.585295\pi$
$480$	3.57839e13	0.0641004
$481$	1.12147e15	1.98605
$482$	1.51011e14	0.264392
$483$	−1.07034e14	−0.185273
$484$	9.76956e14	1.67196
$485$	−8.94598e13	−0.151373
$486$	−6.52862e13	−0.109225
$487$	8.37285e14	1.38505	0.692523	−	0.721396i	$-0.256499\pi$
$487$	8.37285e14	1.38505	0.692523	+	0.721396i	$0.256499\pi$
$488$	−6.46608e13	−0.105763
$489$	−1.29995e14	−0.210246
$490$	−2.85971e13	−0.0457345
$491$	3.30040e14	0.521937	0.260968	−	0.965347i	$-0.415958\pi$
$491$	3.30040e14	0.521937	0.260968	+	0.965347i	$0.415958\pi$
$492$	9.89317e14	1.54713
$493$	3.91305e14	0.605142
$494$	1.24346e15	1.90166
$495$	−1.02760e14	−0.155416
$496$	−1.46858e14	−0.219659
$497$	2.72069e14	0.402457
$498$	6.85664e14	1.00311
$499$	−8.71259e14	−1.26065	−0.630325	−	0.776332i	$-0.717078\pi$
$499$	−8.71259e14	−1.26065	−0.630325	+	0.776332i	$0.717078\pi$
$500$	−8.50203e14	−1.21671
$501$	−1.50416e14	−0.212905
$502$	7.62039e14	1.06686
$503$	−5.40802e14	−0.748884	−0.374442	−	0.927250i	$-0.622166\pi$
$503$	−5.40802e14	−0.748884	−0.374442	+	0.927250i	$0.622166\pi$
$504$	3.57491e14	0.489663
$505$	4.21784e14	0.571462
$506$	−5.82541e14	−0.780726
$507$	−6.04818e14	−0.801828
$508$	1.69807e15	2.22692
$509$	4.27989e14	0.555246	0.277623	−	0.960690i	$-0.410453\pi$
$509$	4.27989e14	0.555246	0.277623	+	0.960690i	$0.410453\pi$
$510$	−1.43252e14	−0.183850
$511$	−2.66568e13	−0.0338449
$512$	−1.04571e15	−1.31349
$513$	−1.11913e14	−0.139071
$514$	−5.19457e14	−0.638634
$515$	3.59911e14	0.437779
$516$	8.44358e13	0.101614
$517$	−1.92152e15	−2.28795
$518$	1.78225e15	2.09969
$519$	8.85819e14	1.03258
$520$	6.97408e14	0.804393
$521$	1.19741e14	0.136658	0.0683291	−	0.997663i	$-0.478233\pi$
$521$	1.19741e14	0.136658	0.0683291	+	0.997663i	$0.478233\pi$
$522$	5.52888e14	0.624380
$523$	−1.02445e15	−1.14480	−0.572401	−	0.819974i	$-0.693988\pi$
$523$	−1.02445e15	−1.14480	−0.572401	+	0.819974i	$0.693988\pi$
$524$	1.50507e15	1.66431
$525$	4.47808e14	0.490022
$526$	1.92656e15	2.08622
$527$	−1.59426e14	−0.170844
$528$	5.27977e14	0.559923
$529$	−8.46274e14	−0.888188
$530$	9.60233e14	0.997377
$531$	−4.22156e13	−0.0433963
$532$	1.29446e15	1.31697
$533$	−2.16596e15	−2.18098
$534$	1.69658e15	1.69082
$535$	7.53902e13	0.0743651
$536$	1.71564e15	1.67502
$537$	2.14531e14	0.207316
$538$	−2.74476e15	−2.62544
$539$	1.14419e14	0.108333
$540$	−1.32587e14	−0.124261
$541$	1.03477e15	0.959974	0.479987	−	0.877276i	$-0.340641\pi$
$541$	1.03477e15	0.959974	0.479987	+	0.877276i	$0.340641\pi$
$542$	−1.58253e15	−1.45330
$543$	−3.55242e14	−0.322942
$544$	−1.99590e14	−0.179616
$545$	4.31025e14	0.383992
$546$	−1.65327e15	−1.45809
$547$	2.36278e14	0.206297	0.103149	−	0.994666i	$-0.467108\pi$
$547$	2.36278e14	0.206297	0.103149	+	0.994666i	$0.467108\pi$
$548$	−3.09405e15	−2.67445
$549$	−2.69134e13	−0.0230315
$550$	2.43722e15	2.06491
$551$	9.47758e14	0.794993
$552$	−3.55826e14	−0.295510
$553$	2.65819e14	0.218574
$554$	−2.82280e15	−2.29814
$555$	−3.12924e14	−0.252248
$556$	3.28839e15	2.62465
$557$	1.31673e15	1.04062	0.520311	−	0.853977i	$-0.325816\pi$
$557$	1.31673e15	1.04062	0.520311	+	0.853977i	$0.325816\pi$
$558$	−2.25258e14	−0.176276
$559$	−1.84860e14	−0.143244
$560$	3.00754e14	0.230769
$561$	5.73160e14	0.435492
$562$	−3.01161e15	−2.26595
$563$	−8.45563e14	−0.630013	−0.315007	−	0.949089i	$-0.602007\pi$
$563$	−8.45563e14	−0.630013	−0.315007	+	0.949089i	$0.602007\pi$
$564$	−2.47924e15	−1.82929
$565$	7.89964e14	0.577220
$566$	3.32183e15	2.40374
$567$	1.48797e14	0.106632
$568$	9.04471e14	0.641917
$569$	−1.89314e15	−1.33065	−0.665326	−	0.746553i	$-0.731707\pi$
$569$	−1.89314e15	−1.33065	−0.665326	+	0.746553i	$0.731707\pi$
$570$	−3.46962e14	−0.241530
$571$	−1.93874e15	−1.33666	−0.668331	−	0.743864i	$-0.732991\pi$
$571$	−1.93874e15	−1.33666	−0.668331	+	0.743864i	$0.732991\pi$
$572$	−5.89421e15	−4.02483
$573$	4.53826e14	0.306930
$574$	−3.44216e15	−2.30577
$575$	−4.45721e14	−0.295727
$576$	−6.40732e14	−0.421068
$577$	−4.83767e14	−0.314897	−0.157449	−	0.987527i	$-0.550327\pi$
$577$	−4.83767e14	−0.314897	−0.157449	+	0.987527i	$0.550327\pi$
$578$	−1.84175e15	−1.18748
$579$	1.46480e15	0.935506
$580$	1.12283e15	0.710332
$581$	−1.56273e15	−0.979300
$582$	7.05018e14	0.437647
$583$	−3.84196e15	−2.36252
$584$	−8.86182e13	−0.0539824
$585$	2.90279e14	0.175169
$586$	−2.90668e15	−1.73764
$587$	1.46781e15	0.869284	0.434642	−	0.900603i	$-0.356875\pi$
$587$	1.46781e15	0.869284	0.434642	+	0.900603i	$0.356875\pi$
$588$	1.47629e14	0.0866158
$589$	−3.86137e14	−0.224443
$590$	−1.30880e14	−0.0753681
$591$	1.27444e14	0.0727092
$592$	1.60779e15	0.908780
$593$	−1.07762e15	−0.603482	−0.301741	−	0.953390i	$-0.597568\pi$
$593$	−1.07762e15	−0.603482	−0.301741	+	0.953390i	$0.597568\pi$
$594$	8.09837e14	0.449337
$595$	3.26492e14	0.179486
$596$	−2.73916e15	−1.49198
$597$	−5.87661e14	−0.317152
$598$	1.64557e15	0.879953
$599$	1.37105e15	0.726448	0.363224	−	0.931702i	$-0.381676\pi$
$599$	1.37105e15	0.726448	0.363224	+	0.931702i	$0.381676\pi$
$600$	1.48870e15	0.781582
$601$	2.09667e15	1.09074	0.545370	−	0.838195i	$-0.316389\pi$
$601$	2.09667e15	1.09074	0.545370	+	0.838195i	$0.316389\pi$
$602$	−2.93780e14	−0.151440
$603$	7.14093e14	0.364762
$604$	9.52200e14	0.481975
$605$	5.96818e14	0.299355
$606$	−3.32401e15	−1.65220
$607$	3.31880e15	1.63472	0.817360	−	0.576127i	$-0.195436\pi$
$607$	3.31880e15	1.63472	0.817360	+	0.576127i	$0.195436\pi$
$608$	−4.83415e14	−0.235966
$609$	−1.26011e15	−0.609558
$610$	−8.34392e13	−0.0399996
$611$	5.42792e15	2.57874
$612$	7.39520e14	0.348191
$613$	1.62912e15	0.760187	0.380093	−	0.924948i	$-0.375892\pi$
$613$	1.62912e15	0.760187	0.380093	+	0.924948i	$0.375892\pi$
$614$	−2.76480e14	−0.127861
$615$	6.04369e14	0.277006
$616$	−4.43447e15	−2.01441
$617$	1.17645e15	0.529671	0.264835	−	0.964294i	$-0.414682\pi$
$617$	1.17645e15	0.529671	0.264835	+	0.964294i	$0.414682\pi$
$618$	−2.83640e15	−1.26570
$619$	1.35218e15	0.598046	0.299023	−	0.954246i	$-0.403339\pi$
$619$	1.35218e15	0.598046	0.299023	+	0.954246i	$0.403339\pi$
$620$	−4.57466e14	−0.200542
$621$	−1.48104e14	−0.0643520
$622$	1.53913e15	0.662868
$623$	−3.86676e15	−1.65068
$624$	−1.49144e15	−0.631087
$625$	1.58918e15	0.666549
$626$	−2.38659e15	−0.992244
$627$	1.38822e15	0.572119
$628$	3.11166e15	1.27120
$629$	1.74538e15	0.706824
$630$	4.61312e14	0.185192
$631$	3.68237e15	1.46543	0.732715	−	0.680535i	$-0.238253\pi$
$631$	3.68237e15	1.46543	0.732715	+	0.680535i	$0.238253\pi$
$632$	8.83692e14	0.348624
$633$	8.03024e14	0.314057
$634$	7.42924e15	2.88040
$635$	1.03734e15	0.398718
$636$	−4.95709e15	−1.88892
$637$	−3.23212e14	−0.122102
$638$	−6.85826e15	−2.56862
$639$	3.76464e14	0.139788
$640$	−1.68486e15	−0.620261
$641$	−1.31159e15	−0.478718	−0.239359	−	0.970931i	$-0.576937\pi$
$641$	−1.31159e15	−0.478718	−0.239359	+	0.970931i	$0.576937\pi$
$642$	−5.94138e14	−0.215003
$643$	2.03714e15	0.730904	0.365452	−	0.930830i	$-0.380914\pi$
$643$	2.03714e15	0.730904	0.365452	+	0.930830i	$0.380914\pi$
$644$	1.71306e15	0.609398
$645$	5.15814e13	0.0181934
$646$	1.93523e15	0.676790
$647$	−2.56874e15	−0.890732	−0.445366	−	0.895348i	$-0.646927\pi$
$647$	−2.56874e15	−0.890732	−0.445366	+	0.895348i	$0.646927\pi$
$648$	4.94663e14	0.170077
$649$	5.23660e14	0.178527
$650$	−6.88470e15	−2.32735
$651$	5.13397e14	0.172091
$652$	2.08055e15	0.691538
$653$	−2.30978e15	−0.761286	−0.380643	−	0.924722i	$-0.624297\pi$
$653$	−2.30978e15	−0.761286	−0.380643	+	0.924722i	$0.624297\pi$
$654$	−3.39684e15	−1.11019
$655$	9.19438e14	0.297986
$656$	−3.10521e15	−0.997976
$657$	−3.68851e13	−0.0117555
$658$	8.62608e15	2.72628
$659$	2.46945e15	0.773981	0.386991	−	0.922084i	$-0.373515\pi$
$659$	2.46945e15	0.773981	0.386991	+	0.922084i	$0.373515\pi$
$660$	1.64466e15	0.511193
$661$	−4.54910e14	−0.140222	−0.0701111	−	0.997539i	$-0.522335\pi$
$661$	−4.54910e14	−0.140222	−0.0701111	+	0.997539i	$0.522335\pi$
$662$	−3.59336e15	−1.09845
$663$	−1.61907e15	−0.490842
$664$	−5.19517e15	−1.56198
$665$	7.90779e14	0.235796
$666$	2.46610e15	0.729295
$667$	1.25424e15	0.367866
$668$	2.40738e15	0.700283
$669$	3.73871e15	1.07864
$670$	2.21389e15	0.633497
$671$	3.33846e14	0.0947485
$672$	6.42736e14	0.180926
$673$	3.04425e14	0.0849959	0.0424979	−	0.999097i	$-0.486468\pi$
$673$	3.04425e14	0.0849959	0.0424979	+	0.999097i	$0.486468\pi$
$674$	2.85912e15	0.791777
$675$	6.19634e14	0.170202
$676$	9.68001e15	2.63736
$677$	3.31684e15	0.896369	0.448184	−	0.893941i	$-0.352071\pi$
$677$	3.31684e15	0.896369	0.448184	+	0.893941i	$0.352071\pi$
$678$	−6.22558e15	−1.66885
$679$	−1.60684e15	−0.427257
$680$	1.08540e15	0.286279
$681$	1.15891e15	0.303208
$682$	2.79420e15	0.725175
$683$	−5.02059e15	−1.29253	−0.646265	−	0.763113i	$-0.723670\pi$
$683$	−5.02059e15	−1.29253	−0.646265	+	0.763113i	$0.723670\pi$
$684$	1.79115e15	0.457429
$685$	−1.89014e15	−0.478846
$686$	−7.01550e15	−1.76310
$687$	3.24911e15	0.810033
$688$	−2.65022e14	−0.0655460
$689$	1.08528e16	2.66279
$690$	−4.59163e14	−0.111763
$691$	−1.47365e15	−0.355848	−0.177924	−	0.984044i	$-0.556938\pi$
$691$	−1.47365e15	−0.355848	−0.177924	+	0.984044i	$0.556938\pi$
$692$	−1.41774e16	−3.39635
$693$	−1.84574e15	−0.438670
$694$	4.83360e14	0.113971
$695$	2.00886e15	0.469930
$696$	−4.18914e15	−0.972241
$697$	−3.37095e15	−0.776197
$698$	8.56470e15	1.95662
$699$	4.48181e15	1.01585
$700$	−7.16708e15	−1.61177
$701$	−3.01534e15	−0.672803	−0.336401	−	0.941719i	$-0.609210\pi$
$701$	−3.01534e15	−0.672803	−0.336401	+	0.941719i	$0.609210\pi$
$702$	−2.28764e15	−0.506446
$703$	4.22739e15	0.928576
$704$	7.94791e15	1.73222
$705$	−1.51455e15	−0.327525
$706$	−3.36765e15	−0.722606
$707$	7.57592e15	1.61298
$708$	6.75653e14	0.142738
$709$	−3.26905e15	−0.685279	−0.342640	−	0.939467i	$-0.611321\pi$
$709$	−3.26905e15	−0.685279	−0.342640	+	0.939467i	$0.611321\pi$
$710$	1.16714e15	0.242775
$711$	3.67815e14	0.0759184
$712$	−1.28547e16	−2.63283
$713$	−5.11005e14	−0.103856
$714$	−2.57303e15	−0.518926
$715$	−3.60074e15	−0.720624
$716$	−3.43353e15	−0.681898
$717$	−3.22852e15	−0.636281
$718$	−1.17701e16	−2.30194
$719$	3.71547e15	0.721116	0.360558	−	0.932737i	$-0.382586\pi$
$719$	3.71547e15	0.721116	0.360558	+	0.932737i	$0.382586\pi$
$720$	4.16155e14	0.0801543
$721$	6.46458e15	1.23565
$722$	−4.28871e15	−0.813527
$723$	−4.76238e14	−0.0896527
$724$	5.68558e15	1.06222
$725$	−5.24748e15	−0.972953
$726$	−4.70342e15	−0.865491
$727$	−8.47326e15	−1.54743	−0.773715	−	0.633534i	$-0.781604\pi$
$727$	−8.47326e15	−1.54743	−0.773715	+	0.633534i	$0.781604\pi$
$728$	1.25266e16	2.27044
$729$	2.05891e14	0.0370370
$730$	−1.14354e14	−0.0204163
$731$	−2.87703e14	−0.0509798
$732$	4.30745e14	0.0757546
$733$	6.60704e15	1.15328	0.576641	−	0.816998i	$-0.304363\pi$
$733$	6.60704e15	1.15328	0.576641	+	0.816998i	$0.304363\pi$
$734$	6.70643e15	1.16188
$735$	9.01860e13	0.0155081
$736$	−6.39742e14	−0.109188
$737$	−8.85792e15	−1.50058
$738$	−4.76293e15	−0.800874
$739$	−4.95816e15	−0.827515	−0.413758	−	0.910387i	$-0.635784\pi$
$739$	−4.95816e15	−0.827515	−0.413758	+	0.910387i	$0.635784\pi$
$740$	5.00830e15	0.829689
$741$	−3.92146e15	−0.644834
$742$	1.72473e16	2.81514
$743$	5.26540e15	0.853086	0.426543	−	0.904467i	$-0.359731\pi$
$743$	5.26540e15	0.853086	0.426543	+	0.904467i	$0.359731\pi$
$744$	1.70674e15	0.274484
$745$	−1.67334e15	−0.267131
$746$	−9.90846e15	−1.57016
$747$	−2.16236e15	−0.340145
$748$	−9.17332e15	−1.43241
$749$	1.35413e15	0.209899
$750$	4.09319e15	0.629832
$751$	1.00067e16	1.52852	0.764260	−	0.644908i	$-0.223104\pi$
$751$	1.00067e16	1.52852	0.764260	+	0.644908i	$0.223104\pi$
$752$	7.78169e15	1.17998
$753$	−2.40322e15	−0.361761
$754$	1.93733e16	2.89508
$755$	5.81694e14	0.0862952
$756$	−2.38147e15	−0.350732
$757$	4.78875e15	0.700156	0.350078	−	0.936721i	$-0.386155\pi$
$757$	4.78875e15	0.700156	0.350078	+	0.936721i	$0.386155\pi$
$758$	−4.26889e15	−0.619632
$759$	1.83714e15	0.264736
$760$	2.62888e15	0.376093
$761$	1.32863e16	1.88708	0.943539	−	0.331261i	$-0.107474\pi$
$761$	1.32863e16	1.88708	0.943539	+	0.331261i	$0.107474\pi$
$762$	−8.17512e15	−1.15277
$763$	7.74190e15	1.08383
$764$	−7.26340e15	−1.00955
$765$	4.51769e14	0.0623417
$766$	−1.81435e16	−2.48578
$767$	−1.47924e15	−0.201217
$768$	7.87805e15	1.06398
$769$	−5.95702e14	−0.0798793	−0.0399397	−	0.999202i	$-0.512717\pi$
$769$	−5.95702e14	−0.0798793	−0.0399397	+	0.999202i	$0.512717\pi$
$770$	−5.72231e15	−0.761855
$771$	1.63820e15	0.216554
$772$	−2.34439e16	−3.07705
$773$	4.14002e15	0.539529	0.269765	−	0.962926i	$-0.413054\pi$
$773$	4.14002e15	0.539529	0.269765	+	0.962926i	$0.413054\pi$
$774$	−4.06505e14	−0.0526006
$775$	2.13793e15	0.274685
$776$	−5.34181e15	−0.681473
$777$	−5.62062e15	−0.711982
$778$	−3.35085e15	−0.421471
$779$	−8.16460e15	−1.01971
$780$	−4.64586e15	−0.576163
$781$	−4.66982e15	−0.575068
$782$	2.56105e15	0.313170
$783$	−1.74363e15	−0.211721
$784$	−4.63370e14	−0.0558714
$785$	1.90090e15	0.227602
$786$	−7.24594e15	−0.861531
$787$	3.68416e15	0.434988	0.217494	−	0.976062i	$-0.430212\pi$
$787$	3.68416e15	0.434988	0.217494	+	0.976062i	$0.430212\pi$
$788$	−2.03972e15	−0.239154
$789$	−6.07573e15	−0.707417
$790$	1.14033e15	0.131850
$791$	1.41890e16	1.62923
$792$	−6.13601e15	−0.699677
$793$	−9.43052e14	−0.106791
$794$	3.85983e15	0.434065
$795$	−3.02826e15	−0.338200
$796$	9.40540e15	1.04317
$797$	−1.23359e16	−1.35878	−0.679389	−	0.733778i	$-0.737755\pi$
$797$	−1.23359e16	−1.35878	−0.679389	+	0.733778i	$0.737755\pi$
$798$	−6.23200e15	−0.681729
$799$	8.44764e15	0.917758
$800$	2.67654e15	0.288788
$801$	−5.35046e15	−0.573340
$802$	−3.44375e15	−0.366499
$803$	4.57539e14	0.0483607
$804$	−1.14289e16	−1.19977
$805$	1.04650e15	0.109109
$806$	−7.89309e15	−0.817343
$807$	8.65607e15	0.890259
$808$	2.51855e16	2.57269
$809$	3.18667e15	0.323311	0.161655	−	0.986847i	$-0.448317\pi$
$809$	3.18667e15	0.323311	0.161655	+	0.986847i	$0.448317\pi$
$810$	6.38320e14	0.0643237
$811$	1.67022e16	1.67170	0.835852	−	0.548955i	$-0.184974\pi$
$811$	1.67022e16	1.67170	0.835852	+	0.548955i	$0.184974\pi$
$812$	2.01679e16	2.00495
$813$	4.99078e15	0.492800
$814$	−3.05906e16	−3.00023
$815$	1.27100e15	0.123816
$816$	−2.32116e15	−0.224600
$817$	−6.96829e14	−0.0669738
$818$	−1.56179e16	−1.49100
$819$	5.21387e15	0.494423
$820$	−9.67281e15	−0.911122
$821$	−1.73340e16	−1.62185	−0.810925	−	0.585151i	$-0.801035\pi$
$821$	−1.73340e16	−1.62185	−0.810925	+	0.585151i	$0.801035\pi$
$822$	1.48959e16	1.38443
$823$	−1.94641e15	−0.179694	−0.0898472	−	0.995956i	$-0.528638\pi$
$823$	−1.94641e15	−0.179694	−0.0898472	+	0.995956i	$0.528638\pi$
$824$	2.14909e16	1.97086
$825$	−7.68620e15	−0.700189
$826$	−2.35082e15	−0.212730
$827$	6.46022e15	0.580720	0.290360	−	0.956917i	$-0.406225\pi$
$827$	6.46022e15	0.580720	0.290360	+	0.956917i	$0.406225\pi$
$828$	2.37037e15	0.211666
$829$	1.94358e16	1.72406	0.862029	−	0.506859i	$-0.169193\pi$
$829$	1.94358e16	1.72406	0.862029	+	0.506859i	$0.169193\pi$
$830$	−6.70392e15	−0.590744
$831$	8.90218e15	0.779275
$832$	−2.24514e16	−1.95238
$833$	−5.03025e14	−0.0434552
$834$	−1.58315e16	−1.35865
$835$	1.47065e15	0.125382
$836$	−2.22182e16	−1.88180
$837$	7.10390e14	0.0597733
$838$	−3.60632e16	−3.01455
$839$	−1.54244e16	−1.28091	−0.640453	−	0.767997i	$-0.721253\pi$
$839$	−1.54244e16	−1.28091	−0.640453	+	0.767997i	$0.721253\pi$
$840$	−3.49529e15	−0.288368
$841$	2.56571e15	0.210295
$842$	3.05138e16	2.48473
$843$	9.49764e15	0.768359
$844$	−1.28523e16	−1.03299
$845$	5.91347e15	0.472205
$846$	1.19360e16	0.946935
$847$	1.07198e16	0.844945
$848$	1.55590e16	1.21844
$849$	−1.04760e16	−0.815082
$850$	−1.07149e16	−0.828290
$851$	5.59444e15	0.429679
$852$	−6.02524e15	−0.459787
$853$	−1.99050e16	−1.50919	−0.754593	−	0.656193i	$-0.772166\pi$
$853$	−1.99050e16	−1.50919	−0.754593	+	0.656193i	$0.772166\pi$
$854$	−1.49870e15	−0.112901
$855$	1.09421e15	0.0819003
$856$	4.50168e15	0.334788
$857$	1.73245e16	1.28017	0.640084	−	0.768305i	$-0.278899\pi$
$857$	1.73245e16	1.28017	0.640084	+	0.768305i	$0.278899\pi$
$858$	2.83769e16	2.08346
$859$	−7.87466e14	−0.0574473	−0.0287236	−	0.999587i	$-0.509144\pi$
$859$	−7.87466e14	−0.0574473	−0.0287236	+	0.999587i	$0.509144\pi$
$860$	−8.25551e14	−0.0598415
$861$	1.08554e16	0.781861
$862$	−3.41823e16	−2.44631
$863$	−2.47354e15	−0.175898	−0.0879488	−	0.996125i	$-0.528031\pi$
$863$	−2.47354e15	−0.175898	−0.0879488	+	0.996125i	$0.528031\pi$
$864$	8.89357e14	0.0628421
$865$	−8.66089e15	−0.608099
$866$	1.06919e15	0.0745948
$867$	5.80826e15	0.402663
$868$	−8.21683e15	−0.566038
$869$	−4.56254e15	−0.312318
$870$	−5.40573e15	−0.367704
$871$	2.50220e16	1.69130
$872$	2.57373e16	1.72871
$873$	−2.22339e15	−0.148401
$874$	6.20297e15	0.411421
$875$	−9.32899e15	−0.614880
$876$	5.90340e14	0.0386660
$877$	−5.53084e15	−0.359992	−0.179996	−	0.983667i	$-0.557609\pi$
$877$	−5.53084e15	−0.359992	−0.179996	+	0.983667i	$0.557609\pi$
$878$	2.17590e16	1.40741
$879$	9.16670e15	0.589216
$880$	−5.16217e15	−0.329744
$881$	9.54401e15	0.605848	0.302924	−	0.953015i	$-0.402037\pi$
$881$	9.54401e15	0.605848	0.302924	+	0.953015i	$0.402037\pi$
$882$	−7.10741e14	−0.0448367
$883$	−9.01504e15	−0.565176	−0.282588	−	0.959241i	$-0.591193\pi$
$883$	−9.01504e15	−0.565176	−0.282588	+	0.959241i	$0.591193\pi$
$884$	2.59129e16	1.61447
$885$	4.12753e14	0.0255565
$886$	−3.36768e16	−2.07226
$887$	−1.44889e16	−0.886042	−0.443021	−	0.896511i	$-0.646093\pi$
$887$	−1.44889e16	−0.886042	−0.443021	+	0.896511i	$0.646093\pi$
$888$	−1.86853e16	−1.13561
$889$	1.86323e16	1.12540
$890$	−1.65879e16	−0.995743
$891$	−2.55396e15	−0.152366
$892$	−5.98374e16	−3.54786
$893$	2.04606e16	1.20569
$894$	1.31873e16	0.772325
$895$	−2.09753e15	−0.122090
$896$	−3.02628e16	−1.75072
$897$	−5.18958e15	−0.298383
$898$	3.37360e16	1.92785
$899$	−6.01607e15	−0.341692
$900$	−9.91713e15	−0.559825
$901$	1.68905e16	0.947671
$902$	5.90814e16	3.29469
$903$	9.26485e14	0.0513518
$904$	4.71702e16	2.59861
$905$	3.47329e15	0.190184
$906$	−4.58424e15	−0.249495
$907$	2.60111e16	1.40708	0.703539	−	0.710657i	$-0.251602\pi$
$907$	2.60111e16	1.40708	0.703539	+	0.710657i	$0.251602\pi$
$908$	−1.85482e16	−0.997307
$909$	1.04828e16	0.560244
$910$	1.61645e16	0.858685
$911$	−7.72715e15	−0.408008	−0.204004	−	0.978970i	$-0.565395\pi$
$911$	−7.72715e15	−0.408008	−0.204004	+	0.978970i	$0.565395\pi$
$912$	−5.62196e15	−0.295064
$913$	2.68228e16	1.39931
$914$	−4.39539e16	−2.27926
$915$	2.63140e14	0.0135635
$916$	−5.20015e16	−2.66435
$917$	1.65146e16	0.841078
$918$	−3.56032e15	−0.180241
$919$	−2.96312e16	−1.49112	−0.745562	−	0.666436i	$-0.767819\pi$
$919$	−2.96312e16	−1.49112	−0.745562	+	0.666436i	$0.767819\pi$
$920$	3.47900e15	0.174029
$921$	8.71928e14	0.0433564
$922$	4.39053e16	2.17018
$923$	1.31914e16	0.648157
$924$	2.95407e16	1.44286
$925$	−2.34059e16	−1.13644
$926$	4.29644e16	2.07371
$927$	8.94507e15	0.429186
$928$	−7.53168e15	−0.359235
$929$	−1.21432e16	−0.575766	−0.287883	−	0.957666i	$-0.592951\pi$
$929$	−1.21432e16	−0.575766	−0.287883	+	0.957666i	$0.592951\pi$
$930$	2.20241e15	0.103811
$931$	−1.21835e15	−0.0570885
$932$	−7.17305e16	−3.34131
$933$	−4.85390e15	−0.224772
$934$	−2.32437e16	−1.07003
$935$	−5.60394e15	−0.256466
$936$	1.73331e16	0.788603
$937$	−9.87785e15	−0.446781	−0.223390	−	0.974729i	$-0.571712\pi$
$937$	−9.87785e15	−0.446781	−0.223390	+	0.974729i	$0.571712\pi$
$938$	3.97650e16	1.78807
$939$	7.52651e15	0.336460
$940$	2.42402e16	1.07729
$941$	−1.67197e16	−0.738730	−0.369365	−	0.929284i	$-0.620425\pi$
$941$	−1.67197e16	−0.738730	−0.369365	+	0.929284i	$0.620425\pi$
$942$	−1.49807e16	−0.658038
$943$	−1.08049e16	−0.471851
$944$	−2.12070e15	−0.0920732
$945$	−1.45483e15	−0.0627966
$946$	5.04246e15	0.216392
$947$	−6.16273e15	−0.262935	−0.131468	−	0.991320i	$-0.541969\pi$
$947$	−6.16273e15	−0.262935	−0.131468	+	0.991320i	$0.541969\pi$
$948$	−5.88682e15	−0.249709
$949$	−1.29246e15	−0.0545072
$950$	−2.59519e16	−1.08815
$951$	−2.34294e16	−0.976715
$952$	1.94955e16	0.808035
$953$	−1.99873e16	−0.823649	−0.411824	−	0.911263i	$-0.635108\pi$
$953$	−1.99873e16	−0.823649	−0.411824	+	0.911263i	$0.635108\pi$
$954$	2.38652e16	0.977799
$955$	−4.43718e15	−0.180754
$956$	5.16720e16	2.09284
$957$	2.16287e16	0.870993
$958$	−2.25179e16	−0.901609
$959$	−3.39499e16	−1.35156
$960$	6.26461e15	0.247972
$961$	−2.29574e16	−0.903533
$962$	8.64128e16	3.38154
$963$	1.87372e15	0.0729053
$964$	7.62210e15	0.294884
$965$	−1.43218e16	−0.550930
$966$	−8.24731e15	−0.315455
$967$	−4.13377e16	−1.57218	−0.786088	−	0.618115i	$-0.787897\pi$
$967$	−4.13377e16	−1.57218	−0.786088	+	0.618115i	$0.787897\pi$
$968$	3.56371e16	1.34768
$969$	−6.10309e15	−0.229493
$970$	−6.89315e15	−0.257735
$971$	−2.40034e16	−0.892415	−0.446208	−	0.894929i	$-0.647226\pi$
$971$	−2.40034e16	−0.892415	−0.446208	+	0.894929i	$0.647226\pi$
$972$	−3.29525e15	−0.121822
$973$	3.60823e16	1.32640
$974$	6.45153e16	2.35824
$975$	2.17121e16	0.789180
$976$	−1.35200e15	−0.0488654
$977$	−4.78397e15	−0.171936	−0.0859682	−	0.996298i	$-0.527398\pi$
$977$	−4.78397e15	−0.171936	−0.0859682	+	0.996298i	$0.527398\pi$
$978$	−1.00165e16	−0.357975
$979$	6.63694e16	2.35865
$980$	−1.44341e15	−0.0510089
$981$	1.07125e16	0.376454
$982$	2.54306e16	0.888675
$983$	−2.39825e15	−0.0833393	−0.0416697	−	0.999131i	$-0.513268\pi$
$983$	−2.39825e15	−0.0833393	−0.0416697	+	0.999131i	$0.513268\pi$
$984$	3.60880e16	1.24707
$985$	−1.24606e15	−0.0428192
$986$	3.01512e16	1.03034
$987$	−2.72038e16	−0.924455
$988$	6.27623e16	2.12098
$989$	−9.22169e14	−0.0309907
$990$	−7.91800e15	−0.264619
$991$	2.16527e16	0.719625	0.359812	−	0.933025i	$-0.382841\pi$
$991$	2.16527e16	0.719625	0.359812	+	0.933025i	$0.382841\pi$
$992$	3.06857e15	0.101419
$993$	1.13323e16	0.372474
$994$	2.09638e16	0.685243
$995$	5.74571e15	0.186774
$996$	3.46082e16	1.11880
$997$	−5.19069e16	−1.66879	−0.834394	−	0.551168i	$-0.814182\pi$
$997$	−5.19069e16	−1.66879	−0.834394	+	0.551168i	$0.814182\pi$
$998$	−6.71332e16	−2.14644
$999$	−7.77728e15	−0.247296

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.c.1.25	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.c.1.25	✓	27	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+77.0530 q^{2} -243.000 q^{3} +3889.17 q^{4} +2375.88 q^{5} -18723.9 q^{6} +42674.5 q^{7} +141868. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+77.0530 q^{2} -243.000 q^{3} +3889.17 q^{4} +2375.88 q^{5} -18723.9 q^{6} +42674.5 q^{7} +141868. q^{8} +59049.0 q^{9} +183068. q^{10} -732469. q^{11} -945069. q^{12} +2.06909e6 q^{13} +3.28820e6 q^{14} -577338. q^{15} +2.96633e6 q^{16} +3.22018e6 q^{17} +4.54991e6 q^{18} +7.79943e6 q^{19} +9.24019e6 q^{20} -1.03699e7 q^{21} -5.64390e7 q^{22} +1.03216e7 q^{23} -3.44739e7 q^{24} -4.31833e7 q^{25} +1.59430e8 q^{26} -1.43489e7 q^{27} +1.65969e8 q^{28} +1.21516e8 q^{29} -4.44856e7 q^{30} -4.95083e7 q^{31} -6.19808e7 q^{32} +1.77990e8 q^{33} +2.48125e8 q^{34} +1.01389e8 q^{35} +2.29652e8 q^{36} +5.42012e8 q^{37} +6.00970e8 q^{38} -5.02788e8 q^{39} +3.37060e8 q^{40} -1.04682e9 q^{41} -7.99033e8 q^{42} -8.93436e7 q^{43} -2.84870e9 q^{44} +1.40293e8 q^{45} +7.95311e8 q^{46} +2.62334e9 q^{47} -7.20818e8 q^{48} -1.56210e8 q^{49} -3.32741e9 q^{50} -7.82504e8 q^{51} +8.04704e9 q^{52} +5.24521e9 q^{53} -1.10563e9 q^{54} -1.74026e9 q^{55} +6.05415e9 q^{56} -1.89526e9 q^{57} +9.36320e9 q^{58} -7.14924e8 q^{59} -2.24537e9 q^{60} -4.55782e8 q^{61} -3.81477e9 q^{62} +2.51989e9 q^{63} -1.08508e10 q^{64} +4.91590e9 q^{65} +1.37147e10 q^{66} +1.20932e10 q^{67} +1.25238e10 q^{68} -2.50815e9 q^{69} +7.81236e9 q^{70} +6.37545e9 q^{71} +8.37716e9 q^{72} -6.24653e8 q^{73} +4.17637e10 q^{74} +1.04936e10 q^{75} +3.03333e10 q^{76} -3.12578e10 q^{77} -3.87414e10 q^{78} +6.22898e9 q^{79} +7.04763e9 q^{80} +3.48678e9 q^{81} -8.06607e10 q^{82} -3.66198e10 q^{83} -4.03304e10 q^{84} +7.65075e9 q^{85} -6.88420e9 q^{86} -2.95285e10 q^{87} -1.03914e11 q^{88} -9.06105e10 q^{89} +1.08100e10 q^{90} +8.82974e10 q^{91} +4.01425e10 q^{92} +1.20305e10 q^{93} +2.02136e11 q^{94} +1.85305e10 q^{95} +1.50613e10 q^{96} -3.76534e10 q^{97} -1.20365e10 q^{98} -4.32516e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9	\( 27 q - 46 q^{2} - 6561 q^{3} + 26142 q^{4} - 2442 q^{5} + 11178 q^{6} + 170093 q^{7} - 19341 q^{8} + 1594323 q^{9} + 140249 q^{10} + 256992 q^{11} - 6352506 q^{12} + 2436978 q^{13} + 5233061 q^{14} + 593406 q^{15} + 28295194 q^{16} - 4565351 q^{17} - 2716254 q^{18} + 33607699 q^{19} - 19208463 q^{20} - 41332599 q^{21} + 79735622 q^{22} + 43966161 q^{23} + 4699863 q^{24} + 406675819 q^{25} + 42605404 q^{26} - 387420489 q^{27} + 635747682 q^{28} - 107217773 q^{29} - 34080507 q^{30} + 570926627 q^{31} + 526569236 q^{32} - 62449056 q^{33} + 129790240 q^{34} + 134356079 q^{35} + 1543658958 q^{36} - 107121371 q^{37} + 208302581 q^{38} - 592185654 q^{39} - 958762162 q^{40} - 1935967559 q^{41} - 1271633823 q^{42} + 1725943824 q^{43} + 196885756 q^{44} - 144197658 q^{45} - 13265966407 q^{46} + 1801256065 q^{47} - 6875732142 q^{48} + 10484289252 q^{49} - 10067682271 q^{50} + 1109380293 q^{51} - 882697024 q^{52} - 6214238922 q^{53} + 660049722 q^{54} + 4460552366 q^{55} + 28328012310 q^{56} - 8166670857 q^{57} + 12220116750 q^{58} - 19302956073 q^{59} + 4667656509 q^{60} + 13167821039 q^{61} - 1162130230 q^{62} + 10043821557 q^{63} - 5337557395 q^{64} - 16849896006 q^{65} - 19375756146 q^{66} - 16856763152 q^{67} - 36171071977 q^{68} - 10683777123 q^{69} - 120177261588 q^{70} - 5198545690 q^{71} - 1142066709 q^{72} - 25075321857 q^{73} - 182979651978 q^{74} - 98822224017 q^{75} - 3501293988 q^{76} - 42787697701 q^{77} - 10353113172 q^{78} + 6850314702 q^{79} - 261464428159 q^{80} + 94143178827 q^{81} - 148881516273 q^{82} + 30908370899 q^{83} - 154486686726 q^{84} - 49419624969 q^{85} - 220725475224 q^{86} + 26053918839 q^{87} - 53091280787 q^{88} + 28988060121 q^{89} + 8281563201 q^{90} + 97120614047 q^{91} + 45374597708 q^{92} - 138735170361 q^{93} + 208966927220 q^{94} - 125253904969 q^{95} - 127956324348 q^{96} + 367722840268 q^{97} - 48265639912 q^{98} + 15175120608 q^{99}+O(q^{100}) \) 27 * q - 46 * q^2 - 6561 * q^3 + 26142 * q^4 - 2442 * q^5 + 11178 * q^6 + 170093 * q^7 - 19341 * q^8 + 1594323 * q^9 + 140249 * q^10 + 256992 * q^11 - 6352506 * q^12 + 2436978 * q^13 + 5233061 * q^14 + 593406 * q^15 + 28295194 * q^16 - 4565351 * q^17 - 2716254 * q^18 + 33607699 * q^19 - 19208463 * q^20 - 41332599 * q^21 + 79735622 * q^22 + 43966161 * q^23 + 4699863 * q^24 + 406675819 * q^25 + 42605404 * q^26 - 387420489 * q^27 + 635747682 * q^28 - 107217773 * q^29 - 34080507 * q^30 + 570926627 * q^31 + 526569236 * q^32 - 62449056 * q^33 + 129790240 * q^34 + 134356079 * q^35 + 1543658958 * q^36 - 107121371 * q^37 + 208302581 * q^38 - 592185654 * q^39 - 958762162 * q^40 - 1935967559 * q^41 - 1271633823 * q^42 + 1725943824 * q^43 + 196885756 * q^44 - 144197658 * q^45 - 13265966407 * q^46 + 1801256065 * q^47 - 6875732142 * q^48 + 10484289252 * q^49 - 10067682271 * q^50 + 1109380293 * q^51 - 882697024 * q^52 - 6214238922 * q^53 + 660049722 * q^54 + 4460552366 * q^55 + 28328012310 * q^56 - 8166670857 * q^57 + 12220116750 * q^58 - 19302956073 * q^59 + 4667656509 * q^60 + 13167821039 * q^61 - 1162130230 * q^62 + 10043821557 * q^63 - 5337557395 * q^64 - 16849896006 * q^65 - 19375756146 * q^66 - 16856763152 * q^67 - 36171071977 * q^68 - 10683777123 * q^69 - 120177261588 * q^70 - 5198545690 * q^71 - 1142066709 * q^72 - 25075321857 * q^73 - 182979651978 * q^74 - 98822224017 * q^75 - 3501293988 * q^76 - 42787697701 * q^77 - 10353113172 * q^78 + 6850314702 * q^79 - 261464428159 * q^80 + 94143178827 * q^81 - 148881516273 * q^82 + 30908370899 * q^83 - 154486686726 * q^84 - 49419624969 * q^85 - 220725475224 * q^86 + 26053918839 * q^87 - 53091280787 * q^88 + 28988060121 * q^89 + 8281563201 * q^90 + 97120614047 * q^91 + 45374597708 * q^92 - 138735170361 * q^93 + 208966927220 * q^94 - 125253904969 * q^95 - 127956324348 * q^96 + 367722840268 * q^97 - 48265639912 * q^98 + 15175120608 * q^99

Introduction

L-functions

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